1 #LyX 2.0 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
154 \font_default_family default
155 \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"
192 \paperorientation portrait
195 \notefontcolor #0000ff
202 \paragraph_separation skip
204 \quotes_language english
207 \paperpagestyle plain
211 \tracking_changes false
212 \output_changes false
215 \html_be_strict false
221 LyX's detailed Math manual
229 \begin_layout Plain Layout
231 If you have comments or error corrections, please send them to the LyX Documenta
235 \begin_inset CommandInset href
237 name "lyx-docs@lists.lyx.org"
238 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
249 \begin_inset Note Note
252 \begin_layout Plain Layout
259 \begin_inset Newline newline
263 \begin_inset Newline newline
271 \begin_layout Standard
272 \begin_inset CommandInset toc
273 LatexCommand tableofcontents
280 \begin_layout Standard
281 \begin_inset Note Note
284 \begin_layout Plain Layout
285 To export this document to PDF, PS or DVI the LaTeX-packages
287 braket, cancel, eurosym, mathdots, mhchem
294 If they are not installed the document can be exported anyway but the sections
295 where the packages are required will not appear in the output.
300 ; if it is not installed, this file cannot be exported.
303 \begin_layout Plain Layout
304 The latest PDF-version of this document can be found here:
305 \begin_inset Newline newline
310 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
318 \begin_layout Standard
319 \begin_inset Newpage newpage
325 \begin_layout Section
329 \begin_layout Standard
330 This document explains LyX's math features and is furthermore a collection
331 of LaTeX-commands used for mathematical characters and constructs.
332 The explanations are designed for the usage of commands.
333 It is therefore required that you have read the section
344 \begin_layout Standard
345 Most of the characters and many constructs explained in this manual are
346 also accessible via the menu
350 \SpecialChar \menuseparator
366 But everybody who has to write lots of formulas will notice that it is
367 much faster to use commands instead of the math toolbar.
368 Therefore this manual is focused on commands but also mentions the correspondin
369 g toolbar buttons when available.
372 \begin_layout Standard
373 If not specially mentioned the commands are only available within formulas.
374 To be able to use all commands explained in this document, the option
378 must be checked in the document settings (menu
380 Document\SpecialChar \menuseparator
381 Settings\SpecialChar \menuseparator
392 \begin_layout Plain Layout
395 Use AMS math package automatically
401 \begin_layout Plain Layout
410 -math when math constructs are found that are supported by LyX.
418 \begin_layout Standard
419 This document doesn't list all
423 \begin_layout Plain Layout
436 \begin_layout Plain Layout
441 \begin_layout Plain Layout
450 -math commands is in the file
453 \begin_inset CommandInset href
456 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
462 , which is part of every LaTeX standard installation.
467 for lucidity reasons.
470 \begin_layout Section
474 \begin_layout Standard
475 To create an inline formula
476 \begin_inset Index idx
479 \begin_layout Plain Layout
485 that is embedded into a text line, use one of the shortcuts
491 or the toolbar button
492 \begin_inset Graphics
493 filename ../images/math-mode.png
499 \begin_inset Newline newline
502 To create a display style formula
503 \begin_inset Index idx
506 \begin_layout Plain Layout
507 Formula ! display style
512 which will appear bigger, has a different format, and will be in a separate
513 paragraph, use one of these shortcuts:
522 \begin_layout Standard
523 To change a display style formula to an inline formula, set the cursor into
524 the formula and use one of the shortcuts
532 Edit\SpecialChar \menuseparator
533 Math\SpecialChar \menuseparator
537 The same way is used to change an inline formula to a display style formula.
540 \begin_layout Standard
541 To display parts of an inline formula in the size of a display style formula,
549 \begin_inset Index idx
552 \begin_layout Plain Layout
561 Then a new blue box appears in which the desired formula part is inserted.
564 \begin_layout Standard
565 Only inline formulas are allowed inside tables.
568 \begin_layout Standard
573 can be turned on in the menu
575 View\SpecialChar \menuseparator
579 When you click there on
580 \begin_inset Quotes eld
584 \begin_inset Quotes erd
587 the toolbar will be shown permanently at the bottom; this state is visualized
592 menu with a checkmark.
593 When you click in this state again on
594 \begin_inset Quotes eld
598 \begin_inset Quotes erd
609 is only shown when the cursor is within a formula; this state is visualized
610 by the renaming of the menu entry from
611 \begin_inset Quotes eld
615 \begin_inset Quotes erd
619 \begin_inset Quotes eld
627 \begin_inset Quotes erd
633 \begin_layout Standard
635 \begin_inset Index idx
638 \begin_layout Plain Layout
644 is invoked by pressing the toolbar button
645 \begin_inset Graphics
646 filename ../images/ert-insert.png
653 Insert\SpecialChar \menuseparator
658 \begin_layout Plain Layout
674 \begin_inset Note Note
677 \begin_layout Plain Layout
678 In LyX there are three
679 \begin_inset Quotes eld
683 \begin_inset Quotes erd
686 that appear in the output with sub- and superscript letters: TeX, LaTeX
690 \begin_layout Plain Layout
691 To avoid that these names are recognized as proper names, a TeX-brace pair
700 \begin_layout Standard
701 To change the LaTeX-preamble
702 \begin_inset Index idx
705 \begin_layout Plain Layout
713 Document\SpecialChar \menuseparator
714 Settings\SpecialChar \menuseparator
719 \begin_layout Plain Layout
735 \begin_layout Standard
736 To edit matrices, case differentiations and multiline formulas subsequently,
739 Edit\SpecialChar \menuseparator
744 Edit\SpecialChar \menuseparator
746 \begin_inset space \thinspace{}
750 \begin_inset space \thinspace{}
760 When lines and columns are swapped via the menu, the column or line where
761 the cursor is in is exchanged with the column to the right or the line
763 Is the cursor in the last column or row, the exchange is done with the
764 column to the left or the line above.
767 \begin_layout Standard
768 To write text in formulas
772 \begin_layout Plain Layout
773 For multiline formulas the command
780 \begin_inset CommandInset ref
782 reference "sub:Text-in-multiline"
796 \begin_inset Index idx
799 \begin_layout Plain Layout
806 \begin_inset Index idx
809 \begin_layout Plain Layout
816 This mode is invoked with the shortcut
822 or by the insertion of the command
829 \begin_inset Index idx
832 \begin_layout Plain Layout
841 The text appears black in LyX and can therefore be distinguished from the
842 other formula parts which appear blue.
843 In the output mathematical text is set upright, in contrary to other formula
847 \begin_layout Subsection*
851 \begin_layout Standard
852 Most of the LaTeX-commands for math constructs have the following scheme:
855 \begin_layout Standard
871 \begin_layout Standard
872 A command always starts with a backslash
873 \begin_inset Quotes gld
883 \begin_inset Quotes grd
887 To omit optional arguments, also omit the associated brackets.
888 The braces around the required arguments are named in this document as
890 \begin_inset Index idx
893 \begin_layout Plain Layout
900 If you add in a formula a left brace to a command name, LyX automatically
902 In all other cases TeX-braces are created in formulas with the command
910 TeX-braces appear red in LyX, in contrary to normal braces which appear
912 In TeX-mode no command is needed to get TeX-braces.
913 TeX-braces don't appear in the output.
916 \begin_layout Standard
917 When commands without arguments, like commands for symbols are entered in
918 TeX-mode, a space character must
922 be behind the command to end it.
923 This space doesn't appear in the output.
924 When the space should appear in the output, the space must be followed
925 by a protected space in normal text.
928 \begin_layout Standard
929 A protected space is inserted with
932 arg "command-alternatives space-insert protected ; math-space"
938 \begin_layout Subsection*
939 \begin_inset Newpage newpage
945 \begin_layout Itemize
950 \begin_layout Plain Layout
951 This visible space character can be created with the command
958 \begin_inset Index idx
961 \begin_layout Plain Layout
969 , inserted in TeX-mode.
978 \begin_layout Plain Layout
991 denotes a space character to be input.
994 \begin_layout Itemize
996 \begin_inset Formula $\to$
999 denotes the usage of the corresponding arrow key on the keyboard.
1004 key can often be used instead of
1005 \begin_inset Formula $\to$
1009 \begin_inset Formula $\downarrow$
1017 \begin_inset Formula $\leftarrow$
1021 \begin_inset Formula $\uparrow$
1027 \begin_layout Subsection*
1031 \begin_layout Standard
1033 \begin_inset Float table
1039 \begin_layout Plain Layout
1041 \begin_inset Caption
1043 \begin_layout Plain Layout
1044 \begin_inset CommandInset label
1046 name "tab:Available-units"
1058 \begin_layout Plain Layout
1060 \begin_inset Tabular
1061 <lyxtabular version="3" rows="13" columns="2">
1062 <features tabularvalignment="middle">
1063 <column alignment="center" valignment="top" width="0">
1064 <column alignment="center" valignment="top" width="0">
1066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1069 \begin_layout Plain Layout
1075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1078 \begin_layout Plain Layout
1086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1089 \begin_layout Plain Layout
1095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1098 \begin_layout Plain Layout
1106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1109 \begin_layout Plain Layout
1115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1118 \begin_layout Plain Layout
1126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1129 \begin_layout Plain Layout
1135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1138 \begin_layout Plain Layout
1140 \begin_inset space \thinspace{}
1144 \begin_inset space \thinspace{}
1154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1157 \begin_layout Plain Layout
1163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1166 \begin_layout Plain Layout
1168 \begin_inset space \thinspace{}
1172 \begin_inset space \thinspace{}
1182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1185 \begin_layout Plain Layout
1191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1194 \begin_layout Plain Layout
1196 \begin_inset space \thinspace{}
1200 \begin_inset space \thinspace{}
1210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1213 \begin_layout Plain Layout
1219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1222 \begin_layout Plain Layout
1224 \begin_inset space \thinspace{}
1228 \begin_inset space \thinspace{}
1238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1241 \begin_layout Plain Layout
1247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1250 \begin_layout Plain Layout
1252 \begin_inset space \thinspace{}
1256 \begin_inset space \thinspace{}
1266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1269 \begin_layout Plain Layout
1275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1278 \begin_layout Plain Layout
1280 \begin_inset space \thinspace{}
1284 \begin_inset Formula $\approx$
1288 \begin_inset space \thinspace{}
1298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1301 \begin_layout Plain Layout
1307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1310 \begin_layout Plain Layout
1312 \begin_inset space \thinspace{}
1316 \begin_inset space \thinspace{}
1326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1329 \begin_layout Plain Layout
1335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1338 \begin_layout Plain Layout
1342 \begin_inset Quotes eld
1348 \begin_inset Quotes erd
1358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1361 \begin_layout Plain Layout
1367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1370 \begin_layout Plain Layout
1372 \begin_inset Quotes eld
1380 \begin_inset Quotes erd
1390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1393 \begin_layout Plain Layout
1399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1402 \begin_layout Plain Layout
1404 \begin_inset space \thinspace{}
1408 \begin_inset Formula $\nicefrac{1}{18}$
1412 \begin_inset space \thinspace{}
1433 \begin_layout Standard
1434 \begin_inset Newpage newpage
1440 \begin_layout Section
1444 \begin_layout Subsection
1446 \begin_inset Index idx
1449 \begin_layout Plain Layout
1456 \begin_inset Index idx
1459 \begin_layout Plain Layout
1466 \begin_inset Index idx
1469 \begin_layout Plain Layout
1474 \begin_layout Plain Layout
1485 \begin_layout Plain Layout
1498 \begin_inset Index idx
1501 \begin_layout Plain Layout
1506 \begin_layout Plain Layout
1517 \begin_layout Plain Layout
1532 \begin_layout Standard
1533 Indices are created with an underscore
1534 \begin_inset Quotes eld
1538 \begin_inset Quotes erd
1541 or via the math toolbar button
1542 \begin_inset Graphics
1543 filename ../images/math-subscript.png
1548 , exponents with a caret
1549 \begin_inset Quotes eld
1553 \begin_inset Quotes erd
1556 or via the math toolbar button
1557 \begin_inset Graphics
1558 filename ../images/math-superscript.png
1566 \begin_layout Standard
1568 \begin_inset Tabular
1569 <lyxtabular version="3" rows="4" columns="2">
1570 <features tabularvalignment="middle">
1571 <column alignment="center" valignment="top" width="0pt">
1572 <column alignment="center" valignment="top" width="0pt">
1574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1577 \begin_layout Plain Layout
1583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1586 \begin_layout Plain Layout
1588 \begin_inset Note Note
1591 \begin_layout Plain Layout
1598 is only used as spacer.
1610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1613 \begin_layout Plain Layout
1619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1622 \begin_layout Plain Layout
1623 \begin_inset Formula $B_{V}$
1633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1636 \begin_layout Plain Layout
1642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1645 \begin_layout Plain Layout
1646 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1659 \begin_layout Plain Layout
1664 \begin_layout Plain Layout
1678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1681 \begin_layout Plain Layout
1682 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1698 \begin_layout Standard
1699 As the caret is in some languages an accent, vowels will be accentuated
1700 in this case and not set as exponents
1704 \begin_layout Plain Layout
1705 Depending on the used keyboard settings this can also happen for characters
1712 To get exponents in this case, press
1716 after the caret as in the last example.
1719 \begin_layout Subsection
1721 \begin_inset CommandInset label
1723 name "sub:Fractions"
1728 \begin_inset Index idx
1731 \begin_layout Plain Layout
1740 \begin_layout Standard
1741 Fractions are generated with the command
1748 \begin_inset Index idx
1751 \begin_layout Plain Layout
1759 or via the math toolbar button
1760 \begin_inset Graphics
1761 filename ../images/math/frac.png
1767 The font size is adjusted automatically, depending on whether the fraction
1768 is in an inline or display style formula.
1769 With the math toolbar button
1770 \begin_inset Graphics
1771 filename ../images/math/frac-square.png
1776 you can select different fraction types.
1779 \begin_layout Standard
1787 \begin_inset Index idx
1790 \begin_layout Plain Layout
1798 a fraction can be created that always has the size of a display style formula.
1806 \begin_inset Index idx
1809 \begin_layout Plain Layout
1817 the fraction appears always with the size of an inline formula.
1821 \begin_layout Standard
1822 A line with the fraction
1823 \begin_inset Formula $\frac{1}{2}$
1826 that was created with the command
1835 \begin_layout Standard
1836 A line with the fraction
1837 \begin_inset Formula $\dfrac{1}{2}$
1840 that was created with the command
1849 \begin_layout Standard
1851 \begin_inset Tabular
1852 <lyxtabular version="3" rows="4" columns="2">
1853 <features tabularvalignment="middle">
1854 <column alignment="center" valignment="top" width="0pt">
1855 <column alignment="center" valignment="top" width="0pt">
1857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1860 \begin_layout Plain Layout
1866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1869 \begin_layout Plain Layout
1871 \begin_inset Note Note
1874 \begin_layout Plain Layout
1881 is only used as spacer.
1893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1896 \begin_layout Plain Layout
1903 \begin_layout Plain Layout
1913 \begin_inset Formula $\downarrow$
1921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1924 \begin_layout Plain Layout
1925 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1938 \begin_layout Plain Layout
1945 \begin_layout Plain Layout
1955 \begin_inset Formula $\downarrow$
1963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1966 \begin_layout Plain Layout
1967 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1980 \begin_layout Plain Layout
1987 \begin_layout Plain Layout
2002 \begin_layout Plain Layout
2012 \begin_inset Formula $\downarrow$
2016 \begin_inset Formula $\downarrow\downarrow$
2024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2027 \begin_layout Plain Layout
2028 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2044 \begin_layout Standard
2045 \begin_inset VSpace bigskip
2049 \begin_inset Newpage newpage
2052 For nested fractions the command
2059 \begin_inset Index idx
2062 \begin_layout Plain Layout
2072 \begin_inset VSpace -3mm
2078 \begin_layout Standard
2079 \begin_inset Formula
2081 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2082 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2090 \begin_layout Standard
2091 The command for the example above is:
2094 \begin_layout Standard
2103 \begin_layout Plain Layout
2113 \begin_inset Formula $\downarrow$
2122 \begin_layout Plain Layout
2137 \begin_layout Plain Layout
2147 \begin_inset Formula $\downarrow$
2151 \begin_inset Formula $\downarrow$
2157 \begin_layout Standard
2158 \begin_inset VSpace medskip
2164 \begin_layout Standard
2171 sets the fraction always in the size of a displayed formula, also when
2172 it is part of another fraction.
2175 \begin_layout Standard
2176 It is possible to specify the alignment of the numerator.
2183 is used to left align it, the command
2196 centers the numerator.
2197 These fractions demonstrate the different alignments:
2200 \begin_layout Standard
2203 \begin_inset Formula
2205 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2213 \begin_layout Standard
2214 \begin_inset Note Greyedout
2217 \begin_layout Plain Layout
2234 are no real LaTeX commands but represent the command
2238 cfrac[alignment]{numerator}{denominator}
2241 Therefore you cannot use them in TeX code.
2249 \begin_layout Standard
2250 \begin_inset VSpace medskip
2253 It is often advantageous to combine
2266 \begin_inset Formula
2268 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2276 \begin_layout Standard
2277 For inline fractions with a sloped fraction stroke you can use the command
2285 \begin_inset Index idx
2288 \begin_layout Plain Layout
2297 \begin_inset Formula $\nicefrac{5}{31}$
2307 \begin_inset Index idx
2310 \begin_layout Plain Layout
2319 \begin_inset Formula $\unitfrac{5}{31}$
2322 There is furthermore the command
2328 that offers to write a fraction in combination with a number:
2329 \begin_inset Formula $\unitfrac[2]{1}{3}$
2335 \begin_layout Standard
2336 \begin_inset Note Greyedout
2339 \begin_layout Plain Layout
2350 is not a real LaTeX command but the command
2351 \begin_inset Newline newline
2358 unitfrac[number]{numerator}{denominator}
2361 Therefore you cannot use it in TeX code.
2369 \begin_layout Standard
2370 How to define own fractions where the fraction stroke can be changed, is
2372 \begin_inset CommandInset ref
2374 reference "sub:Self-defined-Fractions"
2381 \begin_layout Standard
2382 \begin_inset Newpage newpage
2388 \begin_layout Subsection
2390 \begin_inset Index idx
2393 \begin_layout Plain Layout
2402 \begin_layout Standard
2403 Square roots are created with
2410 \begin_inset Index idx
2413 \begin_layout Plain Layout
2421 or the math toolbar button
2422 \begin_inset Graphics
2423 filename ../images/math/sqrt.png
2428 , all other roots with the command
2435 \begin_inset Index idx
2438 \begin_layout Plain Layout
2446 or with the math toolbar button
2447 \begin_inset Graphics
2448 filename ../images/math/root.png
2456 \begin_layout Standard
2458 \begin_inset Tabular
2459 <lyxtabular version="3" rows="3" columns="2">
2460 <features tabularvalignment="middle">
2461 <column alignment="center" valignment="top" width="0pt">
2462 <column alignment="center" valignment="top" width="0pt">
2464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2467 \begin_layout Plain Layout
2473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2476 \begin_layout Plain Layout
2478 \begin_inset Note Note
2481 \begin_layout Plain Layout
2488 is only used as spacer.
2500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2503 \begin_layout Plain Layout
2510 \begin_layout Plain Layout
2524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2527 \begin_layout Plain Layout
2528 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2541 \begin_layout Plain Layout
2548 \begin_layout Plain Layout
2558 \begin_inset Formula $\downarrow$
2566 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2569 \begin_layout Plain Layout
2570 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2586 \begin_layout Standard
2587 A square root can also be created with
2593 when the root index field is left empty.
2596 \begin_layout Standard
2597 With certain indices the distance to the root is too small, like in this
2599 \begin_inset Formula $\sqrt[\beta]{B}$
2603 \begin_inset Newline newline
2607 \begin_inset Formula $\beta$
2611 To avoid this, the commands
2618 \begin_inset Index idx
2621 \begin_layout Plain Layout
2636 \begin_inset Index idx
2639 \begin_layout Plain Layout
2647 are used with the following scheme:
2650 \begin_layout Standard
2664 \begin_layout Standard
2665 Distance is the number of Big Points (unit bp;
2666 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2669 ), that the index should be moved to the left or top, resp..
2670 The commands are written to the index.
2671 This way the command
2672 \begin_inset Newline newline
2682 \begin_inset Formula $\to$
2688 \begin_inset Formula $\to$
2697 \begin_layout Plain Layout
2707 \begin_inset Formula $\to$
2711 \begin_inset Newline newline
2716 produces a correct typeset formula:
2717 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2723 \begin_layout Subsection
2724 Binomial Coefficients
2725 \begin_inset Index idx
2728 \begin_layout Plain Layout
2729 Binomial coefficients
2737 \begin_layout Standard
2738 Binomial coefficients are inserted with the command
2745 \begin_inset Index idx
2748 \begin_layout Plain Layout
2756 or with the submenu of the math toolbar button
2757 \begin_inset Graphics
2758 filename ../images/math/frac-square.png
2776 there are the commands
2783 \begin_inset Index idx
2786 \begin_layout Plain Layout
2801 \begin_inset Index idx
2804 \begin_layout Plain Layout
2813 For other brackets around binomial coeficients there are the commands
2820 \begin_inset Index idx
2823 \begin_layout Plain Layout
2838 \begin_inset Index idx
2841 \begin_layout Plain Layout
2852 \begin_layout Standard
2854 \begin_inset Tabular
2855 <lyxtabular version="3" rows="6" columns="2">
2856 <features tabularvalignment="middle">
2857 <column alignment="center" valignment="top" width="0pt">
2858 <column alignment="center" valignment="top" width="0pt">
2860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2863 \begin_layout Plain Layout
2869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2872 \begin_layout Plain Layout
2874 \begin_inset Note Note
2877 \begin_layout Plain Layout
2884 is only used as spacer.
2896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2899 \begin_layout Plain Layout
2906 \begin_layout Plain Layout
2916 \begin_inset Formula $\downarrow$
2924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2927 \begin_layout Plain Layout
2928 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2941 \begin_layout Plain Layout
2948 \begin_layout Plain Layout
2958 \begin_inset Formula $\downarrow$
2966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2969 \begin_layout Plain Layout
2970 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2983 \begin_layout Plain Layout
2990 \begin_layout Plain Layout
3000 \begin_inset Formula $\downarrow$
3008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3011 \begin_layout Plain Layout
3012 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3025 \begin_layout Plain Layout
3032 \begin_layout Plain Layout
3042 \begin_inset Formula $\downarrow$
3050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3053 \begin_layout Plain Layout
3054 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3067 \begin_layout Plain Layout
3074 \begin_layout Plain Layout
3084 \begin_inset Formula $\downarrow$
3092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3095 \begin_layout Plain Layout
3096 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3112 \begin_layout Subsection
3113 Case Differentiations
3114 \begin_inset Index idx
3117 \begin_layout Plain Layout
3118 Case differentiations
3126 \begin_layout Standard
3128 \begin_inset Tabular
3129 <lyxtabular version="3" rows="3" columns="2">
3130 <features tabularvalignment="middle">
3131 <column alignment="center" valignment="top" width="0pt">
3132 <column alignment="center" valignment="top" width="0pt">
3134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3137 \begin_layout Plain Layout
3143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3146 \begin_layout Plain Layout
3154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3157 \begin_layout Plain Layout
3164 \begin_layout Plain Layout
3174 \begin_inset Formula $\to$
3178 \begin_inset Index idx
3181 \begin_layout Plain Layout
3194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3197 \begin_layout Plain Layout
3198 \begin_inset Formula $\begin{cases}
3209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3212 \begin_layout Plain Layout
3219 \begin_layout Plain Layout
3231 arg "newline-insert newline"
3239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3242 \begin_layout Plain Layout
3243 \begin_inset Formula $\begin{cases}
3244 A & \textrm{for }x>0\\
3245 B & \textrm{for }x=0
3262 \begin_layout Standard
3269 or pressing the math toolbar button
3270 \begin_inset Graphics
3271 filename ../images/math/cases.png
3276 you can create new lines with the shortcut
3279 arg "newline-insert newline"
3282 or the table toolbar button
3283 \begin_inset Graphics
3284 filename ../images/tabular-feature_append-row.png
3292 \begin_layout Standard
3299 is also available via the menu
3301 Insert\SpecialChar \menuseparator
3302 Math\SpecialChar \menuseparator
3308 \begin_layout Subsection
3310 \begin_inset Index idx
3313 \begin_layout Plain Layout
3322 \begin_layout Standard
3330 \begin_inset Index idx
3333 \begin_layout Plain Layout
3341 every character can be displayed canceled.
3342 The characters are quasi accentuated by a slash.
3345 \begin_layout Standard
3347 \begin_inset Tabular
3348 <lyxtabular version="3" rows="4" columns="2">
3349 <features tabularvalignment="middle">
3350 <column alignment="center" valignment="top" width="0pt">
3351 <column alignment="center" valignment="top" width="0pt">
3353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3356 \begin_layout Plain Layout
3362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3365 \begin_layout Plain Layout
3373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3376 \begin_layout Plain Layout
3384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3387 \begin_layout Plain Layout
3388 \begin_inset Formula $\not=$
3398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3401 \begin_layout Plain Layout
3411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3414 \begin_layout Plain Layout
3415 \begin_inset Formula $\not\le$
3425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3428 \begin_layout Plain Layout
3438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3441 \begin_layout Plain Layout
3442 \begin_inset Formula $\not\parallel$
3458 \begin_layout Standard
3459 The last example shows that not all negations look good.
3460 Therefore there are special commands for some negations (see
3461 \begin_inset CommandInset ref
3463 reference "sub:Mathematical-Symbols"
3468 \begin_inset CommandInset ref
3470 reference "sec:Relations"
3477 \begin_layout Subsection
3479 \begin_inset CommandInset label
3481 name "sub:Placeholders"
3486 \begin_inset Index idx
3489 \begin_layout Plain Layout
3496 \begin_inset Index idx
3499 \begin_layout Plain Layout
3500 Chemical characters ! Isotopes
3506 \begin_inset Index idx
3509 \begin_layout Plain Layout
3514 \begin_layout Plain Layout
3525 \begin_layout Plain Layout
3540 \begin_layout Standard
3542 \begin_inset space \thinspace{}
3546 \begin_inset space \space{}
3553 \begin_layout Plain Layout
3554 Typesetting isotopes and chemical symbols is described in
3555 \begin_inset CommandInset ref
3557 reference "sub:Chemical-Symbols-and"
3566 the following problem occurs:
3569 \begin_layout Standard
3571 \begin_inset Tabular
3572 <lyxtabular version="3" rows="2" columns="2">
3573 <features tabularvalignment="middle">
3574 <column alignment="center" valignment="top" width="0pt">
3575 <column alignment="center" valignment="top" width="0pt">
3577 <cell alignment="center" valignment="top" usebox="none">
3580 \begin_layout Plain Layout
3581 Indices created with sub- and superscripts:
3586 <cell alignment="center" valignment="top" usebox="none">
3589 \begin_layout Plain Layout
3590 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3600 <cell alignment="center" valignment="top" usebox="none">
3603 \begin_layout Plain Layout
3609 <cell alignment="center" valignment="top" usebox="none">
3612 \begin_layout Plain Layout
3613 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3627 \begin_inset Note Note
3630 \begin_layout Plain Layout
3637 is only used as spacer.
3645 \begin_layout Standard
3646 The shorter index is by default placed below or above the first character
3647 of the longer index.
3648 To avoid this there is the command
3655 \begin_inset Index idx
3658 \begin_layout Plain Layout
3666 or the math toolbar button
3667 \begin_inset space \thinspace{}
3674 \begin_layout Plain Layout
3675 can be found in the submenu of the toolbar button
3676 \begin_inset Graphics
3677 filename ../images/math/space.png
3688 \begin_inset Graphics
3689 filename ../images/math/phantom.png
3694 that creates one or more phantom characters.
3701 a small blue box appears that is superposed with two red arrows.
3702 The arrows indicate that the complete width and height of the box content
3703 will be created as placeholder.
3704 Phantom characters are accordingly placeholders with the size of the characters.
3707 \begin_layout Standard
3709 \begin_inset Tabular
3710 <lyxtabular version="3" rows="4" columns="2">
3711 <features tabularvalignment="middle">
3712 <column alignment="center" valignment="top" width="0">
3713 <column alignment="center" valignment="top" width="0">
3715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3718 \begin_layout Plain Layout
3724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3727 \begin_layout Plain Layout
3729 \begin_inset Note Note
3732 \begin_layout Plain Layout
3739 is only used as spacer.
3751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3754 \begin_layout Plain Layout
3759 \begin_layout Plain Layout
3774 \begin_layout Plain Layout
3784 \begin_inset Formula $\to$
3791 \begin_layout Plain Layout
3805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3808 \begin_layout Plain Layout
3809 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3822 \begin_layout Plain Layout
3827 \begin_layout Plain Layout
3842 \begin_layout Plain Layout
3852 \begin_inset Formula $\to$
3859 \begin_layout Plain Layout
3873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3876 \begin_layout Plain Layout
3877 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3890 \begin_layout Plain Layout
3897 \begin_layout Plain Layout
3912 \begin_layout Plain Layout
3922 \begin_inset Formula $\to$
3929 \begin_layout Plain Layout
3943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3946 \begin_layout Plain Layout
3947 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3963 \begin_layout Standard
3964 Furthermore there are the commands
3971 \begin_inset Index idx
3974 \begin_layout Plain Layout
3983 \begin_inset space ~
3987 \begin_inset Graphics
3988 filename ../images/math/vphantom.png
4000 \begin_inset Index idx
4003 \begin_layout Plain Layout
4012 \begin_inset space ~
4016 \begin_inset Graphics
4017 filename ../images/math/hphantom.png
4029 creates only space for the maximal height of the characters in the box
4030 but not for its width.
4037 creates only space for the width of the box content.
4038 Therefore the boxes of both commands have only one red arrow.
4041 \begin_layout Standard
4042 For example the command
4052 \begin_layout Plain Layout
4067 creates space for the height of the integral sign,
4071 \begin_layout Plain Layout
4078 creates an integral sign, see
4079 \begin_inset CommandInset ref
4081 reference "sub:Big-Operators"
4090 because this is the larger character.
4091 An example application is in
4092 \begin_inset CommandInset ref
4094 reference "sub:Multiline-Brackets"
4101 \begin_layout Standard
4102 Placeholders can also be used for text when they are inserted via the menu
4105 Insert\SpecialChar \menuseparator
4106 Formatting\SpecialChar \menuseparator
4112 \begin_layout Standard
4114 \begin_inset Newline newline
4118 \begin_inset Phantom Phantom
4121 \begin_layout Plain Layout
4130 \begin_layout Subsection
4132 \begin_inset Index idx
4135 \begin_layout Plain Layout
4142 \begin_inset Index idx
4145 \begin_layout Plain Layout
4146 Formula ! underlined
4154 \begin_layout Standard
4156 \begin_inset Tabular
4157 <lyxtabular version="3" rows="4" columns="2">
4158 <features tabularvalignment="middle">
4159 <column alignment="center" valignment="top" width="0pt">
4160 <column alignment="center" valignment="top" width="0pt">
4162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4165 \begin_layout Plain Layout
4171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4174 \begin_layout Plain Layout
4176 \begin_inset Note Note
4179 \begin_layout Plain Layout
4186 is only used as spacer.
4198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4201 \begin_layout Plain Layout
4208 \begin_layout Plain Layout
4218 \begin_inset Index idx
4221 \begin_layout Plain Layout
4234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4237 \begin_layout Plain Layout
4238 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4248 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4251 \begin_layout Plain Layout
4258 \begin_layout Plain Layout
4268 \begin_inset Index idx
4271 \begin_layout Plain Layout
4284 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4287 \begin_layout Plain Layout
4288 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4301 \begin_layout Plain Layout
4308 \begin_layout Plain Layout
4323 \begin_layout Plain Layout
4337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4340 \begin_layout Plain Layout
4341 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4357 \begin_layout Standard
4358 In the last example it doesn't matter if first
4373 \begin_layout Standard
4374 To double underline use
4383 \begin_layout Standard
4384 It is possible to place up to 6 lines above or below characters.
4387 \begin_layout Standard
4388 \begin_inset VSpace bigskip
4391 Custom lines can be created using the command
4398 \begin_inset Index idx
4401 \begin_layout Plain Layout
4409 which has the following scheme:
4412 \begin_layout Standard
4417 rule[vertical offset]{length}{thickness}
4420 \begin_layout Standard
4421 The optional vertical offset shifts the line upwards (or downwards, when
4422 the value is negative).
4424 \begin_inset CommandInset ref
4426 reference "tab:Available-units"
4430 can be used for the values.
4431 Here are two example lines created with the commands
4432 \begin_inset Newline newline
4439 rule[-2ex]{3cm}{2pt}
4450 \begin_layout Standard
4452 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4458 \begin_layout Standard
4465 can also be used for text when a line is inserted via the menu
4467 Insert\SpecialChar \menuseparator
4468 Formatting\SpecialChar \menuseparator
4470 \begin_inset space ~
4478 \begin_layout Standard
4480 \begin_inset CommandInset line
4491 \begin_layout Subsection
4493 \begin_inset CommandInset label
4500 \begin_inset Index idx
4503 \begin_layout Plain Layout
4512 \begin_layout Standard
4513 There are different types of ellipses available.
4517 \begin_layout Plain Layout
4518 In the math toolbar in the submenu of the button
4519 \begin_inset Graphics
4520 filename ../images/math/ldots.png
4530 For listings dots at the baseline are used (
4537 \begin_inset Index idx
4540 \begin_layout Plain Layout
4548 ), while for operations dots are needed that are on the same height as the
4556 \begin_inset Index idx
4559 \begin_layout Plain Layout
4568 When using the command
4575 \begin_inset Index idx
4578 \begin_layout Plain Layout
4586 , LaTeX decides on the basis of the next character what type is used.
4589 \begin_layout Standard
4591 \begin_inset Tabular
4592 <lyxtabular version="3" rows="9" columns="2">
4593 <features tabularvalignment="middle">
4594 <column alignment="center" valignment="top" width="0pt">
4595 <column alignment="center" valignment="top" width="0pt">
4597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4600 \begin_layout Plain Layout
4606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4609 \begin_layout Plain Layout
4617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4620 \begin_layout Plain Layout
4625 \begin_layout Plain Layout
4640 \begin_layout Plain Layout
4654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4657 \begin_layout Plain Layout
4658 \begin_inset Formula $A_{1},\dots,A_{n}$
4668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4671 \begin_layout Plain Layout
4676 \begin_layout Plain Layout
4691 \begin_layout Plain Layout
4705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4708 \begin_layout Plain Layout
4709 \begin_inset Formula $A_{1}+\dots+A_{n}$
4719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4722 \begin_layout Plain Layout
4727 \begin_layout Plain Layout
4742 \begin_layout Plain Layout
4756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4759 \begin_layout Plain Layout
4760 \begin_inset Formula $A_{1},\ldots,A_{n}$
4770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4773 \begin_layout Plain Layout
4778 \begin_layout Plain Layout
4793 \begin_layout Plain Layout
4807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4810 \begin_layout Plain Layout
4811 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4824 \begin_layout Plain Layout
4832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4835 \begin_layout Plain Layout
4836 \begin_inset Formula $\vdots$
4846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4849 \begin_layout Plain Layout
4857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4860 \begin_layout Plain Layout
4861 \begin_inset Formula $\ddots$
4871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4874 \begin_layout Plain Layout
4882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4885 \begin_layout Plain Layout
4886 \begin_inset Formula $\iddots$
4896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4899 \begin_layout Plain Layout
4901 \begin_inset space \thinspace{}
4904 matrix with the different dots
4909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4912 \begin_layout Plain Layout
4913 \begin_inset Formula $\begin{array}{ccc}
4914 A_{11} & \cdots & A_{1m}\\
4915 \vdots & \ddots & \vdots\\
4916 A_{n1} & \cdots & A_{nm}
4933 \begin_layout Standard
4934 The ellipses available in menu
4936 Insert\SpecialChar \menuseparator
4938 \begin_inset space ~
4952 \begin_layout Standard
4953 \begin_inset VSpace medskip
4962 , one of the options
4964 Use mathdots package (automatically)
4966 must be set in the document settings under
4969 \begin_inset space ~
4975 \begin_inset Newline newline
4980 Use mathdots package
4982 will improve the appearance of all dots in the documents if their font
4983 style or size is not the default.
