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 VSpace bigskip
5833 As all multiline formulas are matrices, the length
5840 \begin_inset Index idx
5843 \begin_layout Plain Layout
5851 that is described in
5852 \begin_inset CommandInset ref
5854 reference "sub:Column-Separation"
5858 can also be used to change the column separation of matrices.
5861 \begin_layout Standard
5862 To change the row separation, the command
5869 \begin_inset Index idx
5872 \begin_layout Plain Layout
5881 It is used as follows:
5884 \begin_layout Standard
5891 arraystretch}{stretch factor}
5892 \begin_inset Index idx
5895 \begin_layout Plain Layout
5906 \begin_layout Standard
5913 assigns the stretch factor to the predefined command
5921 \begin_inset space \thinspace{}
5925 \begin_inset space \space{}
5928 the row separation, use the factor 2.
5929 This is then used for all following matrices.
5930 To go back to the original separation, assign the factor 1 to
5939 \begin_layout Standard
5940 To set matrices into a text line, the command
5947 \begin_inset Index idx
5950 \begin_layout Plain Layout
5959 When it is inserted a blue box with two dashed lines appears.
5960 In this box the matrix is inserted.
5963 \begin_layout Standard
5965 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5967 \end{smallmatrix}\right)$
5973 \begin_layout Section
5974 Brackets and Delimiters
5975 \begin_inset Index idx
5978 \begin_layout Plain Layout
5985 \begin_inset Index idx
5988 \begin_layout Plain Layout
5997 \begin_layout Subsection
5998 Vertical Brackets and Delimiters
5999 \begin_inset Index idx
6002 \begin_layout Plain Layout
6011 \begin_layout Standard
6012 \begin_inset space \hfill{}
6016 \begin_inset Tabular
6017 <lyxtabular version="3" rows="9" columns="2">
6018 <features tabularvalignment="middle">
6019 <column alignment="center" valignment="top" width="0pt">
6020 <column alignment="center" valignment="top" width="0pt">
6022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6025 \begin_layout Plain Layout
6031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6034 \begin_layout Plain Layout
6042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6045 \begin_layout Plain Layout
6051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6054 \begin_layout Plain Layout
6055 \begin_inset Formula $($
6065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6068 \begin_layout Plain Layout
6074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6077 \begin_layout Plain Layout
6078 \begin_inset Formula $\{$
6088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6091 \begin_layout Plain Layout
6097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6100 \begin_layout Plain Layout
6101 \begin_inset Formula $[$
6111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6114 \begin_layout Plain Layout
6122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6125 \begin_layout Plain Layout
6126 \begin_inset Formula $\langle$
6136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6139 \begin_layout Plain Layout
6147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6150 \begin_layout Plain Layout
6151 \begin_inset Formula $\lceil$
6161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6164 \begin_layout Plain Layout
6172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6175 \begin_layout Plain Layout
6176 \begin_inset Formula $\lfloor$
6186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6189 \begin_layout Plain Layout
6195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6198 \begin_layout Plain Layout
6199 \begin_inset Formula $/$
6209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6212 \begin_layout Plain Layout
6218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6221 \begin_layout Plain Layout
6222 \begin_inset Formula $|$
6236 \begin_inset space \hfill{}
6240 \begin_inset Tabular
6241 <lyxtabular version="3" rows="9" columns="2">
6242 <features tabularvalignment="middle">
6243 <column alignment="center" valignment="top" width="0pt">
6244 <column alignment="center" valignment="top" width="0pt">
6246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6249 \begin_layout Plain Layout
6255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6258 \begin_layout Plain Layout
6266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6269 \begin_layout Plain Layout
6275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6278 \begin_layout Plain Layout
6279 \begin_inset Formula $)$
6289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6292 \begin_layout Plain Layout
6298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6301 \begin_layout Plain Layout
6302 \begin_inset Formula $\}$
6312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6315 \begin_layout Plain Layout
6321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6324 \begin_layout Plain Layout
6325 \begin_inset Formula $]$
6335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6338 \begin_layout Plain Layout
6346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6349 \begin_layout Plain Layout
6350 \begin_inset Formula $\rangle$
6360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6363 \begin_layout Plain Layout
6371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6374 \begin_layout Plain Layout
6375 \begin_inset Formula $\rceil$
6385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6388 \begin_layout Plain Layout
6396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6399 \begin_layout Plain Layout
6400 \begin_inset Formula $\rfloor$
6410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6413 \begin_layout Plain Layout
6423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6426 \begin_layout Plain Layout
6427 \begin_inset Formula $\backslash$
6437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6440 \begin_layout Plain Layout
6448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6451 \begin_layout Plain Layout
6452 \begin_inset Formula $\|$
6466 \begin_inset space \hfill{}
6472 \begin_layout Standard
6475 \begin_inset Note Greyedout
6478 \begin_layout Plain Layout
6483 In TeX-mode the command
6490 \begin_inset Index idx
6493 \begin_layout Plain Layout
6501 must be used for the backslash, because the command
6509 produces a line break there.
6517 \begin_layout Standard
6518 For all characters listed above the size can be adjusted with the commands
6519 described in the following two subsections.
6520 When using these commands, the characters < and > can directly be used
6521 instead of the commands
6536 \begin_layout Subsubsection
6538 \begin_inset CommandInset label
6540 name "sub:Manual-Bracket-Size"
6545 \begin_inset Index idx
6548 \begin_layout Plain Layout
6549 Bracket size ! manual
6557 \begin_layout Standard
6558 The bracket size can be specified manually by the LaTeX-commands
6565 \begin_inset Index idx
6568 \begin_layout Plain Layout
6601 denotes the smallest and
6607 the largest bracket size.
6610 \begin_layout Standard
6611 These commands are used to emphasize levels of brackets:
6614 \begin_layout Standard
6616 \begin_inset Tabular
6617 <lyxtabular version="3" rows="2" columns="2">
6618 <features tabularvalignment="middle">
6619 <column alignment="center" valignment="top" width="0pt">
6620 <column alignment="center" valignment="top" width="0pt">
6622 <cell alignment="center" valignment="top" usebox="none">
6625 \begin_layout Plain Layout
6626 all brackets in the same size:
6631 <cell alignment="center" valignment="top" usebox="none">
6634 \begin_layout Plain Layout
6635 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6645 <cell alignment="center" valignment="top" usebox="none">
6648 \begin_layout Plain Layout
6654 <cell alignment="center" valignment="top" usebox="none">
6657 \begin_layout Plain Layout
6658 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6672 \begin_inset Note Note
6675 \begin_layout Plain Layout
6682 is only used as spacer.
6690 \begin_layout Standard
6691 For the second formula the command
6701 \begin_layout Plain Layout
6715 \begin_layout Standard
6716 Here is an overview about all bracket sizes:
6719 \begin_layout Standard
6739 \begin_layout Plain Layout
6756 \begin_layout Plain Layout
6769 \begin_layout Plain Layout
6785 \begin_layout Standard
6787 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6793 \begin_layout Standard
6800 -commands there is the variant
6807 \begin_inset Index idx
6810 \begin_layout Plain Layout
6818 that adds a bit more space between the bracket and its content, and the
6832 \begin_inset Index idx
6835 \begin_layout Plain Layout
6845 , that don't add additional space.
6850 at the end of the command
6856 is for a left bracket; for a right bracket this will be replaced by an
6862 A left or right bracket can each be an opening or closing bracket.
6865 \begin_layout Standard
6866 In the following table is a comparison of the variants:
6869 \begin_layout Standard
6871 \begin_inset Tabular
6872 <lyxtabular version="3" rows="5" columns="2">
6873 <features tabularvalignment="middle">
6874 <column alignment="center" valignment="middle" width="0">
6875 <column alignment="center" valignment="middle" width="0">
6877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6880 \begin_layout Plain Layout
6886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6889 \begin_layout Plain Layout
6891 \begin_inset Note Note
6894 \begin_layout Plain Layout
6901 is only used as spacer.
6913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6916 \begin_layout Plain Layout
6931 \begin_layout Plain Layout
6949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6952 \begin_layout Plain Layout
6953 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6966 \begin_layout Plain Layout
6981 \begin_layout Plain Layout
6999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7002 \begin_layout Plain Layout
7003 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7016 \begin_layout Plain Layout
7031 \begin_layout Plain Layout
7049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7052 \begin_layout Plain Layout
7053 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7066 \begin_layout Plain Layout
7078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7081 \begin_layout Plain Layout
7082 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7098 \begin_layout Subsubsection
7099 Automatic Bracket Size
7100 \begin_inset CommandInset label
7102 name "sub:Automatic-Bracket-Size"
7107 \begin_inset Index idx
7110 \begin_layout Plain Layout
7111 Bracket size ! automatic
7119 \begin_layout Standard
7120 Brackets with variable size can be inserted with the commands
7127 \begin_inset Index idx
7130 \begin_layout Plain Layout
7145 \begin_inset Index idx
7148 \begin_layout Plain Layout
7156 or via the math toolbar button
7157 \begin_inset Graphics
7158 filename ../images/dialog-show_mathdelimiter.png
7176 the wanted bracket must be inserted.
7177 The bracket size will then automatically be calculated for the output.
7180 \begin_layout Standard
7182 normal bracket: The command
7192 \begin_layout Plain Layout
7202 \begin_inset Formula $\downarrow$
7209 \begin_layout Plain Layout
7221 \begin_inset Formula
7231 \begin_layout Standard
7233 multiline bracket: The command
7245 \begin_layout Plain Layout
7255 \begin_inset Formula $\downarrow$
7262 \begin_layout Plain Layout
7276 \begin_inset Formula
7278 \ln\left(\frac{A}{C}\right)
7286 \begin_layout Standard
7302 \begin_inset space ~
7308 This has the advantage that you can see in LyX immediately the real bracket
7309 size and that the matching right bracket will be created too.
7310 \begin_inset Newline newline
7313 The command for the last example would then be:
7327 \begin_layout Plain Layout
7337 \begin_inset Formula $\downarrow$
7343 \begin_layout Standard
7344 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7345 For example the command
7355 \begin_layout Plain Layout
7365 \begin_inset Formula $\downarrow$
7372 \begin_layout Plain Layout
7388 \begin_inset Formula
7390 \left.\frac{A}{B}\right\}
7409 will be converted by LyX to brackets in the right size when the document
7410 is reloaded and an omitted bracket will appear as dashed line.
7413 \begin_layout Standard
7414 \begin_inset VSpace bigskip
7417 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7425 \begin_inset Index idx
7428 \begin_layout Plain Layout
7436 is additionally available for all brackets and limits.
7437 With this command the height of the following character is adapted to the
7438 one of the surrounding brackets, what is e.
7439 \begin_inset space \thinspace{}
7443 \begin_inset space \space{}
7446 needed for physical vectors:
7447 \begin_inset Formula
7449 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
7454 For physical vectors there is a special LaTeX-package, described in
7455 \begin_inset CommandInset ref
7457 reference "sub:Physical-Vectors"
7464 \begin_layout Subsection
7466 \begin_inset Index idx
7469 \begin_layout Plain Layout
7470 Brackets ! horizontal
7478 \begin_layout Standard
7480 \begin_inset Tabular
7481 <lyxtabular version="3" rows="4" columns="2">
7482 <features tabularvalignment="middle">
7483 <column alignment="center" valignment="top" width="0pt">
7484 <column alignment="center" valignment="top" width="0pt">
7486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7489 \begin_layout Plain Layout
7491 \begin_inset Note Note
7494 \begin_layout Plain Layout
7501 is only used as spacer.
7511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7514 \begin_layout Plain Layout
7522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7525 \begin_layout Plain Layout
7529 \begin_layout Plain Layout
7544 \begin_layout Plain Layout
7557 \begin_layout Plain Layout
7570 \begin_layout Plain Layout
7583 \begin_layout Plain Layout
7591 \begin_inset Index idx
7594 \begin_layout Plain Layout
7607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7610 \begin_layout Plain Layout
7611 \begin_inset Formula $\overbrace{A+B}^{3}$
7621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7624 \begin_layout Plain Layout
7628 \begin_layout Plain Layout
7643 \begin_layout Plain Layout
7656 \begin_layout Plain Layout
7669 \begin_layout Plain Layout
7677 \begin_inset Index idx
7680 \begin_layout Plain Layout
7693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7696 \begin_layout Plain Layout
7697 \begin_inset Formula $\underbrace{A+B}_{5}$
7707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7710 \begin_layout Plain Layout
7717 \begin_layout Plain Layout
7732 \begin_layout Plain Layout
7745 \begin_layout Plain Layout
7758 \begin_layout Plain Layout
7771 \begin_layout Plain Layout
7784 \begin_layout Plain Layout
7797 \begin_layout Plain Layout
7811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7814 \begin_layout Plain Layout
7815 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7831 \begin_layout Standard
7832 In the last example it doesn't matter if
7844 is inserted at first.
7847 \begin_layout Standard
7848 \begin_inset VSpace bigskip
7851 When brackets are needed that overlap each other, multiline formulas, as
7853 \begin_inset CommandInset ref
7855 reference "sec:Multiline-Formulas"
7860 \begin_inset Formula
7862 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7863 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7868 In the first row the formula is inserted together with the first brace.
7869 It is hereby important that the space command
7873 \begin_layout Plain Layout
7874 Space commands are explained in
7875 \begin_inset CommandInset ref
7877 reference "sub:Predefined-Space"
7892 is inserted before the first
7893 \begin_inset Formula $d$
7896 , because the brace that ends behind the
7897 \begin_inset Formula $q$
7900 prevents that the following
7901 \begin_inset Quotes eld
7905 \begin_inset Quotes erd
7908 is surrounded by space.
7912 \begin_layout Plain Layout
7913 because a bracket is not handled as a character, see
7914 \begin_inset CommandInset ref
7916 reference "sub:Binary-Operators"
7925 In the second row the second brace is inserted.
7926 As it should begin before the
7927 \begin_inset Formula $b$
7942 \begin_layout Plain Layout
7950 \begin_inset CommandInset ref
7952 reference "sub:Placeholders"
7961 This space is needed because the
7962 \begin_inset Quotes eld
7966 \begin_inset Quotes erd
7969 is also surrounded by space in the formula.
7970 The brace is placed under the command
7979 \begin_layout Standard
7980 It gets more complicated when brackets overlap each other, like in the following
7985 \begin_layout Plain Layout
7997 \begin_inset Formula
7999 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
8000 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
8009 \begin_layout Plain Layout
8020 The first formula row is the same as the second row of the previous example,
8021 with the difference that the brace is above.
8022 The second row contains the formula together with the second brace.
8023 To avoid that there is space between the upper brace in the first row and
8024 the formula, the row spacing needs to be reduced.
8025 This is not easily possible due to a bug in LyX
8029 \begin_layout Plain Layout
8030 \begin_inset CommandInset href
8032 name "LyX-bug #1505"
8033 target "http://www.lyx.org/trac/ticket/1505"
8043 As a solution for the problem, the global formula row separation
8050 \begin_inset Index idx
8053 \begin_layout Plain Layout
8061 must be changed to -6
8062 \begin_inset space \thinspace{}
8065 pt before the formula with the command
8080 is set back after the formula to the standard value of 3
8081 \begin_inset space \thinspace{}
8084 pt using the same command.
8085 More about the row separation in formulas is explained in
8086 \begin_inset CommandInset ref
8088 reference "sub:Line-Separation"
8095 \begin_layout Section
8097 \begin_inset Index idx
8100 \begin_layout Plain Layout
8109 \begin_layout Standard
8110 Arrows can be inserted via the math toolbar button
8111 \begin_inset Graphics
8112 filename ../images/math/leftarrow.png
8117 or the commands listed in the following subsections.
8120 \begin_layout Subsection
8122 \begin_inset Index idx
8125 \begin_layout Plain Layout
8134 \begin_layout Standard
8135 \begin_inset space \hfill{}
8139 \begin_inset Tabular
8140 <lyxtabular version="3" rows="8" columns="2">
8141 <features tabularvalignment="middle">
8142 <column alignment="center" valignment="top" width="0pt">
8143 <column alignment="center" valignment="top" width="0pt">
8145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8148 \begin_layout Plain Layout
8154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8157 \begin_layout Plain Layout
8165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8168 \begin_layout Plain Layout
8176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8179 \begin_layout Plain Layout
8180 \begin_inset Formula $\gets$
8190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8193 \begin_layout Plain Layout
8201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8204 \begin_layout Plain Layout
8205 \begin_inset Formula $\Leftarrow$
8215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8218 \begin_layout Plain Layout
8226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8229 \begin_layout Plain Layout
8230 \begin_inset Formula $\longleftarrow$
8240 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8243 \begin_layout Plain Layout
8251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8254 \begin_layout Plain Layout
8255 \begin_inset Formula $\Longleftarrow$
8265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8268 \begin_layout Plain Layout
8276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8279 \begin_layout Plain Layout
8280 \begin_inset Formula $\leftharpoonup$
8290 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8293 \begin_layout Plain Layout
8301 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8304 \begin_layout Plain Layout
8305 \begin_inset Formula $\leftharpoondown$
8315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8318 \begin_layout Plain Layout
8326 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8329 \begin_layout Plain Layout
8330 \begin_inset Formula $\hookleftarrow$
8344 \begin_inset space \hfill{}
8348 \begin_inset Tabular
8349 <lyxtabular version="3" rows="8" columns="2">
8350 <features tabularvalignment="middle">
8351 <column alignment="center" valignment="top" width="0pt">
8352 <column alignment="center" valignment="top" width="0pt">
8354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8357 \begin_layout Plain Layout
8363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8366 \begin_layout Plain Layout
8374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8377 \begin_layout Plain Layout
8385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8388 \begin_layout Plain Layout
8389 \begin_inset Formula $\to$
8399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8402 \begin_layout Plain Layout
8410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8413 \begin_layout Plain Layout
8414 \begin_inset Formula $\Rightarrow$
8424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8427 \begin_layout Plain Layout
8435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8438 \begin_layout Plain Layout
8439 \begin_inset Formula $\longrightarrow$
8449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8452 \begin_layout Plain Layout
8460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8463 \begin_layout Plain Layout
8464 \begin_inset Formula $\Longrightarrow$
8474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8477 \begin_layout Plain Layout
8485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8488 \begin_layout Plain Layout
8489 \begin_inset Formula $\rightharpoonup$
8499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8502 \begin_layout Plain Layout
8510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8513 \begin_layout Plain Layout
8514 \begin_inset Formula $\rightharpoondown$
8524 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8527 \begin_layout Plain Layout
8535 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8538 \begin_layout Plain Layout
8539 \begin_inset Formula $\hookrightarrow$
8553 \begin_inset space \hfill{}
8559 \begin_layout Standard
8560 \begin_inset space \hfill{}
8564 \begin_inset Tabular
8565 <lyxtabular version="3" rows="6" columns="2">
8566 <features tabularvalignment="middle">
8567 <column alignment="center" valignment="top" width="0pt">
8568 <column alignment="center" valignment="top" width="0pt">
8570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8573 \begin_layout Plain Layout
8579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8582 \begin_layout Plain Layout
8590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8593 \begin_layout Plain Layout
8601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8604 \begin_layout Plain Layout
8605 \begin_inset Formula $\leftrightarrow$
8615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8618 \begin_layout Plain Layout
8626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8629 \begin_layout Plain Layout
8630 \begin_inset Formula $\Leftrightarrow$
8640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8643 \begin_layout Plain Layout
8651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8654 \begin_layout Plain Layout
8655 \begin_inset Formula $\longleftrightarrow$
8665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8668 \begin_layout Plain Layout
8676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8679 \begin_layout Plain Layout
8680 \begin_inset Formula $\Longleftrightarrow$
8690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8693 \begin_layout Plain Layout
8701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8704 \begin_layout Plain Layout
8705 \begin_inset Formula $\rightleftharpoons$
8719 \begin_inset space \hspace{}
8724 \begin_inset space \hfill{}
8728 \begin_inset Tabular
8729 <lyxtabular version="3" rows="5" columns="2">
8730 <features tabularvalignment="middle">
8731 <column alignment="center" valignment="top" width="0pt">
8732 <column alignment="center" valignment="top" width="0pt">
8734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8737 \begin_layout Plain Layout
8743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8746 \begin_layout Plain Layout
8754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8757 \begin_layout Plain Layout
8765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8768 \begin_layout Plain Layout
8769 \begin_inset Formula $\mapsto$
8779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8782 \begin_layout Plain Layout
8790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8793 \begin_layout Plain Layout
8794 \begin_inset Formula $\longmapsto$
8804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8807 \begin_layout Plain Layout
8815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8818 \begin_layout Plain Layout
8819 \begin_inset Formula $\leadsto$
8829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8832 \begin_layout Plain Layout
8840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8843 \begin_layout Plain Layout
8844 \begin_inset Formula $\dasharrow$
8858 \begin_inset space \hfill{}
8864 \begin_layout Standard
8865 \begin_inset VSpace medskip
8868 Arrows used as accents like e.
8869 \begin_inset space \thinspace{}
8873 \begin_inset space \space{}
8876 vector arrows are listed in
8877 \begin_inset CommandInset ref
8879 reference "sec:Accents"
8886 \begin_layout Standard
8887 \begin_inset VSpace bigskip
8890 Furthermore there are the labeled arrows
8891 \begin_inset Index idx
8894 \begin_layout Plain Layout
8907 \begin_inset Index idx
8910 \begin_layout Plain Layout
8925 \begin_inset Index idx
8928 \begin_layout Plain Layout
8935 \begin_layout Plain Layout
8950 When inserting one of these commands in a formula, an arrow with two blue
8951 boxes appear where the label can be inserted.
8952 The length of the arrow adapts to the label width.
8955 \begin_layout Standard
8957 \begin_inset Tabular
8958 <lyxtabular version="3" rows="3" columns="2">
8959 <features tabularvalignment="middle">
8960 <column alignment="center" valignment="top" width="0pt">
8961 <column alignment="center" valignment="top" width="0pt">
8963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8966 \begin_layout Plain Layout
8972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8975 \begin_layout Plain Layout
8977 \begin_inset Note Note
8980 \begin_layout Plain Layout
8987 is only used as spacer.
8999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9002 \begin_layout Plain Layout
9009 \begin_layout Plain Layout
9019 \begin_inset Formula $\downarrow$
9023 \begin_inset Formula $\to$
9031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9034 \begin_layout Plain Layout
9035 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9048 \begin_layout Plain Layout
9055 \begin_layout Plain Layout
9065 \begin_inset Formula $\downarrow$
9069 \begin_inset Formula $\to$
9077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9080 \begin_layout Plain Layout
9081 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9097 \begin_layout Subsection
9098 Vertical and diagonal Arrows
9099 \begin_inset Index idx
9102 \begin_layout Plain Layout
9109 \begin_inset Index idx
9112 \begin_layout Plain Layout
9121 \begin_layout Standard
9122 \begin_inset space \hfill{}
9126 \begin_inset Tabular
9127 <lyxtabular version="3" rows="7" columns="2">
9128 <features tabularvalignment="middle">
9129 <column alignment="center" valignment="top" width="0pt">
9130 <column alignment="center" valignment="top" width="0pt">
9132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9135 \begin_layout Plain Layout
9141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9144 \begin_layout Plain Layout
9152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9155 \begin_layout Plain Layout
9163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9166 \begin_layout Plain Layout
9167 \begin_inset Formula $\uparrow$
9177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9180 \begin_layout Plain Layout
9188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9191 \begin_layout Plain Layout
9192 \begin_inset Formula $\Uparrow$
9202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9205 \begin_layout Plain Layout
9213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9216 \begin_layout Plain Layout
9217 \begin_inset Formula $\updownarrow$
9227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9230 \begin_layout Plain Layout
9238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9241 \begin_layout Plain Layout
9242 \begin_inset Formula $\Updownarrow$
9252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9255 \begin_layout Plain Layout
9263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9266 \begin_layout Plain Layout
9267 \begin_inset Formula $\Downarrow$
9277 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9280 \begin_layout Plain Layout
9288 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9291 \begin_layout Plain Layout
9292 \begin_inset Formula $\downarrow$
9306 \begin_inset space \hfill{}
9310 \begin_inset Tabular
9311 <lyxtabular version="3" rows="5" columns="2">
9312 <features tabularvalignment="middle">
9313 <column alignment="center" valignment="top" width="0pt">
9314 <column alignment="center" valignment="top" width="0pt">
9316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9319 \begin_layout Plain Layout
9325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9328 \begin_layout Plain Layout
9336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9339 \begin_layout Plain Layout
9347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9350 \begin_layout Plain Layout
9351 \begin_inset Formula $\nearrow$
9361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9364 \begin_layout Plain Layout
9372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9375 \begin_layout Plain Layout
9376 \begin_inset Formula $\searrow$
9386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9389 \begin_layout Plain Layout
9397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9400 \begin_layout Plain Layout
9401 \begin_inset Formula $\swarrow$
9411 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9414 \begin_layout Plain Layout
9422 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9425 \begin_layout Plain Layout
9426 \begin_inset Formula $\nwarrow$
9440 \begin_inset space \hfill{}
9446 \begin_layout Standard
9447 \begin_inset VSpace medskip
9450 Vertical arrows can be used also as delimiters together with the commands
9452 \begin_inset CommandInset ref
9454 reference "sub:Manual-Bracket-Size"
9459 \begin_inset CommandInset ref
9461 reference "sub:Automatic-Bracket-Size"
9468 \begin_layout Section
9470 \begin_inset CommandInset label
9477 \begin_inset Index idx
9480 \begin_layout Plain Layout
9489 \begin_layout Standard
9490 Accents can be inserted via the math toolbar button
9491 \begin_inset Graphics
9492 filename ../images/math/hat.png
9497 or the commands listed in the following subsections.
9500 \begin_layout Subsection
9501 Accents for one Character
9505 \begin_layout Plain Layout
9518 \begin_layout Plain Layout
9520 \begin_inset CommandInset ref
9522 reference "sub:Accents-in-Text"
9535 \begin_layout Plain Layout
9543 \begin_inset Note Note
9546 \begin_layout Plain Layout
9553 is used to avoid that the footnote appears in the PDF-bookmark.
9556 \begin_layout Plain Layout
9564 \begin_inset CommandInset ref
9566 reference "sub:Formulas-in-Section"
9576 \begin_inset CommandInset label
9578 name "sub:Accents-for-one"
9583 \begin_inset Index idx
9586 \begin_layout Plain Layout
9587 Accents ! for one character
9595 \begin_layout Standard
9596 \begin_inset space \hfill{}
9600 \begin_inset Tabular
9601 <lyxtabular version="3" rows="8" columns="2">
9602 <features tabularvalignment="middle">
9603 <column alignment="center" valignment="top" width="0pt">
9604 <column alignment="center" valignment="top" width="0pt">
9606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9609 \begin_layout Plain Layout
9615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9618 \begin_layout Plain Layout
9620 \begin_inset Note Note
9623 \begin_layout Plain Layout
9630 is only used as spacer.
9642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9645 \begin_layout Plain Layout
9652 \begin_layout Plain Layout
9666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9669 \begin_layout Plain Layout
9670 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9683 \begin_layout Plain Layout
9690 \begin_layout Plain Layout
9704 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9707 \begin_layout Plain Layout
9708 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
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 $\raisebox{5mm}{}\dddot{A}$
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 $\raisebox{5mm}{}\ddddot{A}$
9794 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9797 \begin_layout Plain Layout
9804 \begin_layout Plain Layout
9814 \begin_inset Index idx
9817 \begin_layout Plain Layout
9828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9831 \begin_layout Plain Layout
9832 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9842 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9845 \begin_layout Plain Layout
9852 \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 $\raisebox{5mm}{}\bar{A}$
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 $\raisebox{5mm}{}\mathring{A}$
9922 \begin_inset space \hfill{}
9926 \begin_inset Tabular
9927 <lyxtabular version="3" rows="7" columns="2">
9928 <features tabularvalignment="middle">
9929 <column alignment="center" valignment="top" width="0pt">
9930 <column alignment="center" valignment="top" width="0pt">
9932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9935 \begin_layout Plain Layout
9941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9944 \begin_layout Plain Layout
9952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9955 \begin_layout Plain Layout
9962 \begin_layout Plain Layout
9976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9979 \begin_layout Plain Layout
9980 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9990 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9993 \begin_layout Plain Layout
10000 \begin_layout Plain Layout
10014 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10017 \begin_layout Plain Layout
10018 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
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 $\raisebox{5mm}{}\check{A}$
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 $\raisebox{5mm}{}\acute{A}$
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 $\raisebox{5mm}{}\grave{A}$
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 $\raisebox{5mm}{}\breve{A}$
10184 \begin_inset space \hfill{}
10190 \begin_layout Standard
10191 \begin_inset VSpace bigskip
10197 \begin_layout Standard
10198 You can directly insert accents like é to formulas.
10199 LyX will transform them to the corresponding accent command.
10201 \begin_inset Index idx
10204 \begin_layout Plain Layout
10210 it is better to insert a quotation mark before the vowel.
10211 These two characters are then treated by LaTeX as
10215 character when the formula part with the umlaut is marked as German.
10223 \begin_inset Quotes eld
10227 \begin_inset Quotes erd
10230 umlauts are created as demonstrated in the following example:
10233 \begin_layout Standard
10234 \begin_inset VSpace -2mm
10240 \begin_layout Standard
10242 \begin_inset Tabular
10243 <lyxtabular version="3" rows="3" columns="2">
10244 <features tabularvalignment="middle">
10245 <column alignment="center" valignment="top" width="0">
10246 <column alignment="center" valignment="top" width="0">
10248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10251 \begin_layout Plain Layout
10257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10260 \begin_layout Plain Layout
10262 \begin_inset Note Note
10265 \begin_layout Plain Layout
10273 \begin_inset space \thinspace{}
10276 pt space are only used as spacer.
10288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10291 \begin_layout Plain Layout
10294 \begin_inset Quotes grd
10302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10305 \begin_layout Plain Layout
10306 \begin_inset space \hspace{}
10313 \begin_inset Formula $"i$
10323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10326 \begin_layout Plain Layout
10333 \begin_layout Plain Layout
10347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10350 \begin_layout Plain Layout
10351 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10367 \begin_layout Standard
10368 Another advantage to
10374 is that umlauts can directly be converted to mathematical text because
10375 the accent commands above are
10381 in mathematical text
10384 To convert an accented character to mathematical text, only the character
10385 under the accent may be converted.