4986 \begin_layout Standard
4987 \begin_inset VSpace medskip
4990 Specially for matrices there are ellipses that span over several columns.
4991 They are created with the command
4998 \begin_inset Index idx
5001 \begin_layout Plain Layout
5009 , that has the following scheme:
5012 \begin_layout Standard
5017 hdotsfor[distance]{number of columns}
5020 \begin_layout Standard
5021 The number of columns specifies how many columns should be spanned.
5022 Distance is a factor for the distance between the dots.
5025 \begin_layout Standard
5026 In the following matrix the command
5032 was inserted in the first box of the second line, to get an ellipsis with
5033 a dot distance twice as long as with the command
5040 \begin_inset Formula
5042 \left(\begin{array}{cccc}
5051 Note that the matrix fields that should be spanned must be empty, otherwise
5052 you get LaTeX-errors.
5055 \begin_layout Standard
5056 \begin_inset VSpace bigskip
5059 Furthermore you can fill with the command
5066 \begin_inset Index idx
5069 \begin_layout Plain Layout
5077 the rest of a line with dots.
5078 The effect of these commands is the same as with
5085 \begin_inset CommandInset ref
5087 reference "sub:Variable-Space"
5094 \begin_layout Standard
5095 For example the command
5103 \begin_layout Plain Layout
5117 \begin_layout Standard
5118 \begin_inset Formula $A\dotfill B$
5124 \begin_layout Standard
5131 there is for a line the command
5138 \begin_inset Index idx
5141 \begin_layout Plain Layout
5152 \begin_layout Standard
5153 \begin_inset Formula $A\hrulefill B$
5159 \begin_layout Standard
5160 To use the commands for text, they have to be inserted in TeX-mode.
5163 \begin_layout Section
5165 \begin_inset CommandInset label
5172 \begin_inset Index idx
5175 \begin_layout Plain Layout
5184 \begin_layout Standard
5185 Matrices can be inserted via the math toolbar button
5186 \begin_inset Graphics
5187 filename ../images/dialog-show_mathmatrix.png
5194 Insert\SpecialChar \menuseparator
5195 Math\SpecialChar \menuseparator
5199 In the matrix dialog you can specify the number of columns and rows, the
5200 alignment and the decoration.
5201 The vertical alignment is only of importance for matrices in inline formulas:
5204 \begin_layout Standard
5205 The first matrix is top
5206 \begin_inset Formula $\begin{array}[t]{cccc}
5214 \begin_inset Formula $\begin{array}{cccc}
5221 and the third bottom
5222 \begin_inset Formula $\begin{array}[b]{cccc}
5232 \begin_layout Standard
5233 The horizontal alignment specifies how the column entries should be aligned.
5234 It is set by entering a letter for every column.
5239 denotes left aligned,
5248 To create for example a 4
5253 \begin_inset space ~
5256 matrix where the first column is left aligned, the second and third are
5257 centered and the last one is right aligned, one enters for the horizontal
5263 Normally in a matrix all columns are centered, therefore the default for
5271 \begin_layout Standard
5272 Horizontal alignment:
5275 \begin_layout Standard
5281 \begin_inset Formula $\begin{array}{lll}
5293 \begin_inset Formula $\begin{array}{ccc}
5305 \begin_inset Formula $\begin{array}{rrr}
5315 \begin_layout Standard
5316 To add or delete rows and columns subsequently, the math toolbar buttons
5318 \begin_inset Graphics
5319 filename ../images/tabular-feature_append-row.png
5325 \begin_inset Graphics
5326 filename ../images/tabular-feature_delete-row.png
5332 \begin_inset space \thinspace{}
5337 Edit\SpecialChar \menuseparator
5341 New rows can also be created with
5344 arg "newline-insert newline"
5350 \begin_layout Standard
5351 \begin_inset VSpace bigskip
5358 adds parentheses in the selected style around the matrix.
5359 Alternatively, parentheses can can either be created with the commands
5367 \begin_inset Index idx
5370 \begin_layout Plain Layout
5385 \begin_inset Index idx
5388 \begin_layout Plain Layout
5399 \begin_inset space ~
5405 \begin_inset CommandInset ref
5407 reference "sub:Automatic-Bracket-Size"
5411 , or by using the following commands:
5412 \begin_inset VSpace medskip
5418 \begin_layout Standard
5419 \begin_inset space \hfill{}
5423 \begin_inset Tabular
5424 <lyxtabular version="3" rows="4" columns="2">
5425 <features tabularvalignment="middle">
5426 <column alignment="center" valignment="top" width="0">
5427 <column alignment="center" valignment="top" width="0">
5429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5432 \begin_layout Plain Layout
5438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5441 \begin_layout Plain Layout
5443 \begin_inset Note Note
5446 \begin_layout Plain Layout
5453 is only used as spacer.
5465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5468 \begin_layout Plain Layout
5475 \begin_layout Plain Layout
5489 \begin_inset space \thinspace{}
5497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5500 \begin_layout Plain Layout
5501 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5502 0 & \textrm{-}\mathrm{i}\\
5504 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5517 \begin_layout Plain Layout
5524 \begin_layout Plain Layout
5538 \begin_inset space \thinspace{}
5546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5549 \begin_layout Plain Layout
5550 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5551 0 & \textrm{-}\mathrm{i}\\
5553 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5566 \begin_layout Plain Layout
5573 \begin_layout Plain Layout
5587 \begin_inset space \thinspace{}
5595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5598 \begin_layout Plain Layout
5599 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5600 0 & \textrm{-}\mathrm{i}\\
5602 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5616 \begin_inset space \hfill{}
5620 \begin_inset Tabular
5621 <lyxtabular version="3" rows="4" columns="2">
5622 <features tabularvalignment="middle">
5623 <column alignment="center" valignment="top" width="0">
5624 <column alignment="center" valignment="top" width="0">
5626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5629 \begin_layout Plain Layout
5635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5638 \begin_layout Plain Layout
5646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5649 \begin_layout Plain Layout
5656 \begin_layout Plain Layout
5670 \begin_inset space \thinspace{}
5678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5681 \begin_layout Plain Layout
5682 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5683 0 & \textrm{-}\mathrm{i}\\
5685 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5698 \begin_layout Plain Layout
5705 \begin_layout Plain Layout
5719 \begin_inset space \thinspace{}
5727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5730 \begin_layout Plain Layout
5731 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5732 0 & \textrm{-}\mathrm{i}\\
5734 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5747 \begin_layout Plain Layout
5754 \begin_layout Plain Layout
5768 \begin_inset space \thinspace{}
5776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5779 \begin_layout Plain Layout
5780 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5781 0 & \textrm{-}\mathrm{i}\\
5783 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5797 \begin_inset space \hfill{}
5803 \begin_layout Standard
5804 \begin_inset VSpace medskip
5808 \begin_inset space \thinspace{}
5812 \begin_inset space \space{}
5821 is inserted, a blue box appears between two vertical lines where the matrix
5823 \begin_inset Newline newline
5826 Note that decorated matrices ignore the vertical alignment.
5829 \begin_layout Standard
5830 \begin_inset Note Greyedout
5833 \begin_layout Plain Layout
5838 LaTeX limits the number of matrix columns with decorations to 10.
5839 If you need more than 10
5840 \begin_inset space ~
5843 columns, you have to add this line to the document preamble:
5846 \begin_layout Plain Layout
5851 setcounter{MaxMatrixCols}{number}
5854 \begin_layout Plain Layout
5859 is the number of columns between 11 and 99.
5867 \begin_layout Standard
5868 \begin_inset VSpace bigskip
5871 As all multiline formulas are matrices, the length
5878 \begin_inset Index idx
5881 \begin_layout Plain Layout
5889 that is described in
5890 \begin_inset CommandInset ref
5892 reference "sub:Column-Separation"
5896 can also be used to change the column separation of matrices.
5899 \begin_layout Standard
5900 To change the row separation, the command
5907 \begin_inset Index idx
5910 \begin_layout Plain Layout
5919 It is used as follows:
5922 \begin_layout Standard
5929 arraystretch}{stretch factor}
5930 \begin_inset Index idx
5933 \begin_layout Plain Layout
5944 \begin_layout Standard
5951 assigns the stretch factor to the predefined command
5959 \begin_inset space \thinspace{}
5963 \begin_inset space \space{}
5966 the row separation, use the factor 2.
5967 This is then used for all following matrices.
5968 To go back to the original separation, assign the factor 1 to
5977 \begin_layout Standard
5978 To set matrices into a text line, the command
5985 \begin_inset Index idx
5988 \begin_layout Plain Layout
5997 When it is inserted a blue box with two dashed lines appears.
5998 In this box the matrix is inserted.
6001 \begin_layout Standard
6003 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
6005 \end{smallmatrix}\right)$
6011 \begin_layout Section
6012 Brackets and Delimiters
6013 \begin_inset Index idx
6016 \begin_layout Plain Layout
6023 \begin_inset Index idx
6026 \begin_layout Plain Layout
6035 \begin_layout Subsection
6036 Vertical Brackets and Delimiters
6037 \begin_inset Index idx
6040 \begin_layout Plain Layout
6049 \begin_layout Standard
6050 \begin_inset space \hfill{}
6054 \begin_inset Tabular
6055 <lyxtabular version="3" rows="9" columns="2">
6056 <features tabularvalignment="middle">
6057 <column alignment="center" valignment="top" width="0pt">
6058 <column alignment="center" valignment="top" width="0pt">
6060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6063 \begin_layout Plain Layout
6069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6072 \begin_layout Plain Layout
6080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6083 \begin_layout Plain Layout
6089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6092 \begin_layout Plain Layout
6093 \begin_inset Formula $($
6103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6106 \begin_layout Plain Layout
6112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6115 \begin_layout Plain Layout
6116 \begin_inset Formula $\{$
6126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6129 \begin_layout Plain Layout
6135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6138 \begin_layout Plain Layout
6139 \begin_inset Formula $[$
6149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6152 \begin_layout Plain Layout
6160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6163 \begin_layout Plain Layout
6164 \begin_inset Formula $\langle$
6174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6177 \begin_layout Plain Layout
6185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6188 \begin_layout Plain Layout
6189 \begin_inset Formula $\lceil$
6199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6202 \begin_layout Plain Layout
6210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6213 \begin_layout Plain Layout
6214 \begin_inset Formula $\lfloor$
6224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6227 \begin_layout Plain Layout
6233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6236 \begin_layout Plain Layout
6237 \begin_inset Formula $/$
6247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6250 \begin_layout Plain Layout
6256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6259 \begin_layout Plain Layout
6260 \begin_inset Formula $|$
6274 \begin_inset space \hfill{}
6278 \begin_inset Tabular
6279 <lyxtabular version="3" rows="9" columns="2">
6280 <features tabularvalignment="middle">
6281 <column alignment="center" valignment="top" width="0pt">
6282 <column alignment="center" valignment="top" width="0pt">
6284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6287 \begin_layout Plain Layout
6293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6296 \begin_layout Plain Layout
6304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6307 \begin_layout Plain Layout
6313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6316 \begin_layout Plain Layout
6317 \begin_inset Formula $)$
6327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6330 \begin_layout Plain Layout
6336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6339 \begin_layout Plain Layout
6340 \begin_inset Formula $\}$
6350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6353 \begin_layout Plain Layout
6359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6362 \begin_layout Plain Layout
6363 \begin_inset Formula $]$
6373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6376 \begin_layout Plain Layout
6384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6387 \begin_layout Plain Layout
6388 \begin_inset Formula $\rangle$
6398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6401 \begin_layout Plain Layout
6409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6412 \begin_layout Plain Layout
6413 \begin_inset Formula $\rceil$
6423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6426 \begin_layout Plain Layout
6434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6437 \begin_layout Plain Layout
6438 \begin_inset Formula $\rfloor$
6448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6451 \begin_layout Plain Layout
6461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6464 \begin_layout Plain Layout
6465 \begin_inset Formula $\backslash$
6475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6478 \begin_layout Plain Layout
6486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6489 \begin_layout Plain Layout
6490 \begin_inset Formula $\|$
6504 \begin_inset space \hfill{}
6510 \begin_layout Standard
6513 \begin_inset Note Greyedout
6516 \begin_layout Plain Layout
6521 In TeX-mode the command
6528 \begin_inset Index idx
6531 \begin_layout Plain Layout
6539 must be used for the backslash, because the command
6547 produces a line break there.
6555 \begin_layout Standard
6556 For all characters listed above the size can be adjusted with the commands
6557 described in the following two subsections.
6558 When using these commands, the characters < and > can directly be used
6559 instead of the commands
6574 \begin_layout Subsubsection
6576 \begin_inset CommandInset label
6578 name "sub:Manual-Bracket-Size"
6583 \begin_inset Index idx
6586 \begin_layout Plain Layout
6587 Bracket size ! manual
6595 \begin_layout Standard
6596 The bracket size can be specified manually by the LaTeX-commands
6603 \begin_inset Index idx
6606 \begin_layout Plain Layout
6639 denotes the smallest and
6645 the largest bracket size.
6648 \begin_layout Standard
6649 These commands are used to emphasize levels of brackets:
6652 \begin_layout Standard
6654 \begin_inset Tabular
6655 <lyxtabular version="3" rows="2" columns="2">
6656 <features tabularvalignment="middle">
6657 <column alignment="center" valignment="top" width="0pt">
6658 <column alignment="center" valignment="top" width="0pt">
6660 <cell alignment="center" valignment="top" usebox="none">
6663 \begin_layout Plain Layout
6664 all brackets in the same size:
6669 <cell alignment="center" valignment="top" usebox="none">
6672 \begin_layout Plain Layout
6673 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6683 <cell alignment="center" valignment="top" usebox="none">
6686 \begin_layout Plain Layout
6692 <cell alignment="center" valignment="top" usebox="none">
6695 \begin_layout Plain Layout
6696 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6710 \begin_inset Note Note
6713 \begin_layout Plain Layout
6720 is only used as spacer.
6728 \begin_layout Standard
6729 For the second formula the command
6739 \begin_layout Plain Layout
6753 \begin_layout Standard
6754 Here is an overview about all bracket sizes:
6757 \begin_layout Standard
6777 \begin_layout Plain Layout
6794 \begin_layout Plain Layout
6807 \begin_layout Plain Layout
6823 \begin_layout Standard
6825 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6831 \begin_layout Standard
6838 -commands there is the variant
6845 \begin_inset Index idx
6848 \begin_layout Plain Layout
6856 that adds a bit more space between the bracket and its content, and the
6870 \begin_inset Index idx
6873 \begin_layout Plain Layout
6883 , that don't add additional space.
6888 at the end of the command
6894 is for a left bracket; for a right bracket this will be replaced by an
6900 A left or right bracket can each be an opening or closing bracket.
6903 \begin_layout Standard
6904 In the following table is a comparison of the variants:
6907 \begin_layout Standard
6909 \begin_inset Tabular
6910 <lyxtabular version="3" rows="5" columns="2">
6911 <features tabularvalignment="middle">
6912 <column alignment="center" valignment="middle" width="0">
6913 <column alignment="center" valignment="middle" width="0">
6915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6918 \begin_layout Plain Layout
6924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6927 \begin_layout Plain Layout
6929 \begin_inset Note Note
6932 \begin_layout Plain Layout
6939 is only used as spacer.
6951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6954 \begin_layout Plain Layout
6969 \begin_layout Plain Layout
6987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6990 \begin_layout Plain Layout
6991 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
7001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7004 \begin_layout Plain Layout
7019 \begin_layout Plain Layout
7037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7040 \begin_layout Plain Layout
7041 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7054 \begin_layout Plain Layout
7069 \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 $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7104 \begin_layout Plain Layout
7116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7119 \begin_layout Plain Layout
7120 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7136 \begin_layout Subsubsection
7137 Automatic Bracket Size
7138 \begin_inset CommandInset label
7140 name "sub:Automatic-Bracket-Size"
7145 \begin_inset Index idx
7148 \begin_layout Plain Layout
7149 Bracket size ! automatic
7157 \begin_layout Standard
7158 Brackets with variable size can be inserted with the commands
7165 \begin_inset Index idx
7168 \begin_layout Plain Layout
7183 \begin_inset Index idx
7186 \begin_layout Plain Layout
7194 or via the math toolbar button
7195 \begin_inset Graphics
7196 filename ../images/dialog-show_mathdelimiter.png
7214 the wanted bracket must be inserted.
7215 The bracket size will then automatically be calculated for the output.
7218 \begin_layout Standard
7220 normal bracket: The command
7230 \begin_layout Plain Layout
7240 \begin_inset Formula $\downarrow$
7247 \begin_layout Plain Layout
7259 \begin_inset Formula
7269 \begin_layout Standard
7271 multiline bracket: The command
7283 \begin_layout Plain Layout
7293 \begin_inset Formula $\downarrow$
7300 \begin_layout Plain Layout
7314 \begin_inset Formula
7316 \ln\left(\frac{A}{C}\right)
7324 \begin_layout Standard
7340 \begin_inset space ~
7346 This has the advantage that you can see in LyX immediately the real bracket
7347 size and that the matching right bracket will be created too.
7348 \begin_inset Newline newline
7351 The command for the last example would then be:
7365 \begin_layout Plain Layout
7375 \begin_inset Formula $\downarrow$
7381 \begin_layout Standard
7382 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7383 For example the command
7393 \begin_layout Plain Layout
7403 \begin_inset Formula $\downarrow$
7410 \begin_layout Plain Layout
7426 \begin_inset Formula
7428 \left.\frac{A}{B}\right\}
7447 will be converted by LyX to brackets in the right size when the document
7448 is reloaded and an omitted bracket will appear as dashed line.
7451 \begin_layout Standard
7452 \begin_inset VSpace bigskip
7455 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7463 \begin_inset Index idx
7466 \begin_layout Plain Layout
7474 is additionally available for all brackets and limits.
7475 With this command the height of the following character is adapted to the
7476 one of the surrounding brackets, what is e.
7477 \begin_inset space \thinspace{}
7481 \begin_inset space \space{}
7484 needed for physical vectors:
7485 \begin_inset Formula
7487 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
7492 For physical vectors there is a special LaTeX-package, described in
7493 \begin_inset CommandInset ref
7495 reference "sub:Physical-Vectors"
7502 \begin_layout Subsection
7504 \begin_inset Index idx
7507 \begin_layout Plain Layout
7508 Brackets ! horizontal
7516 \begin_layout Standard
7518 \begin_inset Tabular
7519 <lyxtabular version="3" rows="4" columns="2">
7520 <features tabularvalignment="middle">
7521 <column alignment="center" valignment="top" width="0pt">
7522 <column alignment="center" valignment="top" width="0pt">
7524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7527 \begin_layout Plain Layout
7529 \begin_inset Note Note
7532 \begin_layout Plain Layout
7539 is only used as spacer.
7549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7552 \begin_layout Plain Layout
7560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7563 \begin_layout Plain Layout
7567 \begin_layout Plain Layout
7582 \begin_layout Plain Layout
7595 \begin_layout Plain Layout
7608 \begin_layout Plain Layout
7621 \begin_layout Plain Layout
7629 \begin_inset Index idx
7632 \begin_layout Plain Layout
7645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7648 \begin_layout Plain Layout
7649 \begin_inset Formula $\overbrace{A+B}^{3}$
7659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7662 \begin_layout Plain Layout
7666 \begin_layout Plain Layout
7681 \begin_layout Plain Layout
7694 \begin_layout Plain Layout
7707 \begin_layout Plain Layout
7715 \begin_inset Index idx
7718 \begin_layout Plain Layout
7731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7734 \begin_layout Plain Layout
7735 \begin_inset Formula $\underbrace{A+B}_{5}$
7745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7748 \begin_layout Plain Layout
7755 \begin_layout Plain Layout
7770 \begin_layout Plain Layout
7783 \begin_layout Plain Layout
7796 \begin_layout Plain Layout
7809 \begin_layout Plain Layout
7822 \begin_layout Plain Layout
7835 \begin_layout Plain Layout
7849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7852 \begin_layout Plain Layout
7853 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7869 \begin_layout Standard
7870 In the last example it doesn't matter if
7882 is inserted at first.
7885 \begin_layout Standard
7886 \begin_inset VSpace bigskip
7889 When brackets are needed that overlap each other, multiline formulas, as
7891 \begin_inset CommandInset ref
7893 reference "sec:Multiline-Formulas"
7898 \begin_inset Formula
7900 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7901 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7906 In the first row the formula is inserted together with the first brace.
7907 It is hereby important that the space command
7911 \begin_layout Plain Layout
7912 Space commands are explained in
7913 \begin_inset CommandInset ref
7915 reference "sub:Predefined-Space"
7930 is inserted before the first
7931 \begin_inset Formula $d$
7934 , because the brace that ends behind the
7935 \begin_inset Formula $q$
7938 prevents that the following
7939 \begin_inset Quotes eld
7943 \begin_inset Quotes erd
7946 is surrounded by space.
7950 \begin_layout Plain Layout
7951 because a bracket is not handled as a character, see
7952 \begin_inset CommandInset ref
7954 reference "sub:Binary-Operators"
7963 In the second row the second brace is inserted.
7964 As it should begin before the
7965 \begin_inset Formula $b$
7980 \begin_layout Plain Layout
7988 \begin_inset CommandInset ref
7990 reference "sub:Placeholders"
7999 This space is needed because the
8000 \begin_inset Quotes eld
8004 \begin_inset Quotes erd
8007 is also surrounded by space in the formula.
8008 The brace is placed under the command
8017 \begin_layout Standard
8018 It gets more complicated when brackets overlap each other, like in the following
8023 \begin_layout Plain Layout
8035 \begin_inset Formula
8037 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
8038 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
8047 \begin_layout Plain Layout
8058 The first formula row is the same as the second row of the previous example,
8059 with the difference that the brace is above.
8060 The second row contains the formula together with the second brace.
8061 To avoid that there is space between the upper brace in the first row and
8062 the formula, the row spacing needs to be reduced.
8063 This is not easily possible due to a bug in LyX
8067 \begin_layout Plain Layout
8068 \begin_inset CommandInset href
8070 name "LyX-bug #1505"
8071 target "http://www.lyx.org/trac/ticket/1505"
8081 As a solution for the problem, the global formula row separation
8088 \begin_inset Index idx
8091 \begin_layout Plain Layout
8099 must be changed to -6
8100 \begin_inset space \thinspace{}
8103 pt before the formula with the command
8118 is set back after the formula to the standard value of 3
8119 \begin_inset space \thinspace{}
8122 pt using the same command.
8123 More about the row separation in formulas is explained in
8124 \begin_inset CommandInset ref
8126 reference "sub:Line-Separation"
8133 \begin_layout Section
8135 \begin_inset Index idx
8138 \begin_layout Plain Layout
8147 \begin_layout Standard
8148 Arrows can be inserted via the math toolbar button
8149 \begin_inset Graphics
8150 filename ../images/math/leftarrow.png
8155 or the commands listed in the following subsections.
8158 \begin_layout Subsection
8160 \begin_inset Index idx
8163 \begin_layout Plain Layout
8172 \begin_layout Standard
8173 \begin_inset space \hfill{}
8177 \begin_inset Tabular
8178 <lyxtabular version="3" rows="8" columns="2">
8179 <features tabularvalignment="middle">
8180 <column alignment="center" valignment="top" width="0pt">
8181 <column alignment="center" valignment="top" width="0pt">
8183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8186 \begin_layout Plain Layout
8192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8195 \begin_layout Plain Layout
8203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8206 \begin_layout Plain Layout
8214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8217 \begin_layout Plain Layout
8218 \begin_inset Formula $\gets$
8228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8231 \begin_layout Plain Layout
8239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8242 \begin_layout Plain Layout
8243 \begin_inset Formula $\Leftarrow$
8253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8256 \begin_layout Plain Layout
8264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8267 \begin_layout Plain Layout
8268 \begin_inset Formula $\longleftarrow$
8278 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8281 \begin_layout Plain Layout
8289 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8292 \begin_layout Plain Layout
8293 \begin_inset Formula $\Longleftarrow$
8303 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8306 \begin_layout Plain Layout
8314 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8317 \begin_layout Plain Layout
8318 \begin_inset Formula $\leftharpoonup$
8328 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8331 \begin_layout Plain Layout
8339 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8342 \begin_layout Plain Layout
8343 \begin_inset Formula $\leftharpoondown$
8353 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8356 \begin_layout Plain Layout
8364 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8367 \begin_layout Plain Layout
8368 \begin_inset Formula $\hookleftarrow$
8382 \begin_inset space \hfill{}
8386 \begin_inset Tabular
8387 <lyxtabular version="3" rows="8" columns="2">
8388 <features tabularvalignment="middle">
8389 <column alignment="center" valignment="top" width="0pt">
8390 <column alignment="center" valignment="top" width="0pt">
8392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8395 \begin_layout Plain Layout
8401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8404 \begin_layout Plain Layout
8412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8415 \begin_layout Plain Layout
8423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8426 \begin_layout Plain Layout
8427 \begin_inset Formula $\to$
8437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8440 \begin_layout Plain Layout
8448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8451 \begin_layout Plain Layout
8452 \begin_inset Formula $\Rightarrow$
8462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8465 \begin_layout Plain Layout
8473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8476 \begin_layout Plain Layout
8477 \begin_inset Formula $\longrightarrow$
8487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8490 \begin_layout Plain Layout
8498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8501 \begin_layout Plain Layout
8502 \begin_inset Formula $\Longrightarrow$
8512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8515 \begin_layout Plain Layout
8523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8526 \begin_layout Plain Layout
8527 \begin_inset Formula $\rightharpoonup$
8537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8540 \begin_layout Plain Layout
8548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8551 \begin_layout Plain Layout
8552 \begin_inset Formula $\rightharpoondown$
8562 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8565 \begin_layout Plain Layout
8573 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8576 \begin_layout Plain Layout
8577 \begin_inset Formula $\hookrightarrow$
8591 \begin_inset space \hfill{}
8597 \begin_layout Standard
8598 \begin_inset space \hfill{}
8602 \begin_inset Tabular
8603 <lyxtabular version="3" rows="6" columns="2">
8604 <features tabularvalignment="middle">
8605 <column alignment="center" valignment="top" width="0pt">
8606 <column alignment="center" valignment="top" width="0pt">
8608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8611 \begin_layout Plain Layout
8617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8620 \begin_layout Plain Layout
8628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8631 \begin_layout Plain Layout
8639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8642 \begin_layout Plain Layout
8643 \begin_inset Formula $\leftrightarrow$
8653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8656 \begin_layout Plain Layout
8664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8667 \begin_layout Plain Layout
8668 \begin_inset Formula $\Leftrightarrow$
8678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8681 \begin_layout Plain Layout
8689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8692 \begin_layout Plain Layout
8693 \begin_inset Formula $\longleftrightarrow$
8703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8706 \begin_layout Plain Layout
8714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8717 \begin_layout Plain Layout
8718 \begin_inset Formula $\Longleftrightarrow$
8728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8731 \begin_layout Plain Layout
8739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8742 \begin_layout Plain Layout
8743 \begin_inset Formula $\rightleftharpoons$
8757 \begin_inset space \hspace{}
8762 \begin_inset space \hfill{}
8766 \begin_inset Tabular
8767 <lyxtabular version="3" rows="5" columns="2">
8768 <features tabularvalignment="middle">
8769 <column alignment="center" valignment="top" width="0pt">
8770 <column alignment="center" valignment="top" width="0pt">
8772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8775 \begin_layout Plain Layout
8781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8784 \begin_layout Plain Layout
8792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8795 \begin_layout Plain Layout
8803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8806 \begin_layout Plain Layout
8807 \begin_inset Formula $\mapsto$
8817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8820 \begin_layout Plain Layout
8828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8831 \begin_layout Plain Layout
8832 \begin_inset Formula $\longmapsto$
8842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8845 \begin_layout Plain Layout
8853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8856 \begin_layout Plain Layout
8857 \begin_inset Formula $\leadsto$
8867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8870 \begin_layout Plain Layout
8878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8881 \begin_layout Plain Layout
8882 \begin_inset Formula $\dasharrow$
8896 \begin_inset space \hfill{}
8902 \begin_layout Standard
8903 \begin_inset VSpace medskip
8906 Arrows used as accents like e.
8907 \begin_inset space \thinspace{}
8911 \begin_inset space \space{}
8914 vector arrows are listed in
8915 \begin_inset CommandInset ref
8917 reference "sec:Accents"
8924 \begin_layout Standard
8925 \begin_inset VSpace bigskip
8928 Furthermore there are the labeled arrows
8929 \begin_inset Index idx
8932 \begin_layout Plain Layout
8945 \begin_inset Index idx
8948 \begin_layout Plain Layout
8963 \begin_inset Index idx
8966 \begin_layout Plain Layout
8973 \begin_layout Plain Layout
8988 When inserting one of these commands in a formula, an arrow with two blue
8989 boxes appear where the label can be inserted.
8990 The length of the arrow adapts to the label width.
8993 \begin_layout Standard
8995 \begin_inset Tabular
8996 <lyxtabular version="3" rows="3" columns="2">
8997 <features tabularvalignment="middle">
8998 <column alignment="center" valignment="top" width="0pt">
8999 <column alignment="center" valignment="top" width="0pt">
9001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9004 \begin_layout Plain Layout
9010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9013 \begin_layout Plain Layout
9015 \begin_inset Note Note
9018 \begin_layout Plain Layout
9025 is only used as spacer.
9037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9040 \begin_layout Plain Layout
9047 \begin_layout Plain Layout
9057 \begin_inset Formula $\downarrow$
9061 \begin_inset Formula $\to$
9069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9072 \begin_layout Plain Layout
9073 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9086 \begin_layout Plain Layout
9093 \begin_layout Plain Layout
9103 \begin_inset Formula $\downarrow$
9107 \begin_inset Formula $\to$
9115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9118 \begin_layout Plain Layout
9119 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9135 \begin_layout Subsection
9136 Vertical and diagonal Arrows
9137 \begin_inset Index idx
9140 \begin_layout Plain Layout
9147 \begin_inset Index idx
9150 \begin_layout Plain Layout
9159 \begin_layout Standard
9160 \begin_inset space \hfill{}
9164 \begin_inset Tabular
9165 <lyxtabular version="3" rows="7" columns="2">
9166 <features tabularvalignment="middle">
9167 <column alignment="center" valignment="top" width="0pt">
9168 <column alignment="center" valignment="top" width="0pt">
9170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9173 \begin_layout Plain Layout
9179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9182 \begin_layout Plain Layout
9190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9193 \begin_layout Plain Layout
9201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9204 \begin_layout Plain Layout
9205 \begin_inset Formula $\uparrow$
9215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9218 \begin_layout Plain Layout
9226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9229 \begin_layout Plain Layout
9230 \begin_inset Formula $\Uparrow$
9240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9243 \begin_layout Plain Layout
9251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9254 \begin_layout Plain Layout
9255 \begin_inset Formula $\updownarrow$
9265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9268 \begin_layout Plain Layout
9276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9279 \begin_layout Plain Layout
9280 \begin_inset Formula $\Updownarrow$
9290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9293 \begin_layout Plain Layout
9301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9304 \begin_layout Plain Layout
9305 \begin_inset Formula $\Downarrow$
9315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9318 \begin_layout Plain Layout
9326 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9329 \begin_layout Plain Layout
9330 \begin_inset Formula $\downarrow$
9344 \begin_inset space \hfill{}
9348 \begin_inset Tabular
9349 <lyxtabular version="3" rows="5" columns="2">
9350 <features tabularvalignment="middle">
9351 <column alignment="center" valignment="top" width="0pt">
9352 <column alignment="center" valignment="top" width="0pt">
9354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9357 \begin_layout Plain Layout
9363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9366 \begin_layout Plain Layout
9374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9377 \begin_layout Plain Layout
9385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9388 \begin_layout Plain Layout
9389 \begin_inset Formula $\nearrow$
9399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9402 \begin_layout Plain Layout
9410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9413 \begin_layout Plain Layout
9414 \begin_inset Formula $\searrow$
9424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9427 \begin_layout Plain Layout
9435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9438 \begin_layout Plain Layout
9439 \begin_inset Formula $\swarrow$
9449 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9452 \begin_layout Plain Layout
9460 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9463 \begin_layout Plain Layout
9464 \begin_inset Formula $\nwarrow$
9478 \begin_inset space \hfill{}
9484 \begin_layout Standard
9485 \begin_inset VSpace medskip
9488 Vertical arrows can be used also as delimiters together with the commands
9490 \begin_inset CommandInset ref
9492 reference "sub:Manual-Bracket-Size"
9497 \begin_inset CommandInset ref
9499 reference "sub:Automatic-Bracket-Size"
9506 \begin_layout Section
9508 \begin_inset CommandInset label
9515 \begin_inset Index idx
9518 \begin_layout Plain Layout
9527 \begin_layout Standard
9528 Accents can be inserted via the math toolbar button
9529 \begin_inset Graphics
9530 filename ../images/math/hat.png
9535 or the commands listed in the following subsections.
9538 \begin_layout Subsection
9539 Accents for one Character
9543 \begin_layout Plain Layout
9556 \begin_layout Plain Layout
9558 \begin_inset CommandInset ref
9560 reference "sub:Accents-in-Text"
9573 \begin_layout Plain Layout
9581 \begin_inset Note Note
9584 \begin_layout Plain Layout
9591 is used to avoid that the footnote appears in the PDF-bookmark.
9594 \begin_layout Plain Layout
9602 \begin_inset CommandInset ref
9604 reference "sub:Formulas-in-Section"
9614 \begin_inset CommandInset label
9616 name "sub:Accents-for-one"
9621 \begin_inset Index idx
9624 \begin_layout Plain Layout
9625 Accents ! for one character
9633 \begin_layout Standard
9634 \begin_inset space \hfill{}
9638 \begin_inset Tabular
9639 <lyxtabular version="3" rows="8" columns="2">
9640 <features tabularvalignment="middle">
9641 <column alignment="center" valignment="top" width="0pt">
9642 <column alignment="center" valignment="top" width="0pt">
9644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9647 \begin_layout Plain Layout
9653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9656 \begin_layout Plain Layout
9658 \begin_inset Note Note
9661 \begin_layout Plain Layout
9668 is only used as spacer.
9680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9683 \begin_layout Plain Layout
9690 \begin_layout Plain Layout
9704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9707 \begin_layout Plain Layout
9708 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9718 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9721 \begin_layout Plain Layout
9728 \begin_layout Plain Layout
9742 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9745 \begin_layout Plain Layout
9746 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9756 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9759 \begin_layout Plain Layout
9766 \begin_layout Plain Layout
9780 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9783 \begin_layout Plain Layout
9784 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9794 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9797 \begin_layout Plain Layout
9804 \begin_layout Plain Layout
9818 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9821 \begin_layout Plain Layout
9822 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9832 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9835 \begin_layout Plain Layout
9842 \begin_layout Plain Layout
9852 \begin_inset Index idx
9855 \begin_layout Plain Layout
9866 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9869 \begin_layout Plain Layout
9870 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9880 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9883 \begin_layout Plain Layout
9890 \begin_layout Plain Layout
9904 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9907 \begin_layout Plain Layout
9908 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9918 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9921 \begin_layout Plain Layout
9928 \begin_layout Plain Layout
9942 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9945 \begin_layout Plain Layout
9946 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9960 \begin_inset space \hfill{}
9964 \begin_inset Tabular
9965 <lyxtabular version="3" rows="7" columns="2">
9966 <features tabularvalignment="middle">
9967 <column alignment="center" valignment="top" width="0pt">
9968 <column alignment="center" valignment="top" width="0pt">
9970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9973 \begin_layout Plain Layout
9979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9982 \begin_layout Plain Layout
9990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9993 \begin_layout Plain Layout
10000 \begin_layout Plain Layout
10014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10017 \begin_layout Plain Layout
10018 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
10028 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10031 \begin_layout Plain Layout
10038 \begin_layout Plain Layout
10052 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10055 \begin_layout Plain Layout
10056 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10066 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10069 \begin_layout Plain Layout
10076 \begin_layout Plain Layout
10090 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10093 \begin_layout Plain Layout
10094 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10104 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10107 \begin_layout Plain Layout
10114 \begin_layout Plain Layout
10128 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10131 \begin_layout Plain Layout
10132 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10142 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10145 \begin_layout Plain Layout
10152 \begin_layout Plain Layout
10166 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10169 \begin_layout Plain Layout
10170 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10180 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10183 \begin_layout Plain Layout
10190 \begin_layout Plain Layout
10204 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10207 \begin_layout Plain Layout
10208 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10222 \begin_inset space \hfill{}
10228 \begin_layout Standard
10229 \begin_inset VSpace bigskip
10235 \begin_layout Standard
10236 You can directly insert accents like é to formulas.
10237 LyX will transform them to the corresponding accent command.
10239 \begin_inset Index idx
10242 \begin_layout Plain Layout
10248 it is better to insert a quotation mark before the vowel.