10386 This applies also for all other conversions, e.
10387 \begin_inset space \thinspace{}
10391 \begin_inset space \space{}
10397 \begin_layout Standard
10398 In mathematical text, umlauts and other accented characters can directly
10402 \begin_layout Subsection
10403 Accents for several Characters
10404 \begin_inset Index idx
10407 \begin_layout Plain Layout
10408 Accents ! for several characters
10416 \begin_layout Standard
10417 \begin_inset space \hfill{}
10421 \begin_inset Tabular
10422 <lyxtabular version="3" rows="5" columns="2">
10423 <features tabularvalignment="middle">
10424 <column alignment="center" valignment="top" width="0pt">
10425 <column alignment="center" valignment="top" width="0pt">
10427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10430 \begin_layout Plain Layout
10436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10439 \begin_layout Plain Layout
10441 \begin_inset Note Note
10444 \begin_layout Plain Layout
10451 is only used as spacer.
10463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10466 \begin_layout Plain Layout
10473 \begin_layout Plain Layout
10487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10490 \begin_layout Plain Layout
10491 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10501 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10504 \begin_layout Plain Layout
10511 \begin_layout Plain Layout
10525 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10528 \begin_layout Plain Layout
10529 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10539 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10542 \begin_layout Plain Layout
10549 \begin_layout Plain Layout
10563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10566 \begin_layout Plain Layout
10567 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10577 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10580 \begin_layout Plain Layout
10583 underleftrightarrow
10587 \begin_layout Plain Layout
10601 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10604 \begin_layout Plain Layout
10605 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10619 \begin_inset space \hfill{}
10623 \begin_inset Tabular
10624 <lyxtabular version="3" rows="5" columns="2">
10625 <features tabularvalignment="middle">
10626 <column alignment="center" valignment="top" width="0pt">
10627 <column alignment="center" valignment="top" width="0pt">
10629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10632 \begin_layout Plain Layout
10638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10641 \begin_layout Plain Layout
10649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10652 \begin_layout Plain Layout
10659 \begin_layout Plain Layout
10673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10676 \begin_layout Plain Layout
10677 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10690 \begin_layout Plain Layout
10697 \begin_layout Plain Layout
10711 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10714 \begin_layout Plain Layout
10715 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10725 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10728 \begin_layout Plain Layout
10735 \begin_layout Plain Layout
10749 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10752 \begin_layout Plain Layout
10753 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10763 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10766 \begin_layout Plain Layout
10773 \begin_layout Plain Layout
10787 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10790 \begin_layout Plain Layout
10791 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10805 \begin_inset space \hfill{}
10811 \begin_layout Standard
10812 \begin_inset VSpace medskip
10815 With these commands as many characters as you like can be accented.
10828 will only be set in the output with a length of three characters, as shown
10829 in the following example:
10830 \begin_inset Formula
10832 \widetilde{A+B=C-D}
10840 \begin_layout Standard
10848 \begin_inset Index idx
10851 \begin_layout Plain Layout
10866 \begin_inset Index idx
10869 \begin_layout Plain Layout
10877 described in the previous subsection it is also possible to accent several
10887 \begin_layout Plain Layout
10897 \begin_inset Formula $\downarrow$
10903 \begin_inset Formula
10905 \underset{***}{A=B}
10913 \begin_layout Standard
10914 \begin_inset Newpage newpage
10920 \begin_layout Section
10922 \begin_inset CommandInset label
10929 \begin_inset Index idx
10932 \begin_layout Plain Layout
10941 \begin_layout Subsection
10943 \begin_inset CommandInset label
10945 name "sub:Predefined-Space"
10950 \begin_inset Index idx
10953 \begin_layout Plain Layout
10954 Space ! horizontal ! predefined
10962 \begin_layout Standard
10963 Sometimes it is necessary to insert horizontal space into a formula.
10964 This is done by inserting a protected space (shortcut
10967 arg "command-alternatives space-insert protected ; math-space"
10972 \begin_inset Quotes eld
10981 \begin_layout Plain Layout
10993 \begin_inset Quotes erd
10996 appears and by pressing
11000 several times one can select one of eight different space sizes.
11001 The spaces can also be inserted using the math toolbar button
11002 \begin_inset Graphics
11003 filename ../images/math/space.png
11008 or special commands.
11009 Independent from the inserted command, one can select the size again by
11017 \begin_layout Standard
11020 \begin_inset VSpace -5mm
11024 \begin_inset Tabular
11025 <lyxtabular version="3" rows="3" columns="7">
11026 <features tabularvalignment="middle">
11027 <column alignment="center" valignment="middle" width="6.8cm">
11028 <column alignment="center" valignment="top" width="0">
11029 <column alignment="center" valignment="top" width="0">
11030 <column alignment="center" valignment="top" width="0">
11031 <column alignment="center" valignment="top" width="0">
11032 <column alignment="center" valignment="top" width="0">
11033 <column alignment="center" valignment="top" width="0">
11035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11038 \begin_layout Plain Layout
11044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11047 \begin_layout Plain Layout
11055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11058 \begin_layout Plain Layout
11066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11069 \begin_layout Plain Layout
11077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11080 \begin_layout Plain Layout
11088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11091 \begin_layout Plain Layout
11099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11102 \begin_layout Plain Layout
11112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11115 \begin_layout Plain Layout
11120 keystrokes after inserting the protected space
11125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11128 \begin_layout Plain Layout
11134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11137 \begin_layout Plain Layout
11143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11146 \begin_layout Plain Layout
11152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11155 \begin_layout Plain Layout
11161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11164 \begin_layout Plain Layout
11170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11173 \begin_layout Plain Layout
11181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11184 \begin_layout Plain Layout
11190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11193 \begin_layout Plain Layout
11194 \begin_inset Formula $A\, B$
11202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11205 \begin_layout Plain Layout
11206 \begin_inset Formula $A\: B$
11214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11217 \begin_layout Plain Layout
11218 \begin_inset Formula $A\; B$
11226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11229 \begin_layout Plain Layout
11230 \begin_inset Formula $A\quad B$
11238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11241 \begin_layout Plain Layout
11242 \begin_inset Formula $A\qquad B$
11250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11253 \begin_layout Plain Layout
11254 \begin_inset Formula $A\! B$
11270 \begin_layout Standard
11271 The last size seem to produce no space.
11272 It is displayed red in LyX contrary to the other sizes, because it is a
11274 There are two more negative spaces:
11277 \begin_layout Standard
11279 \begin_inset Tabular
11280 <lyxtabular version="3" rows="3" columns="3">
11281 <features tabularvalignment="middle">
11282 <column alignment="center" valignment="middle" width="6.8cm">
11283 <column alignment="center" valignment="top" width="0pt">
11284 <column alignment="center" valignment="top" width="0pt">
11286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11289 \begin_layout Plain Layout
11295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11298 \begin_layout Plain Layout
11306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11309 \begin_layout Plain Layout
11319 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11322 \begin_layout Plain Layout
11327 keystrokes after inserting the protected space
11332 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11335 \begin_layout Plain Layout
11341 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11344 \begin_layout Plain Layout
11352 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11355 \begin_layout Plain Layout
11361 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11364 \begin_layout Plain Layout
11365 \begin_inset Formula $A\negmedspace B$
11373 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11376 \begin_layout Plain Layout
11377 \begin_inset Formula $A\negthickspace B$
11393 \begin_layout Standard
11394 Negative spaces can lead to characters overlapping each other.
11395 Thus they can be used to enforce ligatures, which are e.
11396 \begin_inset space \thinspace{}
11400 \begin_inset space \space{}
11403 useful for summation operators:
11406 \begin_layout Standard
11408 \begin_inset Tabular
11409 <lyxtabular version="3" rows="3" columns="2">
11410 <features tabularvalignment="middle">
11411 <column alignment="center" valignment="top" width="0">
11412 <column alignment="center" valignment="top" width="0">
11414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11417 \begin_layout Plain Layout
11423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11426 \begin_layout Plain Layout
11428 \begin_inset Note Note
11431 \begin_layout Plain Layout
11438 is only used as spacer.
11450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11453 \begin_layout Plain Layout
11462 \begin_layout Plain Layout
11476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11479 \begin_layout Plain Layout
11480 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11493 \begin_layout Plain Layout
11504 \begin_layout Plain Layout
11518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11521 \begin_layout Plain Layout
11522 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11538 \begin_layout Standard
11539 Relations like for example equal signs, are always surrounded by space.
11540 To suppress this, the equal sign is placed into a TeX-brace.
11541 The following example demonstrates this:
11544 \begin_layout Standard
11546 \begin_inset Tabular
11547 <lyxtabular version="3" rows="2" columns="2">
11548 <features tabularvalignment="middle">
11549 <column alignment="center" valignment="top" width="0pt">
11550 <column alignment="center" valignment="top" width="0pt">
11552 <cell alignment="center" valignment="top" usebox="none">
11555 \begin_layout Plain Layout
11561 <cell alignment="center" valignment="top" usebox="none">
11564 \begin_layout Plain Layout
11565 \begin_inset Formula $A=B$
11575 <cell alignment="center" valignment="top" usebox="none">
11578 \begin_layout Plain Layout
11579 \begin_inset Note Note
11582 \begin_layout Plain Layout
11589 is only used as spacer.
11595 \begin_inset Formula $\raisebox{5mm}{}$
11598 equation without space
11603 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11606 \begin_layout Plain Layout
11607 \begin_inset Formula $A{=}B$
11623 \begin_layout Standard
11625 The command for the last formula is:
11630 \begin_inset Formula $\to$
11636 \begin_layout Standard
11637 \begin_inset VSpace bigskip
11640 Spaces are needed for physical units, because the space between the value
11641 and the unit is the smallest one and not a normal space.
11642 For units in text, the smallest space is inserted via the menu
11644 Insert\SpecialChar \menuseparator
11645 Formatting\SpecialChar \menuseparator
11647 \begin_inset space ~
11655 arg "space-insert thin"
11661 \begin_layout Standard
11662 An example to visualize the difference:
11665 \begin_layout Standard
11666 \begin_inset Tabular
11667 <lyxtabular version="3" rows="2" columns="2">
11668 <features tabularvalignment="middle">
11669 <column alignment="left" valignment="top" width="0">
11670 <column alignment="left" valignment="top" width="0">
11672 <cell alignment="center" valignment="top" usebox="none">
11675 \begin_layout Plain Layout
11677 \begin_inset Formula $\cdot$
11685 <cell alignment="center" valignment="top" usebox="none">
11688 \begin_layout Plain Layout
11689 space between value and unit
11696 <cell alignment="center" valignment="top" usebox="none">
11699 \begin_layout Plain Layout
11701 \begin_inset space \thinspace{}
11705 \begin_inset Formula $\cdot$
11713 <cell alignment="center" valignment="top" usebox="none">
11716 \begin_layout Plain Layout
11717 smallest space between value and unit
11730 \begin_layout Subsection
11735 \begin_layout Plain Layout
11748 \begin_layout Plain Layout
11749 for vertical space in formulas see
11750 \begin_inset CommandInset ref
11752 reference "sub:Line-Separation"
11765 \begin_layout Plain Layout
11773 \begin_inset Note Note
11776 \begin_layout Plain Layout
11779 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11782 \begin_layout Plain Layout
11785 texorpdfstring is in section
11786 \begin_inset CommandInset ref
11788 reference "sub:Formulas-in-Section"
11798 \begin_inset CommandInset label
11800 name "sub:Variable-Space"
11805 \begin_inset Index idx
11808 \begin_layout Plain Layout
11809 Space ! horizontal ! variable
11817 \begin_layout Standard
11818 Space with a defined length can be inserted with the command
11825 \begin_inset Index idx
11828 \begin_layout Plain Layout
11838 \begin_inset Quotes eld
11847 \begin_layout Plain Layout
11859 \begin_inset Quotes erd
11863 The length can be specified by left-clicking on the
11864 \begin_inset Quotes eld
11873 \begin_layout Plain Layout
11885 \begin_inset Quotes erd
11889 The length may also be negative.
11890 To insert as much space as is available, the command
11897 \begin_inset Index idx
11900 \begin_layout Plain Layout
11911 \begin_layout Standard
11912 \begin_inset VSpace -1mm
11918 \begin_layout Standard
11920 \begin_inset Tabular
11921 <lyxtabular version="3" rows="4" columns="2">
11922 <features tabularvalignment="middle">
11923 <column alignment="center" valignment="top" width="0">
11924 <column alignment="center" valignment="top" width="0">
11926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11929 \begin_layout Plain Layout
11937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11940 \begin_layout Plain Layout
11948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11951 \begin_layout Plain Layout
11958 \begin_layout Plain Layout
11968 \begin_inset Formula $\to$
11974 \begin_inset space \thinspace{}
11982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11985 \begin_layout Plain Layout
11986 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11999 \begin_layout Plain Layout
12006 \begin_layout Plain Layout
12016 \begin_inset Formula $\to$
12022 \begin_inset space \thinspace{}
12030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12033 \begin_layout Plain Layout
12034 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12047 \begin_layout Plain Layout
12054 \begin_layout Plain Layout
12068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12071 \begin_layout Plain Layout
12072 \begin_inset Formula $A=A\hfill B=B$
12088 \begin_layout Standard
12089 In the last example the available space is given by the longest column entry
12091 In an inline formula the space depends on the length of the line in which
12099 Thus, when the line uses the full width, no space will be created.
12106 only has an effect on displayed formulas when the formula style
12111 (Formula styles are explained in
12112 \begin_inset CommandInset ref
12114 reference "sec:Formula-Styles"
12121 \begin_layout Standard
12128 , there are the commands
12140 that fill the space with a pattern, see
12141 \begin_inset CommandInset ref
12143 reference "sub:Ellipses"
12150 \begin_layout Standard
12151 For text, variable space can be inserted via the menu
12153 Insert\SpecialChar \menuseparator
12154 Formatting\SpecialChar \menuseparator
12156 \begin_inset space ~
12164 \begin_layout Standard
12165 This is a line with
12166 \begin_inset space \hspace{}
12171 \begin_inset space \thinspace{}
12177 \begin_layout Standard
12178 This is a line with
12179 \begin_inset space \hfill{}
12185 \begin_layout Subsection
12186 Space besides inline Formulas
12187 \begin_inset Index idx
12190 \begin_layout Plain Layout
12191 Space ! besides inline formulas
12199 \begin_layout Standard
12200 The space that surrounds inline formulas can be adjusted with the length
12208 \begin_inset Index idx
12211 \begin_layout Plain Layout
12220 The value of a length is set with the command
12227 \begin_inset Index idx
12230 \begin_layout Plain Layout
12238 which has the following scheme:
12241 \begin_layout Standard
12246 setlength{length name}{value}
12249 \begin_layout Standard
12257 \begin_inset space \thinspace{}
12263 \begin_layout Standard
12273 \begin_layout Standard
12274 is inserted in TeX-mode.
12276 \begin_inset space \thinspace{}
12279 mm space will now be set around all inline formulas:
12283 \begin_layout Plain Layout
12297 \begin_layout Standard
12298 This is a line with an inline formula
12299 \begin_inset Formula $A=B$
12303 \begin_inset space \thinspace{}
12306 mm surrounding space.
12310 \begin_layout Plain Layout
12324 \begin_layout Standard
12325 To return to the predefined value,
12331 is set to the value 0
12332 \begin_inset space \thinspace{}
12338 \begin_layout Section
12340 \begin_inset Index idx
12343 \begin_layout Plain Layout
12350 \begin_inset Index idx
12353 \begin_layout Plain Layout
12358 \begin_layout Plain Layout
12369 \begin_layout Plain Layout
12384 \begin_layout Standard
12385 Boxes for text are described in chapter
12392 \begin_inset space ~
12400 \begin_layout Subsection
12402 \begin_inset CommandInset label
12404 name "sub:Boxes-with-Frame"
12409 \begin_inset Index idx
12412 \begin_layout Plain Layout
12421 \begin_layout Standard
12422 It is possible to frame a formula or part of one with the commands
12429 \begin_inset Index idx
12432 \begin_layout Plain Layout
12447 \begin_inset Index idx
12450 \begin_layout Plain Layout
12461 \begin_layout Standard
12462 When one of these commands is inserted in a formula, a blue box appears
12463 within a frame to enter formula parts.
12470 an additional formula has to be created by
12474 within this box, because the box content will otherwise be treated as mathemati
12482 is used, a new formula is automatically created inside the frame.
12485 \begin_layout Standard
12492 is not suitable to frame displayed formulas because the formula will always
12493 be set in the size of the text.
12500 is in contrary not suitable to frame inline formulas, because the formula
12501 will always be set in the size of a displayed formula.
12504 \begin_layout Standard
12518 \begin_inset Index idx
12521 \begin_layout Plain Layout
12529 where additionally the frame width and the alignment can be specified.
12536 is used in the following scheme:
12539 \begin_layout Standard
12544 framebox[frame width][position]{box content}
12547 \begin_layout Standard
12548 The position can either be
12565 right aligns the formula in the box.
12566 When no position is given, the formula will be centered.
12567 \begin_inset Newline newline
12570 If no width is given, also no position can be given.
12571 In this case the frame width is adjusted to the box content like for
12580 \begin_layout Standard
12587 is inserted, a box appears containing three blue boxes.
12588 The first two boxes are surrounded by brackets and denote the two optional
12590 The third box is for formula parts like for
12599 \begin_layout Standard
12600 \begin_inset Newpage newpage
12606 \begin_layout Standard
12608 \begin_inset Tabular
12609 <lyxtabular version="3" rows="5" columns="2">
12610 <features tabularvalignment="middle">
12611 <column alignment="center" valignment="top" width="0">
12612 <column alignment="center" valignment="top" width="0">
12614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12617 \begin_layout Plain Layout
12623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12626 \begin_layout Plain Layout
12628 \begin_inset Note Note
12631 \begin_layout Plain Layout
12638 is only used as spacer.
12650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12653 \begin_layout Plain Layout
12660 \begin_layout Plain Layout
12679 \begin_layout Plain Layout
12693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12696 \begin_layout Plain Layout
12697 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12710 \begin_layout Plain Layout
12717 \begin_layout Plain Layout
12732 \begin_layout Plain Layout
12746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12749 \begin_layout Plain Layout
12750 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12763 \begin_layout Plain Layout
12770 \begin_layout Plain Layout
12784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12787 \begin_layout Plain Layout
12788 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12801 \begin_layout Plain Layout
12808 \begin_layout Plain Layout
12818 \begin_inset Formula $\to$
12822 \begin_inset Formula $\to$
12835 \begin_layout Plain Layout
12845 \begin_inset Formula $\downarrow$
12853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12856 \begin_layout Plain Layout
12857 \begin_inset Formula $\raisebox{6mm}{}$
12861 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12865 \begin_inset Formula $\raisebox{-4mm}{}$
12881 \begin_layout Standard
12882 The frame thickness can also be adjusted.
12883 To do this the following commands have to be inserted in TeX-mode before
12887 \begin_layout Standard
12897 \begin_inset Quotes eld
12901 \begin_inset Quotes erd
12915 \begin_inset Quotes eld
12919 \begin_inset Quotes erd
12925 \begin_layout Standard
12926 \begin_inset Quotes eld
12930 \begin_inset Quotes erd
12933 specifies the minimal distance between the frame and the first character
12935 An example for this is the following framed formula:
12939 \begin_layout Plain Layout
12951 \begin_inset Formula
12958 Before this formula the commands
12961 \begin_layout Standard
12983 \begin_layout Standard
12984 were inserted in TeX-mode.
12985 The given values are used for all following boxes.
12988 \begin_layout Standard
12989 To return to the standard frame size, the command
12992 \begin_layout Standard
13017 \begin_layout Plain Layout
13031 \begin_layout Standard
13032 is inserted in TeX-mode before the next formula.
13035 \begin_layout Subsection
13036 Boxes without Frame
13037 \begin_inset CommandInset label
13039 name "sub:Boxes-without-Frame"
13044 \begin_inset Index idx
13047 \begin_layout Plain Layout
13048 Boxes ! without frame
13056 \begin_layout Standard
13057 For boxes without a frame there are the following box commands:
13064 \begin_inset Index idx
13067 \begin_layout Plain Layout
13082 \begin_inset Index idx
13085 \begin_layout Plain Layout
13100 \begin_inset Index idx
13103 \begin_layout Plain Layout
13114 \begin_layout Standard
13121 a box can be super- or subscripted.
13122 But in contrary to normal super- and subscripting, the characters in the
13123 box keep their font size.
13130 is used in the following scheme:
13133 \begin_layout Standard
13138 raisebox{height}{box content}
13141 \begin_layout Standard
13142 When the box should contain a formula, an extra formula is needed like for
13153 \begin_inset Note Greyedout
13156 \begin_layout Plain Layout
13167 this extra formula is created by pressing
13171 twice instead of once because LyX doesn't yet support
13185 \begin_layout Standard
13187 \begin_inset Tabular
13188 <lyxtabular version="3" rows="4" columns="2">
13189 <features tabularvalignment="middle">
13190 <column alignment="center" valignment="top" width="0">
13191 <column alignment="center" valignment="top" width="0">
13193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13196 \begin_layout Plain Layout
13202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13205 \begin_layout Plain Layout
13213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13216 \begin_layout Plain Layout
13220 \begin_inset Formula $\to$
13226 \begin_inset Formula $\to$
13234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13237 \begin_layout Plain Layout
13238 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13251 \begin_layout Plain Layout
13255 \begin_inset Formula $\to$
13261 \begin_inset Formula $\to$
13269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13272 \begin_layout Plain Layout
13273 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13286 \begin_layout Plain Layout
13290 \begin_inset Formula $\to$
13309 \begin_layout Plain Layout
13323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13326 \begin_layout Plain Layout
13327 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13343 \begin_layout Standard
13368 , with the difference that there is no frame.
13371 \begin_layout Subsection
13373 \begin_inset CommandInset label
13375 name "sub:Colored-Boxes"
13380 \begin_inset Index idx
13383 \begin_layout Plain Layout
13392 \begin_layout Standard
13393 To be able to use all commands explained in this section, the LaTeX-package
13402 \begin_layout Plain Layout
13407 is part of every LaTeX standard installation.
13413 \begin_inset Index idx
13416 \begin_layout Plain Layout
13422 has to be loaded in the LaTeX-preamble with the line
13426 \begin_layout Plain Layout
13427 When text is colored somewhere in the document with a predefined color,
13428 LyX loads the LaTeX-package
13433 Thus it is possible that the package is loaded twice, but this does not
13440 \begin_inset Note Note
13443 \begin_layout Plain Layout
13444 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13453 \begin_layout Standard
13461 \begin_layout Standard
13462 \begin_inset VSpace medskip
13465 To color boxes, the command
13472 \begin_inset Index idx
13475 \begin_layout Plain Layout
13483 is used in the following scheme:
13486 \begin_layout Standard
13491 colorbox{color}{box content}
13494 \begin_layout Standard
13495 The box content can also be a box and a
13501 can also be part of another box (see the 2nd and 3rd example).
13502 When the box should contain a formula, an extra formula has to be created,
13503 the same way as for
13513 \begin_layout Plain Layout
13514 This also applies for the command
13528 \begin_layout Standard
13529 One of the following predefined colors can be chosen:
13532 \begin_layout Standard
13566 \begin_layout Standard
13568 \begin_inset Tabular
13569 <lyxtabular version="3" rows="4" columns="2">
13570 <features tabularvalignment="middle">
13571 <column alignment="center" valignment="top" width="0">
13572 <column alignment="center" valignment="top" width="0">
13574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13577 \begin_layout Plain Layout
13583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13586 \begin_layout Plain Layout
13588 \begin_inset Note Note
13591 \begin_layout Plain Layout
13598 is only used as spacer.
13610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13613 \begin_layout Plain Layout
13617 \begin_inset Formula $\to$
13627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13630 \begin_layout Plain Layout
13631 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13644 \begin_layout Plain Layout
13648 \begin_inset Formula $\to$
13659 \begin_layout Plain Layout
13673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13676 \begin_layout Plain Layout
13677 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13690 \begin_layout Plain Layout
13697 \begin_layout Plain Layout
13709 \begin_inset Formula $\to$
13728 \begin_layout Plain Layout
13742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13745 \begin_layout Plain Layout
13746 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13762 \begin_layout Standard
13769 only colors the box but not the characters in the box.
13770 To color all characters, the whole formula is highlighted and the desired
13771 color is chosen in the
13774 \begin_inset space ~
13780 The dialog can be called with the toolbar button
13781 \begin_inset Graphics
13782 filename ../images/dialog-show_character.png
13789 Edit\SpecialChar \menuseparator
13791 \begin_inset space ~
13794 Style\SpecialChar \menuseparator
13798 The formula number then has the same color as the formula.
13799 When the formula number should get another color than the formula characters,
13800 the color must be changed within the formula.
13803 \begin_layout Standard
13807 \begin_layout Standard
13810 \begin_inset Formula
13812 \int A=B\label{eq:red}
13820 \begin_inset Formula
13822 \textcolor{red}{\int A=B}\label{eq:redgreen}
13830 \begin_layout Standard
13832 \begin_inset CommandInset ref
13838 is completely colored red.
13839 \begin_inset Newline newline
13843 \begin_inset CommandInset ref
13845 reference "eq:redgreen"
13849 was first completely colored green to set the color for the formula number.
13850 Subsequently the formula characters were colored red.
13853 \begin_layout Standard
13854 \begin_inset VSpace bigskip
13857 To color the frame different than the rest of the box, the command
13864 \begin_inset Index idx
13867 \begin_layout Plain Layout
13875 is used in the following scheme:
13878 \begin_layout Standard
13883 fcolorbox{frame color}{color}{box content}
13886 \begin_layout Standard
13893 is an extension of the command
13900 The frame width is set, like for
13923 \begin_layout Plain Layout
13935 \begin_inset Formula
13937 \fcolorbox{cyan}{magenta}{A=B}
13946 \begin_layout Plain Layout
13960 \begin_layout Standard
13961 This formula was created with the command
13962 \begin_inset Newline newline
13970 \begin_inset Formula $\to$
13976 \begin_inset Formula $\to$
13986 \begin_layout Standard
13987 \begin_inset VSpace bigskip
13990 To use other colors than the predefined ones, they have to be defined first.
13993 \begin_layout Standard
13994 One can for example define the color
13995 \begin_inset Quotes eld
14003 \begin_inset Quotes erd
14006 with the LaTeX-preamble line:
14009 \begin_layout Standard
14014 definecolor{darkgreen}{cmyk}{0.5,
14029 \begin_inset Index idx
14032 \begin_layout Plain Layout
14043 \begin_layout Standard
14048 is the color space that denotes the colors
14065 The four comma separated numbers are the portion factor for the corresponding
14066 colors of the color space.
14067 The factors can be in the range of 0
14068 \begin_inset space \thinspace{}
14072 \begin_inset space \thinspace{}
14080 also the color space
14084 can be used for definitions.
14101 , so that there are in this case three portion factors for the corresponding
14103 Furthermore there is the color space
14107 with one portion factor for the gray value.
14110 \begin_layout Standard
14111 As example a framed box with the new defined color
14115 where the characters have been colored
14120 \begin_inset Formula
14122 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14130 \begin_layout Standard
14131 Self-defined colors can also be used for text with the help of the command
14139 \begin_inset Index idx
14142 \begin_layout Plain Layout
14151 \begin_layout Standard
14155 \begin_layout Plain Layout
14159 textcolor{darkgreen}{
14165 \begin_inset Quotes eld
14169 \begin_inset Quotes erd
14176 \begin_layout Plain Layout
14186 \begin_layout Standard
14194 \begin_inset Index idx
14197 \begin_layout Plain Layout
14205 is used in the scheme
14209 textcolor{color}{characters to color}
14214 \begin_layout Subsection
14216 \begin_inset CommandInset label
14218 name "sub:Paragraph-Boxes"
14223 \begin_inset Index idx
14226 \begin_layout Plain Layout
14227 Boxes ! as paragraph
14235 \begin_layout Standard
14236 A box that can contain several lines and paragraphs, a so-called paragraph
14237 box (parbox), can be created with the menu
14239 Insert\SpecialChar \menuseparator
14242 or the toolbar button
14243 \begin_inset Graphics
14244 filename ../images/box-insert.png
14252 \begin_layout Standard
14253 The following example shows a framed parbox in a line:
14256 \begin_layout Standard
14257 \begin_inset VSpace medskip
14261 \begin_inset Box Boxed
14271 height_special "totalheight"
14274 \begin_layout Plain Layout
14275 This is a paragraph box.
14277 \begin_inset space \thinspace{}
14280 cm long and can also contain formulas:
14281 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14292 \begin_layout Standard
14293 \begin_inset VSpace medskip
14299 \begin_layout Standard
14300 Such a box is created by right-clicking on the gray box inset.
14301 A dialog pops up showing the box properties.
14315 \begin_inset space \thinspace{}
14320 Vertical Box Alignment
14325 \begin_layout Standard
14326 \begin_inset VSpace medskip
14329 In LaTeX a parbox is created with the command
14336 \begin_inset Index idx
14339 \begin_layout Plain Layout
14347 which has the following scheme:
14350 \begin_layout Standard
14355 parbox[position]{width}{box content}
14358 \begin_layout Standard
14373 \begin_inset Quotes eld
14377 \begin_inset Quotes erd
14380 means that the box is aligned within the surrounding text with its last
14387 \begin_inset Quotes eld
14391 \begin_inset Quotes erd
14394 this is done with the first line.
14395 When no position is given, the box will be vertically centered, see section
14403 \begin_inset space ~
14408 manual for examples.
14411 \begin_layout Standard
14412 \begin_inset VSpace bigskip
14415 To frame formulas completely, including the formula number, the formula
14416 must be set into a parbox.
14417 To do this, the command
14431 is inserted in TeX-mode before the formula.
14439 \begin_inset Index idx
14442 \begin_layout Plain Layout
14450 is hereby the line width set for the document.
14451 Because the frame is outside the parbox, 2
14452 \begin_inset space \thinspace{}
14455 times the frame separation and the frame thickness must be subtracted from
14457 As this is not automatically done by LyX due to a bug
14461 \begin_layout Plain Layout
14462 \begin_inset CommandInset href
14464 name "LyX-bug #4483"
14465 target "http://www.lyx.org/trac/ticket/4483"
14474 , TeX-mode has to be used.
14475 To be able to multiply and subtract in arguments, the LaTeX-package
14483 \begin_layout Plain Layout
14488 is part of every LaTeX standard installation.
14494 \begin_inset Index idx
14497 \begin_layout Plain Layout
14503 must be loaded in the LaTeX-preamble with the line
14506 \begin_layout Standard
14514 \begin_layout Standard
14515 Behind the formula both boxes are closed by entering
14520 Here is an example:
14524 \begin_layout Plain Layout
14538 \begin_layout Standard
14542 \begin_layout Plain Layout
14560 \begin_inset Formula
14562 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14571 \begin_layout Plain Layout
14582 \begin_layout Plain Layout
14596 \begin_layout Standard
14597 \begin_inset VSpace medskip
14600 As a parbox is used as the argument of
14606 , there is in this case no difference between
14621 \begin_layout Standard
14622 \begin_inset VSpace bigskip
14625 Paragraph boxes are very useful to comment formulas directly.
14632 is used in combination with the command
14646 \begin_inset CommandInset ref
14648 reference "sub:User-defined-Numbering"
14655 \begin_layout Standard
14656 An example of a formula commented with
14665 \begin_layout Standard
14669 \begin_layout Plain Layout
14682 This is a description.
14683 It is distinctly separated from the formula and multiline.
14687 \begin_layout Plain Layout
14699 \begin_layout Standard
14700 Such a formula must be inserted completely in TeX-mode because LyX does
14701 not yet support the command
14708 The formula is created with the following command sequence:
14711 \begin_layout Standard
14724 is inserted in TeX-mode.
14728 \begin_layout Plain Layout
14729 When the formula style
14741 can also be replaced by
14748 (formula styles see
14749 \begin_inset CommandInset ref
14751 reference "sec:Formula-Styles"
14760 Then the description follows as normal text and finally
14766 is inserted in TeX-mode.
14779 hereby create a displayed formula.
14782 \begin_layout Standard
14789 can be seen in this example that was
14790 \begin_inset Quotes eld
14794 \begin_inset Quotes erd
14797 using the mathematical textmode:
14798 \begin_inset Formula
14800 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14808 \begin_layout Section
14810 \begin_inset Index idx
14813 \begin_layout Plain Layout
14822 \begin_layout Subsection
14824 \begin_inset CommandInset label
14826 name "sub:Big-Operators"
14831 \begin_inset Index idx
14834 \begin_layout Plain Layout
14841 \begin_inset Index idx
14844 \begin_layout Plain Layout
14851 \begin_inset Index idx
14854 \begin_layout Plain Layout
14863 \begin_layout Standard
14864 To be able to use all integral operators listed here, the option
14866 Use esint package automatically
14868 must be set in the document settings under
14871 \begin_inset space ~
14879 \begin_layout Standard
14880 \begin_inset space \hfill{}
14884 \begin_inset Tabular
14885 <lyxtabular version="3" rows="11" columns="2">
14886 <features tabularvalignment="middle">
14887 <column alignment="center" valignment="top" width="0pt">
14888 <column alignment="center" valignment="top" width="0pt">
14890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14893 \begin_layout Plain Layout
14899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14902 \begin_layout Plain Layout
14910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14913 \begin_layout Plain Layout
14917 \begin_inset Index idx
14920 \begin_layout Plain Layout
14933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14936 \begin_layout Plain Layout
14937 \begin_inset Formula $\int$
14947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14950 \begin_layout Plain Layout
14958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14961 \begin_layout Plain Layout
14962 \begin_inset Formula $\oint$
14972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14975 \begin_layout Plain Layout
14983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14986 \begin_layout Plain Layout
14987 \begin_inset Formula $\ointctrclockwise$
14997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15000 \begin_layout Plain Layout
15008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15011 \begin_layout Plain Layout
15012 \begin_inset Formula $\ointclockwise$
15022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15025 \begin_layout Plain Layout
15033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15036 \begin_layout Plain Layout
15037 \begin_inset Formula $\sqint$
15047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15050 \begin_layout Plain Layout
15058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15061 \begin_layout Plain Layout
15063 \begin_inset Formula $\fint$
15073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15076 \begin_layout Plain Layout
15084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15087 \begin_layout Plain Layout
15089 \begin_inset Formula $\landupint$
15099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15102 \begin_layout Plain Layout
15110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15113 \begin_layout Plain Layout
15115 \begin_inset Formula $\landdownint$
15125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15128 \begin_layout Plain Layout
15136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15139 \begin_layout Plain Layout
15140 \begin_inset Formula $\bigcap$
15150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15153 \begin_layout Plain Layout
15161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15164 \begin_layout Plain Layout
15165 \begin_inset Formula $\bigcup$
15179 \begin_inset space \hfill{}
15183 \begin_inset Tabular
15184 <lyxtabular version="3" rows="11" columns="2">
15185 <features tabularvalignment="middle">
15186 <column alignment="center" valignment="top" width="0pt">
15187 <column alignment="center" valignment="top" width="0pt">
15189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15192 \begin_layout Plain Layout
15198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15201 \begin_layout Plain Layout
15209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15212 \begin_layout Plain Layout
15216 \begin_inset Index idx
15219 \begin_layout Plain Layout
15232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15235 \begin_layout Plain Layout
15236 \begin_inset Formula $\sum$
15246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15249 \begin_layout Plain Layout
15253 \begin_inset Index idx
15256 \begin_layout Plain Layout
15263 \begin_layout Plain Layout
15282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15285 \begin_layout Plain Layout
15286 \begin_inset Formula $\prod$
15296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15299 \begin_layout Plain Layout
15307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15310 \begin_layout Plain Layout
15311 \begin_inset Formula $\coprod$
15321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15324 \begin_layout Plain Layout
15332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15335 \begin_layout Plain Layout
15336 \begin_inset Formula $\bigodot$
15346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15349 \begin_layout Plain Layout
15357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15360 \begin_layout Plain Layout
15361 \begin_inset Formula $\bigotimes$
15371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15374 \begin_layout Plain Layout
15382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15385 \begin_layout Plain Layout
15386 \begin_inset Formula $\bigoplus$
15396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15399 \begin_layout Plain Layout
15407 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15410 \begin_layout Plain Layout
15411 \begin_inset Formula $\bigwedge$
15421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15424 \begin_layout Plain Layout
15432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15435 \begin_layout Plain Layout
15436 \begin_inset Formula $\bigvee$
15446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15449 \begin_layout Plain Layout
15457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15460 \begin_layout Plain Layout
15461 \begin_inset Formula $\bigsqcup$
15471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15474 \begin_layout Plain Layout
15482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15485 \begin_layout Plain Layout
15486 \begin_inset Formula $\biguplus$
15500 \begin_inset space \hfill{}
15506 \begin_layout Standard
15507 All big operators can also be inserted via the math toolbar button
15508 \begin_inset Graphics
15509 filename ../images/math/intop.png
15517 \begin_layout Standard
15518 The operators are called big because they are bigger than the sometimes
15519 equal looking binary operators.
15520 All big operators can have limits as described in the next subsection.
15523 \begin_layout Standard
15524 For all integral operators there is a second version available, ending in
15542 These operators are different from
15549 \begin_inset space \space{}
15552 in the style the operator limits are displayed, see
15553 \begin_inset CommandInset ref
15555 reference "sub:Operator-Limits"
15563 \begin_layout Subsubsection*
15564 Advice for Integrals
15567 \begin_layout Standard
15572 in an integral is an operator, that therefore has to be set upright.
15573 This is done by highlighting the
15577 and using the keyboard shortcut
15587 \begin_layout Plain Layout
15593 \begin_inset CommandInset ref
15595 reference "sub:Font-Styles"
15605 Finally the smallest space is inserted before the
15609 , as this is usual for operators.
15613 \begin_layout Standard
15615 \begin_inset Formula $\int A(x)dx$
15619 \begin_inset Newline newline
15623 \begin_inset Phantom HPhantom
15626 \begin_layout Plain Layout
15633 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15639 \begin_layout Standard
15640 For multiple integrals there are the following commands:
15641 \begin_inset VSpace medskip
15647 \begin_layout Standard
15648 \begin_inset space \hfill{}
15652 \begin_inset Tabular
15653 <lyxtabular version="3" rows="4" columns="2">
15654 <features tabularvalignment="middle">
15655 <column alignment="center" valignment="top" width="0">
15656 <column alignment="center" valignment="top" width="0">
15658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15661 \begin_layout Plain Layout
15667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15670 \begin_layout Plain Layout
15672 \begin_inset Note Note
15675 \begin_layout Plain Layout
15682 is only used as spacer.
15694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15697 \begin_layout Plain Layout
15705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15708 \begin_layout Plain Layout
15709 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15722 \begin_layout Plain Layout
15730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15733 \begin_layout Plain Layout
15734 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15747 \begin_layout Plain Layout
15755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15758 \begin_layout Plain Layout
15759 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15773 \begin_inset space \hfill{}
15777 \begin_inset Tabular
15778 <lyxtabular version="3" rows="4" columns="2">
15779 <features tabularvalignment="middle">
15780 <column alignment="center" valignment="top" width="0">
15781 <column alignment="center" valignment="top" width="0">
15783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15786 \begin_layout Plain Layout
15792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15795 \begin_layout Plain Layout
15803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15806 \begin_layout Plain Layout
15814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15817 \begin_layout Plain Layout
15818 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15831 \begin_layout Plain Layout
15839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15842 \begin_layout Plain Layout
15843 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15856 \begin_layout Plain Layout
15864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15867 \begin_layout Plain Layout
15868 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15882 \begin_inset space \hfill{}
15888 \begin_layout Standard
15889 \begin_inset Newpage newpage
15895 \begin_layout Subsection
15897 \begin_inset CommandInset label
15899 name "sub:Operator-Limits"
15904 \begin_inset Index idx
15907 \begin_layout Plain Layout
15916 \begin_layout Standard
15917 Limits are created by super- and subscripts:
15920 \begin_layout Standard
15922 \begin_inset Tabular
15923 <lyxtabular version="3" rows="2" columns="2">
15924 <features tabularvalignment="middle">
15925 <column alignment="center" valignment="top" width="0pt">
15926 <column alignment="center" valignment="top" width="0pt">
15928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15931 \begin_layout Plain Layout
15937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15940 \begin_layout Plain Layout
15942 \begin_inset Note Note
15945 \begin_layout Plain Layout
15952 is only used as spacer.
15964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15967 \begin_layout Plain Layout
15976 \begin_layout Plain Layout
15986 \begin_inset Formula $\to$
15990 \begin_inset Formula $\to$
15998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16001 \begin_layout Plain Layout
16002 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16018 \begin_layout Standard
16019 Limits of inline formulas are set right beside the operator.
16020 Limits in displayed formulas are set above or below the operator, except
16021 for integral limits.
16024 \begin_layout Standard
16025 To force that the limits are set beside the operator, the cursor is set
16026 directly behind the operator and the limits type is changed with the menu
16029 Edit\SpecialChar \menuseparator
16030 Math\SpecialChar \menuseparator
16049 \begin_layout Standard
16050 The default limits type is this:
16051 \begin_inset Formula
16053 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16058 This is how it looks when the limits type was changed to
16065 \begin_inset Formula
16067 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16072 For integrals, except those ending with
16088 etc., the limits are by default set beside the operator.
16089 But for multiple integrals the limits are often set below the operator.
16090 In the following example the limits type was therefore set to
16094 and so set below the integrals:
16095 \begin_inset Formula
16097 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16105 \begin_layout Standard
16106 \begin_inset VSpace medskip
16109 To specify conditions for limits, the commands
16116 \begin_inset Index idx
16119 \begin_layout Plain Layout
16134 \begin_inset Index idx
16137 \begin_layout Plain Layout
16146 To create for example this expression
16147 \begin_inset Formula
16149 \sum_{\begin{subarray}{c}
16153 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16161 \begin_layout Standard
16162 the following has to be done:
16163 \begin_inset Newline newline
16178 \begin_layout Plain Layout
16190 One is now in a blue box under the summation operator and insert there
16199 \begin_layout Plain Layout
16211 The blue box is now within a purple box and now several lines can be written
16213 A new line is created by inserting a line break (
16216 arg "newline-insert newline"
16221 \begin_inset Newline newline
16226 0<k<1000 Ctrl+Return
16227 \begin_inset Newline newline
16232 is typed in, a new box appears below for the new line.
16235 \begin_layout Standard
16236 The alignment of the lines can be changed to left aligned with the
16246 Edit\SpecialChar \menuseparator
16250 To get right alignment,
16258 \begin_layout Plain Layout
16269 is inserted at the beginning of the line.
16272 \begin_layout Standard
16285 with the difference that the lines are always centered.
16288 \begin_layout Standard
16289 \begin_inset VSpace bigskip
16293 \begin_inset CommandInset ref
16295 reference "eq:substack"
16299 there can be too much space beside an operator, because the characters
16300 following the operator are set beside the limits.
16303 \begin_layout Standard
16304 To avoid this, the following macro can be used in the LaTeX-preamble:
16307 \begin_layout Standard
16321 \begin_inset Newline newline
16333 \begin_inset Newline newline
16340 mathclapinternal #1#2{
16344 mathsurround =0pt #1{#2}$}}
16347 \begin_layout Standard
16348 This defines the command
16355 \begin_inset Index idx
16358 \begin_layout Plain Layout
16366 that sets the width of the limit to 0
16367 \begin_inset space \thinspace{}
16371 The command scheme is
16374 \begin_layout Standard
16382 \begin_layout Standard
16383 where the limit can consist of several conditions.
16386 \begin_layout Standard
16388 \begin_inset CommandInset ref
16390 reference "eq:substack"
16394 , one uses the command
16397 \begin_layout Standard
16410 \begin_layout Plain Layout
16419 0<k<1000 Ctrl+Return
16422 \begin_layout Standard
16423 to create the lower limit.
16424 The summand is now directly behind the summation operator:
16425 \begin_inset Formula
16427 \sum_{\mathclap{\substack{0<k<1000\\
16439 \begin_layout Standard
16440 \begin_inset VSpace bigskip
16443 How to use one limit for several operators is described in
16444 \begin_inset CommandInset ref
16446 reference "sub:Self-defined-Operators"
16453 \begin_layout Subsection
16454 Decoration for Operators
16455 \begin_inset Index idx
16458 \begin_layout Plain Layout
16459 Operators ! Decoration
16467 \begin_layout Standard
16475 \begin_inset Index idx
16478 \begin_layout Plain Layout
16493 \begin_inset Index idx
16496 \begin_layout Plain Layout
16504 characters can be placed above or below an operator, respectively.
16512 \begin_inset Index idx
16515 \begin_layout Plain Layout
16523 characters can be set before and behind a big operator.
16524 The command scheme is:
16527 \begin_layout Standard
16543 \begin_layout Standard
16550 must always be before the operator.
16551 You can decorate with several characters and even with other operators
16553 To place for example only characters behind a big operator, write nothing
16554 between the first braces but don't omit the braces.
16557 \begin_layout Standard
16558 For example the command
16563 \begin_inset Formula $\to$
16573 \begin_inset Formula $\to$
16582 \begin_layout Plain Layout
16598 \begin_inset Formula
16600 \sideset{}{'}\sum_{k=1}^{n}
16608 \begin_layout Standard
16609 \begin_inset Note Greyedout
16612 \begin_layout Plain Layout
16619 can only be used to decorate big operators, binary operators are not allowed.
16627 \begin_layout Standard
16640 can also be used to decorate symbols and characters.
16641 For example, the command
16649 \begin_layout Plain Layout
16664 \begin_layout Plain Layout
16676 \begin_inset Formula $\uparrow$
16684 \begin_inset Formula
16686 \overset{a}{\maltese}
16694 \begin_layout Subsection
16696 \begin_inset CommandInset label
16698 name "sub:Binary-Operators"
16703 \begin_inset Index idx
16706 \begin_layout Plain Layout
16715 \begin_layout Standard
16716 Binary operators are surrounded by space when there is a character before
16718 \begin_inset VSpace medskip
16724 \begin_layout Standard
16725 \begin_inset space \hfill{}
16729 \begin_inset Tabular
16730 <lyxtabular version="3" rows="13" columns="2">
16731 <features tabularvalignment="middle">
16732 <column alignment="center" valignment="top" width="0pt">
16733 <column alignment="center" valignment="top" width="0pt">
16735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16738 \begin_layout Plain Layout
16740 \begin_inset Note Note
16743 \begin_layout Plain Layout
16750 is only used as spacer.
16760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16763 \begin_layout Plain Layout
16771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16774 \begin_layout Plain Layout
16780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16783 \begin_layout Plain Layout
16784 \begin_inset Formula $+$
16794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16797 \begin_layout Plain Layout
16803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16806 \begin_layout Plain Layout
16807 \begin_inset Formula $-$
16817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16820 \begin_layout Plain Layout
16828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16831 \begin_layout Plain Layout
16832 \begin_inset Formula $\pm$
16842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16845 \begin_layout Plain Layout
16853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16856 \begin_layout Plain Layout
16857 \begin_inset Formula $\mp$
16867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16870 \begin_layout Plain Layout
16878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16881 \begin_layout Plain Layout
16882 \begin_inset Formula $\cdot$
16892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16895 \begin_layout Plain Layout
16903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16906 \begin_layout Plain Layout
16907 \begin_inset Formula $\times$
16917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16920 \begin_layout Plain Layout
16928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16931 \begin_layout Plain Layout
16932 \begin_inset Formula $\div$
16942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16945 \begin_layout Plain Layout
16949 \begin_layout Plain Layout
16962 \begin_layout Plain Layout
16974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16977 \begin_layout Plain Layout
16978 \begin_inset Formula $*$
16988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16991 \begin_layout Plain Layout
16999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17002 \begin_layout Plain Layout
17003 \begin_inset Formula $\star$
17013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17016 \begin_layout Plain Layout
17024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17027 \begin_layout Plain Layout
17028 \begin_inset Formula $\circ$
17038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17041 \begin_layout Plain Layout
17049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17052 \begin_layout Plain Layout
17053 \begin_inset Formula $\diamond$
17063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17066 \begin_layout Plain Layout
17074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17077 \begin_layout Plain Layout
17078 \begin_inset Formula $\bullet$
17092 \begin_inset space \hfill{}
17096 \begin_inset Tabular
17097 <lyxtabular version="3" rows="13" columns="2">
17098 <features tabularvalignment="middle">
17099 <column alignment="center" valignment="top" width="0pt">
17100 <column alignment="center" valignment="top" width="0pt">
17102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17105 \begin_layout Plain Layout
17111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17114 \begin_layout Plain Layout
17122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17125 \begin_layout Plain Layout
17133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17136 \begin_layout Plain Layout
17137 \begin_inset Formula $\nabla$
17147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17150 \begin_layout Plain Layout
17158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17161 \begin_layout Plain Layout
17162 \begin_inset Formula $\bigtriangledown$
17172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17175 \begin_layout Plain Layout
17183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17186 \begin_layout Plain Layout
17187 \begin_inset Formula $\bigtriangleup$
17197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17200 \begin_layout Plain Layout
17208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17211 \begin_layout Plain Layout
17212 \begin_inset Formula $\Box$
17222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17225 \begin_layout Plain Layout
17233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17236 \begin_layout Plain Layout
17237 \begin_inset Formula $\cap$
17247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17250 \begin_layout Plain Layout
17258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17261 \begin_layout Plain Layout
17262 \begin_inset Formula $\cup$
17272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17275 \begin_layout Plain Layout
17283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17286 \begin_layout Plain Layout
17287 \begin_inset Formula $\dagger$
17297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17300 \begin_layout Plain Layout
17308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17311 \begin_layout Plain Layout
17312 \begin_inset Formula $\ddagger$
17322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17325 \begin_layout Plain Layout
17333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17336 \begin_layout Plain Layout
17337 \begin_inset Formula $\wr$
17347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17350 \begin_layout Plain Layout
17358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17361 \begin_layout Plain Layout
17362 \begin_inset Formula $\bigcirc$
17372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17375 \begin_layout Plain Layout
17383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17386 \begin_layout Plain Layout
17387 \begin_inset Formula $\wedge$
17397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17400 \begin_layout Plain Layout
17408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17411 \begin_layout Plain Layout
17412 \begin_inset Formula $\vee$
17426 \begin_inset space \hfill{}
17430 \begin_inset Tabular
17431 <lyxtabular version="3" rows="13" columns="2">
17432 <features tabularvalignment="middle">
17433 <column alignment="center" valignment="top" width="0pt">
17434 <column alignment="center" valignment="top" width="0pt">
17436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17439 \begin_layout Plain Layout
17445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17448 \begin_layout Plain Layout
17456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17459 \begin_layout Plain Layout
17467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17470 \begin_layout Plain Layout
17471 \begin_inset Formula $\oplus$
17481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17484 \begin_layout Plain Layout
17492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17495 \begin_layout Plain Layout
17496 \begin_inset Formula $\ominus$
17506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17509 \begin_layout Plain Layout
17517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17520 \begin_layout Plain Layout
17521 \begin_inset Formula $\otimes$
17531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17534 \begin_layout Plain Layout
17542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17545 \begin_layout Plain Layout
17546 \begin_inset Formula $\oslash$
17556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17559 \begin_layout Plain Layout
17567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17570 \begin_layout Plain Layout
17571 \begin_inset Formula $\odot$
17581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17584 \begin_layout Plain Layout
17592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17595 \begin_layout Plain Layout
17596 \begin_inset Formula $\amalg$
17606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17609 \begin_layout Plain Layout
17617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17620 \begin_layout Plain Layout
17621 \begin_inset Formula $\uplus$
17631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17634 \begin_layout Plain Layout
17642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17645 \begin_layout Plain Layout
17646 \begin_inset Formula $\setminus$
17656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17659 \begin_layout Plain Layout
17667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17670 \begin_layout Plain Layout
17671 \begin_inset Formula $\sqcap$
17681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17684 \begin_layout Plain Layout
17692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17695 \begin_layout Plain Layout
17696 \begin_inset Formula $\sqcup$
17706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17709 \begin_layout Plain Layout
17717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17720 \begin_layout Plain Layout
17721 \begin_inset Formula $\triangleleft$
17731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17734 \begin_layout Plain Layout
17742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17745 \begin_layout Plain Layout
17746 \begin_inset Formula $\triangleright$
17760 \begin_inset space \hfill{}
17766 \begin_layout Standard
17767 All binary operators can also be inserted via the math toolbar button
17768 \begin_inset Graphics
17769 filename ../images/math/pm.png
17777 \begin_layout Standard
17778 To typeset the Laplace operator also
17795 \begin_inset Formula $\nabla^{2}$
17798 ) can be used instead of
17807 \begin_layout Standard
17814 Insert\SpecialChar \menuseparator
17826 \begin_layout Subsection
17827 Self-defined Operators
17828 \begin_inset CommandInset label
17830 name "sub:Self-defined-Operators"
17835 \begin_inset Index idx
17838 \begin_layout Plain Layout
17839 Operators ! self-defined
17847 \begin_layout Standard
17848 With the help of the command
17852 DeclareMathOperator
17855 \begin_inset Index idx
17858 \begin_layout Plain Layout
17863 DeclareMathOperator
17868 custom operators can be defined in the LaTeX-preamble.
17869 Its command scheme is:
17872 \begin_layout Standard
17877 DeclareMathOperator{new command}{display}
17880 \begin_layout Standard
17881 Display can be characters or symbols that define how the operator looks
17883 To define a big operator a * is set behind the command.
17884 All self-defined big operators can have limits as described in
17885 \begin_inset CommandInset ref
17887 reference "sub:Operator-Limits"
17894 \begin_layout Standard
17895 For example the LaTeX-preamble line
17898 \begin_layout Standard
17903 DeclareMathOperator*{
17910 \begin_layout Standard
17911 defines the command
17917 , that inserts a big operator consisting of the lozenge symbol from
17918 \begin_inset CommandInset ref
17920 reference "sub:Miscellaneous-Symbols"
17925 \begin_inset Formula
17927 \Lozenge_{n=1}^{\infty}
17932 The command for this formula is:
17943 \begin_inset Formula $\to$
17949 \begin_layout Standard
17950 \begin_inset VSpace bigskip
17953 When self-defined operators are not used several times in the document,
17954 they can also be defined with the commands
17961 \begin_inset Index idx
17964 \begin_layout Plain Layout
17979 \begin_inset Index idx
17982 \begin_layout Plain Layout
17990 , which have the following scheme:
17993 \begin_layout Standard
18007 \begin_layout Standard
18014 defines big operators,
18023 \begin_layout Standard
18031 \begin_inset space \thinspace{}
18035 \begin_inset space \space{}
18038 be used to use one limit for several operators:
18041 \begin_layout Standard
18042 \begin_inset Formula
18044 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18052 \begin_layout Standard
18053 The command for the formula above is:
18054 \begin_inset Newline newline
18073 \begin_layout Plain Layout
18085 \begin_inset Formula $\to$
18094 \begin_layout Plain Layout
18108 \begin_layout Section
18110 \begin_inset Index idx
18113 \begin_layout Plain Layout
18122 \begin_layout Subsection
18124 \begin_inset CommandInset label
18126 name "sub:Font-Styles"
18131 \begin_inset Index idx
18134 \begin_layout Plain Layout
18143 \begin_layout Standard
18144 Latin letters in formulas can be set in one of the following font styles:
18145 \begin_inset VSpace -2mm
18151 \begin_layout Standard
18153 \begin_inset Tabular
18154 <lyxtabular version="3" rows="7" columns="3">
18155 <features tabularvalignment="middle">
18156 <column alignment="center" valignment="top" width="0">
18157 <column alignment="center" valignment="top" width="0">
18158 <column alignment="center" valignment="top" width="0">
18160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18163 \begin_layout Plain Layout
18169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18172 \begin_layout Plain Layout
18178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18181 \begin_layout Plain Layout
18189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18192 \begin_layout Plain Layout
18201 \begin_layout Plain Layout
18217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18220 \begin_layout Plain Layout
18221 \begin_inset Formula $\mathbb{ABC}$
18229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18232 \begin_layout Plain Layout
18245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18248 \begin_layout Plain Layout
18257 \begin_layout Plain Layout
18273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18276 \begin_layout Plain Layout
18277 \begin_inset Formula $\mathbf{AbC}$
18285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18288 \begin_layout Plain Layout
18301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18304 \begin_layout Plain Layout
18313 \begin_layout Plain Layout
18329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18332 \begin_layout Plain Layout
18333 \begin_inset Formula $\boldsymbol{AbC}$
18341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18344 \begin_layout Plain Layout
18347 arg "font-boldsymbol"
18357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18360 \begin_layout Plain Layout
18369 \begin_layout Plain Layout
18385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18388 \begin_layout Plain Layout
18389 \begin_inset Formula $\mathcal{ABC}$
18397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18400 \begin_layout Plain Layout
18413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18416 \begin_layout Plain Layout
18425 \begin_layout Plain Layout
18441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18444 \begin_layout Plain Layout
18445 \begin_inset Formula $\mathfrak{AbC}$
18453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18456 \begin_layout Plain Layout
18464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18467 \begin_layout Plain Layout
18476 \begin_layout Plain Layout
18492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18495 \begin_layout Plain Layout
18496 \begin_inset Formula $\mathscr{AbC}$
18504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18507 \begin_layout Plain Layout
18521 \begin_layout Standard
18523 \begin_inset Tabular
18524 <lyxtabular version="3" rows="5" columns="3">
18525 <features tabularvalignment="middle">
18526 <column alignment="center" valignment="top" width="0">
18527 <column alignment="center" valignment="top" width="0">
18528 <column alignment="center" valignment="top" width="0">
18530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18533 \begin_layout Plain Layout
18539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18542 \begin_layout Plain Layout
18548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18551 \begin_layout Plain Layout
18559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18562 \begin_layout Plain Layout
18571 \begin_layout Plain Layout
18587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18590 \begin_layout Plain Layout
18591 \begin_inset Formula $\mathit{AbC}$
18599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18602 \begin_layout Plain Layout
18610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18613 \begin_layout Plain Layout
18622 \begin_layout Plain Layout
18638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18641 \begin_layout Plain Layout
18642 \begin_inset Formula $\mathrm{AbC}$
18650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18653 \begin_layout Plain Layout
18666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18669 \begin_layout Plain Layout
18678 \begin_layout Plain Layout
18694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18697 \begin_layout Plain Layout
18698 \begin_inset Formula $\mathsf{AbC}$
18706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18709 \begin_layout Plain Layout
18722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18725 \begin_layout Plain Layout
18734 \begin_layout Plain Layout
18750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18753 \begin_layout Plain Layout
18754 \begin_inset Formula $\mathtt{AbC}$
18762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18765 \begin_layout Plain Layout
18768 arg "font-typewriter"
18784 \begin_layout Standard
18785 \begin_inset Note Greyedout
18788 \begin_layout Plain Layout
18805 can only be used for big letters.
18813 \begin_layout Standard
18814 Predefined is the style
18823 \begin_layout Standard
18824 The style commands work also for letters in mathematical constructs:
18825 \begin_inset Formula
18827 \mathfrak{A=\frac{b}{C}}
18835 \begin_layout Standard
18836 Characters in mathematical text don't appear in a math font style but in
18837 the text font style
18844 That their style can't be set correctly via the text style dialog is a
18849 \begin_layout Plain Layout
18850 \begin_inset CommandInset href
18852 name "LyX-bug #4629"
18853 target "http://www.lyx.org/trac/ticket/4629"
18865 \begin_layout Standard
18866 Instead of the style commands the dialog
18868 Edit\SpecialChar \menuseparator
18869 Math\SpecialChar \menuseparator
18872 or the toolbar button
18873 \begin_inset Graphics
18874 filename ../images/math/font.png
18882 \begin_layout Subsection
18884 \begin_inset CommandInset label
18886 name "sub:Bold-Formulas"
18891 \begin_inset Index idx
18894 \begin_layout Plain Layout
18903 \begin_layout Standard
18904 To make a complete formula bold, the command
18910 from the previous subsection cannot be used, because it doesn't work for
18911 small Greek letters.
18912 Furthermore it prints Latin letters always upright, like in the following
18916 \begin_layout Standard
18917 \begin_inset Formula
18919 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18927 \begin_layout Standard
18928 To display the formula correctly, the command
18935 \begin_inset Formula
18937 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18942 It is also possible to set the formula in a
18944 boldmath environment
18947 This environment is created by inserting the command
18954 \begin_inset Index idx
18957 \begin_layout Plain Layout
18966 To end the environment, the command
18973 \begin_inset Index idx
18976 \begin_layout Plain Layout
18984 is inserted in TeX-mode.