10249 These two characters are then treated by LaTeX as
10253 character when the formula part with the umlaut is marked as German.
10261 \begin_inset Quotes eld
10265 \begin_inset Quotes erd
10268 umlauts are created as demonstrated in the following example:
10271 \begin_layout Standard
10272 \begin_inset VSpace -2mm
10278 \begin_layout Standard
10280 \begin_inset Tabular
10281 <lyxtabular version="3" rows="3" columns="2">
10282 <features tabularvalignment="middle">
10283 <column alignment="center" valignment="top" width="0">
10284 <column alignment="center" valignment="top" width="0">
10286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10289 \begin_layout Plain Layout
10295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10298 \begin_layout Plain Layout
10300 \begin_inset Note Note
10303 \begin_layout Plain Layout
10311 \begin_inset space \thinspace{}
10314 pt space are only used as spacer.
10326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10329 \begin_layout Plain Layout
10332 \begin_inset Quotes grd
10340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10343 \begin_layout Plain Layout
10344 \begin_inset space \hspace{}
10351 \begin_inset Formula $"i$
10361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10364 \begin_layout Plain Layout
10371 \begin_layout Plain Layout
10385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10388 \begin_layout Plain Layout
10389 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10405 \begin_layout Standard
10406 Another advantage to
10412 is that umlauts can directly be converted to mathematical text because
10413 the accent commands above are
10419 in mathematical text
10422 To convert an accented character to mathematical text, only the character
10423 under the accent may be converted.
10424 This applies also for all other conversions, e.
10425 \begin_inset space \thinspace{}
10429 \begin_inset space \space{}
10435 \begin_layout Standard
10436 In mathematical text, umlauts and other accented characters can directly
10440 \begin_layout Subsection
10441 Accents for Operators
10442 \begin_inset Index idx
10445 \begin_layout Plain Layout
10446 Accents ! for operators
10454 \begin_layout Standard
10462 \begin_inset Index idx
10465 \begin_layout Plain Layout
10480 \begin_inset Index idx
10483 \begin_layout Plain Layout
10491 characters can be placed above or below an operator, respectively, to accent
10500 \begin_inset Index idx
10503 \begin_layout Plain Layout
10511 characters can be set before and behind an operator.
10512 The command scheme is:
10515 \begin_layout Standard
10531 \begin_layout Standard
10538 must always be before the operator that should be accented.
10539 You can accent with several characters and even with other operators and
10547 for example only characters behind an operator, write nothing between the
10548 first braces but don't omit the braces.
10551 \begin_layout Standard
10552 For example the command
10557 \begin_inset Formula $\to$
10567 \begin_inset Formula $\to$
10576 \begin_layout Plain Layout
10592 \begin_inset Formula
10594 \sideset{}{'}\sum_{k=1}^{n}
10602 \begin_layout Standard
10611 \begin_layout Plain Layout
10626 \begin_layout Plain Layout
10638 \begin_inset Formula $\uparrow$
10646 \begin_inset Formula
10648 \overset{a}{\maltese}
10653 As seen in the last example, with
10665 symbols and characters can also be accented; with
10671 this is not possible.
10674 \begin_layout Subsection
10675 Accents for several Characters
10676 \begin_inset Index idx
10679 \begin_layout Plain Layout
10680 Accents ! for several characters
10688 \begin_layout Standard
10689 \begin_inset space \hfill{}
10693 \begin_inset Tabular
10694 <lyxtabular version="3" rows="5" columns="2">
10695 <features tabularvalignment="middle">
10696 <column alignment="center" valignment="top" width="0pt">
10697 <column alignment="center" valignment="top" width="0pt">
10699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10702 \begin_layout Plain Layout
10708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10711 \begin_layout Plain Layout
10713 \begin_inset Note Note
10716 \begin_layout Plain Layout
10723 is only used as spacer.
10735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10738 \begin_layout Plain Layout
10745 \begin_layout Plain Layout
10759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10762 \begin_layout Plain Layout
10763 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10773 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10776 \begin_layout Plain Layout
10783 \begin_layout Plain Layout
10797 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10800 \begin_layout Plain Layout
10801 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10811 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10814 \begin_layout Plain Layout
10821 \begin_layout Plain Layout
10835 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10838 \begin_layout Plain Layout
10839 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10849 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10852 \begin_layout Plain Layout
10855 underleftrightarrow
10859 \begin_layout Plain Layout
10873 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10876 \begin_layout Plain Layout
10877 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10891 \begin_inset space \hfill{}
10895 \begin_inset Tabular
10896 <lyxtabular version="3" rows="5" columns="2">
10897 <features tabularvalignment="middle">
10898 <column alignment="center" valignment="top" width="0pt">
10899 <column alignment="center" valignment="top" width="0pt">
10901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10904 \begin_layout Plain Layout
10910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10913 \begin_layout Plain Layout
10921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10924 \begin_layout Plain Layout
10931 \begin_layout Plain Layout
10945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10948 \begin_layout Plain Layout
10949 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10962 \begin_layout Plain Layout
10969 \begin_layout Plain Layout
10983 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10986 \begin_layout Plain Layout
10987 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10997 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11000 \begin_layout Plain Layout
11007 \begin_layout Plain Layout
11021 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11024 \begin_layout Plain Layout
11025 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
11035 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11038 \begin_layout Plain Layout
11045 \begin_layout Plain Layout
11059 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11062 \begin_layout Plain Layout
11063 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11077 \begin_inset space \hfill{}
11083 \begin_layout Standard
11084 \begin_inset VSpace medskip
11087 With these commands as many characters as you like can be accented.
11100 will only be set in the output with a length of three characters, as shown
11101 in the following example:
11102 \begin_inset Formula
11104 \widetilde{A+B=C-D}
11112 \begin_layout Standard
11120 \begin_inset Index idx
11123 \begin_layout Plain Layout
11138 \begin_inset Index idx
11141 \begin_layout Plain Layout
11149 described in the previous subsection it is also possible to accent several
11159 \begin_layout Plain Layout
11169 \begin_inset Formula $\downarrow$
11175 \begin_inset Formula
11177 \underset{***}{A=B}
11185 \begin_layout Section
11187 \begin_inset CommandInset label
11194 \begin_inset Index idx
11197 \begin_layout Plain Layout
11206 \begin_layout Subsection
11208 \begin_inset CommandInset label
11210 name "sub:Predefined-Space"
11215 \begin_inset Index idx
11218 \begin_layout Plain Layout
11219 Space ! horizontal ! predefined
11227 \begin_layout Standard
11228 Sometimes it is necessary to insert horizontal space into a formula.
11229 This is done by inserting a protected space (shortcut
11232 arg "command-alternatives space-insert protected ; math-space"
11237 \begin_inset Quotes eld
11246 \begin_layout Plain Layout
11258 \begin_inset Quotes erd
11261 appears and by pressing
11265 several times one can select one of eight different space sizes.
11266 The spaces can also be inserted using the math toolbar button
11267 \begin_inset Graphics
11268 filename ../images/math/space.png
11273 or special commands.
11274 Independent from the inserted command, one can select the size again by
11282 \begin_layout Standard
11285 \begin_inset VSpace -5mm
11289 \begin_inset Tabular
11290 <lyxtabular version="3" rows="3" columns="7">
11291 <features tabularvalignment="middle">
11292 <column alignment="center" valignment="middle" width="6.8cm">
11293 <column alignment="center" valignment="top" width="0">
11294 <column alignment="center" valignment="top" width="0">
11295 <column alignment="center" valignment="top" width="0">
11296 <column alignment="center" valignment="top" width="0">
11297 <column alignment="center" valignment="top" width="0">
11298 <column alignment="center" valignment="top" width="0">
11300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11303 \begin_layout Plain Layout
11309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11312 \begin_layout Plain Layout
11320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11323 \begin_layout Plain Layout
11331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11334 \begin_layout Plain Layout
11342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11345 \begin_layout Plain Layout
11353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11356 \begin_layout Plain Layout
11364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11367 \begin_layout Plain Layout
11377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11380 \begin_layout Plain Layout
11385 keystrokes after inserting the protected space
11390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11393 \begin_layout Plain Layout
11399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11402 \begin_layout Plain Layout
11408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11411 \begin_layout Plain Layout
11417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11420 \begin_layout Plain Layout
11426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11429 \begin_layout Plain Layout
11435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11438 \begin_layout Plain Layout
11446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11449 \begin_layout Plain Layout
11455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11458 \begin_layout Plain Layout
11459 \begin_inset Formula $A\, B$
11467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11470 \begin_layout Plain Layout
11471 \begin_inset Formula $A\: B$
11479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11482 \begin_layout Plain Layout
11483 \begin_inset Formula $A\; B$
11491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11494 \begin_layout Plain Layout
11495 \begin_inset Formula $A\quad B$
11503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11506 \begin_layout Plain Layout
11507 \begin_inset Formula $A\qquad B$
11515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11518 \begin_layout Plain Layout
11519 \begin_inset Formula $A\! B$
11535 \begin_layout Standard
11536 The last size seem to produce no space.
11537 It is displayed red in LyX contrary to the other sizes, because it is a
11539 There are two more negative spaces:
11542 \begin_layout Standard
11544 \begin_inset Tabular
11545 <lyxtabular version="3" rows="3" columns="3">
11546 <features tabularvalignment="middle">
11547 <column alignment="center" valignment="middle" width="6.8cm">
11548 <column alignment="center" valignment="top" width="0pt">
11549 <column alignment="center" valignment="top" width="0pt">
11551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11554 \begin_layout Plain Layout
11560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11563 \begin_layout Plain Layout
11571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11574 \begin_layout Plain Layout
11584 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11587 \begin_layout Plain Layout
11592 keystrokes after inserting the protected space
11597 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11600 \begin_layout Plain Layout
11606 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11609 \begin_layout Plain Layout
11617 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11620 \begin_layout Plain Layout
11626 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11629 \begin_layout Plain Layout
11630 \begin_inset Formula $A\negmedspace B$
11638 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11641 \begin_layout Plain Layout
11642 \begin_inset Formula $A\negthickspace B$
11658 \begin_layout Standard
11659 Negative spaces can lead to characters overlapping each other.
11660 Thus they can be used to enforce ligatures, which are e.
11661 \begin_inset space \thinspace{}
11665 \begin_inset space \space{}
11668 useful for summation operators:
11671 \begin_layout Standard
11673 \begin_inset Tabular
11674 <lyxtabular version="3" rows="3" columns="2">
11675 <features tabularvalignment="middle">
11676 <column alignment="center" valignment="top" width="0">
11677 <column alignment="center" valignment="top" width="0">
11679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11682 \begin_layout Plain Layout
11688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11691 \begin_layout Plain Layout
11693 \begin_inset Note Note
11696 \begin_layout Plain Layout
11703 is only used as spacer.
11715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11718 \begin_layout Plain Layout
11727 \begin_layout Plain Layout
11741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11744 \begin_layout Plain Layout
11745 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11758 \begin_layout Plain Layout
11769 \begin_layout Plain Layout
11783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11786 \begin_layout Plain Layout
11787 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11803 \begin_layout Standard
11804 Relations like for example equal signs, are always surrounded by space.
11805 To suppress this, the equal sign is placed into a TeX-brace.
11806 The following example demonstrates this:
11809 \begin_layout Standard
11811 \begin_inset Tabular
11812 <lyxtabular version="3" rows="2" columns="2">
11813 <features tabularvalignment="middle">
11814 <column alignment="center" valignment="top" width="0pt">
11815 <column alignment="center" valignment="top" width="0pt">
11817 <cell alignment="center" valignment="top" usebox="none">
11820 \begin_layout Plain Layout
11826 <cell alignment="center" valignment="top" usebox="none">
11829 \begin_layout Plain Layout
11830 \begin_inset Formula $A=B$
11840 <cell alignment="center" valignment="top" usebox="none">
11843 \begin_layout Plain Layout
11844 \begin_inset Note Note
11847 \begin_layout Plain Layout
11854 is only used as spacer.
11860 \begin_inset Formula $\raisebox{5mm}{}$
11863 equation without space
11868 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11871 \begin_layout Plain Layout
11872 \begin_inset Formula $A{=}B$
11888 \begin_layout Standard
11890 The command for the last formula is:
11895 \begin_inset Formula $\to$
11901 \begin_layout Standard
11902 \begin_inset VSpace bigskip
11905 Spaces are needed for physical units, because the space between the value
11906 and the unit is the smallest one and not a normal space.
11907 For units in text, the smallest space is inserted via the menu
11909 Insert\SpecialChar \menuseparator
11910 Formatting\SpecialChar \menuseparator
11912 \begin_inset space ~
11920 arg "space-insert thin"
11926 \begin_layout Standard
11927 An example to visualize the difference:
11930 \begin_layout Standard
11931 \begin_inset Tabular
11932 <lyxtabular version="3" rows="2" columns="2">
11933 <features tabularvalignment="middle">
11934 <column alignment="left" valignment="top" width="0">
11935 <column alignment="left" valignment="top" width="0">
11937 <cell alignment="center" valignment="top" usebox="none">
11940 \begin_layout Plain Layout
11942 \begin_inset Formula $\cdot$
11950 <cell alignment="center" valignment="top" usebox="none">
11953 \begin_layout Plain Layout
11954 space between value and unit
11961 <cell alignment="center" valignment="top" usebox="none">
11964 \begin_layout Plain Layout
11966 \begin_inset space \thinspace{}
11970 \begin_inset Formula $\cdot$
11978 <cell alignment="center" valignment="top" usebox="none">
11981 \begin_layout Plain Layout
11982 smallest space between value and unit
11995 \begin_layout Subsection
12000 \begin_layout Plain Layout
12013 \begin_layout Plain Layout
12014 for vertical space in formulas see
12015 \begin_inset CommandInset ref
12017 reference "sub:Line-Separation"
12030 \begin_layout Plain Layout
12038 \begin_inset Note Note
12041 \begin_layout Plain Layout
12044 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12047 \begin_layout Plain Layout
12050 texorpdfstring is in section
12051 \begin_inset CommandInset ref
12053 reference "sub:Formulas-in-Section"
12063 \begin_inset CommandInset label
12065 name "sub:Variable-Space"
12070 \begin_inset Index idx
12073 \begin_layout Plain Layout
12074 Space ! horizontal ! variable
12082 \begin_layout Standard
12083 Space with a defined length can be inserted with the command
12090 \begin_inset Index idx
12093 \begin_layout Plain Layout
12103 \begin_inset Quotes eld
12112 \begin_layout Plain Layout
12124 \begin_inset Quotes erd
12128 The length can be specified by left-clicking on the
12129 \begin_inset Quotes eld
12138 \begin_layout Plain Layout
12150 \begin_inset Quotes erd
12154 The length may also be negative.
12155 To insert as much space as is available, the command
12162 \begin_inset Index idx
12165 \begin_layout Plain Layout
12176 \begin_layout Standard
12177 \begin_inset VSpace -1mm
12183 \begin_layout Standard
12185 \begin_inset Tabular
12186 <lyxtabular version="3" rows="4" columns="2">
12187 <features tabularvalignment="middle">
12188 <column alignment="center" valignment="top" width="0">
12189 <column alignment="center" valignment="top" width="0">
12191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12194 \begin_layout Plain Layout
12202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12205 \begin_layout Plain Layout
12213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12216 \begin_layout Plain Layout
12223 \begin_layout Plain Layout
12233 \begin_inset Formula $\to$
12239 \begin_inset space \thinspace{}
12247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12250 \begin_layout Plain Layout
12251 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12264 \begin_layout Plain Layout
12271 \begin_layout Plain Layout
12281 \begin_inset Formula $\to$
12287 \begin_inset space \thinspace{}
12295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12298 \begin_layout Plain Layout
12299 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12312 \begin_layout Plain Layout
12319 \begin_layout Plain Layout
12333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12336 \begin_layout Plain Layout
12337 \begin_inset Formula $A=A\hfill B=B$
12353 \begin_layout Standard
12354 In the last example the available space is given by the longest column entry
12356 In an inline formula the space depends on the length of the line in which
12364 Thus, when the line uses the full width, no space will be created.
12371 only has an effect on displayed formulas when the formula style
12376 (Formula styles are explained in
12377 \begin_inset CommandInset ref
12379 reference "sec:Formula-Styles"
12386 \begin_layout Standard
12393 , there are the commands
12405 that fill the space with a pattern, see
12406 \begin_inset CommandInset ref
12408 reference "sub:Ellipses"
12415 \begin_layout Standard
12416 For text, variable space can be inserted via the menu
12418 Insert\SpecialChar \menuseparator
12419 Formatting\SpecialChar \menuseparator
12421 \begin_inset space ~
12429 \begin_layout Standard
12430 This is a line with
12431 \begin_inset space \hspace{}
12436 \begin_inset space \thinspace{}
12442 \begin_layout Standard
12443 This is a line with
12444 \begin_inset space \hfill{}
12450 \begin_layout Subsection
12451 Space besides inline Formulas
12452 \begin_inset Index idx
12455 \begin_layout Plain Layout
12456 Space ! besides inline formulas
12464 \begin_layout Standard
12465 The space that surrounds inline formulas can be adjusted with the length
12473 \begin_inset Index idx
12476 \begin_layout Plain Layout
12485 The value of a length is set with the command
12492 \begin_inset Index idx
12495 \begin_layout Plain Layout
12503 which has the following scheme:
12506 \begin_layout Standard
12511 setlength{length name}{value}
12514 \begin_layout Standard
12522 \begin_inset space \thinspace{}
12528 \begin_layout Standard
12538 \begin_layout Standard
12539 is inserted in TeX-mode.
12541 \begin_inset space \thinspace{}
12544 mm space will now be set around all inline formulas:
12548 \begin_layout Plain Layout
12562 \begin_layout Standard
12563 This is a line with an inline formula
12564 \begin_inset Formula $A=B$
12568 \begin_inset space \thinspace{}
12571 mm surrounding space.
12575 \begin_layout Plain Layout
12589 \begin_layout Standard
12590 To return to the predefined value,
12596 is set to the value 0
12597 \begin_inset space \thinspace{}
12603 \begin_layout Section
12605 \begin_inset Index idx
12608 \begin_layout Plain Layout
12615 \begin_inset Index idx
12618 \begin_layout Plain Layout
12623 \begin_layout Plain Layout
12634 \begin_layout Plain Layout
12649 \begin_layout Standard
12650 Boxes for text are described in chapter
12657 \begin_inset space ~
12665 \begin_layout Subsection
12667 \begin_inset CommandInset label
12669 name "sub:Boxes-with-Frame"
12674 \begin_inset Index idx
12677 \begin_layout Plain Layout
12686 \begin_layout Standard
12687 It is possible to frame a formula or part of one with the commands
12694 \begin_inset Index idx
12697 \begin_layout Plain Layout
12712 \begin_inset Index idx
12715 \begin_layout Plain Layout
12726 \begin_layout Standard
12727 When one of these commands is inserted in a formula, a blue box appears
12728 within a frame to enter formula parts.
12735 an additional formula has to be created by
12739 within this box, because the box content will otherwise be treated as mathemati
12747 is used, a new formula is automatically created inside the frame.
12750 \begin_layout Standard
12757 is not suitable to frame displayed formulas because the formula will always
12758 be set in the size of the text.
12765 is in contrary not suitable to frame inline formulas, because the formula
12766 will always be set in the size of a displayed formula.
12769 \begin_layout Standard
12783 \begin_inset Index idx
12786 \begin_layout Plain Layout
12794 where additionally the frame width and the alignment can be specified.
12801 is used in the following scheme:
12804 \begin_layout Standard
12809 framebox[frame width][position]{box content}
12812 \begin_layout Standard
12813 The position can either be
12830 right aligns the formula in the box.
12831 When no position is given, the formula will be centered.
12832 \begin_inset Newline newline
12835 If no width is given, also no position can be given.
12836 In this case the frame width is adjusted to the box content like for
12845 \begin_layout Standard
12852 is inserted, a box appears containing three blue boxes.
12853 The first two boxes are surrounded by brackets and denote the two optional
12855 The third box is for formula parts like for
12864 \begin_layout Standard
12866 \begin_inset Tabular
12867 <lyxtabular version="3" rows="5" columns="2">
12868 <features tabularvalignment="middle">
12869 <column alignment="center" valignment="top" width="0">
12870 <column alignment="center" valignment="top" width="0">
12872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12875 \begin_layout Plain Layout
12881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12884 \begin_layout Plain Layout
12886 \begin_inset Note Note
12889 \begin_layout Plain Layout
12896 is only used as spacer.
12908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12911 \begin_layout Plain Layout
12918 \begin_layout Plain Layout
12937 \begin_layout Plain Layout
12951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12954 \begin_layout Plain Layout
12955 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12968 \begin_layout Plain Layout
12975 \begin_layout Plain Layout
12990 \begin_layout Plain Layout
13004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13007 \begin_layout Plain Layout
13008 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
13018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13021 \begin_layout Plain Layout
13028 \begin_layout Plain Layout
13042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13045 \begin_layout Plain Layout
13046 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13059 \begin_layout Plain Layout
13066 \begin_layout Plain Layout
13076 \begin_inset Formula $\to$
13080 \begin_inset Formula $\to$
13093 \begin_layout Plain Layout
13103 \begin_inset Formula $\downarrow$
13111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13114 \begin_layout Plain Layout
13115 \begin_inset Formula $\raisebox{6mm}{}$
13119 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13123 \begin_inset Formula $\raisebox{-4mm}{}$
13139 \begin_layout Standard
13140 The frame thickness can also be adjusted.
13141 To do this the following commands have to be inserted in TeX-mode before
13145 \begin_layout Standard
13155 \begin_inset Quotes eld
13159 \begin_inset Quotes erd
13173 \begin_inset Quotes eld
13177 \begin_inset Quotes erd
13183 \begin_layout Standard
13184 \begin_inset Quotes eld
13188 \begin_inset Quotes erd
13191 specifies the minimal distance between the frame and the first character
13193 An example for this is the following framed formula:
13197 \begin_layout Plain Layout
13209 \begin_inset Formula
13216 Before this formula the commands
13219 \begin_layout Standard
13241 \begin_layout Standard
13242 were inserted in TeX-mode.
13243 The given values are used for all following boxes.
13246 \begin_layout Standard
13247 To return to the standard frame size, the command
13250 \begin_layout Standard
13275 \begin_layout Plain Layout
13289 \begin_layout Standard
13290 is inserted in TeX-mode before the next formula.
13293 \begin_layout Subsection
13294 Boxes without Frame
13295 \begin_inset CommandInset label
13297 name "sub:Boxes-without-Frame"
13302 \begin_inset Index idx
13305 \begin_layout Plain Layout
13306 Boxes ! without frame
13314 \begin_layout Standard
13315 For boxes without a frame there are the following box commands:
13322 \begin_inset Index idx
13325 \begin_layout Plain Layout
13340 \begin_inset Index idx
13343 \begin_layout Plain Layout
13358 \begin_inset Index idx
13361 \begin_layout Plain Layout
13372 \begin_layout Standard
13379 a box can be super- or subscripted.
13380 But in contrary to normal super- and subscripting, the characters in the
13381 box keep their font size.
13388 is used in the following scheme:
13391 \begin_layout Standard
13396 raisebox{height}{box content}
13399 \begin_layout Standard
13400 When the box should contain a formula, an extra formula is needed like for
13411 \begin_inset Note Greyedout
13414 \begin_layout Plain Layout
13425 this extra formula is created by pressing
13429 twice instead of once because LyX doesn't yet support
13443 \begin_layout Standard
13445 \begin_inset Tabular
13446 <lyxtabular version="3" rows="4" columns="2">
13447 <features tabularvalignment="middle">
13448 <column alignment="center" valignment="top" width="0">
13449 <column alignment="center" valignment="top" width="0">
13451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13454 \begin_layout Plain Layout
13460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13463 \begin_layout Plain Layout
13471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13474 \begin_layout Plain Layout
13478 \begin_inset Formula $\to$
13484 \begin_inset Formula $\to$
13492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13495 \begin_layout Plain Layout
13496 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13509 \begin_layout Plain Layout
13513 \begin_inset Formula $\to$
13519 \begin_inset Formula $\to$
13527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13530 \begin_layout Plain Layout
13531 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13544 \begin_layout Plain Layout
13548 \begin_inset Formula $\to$
13567 \begin_layout Plain Layout
13581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13584 \begin_layout Plain Layout
13585 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13601 \begin_layout Standard
13626 , with the difference that there is no frame.
13629 \begin_layout Subsection
13631 \begin_inset CommandInset label
13633 name "sub:Colored-Boxes"
13638 \begin_inset Index idx
13641 \begin_layout Plain Layout
13650 \begin_layout Standard
13651 To be able to use all commands explained in this section, the LaTeX-package
13660 \begin_layout Plain Layout
13665 is part of every LaTeX standard installation.
13671 \begin_inset Index idx
13674 \begin_layout Plain Layout
13680 has to be loaded in the LaTeX-preamble with the line
13684 \begin_layout Plain Layout
13685 When text is colored somewhere in the document with a predefined color,
13686 LyX loads the LaTeX-package
13691 Thus it is possible that the package is loaded twice, but this does not
13698 \begin_inset Note Note
13701 \begin_layout Plain Layout
13702 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13711 \begin_layout Standard
13719 \begin_layout Standard
13720 \begin_inset VSpace medskip
13723 To color boxes, the command
13730 \begin_inset Index idx
13733 \begin_layout Plain Layout
13741 is used in the following scheme:
13744 \begin_layout Standard
13749 colorbox{color}{box content}
13752 \begin_layout Standard
13753 The box content can also be a box and a
13759 can also be part of another box (see the 2nd and 3rd example).
13760 When the box should contain a formula, an extra formula has to be created,
13761 the same way as for
13771 \begin_layout Plain Layout
13772 This also applies for the command
13786 \begin_layout Standard
13787 One of the following predefined colors can be chosen:
13790 \begin_layout Standard
13824 \begin_layout Standard
13826 \begin_inset Tabular
13827 <lyxtabular version="3" rows="4" columns="2">
13828 <features tabularvalignment="middle">
13829 <column alignment="center" valignment="top" width="0">
13830 <column alignment="center" valignment="top" width="0">
13832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13835 \begin_layout Plain Layout
13841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13844 \begin_layout Plain Layout
13846 \begin_inset Note Note
13849 \begin_layout Plain Layout
13856 is only used as spacer.
13868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13871 \begin_layout Plain Layout
13875 \begin_inset Formula $\to$
13885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13888 \begin_layout Plain Layout
13889 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13902 \begin_layout Plain Layout
13906 \begin_inset Formula $\to$
13917 \begin_layout Plain Layout
13931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13934 \begin_layout Plain Layout
13935 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13948 \begin_layout Plain Layout
13955 \begin_layout Plain Layout
13967 \begin_inset Formula $\to$
13986 \begin_layout Plain Layout
14000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14003 \begin_layout Plain Layout
14004 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
14020 \begin_layout Standard
14027 only colors the box but not the characters in the box.
14028 To color all characters, the whole formula is highlighted and the desired
14029 color is chosen in the
14032 \begin_inset space ~
14038 The dialog can be called with the toolbar button
14039 \begin_inset Graphics
14040 filename ../images/dialog-show_character.png
14047 Edit\SpecialChar \menuseparator
14049 \begin_inset space ~
14052 Style\SpecialChar \menuseparator
14056 The formula number then has the same color as the formula.
14057 When the formula number should get another color than the formula characters,
14058 the color must be changed within the formula.
14061 \begin_layout Standard
14065 \begin_layout Standard
14068 \begin_inset Formula
14070 \int A=B\label{eq:red}
14078 \begin_inset Formula
14080 \textcolor{red}{\int A=B}\label{eq:redgreen}
14088 \begin_layout Standard
14090 \begin_inset CommandInset ref
14096 is completely colored red.
14097 \begin_inset Newline newline
14101 \begin_inset CommandInset ref
14103 reference "eq:redgreen"
14107 was first completely colored green to set the color for the formula number.
14108 Subsequently the formula characters were colored red.
14111 \begin_layout Standard
14112 \begin_inset VSpace bigskip
14115 To color the frame different than the rest of the box, the command
14122 \begin_inset Index idx
14125 \begin_layout Plain Layout
14133 is used in the following scheme:
14136 \begin_layout Standard
14141 fcolorbox{frame color}{color}{box content}
14144 \begin_layout Standard
14151 is an extension of the command
14158 The frame width is set, like for
14181 \begin_layout Plain Layout
14193 \begin_inset Formula
14195 \fcolorbox{cyan}{magenta}{A=B}
14204 \begin_layout Plain Layout
14218 \begin_layout Standard
14219 This formula was created with the command
14220 \begin_inset Newline newline
14228 \begin_inset Formula $\to$
14234 \begin_inset Formula $\to$
14244 \begin_layout Standard
14245 \begin_inset VSpace bigskip
14248 To use other colors than the predefined ones, they have to be defined first.
14251 \begin_layout Standard
14252 One can for example define the color
14253 \begin_inset Quotes eld
14261 \begin_inset Quotes erd
14264 with the LaTeX-preamble line:
14267 \begin_layout Standard
14272 definecolor{darkgreen}{cmyk}{0.5,
14287 \begin_inset Index idx
14290 \begin_layout Plain Layout
14301 \begin_layout Standard
14306 is the color space that denotes the colors
14323 The four comma separated numbers are the portion factor for the corresponding
14324 colors of the color space.
14325 The factors can be in the range of 0
14326 \begin_inset space \thinspace{}
14330 \begin_inset space \thinspace{}
14338 also the color space
14342 can be used for definitions.
14359 , so that there are in this case three portion factors for the corresponding
14361 Furthermore there is the color space
14365 with one portion factor for the gray value.
14368 \begin_layout Standard
14369 As example a framed box with the new defined color
14373 where the characters have been colored
14378 \begin_inset Formula
14380 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14388 \begin_layout Standard
14389 Self-defined colors can also be used for text with the help of the command
14397 \begin_inset Index idx
14400 \begin_layout Plain Layout
14409 \begin_layout Standard
14413 \begin_layout Plain Layout
14417 textcolor{darkgreen}{
14423 \begin_inset Quotes eld
14427 \begin_inset Quotes erd
14434 \begin_layout Plain Layout
14444 \begin_layout Standard
14452 \begin_inset Index idx
14455 \begin_layout Plain Layout
14463 is used in the scheme
14467 textcolor{color}{characters to color}
14472 \begin_layout Subsection
14474 \begin_inset CommandInset label
14476 name "sub:Paragraph-Boxes"
14481 \begin_inset Index idx
14484 \begin_layout Plain Layout
14485 Boxes ! as paragraph
14493 \begin_layout Standard
14494 A box that can contain several lines and paragraphs, a so-called paragraph
14495 box (parbox), can be created with the menu
14497 Insert\SpecialChar \menuseparator
14500 or the toolbar button
14501 \begin_inset Graphics
14502 filename ../images/box-insert.png
14510 \begin_layout Standard
14511 The following example shows a framed parbox in a line:
14514 \begin_layout Standard
14515 \begin_inset VSpace medskip
14519 \begin_inset Box Boxed
14529 height_special "totalheight"
14532 \begin_layout Plain Layout
14533 This is a paragraph box.
14535 \begin_inset space \thinspace{}
14538 cm long and can also contain formulas:
14539 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14550 \begin_layout Standard
14551 \begin_inset VSpace medskip
14557 \begin_layout Standard
14558 Such a box is created by right-clicking on the gray box inset.
14559 A dialog pops up showing the box properties.
14573 \begin_inset space \thinspace{}
14578 Vertical Box Alignment
14583 \begin_layout Standard
14584 \begin_inset VSpace medskip
14587 In LaTeX a parbox is created with the command
14594 \begin_inset Index idx
14597 \begin_layout Plain Layout
14605 which has the following scheme:
14608 \begin_layout Standard
14613 parbox[position]{width}{box content}
14616 \begin_layout Standard
14631 \begin_inset Quotes eld
14635 \begin_inset Quotes erd
14638 means that the box is aligned within the surrounding text with its last
14645 \begin_inset Quotes eld
14649 \begin_inset Quotes erd
14652 this is done with the first line.
14653 When no position is given, the box will be vertically centered, see section
14661 \begin_inset space ~
14666 manual for examples.
14669 \begin_layout Standard
14670 \begin_inset VSpace bigskip
14673 To frame formulas completely, including the formula number, the formula
14674 must be set into a parbox.
14675 To do this, the command
14689 is inserted in TeX-mode before the formula.
14697 \begin_inset Index idx
14700 \begin_layout Plain Layout
14708 is hereby the line width set for the document.
14709 Because the frame is outside the parbox, 2
14710 \begin_inset space \thinspace{}
14713 times the frame separation and the frame thickness must be subtracted from
14715 As this is not automatically done by LyX due to a bug
14719 \begin_layout Plain Layout
14720 \begin_inset CommandInset href
14722 name "LyX-bug #4483"
14723 target "http://www.lyx.org/trac/ticket/4483"
14732 , TeX-mode has to be used.
14733 To be able to multiply and subtract in arguments, the LaTeX-package
14741 \begin_layout Plain Layout
14746 is part of every LaTeX standard installation.
14752 \begin_inset Index idx
14755 \begin_layout Plain Layout
14761 must be loaded in the LaTeX-preamble with the line
14764 \begin_layout Standard
14772 \begin_layout Standard
14773 Behind the formula both boxes are closed by entering
14778 Here is an example:
14782 \begin_layout Plain Layout
14796 \begin_layout Standard
14800 \begin_layout Plain Layout
14818 \begin_inset Formula
14820 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14829 \begin_layout Plain Layout
14840 \begin_layout Plain Layout
14854 \begin_layout Standard
14855 \begin_inset VSpace medskip
14858 As a parbox is used as the argument of
14864 , there is in this case no difference between
14879 \begin_layout Standard
14880 \begin_inset VSpace bigskip
14883 Paragraph boxes are very useful to comment formulas directly.
14890 is used in combination with the command
14904 \begin_inset CommandInset ref
14906 reference "sub:User-defined-Numbering"
14913 \begin_layout Standard
14914 An example of a formula commented with
14923 \begin_layout Standard
14927 \begin_layout Plain Layout
14940 This is a description.
14941 It is distinctly separated from the formula and multiline.
14945 \begin_layout Plain Layout
14957 \begin_layout Standard
14958 Such a formula must be inserted completely in TeX-mode because LyX does
14959 not yet support the command
14966 The formula is created with the following command sequence:
14969 \begin_layout Standard
14982 is inserted in TeX-mode.
14986 \begin_layout Plain Layout
14987 When the formula style
14999 can also be replaced by
15006 (formula styles see
15007 \begin_inset CommandInset ref
15009 reference "sec:Formula-Styles"
15018 Then the description follows as normal text and finally
15024 is inserted in TeX-mode.
15037 hereby create a displayed formula.