18988 \begin_layout Plain Layout
18998 \begin_inset Formula
19000 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19009 \begin_layout Plain Layout
19021 \begin_layout Subsection
19023 \begin_inset Index idx
19026 \begin_layout Plain Layout
19035 \begin_layout Standard
19036 Formulas can be colored like normal text: Highlight a formula or a formula
19042 Here is a formula in magenta:
19043 \begin_inset Formula
19045 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19053 \begin_layout Standard
19054 You can also define your own colors as described in
19055 \begin_inset CommandInset ref
19057 reference "sub:Colored-Boxes"
19062 They can be used with the TeX code command
19069 \begin_inset Index idx
19072 \begin_layout Plain Layout
19083 \begin_layout Standard
19088 textcolor{color}{characters or formula}
19091 \begin_layout Standard
19092 The following example was colored completely dark green and partly red:
19095 \begin_layout Standard
19099 \begin_layout Plain Layout
19103 textcolor{darkgreen}{
19109 \begin_inset Formula
19111 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19120 \begin_layout Plain Layout
19130 \begin_layout Standard
19131 Due to a bug in LyX only complete formulas can be colored with self-defined
19136 \begin_layout Plain Layout
19137 \begin_inset CommandInset href
19139 name "LyX-bug #5269"
19140 target "http://www.lyx.org/trac/ticket/5269"
19152 \begin_layout Subsection
19154 \begin_inset CommandInset label
19156 name "sub:Font-Sizes"
19161 \begin_inset Index idx
19164 \begin_layout Plain Layout
19173 \begin_layout Standard
19174 For characters in formulas there are, analog to characters in text, the
19175 following size commands:
19178 \begin_layout Standard
19222 \begin_inset Newline newline
19244 \begin_layout Standard
19245 The size produced by the commands depends on the document font size, which
19246 corresponds to the command
19253 The other commands produce smaller or larger sizes than
19260 The font size can however not exceed a certain value.
19261 Is for example the document font size 12
19262 \begin_inset space \thinspace{}
19271 switches to the same size as
19281 \begin_layout Standard
19282 A size command is inserted in TeX-mode before the formula and sets the size
19283 for all following formula and text characters.
19284 To switch back to the initial size, the command
19290 is inserted behind the formula in TeX-mode.
19293 \begin_layout Standard
19294 Within a formula the size can be changed using the following size commands:
19297 \begin_layout Standard
19300 \begin_inset Tabular
19301 <lyxtabular version="3" rows="5" columns="2">
19302 <features tabularvalignment="middle">
19303 <column alignment="center" valignment="top" width="0">
19304 <column alignment="center" valignment="top" width="0">
19306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19309 \begin_layout Plain Layout
19315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19318 \begin_layout Plain Layout
19320 \begin_inset Note Note
19323 \begin_layout Plain Layout
19330 is only used as spacer.
19342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19345 \begin_layout Plain Layout
19349 \begin_inset Index idx
19352 \begin_layout Plain Layout
19365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19368 \begin_layout Plain Layout
19369 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19382 \begin_layout Plain Layout
19390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19393 \begin_layout Plain Layout
19394 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19407 \begin_layout Plain Layout
19415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19418 \begin_layout Plain Layout
19419 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19432 \begin_layout Plain Layout
19440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19443 \begin_layout Plain Layout
19444 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19460 \begin_layout Standard
19461 After entering these commands, a blue box appears in which the formula parts
19465 \begin_layout Standard
19466 There is a further method to change the font size, that though only works
19467 for symbols or letters in mathematical text.
19468 To use it, one of the above text size commands is inserted in mathematical
19470 All following characters until the end of the mathematical text or until
19471 another size command will have the selected size.
19473 \begin_inset VSpace -2mm
19479 \begin_layout Standard
19483 \begin_layout Plain Layout
19493 \begin_inset Formula
19495 A=\frac{B}{c}\cdot\maltese
19501 \begin_inset Formula
19503 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19512 \begin_layout Plain Layout
19524 \begin_layout Standard
19525 \begin_inset VSpace medskip
19528 Before both formulas the command
19535 The command for the second formula is:
19536 \begin_inset Newline newline
19547 \begin_layout Plain Layout
19562 \begin_layout Plain Layout
19577 \begin_layout Plain Layout
19592 \begin_layout Plain Layout
19602 \begin_inset Formula $\to$
19606 \begin_inset Formula $\to$
19610 \begin_inset Newline newline
19614 \begin_inset space \hspace*{}
19628 \begin_layout Plain Layout
19643 \begin_layout Plain Layout
19658 \begin_layout Plain Layout
19670 \begin_layout Standard
19671 If a symbol cannot be displayed in different sizes, it will always be displayed
19672 in the default size.
19675 \begin_layout Section
19677 \begin_inset Index idx
19680 \begin_layout Plain Layout
19689 \begin_layout Standard
19690 Greek letters can also be inserted via the toolbar button
19691 \begin_inset Graphics
19692 filename ../images/math/alpha.png
19698 All international typesetting norms purport that Greek letters in math
19699 have to be typeset italic/slanted.
19700 In some languages, like French or Russian, they are nevertheless sometimes
19704 \begin_layout Subsection
19706 \begin_inset Index idx
19709 \begin_layout Plain Layout
19710 Greek letters ! small
19718 \begin_layout Standard
19719 \begin_inset space \hfill{}
19723 \begin_inset Tabular
19724 <lyxtabular version="3" rows="11" columns="2">
19725 <features tabularvalignment="middle">
19726 <column alignment="center" valignment="top" width="0pt">
19727 <column alignment="center" valignment="top" width="0pt">
19729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19732 \begin_layout Plain Layout
19738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19741 \begin_layout Plain Layout
19749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19752 \begin_layout Plain Layout
19760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19763 \begin_layout Plain Layout
19764 \begin_inset Formula $\alpha$
19774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19777 \begin_layout Plain Layout
19785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19788 \begin_layout Plain Layout
19789 \begin_inset Formula $\beta$
19799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19802 \begin_layout Plain Layout
19810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19813 \begin_layout Plain Layout
19814 \begin_inset Formula $\gamma$
19824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19827 \begin_layout Plain Layout
19835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19838 \begin_layout Plain Layout
19839 \begin_inset Formula $\delta$
19849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19852 \begin_layout Plain Layout
19860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19863 \begin_layout Plain Layout
19864 \begin_inset Formula $\epsilon$
19874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19877 \begin_layout Plain Layout
19885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19888 \begin_layout Plain Layout
19889 \begin_inset Formula $\varepsilon$
19899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19902 \begin_layout Plain Layout
19910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19913 \begin_layout Plain Layout
19914 \begin_inset Formula $\zeta$
19924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19927 \begin_layout Plain Layout
19935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19938 \begin_layout Plain Layout
19939 \begin_inset Formula $\eta$
19949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19952 \begin_layout Plain Layout
19960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19963 \begin_layout Plain Layout
19964 \begin_inset Formula $\theta$
19974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19977 \begin_layout Plain Layout
19985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19988 \begin_layout Plain Layout
19989 \begin_inset Formula $\vartheta$
20003 \begin_inset space \hfill{}
20007 \begin_inset Tabular
20008 <lyxtabular version="3" rows="12" columns="2">
20009 <features tabularvalignment="middle">
20010 <column alignment="center" valignment="top" width="0pt">
20011 <column alignment="center" valignment="top" width="0pt">
20013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20016 \begin_layout Plain Layout
20022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20025 \begin_layout Plain Layout
20033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20036 \begin_layout Plain Layout
20044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20047 \begin_layout Plain Layout
20048 \begin_inset Formula $\iota$
20058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20061 \begin_layout Plain Layout
20069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20072 \begin_layout Plain Layout
20073 \begin_inset Formula $\kappa$
20083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20086 \begin_layout Plain Layout
20094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20097 \begin_layout Plain Layout
20098 \begin_inset Formula $\varkappa$
20108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20111 \begin_layout Plain Layout
20119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20122 \begin_layout Plain Layout
20123 \begin_inset Formula $\lambda$
20133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20136 \begin_layout Plain Layout
20144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20147 \begin_layout Plain Layout
20148 \begin_inset Formula $\mu$
20158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20161 \begin_layout Plain Layout
20169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20172 \begin_layout Plain Layout
20173 \begin_inset Formula $\nu$
20183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20186 \begin_layout Plain Layout
20194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20197 \begin_layout Plain Layout
20198 \begin_inset Formula $\xi$
20208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20211 \begin_layout Plain Layout
20217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20220 \begin_layout Plain Layout
20221 \begin_inset Formula $o$
20231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20234 \begin_layout Plain Layout
20242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20245 \begin_layout Plain Layout
20246 \begin_inset Formula $\pi$
20256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20259 \begin_layout Plain Layout
20267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20270 \begin_layout Plain Layout
20271 \begin_inset Formula $\varpi$
20281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20284 \begin_layout Plain Layout
20292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20295 \begin_layout Plain Layout
20296 \begin_inset Formula $\rho$
20310 \begin_inset space \hfill{}
20314 \begin_inset Tabular
20315 <lyxtabular version="3" rows="11" columns="2">
20316 <features tabularvalignment="middle">
20317 <column alignment="center" valignment="top" width="0pt">
20318 <column alignment="center" valignment="top" width="0pt">
20320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20323 \begin_layout Plain Layout
20329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20332 \begin_layout Plain Layout
20340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20343 \begin_layout Plain Layout
20351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20354 \begin_layout Plain Layout
20355 \begin_inset Formula $\varrho$
20365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20368 \begin_layout Plain Layout
20376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20379 \begin_layout Plain Layout
20380 \begin_inset Formula $\sigma$
20390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20393 \begin_layout Plain Layout
20401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20404 \begin_layout Plain Layout
20405 \begin_inset Formula $\varsigma$
20415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20418 \begin_layout Plain Layout
20426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20429 \begin_layout Plain Layout
20430 \begin_inset Formula $\tau$
20440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20443 \begin_layout Plain Layout
20451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20454 \begin_layout Plain Layout
20455 \begin_inset Formula $\upsilon$
20465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20468 \begin_layout Plain Layout
20476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20479 \begin_layout Plain Layout
20480 \begin_inset Formula $\phi$
20490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20493 \begin_layout Plain Layout
20501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20504 \begin_layout Plain Layout
20505 \begin_inset Formula $\varphi$
20515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20518 \begin_layout Plain Layout
20526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20529 \begin_layout Plain Layout
20530 \begin_inset Formula $\chi$
20540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20543 \begin_layout Plain Layout
20551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20554 \begin_layout Plain Layout
20555 \begin_inset Formula $\psi$
20565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20568 \begin_layout Plain Layout
20576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20579 \begin_layout Plain Layout
20580 \begin_inset Formula $\omega$
20594 \begin_inset space \hfill{}
20600 \begin_layout Standard
20601 \begin_inset VSpace medskip
20607 \begin_layout Standard
20608 How to create special upright Greek letters is explained in
20609 \begin_inset CommandInset ref
20611 reference "sub:Upright-small-Greek"
20618 \begin_layout Subsection
20620 \begin_inset Index idx
20623 \begin_layout Plain Layout
20624 Greek letters ! big
20632 \begin_layout Standard
20633 \begin_inset space \hfill{}
20637 \begin_inset Tabular
20638 <lyxtabular version="3" rows="7" columns="2">
20639 <features tabularvalignment="middle">
20640 <column alignment="center" valignment="top" width="0pt">
20641 <column alignment="center" valignment="top" width="0pt">
20643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20646 \begin_layout Plain Layout
20652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20655 \begin_layout Plain Layout
20663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20666 \begin_layout Plain Layout
20674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20677 \begin_layout Plain Layout
20678 \begin_inset Formula $\Gamma$
20688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20691 \begin_layout Plain Layout
20699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20702 \begin_layout Plain Layout
20703 \begin_inset Formula $\Delta$
20713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20716 \begin_layout Plain Layout
20724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20727 \begin_layout Plain Layout
20728 \begin_inset Formula $\Theta$
20738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20741 \begin_layout Plain Layout
20749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20752 \begin_layout Plain Layout
20753 \begin_inset Formula $\Lambda$
20763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20766 \begin_layout Plain Layout
20774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20777 \begin_layout Plain Layout
20778 \begin_inset Formula $\Xi$
20788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20791 \begin_layout Plain Layout
20799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20802 \begin_layout Plain Layout
20803 \begin_inset Formula $\Pi$
20817 \begin_inset space \hfill{}
20821 \begin_inset Tabular
20822 <lyxtabular version="3" rows="6" columns="2">
20823 <features tabularvalignment="middle">
20824 <column alignment="center" valignment="top" width="0pt">
20825 <column alignment="center" valignment="top" width="0pt">
20827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20830 \begin_layout Plain Layout
20836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20839 \begin_layout Plain Layout
20847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20850 \begin_layout Plain Layout
20858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20861 \begin_layout Plain Layout
20862 \begin_inset Formula $\Sigma$
20872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20875 \begin_layout Plain Layout
20883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20886 \begin_layout Plain Layout
20887 \begin_inset Formula $\Upsilon$
20897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20900 \begin_layout Plain Layout
20908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20911 \begin_layout Plain Layout
20912 \begin_inset Formula $\Phi$
20922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20925 \begin_layout Plain Layout
20933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20936 \begin_layout Plain Layout
20937 \begin_inset Formula $\Psi$
20947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20950 \begin_layout Plain Layout
20958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20961 \begin_layout Plain Layout
20962 \begin_inset Formula $\Omega$
20976 \begin_inset space \hfill{}
20982 \begin_layout Standard
20983 \begin_inset VSpace medskip
20986 That the big Greek letters appear upright is caused by a design bug when
20988 To get correct italic big letters, begin every command with
20993 For example the command
21000 \begin_inset Formula $\varGamma$
21004 Another way is to load the package
21012 \begin_layout Plain Layout
21017 is part of the LaTeX-package
21022 \begin_inset Index idx
21025 \begin_layout Plain Layout
21030 \begin_layout Plain Layout
21050 \begin_inset Index idx
21053 \begin_layout Plain Layout
21059 with the LaTeX-preamble line
21062 \begin_layout Standard
21067 usepackage{fixmath}
21070 \begin_layout Standard
21071 Then all big Greek letters in a document will automatically be typeset italic.
21074 \begin_layout Subsection
21076 \begin_inset Index idx
21079 \begin_layout Plain Layout
21080 Greek letters ! bold
21088 \begin_layout Standard
21089 Greek letters cannot be set with different font styles like Latin letters.
21090 They can only be made bold with the command
21097 \begin_inset Index idx
21100 \begin_layout Plain Layout
21111 \begin_layout Standard
21113 \begin_inset Tabular
21114 <lyxtabular version="3" rows="3" columns="2">
21115 <features tabularvalignment="middle">
21116 <column alignment="center" valignment="top" width="0">
21117 <column alignment="center" valignment="top" width="0">
21119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21122 \begin_layout Plain Layout
21128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21131 \begin_layout Plain Layout
21139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21142 \begin_layout Plain Layout
21154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21157 \begin_layout Plain Layout
21158 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21171 \begin_layout Plain Layout
21183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21186 \begin_layout Plain Layout
21187 \begin_inset Formula $\theta\boldsymbol{\theta}$
21203 \begin_layout Section
21208 \begin_layout Plain Layout
21221 \begin_layout Plain Layout
21222 A list with all symbols of most of the LaTeX-packages can be found in
21223 \begin_inset CommandInset citation
21238 \begin_layout Plain Layout
21246 \begin_inset Note Note
21249 \begin_layout Plain Layout
21252 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21255 \begin_layout Plain Layout
21258 texorpdfstring is in section
21259 \begin_inset CommandInset ref
21261 reference "sub:Formulas-in-Section"
21271 \begin_inset Index idx
21274 \begin_layout Plain Layout
21283 \begin_layout Standard
21284 Many of the symbols listed in this section can also be inserted via the
21286 \begin_inset Graphics
21287 filename ../images/math/nabla.png
21293 \begin_inset Graphics
21294 filename ../images/math/digamma.png
21302 \begin_layout Subsection
21303 Mathematical Symbols
21304 \begin_inset CommandInset label
21306 name "sub:Mathematical-Symbols"
21311 \begin_inset Index idx
21314 \begin_layout Plain Layout
21315 Symbols ! mathematical
21323 \begin_layout Standard
21324 \begin_inset space \hfill{}
21328 \begin_inset Tabular
21329 <lyxtabular version="3" rows="10" columns="2">
21330 <features tabularvalignment="middle">
21331 <column alignment="center" valignment="top" width="0pt">
21332 <column alignment="center" valignment="top" width="0pt">
21334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21337 \begin_layout Plain Layout
21343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21346 \begin_layout Plain Layout
21354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21357 \begin_layout Plain Layout
21365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21368 \begin_layout Plain Layout
21369 \begin_inset Formula $\neg$
21379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21382 \begin_layout Plain Layout
21390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21393 \begin_layout Plain Layout
21394 \begin_inset Formula $\Im$
21404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21407 \begin_layout Plain Layout
21415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21418 \begin_layout Plain Layout
21419 \begin_inset Formula $\Re$
21429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21432 \begin_layout Plain Layout
21440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21443 \begin_layout Plain Layout
21444 \begin_inset Formula $\aleph$
21454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21457 \begin_layout Plain Layout
21465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21468 \begin_layout Plain Layout
21469 \begin_inset Formula $\partial$
21479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21482 \begin_layout Plain Layout
21490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21493 \begin_layout Plain Layout
21494 \begin_inset Formula $\infty$
21504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21507 \begin_layout Plain Layout
21515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21518 \begin_layout Plain Layout
21519 \begin_inset Formula $\wp$
21529 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21532 \begin_layout Plain Layout
21540 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21543 \begin_layout Plain Layout
21544 \begin_inset Formula $\imath$
21554 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21557 \begin_layout Plain Layout
21565 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21568 \begin_layout Plain Layout
21569 \begin_inset Formula $\jmath$
21583 \begin_inset space \hfill{}
21587 \begin_inset Tabular
21588 <lyxtabular version="3" rows="10" columns="2">
21589 <features tabularvalignment="middle">
21590 <column alignment="center" valignment="top" width="0pt">
21591 <column alignment="center" valignment="top" width="0pt">
21593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21596 \begin_layout Plain Layout
21602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21605 \begin_layout Plain Layout
21607 \begin_inset Note Note
21610 \begin_layout Plain Layout
21617 is only used as spacer.
21629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21632 \begin_layout Plain Layout
21640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21643 \begin_layout Plain Layout
21644 \begin_inset Formula $\forall$
21654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21657 \begin_layout Plain Layout
21665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21668 \begin_layout Plain Layout
21669 \begin_inset Formula $\exists$
21679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21682 \begin_layout Plain Layout
21690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21693 \begin_layout Plain Layout
21694 \begin_inset Formula $\nexists$
21704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21707 \begin_layout Plain Layout
21715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21718 \begin_layout Plain Layout
21719 \begin_inset Formula $\emptyset$
21729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21732 \begin_layout Plain Layout
21740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21743 \begin_layout Plain Layout
21744 \begin_inset Formula $\varnothing$
21754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21757 \begin_layout Plain Layout
21765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21768 \begin_layout Plain Layout
21769 \begin_inset Formula $\dag$
21779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21782 \begin_layout Plain Layout
21790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21793 \begin_layout Plain Layout
21794 \begin_inset Formula $\ddag$
21804 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21807 \begin_layout Plain Layout
21815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21818 \begin_layout Plain Layout
21822 \begin_layout Plain Layout
21832 \begin_inset Formula $\complement$
21839 \begin_layout Plain Layout
21853 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21856 \begin_layout Plain Layout
21864 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21867 \begin_layout Plain Layout
21868 \begin_inset Formula $\Bbbk$
21882 \begin_inset space \hfill{}
21886 \begin_inset Tabular
21887 <lyxtabular version="3" rows="10" columns="2">
21888 <features tabularvalignment="middle">
21889 <column alignment="center" valignment="top" width="0pt">
21890 <column alignment="center" valignment="top" width="0pt">
21892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21895 \begin_layout Plain Layout
21901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21904 \begin_layout Plain Layout
21912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21915 \begin_layout Plain Layout
21923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21926 \begin_layout Plain Layout
21927 \begin_inset Formula $\prime$
21937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21940 \begin_layout Plain Layout
21948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21951 \begin_layout Plain Layout
21952 \begin_inset Formula $\backprime$
21962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21965 \begin_layout Plain Layout
21973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21976 \begin_layout Plain Layout
21977 \begin_inset Formula $\mho$
21987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21990 \begin_layout Plain Layout
21998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22001 \begin_layout Plain Layout
22002 \begin_inset Formula $\triangle$
22012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22015 \begin_layout Plain Layout
22023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22026 \begin_layout Plain Layout
22027 \begin_inset Formula $\angle$
22037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22040 \begin_layout Plain Layout
22048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22051 \begin_layout Plain Layout
22052 \begin_inset Formula $\measuredangle$
22062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22065 \begin_layout Plain Layout
22073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22076 \begin_layout Plain Layout
22077 \begin_inset Formula $\sphericalangle$
22087 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22090 \begin_layout Plain Layout
22098 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22101 \begin_layout Plain Layout
22102 \begin_inset Formula $\top$
22112 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22115 \begin_layout Plain Layout
22123 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22126 \begin_layout Plain Layout
22127 \begin_inset Formula $\bot$
22141 \begin_inset space \hfill{}
22147 \begin_layout Subsection
22148 Miscellaneous Symbols
22149 \begin_inset CommandInset label
22151 name "sub:Miscellaneous-Symbols"
22156 \begin_inset Index idx
22159 \begin_layout Plain Layout
22160 Symbols ! miscellaneous
22168 \begin_layout Standard
22171 \begin_inset Tabular
22172 <lyxtabular version="3" rows="10" columns="2">
22173 <features tabularvalignment="middle">
22174 <column alignment="center" valignment="top" width="0pt">
22175 <column alignment="center" valignment="top" width="0pt">
22177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22180 \begin_layout Plain Layout
22186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22189 \begin_layout Plain Layout
22197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22200 \begin_layout Plain Layout
22208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22211 \begin_layout Plain Layout
22212 \begin_inset Formula $\flat$
22222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22225 \begin_layout Plain Layout
22233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22236 \begin_layout Plain Layout
22237 \begin_inset Formula $\natural$
22247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22250 \begin_layout Plain Layout
22258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22261 \begin_layout Plain Layout
22262 \begin_inset Formula $\sharp$
22272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22275 \begin_layout Plain Layout
22283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22286 \begin_layout Plain Layout
22287 \begin_inset Formula $\surd$
22297 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22300 \begin_layout Plain Layout
22308 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22311 \begin_layout Plain Layout
22312 \begin_inset Formula $\checkmark$
22322 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22325 \begin_layout Plain Layout
22333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22336 \begin_layout Plain Layout
22337 \begin_inset Formula $\yen$
22347 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22350 \begin_layout Plain Layout
22358 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22361 \begin_layout Plain Layout
22362 \begin_inset Formula $\pounds$
22372 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22375 \begin_layout Plain Layout
22381 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22384 \begin_layout Plain Layout
22385 \begin_inset Formula $\$$
22395 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22398 \begin_layout Plain Layout
22404 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22407 \begin_layout Plain Layout
22408 \begin_inset Formula $§$
22422 \begin_inset Tabular
22423 <lyxtabular version="3" rows="10" columns="2">
22424 <features tabularvalignment="middle">
22425 <column alignment="center" valignment="top" width="0">
22426 <column alignment="center" valignment="top" width="0">
22428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22431 \begin_layout Plain Layout
22437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22440 \begin_layout Plain Layout
22448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22451 \begin_layout Plain Layout
22459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22462 \begin_layout Plain Layout
22463 \begin_inset Formula $\hbar$
22473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22476 \begin_layout Plain Layout
22484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22487 \begin_layout Plain Layout
22488 \begin_inset Formula $\hslash$
22498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22501 \begin_layout Plain Layout
22509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22512 \begin_layout Plain Layout
22513 \begin_inset Formula $\clubsuit$
22523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22526 \begin_layout Plain Layout
22534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22537 \begin_layout Plain Layout
22538 \begin_inset Formula $\spadesuit$
22548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22551 \begin_layout Plain Layout
22559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22562 \begin_layout Plain Layout
22563 \begin_inset Formula $\bigstar$
22573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22576 \begin_layout Plain Layout
22584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22587 \begin_layout Plain Layout
22588 \begin_inset Formula $\blacklozenge$
22598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22601 \begin_layout Plain Layout
22609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22612 \begin_layout Plain Layout
22613 \begin_inset Formula $\blacktriangle$
22623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22626 \begin_layout Plain Layout
22634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22637 \begin_layout Plain Layout
22638 \begin_inset Formula $\blacktriangledown$
22648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22651 \begin_layout Plain Layout
22659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22662 \begin_layout Plain Layout
22663 \begin_inset Formula $\bullet$
22677 \begin_inset Tabular
22678 <lyxtabular version="3" rows="10" columns="2">
22679 <features tabularvalignment="middle">
22680 <column alignment="center" valignment="top" width="0pt">
22681 <column alignment="center" valignment="top" width="0pt">
22683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22686 \begin_layout Plain Layout
22692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22695 \begin_layout Plain Layout
22703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22706 \begin_layout Plain Layout
22714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22717 \begin_layout Plain Layout
22718 \begin_inset Formula $\diamondsuit$
22728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22731 \begin_layout Plain Layout
22739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22742 \begin_layout Plain Layout
22743 \begin_inset Formula $\Diamond$
22753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22756 \begin_layout Plain Layout
22764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22767 \begin_layout Plain Layout
22768 \begin_inset Formula $\heartsuit$
22778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22781 \begin_layout Plain Layout
22789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22792 \begin_layout Plain Layout
22793 \begin_inset Formula $\P$
22803 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22806 \begin_layout Plain Layout
22814 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22817 \begin_layout Plain Layout
22818 \begin_inset Formula $\copyright$
22828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22831 \begin_layout Plain Layout
22839 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22842 \begin_layout Plain Layout
22843 \begin_inset Formula $\circledR$
22853 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22856 \begin_layout Plain Layout
22864 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22867 \begin_layout Plain Layout
22868 \begin_inset Formula $\maltese$
22878 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22881 \begin_layout Plain Layout
22889 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22892 \begin_layout Plain Layout
22893 \begin_inset Formula $\diagup$
22903 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22906 \begin_layout Plain Layout
22914 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22917 \begin_layout Plain Layout
22918 \begin_inset Formula $\diagdown$
22934 \begin_layout Standard
22935 \begin_inset VSpace medskip
22938 More symbols are listed in
22939 \begin_inset CommandInset ref
22941 reference "sub:Miscellaneous-special-Characters"
22948 \begin_layout Standard
22949 Some symbols can be displayed in different sizes, see
22950 \begin_inset CommandInset ref
22952 reference "sub:Font-Sizes"
22959 \begin_layout Subsection
22961 \begin_inset Index idx
22964 \begin_layout Plain Layout
22965 Symbols ! Euro-symbol
22971 \begin_inset Index idx
22974 \begin_layout Plain Layout
22981 \begin_layout Plain Layout
22998 \begin_layout Standard
22999 To use the Euro symbol in formulas, the LaTeX-package
23004 \begin_inset Index idx
23007 \begin_layout Plain Layout
23013 must be installed and loaded with the LaTeX-preamble line
23016 \begin_layout Standard
23021 usepackage[gennarrow]{eurosym}
23024 \begin_layout Standard
23025 The Euro symbol can now be inserted with the command
23032 \begin_inset Index idx
23035 \begin_layout Plain Layout
23046 \begin_layout Standard
23047 The Euro symbol can directly be inserted with the € key in mathematical
23048 text, without having
23063 can also be inserted in TeX-mode.
23064 The official currency symbol can then be inserted with the command
23071 \begin_inset Index idx
23074 \begin_layout Plain Layout
23082 , that is only available in TeX-mode.
23085 \begin_layout Standard
23089 \begin_layout Plain Layout
23099 \begin_inset Note Note
23102 \begin_layout Plain Layout
23103 The following table will only be displayed when the LaTeX-package
23115 \begin_layout Standard
23116 An overview about the different Euro symbols:
23119 \begin_layout Standard
23121 \begin_inset Tabular
23122 <lyxtabular version="3" rows="4" columns="3">
23123 <features tabularvalignment="middle">
23124 <column alignment="center" valignment="top" width="0pt">
23125 <column alignment="center" valignment="top" width="0pt">
23126 <column alignment="center" valignment="top" width="0pt">
23128 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23131 \begin_layout Plain Layout
23137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23140 \begin_layout Plain Layout
23146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23149 \begin_layout Plain Layout
23157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23160 \begin_layout Plain Layout
23166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23169 \begin_layout Plain Layout
23177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23180 \begin_layout Plain Layout
23181 \begin_inset Formula $\euro$
23191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23194 \begin_layout Plain Layout
23200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23203 \begin_layout Plain Layout
23209 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23212 \begin_layout Plain Layout
23213 \begin_inset Formula $\mbox{€}$
23223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23226 \begin_layout Plain Layout
23232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23235 \begin_layout Plain Layout
23243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23246 \begin_layout Plain Layout
23250 \begin_layout Plain Layout
23272 \begin_layout Standard
23276 \begin_layout Plain Layout
23286 \begin_inset Note Note
23289 \begin_layout Plain Layout
23290 The following will be displayed when the LaTeX-package
23302 \begin_layout Standard
23303 You need to install the LaTeX-package
23307 to see the rest of this subsection in the output.