15040 \begin_layout Standard
15047 can be seen in this example that was
15048 \begin_inset Quotes eld
15052 \begin_inset Quotes erd
15055 using the mathematical textmode:
15056 \begin_inset Formula
15058 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15066 \begin_layout Section
15068 \begin_inset Index idx
15071 \begin_layout Plain Layout
15080 \begin_layout Subsection
15082 \begin_inset CommandInset label
15084 name "sub:Big-Operators"
15089 \begin_inset Index idx
15092 \begin_layout Plain Layout
15099 \begin_inset Index idx
15102 \begin_layout Plain Layout
15109 \begin_inset Index idx
15112 \begin_layout Plain Layout
15121 \begin_layout Standard
15122 To be able to use all integral operators listed here, the option
15124 Use esint package automatically
15126 must be set in the document settings under
15129 \begin_inset space ~
15137 \begin_layout Standard
15138 \begin_inset space \hfill{}
15142 \begin_inset Tabular
15143 <lyxtabular version="3" rows="11" columns="2">
15144 <features tabularvalignment="middle">
15145 <column alignment="center" valignment="top" width="0pt">
15146 <column alignment="center" valignment="top" width="0pt">
15148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15151 \begin_layout Plain Layout
15157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15160 \begin_layout Plain Layout
15168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15171 \begin_layout Plain Layout
15175 \begin_inset Index idx
15178 \begin_layout Plain Layout
15191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15194 \begin_layout Plain Layout
15195 \begin_inset Formula $\int$
15205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15208 \begin_layout Plain Layout
15216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15219 \begin_layout Plain Layout
15220 \begin_inset Formula $\oint$
15230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15233 \begin_layout Plain Layout
15241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15244 \begin_layout Plain Layout
15245 \begin_inset Formula $\ointctrclockwise$
15255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15258 \begin_layout Plain Layout
15266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15269 \begin_layout Plain Layout
15270 \begin_inset Formula $\ointclockwise$
15280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15283 \begin_layout Plain Layout
15291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15294 \begin_layout Plain Layout
15295 \begin_inset Formula $\sqint$
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
15321 \begin_inset Formula $\fint$
15331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15334 \begin_layout Plain Layout
15342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15345 \begin_layout Plain Layout
15347 \begin_inset Formula $\landupint$
15357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15360 \begin_layout Plain Layout
15368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15371 \begin_layout Plain Layout
15373 \begin_inset Formula $\landdownint$
15383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15386 \begin_layout Plain Layout
15394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15397 \begin_layout Plain Layout
15398 \begin_inset Formula $\bigcap$
15408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15411 \begin_layout Plain Layout
15419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15422 \begin_layout Plain Layout
15423 \begin_inset Formula $\bigcup$
15437 \begin_inset space \hfill{}
15441 \begin_inset Tabular
15442 <lyxtabular version="3" rows="11" columns="2">
15443 <features tabularvalignment="middle">
15444 <column alignment="center" valignment="top" width="0pt">
15445 <column alignment="center" valignment="top" width="0pt">
15447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15450 \begin_layout Plain Layout
15456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15459 \begin_layout Plain Layout
15467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15470 \begin_layout Plain Layout
15474 \begin_inset Index idx
15477 \begin_layout Plain Layout
15490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15493 \begin_layout Plain Layout
15494 \begin_inset Formula $\sum$
15504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15507 \begin_layout Plain Layout
15511 \begin_inset Index idx
15514 \begin_layout Plain Layout
15527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15530 \begin_layout Plain Layout
15531 \begin_inset Formula $\prod$
15541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15544 \begin_layout Plain Layout
15552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15555 \begin_layout Plain Layout
15556 \begin_inset Formula $\coprod$
15566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15569 \begin_layout Plain Layout
15577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15580 \begin_layout Plain Layout
15581 \begin_inset Formula $\bigodot$
15591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15594 \begin_layout Plain Layout
15602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15605 \begin_layout Plain Layout
15606 \begin_inset Formula $\bigotimes$
15616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15619 \begin_layout Plain Layout
15627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15630 \begin_layout Plain Layout
15631 \begin_inset Formula $\bigoplus$
15641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15644 \begin_layout Plain Layout
15652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15655 \begin_layout Plain Layout
15656 \begin_inset Formula $\bigwedge$
15666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15669 \begin_layout Plain Layout
15677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15680 \begin_layout Plain Layout
15681 \begin_inset Formula $\bigvee$
15691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15694 \begin_layout Plain Layout
15702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15705 \begin_layout Plain Layout
15706 \begin_inset Formula $\bigsqcup$
15716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15719 \begin_layout Plain Layout
15727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15730 \begin_layout Plain Layout
15731 \begin_inset Formula $\biguplus$
15745 \begin_inset space \hfill{}
15751 \begin_layout Standard
15752 All big operators can also be inserted via the math toolbar button
15753 \begin_inset Graphics
15754 filename ../images/math/intop.png
15762 \begin_layout Standard
15763 The operators are called big because they are bigger than the sometimes
15764 equal looking binary operators.
15765 All big operators can have limits as described in the next subsection.
15768 \begin_layout Standard
15769 For all integral operators there is a second version available, ending in
15787 These operators are different from
15794 \begin_inset space \space{}
15797 in the style the operator limits are displayed, see
15798 \begin_inset CommandInset ref
15800 reference "sub:Operator-Limits"
15808 \begin_layout Subsubsection*
15809 Advice for Integrals
15812 \begin_layout Standard
15817 in an integral is an operator, that therefore has to be set upright.
15818 This is done by highlighting the
15822 and using the keyboard shortcut
15832 \begin_layout Plain Layout
15838 \begin_inset CommandInset ref
15840 reference "sub:Font-Styles"
15850 Finally the smallest space is inserted before the
15854 , as this is usual for operators.
15858 \begin_layout Standard
15860 \begin_inset Formula $\int A(x)dx$
15864 \begin_inset Newline newline
15868 \begin_inset Phantom HPhantom
15871 \begin_layout Plain Layout
15878 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15884 \begin_layout Standard
15885 For multiple integrals there are the following commands:
15886 \begin_inset VSpace medskip
15892 \begin_layout Standard
15893 \begin_inset space \hfill{}
15897 \begin_inset Tabular
15898 <lyxtabular version="3" rows="4" columns="2">
15899 <features tabularvalignment="middle">
15900 <column alignment="center" valignment="top" width="0">
15901 <column alignment="center" valignment="top" width="0">
15903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15906 \begin_layout Plain Layout
15912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15915 \begin_layout Plain Layout
15917 \begin_inset Note Note
15920 \begin_layout Plain Layout
15927 is only used as spacer.
15939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15942 \begin_layout Plain Layout
15950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15953 \begin_layout Plain Layout
15954 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15967 \begin_layout Plain Layout
15975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15978 \begin_layout Plain Layout
15979 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15992 \begin_layout Plain Layout
16000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16003 \begin_layout Plain Layout
16004 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
16018 \begin_inset space \hfill{}
16022 \begin_inset Tabular
16023 <lyxtabular version="3" rows="4" columns="2">
16024 <features tabularvalignment="middle">
16025 <column alignment="center" valignment="top" width="0">
16026 <column alignment="center" valignment="top" width="0">
16028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16031 \begin_layout Plain Layout
16037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16040 \begin_layout Plain Layout
16048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16051 \begin_layout Plain Layout
16059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16062 \begin_layout Plain Layout
16063 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16076 \begin_layout Plain Layout
16084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16087 \begin_layout Plain Layout
16088 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16101 \begin_layout Plain Layout
16109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16112 \begin_layout Plain Layout
16113 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16127 \begin_inset space \hfill{}
16133 \begin_layout Subsection
16135 \begin_inset CommandInset label
16137 name "sub:Operator-Limits"
16142 \begin_inset Index idx
16145 \begin_layout Plain Layout
16154 \begin_layout Standard
16155 Limits are created by super- and subscripts:
16158 \begin_layout Standard
16160 \begin_inset Tabular
16161 <lyxtabular version="3" rows="2" columns="2">
16162 <features tabularvalignment="middle">
16163 <column alignment="center" valignment="top" width="0pt">
16164 <column alignment="center" valignment="top" width="0pt">
16166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16169 \begin_layout Plain Layout
16175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16178 \begin_layout Plain Layout
16180 \begin_inset Note Note
16183 \begin_layout Plain Layout
16190 is only used as spacer.
16202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16205 \begin_layout Plain Layout
16214 \begin_layout Plain Layout
16224 \begin_inset Formula $\to$
16228 \begin_inset Formula $\to$
16236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16239 \begin_layout Plain Layout
16240 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16256 \begin_layout Standard
16257 Limits of inline formulas are set right beside the operator.
16258 Limits in displayed formulas are set above or below the operator, except
16259 for integral limits.
16262 \begin_layout Standard
16263 To force that the limits are set beside the operator, the cursor is set
16264 directly behind the operator and the limits type is changed with the menu
16267 Edit\SpecialChar \menuseparator
16268 Math\SpecialChar \menuseparator
16287 \begin_layout Standard
16288 The default limits type is this:
16289 \begin_inset Formula
16291 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16296 This is how it looks when the limits type was changed to
16303 \begin_inset Formula
16305 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16310 For integrals, except those ending with
16326 etc., the limits are by default set beside the operator.
16327 But for multiple integrals the limits are often set below the operator.
16328 In the following example the limits type was therefore set to
16332 and so set below the integrals:
16333 \begin_inset Formula
16335 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16343 \begin_layout Standard
16344 \begin_inset VSpace medskip
16347 To specify conditions for limits, the commands
16354 \begin_inset Index idx
16357 \begin_layout Plain Layout
16372 \begin_inset Index idx
16375 \begin_layout Plain Layout
16384 To create for example this expression
16385 \begin_inset Formula
16387 \sum_{\begin{subarray}{c}
16391 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16399 \begin_layout Standard
16400 the following has to be done:
16401 \begin_inset Newline newline
16416 \begin_layout Plain Layout
16428 One is now in a blue box under the summation operator and insert there
16437 \begin_layout Plain Layout
16449 The blue box is now within a purple box and now several lines can be written
16451 A new line is created by inserting a line break (
16454 arg "newline-insert newline"
16459 \begin_inset Newline newline
16464 0<k<1000 Ctrl+Return
16465 \begin_inset Newline newline
16470 is typed in, a new box appears below for the new line.
16473 \begin_layout Standard
16474 The alignment of the lines can be changed to left aligned with the
16484 Edit\SpecialChar \menuseparator
16488 To get right alignment,
16496 \begin_layout Plain Layout
16507 is inserted at the beginning of the line.
16510 \begin_layout Standard
16523 with the difference that the lines are always centered.
16526 \begin_layout Standard
16527 \begin_inset VSpace bigskip
16531 \begin_inset CommandInset ref
16533 reference "eq:substack"
16537 there can be too much space beside an operator, because the characters
16538 following the operator are set beside the limits.
16541 \begin_layout Standard
16542 To avoid this, the following macro can be used in the LaTeX-preamble:
16545 \begin_layout Standard
16559 \begin_inset Newline newline
16571 \begin_inset Newline newline
16578 mathclapinternal #1#2{
16582 mathsurround =0pt #1{#2}$}}
16585 \begin_layout Standard
16586 This defines the command
16593 \begin_inset Index idx
16596 \begin_layout Plain Layout
16604 that sets the width of the limit to 0
16605 \begin_inset space \thinspace{}
16609 The command scheme is
16612 \begin_layout Standard
16620 \begin_layout Standard
16621 where the limit can consist of several conditions.
16624 \begin_layout Standard
16626 \begin_inset CommandInset ref
16628 reference "eq:substack"
16632 , one uses the command
16635 \begin_layout Standard
16648 \begin_layout Plain Layout
16657 0<k<1000 Ctrl+Return
16660 \begin_layout Standard
16661 to create the lower limit.
16662 The summand is now directly behind the summation operator:
16663 \begin_inset Formula
16665 \sum_{\mathclap{\substack{0<k<1000\\
16677 \begin_layout Standard
16678 \begin_inset VSpace bigskip
16681 How to use one limit for several operators is described in
16682 \begin_inset CommandInset ref
16684 reference "sub:Self-defined-Operators"
16691 \begin_layout Standard
16692 \begin_inset Newpage newpage
16698 \begin_layout Subsection
16700 \begin_inset CommandInset label
16702 name "sub:Binary-Operators"
16707 \begin_inset Index idx
16710 \begin_layout Plain Layout
16719 \begin_layout Standard
16720 Binary operators are surrounded by space when there is a character before
16722 \begin_inset VSpace medskip
16728 \begin_layout Standard
16729 \begin_inset space \hfill{}
16733 \begin_inset Tabular
16734 <lyxtabular version="3" rows="13" columns="2">
16735 <features tabularvalignment="middle">
16736 <column alignment="center" valignment="top" width="0pt">
16737 <column alignment="center" valignment="top" width="0pt">
16739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16742 \begin_layout Plain Layout
16744 \begin_inset Note Note
16747 \begin_layout Plain Layout
16754 is only used as spacer.
16764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16767 \begin_layout Plain Layout
16775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16778 \begin_layout Plain Layout
16784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16787 \begin_layout Plain Layout
16788 \begin_inset Formula $+$
16798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16801 \begin_layout Plain Layout
16807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16810 \begin_layout Plain Layout
16811 \begin_inset Formula $-$
16821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16824 \begin_layout Plain Layout
16832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16835 \begin_layout Plain Layout
16836 \begin_inset Formula $\pm$
16846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16849 \begin_layout Plain Layout
16857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16860 \begin_layout Plain Layout
16861 \begin_inset Formula $\mp$
16871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16874 \begin_layout Plain Layout
16882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16885 \begin_layout Plain Layout
16886 \begin_inset Formula $\cdot$
16896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16899 \begin_layout Plain Layout
16907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16910 \begin_layout Plain Layout
16911 \begin_inset Formula $\times$
16921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16924 \begin_layout Plain Layout
16932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16935 \begin_layout Plain Layout
16936 \begin_inset Formula $\div$
16946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16949 \begin_layout Plain Layout
16953 \begin_layout Plain Layout
16966 \begin_layout Plain Layout
16978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16981 \begin_layout Plain Layout
16982 \begin_inset Formula $*$
16992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16995 \begin_layout Plain Layout
17003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17006 \begin_layout Plain Layout
17007 \begin_inset Formula $\star$
17017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17020 \begin_layout Plain Layout
17028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17031 \begin_layout Plain Layout
17032 \begin_inset Formula $\circ$
17042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17045 \begin_layout Plain Layout
17053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17056 \begin_layout Plain Layout
17057 \begin_inset Formula $\diamond$
17067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17070 \begin_layout Plain Layout
17078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17081 \begin_layout Plain Layout
17082 \begin_inset Formula $\bullet$
17096 \begin_inset space \hfill{}
17100 \begin_inset Tabular
17101 <lyxtabular version="3" rows="13" columns="2">
17102 <features tabularvalignment="middle">
17103 <column alignment="center" valignment="top" width="0pt">
17104 <column alignment="center" valignment="top" width="0pt">
17106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17109 \begin_layout Plain Layout
17115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17118 \begin_layout Plain Layout
17126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17129 \begin_layout Plain Layout
17137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17140 \begin_layout Plain Layout
17141 \begin_inset Formula $\nabla$
17151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17154 \begin_layout Plain Layout
17162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17165 \begin_layout Plain Layout
17166 \begin_inset Formula $\bigtriangledown$
17176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17179 \begin_layout Plain Layout
17187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17190 \begin_layout Plain Layout
17191 \begin_inset Formula $\bigtriangleup$
17201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17204 \begin_layout Plain Layout
17212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17215 \begin_layout Plain Layout
17216 \begin_inset Formula $\Box$
17226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17229 \begin_layout Plain Layout
17237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17240 \begin_layout Plain Layout
17241 \begin_inset Formula $\cap$
17251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17254 \begin_layout Plain Layout
17262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17265 \begin_layout Plain Layout
17266 \begin_inset Formula $\cup$
17276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17279 \begin_layout Plain Layout
17287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17290 \begin_layout Plain Layout
17291 \begin_inset Formula $\dagger$
17301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17304 \begin_layout Plain Layout
17312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17315 \begin_layout Plain Layout
17316 \begin_inset Formula $\ddagger$
17326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17329 \begin_layout Plain Layout
17337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17340 \begin_layout Plain Layout
17341 \begin_inset Formula $\wr$
17351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17354 \begin_layout Plain Layout
17362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17365 \begin_layout Plain Layout
17366 \begin_inset Formula $\bigcirc$
17376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17379 \begin_layout Plain Layout
17387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17390 \begin_layout Plain Layout
17391 \begin_inset Formula $\wedge$
17401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17404 \begin_layout Plain Layout
17412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17415 \begin_layout Plain Layout
17416 \begin_inset Formula $\vee$
17430 \begin_inset space \hfill{}
17434 \begin_inset Tabular
17435 <lyxtabular version="3" rows="13" columns="2">
17436 <features tabularvalignment="middle">
17437 <column alignment="center" valignment="top" width="0pt">
17438 <column alignment="center" valignment="top" width="0pt">
17440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17443 \begin_layout Plain Layout
17449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17452 \begin_layout Plain Layout
17460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17463 \begin_layout Plain Layout
17471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17474 \begin_layout Plain Layout
17475 \begin_inset Formula $\oplus$
17485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17488 \begin_layout Plain Layout
17496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17499 \begin_layout Plain Layout
17500 \begin_inset Formula $\ominus$
17510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17513 \begin_layout Plain Layout
17521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17524 \begin_layout Plain Layout
17525 \begin_inset Formula $\otimes$
17535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17538 \begin_layout Plain Layout
17546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17549 \begin_layout Plain Layout
17550 \begin_inset Formula $\oslash$
17560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17563 \begin_layout Plain Layout
17571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17574 \begin_layout Plain Layout
17575 \begin_inset Formula $\odot$
17585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17588 \begin_layout Plain Layout
17596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17599 \begin_layout Plain Layout
17600 \begin_inset Formula $\amalg$
17610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17613 \begin_layout Plain Layout
17621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17624 \begin_layout Plain Layout
17625 \begin_inset Formula $\uplus$
17635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17638 \begin_layout Plain Layout
17646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17649 \begin_layout Plain Layout
17650 \begin_inset Formula $\setminus$
17660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17663 \begin_layout Plain Layout
17671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17674 \begin_layout Plain Layout
17675 \begin_inset Formula $\sqcap$
17685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17688 \begin_layout Plain Layout
17696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17699 \begin_layout Plain Layout
17700 \begin_inset Formula $\sqcup$
17710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17713 \begin_layout Plain Layout
17721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17724 \begin_layout Plain Layout
17725 \begin_inset Formula $\triangleleft$
17735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17738 \begin_layout Plain Layout
17746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17749 \begin_layout Plain Layout
17750 \begin_inset Formula $\triangleright$
17764 \begin_inset space \hfill{}
17770 \begin_layout Standard
17771 All binary operators can also be inserted via the math toolbar button
17772 \begin_inset Graphics
17773 filename ../images/math/pm.png
17781 \begin_layout Standard
17782 To typeset the Laplace operator also
17799 \begin_inset Formula $\nabla^{2}$
17802 ) can be used instead of
17811 \begin_layout Standard
17818 Insert\SpecialChar \menuseparator
17830 \begin_layout Subsection
17831 Self-defined Operators
17832 \begin_inset CommandInset label
17834 name "sub:Self-defined-Operators"
17839 \begin_inset Index idx
17842 \begin_layout Plain Layout
17843 Operators ! self-defined
17851 \begin_layout Standard
17852 With the help of the command
17856 DeclareMathOperator
17859 \begin_inset Index idx
17862 \begin_layout Plain Layout
17867 DeclareMathOperator
17872 custom operators can be defined in the LaTeX-preamble.
17873 Its command scheme is:
17876 \begin_layout Standard
17881 DeclareMathOperator{new command}{display}
17884 \begin_layout Standard
17885 Display can be characters or symbols that define how the operator looks
17887 To define a big operator a * is set behind the command.
17888 All self-defined big operators can have limits as described in
17889 \begin_inset CommandInset ref
17891 reference "sub:Operator-Limits"
17898 \begin_layout Standard
17899 For example the LaTeX-preamble line
17902 \begin_layout Standard
17907 DeclareMathOperator*{
17914 \begin_layout Standard
17915 defines the command
17921 , that inserts a big operator consisting of the lozenge symbol from
17922 \begin_inset CommandInset ref
17924 reference "sub:Miscellaneous-Symbols"
17929 \begin_inset Formula
17931 \Lozenge_{n=1}^{\infty}
17936 The command for this formula is:
17947 \begin_inset Formula $\to$
17953 \begin_layout Standard
17954 \begin_inset VSpace bigskip
17957 When self-defined operators are not used several times in the document,
17958 they can also be defined with the commands
17965 \begin_inset Index idx
17968 \begin_layout Plain Layout
17983 \begin_inset Index idx
17986 \begin_layout Plain Layout
17994 , which have the following scheme:
17997 \begin_layout Standard
18011 \begin_layout Standard
18018 defines big operators,
18027 \begin_layout Standard
18035 \begin_inset space \thinspace{}
18039 \begin_inset space \space{}
18042 be used to use one limit for several operators:
18045 \begin_layout Standard
18046 \begin_inset Formula
18048 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18056 \begin_layout Standard
18057 The command for the formula above is:
18058 \begin_inset Newline newline
18077 \begin_layout Plain Layout
18089 \begin_inset Formula $\to$
18098 \begin_layout Plain Layout
18112 \begin_layout Section
18114 \begin_inset Index idx
18117 \begin_layout Plain Layout
18126 \begin_layout Subsection
18128 \begin_inset CommandInset label
18130 name "sub:Font-Styles"
18135 \begin_inset Index idx
18138 \begin_layout Plain Layout
18147 \begin_layout Standard
18148 Latin letters in formulas can be set in one of the following font styles:
18149 \begin_inset VSpace -2mm
18155 \begin_layout Standard
18157 \begin_inset Tabular
18158 <lyxtabular version="3" rows="7" columns="3">
18159 <features tabularvalignment="middle">
18160 <column alignment="center" valignment="top" width="0">
18161 <column alignment="center" valignment="top" width="0">
18162 <column alignment="center" valignment="top" width="0">
18164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18167 \begin_layout Plain Layout
18173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18176 \begin_layout Plain Layout
18182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18185 \begin_layout Plain Layout
18193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18196 \begin_layout Plain Layout
18205 \begin_layout Plain Layout
18221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18224 \begin_layout Plain Layout
18225 \begin_inset Formula $\mathbb{ABC}$
18233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18236 \begin_layout Plain Layout
18249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18252 \begin_layout Plain Layout
18261 \begin_layout Plain Layout
18277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18280 \begin_layout Plain Layout
18281 \begin_inset Formula $\mathbf{AbC}$
18289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18292 \begin_layout Plain Layout
18305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18308 \begin_layout Plain Layout
18317 \begin_layout Plain Layout
18333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18336 \begin_layout Plain Layout
18337 \begin_inset Formula $\boldsymbol{AbC}$
18345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18348 \begin_layout Plain Layout
18351 arg "font-boldsymbol"
18361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18364 \begin_layout Plain Layout
18373 \begin_layout Plain Layout
18389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18392 \begin_layout Plain Layout
18393 \begin_inset Formula $\mathcal{ABC}$
18401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18404 \begin_layout Plain Layout
18417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18420 \begin_layout Plain Layout
18429 \begin_layout Plain Layout
18445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18448 \begin_layout Plain Layout
18449 \begin_inset Formula $\mathfrak{AbC}$
18457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18460 \begin_layout Plain Layout
18468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18471 \begin_layout Plain Layout
18480 \begin_layout Plain Layout
18496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18499 \begin_layout Plain Layout
18500 \begin_inset Formula $\mathscr{AbC}$
18508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18511 \begin_layout Plain Layout
18525 \begin_layout Standard
18527 \begin_inset Tabular
18528 <lyxtabular version="3" rows="5" columns="3">
18529 <features tabularvalignment="middle">
18530 <column alignment="center" valignment="top" width="0">
18531 <column alignment="center" valignment="top" width="0">
18532 <column alignment="center" valignment="top" width="0">
18534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18537 \begin_layout Plain Layout
18543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18546 \begin_layout Plain Layout
18552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18555 \begin_layout Plain Layout
18563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18566 \begin_layout Plain Layout
18575 \begin_layout Plain Layout
18591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18594 \begin_layout Plain Layout
18595 \begin_inset Formula $\mathit{AbC}$
18603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18606 \begin_layout Plain Layout
18614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18617 \begin_layout Plain Layout
18626 \begin_layout Plain Layout
18642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18645 \begin_layout Plain Layout
18646 \begin_inset Formula $\mathrm{AbC}$
18654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18657 \begin_layout Plain Layout
18670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18673 \begin_layout Plain Layout
18682 \begin_layout Plain Layout
18698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18701 \begin_layout Plain Layout
18702 \begin_inset Formula $\mathsf{AbC}$
18710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18713 \begin_layout Plain Layout
18726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18729 \begin_layout Plain Layout
18738 \begin_layout Plain Layout
18754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18757 \begin_layout Plain Layout
18758 \begin_inset Formula $\mathtt{AbC}$
18766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18769 \begin_layout Plain Layout
18772 arg "font-typewriter"
18788 \begin_layout Standard
18789 \begin_inset Note Greyedout
18792 \begin_layout Plain Layout
18809 can only be used for big letters.
18817 \begin_layout Standard
18818 Predefined is the style
18827 \begin_layout Standard
18828 The style commands work also for letters in mathematical constructs:
18829 \begin_inset Formula
18831 \mathfrak{A=\frac{b}{C}}
18839 \begin_layout Standard
18840 Characters in mathematical text don't appear in a math font style but in
18841 the text font style
18848 That their style can't be set correctly via the text style dialog is a
18853 \begin_layout Plain Layout
18854 \begin_inset CommandInset href
18856 name "LyX-bug #4629"
18857 target "http://www.lyx.org/trac/ticket/4629"
18869 \begin_layout Standard
18870 Instead of the style commands the dialog
18872 Edit\SpecialChar \menuseparator
18873 Math\SpecialChar \menuseparator
18876 or the toolbar button
18877 \begin_inset Graphics
18878 filename ../images/math/font.png
18886 \begin_layout Subsection
18888 \begin_inset CommandInset label
18890 name "sub:Bold-Formulas"
18895 \begin_inset Index idx
18898 \begin_layout Plain Layout
18907 \begin_layout Standard
18908 To make a complete formula bold, the command
18914 from the previous subsection cannot be used, because it doesn't work for
18915 small Greek letters.
18916 Furthermore it prints Latin letters always upright, like in the following
18920 \begin_layout Standard
18921 \begin_inset Formula
18923 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18931 \begin_layout Standard
18932 To display the formula correctly, the command
18939 \begin_inset Formula
18941 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18946 It is also possible to set the formula in a
18948 boldmath environment
18951 This environment is created by inserting the command
18958 \begin_inset Index idx
18961 \begin_layout Plain Layout
18970 To end the environment, the command
18977 \begin_inset Index idx
18980 \begin_layout Plain Layout
18988 is inserted in TeX-mode.
18992 \begin_layout Plain Layout
19002 \begin_inset Formula
19004 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19013 \begin_layout Plain Layout
19025 \begin_layout Subsection
19027 \begin_inset Index idx
19030 \begin_layout Plain Layout
19039 \begin_layout Standard
19040 Formulas can be colored like normal text: Highlight a formula or a formula
19046 Here is a formula in magenta:
19047 \begin_inset Formula
19049 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19057 \begin_layout Standard
19058 You can also define your own colors as described in
19059 \begin_inset CommandInset ref
19061 reference "sub:Colored-Boxes"
19066 They can be used with the TeX code command
19073 \begin_inset Index idx
19076 \begin_layout Plain Layout
19087 \begin_layout Standard
19092 textcolor{color}{characters or formula}
19095 \begin_layout Standard
19096 The following example was colored completely dark green and partly red:
19099 \begin_layout Standard
19103 \begin_layout Plain Layout
19107 textcolor{darkgreen}{
19113 \begin_inset Formula
19115 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19124 \begin_layout Plain Layout
19134 \begin_layout Standard
19135 Due to a bug in LyX only complete formulas can be colored with self-defined
19140 \begin_layout Plain Layout
19141 \begin_inset CommandInset href
19143 name "LyX-bug #5269"
19144 target "http://www.lyx.org/trac/ticket/5269"
19156 \begin_layout Subsection
19158 \begin_inset CommandInset label
19160 name "sub:Font-Sizes"
19165 \begin_inset Index idx
19168 \begin_layout Plain Layout
19177 \begin_layout Standard
19178 For characters in formulas there are, analog to characters in text, the
19179 following size commands:
19182 \begin_layout Standard
19226 \begin_inset Newline newline
19248 \begin_layout Standard
19249 The size produced by the commands depends on the document font size, which
19250 corresponds to the command
19257 The other commands produce smaller or larger sizes than
19264 The font size can however not exceed a certain value.
19265 Is for example the document font size 12
19266 \begin_inset space \thinspace{}
19275 switches to the same size as
19285 \begin_layout Standard
19286 A size command is inserted in TeX-mode before the formula and sets the size
19287 for all following formula and text characters.
19288 To switch back to the initial size, the command
19294 is inserted behind the formula in TeX-mode.
19297 \begin_layout Standard
19298 Within a formula the size can be changed using the following size commands:
19301 \begin_layout Standard
19304 \begin_inset Tabular
19305 <lyxtabular version="3" rows="5" columns="2">
19306 <features tabularvalignment="middle">
19307 <column alignment="center" valignment="top" width="0">
19308 <column alignment="center" valignment="top" width="0">
19310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19313 \begin_layout Plain Layout
19319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19322 \begin_layout Plain Layout
19324 \begin_inset Note Note
19327 \begin_layout Plain Layout
19334 is only used as spacer.
19346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19349 \begin_layout Plain Layout
19353 \begin_inset Index idx
19356 \begin_layout Plain Layout
19369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19372 \begin_layout Plain Layout
19373 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19386 \begin_layout Plain Layout
19394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19397 \begin_layout Plain Layout
19398 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19411 \begin_layout Plain Layout
19419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19422 \begin_layout Plain Layout
19423 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19436 \begin_layout Plain Layout
19444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19447 \begin_layout Plain Layout
19448 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19464 \begin_layout Standard
19465 After entering these commands, a blue box appears in which the formula parts
19469 \begin_layout Standard
19470 There is a further method to change the font size, that though only works
19471 for symbols or letters in mathematical text.
19472 To use it, one of the above text size commands is inserted in mathematical
19474 All following characters until the end of the mathematical text or until
19475 another size command will have the selected size.
19477 \begin_inset VSpace -2mm
19483 \begin_layout Standard
19487 \begin_layout Plain Layout
19497 \begin_inset Formula
19499 A=\frac{B}{c}\cdot\maltese
19505 \begin_inset Formula
19507 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19516 \begin_layout Plain Layout
19528 \begin_layout Standard
19529 \begin_inset VSpace medskip
19532 Before both formulas the command
19539 The command for the second formula is:
19540 \begin_inset Newline newline
19551 \begin_layout Plain Layout
19566 \begin_layout Plain Layout
19581 \begin_layout Plain Layout
19596 \begin_layout Plain Layout
19606 \begin_inset Formula $\to$
19610 \begin_inset Formula $\to$
19614 \begin_inset Newline newline
19618 \begin_inset space \hspace*{}
19632 \begin_layout Plain Layout
19647 \begin_layout Plain Layout
19662 \begin_layout Plain Layout
19674 \begin_layout Standard
19675 If a symbol cannot be displayed in different sizes, it will always be displayed
19676 in the default size.
19679 \begin_layout Section
19681 \begin_inset Index idx
19684 \begin_layout Plain Layout
19693 \begin_layout Standard
19694 Greek letters can also be inserted via the toolbar button
19695 \begin_inset Graphics
19696 filename ../images/math/alpha.png
19702 All international typesetting norms purport that Greek letters in math
19703 have to be typeset italic/slanted.