23310 \begin_layout Standard
23314 \begin_layout Plain Layout
23326 \begin_layout Section
23328 \begin_inset CommandInset label
23330 name "sec:Relations"
23335 \begin_inset Index idx
23338 \begin_layout Plain Layout
23345 \begin_inset Index idx
23348 \begin_layout Plain Layout
23353 \begin_layout Plain Layout
23364 \begin_layout Plain Layout
23379 \begin_layout Standard
23380 All relations can also be inserted via the toolbar button
23381 \begin_inset Graphics
23382 filename ../images/math/leq.png
23390 \begin_layout Standard
23391 \begin_inset space \hfill{}
23395 \begin_inset Tabular
23396 <lyxtabular version="3" rows="17" columns="2">
23397 <features tabularvalignment="middle">
23398 <column alignment="center" valignment="top" width="0pt">
23399 <column alignment="center" valignment="top" width="0pt">
23401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23404 \begin_layout Plain Layout
23410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23413 \begin_layout Plain Layout
23421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23424 \begin_layout Plain Layout
23430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23433 \begin_layout Plain Layout
23434 \begin_inset Formula $<$
23444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23447 \begin_layout Plain Layout
23455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23458 \begin_layout Plain Layout
23459 \begin_inset Formula $\le$
23469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23472 \begin_layout Plain Layout
23480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23483 \begin_layout Plain Layout
23484 \begin_inset Formula $\ll$
23494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23497 \begin_layout Plain Layout
23505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23508 \begin_layout Plain Layout
23509 \begin_inset Formula $\prec$
23519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23522 \begin_layout Plain Layout
23530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23533 \begin_layout Plain Layout
23534 \begin_inset Formula $\preceq$
23544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23547 \begin_layout Plain Layout
23555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23558 \begin_layout Plain Layout
23559 \begin_inset Formula $\subset$
23569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23572 \begin_layout Plain Layout
23580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23583 \begin_layout Plain Layout
23584 \begin_inset Formula $\subseteq$
23594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23597 \begin_layout Plain Layout
23605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23608 \begin_layout Plain Layout
23609 \begin_inset Formula $\sqsubseteq$
23619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23622 \begin_layout Plain Layout
23630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23633 \begin_layout Plain Layout
23634 \begin_inset Formula $\in$
23644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23647 \begin_layout Plain Layout
23655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23658 \begin_layout Plain Layout
23659 \begin_inset Formula $\vdash$
23669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23672 \begin_layout Plain Layout
23680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23683 \begin_layout Plain Layout
23684 \begin_inset Formula $\smile$
23694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23697 \begin_layout Plain Layout
23705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23708 \begin_layout Plain Layout
23709 \begin_inset Formula $\lhd$
23719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23722 \begin_layout Plain Layout
23730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23733 \begin_layout Plain Layout
23734 \begin_inset Formula $\unlhd$
23744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23747 \begin_layout Plain Layout
23755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23758 \begin_layout Plain Layout
23759 \begin_inset Formula $\gtrless$
23769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23772 \begin_layout Plain Layout
23780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23783 \begin_layout Plain Layout
23784 \begin_inset Formula $\mid$
23794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23797 \begin_layout Plain Layout
23805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23808 \begin_layout Plain Layout
23809 \begin_inset Formula $\nmid$
23823 \begin_inset space \hfill{}
23827 \begin_inset Tabular
23828 <lyxtabular version="3" rows="17" columns="2">
23829 <features tabularvalignment="middle">
23830 <column alignment="center" valignment="top" width="0pt">
23831 <column alignment="center" valignment="top" width="0pt">
23833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23836 \begin_layout Plain Layout
23842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23845 \begin_layout Plain Layout
23853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23856 \begin_layout Plain Layout
23862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23865 \begin_layout Plain Layout
23866 \begin_inset Formula $=$
23876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23879 \begin_layout Plain Layout
23887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23890 \begin_layout Plain Layout
23891 \begin_inset Formula $\not=$
23901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23904 \begin_layout Plain Layout
23912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23915 \begin_layout Plain Layout
23916 \begin_inset Formula $\equiv$
23926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23929 \begin_layout Plain Layout
23937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23940 \begin_layout Plain Layout
23941 \begin_inset Formula $\sim$
23951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23954 \begin_layout Plain Layout
23962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23965 \begin_layout Plain Layout
23966 \begin_inset Formula $\simeq$
23976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23979 \begin_layout Plain Layout
23987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23990 \begin_layout Plain Layout
23991 \begin_inset Formula $\approx$
24001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24004 \begin_layout Plain Layout
24012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24015 \begin_layout Plain Layout
24016 \begin_inset Formula $\cong$
24026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24029 \begin_layout Plain Layout
24037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24040 \begin_layout Plain Layout
24041 \begin_inset Formula $\bowtie$
24051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24054 \begin_layout Plain Layout
24062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24065 \begin_layout Plain Layout
24066 \begin_inset Formula $\notin$
24076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24079 \begin_layout Plain Layout
24087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24090 \begin_layout Plain Layout
24091 \begin_inset Formula $\perp$
24101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24104 \begin_layout Plain Layout
24112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24115 \begin_layout Plain Layout
24116 \begin_inset Formula $\propto$
24126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24129 \begin_layout Plain Layout
24137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24140 \begin_layout Plain Layout
24141 \begin_inset Formula $\asymp$
24151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24154 \begin_layout Plain Layout
24162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24165 \begin_layout Plain Layout
24166 \begin_inset Formula $\doteq$
24176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24179 \begin_layout Plain Layout
24187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24190 \begin_layout Plain Layout
24191 \begin_inset Formula $\circeq$
24201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24204 \begin_layout Plain Layout
24212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24215 \begin_layout Plain Layout
24216 \begin_inset Formula $\models$
24226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24229 \begin_layout Plain Layout
24237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24240 \begin_layout Plain Layout
24241 \begin_inset Formula $\widehat{=}$
24255 \begin_inset space \hfill{}
24259 \begin_inset Tabular
24260 <lyxtabular version="3" rows="17" columns="2">
24261 <features tabularvalignment="middle">
24262 <column alignment="center" valignment="top" width="0pt">
24263 <column alignment="center" valignment="top" width="0pt">
24265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24268 \begin_layout Plain Layout
24274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24277 \begin_layout Plain Layout
24285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24288 \begin_layout Plain Layout
24294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24297 \begin_layout Plain Layout
24298 \begin_inset Formula $>$
24308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24311 \begin_layout Plain Layout
24319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24322 \begin_layout Plain Layout
24323 \begin_inset Formula $\ge$
24333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24336 \begin_layout Plain Layout
24344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24347 \begin_layout Plain Layout
24348 \begin_inset Formula $\gg$
24358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24361 \begin_layout Plain Layout
24369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24372 \begin_layout Plain Layout
24373 \begin_inset Formula $\succ$
24383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24386 \begin_layout Plain Layout
24394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24397 \begin_layout Plain Layout
24398 \begin_inset Formula $\succeq$
24408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24411 \begin_layout Plain Layout
24419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24422 \begin_layout Plain Layout
24423 \begin_inset Formula $\supset$
24433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24436 \begin_layout Plain Layout
24444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24447 \begin_layout Plain Layout
24448 \begin_inset Formula $\supseteq$
24458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24461 \begin_layout Plain Layout
24469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24472 \begin_layout Plain Layout
24473 \begin_inset Formula $\sqsupseteq$
24483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24486 \begin_layout Plain Layout
24494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24497 \begin_layout Plain Layout
24498 \begin_inset Formula $\ni$
24508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24511 \begin_layout Plain Layout
24519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24522 \begin_layout Plain Layout
24523 \begin_inset Formula $\dashv$
24533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24536 \begin_layout Plain Layout
24544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24547 \begin_layout Plain Layout
24548 \begin_inset Formula $\frown$
24558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24561 \begin_layout Plain Layout
24569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24572 \begin_layout Plain Layout
24573 \begin_inset Formula $\rhd$
24583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24586 \begin_layout Plain Layout
24594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24597 \begin_layout Plain Layout
24598 \begin_inset Formula $\unrhd$
24608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24611 \begin_layout Plain Layout
24619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24622 \begin_layout Plain Layout
24623 \begin_inset Formula $\lessgtr$
24633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24636 \begin_layout Plain Layout
24644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24647 \begin_layout Plain Layout
24648 \begin_inset Formula $\parallel$
24658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24661 \begin_layout Plain Layout
24669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24672 \begin_layout Plain Layout
24673 \begin_inset Formula $\nparallel$
24687 \begin_inset space \hfill{}
24693 \begin_layout Standard
24694 \begin_inset VSpace medskip
24709 are bigger than the equal looking operators
24724 \begin_layout Standard
24725 Relations are, in contrary to symbols, always surrounded by space.
24728 \begin_layout Standard
24729 Relations with labels can be created with the command
24736 \begin_inset Index idx
24739 \begin_layout Plain Layout
24750 \begin_layout Standard
24752 \begin_inset Tabular
24753 <lyxtabular version="3" rows="2" columns="2">
24754 <features tabularvalignment="middle">
24755 <column alignment="center" valignment="top" width="0">
24756 <column alignment="center" valignment="top" width="0">
24758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24761 \begin_layout Plain Layout
24767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24770 \begin_layout Plain Layout
24772 \begin_inset Note Note
24775 \begin_layout Plain Layout
24782 is only used as spacer.
24794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24797 \begin_layout Plain Layout
24804 \begin_layout Plain Layout
24821 \begin_layout Plain Layout
24831 \begin_inset Formula $\downarrow$
24840 \begin_layout Plain Layout
24853 \begin_layout Plain Layout
24867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24870 \begin_layout Plain Layout
24871 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24887 \begin_layout Section
24891 \begin_layout Subsection
24892 Predefined Functions
24893 \begin_inset CommandInset label
24895 name "sub:Predefined-Functions"
24900 \begin_inset Index idx
24903 \begin_layout Plain Layout
24904 Functions ! predefined
24912 \begin_layout Standard
24913 In general, variables are set
24917 in mathematical expressions, but not function names, because
24918 \begin_inset Formula $sin$
24921 could be misunderstood as
24922 \begin_inset Formula $s\cdot i\cdot n$
24926 Therefore there are predefined functionswhich are additionally a bit separated
24928 They are inserted as commands starting with a backslash before their name.
24931 \begin_layout Standard
24933 \begin_inset Tabular
24934 <lyxtabular version="3" rows="2" columns="4">
24935 <features tabularvalignment="middle">
24936 <column alignment="center" valignment="top" width="0pt">
24937 <column alignment="center" valignment="top" width="0pt">
24938 <column alignment="center" valignment="top" width="0pt">
24939 <column alignment="center" valignment="top" width="0pt">
24941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24944 \begin_layout Plain Layout
24950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24953 \begin_layout Plain Layout
24959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24962 \begin_layout Plain Layout
24968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24971 \begin_layout Plain Layout
24979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24982 \begin_layout Plain Layout
24988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24991 \begin_layout Plain Layout
24992 \begin_inset Formula $Asin(x)+B$
25000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25003 \begin_layout Plain Layout
25011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25014 \begin_layout Plain Layout
25015 \begin_inset Formula $A\sin(x)+B$
25031 \begin_layout Standard
25032 The following functions are predefined:
25035 \begin_layout Standard
25036 \begin_inset VSpace -2mm
25042 \begin_layout Standard
25044 \begin_inset Tabular
25045 <lyxtabular version="3" rows="9" columns="4">
25046 <features tabularvalignment="middle">
25047 <column alignment="center" valignment="top" width="0pt">
25048 <column alignment="center" valignment="top" width="0pt">
25049 <column alignment="center" valignment="top" width="0pt">
25050 <column alignment="center" valignment="top" width="0pt">
25052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25055 \begin_layout Plain Layout
25061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25064 \begin_layout Plain Layout
25070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25073 \begin_layout Plain Layout
25079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25082 \begin_layout Plain Layout
25090 <cell alignment="center" valignment="top" topline="true" leftline="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" rightline="true" usebox="none">
25126 \begin_layout Plain Layout
25136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25139 \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" rightline="true" usebox="none">
25172 \begin_layout Plain Layout
25182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25185 \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" rightline="true" usebox="none">
25218 \begin_layout Plain Layout
25228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25231 \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" rightline="true" usebox="none">
25264 \begin_layout Plain Layout
25274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25277 \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" rightline="true" usebox="none">
25310 \begin_layout Plain Layout
25320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25323 \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" rightline="true" usebox="none">
25356 \begin_layout Plain Layout
25366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25369 \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" rightline="true" usebox="none">
25402 \begin_layout Plain Layout
25412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25415 \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" rightline="true" usebox="none">
25448 \begin_layout Plain Layout
25464 \begin_layout Standard
25465 They can also be inserted with the math toolbar button
25466 \begin_inset Graphics
25467 filename ../images/math/functions.png
25475 \begin_layout Subsection
25476 Self-defined Functions
25477 \begin_inset Index idx
25480 \begin_layout Plain Layout
25481 Functions ! self-defined
25489 \begin_layout Standard
25490 To use a function that is not predefined, like for example the sign function
25491 sgn(x), there are two possibilities:
25494 \begin_layout Itemize
25495 Define the function by inserting the following line to the LaTeX-preamble
25499 \begin_layout Plain Layout
25504 DeclareMathOperator
25507 \begin_inset CommandInset ref
25509 reference "sub:Self-defined-Operators"
25519 \begin_inset Newline newline
25523 \begin_inset VSpace -3mm
25527 \begin_inset Newline newline
25534 DeclareMathOperator{
25539 \begin_inset Index idx
25542 \begin_layout Plain Layout
25547 DeclareMathOperator
25553 \begin_inset Newline newline
25557 \begin_inset VSpace -2mm
25561 \begin_inset Newline newline
25564 Now the new defined function can be called with the command
25573 \begin_layout Itemize
25574 Write the formula as usual, mark the formula name, in our example the letters
25579 , and change it to mathematical text.
25580 Finally, a space is inserted between prefactor and function.
25583 \begin_layout Standard
25584 The result is the same with both methods as with a predefined function
25588 \begin_layout Plain Layout
25589 In LyX self-defined functions are displayed red, predefined ones black.
25597 \begin_layout Standard
25599 \begin_inset Tabular
25600 <lyxtabular version="3" rows="3" columns="2">
25601 <features tabularvalignment="middle">
25602 <column alignment="center" valignment="top" width="0pt">
25603 <column alignment="center" valignment="top" width="0pt">
25605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25608 \begin_layout Plain Layout
25614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25617 \begin_layout Plain Layout
25625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25628 \begin_layout Plain Layout
25636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25639 \begin_layout Plain Layout
25640 \begin_inset Formula $A\sgn(x)+B$
25650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25653 \begin_layout Plain Layout
25657 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25668 \begin_layout Plain Layout
25669 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25685 \begin_layout Standard
25686 The first method is more suitable when the self-defined function should
25687 be used several times.
25690 \begin_layout Subsection
25692 \begin_inset Index idx
25695 \begin_layout Plain Layout
25704 \begin_layout Standard
25705 For limits, in addition to the commands
25712 \begin_inset Index idx
25715 \begin_layout Plain Layout
25735 the following functions are defined:
25738 \begin_layout Standard
25740 \begin_inset Tabular
25741 <lyxtabular version="3" rows="5" columns="2">
25742 <features tabularvalignment="middle">
25743 <column alignment="center" valignment="top" width="0">
25744 <column alignment="center" valignment="top" width="0">
25746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25749 \begin_layout Plain Layout
25755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25758 \begin_layout Plain Layout
25760 \begin_inset Note Note
25763 \begin_layout Plain Layout
25770 is only used as spacer.
25782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25785 \begin_layout Plain Layout
25793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25796 \begin_layout Plain Layout
25797 \begin_inset Formula $\varliminf$
25807 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25810 \begin_layout Plain Layout
25818 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25821 \begin_layout Plain Layout
25822 \begin_inset Formula $\varlimsup$
25832 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25835 \begin_layout Plain Layout
25843 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25846 \begin_layout Plain Layout
25847 \begin_inset Formula $\varprojlim$
25857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25860 \begin_layout Plain Layout
25868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25871 \begin_layout Plain Layout
25872 \begin_inset Formula $\varinjlim$
25876 \begin_inset Formula $\raisebox{-2.5mm}{}$
25892 \begin_layout Standard
25893 \begin_inset VSpace medskip
25896 The limit is created by inserting a subscript.
25897 It is set right beside the function in an inline formula:
25900 \begin_layout Standard
25902 \begin_inset Tabular
25903 <lyxtabular version="3" rows="2" columns="2">
25904 <features tabularvalignment="middle">
25905 <column alignment="center" valignment="top" width="0pt">
25906 <column alignment="center" valignment="top" width="0pt">
25908 <cell alignment="center" valignment="top" usebox="none">
25911 \begin_layout Plain Layout
25917 <cell alignment="center" valignment="top" usebox="none">
25920 \begin_layout Plain Layout
25921 \begin_inset space \hspace{}
25926 \begin_inset Note Note
25929 \begin_layout Plain Layout
25936 are used here as spacer.
25948 <cell alignment="center" valignment="top" usebox="none">
25951 \begin_layout Plain Layout
25960 \begin_layout Plain Layout
25973 \begin_layout Plain Layout
25987 <cell alignment="center" valignment="top" usebox="none">
25990 \begin_layout Plain Layout
25991 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
26007 \begin_layout Standard
26008 In a displayed formula the limit is set below the formula, as usual:
26009 \begin_inset Formula
26019 \begin_layout Subsection
26021 \begin_inset Index idx
26024 \begin_layout Plain Layout
26025 Functions ! modulo-
26033 \begin_layout Standard
26034 The modulo-function is special, because it exists in four variants.
26035 The variants in a displayed formula are:
26036 \begin_inset Formula
26038 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26039 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
26040 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
26041 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
26042 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
26050 \begin_layout Standard
26051 In an inline formula less space is set before the function names for all
26053 By default the modulo-functions take only the first following character
26055 To use more than one character, one has to put them into TeX-braces:
26056 \begin_inset Formula
26058 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26059 \mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\
26060 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26068 \begin_layout Section
26070 \begin_inset Index idx
26073 \begin_layout Plain Layout
26082 \begin_layout Subsection
26083 Special Characters in Mathematical Text
26086 \begin_layout Standard
26087 The following commands can only be used in mathematical text or in TeX-mode:
26090 \begin_layout Standard
26091 \begin_inset space \hfill{}
26095 \begin_inset Tabular
26096 <lyxtabular version="3" rows="8" columns="2">
26097 <features tabularvalignment="middle">
26098 <column alignment="block" valignment="top" width="0">
26099 <column alignment="block" valignment="top" width="0">
26101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26104 \begin_layout Plain Layout
26110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26113 \begin_layout Plain Layout
26121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26124 \begin_layout Plain Layout
26132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26135 \begin_layout Plain Layout
26136 \begin_inset Formula $\textrm{œ}$
26146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26149 \begin_layout Plain Layout
26157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26160 \begin_layout Plain Layout
26161 \begin_inset Formula $\textrm{Œ}$
26171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26174 \begin_layout Plain Layout
26182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26185 \begin_layout Plain Layout
26186 \begin_inset Formula $\textrm{æ}$
26196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26199 \begin_layout Plain Layout
26207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26210 \begin_layout Plain Layout
26211 \begin_inset Formula $\textrm{Æ}$
26221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26224 \begin_layout Plain Layout
26232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26235 \begin_layout Plain Layout
26236 \begin_inset Formula $\textrm{\aa}$
26246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26249 \begin_layout Plain Layout
26253 \begin_inset Index idx
26256 \begin_layout Plain Layout
26263 \begin_layout Plain Layout
26284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26287 \begin_layout Plain Layout
26288 \begin_inset Formula $\textrm{Å}$
26298 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26301 \begin_layout Plain Layout
26309 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26312 \begin_layout Plain Layout
26313 \begin_inset Formula $\textrm{ı}$
26327 \begin_inset space \hfill{}
26331 \begin_inset Tabular
26332 <lyxtabular version="3" rows="8" columns="2">
26333 <features tabularvalignment="middle">
26334 <column alignment="block" valignment="top" width="0">
26335 <column alignment="center" valignment="top" width="0">
26337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26340 \begin_layout Plain Layout
26342 \begin_inset Note Note
26345 \begin_layout Plain Layout
26347 \begin_inset space \thinspace{}
26350 mm is used for separation, because otherwise the output will be ¡ and ¿
26361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26364 \begin_layout Plain Layout
26372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26375 \begin_layout Plain Layout
26383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26386 \begin_layout Plain Layout
26387 \begin_inset Formula $\textrm{ø}$
26397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26400 \begin_layout Plain Layout
26408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26411 \begin_layout Plain Layout
26412 \begin_inset Formula $\textrm{Ø}$
26422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26425 \begin_layout Plain Layout
26433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26436 \begin_layout Plain Layout
26437 \begin_inset Formula $\textrm{ł}$
26447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26450 \begin_layout Plain Layout
26458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26461 \begin_layout Plain Layout
26462 \begin_inset Formula $\textrm{Ł}$
26472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26475 \begin_layout Plain Layout
26477 \begin_inset space \hspace{}
26485 \begin_layout Plain Layout
26499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26502 \begin_layout Plain Layout
26503 \begin_inset Formula $\textrm{!`}$
26513 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26516 \begin_layout Plain Layout
26518 \begin_inset space \hspace{}
26526 \begin_layout Plain Layout
26540 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26543 \begin_layout Plain Layout
26544 \begin_inset Formula $\textrm{?`}$
26554 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26557 \begin_layout Plain Layout
26565 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26568 \begin_layout Plain Layout
26569 \begin_inset Formula $\textrm{ȷ}$
26583 \begin_inset space \hfill{}
26589 \begin_layout Standard
26591 \begin_inset Formula $\textrm{\textrm{Å}}$
26595 \begin_inset Formula $\textrm{\textrm{Ø}}$
26598 can also be inserted via the math toolbar button
26599 \begin_inset Graphics
26600 filename ../images/math/digamma.png
26608 \begin_layout Standard
26609 An exception are the commands
26612 \begin_inset space \hspace{}
26621 \begin_inset space \hspace{}
26627 , because they can be inserted in LyX directly to text.
26630 \begin_layout Subsection
26632 \begin_inset CommandInset label
26634 name "sub:Accents-in-Text"
26639 \begin_inset Index idx
26642 \begin_layout Plain Layout
26651 \begin_layout Standard
26652 With the following commands all letters can be accented.
26653 The commands must be inserted in TeX-mode.
26656 \begin_layout Standard
26657 \begin_inset space \hfill{}
26661 \begin_inset Tabular
26662 <lyxtabular version="3" rows="8" columns="2">
26663 <features tabularvalignment="middle">
26664 <column alignment="block" valignment="top" width="0">
26665 <column alignment="block" valignment="top" width="0">
26667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26670 \begin_layout Plain Layout
26676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26679 \begin_layout Plain Layout
26687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26690 \begin_layout Plain Layout
26694 \begin_inset Quotes grd
26702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26705 \begin_layout Plain Layout
26709 \begin_layout Plain Layout
26725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26728 \begin_layout Plain Layout
26736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26739 \begin_layout Plain Layout
26743 \begin_layout Plain Layout
26759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26762 \begin_layout Plain Layout
26769 \begin_layout Plain Layout
26783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26786 \begin_layout Plain Layout
26790 \begin_layout Plain Layout
26806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26809 \begin_layout Plain Layout
26817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26820 \begin_layout Plain Layout
26824 \begin_layout Plain Layout
26840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26843 \begin_layout Plain Layout
26850 \begin_layout Plain Layout
26864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26867 \begin_layout Plain Layout
26871 \begin_layout Plain Layout
26887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26890 \begin_layout Plain Layout
26897 \begin_layout Plain Layout
26911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26914 \begin_layout Plain Layout
26918 \begin_layout Plain Layout
26934 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26937 \begin_layout Plain Layout
26944 \begin_layout Plain Layout
26958 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26961 \begin_layout Plain Layout
26965 \begin_layout Plain Layout
26985 \begin_inset space \hfill{}
26989 \begin_inset Tabular
26990 <lyxtabular version="3" rows="8" columns="2">
26991 <features tabularvalignment="middle">
26992 <column alignment="block" valignment="top" width="0">
26993 <column alignment="center" valignment="top" width="0">
26995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26998 \begin_layout Plain Layout
27004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27007 \begin_layout Plain Layout
27015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27018 \begin_layout Plain Layout
27025 \begin_layout Plain Layout
27039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27042 \begin_layout Plain Layout
27046 \begin_layout Plain Layout
27062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27065 \begin_layout Plain Layout
27073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27076 \begin_layout Plain Layout
27080 \begin_layout Plain Layout
27096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27099 \begin_layout Plain Layout
27103 \begin_inset Index idx
27106 \begin_layout Plain Layout
27117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27120 \begin_layout Plain Layout
27124 \begin_layout Plain Layout
27140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27143 \begin_layout Plain Layout
27151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27154 \begin_layout Plain Layout
27158 \begin_layout Plain Layout
27174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27177 \begin_layout Plain Layout
27184 \begin_layout Plain Layout
27198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27201 \begin_layout Plain Layout
27205 \begin_layout Plain Layout
27221 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27224 \begin_layout Plain Layout
27231 \begin_layout Plain Layout
27245 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27248 \begin_layout Plain Layout
27252 \begin_layout Plain Layout
27268 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27271 \begin_layout Plain Layout
27278 \begin_layout Plain Layout
27292 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27295 \begin_layout Plain Layout
27299 \begin_layout Plain Layout
27319 \begin_inset space \hfill{}
27325 \begin_layout Standard
27326 \begin_inset VSpace medskip
27335 also two different characters can be accented.
27344 \begin_layout Plain Layout
27359 \begin_layout Plain Layout
27371 \begin_layout Standard
27384 can in combination with vowels directly be inserted with the keyboard without
27386 The same applies for the tilde
27390 \begin_layout Plain Layout
27391 This only applies for keyboards where the tilde is defined as accent.
27400 in combination with
27415 \begin_layout Standard
27458 and accents that are inserted directly with the keyboard are also available
27459 in mathematical text.
27460 For the other accents there are special math commands to be used in formulas,
27462 \begin_inset CommandInset ref
27464 reference "sub:Accents-for-one"
27471 \begin_layout Standard
27472 \begin_inset VSpace bigskip
27475 Furthermore, with the command
27482 \begin_inset Index idx
27485 \begin_layout Plain Layout
27493 all numbers and letters can be set into a circle, quasi accented with a
27494 circle, similar to the copyright symbol.
27497 \begin_layout Standard
27499 \begin_inset Tabular
27500 <lyxtabular version="3" rows="3" columns="2">
27501 <features tabularvalignment="middle">
27502 <column alignment="center" valignment="top" width="0">
27503 <column alignment="center" valignment="top" width="0">
27505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27508 \begin_layout Plain Layout
27514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27517 \begin_layout Plain Layout
27519 \begin_inset Note Note
27522 \begin_layout Plain Layout
27529 is only used as spacer.
27541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27544 \begin_layout Plain Layout
27552 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27555 \begin_layout Plain Layout
27559 \begin_layout Plain Layout
27575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27578 \begin_layout Plain Layout
27589 raisebox{-1.5pt}{W}}
27594 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27597 \begin_layout Plain Layout
27598 \begin_inset Formula $\raisebox{4.5mm}{}$
27605 \begin_layout Plain Layout
27623 \begin_inset Formula $\raisebox{-2mm}{}$
27639 \begin_layout Standard
27640 One has to take care that the character fits in the circle.
27651 \begin_layout Plain Layout
27653 \begin_inset CommandInset ref
27655 reference "sub:Font-Sizes"
27664 specifies thereby the size of the circle.
27675 \begin_layout Plain Layout
27677 \begin_inset CommandInset ref
27679 reference "sub:Boxes-without-Frame"
27688 the character can be centered.
27691 \begin_layout Subsection
27693 \begin_inset Index idx
27696 \begin_layout Plain Layout
27705 \begin_layout Standard
27706 Old-style figures (also known as old-style numerals) are created with the
27714 \begin_inset Index idx
27717 \begin_layout Plain Layout
27726 The command can be used in formulas and in TeX-mode.
27727 The command scheme is:
27730 \begin_layout Standard
27735 oldstylenums{number}
27738 \begin_layout Standard
27743 oldstylenums{0123456789
27746 \begin_inset Formula $\oldstylenums{0123456789}$
27752 \begin_layout Subsection
27753 Miscellaneous special Characters
27754 \begin_inset CommandInset label
27756 name "sub:Miscellaneous-special-Characters"
27761 \begin_inset Index idx
27764 \begin_layout Plain Layout
27765 Special characters ! miscellaneous
27773 \begin_layout Standard
27774 The following characters can only be inserted to formulas by using commands:
27777 \begin_layout Standard
27779 \begin_inset Tabular
27780 <lyxtabular version="3" rows="4" columns="2">
27781 <features tabularvalignment="middle">
27782 <column alignment="center" valignment="top" width="0">
27783 <column alignment="center" valignment="top" width="0">
27785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27788 \begin_layout Plain Layout
27794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27797 \begin_layout Plain Layout
27805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27808 \begin_layout Plain Layout
27815 \begin_layout Plain Layout
27829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27832 \begin_layout Plain Layout
27833 \begin_inset Formula $\mathcircumflex$
27843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27846 \begin_layout Plain Layout
27854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27857 \begin_layout Plain Layout
27858 \begin_inset Formula $\_$
27868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27871 \begin_layout Plain Layout
27876 \begin_layout Plain Layout
27888 \begin_inset Index idx
27891 \begin_layout Plain Layout
27904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27907 \begin_layout Plain Layout
27908 \begin_inset Formula $^{\circ}$
27924 \begin_layout Standard
27925 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27926 contains the following line
27930 \begin_layout Plain Layout
27931 More about this is described in
27932 \begin_inset CommandInset ref
27934 reference "sub:Text-Characters-in"
27946 \begin_layout Standard
27951 DeclareInputtext{176}{
27964 \begin_layout Section
27966 \begin_inset CommandInset label
27968 name "sec:Formula-Styles"
27973 \begin_inset Index idx
27976 \begin_layout Plain Layout
27985 \begin_layout Itemize
27986 There are two different alignment styles:
27990 \begin_layout Description
27991 Centered is the predefined standard
27994 \begin_layout Description
27995 Indented for this the option
27999 must be inserted in the menu
28001 Document\SpecialChar \menuseparator
28007 \begin_inset space ~
28013 \begin_layout Standard
28018 is used, the indentation can be adjusted with the length
28025 \begin_inset Index idx
28028 \begin_layout Plain Layout
28037 Should the distance be 15
28038 \begin_inset space \thinspace{}
28041 mm, the following command line is inserted in the LaTeX-preamble
28044 \begin_layout Standard
28054 \begin_layout Standard
28055 When no length is specified, the predefined value of 30
28056 \begin_inset space \thinspace{}
28063 \begin_layout Itemize
28064 And two different numbering styles:
28068 \begin_layout Description
28069 Right is the predefined standard
28072 \begin_layout Description
28073 Left for this the option
28077 must be inserted in the menu
28079 Document\SpecialChar \menuseparator
28085 \begin_inset space ~
28092 \begin_layout Standard
28101 can also be used together.
28102 In this case both options are inserted, separated by a comma.
28105 \begin_layout Standard
28106 The chosen styles are used for all displayed formulas of the document.
28107 When both, centered and indented formulas should be created in a document,
28113 The indented formulas are then set in a flalign environment, see
28114 \begin_inset CommandInset ref
28116 reference "sub:Flalign-Environment"
28123 \begin_layout Section
28125 \begin_inset CommandInset label
28127 name "sec:Multiline-Formulas"
28132 \begin_inset Index idx
28135 \begin_layout Plain Layout
28136 Formula ! multiline
28144 \begin_layout Subsection
28148 \begin_layout Standard
28149 In LyX multiline formulas are created by pressing
28154 arg "newline-insert newline"
28160 This creates either an
28162 eqnarray environment
28164 that is described in
28165 \begin_inset CommandInset ref
28167 reference "sub:Eqnarray-Environment"
28171 or, when the option
28173 Use AMS math package
28175 in the document settings is selected, an
28179 that is described in
28180 \begin_inset CommandInset ref
28182 reference "sub:Standard-align-Environment"
28187 The align environment is recommended because it provides in any case a
28188 typographically correct output.
28191 \begin_layout Standard
28192 There are other multiline formula environments that can be created via the
28195 Insert\SpecialChar \menuseparator
28199 These environments are described in the following sections.
28202 \begin_layout Standard
28203 In all multiline formula environments a new line is created by pressing
28207 arg "newline-insert newline"
28211 To add or delete lines, the math toolbar buttons
28212 \begin_inset Graphics
28213 filename ../images/tabular-feature_append-row.png
28219 \begin_inset Graphics
28220 filename ../images/tabular-feature_delete-row.png
28225 , respectively, or the menu
28227 Edit\SpecialChar \menuseparator
28233 \begin_layout Subsubsection
28235 \begin_inset CommandInset label
28237 name "sub:Line-Separation"
28242 \begin_inset Index idx
28245 \begin_layout Plain Layout
28246 Formula ! multiline ! Line separation
28254 \begin_layout Standard
28255 There is sometimes not enough space in multiline formulas between the lines:
28256 \begin_inset Formula
28258 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}\\
28259 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
28267 \begin_layout Standard
28268 In LaTeX additional line space is specified as optional argument of the
28270 This is not yet possible in LyX
28274 \begin_layout Plain Layout
28276 \begin_inset CommandInset href
28278 name "LyX-bug #1505"
28279 target "http://www.lyx.org/trac/ticket/1505"
28288 , therefore the whole formula must be inserted in TeX-mode.
28289 To add in our example space, the command
28297 is inserted at the end of the first line.
28302 \begin_layout Plain Layout
28309 \begin_layout Plain Layout
28311 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28314 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28321 \begin_layout Plain Layout
28325 left(B^{2}+x_{0}^{2}
28333 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28338 \begin_layout Plain Layout
28350 \begin_layout Standard
28351 \begin_inset VSpace bigskip
28354 To set the line separation for all lines in a formula, the length
28361 \begin_inset Index idx
28364 \begin_layout Plain Layout
28374 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28385 \begin_inset space \thinspace{}
28390 \begin_inset space \thinspace{}
28393 mm additional line separation as in the previous example, the command
28396 \begin_layout Standard
28406 \begin_layout Standard
28407 is inserted in TeX-mode before the formula.
28408 This requires that the LaTeX-package
28416 \begin_layout Plain Layout
28421 is part of every LaTeX standard installation.
28427 \begin_inset Index idx
28430 \begin_layout Plain Layout
28436 was loaded in LaTeX-preamble with the line
28439 \begin_layout Standard
28447 \begin_layout Standard
28452 \begin_layout Plain Layout
28464 \begin_inset Formula
28466 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}\\
28467 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
28475 \begin_layout Standard
28479 \begin_layout Plain Layout
28490 To get back to the predefined distance,
28496 is set to the value 3
28497 \begin_inset space \thinspace{}
28503 \begin_layout Subsubsection
28505 \begin_inset CommandInset label
28507 name "sub:Column-Separation"
28512 \begin_inset Index idx
28515 \begin_layout Plain Layout
28516 Formula ! multiline ! Column separation
28524 \begin_layout Standard
28525 Multiline formulas form a matrix.
28526 A formula in the eqnarray environment is for example a matrix with three
28528 By changing the column separation in this environment, the space beside
28529 the relation sign can be changed.
28532 \begin_layout Standard
28533 The column separation is specified with the length
28540 \begin_inset Index idx
28543 \begin_layout Plain Layout
28552 \begin_inset Newline newline
28555 column separation = 2
28556 \begin_inset space \thinspace{}
28566 \begin_inset Newline newline
28572 \begin_layout Standard
28582 \begin_layout Standard
28583 inserted in TeX-mode, sets for all following formulas a column separation
28585 \begin_inset space \thinspace{}
28589 To get back to the predefined distance,
28596 \begin_inset space \thinspace{}
28602 \begin_layout Standard
28604 \begin_inset space \thinspace{}
28607 cm column separation:
28611 \begin_layout Plain Layout
28623 \begin_inset Formula
28631 A formula with the predefined column separation for matrices of 10
28632 \begin_inset space \thinspace{}
28639 \begin_layout Plain Layout
28651 \begin_inset Formula
28662 \begin_layout Subsubsection
28664 \begin_inset Index idx
28667 \begin_layout Plain Layout
28676 \begin_layout Standard
28677 Long formulas can be typeset using these methods:
28680 \begin_layout Itemize
28681 When one side of the equation is much shorter than the line width, this
28682 one is chosen for the left side and the right side is typeset over two
28684 \begin_inset Formula
28686 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 \\
28687 & & -\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}
28692 The minus sign at the beginning of the second line does normally not appear
28693 as an operator because it is the first character of the line.
28694 Thus it would not be surrounded by space and could not be distinguished
28695 from the fraction bar.
28697 \begin_inset space \thinspace{}
28700 pt space was inserted behind the minus sign with the command
28710 \begin_layout Plain Layout
28718 \begin_inset CommandInset ref
28720 reference "sub:Variable-Space"
28730 \begin_inset Index idx
28733 \begin_layout Plain Layout
28744 \begin_layout Itemize
28745 When both sides of the equation are too long, the command
28752 \begin_inset Index idx
28755 \begin_layout Plain Layout
28764 It is inserted in the first column of the first line and causes all further
28765 insertions to overwrite the following columns:
28766 \begin_inset Formula
28768 \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 \\
28769 & & -\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 \\
28770 & & =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}
28775 After the insertion of
28781 , the cursor is in a purple box that is a bit shifted to the left from the
28783 In this the formula is inserted.
28784 \begin_inset Newline newline
28787 The content of the further lines is inserted to the second or another formula
28789 The greater the column number where it was inserted, the larger the indentation.
28790 \begin_inset VSpace medskip
28794 \begin_inset Newline newline
28798 \begin_inset Note Greyedout
28801 \begin_layout Plain Layout
28802 Note the following when using
28811 \begin_layout Itemize
28812 The formula doesn't use the full page width.
28814 \begin_inset space \thinspace{}
28818 \begin_inset space \space{}
28822 \begin_inset Formula $-B^{2}$
28825 is added to the first line in the above example, it would have been outside
28827 To better use the width, negative space can be inserted at the beginning
28831 \begin_layout Itemize
28832 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28837 \begin_layout Plain Layout
28838 \begin_inset CommandInset href
28840 name "LyX-bug #1429"
28841 target "http://www.lyx.org/trac/ticket/1429"
28850 One can only set the cursor at the beginning of the line and move it with
28859 \begin_layout Itemize
28860 Other methods to set long formulas are offered by the environments described
28862 \begin_inset CommandInset ref
28864 reference "sub:Multline-Environment"
28869 \begin_inset CommandInset ref
28871 reference "sub:Multiline-Formula-Parts"
28878 \begin_layout Subsubsection
28880 \begin_inset CommandInset label
28882 name "sub:Multiline-Brackets"
28887 \begin_inset Index idx
28890 \begin_layout Plain Layout
28891 Brackets ! for multiline expressions
28899 \begin_layout Standard
28900 For brackets spanning multiple lines the following problem occurs:
28901 \begin_inset Formula
28903 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28904 & & \left.\cdots+B-D\right]
28912 \begin_layout Standard
28913 The closing bracket is smaller than the opening bracket because brackets
28914 with variable size may not span multiple lines.
28917 \begin_layout Standard
28918 To set the bracket size for the second line correctly, the first line is
28926 \begin_inset Index idx
28929 \begin_layout Plain Layout
28937 and the second line with
28945 \begin_layout Plain Layout
28959 \begin_inset CommandInset ref
28961 reference "sub:Automatic-Bracket-Size"
28973 \begin_inset Index idx
28976 \begin_layout Plain Layout
29002 \begin_layout Plain Layout
29021 \begin_layout Plain Layout
29040 \begin_layout Plain Layout
29052 \begin_inset Formula $\downarrow$
29058 \begin_inset Index idx
29061 \begin_layout Plain Layout
29069 is inserted, because the multiplication operator with its limits is the
29070 largest symbol in the first line and this should be the size for the bracket
29071 in the second line.
29074 \begin_layout Standard
29075 The result is this:
29076 \begin_inset Formula
29078 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29079 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29087 \begin_layout Subsection
29091 \begin_layout Standard
29092 Align environments can be used for every kind of multiline formulas.
29093 They are especially useful to set several formulas side by side.
29096 \begin_layout Standard
29097 Align environments consist of columns.
29098 The odd columns are right aligned, the even ones left aligned.
29099 Every line in an Align environment can be numbered.
29102 \begin_layout Standard
29103 Align environments are created via the menu
29105 Insert\SpecialChar \menuseparator
29111 Edit\SpecialChar \menuseparator
29112 Math\SpecialChar \menuseparator
29113 Change Formula Type
29115 already existing formulas can be converted to Align environments.
29118 \begin_layout Standard
29119 To add or delete columns, the math toolbar buttons
29120 \begin_inset Graphics
29121 filename ../images/tabular-feature_append-column.png
29127 \begin_inset Graphics
29128 filename ../images/tabular-feature_delete-column.png
29133 , respectively, or the menu
29135 Edit\SpecialChar \menuseparator
29141 \begin_layout Subsubsection
29142 Standard align Environment
29143 \begin_inset CommandInset label
29145 name "sub:Standard-align-Environment"
29150 \begin_inset Index idx
29153 \begin_layout Plain Layout
29154 Formula ! multiline ! align environment
29162 \begin_layout Standard
29163 This Align environment is created by pressing
29166 arg "newline-insert newline"
29169 in a formula or by the menu
29171 Insert\SpecialChar \menuseparator
29172 Math\SpecialChar \menuseparator
29173 AMS align Environment
29178 \begin_layout Standard
29179 An example for two formulas set side by side, that are created with a four
29180 column align environment:
29181 \begin_inset Formula
29183 A & =\sin(B) & C & =D\\
29184 C & \ne A & B & \ne D
29189 As it can be seen, the formulas in this environment are placed so as if
29198 \begin_layout Plain Layout
29206 \begin_inset CommandInset ref
29208 reference "sub:Variable-Space"
29219 before the first and after every even column.
29220 When the formula style
29226 \begin_layout Plain Layout
29228 \begin_inset CommandInset ref
29230 reference "sec:Formula-Styles"
29241 is used, the formula is set without the
29247 before the first column.
29250 \begin_layout Subsubsection
29251 Alignat Environment
29252 \begin_inset Index idx
29255 \begin_layout Plain Layout
29256 Formula ! multiline ! alignat environment
29264 \begin_layout Standard
29265 The alignat environment has no predefined column separation.
29266 It can be inserted manually with the spaces that are described
29267 \begin_inset CommandInset ref
29269 reference "sub:Space"
29276 \begin_layout Standard
29277 The above example in the alignat environment where 1
29278 \begin_inset space \thinspace{}
29281 cm space was inserted at the beginning of the second formula:
29282 \begin_inset Formula
29283 \begin{alignat*}{2}
29284 A & =\sin(B) & \hspace{1cm}C & =D\\
29285 C & \ne A & B & \ne D
29290 Because the column separation can be set separately for every column, this
29291 environment is especially suitable to set three and more formulas side
29295 \begin_layout Subsubsection
29296 Flalign Environment
29297 \begin_inset CommandInset label
29299 name "sub:Flalign-Environment"
29304 \begin_inset Index idx
29307 \begin_layout Plain Layout
29308 Formula ! multiline ! flalign environment
29316 \begin_layout Standard
29317 In this environment the first two columns are always set as much as possible
29318 to the left and the last two ones to the right.
29320 \begin_inset Formula
29322 A & =1 & B & =2 & C & =3\\
29323 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29331 \begin_layout Standard
29332 By creating a flalign environment with an odd number of columns where an
29333 empty TeX-brace is inserted to the last column, several formulas in a document
29334 can be set to the left, although the formula style
29339 As example the indented formula
29340 \begin_inset CommandInset ref
29342 reference "eq:VolInt"
29347 \begin_inset Formula
29349 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29354 The first two columns contain the formula.
29355 To indent it as with the formula style
29360 \begin_inset space \thinspace{}
29363 pt space was inserted at the beginning of the first column.
29366 \begin_layout Subsection
29367 Eqnarray Environment
29368 \begin_inset CommandInset label
29370 name "sub:Eqnarray-Environment"
29375 \begin_inset Index idx
29378 \begin_layout Plain Layout
29379 Formula ! multiline ! eqnarray environment
29387 \begin_layout Standard
29388 When this environment has been created, three blue boxes appear.
29389 The content of the first box is right aligned, the content of the last
29391 The content of the middle box appears centered and a bit smaller, because
29392 it is designed to insert there only relation characters.
29393 \begin_inset Formula
29395 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29405 \begin_layout Subsection
29407 \begin_inset Index idx
29410 \begin_layout Plain Layout
29411 Formula ! multiline ! gather environment
29419 \begin_layout Standard
29420 This environment consists of only one centered column.
29421 Every line can be numbered.
29422 \begin_inset Formula
29433 \begin_layout Subsection
29434 Multline Environment
29435 \begin_inset CommandInset label
29437 name "sub:Multline-Environment"
29442 \begin_inset Index idx
29445 \begin_layout Plain Layout
29446 Formula ! multiline ! multline environment
29454 \begin_layout Standard
29455 The multline environment consists, like the gather environment, of only
29457 But the first line is left aligned, the last one right aligned.
29458 All other lines are centered.
29459 Therefore this environment is suitable for long formulas.
29461 \begin_inset CommandInset ref
29463 reference "eq:lefteqn"
29467 in the multline environment:
29468 \begin_inset Formula
29470 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}\\
29471 -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}\\
29472 =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}}
29480 \begin_layout Standard
29481 In the output only the last (first) line of a multline environment appears
29482 numbered when the document numbering is right (left).
29486 \begin_layout Plain Layout
29487 numbering styles see
29488 \begin_inset CommandInset ref
29490 reference "sec:Formula-Styles"
29502 \begin_layout Standard
29510 \begin_inset Index idx
29513 \begin_layout Plain Layout
29528 \begin_inset Index idx
29531 \begin_layout Plain Layout
29539 a centered line can be right or left aligned, respectively.
29540 The commands are used as follows:
29543 \begin_layout Standard
29548 shoveright{line content}
29554 shoveleft{line content}
29557 \begin_layout Standard
29558 \begin_inset VSpace medskip
29568 \begin_inset Index idx
29571 \begin_layout Plain Layout
29579 specifies the distance of the first line from the left page margin.
29580 Predefined is the length 0
29581 \begin_inset space \thinspace{}
29587 \begin_layout Standard
29588 As example the above formula where the command
29591 \begin_layout Standard
29601 \begin_layout Standard
29602 was inserted in TeX-mode before:
29606 \begin_layout Plain Layout
29618 \begin_inset Formula
29620 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}\\
29621 \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}}\\
29622 =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}}
29631 \begin_layout Plain Layout
29642 The second line was left aligned using
29651 \begin_layout Subsection
29652 Multiline Formula Parts
29653 \begin_inset CommandInset label
29655 name "sub:Multiline-Formula-Parts"
29660 \begin_inset Index idx
29663 \begin_layout Plain Layout
29664 Formula ! multiline ! formula parts
29672 \begin_layout Standard
29673 To display only parts of a formula with multiple lines, one of the following
29674 environments is used:
29691 They can be inserted via the menu
29693 Insert\SpecialChar \menuseparator
29696 or by using the commands described in this section.
29699 \begin_layout Standard
29700 The first three have the same properties as the corresponding multiline
29701 formula environments, but it is possible to set further formula parts beside
29704 \begin_inset Formula
29706 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29707 \Delta E\Delta t & \ge\frac{\hbar}{2}
29709 \right\} \textrm{Uncertainty relations}
29717 \begin_layout Standard
29718 To get this formula, a displayed formula is created where the command
29725 \begin_inset Index idx
29728 \begin_layout Plain Layout
29737 A purple box appears around the blue formula box where now columns and
29738 lines can be added.
29739 Outside the multiline environment other formula parts can be set, like
29743 \begin_layout Standard
29744 The aligned environment is also suitable for long formulas whose lines are
29745 horizontally aligned.
29746 Using aligned in a displayed formula has the advantage that the formula
29747 number is vertically centered behind the lines.
29749 \begin_inset CommandInset ref
29751 reference "eq:shortlong"
29755 in the aligned environment:
29756 \begin_inset Formula
29758 \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}|}\\
29759 & -\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}|}
29768 \begin_layout Standard
29769 To use the environments
29788 \begin_inset Index idx
29791 \begin_layout Plain Layout
29806 \begin_inset Index idx
29809 \begin_layout Plain Layout
29824 \begin_inset Index idx
29827 \begin_layout Plain Layout
29835 are inserted, respectively.
29836 The split environment has the same properties as the aligned environment
29837 but it can only have two columns.
29840 \begin_layout Subsection
29841 Text in multiline Formulas
29842 \begin_inset CommandInset label
29844 name "sub:Text-in-multiline"
29849 \begin_inset Index idx
29852 \begin_layout Plain Layout
29859 \begin_inset Index idx
29862 \begin_layout Plain Layout
29863 Formula ! multiline ! text
29871 \begin_layout Standard
29872 In the Align environments, and the multline and gather environment, text
29873 can be inserted that will appear in a separate line and doesn't affect
29874 the column alignment.
29875 To do this, the command
29882 \begin_inset Index idx
29885 \begin_layout Plain Layout
29893 is used in the following scheme:
29896 \begin_layout Standard
29904 \begin_layout Standard
29905 The text should not be longer than a line because it cannot be hyphenated.
29906 As LyX doesn't yet support
29912 directly, the text is written as mathematical text.
29919 must hereby be at the beginning of a line and appears in the output above
29921 An example where the text was inserted at the beginning of the second line:
29922 \begin_inset Formula
29924 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29925 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29933 \begin_layout Section
29935 \begin_inset Index idx
29938 \begin_layout Plain Layout
29945 \begin_inset Index idx
29948 \begin_layout Plain Layout
29949 Formula ! numbering|see
29953 \begin_layout Plain Layout
29964 \begin_layout Plain Layout
29979 \begin_layout Subsection
29983 \begin_layout Standard
29984 Numbered formulas can be created with the menu
29986 Insert\SpecialChar \menuseparator
29987 Math\SpecialChar \menuseparator
29989 \begin_inset space ~
29997 \begin_inset space ~
30003 Existing formulas can be numbered with the menu
30005 Edit\SpecialChar \menuseparator
30006 Math\SpecialChar \menuseparator
30008 \begin_inset space ~
30016 arg "math-number-toggle"
30020 The formula number is displayed in LyX behind the formula as a number sign
30022 The number sign is replaced in the output by the formula number.
30025 \begin_layout Standard
30026 When numbering is turned on in multiline formulas, all lines will be numbered.
30027 But the numbering can be controlled with the menu
30029 Edit\SpecialChar \menuseparator
30030 Math\SpecialChar \menuseparator
30032 \begin_inset space ~
30036 \begin_inset space ~
30040 \begin_inset space ~
30048 arg "math-number-line-toggle"
30054 \begin_layout Standard
30055 Except for inline formulas, all formulas can be numbered with two different
30057 \begin_inset CommandInset ref
30059 reference "sec:Formula-Styles"
30066 \begin_layout Subsection
30068 \begin_inset Index idx
30071 \begin_layout Plain Layout
30072 Cross-references ! to formulas
30080 \begin_layout Standard
30081 All labeled formulas can be cross-referenced.
30082 A label is added by the menu
30084 Insert\SpecialChar \menuseparator
30087 or the toolbar button
30088 \begin_inset Graphics
30089 filename ../images/label-insert.png
30095 The cursor must hereby be inside a displayed formula.
30096 Alternatively you can right-click on the formula and choose
30101 A dialog pops up displaying the prefix
30106 The label is inserted there behind the prefix.
30107 The predefined prefix means
30108 \begin_inset Quotes eld
30112 \begin_inset Quotes erd
30115 and makes it easier to find labels in large documents because it marks
30116 it as formula label to divide it from e.
30117 \begin_inset space \thinspace{}
30121 \begin_inset space \space{}
30125 To change a label, the menu
30127 Insert\SpecialChar \menuseparator
30130 is used again or you right-click on a formula and then on
30137 \begin_layout Standard
30138 The name of the label is displayed in LyX within two parentheses behind
30140 A formula with a label is always numbered.
30143 \begin_layout Standard
30144 Cross-references are inserted via the menu
30146 Insert\SpecialChar \menuseparator
30149 or with the toolbar button
30150 \begin_inset Graphics
30151 filename ../images/dialog-show-new-inset_ref.png
30157 A formula cross-reference appears in the output as formula number.
30158 When in the cross-reference dialog window the format
30162 is chosen, the cross-reference appears in the output as formula number
30164 \begin_inset Newline newline
30167 By right-clicking on a cross-reference in LyX, one jumps to the formula
30168 that is referenced.
30171 \begin_layout Standard
30172 Here are as examples cross-references to formulas of the following subsections:
30173 \begin_inset Note Note
30176 \begin_layout Plain Layout
30177 Note the different cross-reference types.
30185 \begin_layout Standard
30187 \begin_inset CommandInset ref
30194 \begin_inset CommandInset ref
30202 \begin_inset CommandInset ref
30208 ) big Latin letters are used for the numbering in contrary to (
30209 \begin_inset CommandInset ref
30218 \begin_layout Standard
30219 \begin_inset VSpace medskip
30222 When the argument of
30230 \begin_layout Plain Layout
30238 \begin_inset CommandInset ref
30240 reference "sub:User-defined-Numbering"
30251 contains a box like in
30252 \begin_inset CommandInset ref
30254 reference "sub:Paragraph-Boxes"
30258 , the formula cannot be referenced.
30261 \begin_layout Subsection
30263 \begin_inset Index idx
30266 \begin_layout Plain Layout
30267 Formula numbering ! subnumbering
30275 \begin_layout Standard
30276 With the help of the commands
30280 begin{subequations}
30288 formulas can be subnumbered.
30289 Both commands are inserted in TeX-mode.
30292 \begin_layout Standard
30294 \begin_inset Formula
30305 \begin_layout Plain Layout
30309 addtocounter{equation}{-1}
30318 \begin_layout Plain Layout
30322 begin{subequations}
30328 \begin_inset VSpace -5mm
30332 \begin_inset Formula
30340 \begin_inset Formula
30350 \begin_layout Standard
30354 \begin_layout Plain Layout
30366 \begin_layout Standard
30367 To create the example, the following is done:
30370 \begin_layout Enumerate
30371 first formula is inserted
30374 \begin_layout Enumerate
30379 addtocounter{equation}{-1}
30381 begin{subequations}
30382 \begin_inset Index idx
30385 \begin_layout Plain Layout
30394 \begin_inset Newline newline
30399 is inserted after the first formula
30402 \begin_layout Enumerate
30403 second formula is inserted
30406 \begin_layout Enumerate
30407 third formula is inserted
30410 \begin_layout Enumerate
30417 is inserted after the third formula
30420 \begin_layout Standard
30421 Every formula between the commands
30433 is subnumbered as a, b,
30434 \begin_inset Newline linebreak
30437 c, \SpecialChar \ldots{}
30438 For multiline formulas every line will be subnumbered.
30439 All subnumbered formulas are treated as
30444 But as every numbered formula increases the counter
30448 by one, the command
30454 is needed to decrease it.
30455 Otherwise the formulas
30456 \begin_inset CommandInset ref
30463 \begin_inset CommandInset ref
30470 \begin_inset CommandInset ref
30476 would be numbered as
30477 \begin_inset CommandInset ref
30484 \begin_inset CommandInset ref
30491 \begin_inset CommandInset ref
30500 \begin_layout Standard
30501 By inserting the commands in TeX-mode, a space is created between the first
30504 \begin_inset space \thinspace{}
30507 mm vertical space is inserted after the command
30511 begin{subequations}
30514 When the formula style
30520 \begin_layout Plain Layout
30522 \begin_inset CommandInset ref
30524 reference "sec:Formula-Styles"
30536 \begin_inset space \thinspace{}
30539 mm space is inserted instead.
30542 \begin_layout Standard
30543 Here is an example for a multiline formula where the numbering was turned
30544 off for the second line:
30548 \begin_layout Plain Layout
30552 begin{subequations}
30558 \begin_inset Formula
30560 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30561 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30562 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30571 \begin_layout Plain Layout
30583 \begin_layout Subsection
30584 User-defined Numbering
30585 \begin_inset CommandInset label
30587 name "sub:User-defined-Numbering"
30592 \begin_inset Index idx
30595 \begin_layout Plain Layout
30596 Formula numbering ! user-defined
30604 \begin_layout Standard
30605 \begin_inset Index idx
30608 \begin_layout Plain Layout
30609 Formula numbering ! self-defined delimiters
30614 With the standard numbering parentheses are set around the formula number.
30615 To replace the parentheses for example by vertical bars, the following
30616 line is added to the LaTeX-preamble:
30619 \begin_layout Standard
30631 \begin_inset Note Note
30634 \begin_layout Plain Layout
30635 This macro is already declared in the LaTeX-preamble for testing.
30636 To activate it, remove the percent sign at the beginning.
30644 \begin_layout Standard
30645 To use other characters, the vertical bars besides the
30649 are replaced by one ore more characters.
30650 To get only the formula number the vertical bars are omitted.
30653 \begin_layout Standard
30654 \begin_inset VSpace bigskip
30657 When there should be an expression of your choice instead of the consecutive
30658 formula number in parentheses behind the formula, the command
30665 \begin_inset Index idx
30668 \begin_layout Plain Layout
30677 \begin_inset Formula
30679 A+B=C\tag{something}\label{eq:tag}
30684 In this example the command
30692 \begin_layout Plain Layout
30703 was inserted in the formula.
30706 \begin_layout Standard
30715 \begin_layout Plain Layout
30726 is inserted instead, the star prevents the parentheses around the expression:
30727 \begin_inset Formula
30729 A+B=C\tag*{something}
30737 \begin_layout Standard
30738 \begin_inset VSpace bigskip
30741 To restart the formula numbering with new document parts or sections, the
30742 following command is used:
30745 \begin_layout Standard
30750 @addtoreset{equation}{part}
30753 \begin_inset Index idx
30756 \begin_layout Plain Layout
30761 \begin_layout Plain Layout
30772 \begin_layout Plain Layout
30785 \begin_layout Plain Layout
30796 \begin_layout Plain Layout
30809 \begin_inset Newline newline
30813 \begin_inset Newline newline
30820 @addtoreset{equation}{section}
30823 \begin_layout Standard
30824 To be able to use these commands in TeX-mode, the
30825 \begin_inset Quotes eld
30829 \begin_inset Quotes erd
30832 character has to be made
30833 \begin_inset Quotes eld
30837 \begin_inset Quotes erd
30840 for LaTeX using the command
30854 So the command sequence in TeX-mode is:
30857 \begin_layout Standard
30863 \begin_inset Newline newline
30868 @addtoreset{equation}{section}
30869 \begin_inset Newline newline
30877 \begin_layout Standard
30878 In the LaTeX-preamble
30890 can be omitted as they are automatically internally inserted by LyX.
30893 \begin_layout Standard
30908 \begin_layout Plain Layout
30913 is part of the LaTeX-package
30918 \begin_inset Index idx
30921 \begin_layout Plain Layout
30922 Packages ! carlisle
30927 that is part of every LaTeX standard installation.
30933 \begin_inset Index idx
30936 \begin_layout Plain Layout
30937 Packages ! remreset
30942 has to be loaded in the LaTeX-preamble with the line
30945 \begin_layout Standard
30950 usepackage{remreset}
30953 \begin_layout Standard
30961 \begin_inset Index idx
30964 \begin_layout Plain Layout
30969 \begin_layout Plain Layout
30980 \begin_layout Plain Layout
30993 \begin_layout Plain Layout
31004 \begin_layout Plain Layout
31016 can be used with the same scheme as
31025 \begin_layout Standard
31026 \begin_inset VSpace bigskip
31029 Sometimes formulas should be numbered in the following form:
31032 \begin_layout Standard
31035 (section number.formula number)
31038 \begin_layout Standard
31039 The formula number should start with every section with
31040 \begin_inset Quotes eld
31044 \begin_inset Quotes erd
31050 \begin_layout Standard
31051 For this case there is the command
31058 \begin_inset Index idx
31061 \begin_layout Plain Layout
31069 , which is used with the following scheme:
31072 \begin_layout Standard
31077 numberwithin{counter}{sectioning}
31080 \begin_layout Standard
31081 Counter denotes what kind of numbering is affected, sectioning denotes what
31082 number is before the dot.
31085 \begin_layout Standard
31086 Thus in our case the following LaTeX-preamble or TeX code line is used:
31089 \begin_layout Standard
31094 numberwithin{equation}{section}
31097 \begin_layout Standard
31098 This is the result:
31102 \begin_layout Plain Layout
31106 numberwithin{equation}{section}
31112 \begin_inset Formula
31122 \begin_layout Standard
31124 \begin_inset space \thinspace{}
31128 \begin_inset space \space{}
31131 tables so that the number of the part is the sectioning,
31132 \begin_inset Newline newline
31139 numberwithin{table}{part}
31144 \begin_layout Standard
31145 To go back to the standard numbering or to prevent this kind of numbering
31146 when it is defined by the document class, the following command is inserted
31147 as TeX code or to the LaTeX-preamble:
31150 \begin_layout Standard
31160 \begin_inset Index idx
31163 \begin_layout Plain Layout
31177 \begin_layout Plain Layout
31193 \begin_inset Newline newline
31201 \begin_inset Newline newline
31213 \begin_layout Standard
31220 uses internally the command
31226 , described above, that also needs to be reverted.
31230 \begin_layout Plain Layout
31237 \begin_layout Plain Layout
31241 @removefromreset{equation}{section}
31244 \begin_layout Plain Layout
31256 \begin_layout Subsection
31257 Numbering with Roman Numbers and Letters
31258 \begin_inset Index idx
31261 \begin_layout Plain Layout
31262 Formula numbering ! with letters
31268 \begin_inset Index idx
31271 \begin_layout Plain Layout
31272 Formula numbering ! with Roman numbers
31280 \begin_layout Standard
31281 Formulas can also be numbered with Roman numbers and Latin letters.
31282 To number for example with small Roman numbers, the command
31285 \begin_layout Standard
31297 \begin_layout Standard
31298 is inserted before the formula in TeX-mode.