19704 In some languages, like French or Russian, they are nevertheless sometimes
19708 \begin_layout Subsection
19710 \begin_inset Index idx
19713 \begin_layout Plain Layout
19714 Greek letters ! small
19722 \begin_layout Standard
19723 \begin_inset space \hfill{}
19727 \begin_inset Tabular
19728 <lyxtabular version="3" rows="11" columns="2">
19729 <features tabularvalignment="middle">
19730 <column alignment="center" valignment="top" width="0pt">
19731 <column alignment="center" valignment="top" width="0pt">
19733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19736 \begin_layout Plain Layout
19742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19745 \begin_layout Plain Layout
19753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19756 \begin_layout Plain Layout
19764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19767 \begin_layout Plain Layout
19768 \begin_inset Formula $\alpha$
19778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19781 \begin_layout Plain Layout
19789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19792 \begin_layout Plain Layout
19793 \begin_inset Formula $\beta$
19803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19806 \begin_layout Plain Layout
19814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19817 \begin_layout Plain Layout
19818 \begin_inset Formula $\gamma$
19828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19831 \begin_layout Plain Layout
19839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19842 \begin_layout Plain Layout
19843 \begin_inset Formula $\delta$
19853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19856 \begin_layout Plain Layout
19864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19867 \begin_layout Plain Layout
19868 \begin_inset Formula $\epsilon$
19878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19881 \begin_layout Plain Layout
19889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19892 \begin_layout Plain Layout
19893 \begin_inset Formula $\varepsilon$
19903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19906 \begin_layout Plain Layout
19914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19917 \begin_layout Plain Layout
19918 \begin_inset Formula $\zeta$
19928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19931 \begin_layout Plain Layout
19939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19942 \begin_layout Plain Layout
19943 \begin_inset Formula $\eta$
19953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19956 \begin_layout Plain Layout
19964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19967 \begin_layout Plain Layout
19968 \begin_inset Formula $\theta$
19978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19981 \begin_layout Plain Layout
19989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19992 \begin_layout Plain Layout
19993 \begin_inset Formula $\vartheta$
20007 \begin_inset space \hfill{}
20011 \begin_inset Tabular
20012 <lyxtabular version="3" rows="12" columns="2">
20013 <features tabularvalignment="middle">
20014 <column alignment="center" valignment="top" width="0pt">
20015 <column alignment="center" valignment="top" width="0pt">
20017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20020 \begin_layout Plain Layout
20026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20029 \begin_layout Plain Layout
20037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20040 \begin_layout Plain Layout
20048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20051 \begin_layout Plain Layout
20052 \begin_inset Formula $\iota$
20062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20065 \begin_layout Plain Layout
20073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20076 \begin_layout Plain Layout
20077 \begin_inset Formula $\kappa$
20087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20090 \begin_layout Plain Layout
20098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20101 \begin_layout Plain Layout
20102 \begin_inset Formula $\varkappa$
20112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20115 \begin_layout Plain Layout
20123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20126 \begin_layout Plain Layout
20127 \begin_inset Formula $\lambda$
20137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20140 \begin_layout Plain Layout
20148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20151 \begin_layout Plain Layout
20152 \begin_inset Formula $\mu$
20162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20165 \begin_layout Plain Layout
20173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20176 \begin_layout Plain Layout
20177 \begin_inset Formula $\nu$
20187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20190 \begin_layout Plain Layout
20198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20201 \begin_layout Plain Layout
20202 \begin_inset Formula $\xi$
20212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20215 \begin_layout Plain Layout
20221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20224 \begin_layout Plain Layout
20225 \begin_inset Formula $o$
20235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20238 \begin_layout Plain Layout
20246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20249 \begin_layout Plain Layout
20250 \begin_inset Formula $\pi$
20260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20263 \begin_layout Plain Layout
20271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20274 \begin_layout Plain Layout
20275 \begin_inset Formula $\varpi$
20285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20288 \begin_layout Plain Layout
20296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20299 \begin_layout Plain Layout
20300 \begin_inset Formula $\rho$
20314 \begin_inset space \hfill{}
20318 \begin_inset Tabular
20319 <lyxtabular version="3" rows="11" columns="2">
20320 <features tabularvalignment="middle">
20321 <column alignment="center" valignment="top" width="0pt">
20322 <column alignment="center" valignment="top" width="0pt">
20324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20327 \begin_layout Plain Layout
20333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20336 \begin_layout Plain Layout
20344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20347 \begin_layout Plain Layout
20355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20358 \begin_layout Plain Layout
20359 \begin_inset Formula $\varrho$
20369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20372 \begin_layout Plain Layout
20380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20383 \begin_layout Plain Layout
20384 \begin_inset Formula $\sigma$
20394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20397 \begin_layout Plain Layout
20405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20408 \begin_layout Plain Layout
20409 \begin_inset Formula $\varsigma$
20419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20422 \begin_layout Plain Layout
20430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20433 \begin_layout Plain Layout
20434 \begin_inset Formula $\tau$
20444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20447 \begin_layout Plain Layout
20455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20458 \begin_layout Plain Layout
20459 \begin_inset Formula $\upsilon$
20469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20472 \begin_layout Plain Layout
20480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20483 \begin_layout Plain Layout
20484 \begin_inset Formula $\phi$
20494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20497 \begin_layout Plain Layout
20505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20508 \begin_layout Plain Layout
20509 \begin_inset Formula $\varphi$
20519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20522 \begin_layout Plain Layout
20530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20533 \begin_layout Plain Layout
20534 \begin_inset Formula $\chi$
20544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20547 \begin_layout Plain Layout
20555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20558 \begin_layout Plain Layout
20559 \begin_inset Formula $\psi$
20569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20572 \begin_layout Plain Layout
20580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20583 \begin_layout Plain Layout
20584 \begin_inset Formula $\omega$
20598 \begin_inset space \hfill{}
20604 \begin_layout Standard
20605 \begin_inset VSpace medskip
20611 \begin_layout Standard
20612 How to create special upright Greek letters is explained in
20613 \begin_inset CommandInset ref
20615 reference "sub:Upright-small-Greek"
20622 \begin_layout Subsection
20624 \begin_inset Index idx
20627 \begin_layout Plain Layout
20628 Greek letters ! big
20636 \begin_layout Standard
20637 \begin_inset space \hfill{}
20641 \begin_inset Tabular
20642 <lyxtabular version="3" rows="7" columns="2">
20643 <features tabularvalignment="middle">
20644 <column alignment="center" valignment="top" width="0pt">
20645 <column alignment="center" valignment="top" width="0pt">
20647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20650 \begin_layout Plain Layout
20656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20659 \begin_layout Plain Layout
20667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20670 \begin_layout Plain Layout
20678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20681 \begin_layout Plain Layout
20682 \begin_inset Formula $\Gamma$
20692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20695 \begin_layout Plain Layout
20703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20706 \begin_layout Plain Layout
20707 \begin_inset Formula $\Delta$
20717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20720 \begin_layout Plain Layout
20728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20731 \begin_layout Plain Layout
20732 \begin_inset Formula $\Theta$
20742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20745 \begin_layout Plain Layout
20753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20756 \begin_layout Plain Layout
20757 \begin_inset Formula $\Lambda$
20767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20770 \begin_layout Plain Layout
20778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20781 \begin_layout Plain Layout
20782 \begin_inset Formula $\Xi$
20792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20795 \begin_layout Plain Layout
20803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20806 \begin_layout Plain Layout
20807 \begin_inset Formula $\Pi$
20821 \begin_inset space \hfill{}
20825 \begin_inset Tabular
20826 <lyxtabular version="3" rows="6" columns="2">
20827 <features tabularvalignment="middle">
20828 <column alignment="center" valignment="top" width="0pt">
20829 <column alignment="center" valignment="top" width="0pt">
20831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20834 \begin_layout Plain Layout
20840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20843 \begin_layout Plain Layout
20851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20854 \begin_layout Plain Layout
20862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20865 \begin_layout Plain Layout
20866 \begin_inset Formula $\Sigma$
20876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20879 \begin_layout Plain Layout
20887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20890 \begin_layout Plain Layout
20891 \begin_inset Formula $\Upsilon$
20901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20904 \begin_layout Plain Layout
20912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20915 \begin_layout Plain Layout
20916 \begin_inset Formula $\Phi$
20926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20929 \begin_layout Plain Layout
20937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20940 \begin_layout Plain Layout
20941 \begin_inset Formula $\Psi$
20951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20954 \begin_layout Plain Layout
20962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20965 \begin_layout Plain Layout
20966 \begin_inset Formula $\Omega$
20980 \begin_inset space \hfill{}
20986 \begin_layout Standard
20987 \begin_inset VSpace medskip
20990 That the big Greek letters appear upright is caused by a design bug when
20992 To get correct italic big letters, begin every command with
20997 For example the command
21004 \begin_inset Formula $\varGamma$
21008 Another way is to load the package
21016 \begin_layout Plain Layout
21021 is part of the LaTeX-package
21026 \begin_inset Index idx
21029 \begin_layout Plain Layout
21034 \begin_layout Plain Layout
21054 \begin_inset Index idx
21057 \begin_layout Plain Layout
21063 with the LaTeX-preamble line
21066 \begin_layout Standard
21071 usepackage{fixmath}
21074 \begin_layout Standard
21075 Then all big Greek letters in a document will automatically be typeset italic.
21078 \begin_layout Subsection
21080 \begin_inset Index idx
21083 \begin_layout Plain Layout
21084 Greek letters ! bold
21092 \begin_layout Standard
21093 Greek letters cannot be set with different font styles like Latin letters.
21094 They can only be made bold with the command
21101 \begin_inset Index idx
21104 \begin_layout Plain Layout
21115 \begin_layout Standard
21117 \begin_inset Tabular
21118 <lyxtabular version="3" rows="3" columns="2">
21119 <features tabularvalignment="middle">
21120 <column alignment="center" valignment="top" width="0">
21121 <column alignment="center" valignment="top" width="0">
21123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21126 \begin_layout Plain Layout
21132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21135 \begin_layout Plain Layout
21143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21146 \begin_layout Plain Layout
21158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21161 \begin_layout Plain Layout
21162 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21175 \begin_layout Plain Layout
21187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21190 \begin_layout Plain Layout
21191 \begin_inset Formula $\theta\boldsymbol{\theta}$
21207 \begin_layout Standard
21208 \begin_inset Newpage newpage
21214 \begin_layout Section
21219 \begin_layout Plain Layout
21232 \begin_layout Plain Layout
21233 A list with all symbols of most of the LaTeX-packages can be found in
21234 \begin_inset CommandInset citation
21249 \begin_layout Plain Layout
21257 \begin_inset Note Note
21260 \begin_layout Plain Layout
21263 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21266 \begin_layout Plain Layout
21269 texorpdfstring is in section
21270 \begin_inset CommandInset ref
21272 reference "sub:Formulas-in-Section"
21282 \begin_inset Index idx
21285 \begin_layout Plain Layout
21294 \begin_layout Standard
21295 Many of the symbols listed in this section can also be inserted via the
21297 \begin_inset Graphics
21298 filename ../images/math/nabla.png
21304 \begin_inset Graphics
21305 filename ../images/math/digamma.png
21313 \begin_layout Subsection
21314 Mathematical Symbols
21315 \begin_inset CommandInset label
21317 name "sub:Mathematical-Symbols"
21322 \begin_inset Index idx
21325 \begin_layout Plain Layout
21326 Symbols ! mathematical
21334 \begin_layout Standard
21335 \begin_inset space \hfill{}
21339 \begin_inset Tabular
21340 <lyxtabular version="3" rows="10" columns="2">
21341 <features tabularvalignment="middle">
21342 <column alignment="center" valignment="top" width="0pt">
21343 <column alignment="center" valignment="top" width="0pt">
21345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21348 \begin_layout Plain Layout
21354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21357 \begin_layout Plain Layout
21365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21368 \begin_layout Plain Layout
21376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21379 \begin_layout Plain Layout
21380 \begin_inset Formula $\neg$
21390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21393 \begin_layout Plain Layout
21401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21404 \begin_layout Plain Layout
21405 \begin_inset Formula $\Im$
21415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21418 \begin_layout Plain Layout
21426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21429 \begin_layout Plain Layout
21430 \begin_inset Formula $\Re$
21440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21443 \begin_layout Plain Layout
21451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21454 \begin_layout Plain Layout
21455 \begin_inset Formula $\aleph$
21465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21468 \begin_layout Plain Layout
21476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21479 \begin_layout Plain Layout
21480 \begin_inset Formula $\partial$
21490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21493 \begin_layout Plain Layout
21501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21504 \begin_layout Plain Layout
21505 \begin_inset Formula $\infty$
21515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21518 \begin_layout Plain Layout
21526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21529 \begin_layout Plain Layout
21530 \begin_inset Formula $\wp$
21540 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21543 \begin_layout Plain Layout
21551 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21554 \begin_layout Plain Layout
21555 \begin_inset Formula $\imath$
21565 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21568 \begin_layout Plain Layout
21576 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21579 \begin_layout Plain Layout
21580 \begin_inset Formula $\jmath$
21594 \begin_inset space \hfill{}
21598 \begin_inset Tabular
21599 <lyxtabular version="3" rows="10" columns="2">
21600 <features tabularvalignment="middle">
21601 <column alignment="center" valignment="top" width="0pt">
21602 <column alignment="center" valignment="top" width="0pt">
21604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21607 \begin_layout Plain Layout
21613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21616 \begin_layout Plain Layout
21618 \begin_inset Note Note
21621 \begin_layout Plain Layout
21628 is only used as spacer.
21640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21643 \begin_layout Plain Layout
21651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21654 \begin_layout Plain Layout
21655 \begin_inset Formula $\forall$
21665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21668 \begin_layout Plain Layout
21676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21679 \begin_layout Plain Layout
21680 \begin_inset Formula $\exists$
21690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21693 \begin_layout Plain Layout
21701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21704 \begin_layout Plain Layout
21705 \begin_inset Formula $\nexists$
21715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21718 \begin_layout Plain Layout
21726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21729 \begin_layout Plain Layout
21730 \begin_inset Formula $\emptyset$
21740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21743 \begin_layout Plain Layout
21751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21754 \begin_layout Plain Layout
21755 \begin_inset Formula $\varnothing$
21765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21768 \begin_layout Plain Layout
21776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21779 \begin_layout Plain Layout
21780 \begin_inset Formula $\dag$
21790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21793 \begin_layout Plain Layout
21801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21804 \begin_layout Plain Layout
21805 \begin_inset Formula $\ddag$
21815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21818 \begin_layout Plain Layout
21826 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21829 \begin_layout Plain Layout
21833 \begin_layout Plain Layout
21843 \begin_inset Formula $\complement$
21850 \begin_layout Plain Layout
21864 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21867 \begin_layout Plain Layout
21875 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21878 \begin_layout Plain Layout
21879 \begin_inset Formula $\Bbbk$
21893 \begin_inset space \hfill{}
21897 \begin_inset Tabular
21898 <lyxtabular version="3" rows="10" columns="2">
21899 <features tabularvalignment="middle">
21900 <column alignment="center" valignment="top" width="0pt">
21901 <column alignment="center" valignment="top" width="0pt">
21903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21906 \begin_layout Plain Layout
21912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21915 \begin_layout Plain Layout
21923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21926 \begin_layout Plain Layout
21934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21937 \begin_layout Plain Layout
21938 \begin_inset Formula $\prime$
21948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21951 \begin_layout Plain Layout
21959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21962 \begin_layout Plain Layout
21963 \begin_inset Formula $\backprime$
21973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21976 \begin_layout Plain Layout
21984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21987 \begin_layout Plain Layout
21988 \begin_inset Formula $\mho$
21998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22001 \begin_layout Plain Layout
22009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22012 \begin_layout Plain Layout
22013 \begin_inset Formula $\triangle$
22023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22026 \begin_layout Plain Layout
22034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22037 \begin_layout Plain Layout
22038 \begin_inset Formula $\angle$
22048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22051 \begin_layout Plain Layout
22059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22062 \begin_layout Plain Layout
22063 \begin_inset Formula $\measuredangle$
22073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22076 \begin_layout Plain Layout
22084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22087 \begin_layout Plain Layout
22088 \begin_inset Formula $\sphericalangle$
22098 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22101 \begin_layout Plain Layout
22109 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22112 \begin_layout Plain Layout
22113 \begin_inset Formula $\top$
22123 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22126 \begin_layout Plain Layout
22134 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22137 \begin_layout Plain Layout
22138 \begin_inset Formula $\bot$
22152 \begin_inset space \hfill{}
22158 \begin_layout Subsection
22159 Miscellaneous Symbols
22160 \begin_inset CommandInset label
22162 name "sub:Miscellaneous-Symbols"
22167 \begin_inset Index idx
22170 \begin_layout Plain Layout
22171 Symbols ! miscellaneous
22179 \begin_layout Standard
22182 \begin_inset Tabular
22183 <lyxtabular version="3" rows="10" columns="2">
22184 <features tabularvalignment="middle">
22185 <column alignment="center" valignment="top" width="0pt">
22186 <column alignment="center" valignment="top" width="0pt">
22188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22191 \begin_layout Plain Layout
22197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22200 \begin_layout Plain Layout
22208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22211 \begin_layout Plain Layout
22219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22222 \begin_layout Plain Layout
22223 \begin_inset Formula $\flat$
22233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22236 \begin_layout Plain Layout
22244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22247 \begin_layout Plain Layout
22248 \begin_inset Formula $\natural$
22258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22261 \begin_layout Plain Layout
22269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22272 \begin_layout Plain Layout
22273 \begin_inset Formula $\sharp$
22283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22286 \begin_layout Plain Layout
22294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22297 \begin_layout Plain Layout
22298 \begin_inset Formula $\surd$
22308 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22311 \begin_layout Plain Layout
22319 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22322 \begin_layout Plain Layout
22323 \begin_inset Formula $\checkmark$
22333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22336 \begin_layout Plain Layout
22344 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22347 \begin_layout Plain Layout
22348 \begin_inset Formula $\yen$
22358 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22361 \begin_layout Plain Layout
22369 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22372 \begin_layout Plain Layout
22373 \begin_inset Formula $\pounds$
22383 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22386 \begin_layout Plain Layout
22392 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22395 \begin_layout Plain Layout
22396 \begin_inset Formula $\$$
22406 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22409 \begin_layout Plain Layout
22415 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22418 \begin_layout Plain Layout
22419 \begin_inset Formula $§$
22433 \begin_inset Tabular
22434 <lyxtabular version="3" rows="10" columns="2">
22435 <features tabularvalignment="middle">
22436 <column alignment="center" valignment="top" width="0">
22437 <column alignment="center" valignment="top" width="0">
22439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22442 \begin_layout Plain Layout
22448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22451 \begin_layout Plain Layout
22459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22462 \begin_layout Plain Layout
22470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22473 \begin_layout Plain Layout
22474 \begin_inset Formula $\hbar$
22484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22487 \begin_layout Plain Layout
22495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22498 \begin_layout Plain Layout
22499 \begin_inset Formula $\hslash$
22509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22512 \begin_layout Plain Layout
22520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22523 \begin_layout Plain Layout
22524 \begin_inset Formula $\clubsuit$
22534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22537 \begin_layout Plain Layout
22545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22548 \begin_layout Plain Layout
22549 \begin_inset Formula $\spadesuit$
22559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22562 \begin_layout Plain Layout
22570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22573 \begin_layout Plain Layout
22574 \begin_inset Formula $\bigstar$
22584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22587 \begin_layout Plain Layout
22595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22598 \begin_layout Plain Layout
22599 \begin_inset Formula $\blacklozenge$
22609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22612 \begin_layout Plain Layout
22620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22623 \begin_layout Plain Layout
22624 \begin_inset Formula $\blacktriangle$
22634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22637 \begin_layout Plain Layout
22645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22648 \begin_layout Plain Layout
22649 \begin_inset Formula $\blacktriangledown$
22659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22662 \begin_layout Plain Layout
22670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22673 \begin_layout Plain Layout
22674 \begin_inset Formula $\bullet$
22688 \begin_inset Tabular
22689 <lyxtabular version="3" rows="10" columns="2">
22690 <features tabularvalignment="middle">
22691 <column alignment="center" valignment="top" width="0pt">
22692 <column alignment="center" valignment="top" width="0pt">
22694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22697 \begin_layout Plain Layout
22703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22706 \begin_layout Plain Layout
22714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22717 \begin_layout Plain Layout
22725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22728 \begin_layout Plain Layout
22729 \begin_inset Formula $\diamondsuit$
22739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22742 \begin_layout Plain Layout
22750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22753 \begin_layout Plain Layout
22754 \begin_inset Formula $\Diamond$
22764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22767 \begin_layout Plain Layout
22775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22778 \begin_layout Plain Layout
22779 \begin_inset Formula $\heartsuit$
22789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22792 \begin_layout Plain Layout
22800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22803 \begin_layout Plain Layout
22804 \begin_inset Formula $\P$
22814 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22817 \begin_layout Plain Layout
22825 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22828 \begin_layout Plain Layout
22829 \begin_inset Formula $\copyright$
22839 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22842 \begin_layout Plain Layout
22850 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22853 \begin_layout Plain Layout
22854 \begin_inset Formula $\circledR$
22864 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22867 \begin_layout Plain Layout
22875 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22878 \begin_layout Plain Layout
22879 \begin_inset Formula $\maltese$
22889 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22892 \begin_layout Plain Layout
22900 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22903 \begin_layout Plain Layout
22904 \begin_inset Formula $\diagup$
22914 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22917 \begin_layout Plain Layout
22925 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22928 \begin_layout Plain Layout
22929 \begin_inset Formula $\diagdown$
22945 \begin_layout Standard
22946 \begin_inset VSpace medskip
22949 More symbols are listed in
22950 \begin_inset CommandInset ref
22952 reference "sub:Miscellaneous-special-Characters"
22959 \begin_layout Standard
22960 Some symbols can be displayed in different sizes, see
22961 \begin_inset CommandInset ref
22963 reference "sub:Font-Sizes"
22970 \begin_layout Subsection
22972 \begin_inset Index idx
22975 \begin_layout Plain Layout
22976 Symbols ! Euro-symbol
22982 \begin_inset Index idx
22985 \begin_layout Plain Layout
22992 \begin_layout Plain Layout
23009 \begin_layout Standard
23010 To use the Euro symbol in formulas, the LaTeX-package
23015 \begin_inset Index idx
23018 \begin_layout Plain Layout
23024 must be installed and loaded with the LaTeX-preamble line
23027 \begin_layout Standard
23032 usepackage[gennarrow]{eurosym}
23035 \begin_layout Standard
23036 The Euro symbol can now be inserted with the command
23043 \begin_inset Index idx
23046 \begin_layout Plain Layout
23057 \begin_layout Standard
23058 The Euro symbol can directly be inserted with the € key in mathematical
23059 text, without having
23074 can also be inserted in TeX-mode.
23075 The official currency symbol can then be inserted with the command
23082 \begin_inset Index idx
23085 \begin_layout Plain Layout
23093 , that is only available in TeX-mode.
23096 \begin_layout Standard
23100 \begin_layout Plain Layout
23110 \begin_inset Note Note
23113 \begin_layout Plain Layout
23114 The following table will only be displayed when the LaTeX-package
23126 \begin_layout Standard
23127 An overview about the different Euro symbols:
23130 \begin_layout Standard
23132 \begin_inset Tabular
23133 <lyxtabular version="3" rows="4" columns="3">
23134 <features tabularvalignment="middle">
23135 <column alignment="center" valignment="top" width="0pt">
23136 <column alignment="center" valignment="top" width="0pt">
23137 <column alignment="center" valignment="top" width="0pt">
23139 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23142 \begin_layout Plain Layout
23148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23151 \begin_layout Plain Layout
23157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23160 \begin_layout Plain Layout
23168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23171 \begin_layout Plain Layout
23177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23180 \begin_layout Plain Layout
23188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23191 \begin_layout Plain Layout
23192 \begin_inset Formula $\euro$
23202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23205 \begin_layout Plain Layout
23211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23214 \begin_layout Plain Layout
23220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23223 \begin_layout Plain Layout
23224 \begin_inset Formula $\mbox{€}$
23234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23237 \begin_layout Plain Layout
23243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23246 \begin_layout Plain Layout
23254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23257 \begin_layout Plain Layout
23261 \begin_layout Plain Layout
23283 \begin_layout Standard
23287 \begin_layout Plain Layout
23297 \begin_inset Note Note
23300 \begin_layout Plain Layout
23301 The following will be displayed when the LaTeX-package
23313 \begin_layout Standard
23314 You need to install the LaTeX-package
23318 to see the rest of this subsection in the output.
23321 \begin_layout Standard
23325 \begin_layout Plain Layout
23337 \begin_layout Section
23339 \begin_inset CommandInset label
23341 name "sec:Relations"
23346 \begin_inset Index idx
23349 \begin_layout Plain Layout
23356 \begin_inset Index idx
23359 \begin_layout Plain Layout
23364 \begin_layout Plain Layout
23375 \begin_layout Plain Layout
23390 \begin_layout Standard
23391 All relations can also be inserted via the toolbar button
23392 \begin_inset Graphics
23393 filename ../images/math/leq.png
23401 \begin_layout Standard
23402 \begin_inset space \hfill{}
23406 \begin_inset Tabular
23407 <lyxtabular version="3" rows="17" columns="2">
23408 <features tabularvalignment="middle">
23409 <column alignment="center" valignment="top" width="0pt">
23410 <column alignment="center" valignment="top" width="0pt">
23412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23415 \begin_layout Plain Layout
23421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23424 \begin_layout Plain Layout
23432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23435 \begin_layout Plain Layout
23441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23444 \begin_layout Plain Layout
23445 \begin_inset Formula $<$
23455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23458 \begin_layout Plain Layout
23466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23469 \begin_layout Plain Layout
23470 \begin_inset Formula $\le$
23480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23483 \begin_layout Plain Layout
23491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23494 \begin_layout Plain Layout
23495 \begin_inset Formula $\ll$
23505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23508 \begin_layout Plain Layout
23516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23519 \begin_layout Plain Layout
23520 \begin_inset Formula $\prec$
23530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23533 \begin_layout Plain Layout
23541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23544 \begin_layout Plain Layout
23545 \begin_inset Formula $\preceq$
23555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23558 \begin_layout Plain Layout
23566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23569 \begin_layout Plain Layout
23570 \begin_inset Formula $\subset$
23580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23583 \begin_layout Plain Layout
23591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23594 \begin_layout Plain Layout
23595 \begin_inset Formula $\subseteq$
23605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23608 \begin_layout Plain Layout
23616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23619 \begin_layout Plain Layout
23620 \begin_inset Formula $\sqsubseteq$
23630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23633 \begin_layout Plain Layout
23641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23644 \begin_layout Plain Layout
23645 \begin_inset Formula $\in$
23655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23658 \begin_layout Plain Layout
23666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23669 \begin_layout Plain Layout
23670 \begin_inset Formula $\vdash$
23680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23683 \begin_layout Plain Layout
23691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23694 \begin_layout Plain Layout
23695 \begin_inset Formula $\smile$
23705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23708 \begin_layout Plain Layout
23716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23719 \begin_layout Plain Layout
23720 \begin_inset Formula $\lhd$
23730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23733 \begin_layout Plain Layout
23741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23744 \begin_layout Plain Layout
23745 \begin_inset Formula $\unlhd$
23755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23758 \begin_layout Plain Layout
23766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23769 \begin_layout Plain Layout
23770 \begin_inset Formula $\gtrless$
23780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23783 \begin_layout Plain Layout
23791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23794 \begin_layout Plain Layout
23795 \begin_inset Formula $\mid$
23805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23808 \begin_layout Plain Layout
23816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23819 \begin_layout Plain Layout
23820 \begin_inset Formula $\nmid$
23834 \begin_inset space \hfill{}
23838 \begin_inset Tabular
23839 <lyxtabular version="3" rows="17" columns="2">
23840 <features tabularvalignment="middle">
23841 <column alignment="center" valignment="top" width="0pt">
23842 <column alignment="center" valignment="top" width="0pt">
23844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23847 \begin_layout Plain Layout
23853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23856 \begin_layout Plain Layout
23864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23867 \begin_layout Plain Layout
23873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23876 \begin_layout Plain Layout
23877 \begin_inset Formula $=$
23887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23890 \begin_layout Plain Layout
23898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23901 \begin_layout Plain Layout
23902 \begin_inset Formula $\not=$
23912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23915 \begin_layout Plain Layout
23923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23926 \begin_layout Plain Layout
23927 \begin_inset Formula $\equiv$
23937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23940 \begin_layout Plain Layout
23948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23951 \begin_layout Plain Layout
23952 \begin_inset Formula $\sim$
23962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23965 \begin_layout Plain Layout
23973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23976 \begin_layout Plain Layout
23977 \begin_inset Formula $\simeq$
23987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23990 \begin_layout Plain Layout
23998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24001 \begin_layout Plain Layout
24002 \begin_inset Formula $\approx$
24012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24015 \begin_layout Plain Layout
24023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24026 \begin_layout Plain Layout
24027 \begin_inset Formula $\cong$
24037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24040 \begin_layout Plain Layout
24048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24051 \begin_layout Plain Layout
24052 \begin_inset Formula $\bowtie$
24062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24065 \begin_layout Plain Layout
24073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24076 \begin_layout Plain Layout
24077 \begin_inset Formula $\notin$
24087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24090 \begin_layout Plain Layout
24098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24101 \begin_layout Plain Layout
24102 \begin_inset Formula $\perp$
24112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24115 \begin_layout Plain Layout
24123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24126 \begin_layout Plain Layout
24127 \begin_inset Formula $\propto$
24137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24140 \begin_layout Plain Layout
24148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24151 \begin_layout Plain Layout
24152 \begin_inset Formula $\asymp$
24162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24165 \begin_layout Plain Layout
24173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24176 \begin_layout Plain Layout
24177 \begin_inset Formula $\doteq$
24187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24190 \begin_layout Plain Layout
24198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24201 \begin_layout Plain Layout
24202 \begin_inset Formula $\circeq$
24212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24215 \begin_layout Plain Layout
24223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24226 \begin_layout Plain Layout
24227 \begin_inset Formula $\models$
24237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24240 \begin_layout Plain Layout
24248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24251 \begin_layout Plain Layout
24252 \begin_inset Formula $\widehat{=}$
24266 \begin_inset space \hfill{}
24270 \begin_inset Tabular
24271 <lyxtabular version="3" rows="17" columns="2">
24272 <features tabularvalignment="middle">
24273 <column alignment="center" valignment="top" width="0pt">
24274 <column alignment="center" valignment="top" width="0pt">
24276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24279 \begin_layout Plain Layout
24285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24288 \begin_layout Plain Layout
24296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24299 \begin_layout Plain Layout
24305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24308 \begin_layout Plain Layout
24309 \begin_inset Formula $>$
24319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24322 \begin_layout Plain Layout
24330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24333 \begin_layout Plain Layout
24334 \begin_inset Formula $\ge$
24344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24347 \begin_layout Plain Layout
24355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24358 \begin_layout Plain Layout
24359 \begin_inset Formula $\gg$
24369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24372 \begin_layout Plain Layout
24380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24383 \begin_layout Plain Layout
24384 \begin_inset Formula $\succ$
24394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24397 \begin_layout Plain Layout
24405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24408 \begin_layout Plain Layout
24409 \begin_inset Formula $\succeq$
24419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24422 \begin_layout Plain Layout
24430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24433 \begin_layout Plain Layout
24434 \begin_inset Formula $\supset$
24444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24447 \begin_layout Plain Layout
24455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24458 \begin_layout Plain Layout
24459 \begin_inset Formula $\supseteq$
24469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24472 \begin_layout Plain Layout
24480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24483 \begin_layout Plain Layout
24484 \begin_inset Formula $\sqsupseteq$
24494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24497 \begin_layout Plain Layout
24505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24508 \begin_layout Plain Layout
24509 \begin_inset Formula $\ni$
24519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24522 \begin_layout Plain Layout
24530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24533 \begin_layout Plain Layout
24534 \begin_inset Formula $\dashv$
24544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24547 \begin_layout Plain Layout
24555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24558 \begin_layout Plain Layout
24559 \begin_inset Formula $\frown$
24569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24572 \begin_layout Plain Layout
24580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24583 \begin_layout Plain Layout
24584 \begin_inset Formula $\rhd$
24594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24597 \begin_layout Plain Layout
24605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24608 \begin_layout Plain Layout
24609 \begin_inset Formula $\unrhd$
24619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24622 \begin_layout Plain Layout
24630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24633 \begin_layout Plain Layout
24634 \begin_inset Formula $\lessgtr$
24644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24647 \begin_layout Plain Layout
24655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24658 \begin_layout Plain Layout
24659 \begin_inset Formula $\parallel$
24669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24672 \begin_layout Plain Layout
24680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24683 \begin_layout Plain Layout
24684 \begin_inset Formula $\nparallel$
24698 \begin_inset space \hfill{}
24704 \begin_layout Standard
24705 \begin_inset VSpace medskip
24720 are bigger than the equal looking operators
24735 \begin_layout Standard
24736 Relations are, in contrary to symbols, always surrounded by space.
24739 \begin_layout Standard
24740 Relations with labels can be created with the command
24747 \begin_inset Index idx
24750 \begin_layout Plain Layout
24761 \begin_layout Standard
24763 \begin_inset Tabular
24764 <lyxtabular version="3" rows="2" columns="2">
24765 <features tabularvalignment="middle">
24766 <column alignment="center" valignment="top" width="0">
24767 <column alignment="center" valignment="top" width="0">
24769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24772 \begin_layout Plain Layout
24778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24781 \begin_layout Plain Layout
24783 \begin_inset Note Note
24786 \begin_layout Plain Layout
24793 is only used as spacer.
24805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24808 \begin_layout Plain Layout
24815 \begin_layout Plain Layout
24832 \begin_layout Plain Layout
24842 \begin_inset Formula $\downarrow$
24851 \begin_layout Plain Layout
24864 \begin_layout Plain Layout
24878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24881 \begin_layout Plain Layout
24882 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24898 \begin_layout Section
24902 \begin_layout Subsection
24903 Predefined Functions
24904 \begin_inset CommandInset label
24906 name "sub:Predefined-Functions"
24911 \begin_inset Index idx
24914 \begin_layout Plain Layout
24915 Functions ! predefined
24923 \begin_layout Standard
24924 In general, variables are set
24928 in mathematical expressions, but not function names, because
24929 \begin_inset Formula $sin$
24932 could be misunderstood as
24933 \begin_inset Formula $s\cdot i\cdot n$
24937 Therefore there are predefined functionswhich are additionally a bit separated
24939 They are inserted as commands starting with a backslash before their name.
24942 \begin_layout Standard
24944 \begin_inset Tabular
24945 <lyxtabular version="3" rows="2" columns="4">
24946 <features tabularvalignment="middle">
24947 <column alignment="center" valignment="top" width="0pt">
24948 <column alignment="center" valignment="top" width="0pt">
24949 <column alignment="center" valignment="top" width="0pt">
24950 <column alignment="center" valignment="top" width="0pt">
24952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24955 \begin_layout Plain Layout
24961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24964 \begin_layout Plain Layout
24970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24973 \begin_layout Plain Layout
24979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24982 \begin_layout Plain Layout
24990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24993 \begin_layout Plain Layout
24999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25002 \begin_layout Plain Layout
25003 \begin_inset Formula $Asin(x)+B$
25011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25014 \begin_layout Plain Layout
25022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25025 \begin_layout Plain Layout
25026 \begin_inset Formula $A\sin(x)+B$
25042 \begin_layout Standard
25043 The following functions are predefined:
25046 \begin_layout Standard
25047 \begin_inset VSpace -2mm
25053 \begin_layout Standard
25055 \begin_inset Tabular
25056 <lyxtabular version="3" rows="9" columns="4">
25057 <features tabularvalignment="middle">
25058 <column alignment="center" valignment="top" width="0pt">
25059 <column alignment="center" valignment="top" width="0pt">
25060 <column alignment="center" valignment="top" width="0pt">
25061 <column alignment="center" valignment="top" width="0pt">
25063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25066 \begin_layout Plain Layout
25072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25075 \begin_layout Plain Layout
25081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25084 \begin_layout Plain Layout
25090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25093 \begin_layout Plain Layout
25101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25104 \begin_layout Plain Layout
25112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25115 \begin_layout Plain Layout
25123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25126 \begin_layout Plain Layout
25134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25137 \begin_layout Plain Layout
25147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25150 \begin_layout Plain Layout
25158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25161 \begin_layout Plain Layout
25169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25172 \begin_layout Plain Layout
25180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25183 \begin_layout Plain Layout
25193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25196 \begin_layout Plain Layout
25204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25207 \begin_layout Plain Layout
25215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25218 \begin_layout Plain Layout
25226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25229 \begin_layout Plain Layout
25239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25242 \begin_layout Plain Layout
25250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25253 \begin_layout Plain Layout
25261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25264 \begin_layout Plain Layout
25272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25275 \begin_layout Plain Layout
25285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25288 \begin_layout Plain Layout
25296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25299 \begin_layout Plain Layout
25307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25310 \begin_layout Plain Layout
25318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25321 \begin_layout Plain Layout
25331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25334 \begin_layout Plain Layout
25342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25345 \begin_layout Plain Layout
25353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25356 \begin_layout Plain Layout
25364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25367 \begin_layout Plain Layout
25377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25380 \begin_layout Plain Layout
25388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25391 \begin_layout Plain Layout
25399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25402 \begin_layout Plain Layout
25410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25413 \begin_layout Plain Layout
25423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25426 \begin_layout Plain Layout
25434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25437 \begin_layout Plain Layout
25445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25448 \begin_layout Plain Layout
25456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25459 \begin_layout Plain Layout
25475 \begin_layout Standard
25476 They can also be inserted with the math toolbar button
25477 \begin_inset Graphics
25478 filename ../images/math/functions.png
25486 \begin_layout Subsection
25487 Self-defined Functions
25488 \begin_inset Index idx
25491 \begin_layout Plain Layout
25492 Functions ! self-defined
25500 \begin_layout Standard
25501 To use a function that is not predefined, like for example the sign function
25502 sgn(x), there are two possibilities:
25505 \begin_layout Itemize
25506 Define the function by inserting the following line to the LaTeX-preamble
25510 \begin_layout Plain Layout
25515 DeclareMathOperator
25518 \begin_inset CommandInset ref
25520 reference "sub:Self-defined-Operators"
25530 \begin_inset Newline newline
25534 \begin_inset VSpace -3mm
25538 \begin_inset Newline newline
25545 DeclareMathOperator{
25550 \begin_inset Index idx
25553 \begin_layout Plain Layout
25558 DeclareMathOperator
25564 \begin_inset Newline newline
25568 \begin_inset VSpace -2mm
25572 \begin_inset Newline newline
25575 Now the new defined function can be called with the command
25584 \begin_layout Itemize
25585 Write the formula as usual, mark the formula name, in our example the letters
25590 , and change it to mathematical text.
25591 Finally, a space is inserted between prefactor and function.
25594 \begin_layout Standard
25595 The result is the same with both methods as with a predefined function
25599 \begin_layout Plain Layout
25600 In LyX self-defined functions are displayed red, predefined ones black.
25608 \begin_layout Standard
25610 \begin_inset Tabular
25611 <lyxtabular version="3" rows="3" columns="2">
25612 <features tabularvalignment="middle">
25613 <column alignment="center" valignment="top" width="0pt">
25614 <column alignment="center" valignment="top" width="0pt">
25616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25619 \begin_layout Plain Layout
25625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25628 \begin_layout Plain Layout
25636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25639 \begin_layout Plain Layout
25647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25650 \begin_layout Plain Layout
25651 \begin_inset Formula $A\sgn(x)+B$
25661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25664 \begin_layout Plain Layout
25668 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25679 \begin_layout Plain Layout
25680 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25696 \begin_layout Standard
25697 The first method is more suitable when the self-defined function should
25698 be used several times.
25701 \begin_layout Subsection
25703 \begin_inset Index idx
25706 \begin_layout Plain Layout
25715 \begin_layout Standard
25716 For limits, in addition to the commands
25723 \begin_inset Index idx
25726 \begin_layout Plain Layout
25746 the following functions are defined:
25749 \begin_layout Standard
25751 \begin_inset Tabular
25752 <lyxtabular version="3" rows="5" columns="2">
25753 <features tabularvalignment="middle">
25754 <column alignment="center" valignment="top" width="0">
25755 <column alignment="center" valignment="top" width="0">
25757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25760 \begin_layout Plain Layout
25766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25769 \begin_layout Plain Layout
25771 \begin_inset Note Note
25774 \begin_layout Plain Layout
25781 is only used as spacer.
25793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25796 \begin_layout Plain Layout
25804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25807 \begin_layout Plain Layout
25808 \begin_inset Formula $\varliminf$
25818 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25821 \begin_layout Plain Layout
25829 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25832 \begin_layout Plain Layout
25833 \begin_inset Formula $\varlimsup$
25843 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25846 \begin_layout Plain Layout
25854 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25857 \begin_layout Plain Layout
25858 \begin_inset Formula $\varprojlim$
25868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25871 \begin_layout Plain Layout
25879 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25882 \begin_layout Plain Layout
25883 \begin_inset Formula $\varinjlim$
25887 \begin_inset Formula $\raisebox{-2.5mm}{}$
25903 \begin_layout Standard
25904 \begin_inset VSpace medskip
25907 The limit is created by inserting a subscript.
25908 It is set right beside the function in an inline formula:
25911 \begin_layout Standard
25913 \begin_inset Tabular
25914 <lyxtabular version="3" rows="2" columns="2">
25915 <features tabularvalignment="middle">
25916 <column alignment="center" valignment="top" width="0pt">
25917 <column alignment="center" valignment="top" width="0pt">
25919 <cell alignment="center" valignment="top" usebox="none">
25922 \begin_layout Plain Layout
25928 <cell alignment="center" valignment="top" usebox="none">
25931 \begin_layout Plain Layout
25932 \begin_inset space \hspace{}
25937 \begin_inset Note Note
25940 \begin_layout Plain Layout
25947 are used here as spacer.
25959 <cell alignment="center" valignment="top" usebox="none">
25962 \begin_layout Plain Layout
25971 \begin_layout Plain Layout
25984 \begin_layout Plain Layout
25998 <cell alignment="center" valignment="top" usebox="none">
26001 \begin_layout Plain Layout
26002 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
26018 \begin_layout Standard
26019 In a displayed formula the limit is set below the formula, as usual:
26020 \begin_inset Formula
26030 \begin_layout Subsection
26032 \begin_inset Index idx
26035 \begin_layout Plain Layout
26036 Functions ! modulo-
26044 \begin_layout Standard
26045 The modulo-function is special, because it exists in four variants.
26046 The variants in a displayed formula are:
26047 \begin_inset Formula
26049 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26050 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
26051 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
26052 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
26053 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
26061 \begin_layout Standard
26062 In an inline formula less space is set before the function names for all
26064 By default the modulo-functions take only the first following character
26066 To use more than one character, one has to put them into TeX-braces:
26067 \begin_inset Formula
26069 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26070 \mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\
26071 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26079 \begin_layout Section
26081 \begin_inset Index idx
26084 \begin_layout Plain Layout
26093 \begin_layout Subsection
26094 Special Characters in Mathematical Text
26097 \begin_layout Standard
26098 The following commands can only be used in mathematical text or in TeX-mode:
26101 \begin_layout Standard
26102 \begin_inset space \hfill{}
26106 \begin_inset Tabular
26107 <lyxtabular version="3" rows="8" columns="2">
26108 <features tabularvalignment="middle">
26109 <column alignment="block" valignment="top" width="0">
26110 <column alignment="block" valignment="top" width="0">
26112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26115 \begin_layout Plain Layout
26121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26124 \begin_layout Plain Layout
26132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26135 \begin_layout Plain Layout
26143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26146 \begin_layout Plain Layout
26147 \begin_inset Formula $\textrm{œ}$
26157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26160 \begin_layout Plain Layout
26168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26171 \begin_layout Plain Layout
26172 \begin_inset Formula $\textrm{Œ}$
26182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26185 \begin_layout Plain Layout
26193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26196 \begin_layout Plain Layout
26197 \begin_inset Formula $\textrm{æ}$
26207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26210 \begin_layout Plain Layout
26218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26221 \begin_layout Plain Layout
26222 \begin_inset Formula $\textrm{Æ}$
26232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26235 \begin_layout Plain Layout
26243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26246 \begin_layout Plain Layout
26247 \begin_inset Formula $\textrm{\aa}$
26257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26260 \begin_layout Plain Layout
26264 \begin_inset Index idx
26267 \begin_layout Plain Layout
26274 \begin_layout Plain Layout
26295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26298 \begin_layout Plain Layout
26299 \begin_inset Formula $\textrm{Å}$
26309 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26312 \begin_layout Plain Layout
26320 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26323 \begin_layout Plain Layout
26324 \begin_inset Formula $\textrm{ı}$
26338 \begin_inset space \hfill{}
26342 \begin_inset Tabular
26343 <lyxtabular version="3" rows="8" columns="2">
26344 <features tabularvalignment="middle">
26345 <column alignment="block" valignment="top" width="0">
26346 <column alignment="center" valignment="top" width="0">
26348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26351 \begin_layout Plain Layout
26353 \begin_inset Note Note
26356 \begin_layout Plain Layout
26358 \begin_inset space \thinspace{}
26361 mm is used for separation, because otherwise the output will be ¡ and ¿
26372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26375 \begin_layout Plain Layout
26383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26386 \begin_layout Plain Layout
26394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26397 \begin_layout Plain Layout
26398 \begin_inset Formula $\textrm{ø}$
26408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26411 \begin_layout Plain Layout
26419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26422 \begin_layout Plain Layout
26423 \begin_inset Formula $\textrm{Ø}$
26433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26436 \begin_layout Plain Layout
26444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26447 \begin_layout Plain Layout
26448 \begin_inset Formula $\textrm{ł}$
26458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26461 \begin_layout Plain Layout
26469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26472 \begin_layout Plain Layout
26473 \begin_inset Formula $\textrm{Ł}$
26483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26486 \begin_layout Plain Layout
26488 \begin_inset space \hspace{}
26496 \begin_layout Plain Layout
26510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26513 \begin_layout Plain Layout
26514 \begin_inset Formula $\textrm{!`}$
26524 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26527 \begin_layout Plain Layout
26529 \begin_inset space \hspace{}
26537 \begin_layout Plain Layout
26551 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26554 \begin_layout Plain Layout
26555 \begin_inset Formula $\textrm{?`}$
26565 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26568 \begin_layout Plain Layout
26576 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26579 \begin_layout Plain Layout
26580 \begin_inset Formula $\textrm{ȷ}$
26594 \begin_inset space \hfill{}
26600 \begin_layout Standard
26602 \begin_inset Formula $\textrm{\textrm{Å}}$
26606 \begin_inset Formula $\textrm{\textrm{Ø}}$
26609 can also be inserted via the math toolbar button
26610 \begin_inset Graphics
26611 filename ../images/math/digamma.png
26619 \begin_layout Standard
26620 An exception are the commands
26623 \begin_inset space \hspace{}
26632 \begin_inset space \hspace{}
26638 , because they can be inserted in LyX directly to text.
26641 \begin_layout Subsection
26643 \begin_inset CommandInset label
26645 name "sub:Accents-in-Text"
26650 \begin_inset Index idx
26653 \begin_layout Plain Layout
26662 \begin_layout Standard
26663 With the following commands all letters can be accented.
26664 The commands must be inserted in TeX-mode.
26667 \begin_layout Standard
26668 \begin_inset space \hfill{}
26672 \begin_inset Tabular
26673 <lyxtabular version="3" rows="8" columns="2">
26674 <features tabularvalignment="middle">
26675 <column alignment="block" valignment="top" width="0">
26676 <column alignment="block" valignment="top" width="0">
26678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26681 \begin_layout Plain Layout
26687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26690 \begin_layout Plain Layout
26698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26701 \begin_layout Plain Layout
26705 \begin_inset Quotes grd
26713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26716 \begin_layout Plain Layout
26720 \begin_layout Plain Layout
26736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26739 \begin_layout Plain Layout
26747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26750 \begin_layout Plain Layout
26754 \begin_layout Plain Layout
26770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26773 \begin_layout Plain Layout
26780 \begin_layout Plain Layout
26794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26797 \begin_layout Plain Layout
26801 \begin_layout Plain Layout
26817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26820 \begin_layout Plain Layout
26828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26831 \begin_layout Plain Layout
26835 \begin_layout Plain Layout
26851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26854 \begin_layout Plain Layout
26861 \begin_layout Plain Layout
26875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26878 \begin_layout Plain Layout
26882 \begin_layout Plain Layout
26898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26901 \begin_layout Plain Layout
26908 \begin_layout Plain Layout
26922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26925 \begin_layout Plain Layout
26929 \begin_layout Plain Layout
26945 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26948 \begin_layout Plain Layout
26955 \begin_layout Plain Layout
26969 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26972 \begin_layout Plain Layout
26976 \begin_layout Plain Layout
26996 \begin_inset space \hfill{}
27000 \begin_inset Tabular
27001 <lyxtabular version="3" rows="8" columns="2">
27002 <features tabularvalignment="middle">
27003 <column alignment="block" valignment="top" width="0">
27004 <column alignment="center" valignment="top" width="0">
27006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27009 \begin_layout Plain Layout
27015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27018 \begin_layout Plain Layout
27026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27029 \begin_layout Plain Layout
27036 \begin_layout Plain Layout
27050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27053 \begin_layout Plain Layout
27057 \begin_layout Plain Layout
27073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27076 \begin_layout Plain Layout
27084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27087 \begin_layout Plain Layout
27091 \begin_layout Plain Layout
27107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27110 \begin_layout Plain Layout
27114 \begin_inset Index idx
27117 \begin_layout Plain Layout
27128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27131 \begin_layout Plain Layout
27135 \begin_layout Plain Layout
27151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27154 \begin_layout Plain Layout
27162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27165 \begin_layout Plain Layout
27169 \begin_layout Plain Layout
27185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27188 \begin_layout Plain Layout
27195 \begin_layout Plain Layout
27209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27212 \begin_layout Plain Layout
27216 \begin_layout Plain Layout
27232 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27235 \begin_layout Plain Layout
27242 \begin_layout Plain Layout
27256 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27259 \begin_layout Plain Layout
27263 \begin_layout Plain Layout
27279 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27282 \begin_layout Plain Layout
27289 \begin_layout Plain Layout
27303 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27306 \begin_layout Plain Layout
27310 \begin_layout Plain Layout
27330 \begin_inset space \hfill{}
27336 \begin_layout Standard
27337 \begin_inset VSpace medskip
27346 also two different characters can be accented.
27355 \begin_layout Plain Layout
27370 \begin_layout Plain Layout
27382 \begin_layout Standard
27395 can in combination with vowels directly be inserted with the keyboard without
27397 The same applies for the tilde
27401 \begin_layout Plain Layout
27402 This only applies for keyboards where the tilde is defined as accent.
27411 in combination with
27426 \begin_layout Standard
27469 and accents that are inserted directly with the keyboard are also available
27470 in mathematical text.
27471 For the other accents there are special math commands to be used in formulas,
27473 \begin_inset CommandInset ref
27475 reference "sub:Accents-for-one"
27482 \begin_layout Standard
27483 \begin_inset VSpace bigskip
27486 Furthermore, with the command
27493 \begin_inset Index idx
27496 \begin_layout Plain Layout
27504 all numbers and letters can be set into a circle, quasi accented with a
27505 circle, similar to the copyright symbol.
27508 \begin_layout Standard
27510 \begin_inset Tabular
27511 <lyxtabular version="3" rows="3" columns="2">
27512 <features tabularvalignment="middle">
27513 <column alignment="center" valignment="top" width="0">
27514 <column alignment="center" valignment="top" width="0">
27516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27519 \begin_layout Plain Layout
27525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27528 \begin_layout Plain Layout
27530 \begin_inset Note Note
27533 \begin_layout Plain Layout
27540 is only used as spacer.
27552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27555 \begin_layout Plain Layout
27563 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27566 \begin_layout Plain Layout
27570 \begin_layout Plain Layout
27586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27589 \begin_layout Plain Layout
27600 raisebox{-1.5pt}{W}}
27605 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27608 \begin_layout Plain Layout
27609 \begin_inset Formula $\raisebox{4.5mm}{}$
27616 \begin_layout Plain Layout
27634 \begin_inset Formula $\raisebox{-2mm}{}$
27650 \begin_layout Standard
27651 One has to take care that the character fits in the circle.
27662 \begin_layout Plain Layout
27664 \begin_inset CommandInset ref
27666 reference "sub:Font-Sizes"
27675 specifies thereby the size of the circle.
27686 \begin_layout Plain Layout
27688 \begin_inset CommandInset ref
27690 reference "sub:Boxes-without-Frame"
27699 the character can be centered.
27702 \begin_layout Subsection
27704 \begin_inset Index idx
27707 \begin_layout Plain Layout
27716 \begin_layout Standard
27717 Old-style figures (also known as old-style numerals) are created with the
27725 \begin_inset Index idx
27728 \begin_layout Plain Layout
27737 The command can be used in formulas and in TeX-mode.
27738 The command scheme is:
27741 \begin_layout Standard
27746 oldstylenums{number}
27749 \begin_layout Standard
27754 oldstylenums{0123456789
27757 \begin_inset Formula $\oldstylenums{0123456789}$
27763 \begin_layout Subsection
27764 Miscellaneous special Characters
27765 \begin_inset CommandInset label
27767 name "sub:Miscellaneous-special-Characters"
27772 \begin_inset Index idx
27775 \begin_layout Plain Layout
27776 Special characters ! miscellaneous
27784 \begin_layout Standard
27785 The following characters can only be inserted to formulas by using commands:
27788 \begin_layout Standard
27790 \begin_inset Tabular
27791 <lyxtabular version="3" rows="4" columns="2">
27792 <features tabularvalignment="middle">
27793 <column alignment="center" valignment="top" width="0">
27794 <column alignment="center" valignment="top" width="0">
27796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27799 \begin_layout Plain Layout
27805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27808 \begin_layout Plain Layout
27816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27819 \begin_layout Plain Layout
27826 \begin_layout Plain Layout
27840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27843 \begin_layout Plain Layout
27844 \begin_inset Formula $\mathcircumflex$
27854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27857 \begin_layout Plain Layout
27865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27868 \begin_layout Plain Layout
27869 \begin_inset Formula $\_$
27879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27882 \begin_layout Plain Layout
27887 \begin_layout Plain Layout
27899 \begin_inset Index idx
27902 \begin_layout Plain Layout
27915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27918 \begin_layout Plain Layout
27919 \begin_inset Formula $^{\circ}$
27935 \begin_layout Standard
27936 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27937 contains the following line
27941 \begin_layout Plain Layout
27942 More about this is described in
27943 \begin_inset CommandInset ref
27945 reference "sub:Text-Characters-in"
27957 \begin_layout Standard
27962 DeclareInputtext{176}{
27975 \begin_layout Standard
27976 \begin_inset Newpage newpage
27982 \begin_layout Section
27984 \begin_inset CommandInset label
27986 name "sec:Formula-Styles"
27991 \begin_inset Index idx
27994 \begin_layout Plain Layout
28003 \begin_layout Itemize
28004 There are two different alignment styles:
28008 \begin_layout Description
28009 Centered is the predefined standard
28012 \begin_layout Description
28013 Indented for this the option
28017 must be inserted in the menu
28019 Document\SpecialChar \menuseparator
28025 \begin_inset space ~
28031 \begin_layout Standard
28036 is used, the indentation can be adjusted with the length
28043 \begin_inset Index idx
28046 \begin_layout Plain Layout
28055 Should the distance be 15
28056 \begin_inset space \thinspace{}
28059 mm, the following command line is inserted in the LaTeX-preamble
28062 \begin_layout Standard
28072 \begin_layout Standard
28073 When no length is specified, the predefined value of 30
28074 \begin_inset space \thinspace{}
28081 \begin_layout Itemize
28082 And two different numbering styles:
28086 \begin_layout Description
28087 Right is the predefined standard
28090 \begin_layout Description
28091 Left for this the option
28095 must be inserted in the menu
28097 Document\SpecialChar \menuseparator
28103 \begin_inset space ~
28110 \begin_layout Standard
28119 can also be used together.
28120 In this case both options are inserted, separated by a comma.
28123 \begin_layout Standard
28124 The chosen styles are used for all displayed formulas of the document.
28125 When both, centered and indented formulas should be created in a document,
28131 The indented formulas are then set in a flalign environment, see
28132 \begin_inset CommandInset ref
28134 reference "sub:Flalign-Environment"
28141 \begin_layout Section
28143 \begin_inset CommandInset label
28145 name "sec:Multiline-Formulas"
28150 \begin_inset Index idx
28153 \begin_layout Plain Layout
28154 Formula ! multiline
28162 \begin_layout Subsection
28166 \begin_layout Standard
28167 In LyX multiline formulas are created by pressing
28172 arg "newline-insert newline"
28178 This creates either an
28180 eqnarray environment
28182 that is described in
28183 \begin_inset CommandInset ref
28185 reference "sub:Eqnarray-Environment"
28189 or, when the option
28191 Use AMS math package
28193 in the document settings is selected, an
28197 that is described in
28198 \begin_inset CommandInset ref
28200 reference "sub:Standard-align-Environment"
28205 The align environment is recommended because it provides in any case a
28206 typographically correct output.
28209 \begin_layout Standard
28210 There are other multiline formula environments that can be created via the
28213 Insert\SpecialChar \menuseparator
28217 These environments are described in the following sections.
28220 \begin_layout Standard
28221 In all multiline formula environments a new line is created by pressing
28225 arg "newline-insert newline"
28229 To add or delete lines, the math toolbar buttons
28230 \begin_inset Graphics
28231 filename ../images/tabular-feature_append-row.png
28237 \begin_inset Graphics
28238 filename ../images/tabular-feature_delete-row.png
28243 , respectively, or the menu
28245 Edit\SpecialChar \menuseparator
28251 \begin_layout Subsubsection
28253 \begin_inset CommandInset label
28255 name "sub:Line-Separation"
28260 \begin_inset Index idx
28263 \begin_layout Plain Layout
28264 Formula ! multiline ! Line separation
28272 \begin_layout Standard
28273 There is sometimes not enough space in multiline formulas between the lines:
28274 \begin_inset Formula
28276 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}\\
28277 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
28285 \begin_layout Standard
28286 In LaTeX additional line space is specified as optional argument of the
28288 This is not yet possible in LyX
28292 \begin_layout Plain Layout
28294 \begin_inset CommandInset href
28296 name "LyX-bug #1505"
28297 target "http://www.lyx.org/trac/ticket/1505"
28306 , therefore the whole formula must be inserted in TeX-mode.
28307 To add in our example space, the command
28315 is inserted at the end of the first line.
28320 \begin_layout Plain Layout
28327 \begin_layout Plain Layout
28329 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28332 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28339 \begin_layout Plain Layout
28343 left(B^{2}+x_{0}^{2}
28351 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28356 \begin_layout Plain Layout
28368 \begin_layout Standard
28369 \begin_inset VSpace bigskip
28372 To set the line separation for all lines in a formula, the length
28379 \begin_inset Index idx
28382 \begin_layout Plain Layout
28392 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28403 \begin_inset space \thinspace{}
28408 \begin_inset space \thinspace{}
28411 mm additional line separation as in the previous example, the command
28414 \begin_layout Standard
28424 \begin_layout Standard
28425 is inserted in TeX-mode before the formula.
28426 This requires that the LaTeX-package
28434 \begin_layout Plain Layout
28439 is part of every LaTeX standard installation.
28445 \begin_inset Index idx
28448 \begin_layout Plain Layout
28454 was loaded in LaTeX-preamble with the line
28457 \begin_layout Standard
28465 \begin_layout Standard
28470 \begin_layout Plain Layout
28482 \begin_inset Formula
28484 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}\\
28485 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
28493 \begin_layout Standard
28497 \begin_layout Plain Layout
28508 To get back to the predefined distance,
28514 is set to the value 3
28515 \begin_inset space \thinspace{}
28521 \begin_layout Subsubsection
28523 \begin_inset CommandInset label
28525 name "sub:Column-Separation"
28530 \begin_inset Index idx
28533 \begin_layout Plain Layout
28534 Formula ! multiline ! Column separation
28542 \begin_layout Standard
28543 Multiline formulas form a matrix.
28544 A formula in the eqnarray environment is for example a matrix with three
28546 By changing the column separation in this environment, the space beside
28547 the relation sign can be changed.
28550 \begin_layout Standard
28551 The column separation is specified with the length
28558 \begin_inset Index idx
28561 \begin_layout Plain Layout
28570 \begin_inset Newline newline
28573 column separation = 2
28574 \begin_inset space \thinspace{}
28584 \begin_inset Newline newline
28590 \begin_layout Standard
28600 \begin_layout Standard
28601 inserted in TeX-mode, sets for all following formulas a column separation
28603 \begin_inset space \thinspace{}
28607 To get back to the predefined distance,
28614 \begin_inset space \thinspace{}
28620 \begin_layout Standard
28622 \begin_inset space \thinspace{}
28625 cm column separation:
28629 \begin_layout Plain Layout
28641 \begin_inset Formula
28649 A formula with the predefined column separation for matrices of 10
28650 \begin_inset space \thinspace{}
28657 \begin_layout Plain Layout
28669 \begin_inset Formula
28680 \begin_layout Subsubsection
28682 \begin_inset Index idx
28685 \begin_layout Plain Layout
28694 \begin_layout Standard
28695 Long formulas can be typeset using these methods:
28698 \begin_layout Itemize
28699 When one side of the equation is much shorter than the line width, this
28700 one is chosen for the left side and the right side is typeset over two
28702 \begin_inset Formula
28704 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 \\
28705 & & -\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}
28710 The minus sign at the beginning of the second line does normally not appear
28711 as an operator because it is the first character of the line.
28712 Thus it would not be surrounded by space and could not be distinguished
28713 from the fraction bar.
28715 \begin_inset space \thinspace{}
28718 pt space was inserted behind the minus sign with the command
28728 \begin_layout Plain Layout
28736 \begin_inset CommandInset ref
28738 reference "sub:Variable-Space"
28748 \begin_inset Index idx
28751 \begin_layout Plain Layout
28762 \begin_layout Itemize
28763 When both sides of the equation are too long, the command
28770 \begin_inset Index idx
28773 \begin_layout Plain Layout
28782 It is inserted in the first column of the first line and causes all further
28783 insertions to overwrite the following columns:
28784 \begin_inset Formula
28786 \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 \\
28787 & & -\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 \\
28788 & & =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}
28793 After the insertion of
28799 , the cursor is in a purple box that is a bit shifted to the left from the
28801 In this the formula is inserted.
28802 \begin_inset Newline newline
28805 The content of the further lines is inserted to the second or another formula
28807 The greater the column number where it was inserted, the larger the indentation.
28808 \begin_inset VSpace medskip
28812 \begin_inset Newline newline
28816 \begin_inset Note Greyedout
28819 \begin_layout Plain Layout
28820 Note the following when using
28829 \begin_layout Itemize
28830 The formula doesn't use the full page width.
28832 \begin_inset space \thinspace{}
28836 \begin_inset space \space{}
28840 \begin_inset Formula $-B^{2}$
28843 is added to the first line in the above example, it would have been outside
28845 To better use the width, negative space can be inserted at the beginning
28849 \begin_layout Itemize
28850 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28855 \begin_layout Plain Layout
28856 \begin_inset CommandInset href
28858 name "LyX-bug #1429"
28859 target "http://www.lyx.org/trac/ticket/1429"
28868 One can only set the cursor at the beginning of the line and move it with
28877 \begin_layout Itemize
28878 Other methods to set long formulas are offered by the environments described
28880 \begin_inset CommandInset ref
28882 reference "sub:Multline-Environment"
28887 \begin_inset CommandInset ref
28889 reference "sub:Multiline-Formula-Parts"
28896 \begin_layout Subsubsection
28898 \begin_inset CommandInset label
28900 name "sub:Multiline-Brackets"
28905 \begin_inset Index idx
28908 \begin_layout Plain Layout
28909 Brackets ! for multiline expressions
28917 \begin_layout Standard
28918 For brackets spanning multiple lines the following problem occurs:
28919 \begin_inset Formula
28921 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28922 & & \left.\cdots+B-D\right]
28930 \begin_layout Standard
28931 The closing bracket is smaller than the opening bracket because brackets
28932 with variable size may not span multiple lines.
28935 \begin_layout Standard
28936 To set the bracket size for the second line correctly, the first line is
28944 \begin_inset Index idx
28947 \begin_layout Plain Layout
28955 and the second line with
28963 \begin_layout Plain Layout
28977 \begin_inset CommandInset ref
28979 reference "sub:Automatic-Bracket-Size"
28991 \begin_inset Index idx
28994 \begin_layout Plain Layout
29020 \begin_layout Plain Layout
29039 \begin_layout Plain Layout
29058 \begin_layout Plain Layout
29070 \begin_inset Formula $\downarrow$
29076 \begin_inset Index idx
29079 \begin_layout Plain Layout
29087 is inserted, because the multiplication operator with its limits is the
29088 largest symbol in the first line and this should be the size for the bracket
29089 in the second line.
29092 \begin_layout Standard
29093 The result is this:
29094 \begin_inset Formula
29096 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29097 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29105 \begin_layout Subsection
29109 \begin_layout Standard
29110 Align environments can be used for every kind of multiline formulas.
29111 They are especially useful to set several formulas side by side.
29114 \begin_layout Standard
29115 Align environments consist of columns.
29116 The odd columns are right aligned, the even ones left aligned.
29117 Every line in an Align environment can be numbered.
29120 \begin_layout Standard
29121 Align environments are created via the menu
29123 Insert\SpecialChar \menuseparator
29129 Edit\SpecialChar \menuseparator
29130 Math\SpecialChar \menuseparator
29131 Change Formula Type
29133 already existing formulas can be converted to Align environments.
29136 \begin_layout Standard
29137 To add or delete columns, the math toolbar buttons
29138 \begin_inset Graphics
29139 filename ../images/tabular-feature_append-column.png
29145 \begin_inset Graphics
29146 filename ../images/tabular-feature_delete-column.png
29151 , respectively, or the menu
29153 Edit\SpecialChar \menuseparator
29159 \begin_layout Subsubsection
29160 Standard align Environment
29161 \begin_inset CommandInset label
29163 name "sub:Standard-align-Environment"
29168 \begin_inset Index idx
29171 \begin_layout Plain Layout
29172 Formula ! multiline ! align environment
29180 \begin_layout Standard
29181 This Align environment is created by presssing
29184 arg "newline-insert newline"
29187 in a formula or by the menu
29189 Insert\SpecialChar \menuseparator
29190 Math\SpecialChar \menuseparator
29191 AMS align Environment
29196 \begin_layout Standard
29197 An example for two formulas set side by side, that are created with a four
29198 column align environment:
29199 \begin_inset Formula
29201 A & =\sin(B) & C & =D\\
29202 C & \ne A & B & \ne D
29207 As it can be seen, the formulas in this environment are placed so as if
29216 \begin_layout Plain Layout
29224 \begin_inset CommandInset ref
29226 reference "sub:Variable-Space"
29237 before the first and after every even column.
29238 When the formula style
29244 \begin_layout Plain Layout
29246 \begin_inset CommandInset ref
29248 reference "sec:Formula-Styles"
29259 is used, the formula is set without the
29265 before the first column.
29268 \begin_layout Subsubsection
29269 Alignat Environment
29270 \begin_inset Index idx
29273 \begin_layout Plain Layout
29274 Formula ! multiline ! alignat environment
29282 \begin_layout Standard
29283 The alignat environment has no predefined column separation.
29284 It can be inserted manually with the spaces that are described
29285 \begin_inset CommandInset ref
29287 reference "sub:Space"
29294 \begin_layout Standard
29295 The above example in the alignat environment where 1
29296 \begin_inset space \thinspace{}
29299 cm space was inserted at the beginning of the second formula:
29300 \begin_inset Formula
29301 \begin{alignat*}{2}
29302 A & =\sin(B) & \hspace{1cm}C & =D\\
29303 C & \ne A & B & \ne D
29308 Because the column separation can be set separately for every column, this
29309 environment is especially suitable to set three and more formulas side
29313 \begin_layout Subsubsection
29314 Flalign Environment
29315 \begin_inset CommandInset label
29317 name "sub:Flalign-Environment"
29322 \begin_inset Index idx
29325 \begin_layout Plain Layout
29326 Formula ! multiline ! flalign environment
29334 \begin_layout Standard
29335 In this environment the first two columns are always set as much as possible
29336 to the left and the last two ones to the right.
29338 \begin_inset Formula
29340 A & =1 & B & =2 & C & =3\\
29341 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29349 \begin_layout Standard
29350 By creating a flalign environment with an odd number of columns where an
29351 empty TeX-brace is inserted to the last column, several formulas in a document
29352 can be set to the left, although the formula style
29357 As example the indented formula
29358 \begin_inset CommandInset ref
29360 reference "eq:VolInt"
29365 \begin_inset Formula
29367 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29372 The first two columns contain the formula.
29373 To indent it as with the formula style
29378 \begin_inset space \thinspace{}
29381 pt space was inserted at the beginning of the first column.
29384 \begin_layout Subsection
29385 Eqnarray Environment
29386 \begin_inset CommandInset label
29388 name "sub:Eqnarray-Environment"
29393 \begin_inset Index idx
29396 \begin_layout Plain Layout
29397 Formula ! multiline ! eqnarray environment
29405 \begin_layout Standard
29406 When this environment has been created, three blue boxes appear.
29407 The content of the first box is right aligned, the content of the last
29409 The content of the middle box appears centered and a bit smaller, because
29410 it is designed to insert there only relation characters.
29411 \begin_inset Formula
29413 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29423 \begin_layout Subsection
29425 \begin_inset Index idx
29428 \begin_layout Plain Layout
29429 Formula ! multiline ! gather environment
29437 \begin_layout Standard
29438 This environment consists of only one centered column.
29439 Every line can be numbered.
29440 \begin_inset Formula
29451 \begin_layout Subsection
29452 Multline Environment
29453 \begin_inset CommandInset label
29455 name "sub:Multline-Environment"
29460 \begin_inset Index idx
29463 \begin_layout Plain Layout
29464 Formula ! multiline ! multline environment
29472 \begin_layout Standard
29473 The multline environment consists, like the gather environment, of only
29475 But the first line is left aligned, the last one right aligned.
29476 All other lines are centered.
29477 Therefore this environment is suitable for long formulas.
29479 \begin_inset CommandInset ref
29481 reference "eq:lefteqn"
29485 in the multline environment:
29486 \begin_inset Formula
29488 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}\\
29489 -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}\\
29490 =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}}
29498 \begin_layout Standard
29499 In the output only the last (first) line of a multline environment appears
29500 numbered when the document numbering is right (left).
29504 \begin_layout Plain Layout
29505 numbering styles see
29506 \begin_inset CommandInset ref
29508 reference "sec:Formula-Styles"
29520 \begin_layout Standard
29528 \begin_inset Index idx
29531 \begin_layout Plain Layout
29546 \begin_inset Index idx
29549 \begin_layout Plain Layout
29557 a centered line can be right or left aligned, respectively.
29558 The commands are used as follows:
29561 \begin_layout Standard
29566 shoveright{line content}
29572 shoveleft{line content}
29575 \begin_layout Standard
29576 \begin_inset VSpace medskip
29586 \begin_inset Index idx
29589 \begin_layout Plain Layout
29597 specifies the distance of the first line from the left page margin.
29598 Predefined is the length 0
29599 \begin_inset space \thinspace{}
29605 \begin_layout Standard
29606 As example the above formula where the command
29609 \begin_layout Standard
29619 \begin_layout Standard
29620 was inserted in TeX-mode before:
29624 \begin_layout Plain Layout
29636 \begin_inset Formula
29638 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}\\
29639 \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}}\\
29640 =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}}
29649 \begin_layout Plain Layout
29660 The second line was left aligned using
29669 \begin_layout Subsection
29670 Multiline Formula Parts
29671 \begin_inset CommandInset label
29673 name "sub:Multiline-Formula-Parts"
29678 \begin_inset Index idx
29681 \begin_layout Plain Layout
29682 Formula ! multiline ! formula parts
29690 \begin_layout Standard
29691 To display only parts of a formula with multiple lines, one of the following
29692 environments is used:
29709 They can be inserted via the menu
29711 Insert\SpecialChar \menuseparator
29714 or by using the commands described in this section.
29717 \begin_layout Standard
29718 The first three have the same properties as the corresponding multiline
29719 formula environments, but it is possible to set further formula parts beside
29722 \begin_inset Formula
29724 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29725 \Delta E\Delta t & \ge\frac{\hbar}{2}
29727 \right\} \textrm{Uncertainty relations}
29735 \begin_layout Standard
29736 To get this formula, a displayed formula is created where the command
29743 \begin_inset Index idx
29746 \begin_layout Plain Layout
29755 A purple box appears around the blue formula box where now columns and
29756 lines can be added.
29757 Outside the multiline environment other formula parts can be set, like
29761 \begin_layout Standard
29762 The aligned environment is also suitable for long formulas whose lines are
29763 horizontally aligned.
29764 Using aligned in a displayed formula has the advantage that the formula
29765 number is vertically centered behind the lines.
29767 \begin_inset CommandInset ref
29769 reference "eq:shortlong"
29773 in the aligned environment:
29774 \begin_inset Formula
29776 \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}|}\\
29777 & -\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}|}
29786 \begin_layout Standard
29787 To use the environments
29806 \begin_inset Index idx
29809 \begin_layout Plain Layout
29824 \begin_inset Index idx
29827 \begin_layout Plain Layout
29842 \begin_inset Index idx
29845 \begin_layout Plain Layout
29853 are inserted, respectively.
29854 The split environment has the same properties as the aligned environment
29855 but it can only have two columns.
29858 \begin_layout Subsection
29859 Text in multiline Formulas
29860 \begin_inset CommandInset label
29862 name "sub:Text-in-multiline"
29867 \begin_inset Index idx
29870 \begin_layout Plain Layout
29877 \begin_inset Index idx
29880 \begin_layout Plain Layout
29881 Formula ! multiline ! text
29889 \begin_layout Standard
29890 In the Align environments, and the multline and gather environment, text
29891 can be inserted that will appear in a separate line and doesn't affect
29892 the column alignment.
29893 To do this, the command
29900 \begin_inset Index idx
29903 \begin_layout Plain Layout
29911 is used in the following scheme:
29914 \begin_layout Standard
29922 \begin_layout Standard
29923 The text should not be longer than a line because it cannot be hyphenated.
29924 As LyX doesn't yet support
29930 directly, the text is written as mathematical text.
29937 must hereby be at the beginning of a line and appears in the output above
29939 An example where the text was inserted at the beginning of the second line:
29940 \begin_inset Formula
29942 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29943 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29951 \begin_layout Standard
29952 \begin_inset Newpage newpage
29958 \begin_layout Section
29960 \begin_inset Index idx
29963 \begin_layout Plain Layout
29970 \begin_inset Index idx
29973 \begin_layout Plain Layout
29974 Formula ! numbering|see
29978 \begin_layout Plain Layout
29989 \begin_layout Plain Layout
30004 \begin_layout Subsection
30008 \begin_layout Standard
30009 Numbered formulas can be created with the menu
30011 Insert\SpecialChar \menuseparator
30012 Math\SpecialChar \menuseparator
30014 \begin_inset space ~
30022 \begin_inset space ~
30028 Existing formulas can be numbered with the menu
30030 Edit\SpecialChar \menuseparator
30031 Math\SpecialChar \menuseparator
30033 \begin_inset space ~
30041 arg "math-number-toggle"
30045 The formula number is displayed in LyX behind the formula as a number sign
30047 The number sign is replaced in the output by the formula number.
30050 \begin_layout Standard
30051 When numbering is turned on in multiline formulas, all lines will be numbered.
30052 But the numbering can be controlled with the menu
30054 Edit\SpecialChar \menuseparator
30055 Math\SpecialChar \menuseparator
30057 \begin_inset space ~
30061 \begin_inset space ~
30065 \begin_inset space ~
30073 arg "math-number-line-toggle"
30079 \begin_layout Standard
30080 Except for inline formulas, all formulas can be numbered with two different
30082 \begin_inset CommandInset ref
30084 reference "sec:Formula-Styles"
30091 \begin_layout Subsection
30093 \begin_inset Index idx
30096 \begin_layout Plain Layout
30097 Cross-references ! to formulas
30105 \begin_layout Standard
30106 All labeled formulas can be cross-referenced.
30107 A label is added by the menu
30109 Insert\SpecialChar \menuseparator
30112 or the toolbar button
30113 \begin_inset Graphics
30114 filename ../images/label-insert.png
30120 The cursor must hereby be inside a displayed formula.
30121 Alternatively you can right-click on the formula and choose
30126 A dialog pops up displaying the prefix
30131 The label is inserted there behind the prefix.
30132 The predefined prefix means
30133 \begin_inset Quotes eld
30137 \begin_inset Quotes erd
30140 and makes it easier to find labels in large documents because it marks
30141 it as formula label to divide it from e.