31306 \begin_inset Index idx
31309 \begin_layout Plain Layout
31317 redefines the predefined command
31333 \begin_layout Plain Layout
31340 has the same scheme like the command
31346 that is described in
31347 \begin_inset CommandInset ref
31349 reference "sub:The-Command-newcommand"
31362 is the formula counter.
31369 is used as prefix for a counter, the value of the counter is output as
31371 When a formula is numbered, LaTeX sets internally the command
31377 behind the formula.
31383 \begin_inset Index idx
31386 \begin_layout Plain Layout
31396 outputs the counter as small Roman number.
31399 \begin_layout Standard
31400 All formulas behind the command
31410 are now numbered Roman.
31411 To switch to numbering with big Roman numbers, the command is inserted
31425 \begin_inset Index idx
31428 \begin_layout Plain Layout
31440 \begin_inset Quotes eld
31444 \begin_inset Quotes erd
31447 with small Latin letters there is the command
31454 \begin_inset Index idx
31457 \begin_layout Plain Layout
31465 , for big ones there is the command
31472 \begin_inset Index idx
31475 \begin_layout Plain Layout
31488 \begin_layout Standard
31489 \begin_inset Note Greyedout
31492 \begin_layout Plain Layout
31499 \begin_inset space ~
31502 formulas can be numbered with Latin letters in one document.
31510 \begin_layout Standard
31514 \begin_layout Plain Layout
31530 \begin_layout Standard
31531 \begin_inset Formula
31533 A=\textrm{small roman}
31542 \begin_layout Plain Layout
31556 \begin_inset Formula
31558 B=\textrm{big Roman}\label{eq:Rom}
31567 \begin_layout Plain Layout
31581 \begin_inset Formula
31583 C=\textrm{small Latin}
31592 \begin_layout Plain Layout
31606 \begin_inset Formula
31608 D=\textrm{big Latin}\label{eq:Lat}
31616 \begin_layout Standard
31617 To switch back to the default numbering, insert the command:
31620 \begin_layout Standard
31630 \begin_inset Index idx
31633 \begin_layout Plain Layout
31644 \begin_layout Standard
31648 \begin_layout Plain Layout
31662 \begin_inset Formula
31672 \begin_layout Standard
31673 \begin_inset VSpace medskip
31676 As you see, formulas are numbered serially independent from the numbering
31678 When then numbering should start with
31679 \begin_inset Quotes eld
31683 \begin_inset Quotes erd
31686 when the style is changed, new equation counters have to be defined.
31687 A description about this can be found in the file
31688 \begin_inset CommandInset href
31690 name "Formula-numbering.lyx"
31691 target "run:Formula-numbering.lyx"
31698 \begin_layout Standard
31699 \begin_inset Newpage newpage
31705 \begin_layout Section
31706 Chemical Symbols and Equations
31707 \begin_inset CommandInset label
31709 name "sub:Chemical-Symbols-and"
31714 \begin_inset Index idx
31717 \begin_layout Plain Layout
31718 Chemical characters ! Symbols
31724 \begin_inset Index idx
31727 \begin_layout Plain Layout
31734 \begin_inset Index idx
31737 \begin_layout Plain Layout
31746 \begin_layout Standard
31747 An example text from chemistry:
31750 \begin_layout Quote
31752 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31755 -ion reacts with two
31756 \begin_inset Formula $\mathrm{Na^{+}}$
31759 -ions to sodium sulfate
31760 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31764 The chemical equation for this is:
31765 \begin_inset Formula
31767 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31775 \begin_layout Standard
31776 This chemical equation can directly be created as formula.
31777 To avoid that the symbols appear italic, everything is highlighted and
31778 changed by the shortcut
31784 to the upright font style.
31788 \begin_layout Plain Layout
31794 \begin_inset CommandInset ref
31796 reference "sub:Font-Styles"
31808 \begin_layout Standard
31809 A more convenient way to typeset chemical formulas is to use the command
31817 \begin_inset Index idx
31820 \begin_layout Plain Layout
31828 that is available when the LaTeX-package
31833 \begin_inset Index idx
31836 \begin_layout Plain Layout
31849 to a formula a new blue box appears where chemical formulas can be inserted
31850 in an intuitive way.
31853 \begin_layout Standard
31855 \begin_inset Tabular
31856 <lyxtabular version="3" rows="9" columns="2">
31857 <features tabularvalignment="middle">
31858 <column alignment="center" valignment="top" width="0">
31859 <column alignment="center" valignment="top" width="0">
31861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31864 \begin_layout Plain Layout
31870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31873 \begin_layout Plain Layout
31875 \begin_inset Note Note
31878 \begin_layout Plain Layout
31885 is only used as spacer.
31897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31900 \begin_layout Plain Layout
31907 \begin_layout Plain Layout
31921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31924 \begin_layout Plain Layout
31925 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31938 \begin_layout Plain Layout
31945 \begin_layout Plain Layout
31959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31962 \begin_layout Plain Layout
31963 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31976 \begin_layout Plain Layout
31983 \begin_layout Plain Layout
31997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32000 \begin_layout Plain Layout
32001 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
32011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32014 \begin_layout Plain Layout
32021 \begin_layout Plain Layout
32035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32038 \begin_layout Plain Layout
32039 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32052 \begin_layout Plain Layout
32059 \begin_layout Plain Layout
32074 \begin_layout Plain Layout
32089 \begin_layout Plain Layout
32103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32106 \begin_layout Plain Layout
32107 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32120 \begin_layout Plain Layout
32127 \begin_layout Plain Layout
32137 \begin_inset Formula $\downarrow$
32141 \begin_inset Formula $\to$
32149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32152 \begin_layout Plain Layout
32153 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32166 \begin_layout Plain Layout
32173 \begin_layout Plain Layout
32186 \begin_layout Plain Layout
32199 \begin_layout Plain Layout
32212 \begin_layout Plain Layout
32225 \begin_layout Plain Layout
32239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32242 \begin_layout Plain Layout
32243 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32256 \begin_layout Plain Layout
32263 \begin_layout Plain Layout
32276 \begin_layout Plain Layout
32289 \begin_layout Plain Layout
32302 \begin_layout Plain Layout
32319 \begin_layout Plain Layout
32333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32336 \begin_layout Plain Layout
32337 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32353 \begin_layout Standard
32354 \begin_inset Note Greyedout
32357 \begin_layout Plain Layout
32363 Inserting a formula to a
32369 box will lead to LaTeX errors due to a LyX bug.
32375 \begin_layout Plain Layout
32376 \begin_inset CommandInset href
32378 name "LyX-bug #8566"
32379 target "http://www.lyx.org/trac/ticket/8566"
32390 In this case TeX code has to be used like for
32404 \begin_layout Plain Layout
32425 \begin_layout Standard
32426 \begin_inset Note Greyedout
32429 \begin_layout Plain Layout
32435 It is not possible in LyX to use the character ^ to get an up-arrow as
32441 One instead uses a negative thin space followed by the command
32448 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32459 \begin_layout Standard
32466 the command for equation
32467 \begin_inset space ~
32471 \begin_inset CommandInset ref
32473 reference "eq:chem-reaction"
32478 \begin_inset Newline newline
32489 \begin_layout Plain Layout
32502 \begin_layout Plain Layout
32515 \begin_layout Plain Layout
32528 \begin_layout Plain Layout
32541 \begin_layout Plain Layout
32554 \begin_layout Plain Layout
32566 \begin_layout Standard
32567 To create multiline chemical equations first a multiline formula is created
32569 \begin_inset CommandInset ref
32571 reference "sec:Multiline-Formulas"
32576 Afterwards the command
32582 is used in every small blue box of the formula.
32584 \begin_inset CommandInset ref
32586 reference "eq:TEOS-reaction-1"
32591 \begin_inset CommandInset ref
32593 reference "eq:TEOS-reaction-2"
32597 are an example of a multi-stage chemical reaction where every equation
32598 has its own number.
32599 \begin_inset Formula
32601 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32602 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32610 \begin_layout Standard
32621 package provides the command
32628 \begin_inset Index idx
32631 \begin_layout Plain Layout
32639 that has to be used for special cases.
32640 For more information about
32646 and more examples have a look at the documentation of
32651 \begin_inset CommandInset citation
32660 \begin_layout Section
32664 \begin_layout Standard
32665 LyX supports two types of commutative diagrams:
32673 that are explained in the following.
32676 \begin_layout Subsection
32678 \begin_inset Index idx
32681 \begin_layout Plain Layout
32690 \begin_layout Standard
32691 Diagrams of this type visualize relations by vertical and horizontal lines
32693 \begin_inset Formula
32695 \begin{CD}A@>>>B@>>>C\\
32706 \begin_layout Standard
32707 To get them, the command
32712 \begin_inset Index idx
32715 \begin_layout Plain Layout
32725 is inserted to a formula.
32726 A blue box appears with two dashed lines where further commands can be
32731 arg "newline-insert newline"
32734 a new line is created.
32735 Horizontal relations are inserted in odd, vertical in even formula lines.
32738 \begin_layout Standard
32739 To create the relations there are the following commands:
32742 \begin_layout Itemize
32747 creates a left arrow,
32758 \begin_layout Itemize
32763 creates an up arrow,
32771 a vertical equal sign
32774 \begin_layout Itemize
32780 is a placeholder for non-existent relations
32783 \begin_layout Standard
32784 All arrows can be labeled as follows:
32787 \begin_layout Itemize
32788 If text inserted between the first and second < or >, resp., it is placed
32790 When it is inserted between the second and third one, it appears under
32794 \begin_layout Itemize
32795 When text for vertical arrows is inserted between the first and second A
32796 or V, resp., it is placed left beside the arrow.
32797 When it is inserted between the second and third one, it appears right
32799 If the text contains an A or V, these letters must be set into a TeX-brace.
32802 \begin_layout Standard
32803 As example a diagram with all possible relations:
32806 \begin_layout Standard
32807 \begin_inset Formula
32809 \begin{CD}A@>j>>B@>>k>C@=F\\
32820 \begin_layout Standard
32821 The command for this is:
32822 \begin_inset Newline newline
32833 \begin_layout Plain Layout
32842 A@>j>>B@>>k>C@=F Ctrl+Return
32843 \begin_inset Newline newline
32847 \begin_inset Phantom HPhantom
32850 \begin_layout Plain Layout
32859 \begin_layout Plain Layout
32878 \begin_inset Formula $\to$
32884 \begin_inset Newline newline
32888 \begin_inset Phantom HPhantom
32891 \begin_layout Plain Layout
32900 \begin_layout Plain Layout
32917 \begin_layout Subsection
32919 \begin_inset Index idx
32922 \begin_layout Plain Layout
32923 Diagrams ! xymatrix
32931 \begin_layout Standard
32932 To be able to use xymatrices, the LaTeX-package
32937 A xymatrix is created by inserting the command
32944 Then you are able to add new matrix columns and rows like for normal matrices,
32946 \begin_inset CommandInset ref
32948 reference "sec:Matrices"
32955 \begin_layout Standard
32956 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32958 All possibilities to create commutative diagrams and decorations are explained
32963 that you find in the menu
32965 Help\SpecialChar \menuseparator
32967 \begin_inset space ~
32975 \begin_layout Subsection
32981 \begin_inset Index idx
32984 \begin_layout Plain Layout
32993 \begin_layout Standard
32998 -diagrams, the LaTeX-package
33007 -diagram is created by inserting the command
33014 Then you are able to add new matrix columns and rows like for normal matrices,
33016 \begin_inset CommandInset ref
33018 reference "sec:Matrices"
33025 \begin_layout Standard
33026 Examples how to create
33030 diagrams in LyX is given in the
33032 Feynman-diagram manual
33034 that you find in the menu
33036 Help\SpecialChar \menuseparator
33038 \begin_inset space ~
33046 \begin_layout Standard
33047 \begin_inset Newpage newpage
33053 \begin_layout Section
33054 User-defined Commands
33055 \begin_inset Index idx
33058 \begin_layout Plain Layout
33059 User-defined commands
33067 \begin_layout Standard
33068 \begin_inset Note Greyedout
33071 \begin_layout Plain Layout
33076 The names of user-defined commands and macros may only consist of Latin
33085 \begin_layout Subsection
33089 \begin_inset CommandInset label
33091 name "sub:The-Command-newcommand"
33096 \begin_inset Index idx
33099 \begin_layout Plain Layout
33100 User-defined commands !
33108 \begin_inset Index idx
33111 \begin_layout Plain Layout
33122 \begin_layout Standard
33123 Many LaTeX-commands are too long to be used frequently.
33124 But it is possible to define with the command
33130 new shorter commands.
33133 \begin_layout Standard
33134 The command scheme of
33143 \begin_layout Standard
33148 newcommand{new command name}[number of arguments][optional
33153 \begin_inset Newline newline
33157 \begin_inset Phantom HPhantom
33160 \begin_layout Plain Layout
33170 {command definition}
33173 \begin_layout Standard
33174 \begin_inset Note Greyedout
33177 \begin_layout Plain Layout
33182 Assure that the name of the new command is not already used in your document
33183 or by LaTeX-packages that you use.
33184 When you for example define the command
33196 , you get an error message because
33202 is already defined as command for
33203 \begin_inset Quotes eld
33207 \begin_inset Formula $\le$
33211 \begin_inset Quotes erd
33222 \begin_layout Standard
33223 The number of arguments is an integer in the range 0
33224 \begin_inset space \thinspace{}
33228 \begin_inset space \thinspace{}
33231 9 and specifies how many arguments the new command should have.
33232 With the optional value a value for an optional argument can be predefined.
33233 When this is done, the
33241 rgument of the new command is automatically an optional one.
33244 \begin_layout Standard
33245 Here are some examples:
33248 \begin_layout Itemize
33249 To define the command
33261 , the LaTeX-preamble line is:
33262 \begin_inset VSpace medskip
33266 \begin_inset Newline newline
33280 \begin_layout Itemize
33281 To define the command
33293 , the argument (that should be underlined) must be taken into account.
33294 For this the preamble line is:
33295 \begin_inset VSpace medskip
33299 \begin_inset Newline newline
33313 \begin_inset VSpace medskip
33317 \begin_inset Newline newline
33324 acts as argument placeholder, the
33328 behind it denotes that it is the placeholder for the first argument.
33331 \begin_layout Itemize
33339 \begin_inset space \thinspace{}
33343 \begin_inset space \space{}
33353 \begin_inset VSpace medskip
33357 \begin_inset Newline newline
33368 framebox#1#2{$#3$}}
33371 \begin_inset VSpace medskip
33375 \begin_inset Newline newline
33378 The two Dollar signs creates the extra formula needed for
33385 \begin_inset CommandInset ref
33387 reference "sub:Boxes-with-Frame"
33394 \begin_layout Itemize
33395 To create a new command for
33401 where the color for the box need not be specified, the argument for the
33402 color is defined optional:
33403 \begin_inset VSpace medskip
33407 \begin_inset Newline newline
33418 fcolorbox{#2}{#1}{$#3$}}
33421 \begin_inset VSpace medskip
33425 \begin_inset Newline newline
33428 When the color is not specified when using
33434 , the predefined color
33441 \begin_layout Standard
33442 A test of the new defined commands:
33445 \begin_layout Standard
33447 \begin_inset Tabular
33448 <lyxtabular version="3" rows="6" columns="2">
33449 <features tabularvalignment="middle">
33450 <column alignment="center" valignment="top" width="0">
33451 <column alignment="center" valignment="top" width="0">
33453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33456 \begin_layout Plain Layout
33462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33465 \begin_layout Plain Layout
33467 \begin_inset Note Note
33470 \begin_layout Plain Layout
33477 is only used as spacer.
33489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33492 \begin_layout Plain Layout
33499 \begin_layout Plain Layout
33513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33516 \begin_layout Plain Layout
33517 \begin_inset Formula $A\gr B$
33527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33530 \begin_layout Plain Layout
33538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33541 \begin_layout Plain Layout
33542 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33555 \begin_layout Plain Layout
33559 \begin_inset Formula $\to$
33565 \begin_inset Formula $\to$
33576 \begin_layout Plain Layout
33590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33593 \begin_layout Plain Layout
33594 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33607 \begin_layout Plain Layout
33611 \begin_inset Formula $\to$
33622 \begin_layout Plain Layout
33636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33639 \begin_layout Plain Layout
33640 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33653 \begin_layout Plain Layout
33659 \begin_inset Formula $\to$
33670 \begin_layout Plain Layout
33684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33687 \begin_layout Plain Layout
33688 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33704 \begin_layout Subsection
33706 \begin_inset Index idx
33709 \begin_layout Plain Layout
33710 User-defined commands! Math macros
33716 \begin_inset Index idx
33719 \begin_layout Plain Layout
33728 \begin_layout Standard
33729 User-defined commands are especially convenient for complex expressions.
33730 When you are for example dealing with a document that has quadratic equations,
33731 the same solution type occurs several times.
33732 The general form of a quadratic equation is
33733 \begin_inset Formula
33735 0=\lambda^{2}+p\lambda+q
33740 The general form of the solution is
33741 \begin_inset Formula
33743 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33751 \begin_layout Standard
33752 To define a command for the solution formula where only the three parameters
33754 \begin_inset Formula $\lambda$
33758 \begin_inset Formula $p$
33762 \begin_inset Formula $q$
33765 need to be specified and the index of
33766 \begin_inset Formula $\lambda$
33769 can be given optionally, the LaTeX-preamble line is
33770 \begin_inset Newline newline
33786 \begin_inset Newline newline
33790 \begin_inset Phantom HPhantom
33793 \begin_layout Plain Layout
33807 frac{#3^{2}}{4}-#4}}
33810 \begin_layout Standard
33811 To create with this the solution formula, the command
33812 \begin_inset Newline newline
33822 \begin_inset Formula $\to$
33828 \begin_inset Formula $\to$
33835 is inserted to a formula
33840 \begin_layout Standard
33841 The definition of the new command is unintuitive because one has to know
33842 the schemes of all used LaTeX commands, e.
33843 \begin_inset space \thinspace{}
33847 \begin_inset space \space{}
33850 that a fraction is inserted in LaTeX as
33854 frac{numerator}{denominator}
33857 Furthermore one can easily forget a brace in the definition and cannot
33858 see in LyX what the new command is doing.
33859 To avoid these problems LyX offers the possibility to use math macros instead
33869 \begin_layout Standard
33870 A math macro is created by using the menu
33872 Insert\SpecialChar \menuseparator
33873 Math\SpecialChar \menuseparator
33876 or the toolbar button
33877 \begin_inset Graphics
33878 filename ../images/math-macro_newmacroname_newcommand.png
33884 The math macro toolbar appears together with the following box where the
33886 \begin_inset Newline newline
33890 \begin_inset space \hspace*{\fill}
33894 \begin_inset Graphics
33895 filename clipart/macrobox.png
33900 \begin_inset space \hspace*{\fill}
33904 \begin_inset Newline newline
33908 \begin_inset FormulaMacro
33909 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33914 newmacroname is the default name of the macro that should be changed to
33915 something sensible.
33916 The wanted formula is inserted in the first blue box.
33917 An argument placeholder is inserted with the command
33924 \begin_inset space \thinspace{}
33928 \begin_inset space \space{}
33937 or by using the macro toolbar button
33938 \begin_inset Graphics
33939 filename ../images/math-macro-add-param.png
33945 Argument placeholders are displayed red.
33947 \begin_inset space ~
33950 arguments are possible.
33951 Optional arguments are created with the toolbar button
33952 \begin_inset Graphics
33953 filename ../images/math-macro-add-optional-param.png
33959 The first non-optional argument can be transformed to an optional one with
33961 \begin_inset Graphics
33962 filename ../images/math-macro-make-optional.png
33968 In the second blue box the appearance of the macro in LyX can be defined.
33969 Normally you want to see it as it is defined, so the box is kept empty.
33970 But when you have created a macro that needs lot of space on the screen,
33971 you can insert in the box for example
33972 \begin_inset Newline newline
34002 \begin_inset Newline newline
34007 For the macro only the arguments with the macro name in front of them will
34008 then be displayed in LyX, leading to a better overview.
34009 The formula appears in the output as defined in the first box.
34010 \begin_inset Newline newline
34013 The appearance of macros in formulas can furthermore be changed for single
34014 macros by setting the cursor in the macro and using the menu
34016 View\SpecialChar \menuseparator
34018 \begin_inset space ~
34022 \begin_inset space ~
34030 \begin_layout Standard
34031 To use a macro, the macro name is inserted as command to a formula, in our
34039 Our macro looks in LyX like this:
34040 \begin_inset Newline newline
34044 \begin_inset space \hspace*{\fill}
34048 \begin_inset Graphics
34049 filename clipart/macrouse.png
34054 \begin_inset space \hspace*{\fill}
34058 \begin_inset Newline newline
34061 Here is our macro example with the arguments
34062 \begin_inset Formula $x$
34066 \begin_inset Formula $\ln(x)$
34070 \begin_inset Formula $B$
34076 \begin_layout Standard
34077 \begin_inset Formula
34087 \begin_layout Standard
34088 LyX offers in the menu
34090 Tools\SpecialChar \menuseparator
34091 Preferences\SpecialChar \menuseparator
34092 Editing\SpecialChar \menuseparator
34095 different styles to edit macros.
34096 To find the style that suits you the most, choose a style and set the cursor
34097 in a macro formula to see the difference.
34100 \begin_layout Standard
34101 A math macro is transformed internally to a
34107 command when exporting the document.
34114 command is not placed in the LaTeX-preamble, therefore macros can only
34115 be used in formulas that are in the document below the macro definition
34119 \begin_layout Standard
34120 Math macros can also be directly created from a
34127 When writing for example the command
34130 \begin_inset Newline newline
34139 xleftarrow[#2]{#1}}
34140 \begin_inset Newline newline
34145 in LyX as normal text, highlighting it completely and using then the shortcut
34150 , the command will be transformed to a math macro.
34151 Using this method you need to be careful that the
34157 command is typed correctly, otherwise you get a faulty macro leading to
34161 \begin_layout Standard
34162 Math macros currently have the problem that further formulas in macro definition
34163 s are handled wrongly.
34164 Therefore the example
34171 \begin_inset CommandInset ref
34173 reference "sub:The-Command-newcommand"
34177 cannot be created as macro.
34180 \begin_layout Standard
34181 When the cursor is in a macro definition box, you will see the macro toolbar
34185 \begin_layout Standard
34186 \begin_inset VSpace defskip
34192 \begin_layout Standard
34193 \begin_inset Graphics
34194 filename clipart/MacroToolbar.png
34199 \begin_inset Index idx
34202 \begin_layout Plain Layout
34211 \begin_layout Standard
34212 \begin_inset VSpace defskip
34218 \begin_layout Standard
34219 The macro toolbar contains from left to right the following buttons:
34222 \begin_layout Standard
34223 \begin_inset VSpace defskip
34229 \begin_layout Standard
34230 \begin_inset Tabular
34231 <lyxtabular version="3" rows="9" columns="2">
34232 <features islongtable="true" longtabularalignment="center">
34233 <column alignment="left" valignment="top" width="0">
34234 <column alignment="left" valignment="top" width="85col%">
34235 <row interlinespace="2.5mm">
34236 <cell alignment="center" valignment="top" usebox="none">
34239 \begin_layout Plain Layout
34240 \begin_inset Graphics
34241 filename ../images/math-macro-remove-param.png
34242 rotateOrigin center
34251 <cell alignment="center" valignment="top" usebox="none">
34254 \begin_layout Plain Layout
34257 Edit\SpecialChar \menuseparator
34258 Math\SpecialChar \menuseparator
34260 \begin_inset space ~
34263 Definition\SpecialChar \menuseparator
34264 Remove Last Argument
34270 <row interlinespace="2.5mm">
34271 <cell alignment="center" valignment="top" usebox="none">
34274 \begin_layout Plain Layout
34275 \begin_inset Graphics
34276 filename ../images/math-macro-add-param.png
34277 rotateOrigin center
34286 <cell alignment="center" valignment="top" usebox="none">
34289 \begin_layout Plain Layout
34292 Edit\SpecialChar \menuseparator
34293 Math\SpecialChar \menuseparator
34295 \begin_inset space ~
34298 Definition\SpecialChar \menuseparator
34305 <row interlinespace="2.5mm">
34306 <cell alignment="center" valignment="top" usebox="none">
34309 \begin_layout Plain Layout
34310 \begin_inset Graphics
34311 filename ../images/math-macro-make-optional.png
34312 rotateOrigin center
34321 <cell alignment="center" valignment="top" usebox="none">
34324 \begin_layout Plain Layout
34327 Edit\SpecialChar \menuseparator
34328 Math\SpecialChar \menuseparator
34330 \begin_inset space ~
34333 Definition\SpecialChar \menuseparator
34334 Make First Non-Optional into
34335 \begin_inset Newline newline
34339 \begin_inset Phantom HPhantom
34342 \begin_layout Plain Layout
34345 Edit\SpecialChar \menuseparator
34346 Math\SpecialChar \menuseparator
34348 \begin_inset space ~
34351 Definition\SpecialChar \menuseparator
34363 <row interlinespace="2.5mm">
34364 <cell alignment="center" valignment="top" usebox="none">
34367 \begin_layout Plain Layout
34368 \begin_inset Graphics
34369 filename ../images/math-macro-make-nonoptional.png
34370 rotateOrigin center
34379 <cell alignment="center" valignment="top" usebox="none">
34382 \begin_layout Plain Layout
34385 Edit\SpecialChar \menuseparator
34386 Math\SpecialChar \menuseparator
34388 \begin_inset space ~
34391 Definition\SpecialChar \menuseparator
34392 Make Last Optional into
34393 \begin_inset Newline newline
34397 \begin_inset Phantom HPhantom
34400 \begin_layout Plain Layout
34403 Edit\SpecialChar \menuseparator
34404 Math\SpecialChar \menuseparator
34406 \begin_inset space ~
34409 Definition\SpecialChar \menuseparator
34415 Non-Optional Argument
34421 <row interlinespace="2.5mm">
34422 <cell alignment="center" valignment="top" usebox="none">
34425 \begin_layout Plain Layout
34426 \begin_inset Graphics
34427 filename ../images/math-macro-remove-optional-param.png
34428 rotateOrigin center
34437 <cell alignment="center" valignment="top" usebox="none">
34440 \begin_layout Plain Layout
34443 Edit\SpecialChar \menuseparator
34444 Math\SpecialChar \menuseparator
34446 \begin_inset space ~
34449 Definition\SpecialChar \menuseparator
34450 Remove Optional Argument
34456 <row interlinespace="2.5mm">
34457 <cell alignment="center" valignment="top" usebox="none">
34460 \begin_layout Plain Layout
34461 \begin_inset Graphics
34462 filename ../images/math-macro-add-optional-param.png
34463 rotateOrigin center
34472 <cell alignment="center" valignment="top" usebox="none">
34475 \begin_layout Plain Layout
34478 Edit\SpecialChar \menuseparator
34479 Math\SpecialChar \menuseparator
34481 \begin_inset space ~
34484 Definition\SpecialChar \menuseparator
34485 Insert Optional Argument
34491 <row interlinespace="2.5mm">
34492 <cell alignment="center" valignment="top" usebox="none">
34495 \begin_layout Plain Layout
34496 \begin_inset Graphics
34497 filename ../images/math-macro-remove-greedy-param.png
34498 rotateOrigin center
34507 <cell alignment="center" valignment="top" usebox="none">
34510 \begin_layout Plain Layout
34513 Edit\SpecialChar \menuseparator
34514 Math\SpecialChar \menuseparator
34516 \begin_inset space ~
34519 Definition\SpecialChar \menuseparator
34520 Remove Last Argument
34521 \begin_inset Newline newline
34525 \begin_inset Phantom HPhantom
34528 \begin_layout Plain Layout
34531 Edit\SpecialChar \menuseparator
34532 Math\SpecialChar \menuseparator
34534 \begin_inset space ~
34537 Definition\SpecialChar \menuseparator
34543 Spitting Out To The Right
34549 <row interlinespace="2.5mm">
34550 <cell alignment="center" valignment="top" usebox="none">
34553 \begin_layout Plain Layout
34554 \begin_inset Graphics
34555 filename ../images/math-macro-append-greedy-param.png
34556 rotateOrigin center
34565 <cell alignment="center" valignment="top" usebox="none">
34568 \begin_layout Plain Layout
34571 Edit\SpecialChar \menuseparator
34572 Math\SpecialChar \menuseparator
34574 \begin_inset space ~
34577 Definition\SpecialChar \menuseparator
34579 \begin_inset Newline newline
34583 \begin_inset Phantom HPhantom
34586 \begin_layout Plain Layout
34589 Edit\SpecialChar \menuseparator
34590 Math\SpecialChar \menuseparator
34592 \begin_inset space ~
34595 Definition\SpecialChar \menuseparator
34601 Eating From The Right
34607 <row interlinespace="2.5mm">
34608 <cell alignment="center" valignment="top" usebox="none">
34611 \begin_layout Plain Layout
34612 \begin_inset Graphics
34613 filename ../images/math-macro-add-greedy-optional-param.png
34614 rotateOrigin center
34623 <cell alignment="center" valignment="top" usebox="none">
34626 \begin_layout Plain Layout
34629 Edit\SpecialChar \menuseparator
34630 Math\SpecialChar \menuseparator
34632 \begin_inset space ~
34635 Definition\SpecialChar \menuseparator
34636 Append Optional Argument
34637 \begin_inset Newline newline
34641 \begin_inset Phantom HPhantom
34644 \begin_layout Plain Layout
34647 Edit\SpecialChar \menuseparator
34648 Math\SpecialChar \menuseparator
34650 \begin_inset space ~
34653 Definition\SpecialChar \menuseparator
34659 Eating From The Right
34672 \begin_layout Section
34673 Computer Algebra Systems
34676 \begin_layout Standard
34677 LyX offers the exchange between mathematical expressions written in LyX's
34678 math editor and external applications or user defined scripts.
34679 Currently supported applications are
34696 Note that the set of supported mathematical constructs is limited only
34697 to very simple cases.
34700 \begin_layout Subsection
34704 \begin_layout Standard
34705 Write some expression in a formula, go to the
34707 Edit\SpecialChar \menuseparator
34708 Math\SpecialChar \menuseparator
34709 Use Computer Algebra System
34711 menu and choose the application you have installed on the computer.