30142 \begin_inset space \thinspace{}
30146 \begin_inset space \space{}
30150 To change a label, the menu
30152 Insert\SpecialChar \menuseparator
30155 is used again or you right-click on a formula and then on
30162 \begin_layout Standard
30163 The name of the label is displayed in LyX within two parentheses behind
30165 A formula with a label is always numbered.
30168 \begin_layout Standard
30169 Cross-references are inserted via the menu
30171 Insert\SpecialChar \menuseparator
30174 or with the toolbar button
30175 \begin_inset Graphics
30176 filename ../images/dialog-show-new-inset_ref.png
30182 A formula cross-reference appears in the output as formula number.
30183 When in the cross-reference dialog window the format
30187 is chosen, the cross-reference appears in the output as formula number
30189 \begin_inset Newline newline
30192 By right-clicking on a cross-reference in LyX, one jumps to the formula
30193 that is referenced.
30196 \begin_layout Standard
30197 Here are as examples cross-references to formulas of the following subsections:
30198 \begin_inset Note Note
30201 \begin_layout Plain Layout
30202 Note the different cross-reference types.
30210 \begin_layout Standard
30212 \begin_inset CommandInset ref
30219 \begin_inset CommandInset ref
30227 \begin_inset CommandInset ref
30233 ) big Latin letters are used for the numbering in contrary to (
30234 \begin_inset CommandInset ref
30243 \begin_layout Standard
30244 \begin_inset VSpace medskip
30247 When the argument of
30255 \begin_layout Plain Layout
30263 \begin_inset CommandInset ref
30265 reference "sub:User-defined-Numbering"
30276 contains a box like in
30277 \begin_inset CommandInset ref
30279 reference "sub:Paragraph-Boxes"
30283 , the formula cannot be referenced.
30286 \begin_layout Subsection
30288 \begin_inset Index idx
30291 \begin_layout Plain Layout
30292 Formula numbering ! subnumbering
30300 \begin_layout Standard
30301 With the help of the commands
30305 begin{subequations}
30313 formulas can be subnumbered.
30314 Both commands are inserted in TeX-mode.
30317 \begin_layout Standard
30319 \begin_inset Formula
30330 \begin_layout Plain Layout
30334 addtocounter{equation}{-1}
30343 \begin_layout Plain Layout
30347 begin{subequations}
30353 \begin_inset VSpace -5mm
30357 \begin_inset Formula
30365 \begin_inset Formula
30375 \begin_layout Standard
30379 \begin_layout Plain Layout
30391 \begin_layout Standard
30392 To create the example, the following is done:
30395 \begin_layout Enumerate
30396 first formula is inserted
30399 \begin_layout Enumerate
30404 addtocounter{equation}{-1}
30406 begin{subequations}
30407 \begin_inset Index idx
30410 \begin_layout Plain Layout
30419 \begin_inset Newline newline
30424 is inserted after the first formula
30427 \begin_layout Enumerate
30428 second formula is inserted
30431 \begin_layout Enumerate
30432 third formula is inserted
30435 \begin_layout Enumerate
30442 is inserted after the third formula
30445 \begin_layout Standard
30446 Every formula between the commands
30458 is subnumbered as a, b,
30459 \begin_inset Newline linebreak
30462 c, \SpecialChar \ldots{}
30463 For multiline formulas every line will be subnumbered.
30464 All subnumbered formulas are treated as
30469 But as every numbered formula increases the counter
30473 by one, the command
30479 is needed to decrease it.
30480 Otherwise the formulas
30481 \begin_inset CommandInset ref
30488 \begin_inset CommandInset ref
30495 \begin_inset CommandInset ref
30501 would be numbered as
30502 \begin_inset CommandInset ref
30509 \begin_inset CommandInset ref
30516 \begin_inset CommandInset ref
30525 \begin_layout Standard
30526 By inserting the commands in TeX-mode, a space is created between the first
30529 \begin_inset space \thinspace{}
30532 mm vertical space is inserted after the command
30536 begin{subequations}
30539 When the formula style
30545 \begin_layout Plain Layout
30547 \begin_inset CommandInset ref
30549 reference "sec:Formula-Styles"
30561 \begin_inset space \thinspace{}
30564 mm space is inserted instead.
30567 \begin_layout Standard
30568 Here is an example for a multiline formula where the numbering was turned
30569 off for the second line:
30573 \begin_layout Plain Layout
30577 begin{subequations}
30583 \begin_inset Formula
30585 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30586 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30587 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30596 \begin_layout Plain Layout
30608 \begin_layout Subsection
30609 User-defined Numbering
30610 \begin_inset CommandInset label
30612 name "sub:User-defined-Numbering"
30617 \begin_inset Index idx
30620 \begin_layout Plain Layout
30621 Formula numbering ! user-defined
30629 \begin_layout Standard
30630 \begin_inset Index idx
30633 \begin_layout Plain Layout
30634 Formula numbering ! self-defined delimiters
30639 With the standard numbering parentheses are set around the formula number.
30640 To replace the parentheses for example by vertical bars, the following
30641 line is added to the LaTeX-preamble:
30644 \begin_layout Standard
30656 \begin_inset Note Note
30659 \begin_layout Plain Layout
30660 This macro is already declared in the LaTeX-preamble for testing.
30661 To activate it, remove the percent sign at the beginning.
30669 \begin_layout Standard
30670 To use other characters, the vertical bars besides the
30674 are replaced by one ore more characters.
30675 To get only the formula number the vertical bars are omitted.
30678 \begin_layout Standard
30679 \begin_inset VSpace bigskip
30682 When there should be an expression of your choice instead of the consecutive
30683 formula number in parentheses behind the formula, the command
30690 \begin_inset Index idx
30693 \begin_layout Plain Layout
30702 \begin_inset Formula
30704 A+B=C\tag{something}\label{eq:tag}
30709 In this example the command
30717 \begin_layout Plain Layout
30728 was inserted in the formula.
30731 \begin_layout Standard
30740 \begin_layout Plain Layout
30751 is inserted instead, the star prevents the parentheses around the expression:
30752 \begin_inset Formula
30754 A+B=C\tag*{something}
30762 \begin_layout Standard
30763 \begin_inset VSpace bigskip
30766 To restart the formula numbering with new document parts or sections, the
30767 following command is used:
30770 \begin_layout Standard
30775 @addtoreset{equation}{part}
30778 \begin_inset Index idx
30781 \begin_layout Plain Layout
30786 \begin_layout Plain Layout
30797 \begin_layout Plain Layout
30810 \begin_layout Plain Layout
30821 \begin_layout Plain Layout
30834 \begin_inset Newline newline
30838 \begin_inset Newline newline
30845 @addtoreset{equation}{section}
30848 \begin_layout Standard
30849 To be able to use these commands in TeX-mode, the
30850 \begin_inset Quotes eld
30854 \begin_inset Quotes erd
30857 character has to be made
30858 \begin_inset Quotes eld
30862 \begin_inset Quotes erd
30865 for LaTeX using the command
30879 So the command sequence in TeX-mode is:
30882 \begin_layout Standard
30888 \begin_inset Newline newline
30893 @addtoreset{equation}{section}
30894 \begin_inset Newline newline
30902 \begin_layout Standard
30903 In the LaTeX-preamble
30915 can be omitted as they are automatically internally inserted by LyX.
30918 \begin_layout Standard
30933 \begin_layout Plain Layout
30938 is part of the LaTeX-package
30943 \begin_inset Index idx
30946 \begin_layout Plain Layout
30947 Packages ! carlisle
30952 that is part of every LaTeX standard installation.
30958 \begin_inset Index idx
30961 \begin_layout Plain Layout
30962 Packages ! remreset
30967 has to be loaded in the LaTeX-preamble with the line
30970 \begin_layout Standard
30975 usepackage{remreset}
30978 \begin_layout Standard
30986 \begin_inset Index idx
30989 \begin_layout Plain Layout
30994 \begin_layout Plain Layout
31005 \begin_layout Plain Layout
31018 \begin_layout Plain Layout
31029 \begin_layout Plain Layout
31041 can be used with the same scheme as
31050 \begin_layout Standard
31051 \begin_inset VSpace bigskip
31054 Sometimes formulas should be numbered in the following form:
31057 \begin_layout Standard
31060 (section number.formula number)
31063 \begin_layout Standard
31064 The formula number should start with every section with
31065 \begin_inset Quotes eld
31069 \begin_inset Quotes erd
31075 \begin_layout Standard
31076 For this case there is the command
31083 \begin_inset Index idx
31086 \begin_layout Plain Layout
31094 , which is used with the following scheme:
31097 \begin_layout Standard
31102 numberwithin{counter}{sectioning}
31105 \begin_layout Standard
31106 Counter denotes what kind of numbering is affected, sectioning denotes what
31107 number is before the dot.
31110 \begin_layout Standard
31111 Thus in our case the following LaTeX-preamble or TeX code line is used:
31114 \begin_layout Standard
31119 numberwithin{equation}{section}
31122 \begin_layout Standard
31123 This is the result:
31127 \begin_layout Plain Layout
31131 numberwithin{equation}{section}
31137 \begin_inset Formula
31147 \begin_layout Standard
31149 \begin_inset space \thinspace{}
31153 \begin_inset space \space{}
31156 tables so that the number of the part is the sectioning,
31157 \begin_inset Newline newline
31164 numberwithin{table}{part}
31169 \begin_layout Standard
31170 To go back to the standard numbering or to prevent this kind of numbering
31171 when it is defined by the document class, the following command is inserted
31172 as TeX code or to the LaTeX-preamble:
31175 \begin_layout Standard
31185 \begin_inset Index idx
31188 \begin_layout Plain Layout
31202 \begin_layout Plain Layout
31218 \begin_inset Newline newline
31226 \begin_inset Newline newline
31238 \begin_layout Standard
31245 uses internally the command
31251 , described above, that also needs to be reverted.
31255 \begin_layout Plain Layout
31262 \begin_layout Plain Layout
31266 @removefromreset{equation}{section}
31269 \begin_layout Plain Layout
31281 \begin_layout Subsection
31282 Numbering with Roman Numbers and Letters
31283 \begin_inset Index idx
31286 \begin_layout Plain Layout
31287 Formula numbering ! with letters
31293 \begin_inset Index idx
31296 \begin_layout Plain Layout
31297 Formula numbering ! with Roman numbers
31305 \begin_layout Standard
31306 Formulas can also be numbered with Roman numbers and Latin letters.
31307 To number for example with small Roman numbers, the command
31310 \begin_layout Standard
31322 \begin_layout Standard
31323 is inserted before the formula in TeX-mode.
31331 \begin_inset Index idx
31334 \begin_layout Plain Layout
31342 redefines the predefined command
31358 \begin_layout Plain Layout
31365 has the same scheme like the command
31371 that is described in
31372 \begin_inset CommandInset ref
31374 reference "sub:The-Command-newcommand"
31387 is the formula counter.
31394 is used as prefix for a counter, the value of the counter is output as
31396 When a formula is numbered, LaTeX sets internally the command
31402 behind the formula.
31408 \begin_inset Index idx
31411 \begin_layout Plain Layout
31421 outputs the counter as small Roman number.
31424 \begin_layout Standard
31425 All formulas behind the command
31435 are now numbered Roman.
31436 To switch to numbering with big Roman numbers, the command is inserted
31450 \begin_inset Index idx
31453 \begin_layout Plain Layout
31465 \begin_inset Quotes eld
31469 \begin_inset Quotes erd
31472 with small Latin letters there is the command
31479 \begin_inset Index idx
31482 \begin_layout Plain Layout
31490 , for big ones there is the command
31497 \begin_inset Index idx
31500 \begin_layout Plain Layout
31513 \begin_layout Standard
31514 \begin_inset Note Greyedout
31517 \begin_layout Plain Layout
31524 \begin_inset space ~
31527 formulas can be numbered with Latin letters in one document.
31535 \begin_layout Standard
31539 \begin_layout Plain Layout
31555 \begin_layout Standard
31556 \begin_inset Formula
31558 A=\textrm{small roman}
31567 \begin_layout Plain Layout
31581 \begin_inset Formula
31583 B=\textrm{big Roman}\label{eq:Rom}
31592 \begin_layout Plain Layout
31606 \begin_inset Formula
31608 C=\textrm{small Latin}
31617 \begin_layout Plain Layout
31631 \begin_inset Formula
31633 D=\textrm{big Latin}\label{eq:Lat}
31641 \begin_layout Standard
31642 To switch back to the default numbering, insert the command:
31645 \begin_layout Standard
31655 \begin_inset Index idx
31658 \begin_layout Plain Layout
31669 \begin_layout Standard
31673 \begin_layout Plain Layout
31687 \begin_inset Formula
31697 \begin_layout Standard
31698 \begin_inset VSpace medskip
31701 As you see, formulas are numbered serially independent from the numbering
31703 When then numbering should start with
31704 \begin_inset Quotes eld
31708 \begin_inset Quotes erd
31711 when the style is changed, new equation counters have to be defined.
31712 A description about this can be found in the file
31713 \begin_inset CommandInset href
31715 name "Formula-numbering.lyx"
31716 target "run:Formula-numbering.lyx"
31723 \begin_layout Section
31724 Chemical Symbols and Equations
31725 \begin_inset CommandInset label
31727 name "sub:Chemical-Symbols-and"
31732 \begin_inset Index idx
31735 \begin_layout Plain Layout
31736 Chemical characters ! Symbols
31742 \begin_inset Index idx
31745 \begin_layout Plain Layout
31752 \begin_inset Index idx
31755 \begin_layout Plain Layout
31764 \begin_layout Standard
31765 An example text from chemistry:
31768 \begin_layout Quote
31770 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31773 -ion reacts with two
31774 \begin_inset Formula $\mathrm{Na^{+}}$
31777 -ions to sodium sulfate
31778 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31782 The chemical equation for this is:
31783 \begin_inset Formula
31785 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31793 \begin_layout Standard
31794 This chemical equation can directly be created as formula.
31795 To avoid that the symbols appear italic, everything is highlighted and
31796 changed by the shortcut
31802 to the upright font style.
31806 \begin_layout Plain Layout
31812 \begin_inset CommandInset ref
31814 reference "sub:Font-Styles"
31826 \begin_layout Standard
31827 A more convenient way to typeset chemical formulas is to use the command
31835 \begin_inset Index idx
31838 \begin_layout Plain Layout
31846 that is available when the LaTeX-package
31851 \begin_inset Index idx
31854 \begin_layout Plain Layout
31867 to a formula a new blue box appears where chemical formulas can be inserted
31868 in an intuitive way.
31871 \begin_layout Standard
31873 \begin_inset Tabular
31874 <lyxtabular version="3" rows="9" columns="2">
31875 <features tabularvalignment="middle">
31876 <column alignment="center" valignment="top" width="0">
31877 <column alignment="center" valignment="top" width="0">
31879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31882 \begin_layout Plain Layout
31888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31891 \begin_layout Plain Layout
31893 \begin_inset Note Note
31896 \begin_layout Plain Layout
31903 is only used as spacer.
31915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31918 \begin_layout Plain Layout
31925 \begin_layout Plain Layout
31939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31942 \begin_layout Plain Layout
31943 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31956 \begin_layout Plain Layout
31963 \begin_layout Plain Layout
31977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31980 \begin_layout Plain Layout
31981 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31994 \begin_layout Plain Layout
32001 \begin_layout Plain Layout
32015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32018 \begin_layout Plain Layout
32019 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
32029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32032 \begin_layout Plain Layout
32039 \begin_layout Plain Layout
32053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32056 \begin_layout Plain Layout
32057 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32070 \begin_layout Plain Layout
32077 \begin_layout Plain Layout
32092 \begin_layout Plain Layout
32107 \begin_layout Plain Layout
32121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32124 \begin_layout Plain Layout
32125 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32138 \begin_layout Plain Layout
32145 \begin_layout Plain Layout
32155 \begin_inset Formula $\downarrow$
32159 \begin_inset Formula $\to$
32167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32170 \begin_layout Plain Layout
32171 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32184 \begin_layout Plain Layout
32191 \begin_layout Plain Layout
32204 \begin_layout Plain Layout
32217 \begin_layout Plain Layout
32230 \begin_layout Plain Layout
32243 \begin_layout Plain Layout
32257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32260 \begin_layout Plain Layout
32261 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32274 \begin_layout Plain Layout
32281 \begin_layout Plain Layout
32294 \begin_layout Plain Layout
32307 \begin_layout Plain Layout
32320 \begin_layout Plain Layout
32337 \begin_layout Plain Layout
32351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32354 \begin_layout Plain Layout
32355 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32371 \begin_layout Standard
32372 \begin_inset Note Greyedout
32375 \begin_layout Plain Layout
32381 Inserting a formula to a
32387 box will lead to LaTeX errors.
32388 In this case TeX code has to be used like for
32402 \begin_layout Plain Layout
32423 \begin_layout Standard
32424 \begin_inset Note Greyedout
32427 \begin_layout Plain Layout
32433 It is not possible in LyX to use the character ^ to get an up-arrow as
32439 One instead uses a negative thin space followed by the command
32446 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32457 \begin_layout Standard
32464 the command for equation
32465 \begin_inset space ~
32469 \begin_inset CommandInset ref
32471 reference "eq:chem-reaction"
32476 \begin_inset Newline newline
32487 \begin_layout Plain Layout
32500 \begin_layout Plain Layout
32513 \begin_layout Plain Layout
32526 \begin_layout Plain Layout
32539 \begin_layout Plain Layout
32552 \begin_layout Plain Layout
32564 \begin_layout Standard
32565 To create multiline chemical equations first a multiline formula is created
32567 \begin_inset CommandInset ref
32569 reference "sec:Multiline-Formulas"
32574 Afterwards the command
32580 is used in every small blue box of the formula.
32582 \begin_inset CommandInset ref
32584 reference "eq:TEOS-reaction-1"
32589 \begin_inset CommandInset ref
32591 reference "eq:TEOS-reaction-2"
32595 are an example of a multi-stage chemical reaction where every equation
32596 has its own number.
32597 \begin_inset Formula
32599 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32600 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32608 \begin_layout Standard
32619 package provides the command
32626 \begin_inset Index idx
32629 \begin_layout Plain Layout
32637 that has to be used for special cases.
32638 For more information about
32644 and more examples have a look at the documentation of
32649 \begin_inset CommandInset citation
32658 \begin_layout Section
32662 \begin_layout Standard
32663 LyX supports two types of commutative diagrams:
32671 that are explained in the following.
32674 \begin_layout Subsection
32676 \begin_inset Index idx
32679 \begin_layout Plain Layout
32688 \begin_layout Standard
32689 Diagrams of this type visualize relations by vertical and horizontal lines
32691 \begin_inset Formula
32693 \begin{CD}A@>>>B@>>>C\\
32704 \begin_layout Standard
32705 To get them, the command
32710 \begin_inset Index idx
32713 \begin_layout Plain Layout
32723 is inserted to a formula.
32724 A blue box appears with two dashed lines where further commands can be
32729 arg "newline-insert newline"
32732 a new line is created.
32733 Horizontal relations are inserted in odd, vertical in even formula lines.
32736 \begin_layout Standard
32737 To create the relations there are the following commands:
32740 \begin_layout Itemize
32745 creates a left arrow,
32756 \begin_layout Itemize
32761 creates an up arrow,
32769 a vertical equal sign
32772 \begin_layout Itemize
32778 is a placeholder for non-existent relations
32781 \begin_layout Standard
32782 All arrows can be labeled as follows:
32785 \begin_layout Itemize
32786 If text inserted between the first and second < or >, resp., it is placed
32788 When it is inserted between the second and third one, it appears under
32792 \begin_layout Itemize
32793 When text for vertical arrows is inserted between the first and second A
32794 or V, resp., it is placed left beside the arrow.
32795 When it is inserted between the second and third one, it appears right
32797 If the text contains an A or V, these letters must be set into a TeX-brace.
32800 \begin_layout Standard
32801 As example a diagram with all possible relations:
32804 \begin_layout Standard
32805 \begin_inset Formula
32807 \begin{CD}A@>j>>B@>>k>C@=F\\
32818 \begin_layout Standard
32819 The command for this is:
32820 \begin_inset Newline newline
32831 \begin_layout Plain Layout
32840 A@>j>>B@>>k>C@=F Ctrl+Return
32841 \begin_inset Newline newline
32845 \begin_inset Phantom HPhantom
32848 \begin_layout Plain Layout
32857 \begin_layout Plain Layout
32876 \begin_inset Formula $\to$
32882 \begin_inset Newline newline
32886 \begin_inset Phantom HPhantom
32889 \begin_layout Plain Layout
32898 \begin_layout Plain Layout
32915 \begin_layout Subsection
32917 \begin_inset Index idx
32920 \begin_layout Plain Layout
32921 Diagrams ! xymatrix
32929 \begin_layout Standard
32930 To be able to use xymatrices, the LaTeX-package
32935 A xymatrix is created by inserting the command
32942 Then you are able to add new matrix columns and rows like for normal matrices,
32944 \begin_inset CommandInset ref
32946 reference "sec:Matrices"
32953 \begin_layout Standard
32954 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32956 All possibilities to create commutative diagrams and decorations are explained
32961 that you find in the menu
32963 Help\SpecialChar \menuseparator
32965 \begin_inset space ~
32973 \begin_layout Subsection
32979 \begin_inset Index idx
32982 \begin_layout Plain Layout
32991 \begin_layout Standard
32996 -diagrams, the LaTeX-package
33005 -diagram is created by inserting the command
33012 Then you are able to add new matrix columns and rows like for normal matrices,
33014 \begin_inset CommandInset ref
33016 reference "sec:Matrices"
33023 \begin_layout Standard
33024 Examples how to create
33028 diagrams in LyX is given in the
33030 Feynman-diagram manual
33032 that you find in the menu
33034 Help\SpecialChar \menuseparator
33036 \begin_inset space ~
33044 \begin_layout Section
33045 User-defined Commands
33046 \begin_inset Index idx
33049 \begin_layout Plain Layout
33050 User-defined commands
33058 \begin_layout Standard
33059 \begin_inset Note Greyedout
33062 \begin_layout Plain Layout
33067 The names of user-defined commands and macros may only consist of Latin
33076 \begin_layout Subsection
33080 \begin_inset CommandInset label
33082 name "sub:The-Command-newcommand"
33087 \begin_inset Index idx
33090 \begin_layout Plain Layout
33091 User-defined commands !
33099 \begin_inset Index idx
33102 \begin_layout Plain Layout
33113 \begin_layout Standard
33114 Many LaTeX-commands are too long to be used frequently.
33115 But it is possible to define with the command
33121 new shorter commands.
33124 \begin_layout Standard
33125 The command scheme of
33134 \begin_layout Standard
33139 newcommand{new command name}[number of arguments][optional
33144 \begin_inset Newline newline
33148 \begin_inset Phantom HPhantom
33151 \begin_layout Plain Layout
33161 {command definition}
33164 \begin_layout Standard
33165 \begin_inset Note Greyedout
33168 \begin_layout Plain Layout
33173 Assure that the name of the new command is not already used in your document
33174 or by LaTeX-packages that you use.
33175 When you for example define the command
33187 , you get an error message because
33193 is already defined as command for
33194 \begin_inset Quotes eld
33198 \begin_inset Formula $\le$
33202 \begin_inset Quotes erd
33213 \begin_layout Standard
33214 The number of arguments is an integer in the range 0
33215 \begin_inset space \thinspace{}
33219 \begin_inset space \thinspace{}
33222 9 and specifies how many arguments the new command should have.
33223 With the optional value a value for an optional argument can be predefined.
33224 When this is done, the
33232 rgument of the new command is automatically an optional one.
33235 \begin_layout Standard
33236 Here are some examples:
33239 \begin_layout Itemize
33240 To define the command
33252 , the LaTeX-preamble line is:
33253 \begin_inset VSpace medskip
33257 \begin_inset Newline newline
33271 \begin_layout Itemize
33272 To define the command
33284 , the argument (that should be underlined) must be taken into account.
33285 For this the preamble line is:
33286 \begin_inset VSpace medskip
33290 \begin_inset Newline newline
33304 \begin_inset VSpace medskip
33308 \begin_inset Newline newline
33315 acts as argument placeholder, the
33319 behind it denotes that it is the placeholder for the first argument.
33322 \begin_layout Itemize
33330 \begin_inset space \thinspace{}
33334 \begin_inset space \space{}
33344 \begin_inset VSpace medskip
33348 \begin_inset Newline newline
33359 framebox#1#2{$#3$}}
33362 \begin_inset VSpace medskip
33366 \begin_inset Newline newline
33369 The two Dollar signs creates the extra formula needed for
33376 \begin_inset CommandInset ref
33378 reference "sub:Boxes-with-Frame"
33385 \begin_layout Itemize
33386 To create a new command for
33392 where the color for the box need not be specified, the argument for the
33393 color is defined optional:
33394 \begin_inset VSpace medskip
33398 \begin_inset Newline newline
33409 fcolorbox{#2}{#1}{$#3$}}
33412 \begin_inset VSpace medskip
33416 \begin_inset Newline newline
33419 When the color is not specified when using
33425 , the predefined color
33432 \begin_layout Standard
33433 A test of the new defined commands:
33436 \begin_layout Standard
33438 \begin_inset Tabular
33439 <lyxtabular version="3" rows="6" columns="2">
33440 <features tabularvalignment="middle">
33441 <column alignment="center" valignment="top" width="0">
33442 <column alignment="center" valignment="top" width="0">
33444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33447 \begin_layout Plain Layout
33453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33456 \begin_layout Plain Layout
33458 \begin_inset Note Note
33461 \begin_layout Plain Layout
33468 is only used as spacer.
33480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33483 \begin_layout Plain Layout
33490 \begin_layout Plain Layout
33504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33507 \begin_layout Plain Layout
33508 \begin_inset Formula $A\gr B$
33518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33521 \begin_layout Plain Layout
33529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33532 \begin_layout Plain Layout
33533 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33546 \begin_layout Plain Layout
33550 \begin_inset Formula $\to$
33556 \begin_inset Formula $\to$
33567 \begin_layout Plain Layout
33581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33584 \begin_layout Plain Layout
33585 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33598 \begin_layout Plain Layout
33602 \begin_inset Formula $\to$
33613 \begin_layout Plain Layout
33627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33630 \begin_layout Plain Layout
33631 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33644 \begin_layout Plain Layout
33650 \begin_inset Formula $\to$
33661 \begin_layout Plain Layout
33675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33678 \begin_layout Plain Layout
33679 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33695 \begin_layout Subsection
33697 \begin_inset Index idx
33700 \begin_layout Plain Layout
33701 User-defined commands! Math macros
33707 \begin_inset Index idx
33710 \begin_layout Plain Layout
33719 \begin_layout Standard
33720 User-defined commands are especially convenient for complex expressions.
33721 When you are for example dealing with a document that has quadratic equations,
33722 the same solution type occurs several times.
33723 The general form of a quadratic equation is
33724 \begin_inset Formula
33726 0=\lambda^{2}+p\lambda+q
33731 The general form of the solution is
33732 \begin_inset Formula
33734 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33742 \begin_layout Standard
33743 To define a command for the solution formula where only the three parameters
33745 \begin_inset Formula $\lambda$
33749 \begin_inset Formula $p$
33753 \begin_inset Formula $q$
33756 need to be specified and the index of
33757 \begin_inset Formula $\lambda$
33760 can be given optionally, the LaTeX-preamble line is
33761 \begin_inset Newline newline
33777 \begin_inset Newline newline
33781 \begin_inset Phantom HPhantom
33784 \begin_layout Plain Layout
33798 frac{#3^{2}}{4}-#4}}
33801 \begin_layout Standard
33802 To create with this the solution formula, the command
33803 \begin_inset Newline newline
33813 \begin_inset Formula $\to$
33819 \begin_inset Formula $\to$
33826 is inserted to a formula
33831 \begin_layout Standard
33832 The definition of the new command is unintuitive because one has to know
33833 the schemes of all used LaTeX commands, e.
33834 \begin_inset space \thinspace{}
33838 \begin_inset space \space{}
33841 that a fraction is inserted in LaTeX as
33845 frac{numerator}{denominator}
33848 Furthermore one can easily forget a brace in the definition and cannot
33849 see in LyX what the new command is doing.
33850 To avoid these problems LyX offers the possibility to use math macros instead
33860 \begin_layout Standard
33861 A math macro is created by using the menu
33863 Insert\SpecialChar \menuseparator
33864 Math\SpecialChar \menuseparator
33867 or the toolbar button
33868 \begin_inset Graphics
33869 filename ../images/math-macro_newmacroname_newcommand.png
33875 The math macro toolbar appears together with the following box where the
33877 \begin_inset Newline newline
33881 \begin_inset space \hspace*{\fill}
33885 \begin_inset Graphics
33886 filename clipart/macrobox.png
33891 \begin_inset space \hspace*{\fill}
33895 \begin_inset Newline newline
33899 \begin_inset FormulaMacro
33900 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33905 newmacroname is the default name of the macro that should be changed to
33906 something sensible.
33907 The wanted formula is inserted in the first blue box.
33908 An argument placeholder is inserted with the command
33915 \begin_inset space \thinspace{}
33919 \begin_inset space \space{}
33928 or by using the macro toolbar button
33929 \begin_inset Graphics
33930 filename ../images/math-macro-add-param.png
33936 Argument placeholders are displayed red.
33938 \begin_inset space ~
33941 arguments are possible.
33942 Optional arguments are created with the toolbar button
33943 \begin_inset Graphics
33944 filename ../images/math-macro-add-optional-param.png
33950 The first non-optional argument can be transformed to an optional one with
33952 \begin_inset Graphics
33953 filename ../images/math-macro-make-optional.png
33959 In the second blue box the appearance of the macro in LyX can be defined.
33960 Normally you want to see it as it is defined, so the box is kept empty.
33961 But when you have created a macro that needs lot of space on the screen,
33962 you can insert in the box for example
33963 \begin_inset Newline newline
33993 \begin_inset Newline newline
33998 For the macro only the arguments with the macro name in front of them will
33999 then be displayed in LyX, leading to a better overview.
34000 The formula appears in the output as defined in the first box.
34001 \begin_inset Newline newline
34004 The appearance of macros in formulas can furthermore be changed for single
34005 macros by setting the cursor in the macro and using the menu
34007 View\SpecialChar \menuseparator
34009 \begin_inset space ~
34013 \begin_inset space ~
34021 \begin_layout Standard
34022 To use a macro, the macro name is inserted as command to a formula, in our
34030 Our macro looks in LyX like this:
34031 \begin_inset Newline newline
34035 \begin_inset space \hspace*{\fill}
34039 \begin_inset Graphics
34040 filename clipart/macrouse.png
34045 \begin_inset space \hspace*{\fill}
34049 \begin_inset Newline newline
34052 Here is our macro example with the arguments
34053 \begin_inset Formula $x$
34057 \begin_inset Formula $\ln(x)$
34061 \begin_inset Formula $B$
34067 \begin_layout Standard
34068 \begin_inset Formula
34078 \begin_layout Standard
34079 LyX offers in the menu
34081 Tools\SpecialChar \menuseparator
34082 Preferences\SpecialChar \menuseparator
34083 Editing\SpecialChar \menuseparator
34086 different styles to edit macros.
34087 To find the style that suits you the most, choose a style and set the cursor
34088 in a macro formula to see the difference.
34091 \begin_layout Standard
34092 A math macro is transformed internally to a
34098 command when exporting the document.
34105 command is not placed in the LaTeX-preamble, therefore macros can only
34106 be used in formulas that are in the document below the macro definition
34110 \begin_layout Standard
34111 Math macros can also be directly created from a
34118 When writing for example the command
34121 \begin_inset Newline newline
34130 xleftarrow[#2]{#1}}
34131 \begin_inset Newline newline
34136 in LyX as normal text, highlighting it completely and using then the shortcut
34141 , the command will be transformed to a math macro.
34142 Using this method you need to be careful that the
34148 command is typed correctly, otherwise you get a faulty macro leading to
34152 \begin_layout Standard
34153 Math macros currently have the problem that further formulas in macro definition
34154 s are handled wrongly.
34155 Therefore the example
34162 \begin_inset CommandInset ref
34164 reference "sub:The-Command-newcommand"
34168 cannot be created as macro.