34712 After that the result of computation should show on the right side of the
34713 expression together with the
34714 \begin_inset Quotes eld
34718 \begin_inset Quotes erd
34724 \begin_layout Standard
34725 Here are few simple examples (with results from
34729 ) to show what kind of computations can be performed:
34732 \begin_layout Itemize
34733 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34739 \begin_layout Itemize
34740 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34746 \begin_layout Itemize
34747 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34753 \begin_layout Itemize
34754 \begin_inset Formula $\det\left[\begin{array}{ccc}
34758 \end{array}\right]=-56$
34764 \begin_layout Itemize
34765 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34771 \begin_layout Subsection
34775 \begin_layout Standard
34776 Currently there is no keyboard shortcut for calling the algebra applications.
34777 One can easily bind a shortcut to the
34781 LyX function (see the
34789 \begin_inset space \thinspace{}
34793 \begin_inset space \space{}
34800 key inside the math editor.
34805 one would use this shortcut definition command:
34808 \begin_layout Standard
34811 command-alternatives break-paragraph;math-extern maxima
34814 \begin_layout Section
34816 \begin_inset Index idx
34819 \begin_layout Plain Layout
34828 \begin_layout Subsection
34830 \begin_inset Index idx
34833 \begin_layout Plain Layout
34842 \begin_layout Standard
34843 Negative numbers often look ugly in formulas because the minus sign before
34844 the number is set with the same length as the minus operator sign.
34845 When writing the negative number in normal text, the minus sign appears
34849 \begin_layout Standard
34850 Thus, the problem disappears when converting the minus sign to mathematical
34854 \begin_layout Standard
34855 An example to visualize the problem:
34858 \begin_layout Standard
34860 \begin_inset Tabular
34861 <lyxtabular version="3" rows="3" columns="2">
34862 <features tabularvalignment="middle">
34863 <column alignment="right" valignment="top" width="0">
34864 <column alignment="left" valignment="top" width="0">
34866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34869 \begin_layout Plain Layout
34875 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34878 \begin_layout Plain Layout
34886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34889 \begin_layout Plain Layout
34895 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34898 \begin_layout Plain Layout
34899 \begin_inset Formula $x=-2$
34909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34912 \begin_layout Plain Layout
34918 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34921 \begin_layout Plain Layout
34922 \begin_inset Formula $x=\textrm{-}2$
34938 \begin_layout Subsection
34939 Comma as decimal Separator
34940 \begin_inset Index idx
34943 \begin_layout Plain Layout
34952 \begin_layout Standard
34953 In LaTeX a comma inside a formula is used, according to the English convention,
34954 as number group separator.
34955 So there will be space added behind all commas in formulas.
34958 \begin_layout Standard
34959 To avoid this, the comma is highlighted and changed to mathematical text
34969 \begin_layout Standard
34970 To use all formula commas in the document as decimal separator, the file
34979 \begin_layout Plain Layout
34984 is part of the LaTeX-package
34989 \begin_inset Index idx
34992 \begin_layout Plain Layout
34997 \begin_layout Plain Layout
35017 \begin_inset Index idx
35020 \begin_layout Plain Layout
35026 is loaded with the LaTeX-preamble line
35029 \begin_layout Standard
35037 \begin_layout Subsection
35039 \begin_inset CommandInset label
35041 name "sub:Physical-Vectors"
35046 \begin_inset Index idx
35049 \begin_layout Plain Layout
35058 \begin_layout Standard
35059 Predefined vectors are offered by the LaTeX-package
35064 \begin_inset Index idx
35067 \begin_layout Plain Layout
35073 that is loaded with the LaTeX-preamble line
35076 \begin_layout Standard
35084 \begin_layout Standard
35088 \begin_layout Plain Layout
35098 \begin_inset Note Note
35101 \begin_layout Plain Layout
35102 The following table will only be displayed when the LaTeX-package
35114 \begin_layout Standard
35115 The following commands are defined:
35118 \begin_layout Standard
35120 \begin_inset Tabular
35121 <lyxtabular version="3" rows="4" columns="2">
35122 <features tabularvalignment="middle">
35123 <column alignment="center" valignment="top" width="0">
35124 <column alignment="center" valignment="top" width="0">
35126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35129 \begin_layout Plain Layout
35135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35138 \begin_layout Plain Layout
35146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35149 \begin_layout Plain Layout
35159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35162 \begin_layout Plain Layout
35163 \begin_inset Formula $\Bra{\psi}$
35173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35176 \begin_layout Plain Layout
35186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35189 \begin_layout Plain Layout
35190 \begin_inset Formula $\Ket{\psi}$
35200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35203 \begin_layout Plain Layout
35215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35218 \begin_layout Plain Layout
35219 \begin_inset Formula $\Braket{\psi|\phi}$
35235 \begin_layout Standard
35242 assures that all vertical bars are set in the size of the surrounding brackets:
35243 \begin_inset Formula
35245 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
35254 \begin_layout Plain Layout
35264 \begin_inset Note Note
35267 \begin_layout Plain Layout
35268 The following will be displayed when the LaTeX-package
35280 \begin_layout Standard
35281 You need to install the LaTeX-package
35285 to see the rest of this subsection in the output.
35288 \begin_layout Standard
35292 \begin_layout Plain Layout
35304 \begin_layout Standard
35311 can also be achieved using the command
35317 , that is described in
35318 \begin_inset CommandInset ref
35320 reference "sub:Automatic-Bracket-Size"
35327 \begin_layout Subsection
35328 Self-defined Fractions
35329 \begin_inset CommandInset label
35331 name "sub:Self-defined-Fractions"
35336 \begin_inset Index idx
35339 \begin_layout Plain Layout
35340 Fractions ! self-defined
35348 \begin_layout Standard
35349 To define custom commands for fractions, the command
35356 \begin_inset Index idx
35359 \begin_layout Plain Layout
35366 \begin_layout Plain Layout
35380 is used in the following scheme:
35383 \begin_layout Standard
35396 bracket}{fraction bar thickness}{style}
35397 \begin_inset Newline newline
35401 \begin_inset Phantom HPhantom
35404 \begin_layout Plain Layout
35414 {numerator}{denominator}
35417 \begin_layout Standard
35418 The style is a number in the range of 0
35419 \begin_inset space \thinspace{}
35423 \begin_inset space \thinspace{}
35429 \begin_layout Standard
35431 \begin_inset Tabular
35432 <lyxtabular version="3" rows="5" columns="2">
35433 <features tabularvalignment="middle">
35434 <column alignment="center" valignment="top" width="0">
35435 <column alignment="center" valignment="top" width="0">
35437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35440 \begin_layout Plain Layout
35446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35449 \begin_layout Plain Layout
35457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35460 \begin_layout Plain Layout
35466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35469 \begin_layout Plain Layout
35470 display style formula
35477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35480 \begin_layout Plain Layout
35486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35489 \begin_layout Plain Layout
35497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35500 \begin_layout Plain Layout
35506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35509 \begin_layout Plain Layout
35517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35520 \begin_layout Plain Layout
35526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35529 \begin_layout Plain Layout
35543 \begin_layout Standard
35544 When no style is given, the size is adjusted to the surrounding environment
35545 like for the command
35554 \begin_layout Standard
35555 When no fraction bar thickness is given, the predefined value of 0.4
35556 \begin_inset space \thinspace{}
35562 \begin_layout Standard
35563 \begin_inset VSpace medskip
35566 For example, the commands
35579 \begin_inset CommandInset ref
35581 reference "sub:Fractions"
35585 are defined with the commands
35588 \begin_layout Standard
35597 genfrac{}{}{}{0}{#1}{#2}}
35600 \begin_layout Standard
35604 \begin_layout Standard
35613 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35616 \begin_layout Standard
35617 \begin_inset VSpace medskip
35620 To define a fraction where the fraction bar thickness can be given as optional
35621 argument, the following line is inserted to the LaTeX-preamble:
35624 \begin_layout Standard
35633 genfrac{}{}{#1}{}{#2}{#3}}
35636 \begin_layout Standard
35638 \begin_inset Formula
35640 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35641 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35646 As one can see, the distance of the numerator and the denominator to the
35647 fraction bar is round about three times the bar thickness.
35650 \begin_layout Subsection
35652 \begin_inset Index idx
35655 \begin_layout Plain Layout
35664 \begin_layout Standard
35665 To cancel formulas or formula parts, the LaTeX-package
35670 \begin_inset Index idx
35673 \begin_layout Plain Layout
35679 has to be loaded with the LaTeX-preamble line
35682 \begin_layout Standard
35690 \begin_layout Standard
35694 \begin_layout Plain Layout
35704 \begin_inset Note Note
35707 \begin_layout Plain Layout
35708 The following table will only be displayed when the LaTeX-package
35720 \begin_layout Standard
35721 There are four ways to cancel formulas:
35724 \begin_layout Standard
35726 \begin_inset Tabular
35727 <lyxtabular version="3" rows="5" columns="2">
35728 <features tabularvalignment="middle">
35729 <column alignment="center" valignment="top" width="0">
35730 <column alignment="center" valignment="top" width="0">
35732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35735 \begin_layout Plain Layout
35741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35744 \begin_layout Plain Layout
35746 \begin_inset Note Note
35749 \begin_layout Plain Layout
35756 are used here as spacer.
35768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35771 \begin_layout Plain Layout
35780 \begin_layout Plain Layout
35794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35797 \begin_layout Plain Layout
35798 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35811 \begin_layout Plain Layout
35820 \begin_layout Plain Layout
35834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35837 \begin_layout Plain Layout
35838 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35851 \begin_layout Plain Layout
35860 \begin_layout Plain Layout
35874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35877 \begin_layout Plain Layout
35878 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35891 \begin_layout Plain Layout
35895 \begin_inset Formula $\to$
35906 \begin_layout Plain Layout
35920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35923 \begin_layout Plain Layout
35924 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35940 \begin_layout Standard
35947 is especially suitable to visualize the reduction of fractions within formulas:
35948 \begin_inset Formula
35950 \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}}}
35958 \begin_layout Standard
35959 To change the size of
35966 \begin_inset Quotes eld
35970 \begin_inset Quotes erd
35973 value one can load the package
35977 with either the option
35981 which leads to the same size as for the canceled value or with the option
35986 which makes is it a bit smaller than the size one gets without using a
35992 was loaded with this line:
35995 \begin_layout Standard
36000 usepackage[samesize]{cancel}
36003 \begin_layout Standard
36004 To color the cancellation bar one adds this command as TeX code:
36007 \begin_layout Standard
36019 \begin_layout Standard
36024 can be replaced by a color of your choice.
36027 \begin_layout Standard
36031 \begin_layout Plain Layout
36047 \begin_layout Standard
36048 \begin_inset Formula
36050 \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}}}
36058 \begin_layout Standard
36062 \begin_layout Plain Layout
36076 \begin_inset Note Note
36079 \begin_layout Plain Layout
36088 \begin_layout Standard
36089 For further customizations, see the documentation of the package
36094 \begin_inset CommandInset citation
36103 \begin_layout Standard
36107 \begin_layout Plain Layout
36117 \begin_inset Note Note
36120 \begin_layout Plain Layout
36121 The following will be displayed when the LaTeX-package
36133 \begin_layout Standard
36134 You need to install the LaTeX-package
36138 to see the rest of this subsection in the output.
36141 \begin_layout Standard
36145 \begin_layout Plain Layout
36157 \begin_layout Standard
36158 \begin_inset Newpage newpage
36164 \begin_layout Subsection
36165 Formulas in Section Headings
36166 \begin_inset CommandInset label
36168 name "sub:Formulas-in-Section"
36173 \begin_inset Index idx
36176 \begin_layout Plain Layout
36177 Formula ! in section headings
36185 \begin_layout Standard
36186 When formulas are used in section headings, the following has to be taken
36190 \begin_layout Standard
36191 \begin_inset Note Greyedout
36194 \begin_layout Plain Layout
36200 \begin_inset Index idx
36203 \begin_layout Plain Layout
36204 Packages ! hyperref
36209 support is enabled in the document settings dialog under
36212 \begin_inset space ~
36217 , PDF-bookmarks are created for every section heading in the table of contents.
36218 If a section heading contains formulas, they are incorrectly displayed
36219 in the bookmark text, because formulas in bookmarks infringe the PDF convention
36228 \begin_layout Standard
36229 Both problems can be solved by inserting at the end of the section heading
36230 a short title with the menu
36232 Insert\SpecialChar \menuseparator
36234 \begin_inset space ~
36240 Short titles are used as alternative for multiline section headings to
36241 keep the table of contents clearly arranged.
36242 Only the short title appears in the table of contents and therefore also
36243 in the PDF-bookmark.
36246 \begin_layout Standard
36247 When formulas should be used in the table of contents but
36251 is used, one can use the following command in TeX-mode:
36254 \begin_layout Standard
36259 texorpdfstring{part}{alternative}
36260 \begin_inset Index idx
36263 \begin_layout Plain Layout
36274 \begin_layout Standard
36275 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36276 This can be characters, formulas, footnotes, but also cross-references.
36277 The alternative is used instead of the part for the bookmark.
36280 \begin_layout Standard
36281 Here are two example headings:
36282 \begin_inset VSpace -3mm
36289 \begin_layout Plain Layout
36301 \begin_layout Subsubsection
36302 Heading without formula in table of contents
36303 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36307 \begin_inset Argument
36310 \begin_layout Plain Layout
36311 Heading without formula in table of contents
36319 \begin_layout Subsubsection
36320 Heading with formula in table of contents
36324 \begin_layout Plain Layout
36334 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36341 \begin_layout Plain Layout
36351 \begin_layout Standard
36355 \begin_layout Plain Layout
36364 In the first heading a short title was used, in the second one
36373 \begin_layout Standard
36374 To get the same formatting as for the other headings, the complete heading
36383 \begin_layout Plain Layout
36385 \begin_inset CommandInset ref
36387 reference "sub:Bold-Formulas"
36399 \begin_layout Subsection
36400 Formulas in multi-column Text
36401 \begin_inset Index idx
36404 \begin_layout Plain Layout
36405 Formula ! in multi-column text
36413 \begin_layout Standard
36414 Formulas in multi-column text are often too wide to fit into a column and
36415 thus need to be set over the whole page width.
36416 This is done by using the LaTeX-package
36424 \begin_layout Plain Layout
36429 is part of every LaTeX standard installation.
36435 \begin_inset Index idx
36438 \begin_layout Plain Layout
36439 Packages ! multicol
36444 , that is loaded with the LaTeX-preamble line
36447 \begin_layout Standard
36452 usepackage{multicol}
36455 \begin_layout Standard
36456 \begin_inset Note Greyedout
36459 \begin_layout Plain Layout
36460 Note that in this case the setting
36463 \begin_inset space ~
36470 Document\SpecialChar \menuseparator
36476 \begin_inset space ~
36496 \begin_layout Standard
36497 Before the multi-column text the command
36500 \begin_layout Standard
36505 begin{multicols}{column number}
36508 \begin_layout Standard
36509 is written in TeX-mode.
36510 The column number is a number in the range of 2
36511 \begin_inset space \thinspace{}
36515 \begin_inset space \thinspace{}
36519 Before the formula the multi-column text is ended by inserting the command
36522 \begin_layout Standard
36530 \begin_layout Standard
36534 \begin_layout Standard
36535 Due to the command some space is automatically added before the formula.
36537 \begin_inset space \thinspace{}
36540 mm vertical space is inserted before the formula.
36541 When the formula style
36547 \begin_layout Plain Layout
36549 \begin_inset CommandInset ref
36551 reference "sec:Formula-Styles"
36563 \begin_inset space \thinspace{}
36566 mm space is inserted instead.
36569 \begin_layout Standard
36570 As example a multi-column text with a displayed formula:
36573 \begin_layout Standard
36579 \begin_layout Plain Layout
36583 begin{multicols}{2}
36588 Das Spektrum wird fouriertransformiert.
36589 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36590 , Lösungsmittel) zu trennen.
36591 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36592 nun das Aussehen des Ausgangssignals.
36593 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36594 über alle Phasen integrieren muss.
36596 \begin_inset Formula $S$
36599 unser normiertes Ausgangssignal und
36600 \begin_inset Formula $P$
36603 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36607 \begin_layout Plain Layout
36617 \begin_inset VSpace -6mm
36621 \begin_inset Formula
36623 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36632 \begin_layout Plain Layout
36636 begin{multicols}{2}
36642 \begin_inset Formula $S_{0}$
36645 das Signal ohne Gradient ist und die Normierungsbedingung
36646 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36650 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36652 \begin_inset Formula $\nicefrac{\pi}{2}$
36656 \begin_inset space \thinspace{}
36659 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36660 das Signal zusätzlich abschwächt.
36661 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36663 \begin_inset Formula $T_{2}$
36669 \begin_layout Standard
36675 \begin_layout Plain Layout
36687 \begin_layout Subsection
36688 Formulas with Description of Variables
36689 \begin_inset Index idx
36692 \begin_layout Plain Layout
36693 Formula ! with description of variables
36701 \begin_layout Standard
36702 To describe variables within a formula, like in formula
36703 \begin_inset CommandInset ref
36705 reference "eq:within"
36714 \begin_inset Formula $n$
36718 \begin_inset space ~
36721 matrix is used with left aligned columns for the
36722 \begin_inset Formula $n$
36729 \begin_layout Plain Layout
36731 \begin_inset CommandInset ref
36733 reference "sec:Matrices"
36742 To set the description in a smaller size, before the matrix e.
36743 \begin_inset space \thinspace{}
36747 \begin_inset space \space{}
36760 \begin_layout Plain Layout
36762 \begin_inset CommandInset ref
36764 reference "sub:Font-Sizes"
36776 \begin_layout Standard
36777 When the formula style
36783 \begin_layout Plain Layout
36785 \begin_inset CommandInset ref
36787 reference "sec:Formula-Styles"
36808 \begin_layout Plain Layout
36815 only works in formulas with the style
36820 \begin_inset CommandInset ref
36822 reference "sub:Variable-Space"
36831 is inserted before and after the matrix to have the same separation of
36832 the matrix from the equation and the side margin.
36835 \begin_layout Standard
36836 When the formula style
36840 is used, the method described in
36841 \begin_inset CommandInset ref
36843 reference "sub:Flalign-Environment"
36847 is used to indent formulas.
36849 \begin_inset CommandInset ref
36851 reference "eq:within"
36855 consists of five columns where in the first two columns contain the equation,
36856 the third the matrix and the last one an empty TeX-brace.
36857 \begin_inset Formula
36859 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36860 \rho & \textrm{density}\\
36861 V & \textrm{volume}\\
36862 g & \textrm{gravitational acceleration}
36863 \end{array} & & {}\label{eq:within}
36871 \begin_layout Subsection
36872 Upright small Greek Letters
36873 \begin_inset CommandInset label
36875 name "sub:Upright-small-Greek"
36880 \begin_inset Index idx
36883 \begin_layout Plain Layout
36884 Greek letters ! upright
36892 \begin_layout Standard
36893 Most of the math fonts only provide italic small Greek letters.
36894 But for symbols of elementary particles like pions and neutrinos, upright
36895 Greek letters are needed.
36904 \begin_layout Plain Layout
36909 is part of the LaTeX-package
36914 \begin_inset Index idx
36917 \begin_layout Plain Layout
36922 \begin_layout Plain Layout
36942 \begin_inset Index idx
36945 \begin_layout Plain Layout
36951 that is loaded with the LaTeX-preamble line
36954 \begin_layout Standard
36959 usepackage{upgreek}
36962 \begin_layout Standard
36968 \begin_layout Plain Layout
36978 \begin_inset Note Note
36981 \begin_layout Plain Layout
36982 The following table will only be displayed when the LaTeX-package
36991 They are created when the command for a small Greek letter is started with
36997 For example the command
37004 \begin_inset Formula $\uptau$
37010 \begin_layout Standard
37011 With these commands reactions of elementary particles can be typeset:
37012 \begin_inset Formula
37014 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
37022 \begin_layout Standard
37023 The upright letters are more bold and wider than the italic ones.
37024 They should therefore not be used for units like
37025 \begin_inset Quotes eld
37029 \begin_inset Quotes erd
37035 \begin_layout Standard
37039 \begin_layout Plain Layout
37049 \begin_inset Note Note
37052 \begin_layout Plain Layout
37053 The following will be displayed when the LaTeX-package
37065 \begin_layout Standard
37066 You need to install the LaTeX-package
37070 to see the rest of this subsection in the output.
37073 \begin_layout Standard
37077 \begin_layout Plain Layout
37089 \begin_layout Subsection
37090 Text Characters in Formulas
37091 \begin_inset CommandInset label
37093 name "sub:Text-Characters-in"
37098 \begin_inset Index idx
37101 \begin_layout Plain Layout
37110 \begin_layout Standard
37111 In some cases you might want to insert text characters directly into formulas.
37112 When for example the centered dot · is often used in formulas like
37113 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
37116 , one would have to insert the command
37126 \begin_layout Plain Layout
37128 \begin_inset CommandInset ref
37130 reference "sub:Binary-Operators"
37139 all the time, because this character is defined in all encodings as text
37141 But the encoding can be changed by this LaTeX-preamble line:
37144 \begin_layout Standard
37149 Declare Inputtext{183}{
37159 f\SpecialChar \textcompwordmark{}
37163 \begin_layout Standard
37164 The character encoding (menu
37166 Document\SpecialChar \menuseparator
37167 Settings\SpecialChar \menuseparator
37170 ) specifies what character appears when a keyboard key is pressed.
37171 When the key for the character '·' is pressed, internally the command
37178 But this command is not available in a formula so that you would get LaTeX-erro
37180 With the changed encoding the right command is chosen automatically, depending
37181 on if the character was inserted into a formula or not.
37184 \begin_layout Standard
37185 The encoding of several characters is saved in definition files.
37186 For example the encoding
37190 is defined in the file
37194 which is in the installation folder of LaTeX.
37195 Encodings should only be changed via the LaTeX-preamble and not in the
37197 Otherwise documents could not be edited by other LyX users working on other
37201 \begin_layout Standard
37202 \begin_inset VSpace medskip
37205 Besides the centered dot, in this document the degree sign ° is defined
37206 with the following LaTeX-preamble line so that it can be directly inserted
37210 \begin_layout Standard
37215 DeclareInputtext{176}{
37225 f\SpecialChar \textcompwordmark{}
37229 \begin_layout Standard
37230 \begin_inset Newpage newpage
37236 \begin_layout Section
37239 \begin_inset Index idx
37242 \begin_layout Plain Layout
37251 \begin_layout Standard
37252 This section is a summary of the most important typographic rules, listed
37257 \begin_layout Plain Layout
37258 This collection was partly taken from the German semi-official dictionary
37260 \begin_inset Quotes eld
37264 \begin_inset Quotes erd
37268 \begin_inset CommandInset citation
37274 that lists some of the ISO rules.
37275 More rules are listed in
37276 \begin_inset CommandInset citation
37290 \begin_layout Itemize
37299 \begin_layout Plain Layout
37300 done with font styles, see
37301 \begin_inset CommandInset ref
37303 reference "sub:Font-Styles"
37312 , no matter if they appear in italic text: 30
37313 \begin_inset space \thinspace{}
37317 \begin_inset Newline newline
37320 Between the value and the unit is the smallest space, see
37321 \begin_inset CommandInset ref
37323 reference "sub:Predefined-Space"
37328 \begin_inset Newline newline
37331 This convention is automatically fulfilled when the command
37338 When it is entered to a formula, two boxes appear.
37339 In the first one the value is inserted, in the second one the unit, and
37341 \begin_inset Formula $\unit[30]{km/h}$
37345 \begin_inset space \thinspace{}
37355 is not a real LaTeX command but the command
37361 , therefore you cannot use it in TeX code.
37364 \begin_layout Itemize
37365 Percent and perthousand signs are set like physical units:
37366 \begin_inset Newline newline
37370 \begin_inset space \thinspace{}
37376 \begin_layout Itemize
37377 The degree sign follows directly on the value: 15°, but not when it is used
37379 \begin_inset space \thinspace{}
37385 \begin_layout Itemize
37386 In numbers with more than four digits the smallest space is inserted before
37387 every third digit to group them:
37397 \begin_inset space \thinspace{}
37401 \begin_inset space \thinspace{}
37407 \begin_layout Itemize
37408 For dimensions like 120×90×40
37409 \begin_inset space \thinspace{}
37412 cm the multiplication sign
37413 \begin_inset Quotes eld
37417 \begin_inset Quotes erd
37421 It is available either via the command
37429 Insert\SpecialChar \menuseparator
37430 Special Character\SpecialChar \menuseparator
37436 \begin_layout Itemize
37437 Functions with names consisting of several letters are set upright to avoid
37439 \begin_inset CommandInset ref
37441 reference "sub:Predefined-Functions"
37448 \begin_layout Itemize
37449 Indices consisting of several letters, are set upright:
37450 \begin_inset Formula $E_{\mathrm{kin}}$
37454 \begin_inset Newline newline
37457 Components of matrices are set italic:
37458 \begin_inset Formula $\hat{H}_{kl}$
37464 \begin_layout Itemize
37465 The differentiation/integration operator 'd', the Euler's number 'e' and
37466 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37470 \begin_layout Itemize
37471 The character that denotes a
37475 transformation is inserted either by the command
37483 \begin_layout Plain Layout
37496 Insert\SpecialChar \menuseparator
37497 Special Character\SpecialChar \menuseparator
37498 Symbols\SpecialChar \menuseparator
37500 \begin_inset space ~
37506 \begin_inset Formula $\mathscr{F}$
37512 \begin_layout Standard
37513 \begin_inset Newpage newpage
37519 \begin_layout Section
37521 \begin_inset Index idx
37524 \begin_layout Plain Layout
37533 \begin_layout Standard
37534 Some characters and symbols can be created with several commands.
37535 Here is a list of the synonym commands:
37538 \begin_layout Standard
37539 \begin_inset VSpace bigskip
37543 \begin_inset space \hfill{}
37547 \begin_inset Tabular
37548 <lyxtabular version="3" rows="12" columns="2">
37549 <features tabularvalignment="middle">
37550 <column alignment="center" valignment="top" width="0pt">
37551 <column alignment="center" valignment="top" width="0pt">
37553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37556 \begin_layout Plain Layout
37562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37565 \begin_layout Plain Layout
37567 \begin_inset Note Note
37570 \begin_layout Plain Layout
37577 is only used as spacer.
37589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37592 \begin_layout Plain Layout
37600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37603 \begin_layout Plain Layout
37607 \begin_layout Plain Layout
37620 \begin_layout Plain Layout
37634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37637 \begin_layout Plain Layout
37645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37648 \begin_layout Plain Layout
37658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37661 \begin_layout Plain Layout
37669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37672 \begin_layout Plain Layout
37682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37685 \begin_layout Plain Layout
37693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37696 \begin_layout Plain Layout
37704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37707 \begin_layout Plain Layout
37715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37718 \begin_layout Plain Layout
37726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37729 \begin_layout Plain Layout
37737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37740 \begin_layout Plain Layout
37750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37753 \begin_layout Plain Layout
37761 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37764 \begin_layout Plain Layout
37774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37777 \begin_layout Plain Layout
37785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37788 \begin_layout Plain Layout
37798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37801 \begin_layout Plain Layout
37809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37812 \begin_layout Plain Layout
37822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37825 \begin_layout Plain Layout
37833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37836 \begin_layout Plain Layout
37844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37847 \begin_layout Plain Layout
37855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37858 \begin_layout Plain Layout
37870 \begin_inset space \hfill{}
37874 \begin_inset Tabular
37875 <lyxtabular version="3" rows="12" columns="2">
37876 <features tabularvalignment="middle">
37877 <column alignment="center" valignment="top" width="0pt">
37878 <column alignment="center" valignment="top" width="0pt">
37880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37883 \begin_layout Plain Layout
37889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37892 \begin_layout Plain Layout
37900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37903 \begin_layout Plain Layout
37911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37914 \begin_layout Plain Layout
37926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37929 \begin_layout Plain Layout
37937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37940 \begin_layout Plain Layout
37950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37953 \begin_layout Plain Layout
37961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37964 \begin_layout Plain Layout
37974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37977 \begin_layout Plain Layout
37985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37988 \begin_layout Plain Layout
37996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37999 \begin_layout Plain Layout
38007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38010 \begin_layout Plain Layout
38018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38021 \begin_layout Plain Layout
38029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38032 \begin_layout Plain Layout
38042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38045 \begin_layout Plain Layout
38053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38056 \begin_layout Plain Layout
38066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38069 \begin_layout Plain Layout
38077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38080 \begin_layout Plain Layout
38090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38093 \begin_layout Plain Layout
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38149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
38152 \begin_layout Plain Layout
38166 \begin_inset space \hfill{}
38172 \begin_layout Standard
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38181 LatexCommand bibitem
38193 The LaTeX Companion
38196 Addison Wesley, 2004
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38200 \begin_inset CommandInset bibitem
38201 LatexCommand bibitem
38207 \begin_inset CommandInset href
38210 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
38214 of LaTeX's math abilities
38217 \begin_layout Bibliography
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38219 LatexCommand bibitem
38225 \begin_inset CommandInset href
38228 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
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38248 \begin_layout Bibliography
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38250 LatexCommand bibitem
38256 \begin_inset CommandInset href
38259 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38263 of all symbols available with LaTeX-packages
38266 \begin_layout Bibliography
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38268 LatexCommand bibitem
38274 \begin_inset CommandInset href
38276 name "Documentation"
38277 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
38281 of the LaTeX-package
38286 \begin_inset Index idx
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38299 \begin_inset CommandInset bibitem
38300 LatexCommand bibitem
38306 \begin_inset CommandInset href
38308 name "Documentation"
38309 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38313 of the LaTeX-package
38318 \begin_inset Index idx
38321 \begin_layout Plain Layout
38322 Packages ! hyperref
38330 \begin_layout Bibliography
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38332 LatexCommand bibitem
38338 \begin_inset CommandInset href
38340 name "Documentation"
38341 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38345 of the LaTeX-package
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38363 \begin_inset CommandInset bibitem
38364 LatexCommand bibitem
38370 \begin_inset CommandInset href
38373 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
38384 \begin_inset CommandInset ref
38386 reference "sub:Operator-Limits"
38391 \begin_inset Index idx
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38407 LatexCommand bibitem
38418 Auflage, Duden 2001
38421 \begin_layout Bibliography
38422 \begin_inset CommandInset bibitem
38423 LatexCommand bibitem
38429 \begin_inset CommandInset href
38432 target "http://physics.nist.gov/Document/checklist.pdf"
38436 for reviewing manuscripts
38439 \begin_layout Standard
38440 \begin_inset CommandInset index_print
38441 LatexCommand printindex