34171 \begin_layout Standard
34172 When the cursor is in a macro definition box, you will see the macro toolbar
34176 \begin_layout Standard
34177 \begin_inset VSpace defskip
34183 \begin_layout Standard
34184 \begin_inset Graphics
34185 filename clipart/MacroToolbar.png
34190 \begin_inset Index idx
34193 \begin_layout Plain Layout
34202 \begin_layout Standard
34203 \begin_inset VSpace defskip
34209 \begin_layout Standard
34210 The macro toolbar contains from left to right the following buttons:
34213 \begin_layout Standard
34214 \begin_inset VSpace defskip
34220 \begin_layout Standard
34221 \begin_inset Tabular
34222 <lyxtabular version="3" rows="9" columns="2">
34223 <features islongtable="true" longtabularalignment="center">
34224 <column alignment="left" valignment="top" width="0">
34225 <column alignment="left" valignment="top" width="85col%">
34226 <row interlinespace="2.5mm">
34227 <cell alignment="center" valignment="top" usebox="none">
34230 \begin_layout Plain Layout
34231 \begin_inset Graphics
34232 filename ../images/math-macro-remove-param.png
34233 rotateOrigin center
34242 <cell alignment="center" valignment="top" usebox="none">
34245 \begin_layout Plain Layout
34248 Edit\SpecialChar \menuseparator
34249 Math\SpecialChar \menuseparator
34251 \begin_inset space ~
34254 Definition\SpecialChar \menuseparator
34255 Remove Last Argument
34261 <row interlinespace="2.5mm">
34262 <cell alignment="center" valignment="top" usebox="none">
34265 \begin_layout Plain Layout
34266 \begin_inset Graphics
34267 filename ../images/math-macro-add-param.png
34268 rotateOrigin center
34277 <cell alignment="center" valignment="top" usebox="none">
34280 \begin_layout Plain Layout
34283 Edit\SpecialChar \menuseparator
34284 Math\SpecialChar \menuseparator
34286 \begin_inset space ~
34289 Definition\SpecialChar \menuseparator
34296 <row interlinespace="2.5mm">
34297 <cell alignment="center" valignment="top" usebox="none">
34300 \begin_layout Plain Layout
34301 \begin_inset Graphics
34302 filename ../images/math-macro-make-optional.png
34303 rotateOrigin center
34312 <cell alignment="center" valignment="top" usebox="none">
34315 \begin_layout Plain Layout
34318 Edit\SpecialChar \menuseparator
34319 Math\SpecialChar \menuseparator
34321 \begin_inset space ~
34324 Definition\SpecialChar \menuseparator
34325 Make First Non-Optional into
34326 \begin_inset Newline newline
34330 \begin_inset Phantom HPhantom
34333 \begin_layout Plain Layout
34336 Edit\SpecialChar \menuseparator
34337 Math\SpecialChar \menuseparator
34339 \begin_inset space ~
34342 Definition\SpecialChar \menuseparator
34354 <row interlinespace="2.5mm">
34355 <cell alignment="center" valignment="top" usebox="none">
34358 \begin_layout Plain Layout
34359 \begin_inset Graphics
34360 filename ../images/math-macro-make-nonoptional.png
34361 rotateOrigin center
34370 <cell alignment="center" valignment="top" usebox="none">
34373 \begin_layout Plain Layout
34376 Edit\SpecialChar \menuseparator
34377 Math\SpecialChar \menuseparator
34379 \begin_inset space ~
34382 Definition\SpecialChar \menuseparator
34383 Make Last Optional into
34384 \begin_inset Newline newline
34388 \begin_inset Phantom HPhantom
34391 \begin_layout Plain Layout
34394 Edit\SpecialChar \menuseparator
34395 Math\SpecialChar \menuseparator
34397 \begin_inset space ~
34400 Definition\SpecialChar \menuseparator
34406 Non-Optional Argument
34412 <row interlinespace="2.5mm">
34413 <cell alignment="center" valignment="top" usebox="none">
34416 \begin_layout Plain Layout
34417 \begin_inset Graphics
34418 filename ../images/math-macro-remove-optional-param.png
34419 rotateOrigin center
34428 <cell alignment="center" valignment="top" usebox="none">
34431 \begin_layout Plain Layout
34434 Edit\SpecialChar \menuseparator
34435 Math\SpecialChar \menuseparator
34437 \begin_inset space ~
34440 Definition\SpecialChar \menuseparator
34441 Remove Optional Argument
34447 <row interlinespace="2.5mm">
34448 <cell alignment="center" valignment="top" usebox="none">
34451 \begin_layout Plain Layout
34452 \begin_inset Graphics
34453 filename ../images/math-macro-add-optional-param.png
34454 rotateOrigin center
34463 <cell alignment="center" valignment="top" usebox="none">
34466 \begin_layout Plain Layout
34469 Edit\SpecialChar \menuseparator
34470 Math\SpecialChar \menuseparator
34472 \begin_inset space ~
34475 Definition\SpecialChar \menuseparator
34476 Insert Optional Argument
34482 <row interlinespace="2.5mm">
34483 <cell alignment="center" valignment="top" usebox="none">
34486 \begin_layout Plain Layout
34487 \begin_inset Graphics
34488 filename ../images/math-macro-remove-greedy-param.png
34489 rotateOrigin center
34498 <cell alignment="center" valignment="top" usebox="none">
34501 \begin_layout Plain Layout
34504 Edit\SpecialChar \menuseparator
34505 Math\SpecialChar \menuseparator
34507 \begin_inset space ~
34510 Definition\SpecialChar \menuseparator
34511 Remove Last Argument
34512 \begin_inset Newline newline
34516 \begin_inset Phantom HPhantom
34519 \begin_layout Plain Layout
34522 Edit\SpecialChar \menuseparator
34523 Math\SpecialChar \menuseparator
34525 \begin_inset space ~
34528 Definition\SpecialChar \menuseparator
34534 Spitting Out To The Right
34540 <row interlinespace="2.5mm">
34541 <cell alignment="center" valignment="top" usebox="none">
34544 \begin_layout Plain Layout
34545 \begin_inset Graphics
34546 filename ../images/math-macro-append-greedy-param.png
34547 rotateOrigin center
34556 <cell alignment="center" valignment="top" usebox="none">
34559 \begin_layout Plain Layout
34562 Edit\SpecialChar \menuseparator
34563 Math\SpecialChar \menuseparator
34565 \begin_inset space ~
34568 Definition\SpecialChar \menuseparator
34570 \begin_inset Newline newline
34574 \begin_inset Phantom HPhantom
34577 \begin_layout Plain Layout
34580 Edit\SpecialChar \menuseparator
34581 Math\SpecialChar \menuseparator
34583 \begin_inset space ~
34586 Definition\SpecialChar \menuseparator
34592 Eating From The Right
34598 <row interlinespace="2.5mm">
34599 <cell alignment="center" valignment="top" usebox="none">
34602 \begin_layout Plain Layout
34603 \begin_inset Graphics
34604 filename ../images/math-macro-add-greedy-optional-param.png
34605 rotateOrigin center
34614 <cell alignment="center" valignment="top" usebox="none">
34617 \begin_layout Plain Layout
34620 Edit\SpecialChar \menuseparator
34621 Math\SpecialChar \menuseparator
34623 \begin_inset space ~
34626 Definition\SpecialChar \menuseparator
34627 Append Optional Argument
34628 \begin_inset Newline newline
34632 \begin_inset Phantom HPhantom
34635 \begin_layout Plain Layout
34638 Edit\SpecialChar \menuseparator
34639 Math\SpecialChar \menuseparator
34641 \begin_inset space ~
34644 Definition\SpecialChar \menuseparator
34650 Eating From The Right
34663 \begin_layout Section
34664 Computer Algebra Systems
34667 \begin_layout Standard
34668 LyX offers the exchange between mathematical expressions written in LyX's
34669 math editor and external applications or user defined scripts.
34670 Currently supported applications are
34687 Note that the set of supported mathematical constructs is limited only
34688 to very simple cases.
34691 \begin_layout Subsection
34695 \begin_layout Standard
34696 Write some expression in a formula, go to the
34698 Edit\SpecialChar \menuseparator
34699 Math\SpecialChar \menuseparator
34700 Use Computer Algebra System
34702 menu and choose the application you have installed on the computer.
34703 After that the result of computation should show on the right side of the
34704 expression together with the
34705 \begin_inset Quotes eld
34709 \begin_inset Quotes erd
34715 \begin_layout Standard
34716 Here are few simple examples (with results from
34720 ) to show what kind of computations can be performed:
34723 \begin_layout Itemize
34724 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34730 \begin_layout Itemize
34731 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34737 \begin_layout Itemize
34738 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34744 \begin_layout Itemize
34745 \begin_inset Formula $\det\left[\begin{array}{ccc}
34749 \end{array}\right]=-56$
34755 \begin_layout Itemize
34756 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34762 \begin_layout Subsection
34766 \begin_layout Standard
34767 Currently there is no keyboard shortcut for calling the algebra applications.
34768 One can easily bind a shortcut to the
34772 LyX function (see the
34780 \begin_inset space \thinspace{}
34784 \begin_inset space ~
34791 key inside the math editor.
34796 one would use this shortcut definition command:
34799 \begin_layout Standard
34802 command-alternatives break-paragraph;math-extern maxima
34805 \begin_layout Standard
34806 \begin_inset Newpage newpage
34812 \begin_layout Section
34814 \begin_inset Index idx
34817 \begin_layout Plain Layout
34826 \begin_layout Subsection
34828 \begin_inset Index idx
34831 \begin_layout Plain Layout
34840 \begin_layout Standard
34841 Negative numbers often look ugly in formulas because the minus sign before
34842 the number is set with the same length as the minus operator sign.
34843 When writing the negative number in normal text, the minus sign appears
34847 \begin_layout Standard
34848 Thus, the problem disappears when converting the minus sign to mathematical
34852 \begin_layout Standard
34853 An example to visualize the problem:
34856 \begin_layout Standard
34858 \begin_inset Tabular
34859 <lyxtabular version="3" rows="3" columns="2">
34860 <features tabularvalignment="middle">
34861 <column alignment="right" valignment="top" width="0">
34862 <column alignment="left" valignment="top" width="0">
34864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34867 \begin_layout Plain Layout
34873 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34876 \begin_layout Plain Layout
34884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34887 \begin_layout Plain Layout
34893 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34896 \begin_layout Plain Layout
34897 \begin_inset Formula $x=-2$
34907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34910 \begin_layout Plain Layout
34916 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34919 \begin_layout Plain Layout
34920 \begin_inset Formula $x=\textrm{-}2$
34936 \begin_layout Subsection
34937 Comma as decimal Separator
34938 \begin_inset Index idx
34941 \begin_layout Plain Layout
34950 \begin_layout Standard
34951 In LaTeX a comma inside a formula is used, according to the English convention,
34952 as number group separator.
34953 So there will be space added behind all commas in formulas.
34956 \begin_layout Standard
34957 To avoid this, the comma is highlighted and changed to mathematical text
34967 \begin_layout Standard
34968 To use all formula commas in the document as decimal separator, the file
34977 \begin_layout Plain Layout
34982 is part of the LaTeX-package
34987 \begin_inset Index idx
34990 \begin_layout Plain Layout
34995 \begin_layout Plain Layout
35015 \begin_inset Index idx
35018 \begin_layout Plain Layout
35024 is loaded with the LaTeX-preamble line
35027 \begin_layout Standard
35035 \begin_layout Subsection
35037 \begin_inset CommandInset label
35039 name "sub:Physical-Vectors"
35044 \begin_inset Index idx
35047 \begin_layout Plain Layout
35056 \begin_layout Standard
35057 Predefined vectors are offered by the LaTeX-package
35062 \begin_inset Index idx
35065 \begin_layout Plain Layout
35071 that is loaded with the LaTeX-preamble line
35074 \begin_layout Standard
35082 \begin_layout Standard
35086 \begin_layout Plain Layout
35096 \begin_inset Note Note
35099 \begin_layout Plain Layout
35100 The following table will only be displayed when the LaTeX-package
35112 \begin_layout Standard
35113 The following commands are defined:
35116 \begin_layout Standard
35118 \begin_inset Tabular
35119 <lyxtabular version="3" rows="4" columns="2">
35120 <features tabularvalignment="middle">
35121 <column alignment="center" valignment="top" width="0">
35122 <column alignment="center" valignment="top" width="0">
35124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35127 \begin_layout Plain Layout
35133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35136 \begin_layout Plain Layout
35144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35147 \begin_layout Plain Layout
35157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35160 \begin_layout Plain Layout
35161 \begin_inset Formula $\Bra{\psi}$
35171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35174 \begin_layout Plain Layout
35184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35187 \begin_layout Plain Layout
35188 \begin_inset Formula $\Ket{\psi}$
35198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35201 \begin_layout Plain Layout
35213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35216 \begin_layout Plain Layout
35217 \begin_inset Formula $\Braket{\psi|\phi}$
35233 \begin_layout Standard
35240 assures that all vertical bars are set in the size of the surrounding brackets:
35241 \begin_inset Formula
35243 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
35252 \begin_layout Plain Layout
35262 \begin_inset Note Note
35265 \begin_layout Plain Layout
35266 The following will be displayed when the LaTeX-package
35278 \begin_layout Standard
35279 You need to install the LaTeX-package
35283 to see the rest of this subsection in the output.
35286 \begin_layout Standard
35290 \begin_layout Plain Layout
35302 \begin_layout Standard
35309 can also be achieved using the command
35315 , that is described in
35316 \begin_inset CommandInset ref
35318 reference "sub:Automatic-Bracket-Size"
35325 \begin_layout Subsection
35326 Self-defined Fractions
35327 \begin_inset CommandInset label
35329 name "sub:Self-defined-Fractions"
35334 \begin_inset Index idx
35337 \begin_layout Plain Layout
35338 Fractions ! self-defined
35346 \begin_layout Standard
35347 To define custom commands for fractions, the command
35354 \begin_inset Index idx
35357 \begin_layout Plain Layout
35365 is used in the following scheme:
35368 \begin_layout Standard
35381 bracket}{fraction bar thickness}{style}
35382 \begin_inset Newline newline
35386 \begin_inset Phantom HPhantom
35389 \begin_layout Plain Layout
35399 {numerator}{denominator}
35402 \begin_layout Standard
35403 The style is a number in the range of 0
35404 \begin_inset space \thinspace{}
35408 \begin_inset space \thinspace{}
35414 \begin_layout Standard
35416 \begin_inset Tabular
35417 <lyxtabular version="3" rows="5" columns="2">
35418 <features tabularvalignment="middle">
35419 <column alignment="center" valignment="top" width="0">
35420 <column alignment="center" valignment="top" width="0">
35422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35425 \begin_layout Plain Layout
35431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35434 \begin_layout Plain Layout
35442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35445 \begin_layout Plain Layout
35451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35454 \begin_layout Plain Layout
35455 display style formula
35462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35465 \begin_layout Plain Layout
35471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35474 \begin_layout Plain Layout
35482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35485 \begin_layout Plain Layout
35491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35494 \begin_layout Plain Layout
35502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35505 \begin_layout Plain Layout
35511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35514 \begin_layout Plain Layout
35528 \begin_layout Standard
35529 When no style is given, the size is adjusted to the surrounding environment
35530 like for the command
35539 \begin_layout Standard
35540 When no fraction bar thickness is given, the predefined value of 0.4
35541 \begin_inset space \thinspace{}
35547 \begin_layout Standard
35548 \begin_inset VSpace medskip
35551 For example, the commands
35564 \begin_inset CommandInset ref
35566 reference "sub:Fractions"
35570 are defined with the commands
35573 \begin_layout Standard
35582 genfrac{}{}{}{0}{#1}{#2}}
35585 \begin_layout Standard
35589 \begin_layout Standard
35598 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35601 \begin_layout Standard
35602 \begin_inset VSpace medskip
35605 To define a fraction where the fraction bar thickness can be given as optional
35606 argument, the following line is inserted to the LaTeX-preamble:
35609 \begin_layout Standard
35618 genfrac{}{}{#1}{}{#2}{#3}}
35621 \begin_layout Standard
35622 \begin_inset Newpage newpage
35628 \begin_layout Standard
35630 \begin_inset Formula
35632 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35633 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35638 As one can see, the distance of the numerator and the denominator to the
35639 fraction bar is round about three times the bar thickness.
35642 \begin_layout Subsection
35644 \begin_inset Index idx
35647 \begin_layout Plain Layout
35656 \begin_layout Standard
35657 To cancel formulas or formula parts, the LaTeX-package
35662 \begin_inset Index idx
35665 \begin_layout Plain Layout
35671 has to be loaded with the LaTeX-preamble line
35674 \begin_layout Standard
35682 \begin_layout Standard
35686 \begin_layout Plain Layout
35696 \begin_inset Note Note
35699 \begin_layout Plain Layout
35700 The following table will only be displayed when the LaTeX-package
35712 \begin_layout Standard
35713 There are four ways to cancel formulas:
35716 \begin_layout Standard
35718 \begin_inset Tabular
35719 <lyxtabular version="3" rows="5" columns="2">
35720 <features tabularvalignment="middle">
35721 <column alignment="center" valignment="top" width="0">
35722 <column alignment="center" valignment="top" width="0">
35724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35727 \begin_layout Plain Layout
35733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35736 \begin_layout Plain Layout
35738 \begin_inset Note Note
35741 \begin_layout Plain Layout
35748 are used here as spacer.
35760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35763 \begin_layout Plain Layout
35772 \begin_layout Plain Layout
35786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35789 \begin_layout Plain Layout
35790 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35803 \begin_layout Plain Layout
35812 \begin_layout Plain Layout
35826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35829 \begin_layout Plain Layout
35830 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35843 \begin_layout Plain Layout
35852 \begin_layout Plain Layout
35866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35869 \begin_layout Plain Layout
35870 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35883 \begin_layout Plain Layout
35887 \begin_inset Formula $\to$
35898 \begin_layout Plain Layout
35912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35915 \begin_layout Plain Layout
35916 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35932 \begin_layout Standard
35939 is especially suitable to visualize the reduction of fractions within formulas:
35940 \begin_inset Formula
35942 \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}}}
35950 \begin_layout Standard
35951 To change the size of
35958 \begin_inset Quotes eld
35962 \begin_inset Quotes erd
35965 value one can load the package
35969 with either the option
35973 which leads to the same size as for the canceled value or with the option
35978 which makes is it a bit smaller than the size one gets without using a
35984 was loaded with this line:
35987 \begin_layout Standard
35992 usepackage[samesize]{cancel}
35995 \begin_layout Standard
35996 To color the cancellation bar one adds this command as TeX code:
35999 \begin_layout Standard
36011 \begin_layout Standard
36016 can be replaced by a color of your choice.
36019 \begin_layout Standard
36023 \begin_layout Plain Layout
36039 \begin_layout Standard
36040 \begin_inset Formula
36042 \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}}}
36050 \begin_layout Standard
36054 \begin_layout Plain Layout
36068 \begin_inset Note Note
36071 \begin_layout Plain Layout
36080 \begin_layout Standard
36081 For further customizations, see the documentation of the package
36086 \begin_inset CommandInset citation
36095 \begin_layout Standard
36099 \begin_layout Plain Layout
36109 \begin_inset Note Note
36112 \begin_layout Plain Layout
36113 The following will be displayed when the LaTeX-package
36125 \begin_layout Standard
36126 You need to install the LaTeX-package
36130 to see the rest of this subsection in the output.
36133 \begin_layout Standard
36137 \begin_layout Plain Layout
36149 \begin_layout Subsection
36150 Formulas in Section Headings
36151 \begin_inset CommandInset label
36153 name "sub:Formulas-in-Section"
36158 \begin_inset Index idx
36161 \begin_layout Plain Layout
36162 Formula ! in section headings
36170 \begin_layout Standard
36171 When formulas are used in section headings, the following has to be taken
36175 \begin_layout Standard
36176 \begin_inset Note Greyedout
36179 \begin_layout Plain Layout
36185 \begin_inset Index idx
36188 \begin_layout Plain Layout
36189 Packages ! hyperref
36194 support is enabled in the document settings dialog under
36197 \begin_inset space ~
36202 , PDF-bookmarks are created for every section heading in the table of contents.
36203 If a section heading contains formulas, they are incorrectly displayed
36204 in the bookmark text, because formulas in bookmarks infringe the PDF convention
36213 \begin_layout Standard
36214 Both problems can be solved by inserting at the end of the section heading
36215 a short title with the menu
36217 Insert\SpecialChar \menuseparator
36219 \begin_inset space ~
36225 Short titles are used as alternative for multiline section headings to
36226 keep the table of contents clearly arranged.
36227 Only the short title appears in the table of contents and therefore also
36228 in the PDF-bookmark.
36231 \begin_layout Standard
36232 When formulas should be used in the table of contents but
36236 is used, one can use the following command in TeX-mode:
36239 \begin_layout Standard
36244 texorpdfstring{part}{alternative}
36245 \begin_inset Index idx
36248 \begin_layout Plain Layout
36259 \begin_layout Standard
36260 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36261 This can be characters, formulas, footnotes, but also cross-references.
36262 The alternative is used instead of the part for the bookmark.
36265 \begin_layout Standard
36266 Here are two example headings:
36267 \begin_inset VSpace -3mm
36274 \begin_layout Plain Layout
36286 \begin_layout Subsubsection
36287 Heading without formula in table of contents
36288 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36292 \begin_inset Argument
36295 \begin_layout Plain Layout
36296 Heading without formula in table of contents
36304 \begin_layout Subsubsection
36305 Heading with formula in table of contents
36309 \begin_layout Plain Layout
36319 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36326 \begin_layout Plain Layout
36336 \begin_layout Standard
36340 \begin_layout Plain Layout
36349 In the first heading a short title was used, in the second one
36358 \begin_layout Standard
36359 To get the same formatting as for the other headings, the complete heading
36368 \begin_layout Plain Layout
36370 \begin_inset CommandInset ref
36372 reference "sub:Bold-Formulas"
36384 \begin_layout Subsection
36385 Formulas in multi-column Text
36386 \begin_inset Index idx
36389 \begin_layout Plain Layout
36390 Formula ! in multi-column text
36398 \begin_layout Standard
36399 Formulas in multi-column text are often too wide to fit into a column and
36400 thus need to be set over the whole page width.
36401 This is done by using the LaTeX-package
36409 \begin_layout Plain Layout
36414 is part of every LaTeX standard installation.
36420 \begin_inset Index idx
36423 \begin_layout Plain Layout
36424 Packages ! multicol
36429 , that is loaded with the LaTeX-preamble line
36432 \begin_layout Standard
36437 usepackage{multicol}
36440 \begin_layout Standard
36441 \begin_inset Note Greyedout
36444 \begin_layout Plain Layout
36445 Note that in this case the setting
36448 \begin_inset space ~
36455 Document\SpecialChar \menuseparator
36461 \begin_inset space ~
36481 \begin_layout Standard
36482 Before the multi-column text the command
36485 \begin_layout Standard
36490 begin{multicols}{column number}
36493 \begin_layout Standard
36494 is written in TeX-mode.
36495 The column number is a number in the range of 2
36496 \begin_inset space \thinspace{}
36500 \begin_inset space \thinspace{}
36504 Before the formula the multi-column text is ended by inserting the command
36507 \begin_layout Standard
36515 \begin_layout Standard
36519 \begin_layout Standard
36520 Due to the command some space is automatically added before the formula.
36522 \begin_inset space \thinspace{}
36525 mm vertical space is inserted before the formula.
36526 When the formula style
36532 \begin_layout Plain Layout
36534 \begin_inset CommandInset ref
36536 reference "sec:Formula-Styles"
36548 \begin_inset space \thinspace{}
36551 mm space is inserted instead.
36554 \begin_layout Standard
36555 As example a multi-column text with a displayed formula:
36558 \begin_layout Standard
36564 \begin_layout Plain Layout
36568 begin{multicols}{2}
36573 Das Spektrum wird fouriertransformiert.
36574 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36575 , Lösungsmittel) zu trennen.
36576 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36577 nun das Aussehen des Ausgangssignals.
36578 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36579 über alle Phasen integrieren muss.
36581 \begin_inset Formula $S$
36584 unser normiertes Ausgangssignal und
36585 \begin_inset Formula $P$
36588 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36592 \begin_layout Plain Layout
36602 \begin_inset VSpace -6mm
36606 \begin_inset Formula
36608 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36617 \begin_layout Plain Layout
36621 begin{multicols}{2}
36627 \begin_inset Formula $S_{0}$
36630 das Signal ohne Gradient ist und die Normierungsbedingung
36631 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36635 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36637 \begin_inset Formula $\nicefrac{\pi}{2}$
36641 \begin_inset space \thinspace{}
36644 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36645 das Signal zusätzlich abschwächt.
36646 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36648 \begin_inset Formula $T_{2}$
36654 \begin_layout Standard
36660 \begin_layout Plain Layout
36672 \begin_layout Subsection
36673 Formulas with Description of Variables
36674 \begin_inset Index idx
36677 \begin_layout Plain Layout
36678 Formula ! with description of variables
36686 \begin_layout Standard
36687 To describe variables within a formula, like in formula
36688 \begin_inset CommandInset ref
36690 reference "eq:within"
36699 \begin_inset Formula $n$
36703 \begin_inset space ~
36706 matrix is used with left aligned columns for the
36707 \begin_inset Formula $n$
36714 \begin_layout Plain Layout
36716 \begin_inset CommandInset ref
36718 reference "sec:Matrices"
36727 To set the description in a smaller size, before the matrix e.
36728 \begin_inset space \thinspace{}
36732 \begin_inset space \space{}
36745 \begin_layout Plain Layout
36747 \begin_inset CommandInset ref
36749 reference "sub:Font-Sizes"
36761 \begin_layout Standard
36762 When the formula style
36768 \begin_layout Plain Layout
36770 \begin_inset CommandInset ref
36772 reference "sec:Formula-Styles"
36793 \begin_layout Plain Layout
36800 only works in formulas with the style
36805 \begin_inset CommandInset ref
36807 reference "sub:Variable-Space"
36816 is inserted before and after the matrix to have the same separation of
36817 the matrix from the equation and the side margin.
36820 \begin_layout Standard
36821 When the formula style
36825 is used, the method described in
36826 \begin_inset CommandInset ref
36828 reference "sub:Flalign-Environment"
36832 is used to indent formulas.
36834 \begin_inset CommandInset ref
36836 reference "eq:within"
36840 consists of five columns where in the first two columns contain the equation,
36841 the third the matrix and the last one an empty TeX-brace.
36842 \begin_inset Formula
36844 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36845 \rho & \textrm{density}\\
36846 V & \textrm{volume}\\
36847 g & \textrm{gravitational acceleration}
36848 \end{array} & & {}\label{eq:within}
36856 \begin_layout Subsection
36857 Upright small Greek Letters
36858 \begin_inset CommandInset label
36860 name "sub:Upright-small-Greek"
36865 \begin_inset Index idx
36868 \begin_layout Plain Layout
36869 Greek letters ! upright
36877 \begin_layout Standard
36878 Most of the math fonts only provide italic small Greek letters.
36879 But for symbols of elementary particles like pions and neutrinos, upright
36880 Greek letters are needed.
36889 \begin_layout Plain Layout
36894 is part of the LaTeX-package
36899 \begin_inset Index idx
36902 \begin_layout Plain Layout
36907 \begin_layout Plain Layout
36927 \begin_inset Index idx
36930 \begin_layout Plain Layout
36936 that is loaded with the LaTeX-preamble line
36939 \begin_layout Standard
36944 usepackage{upgreek}
36947 \begin_layout Standard
36953 \begin_layout Plain Layout
36963 \begin_inset Note Note
36966 \begin_layout Plain Layout
36967 The following table will only be displayed when the LaTeX-package
36976 They are created when the command for a small Greek letter is started with
36982 For example the command
36989 \begin_inset Formula $\uptau$
36995 \begin_layout Standard
36996 With these commands reactions of elementary particles can be typeset:
36997 \begin_inset Formula
36999 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
37007 \begin_layout Standard
37008 The upright letters are more bold and wider than the italic ones.
37009 They should therefore not be used for units like
37010 \begin_inset Quotes eld
37014 \begin_inset Quotes erd
37020 \begin_layout Standard
37024 \begin_layout Plain Layout
37034 \begin_inset Note Note
37037 \begin_layout Plain Layout
37038 The following will be displayed when the LaTeX-package
37050 \begin_layout Standard
37051 You need to install the LaTeX-package
37055 to see the rest of this subsection in the output.
37058 \begin_layout Standard
37062 \begin_layout Plain Layout
37074 \begin_layout Standard
37075 \begin_inset Newpage newpage
37081 \begin_layout Subsection
37082 Text Characters in Formulas
37083 \begin_inset CommandInset label
37085 name "sub:Text-Characters-in"
37090 \begin_inset Index idx
37093 \begin_layout Plain Layout
37102 \begin_layout Standard
37103 In some cases you might want to insert text characters directly into formulas.
37104 When for example the centered dot · is often used in formulas like
37105 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
37108 , one would have to insert the command
37118 \begin_layout Plain Layout
37120 \begin_inset CommandInset ref
37122 reference "sub:Binary-Operators"
37131 all the time, because this character is defined in all encodings as text
37133 But the encoding can be changed by this LaTeX-preamble line:
37136 \begin_layout Standard
37141 Declare Inputtext{183}{
37151 f\SpecialChar \textcompwordmark{}
37155 \begin_layout Standard
37156 The character encoding (menu
37158 Document\SpecialChar \menuseparator
37159 Settings\SpecialChar \menuseparator
37162 ) specifies what character appears when a keyboard key is pressed.
37163 When the key for the character '·' is pressed, internally the command
37170 But this command is not available in a formula so that you would get LaTeX-erro
37172 With the changed encoding the right command is chosen automatically, depending
37173 on if the character was inserted into a formula or not.
37176 \begin_layout Standard
37177 The encoding of several characters is saved in definition files.
37178 For example the encoding
37182 is defined in the file
37186 which is in the installation folder of LaTeX.
37187 Encodings should only be changed via the LaTeX-preamble and not in the
37189 Otherwise documents could not be edited by other LyX users working on other
37193 \begin_layout Standard
37194 \begin_inset VSpace medskip
37197 Besides the centered dot, in this document the degree sign ° is defined
37198 with the following LaTeX-preamble line so that it can be directly inserted
37202 \begin_layout Standard
37207 DeclareInputtext{176}{
37217 f\SpecialChar \textcompwordmark{}
37221 \begin_layout Standard
37222 \begin_inset Newpage newpage
37228 \begin_layout Section
37231 \begin_inset Index idx
37234 \begin_layout Plain Layout
37243 \begin_layout Standard
37244 This section is a summary of the most important typographic rules, listed
37249 \begin_layout Plain Layout
37250 This collection was partly taken from the German semi-official dictionary
37252 \begin_inset Quotes eld
37256 \begin_inset Quotes erd
37260 \begin_inset CommandInset citation
37266 that lists some of the ISO rules.
37267 More rules are listed in
37268 \begin_inset CommandInset citation
37282 \begin_layout Itemize
37291 \begin_layout Plain Layout
37292 done with font styles, see
37293 \begin_inset CommandInset ref
37295 reference "sub:Font-Styles"
37304 , no matter if they appear in italic text: 30
37305 \begin_inset space \thinspace{}
37309 \begin_inset Newline newline
37312 Between the value and the unit is the smallest space, see
37313 \begin_inset CommandInset ref
37315 reference "sub:Predefined-Space"
37320 \begin_inset Newline newline
37323 This convention is automatically fulfilled when the command
37330 When it is entered to a formula, two boxes appear.
37331 In the first one the value is inserted, in the second one the unit, and
37333 \begin_inset Formula $\unit[30]{km/h}$
37337 \begin_inset space \thinspace{}
37347 is not a real LaTeX command but the command
37353 , therefore you cannot use it in TeX code.
37356 \begin_layout Itemize
37357 Percent and perthousand signs are set like physical units:
37358 \begin_inset Newline newline
37362 \begin_inset space \thinspace{}
37368 \begin_layout Itemize
37369 The degree sign follows directly on the value: 15°, but not when it is used
37371 \begin_inset space \thinspace{}
37377 \begin_layout Itemize
37378 In numbers with more than four digits the smallest space is inserted before
37379 every third digit to group them:
37389 \begin_inset space \thinspace{}
37393 \begin_inset space \thinspace{}
37399 \begin_layout Itemize
37400 For dimensions like 120×90×40
37401 \begin_inset space \thinspace{}
37404 cm the multiplication sign
37405 \begin_inset Quotes eld
37409 \begin_inset Quotes erd
37413 It is available either via the command
37421 Insert\SpecialChar \menuseparator
37422 Special Character\SpecialChar \menuseparator
37428 \begin_layout Itemize
37429 Functions with names consisting of several letters are set upright to avoid
37431 \begin_inset CommandInset ref
37433 reference "sub:Predefined-Functions"
37440 \begin_layout Itemize
37441 Indices consisting of several letters, are set upright:
37442 \begin_inset Formula $E_{\mathrm{kin}}$
37446 \begin_inset Newline newline
37449 Components of matrices are set italic:
37450 \begin_inset Formula $\hat{H}_{kl}$
37456 \begin_layout Itemize
37457 The differentiation/integration operator 'd', the Euler's number 'e' and
37458 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37462 \begin_layout Itemize
37463 The character that denotes a
37467 transformation is inserted either by the command
37475 \begin_layout Plain Layout
37488 Insert\SpecialChar \menuseparator
37489 Special Character\SpecialChar \menuseparator
37490 Symbols\SpecialChar \menuseparator
37492 \begin_inset space ~
37498 \begin_inset Formula $\mathscr{F}$
37504 \begin_layout Standard
37505 \begin_inset Newpage newpage
37511 \begin_layout Section
37513 \begin_inset Index idx
37516 \begin_layout Plain Layout
37525 \begin_layout Standard
37526 Some characters and symbols can be created with several commands.
37527 Here is a list of the synonym commands:
37530 \begin_layout Standard
37531 \begin_inset VSpace bigskip
37535 \begin_inset space \hfill{}
37539 \begin_inset Tabular
37540 <lyxtabular version="3" rows="12" columns="2">
37541 <features tabularvalignment="middle">
37542 <column alignment="center" valignment="top" width="0pt">
37543 <column alignment="center" valignment="top" width="0pt">
37545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37548 \begin_layout Plain Layout
37554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37557 \begin_layout Plain Layout
37559 \begin_inset Note Note
37562 \begin_layout Plain Layout
37569 is only used as spacer.
37581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37584 \begin_layout Plain Layout
37592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37595 \begin_layout Plain Layout
37599 \begin_layout Plain Layout
37612 \begin_layout Plain Layout
37626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37629 \begin_layout Plain Layout
37637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37640 \begin_layout Plain Layout
37650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37653 \begin_layout Plain Layout
37661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37664 \begin_layout Plain Layout
37674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37677 \begin_layout Plain Layout
37685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37688 \begin_layout Plain Layout
37696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37699 \begin_layout Plain Layout
37707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37710 \begin_layout Plain Layout
37718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37721 \begin_layout Plain Layout
37729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37732 \begin_layout Plain Layout
37742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37745 \begin_layout Plain Layout
37753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37756 \begin_layout Plain Layout
37766 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37769 \begin_layout Plain Layout
37777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37780 \begin_layout Plain Layout
37790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37793 \begin_layout Plain Layout
37801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37804 \begin_layout Plain Layout
37814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37817 \begin_layout Plain Layout
37825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37828 \begin_layout Plain Layout
37836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37839 \begin_layout Plain Layout
37847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37850 \begin_layout Plain Layout
37862 \begin_inset space \hfill{}
37866 \begin_inset Tabular
37867 <lyxtabular version="3" rows="12" columns="2">
37868 <features tabularvalignment="middle">
37869 <column alignment="center" valignment="top" width="0pt">
37870 <column alignment="center" valignment="top" width="0pt">
37872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37875 \begin_layout Plain Layout
37881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37884 \begin_layout Plain Layout
37892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37895 \begin_layout Plain Layout
37903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37906 \begin_layout Plain Layout
37918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37921 \begin_layout Plain Layout
37929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37932 \begin_layout Plain Layout
37942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37945 \begin_layout Plain Layout
37953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37956 \begin_layout Plain Layout
37966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37969 \begin_layout Plain Layout
37977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37980 \begin_layout Plain Layout
37988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37991 \begin_layout Plain Layout
37999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38002 \begin_layout Plain Layout
38010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38013 \begin_layout Plain Layout
38021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38024 \begin_layout Plain Layout
38034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38037 \begin_layout Plain Layout
38045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38048 \begin_layout Plain Layout
38058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38061 \begin_layout Plain Layout
38069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38072 \begin_layout Plain Layout
38082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38085 \begin_layout Plain Layout
38093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38096 \begin_layout Plain Layout
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38109 \begin_layout Plain Layout
38117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38120 \begin_layout Plain Layout
38130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
38133 \begin_layout Plain Layout
38141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
38144 \begin_layout Plain Layout
38158 \begin_inset space \hfill{}
38164 \begin_layout Standard
38165 \begin_inset Newpage newpage
38171 \begin_layout Bibliography
38172 \begin_inset CommandInset bibitem
38173 LatexCommand bibitem
38185 The LaTeX Companion
38188 Addison Wesley, 2004
38191 \begin_layout Bibliography
38192 \begin_inset CommandInset bibitem
38193 LatexCommand bibitem
38199 \begin_inset CommandInset href
38202 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
38206 of LaTeX's math abilities
38209 \begin_layout Bibliography
38210 \begin_inset CommandInset bibitem
38211 LatexCommand bibitem
38217 \begin_inset CommandInset href
38220 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
38228 \begin_layout Plain Layout
38240 \begin_layout Bibliography
38241 \begin_inset CommandInset bibitem
38242 LatexCommand bibitem
38248 \begin_inset CommandInset href
38251 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38255 of all symbols available with LaTeX-packages
38258 \begin_layout Bibliography
38259 \begin_inset CommandInset bibitem
38260 LatexCommand bibitem
38266 \begin_inset CommandInset href
38268 name "Documentation"
38269 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
38273 of the LaTeX-package
38278 \begin_inset Index idx
38281 \begin_layout Plain Layout
38290 \begin_layout Bibliography
38291 \begin_inset CommandInset bibitem
38292 LatexCommand bibitem
38298 \begin_inset CommandInset href
38300 name "Documentation"
38301 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38305 of the LaTeX-package
38310 \begin_inset Index idx
38313 \begin_layout Plain Layout
38314 Packages ! hyperref
38322 \begin_layout Bibliography
38323 \begin_inset CommandInset bibitem
38324 LatexCommand bibitem
38330 \begin_inset CommandInset href
38332 name "Documentation"
38333 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38337 of the LaTeX-package
38342 \begin_inset Index idx
38345 \begin_layout Plain Layout
38354 \begin_layout Bibliography
38355 \begin_inset CommandInset bibitem
38356 LatexCommand bibitem
38362 \begin_inset CommandInset href
38365 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
38376 \begin_inset CommandInset ref
38378 reference "sub:Operator-Limits"
38383 \begin_inset Index idx
38386 \begin_layout Plain Layout
38397 \begin_layout Bibliography
38398 \begin_inset CommandInset bibitem
38399 LatexCommand bibitem
38410 Auflage, Duden 2001
38413 \begin_layout Bibliography
38414 \begin_inset CommandInset bibitem
38415 LatexCommand bibitem
38421 \begin_inset CommandInset href
38424 target "http://physics.nist.gov/Document/checklist.pdf"
38428 for reviewing manuscripts
38431 \begin_layout Standard
38432 \begin_inset CommandInset index_print
38433 LatexCommand printindex