1 #LyX 2.1 created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % solves the following problem:
27 % If the dection number consits of too many numerals the section heading
28 % will be printed in the TOC without a space between it and the section number.
29 % As solution more space between the number and the heading is inserted:
30 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
31 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
33 % increase link area for cross-references and autoname them,
34 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
35 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
36 \addto\extrasenglish{%
37 \renewcommand*{\equationautorefname}[1]{}%
38 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
39 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
40 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
43 % don't load packages twice
44 % see first footnote in sec. 9.3
45 \@ifundefined{textcolor}{\usepackage{color}}{}
47 % the pages of the TOC are numbered roman
48 % and a PDF-bookmark for the TOC is added
50 \let\myTOC\tableofcontents
51 \renewcommand{\tableofcontents}{%
53 \pdfbookmark[1]{\contentsname}{}
56 \pagenumbering{arabic}}
58 % insert additional vertical space of 1.5 mm between footnotes,
60 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
62 % provides caption formatting
63 \setkomafont{captionlabel}{\bfseries}
66 \usepackage[samesize]{cancel}
68 % enables calculation of values
71 % for multiple columns used in sec. 24.7
77 % for the Fourier transformation symbol
80 % define a color, used in sec.9.3
81 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
83 % declare operators (see sec. 10.4 and sec. 15.2)
84 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
85 \DeclareMathOperator{\sgn}{sgn}
87 \newcommand{\spce}{\textvisiblespace}
89 % example definitions for sec. 20.1
90 \newcommand{\gr}{\Longrightarrow}
91 \newcommand{\us}[1]{\underline{#1}}
92 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
93 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
94 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
96 % example macro from sec. 19.4
97 %\def\tagform@#1{\maketag@@@{|#1|}}
99 % macro from sec. 10.2
100 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
101 \def\mathclap {\mathpalette \mathclapinternal}
102 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
105 % ------------------------------------
106 % used to check for needed LaTeX packages
109 % check for package eurosym
110 % used for the Euro symbol
112 \IfFileExists{eurosym.sty}
113 {\usepackage[gennarrow]{eurosym}
114 \setboolean{eurosym}{true}}
115 {\setboolean{eurosym}{false}}
117 % check for package braket
118 % used for physical vectors
120 \IfFileExists{braket.sty}
122 \setboolean{braket}{true}}
123 {\setboolean{braket}{false}}
125 % check for package cancel
127 \IfFileExists{cancel.sty}
129 \setboolean{cancel}{true}}
130 {\setboolean{cancel}{false}}
132 % check for package upgreek
134 \IfFileExists{upgreek.sty}
135 {\usepackage{upgreek}
136 \setboolean{upgreek}{true}}
137 {\setboolean{upgreek}{false}}
139 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
140 \use_default_options false
141 \maintain_unincluded_children false
143 \language_package default
148 \font_typewriter default
150 \font_default_family default
151 \use_non_tex_fonts false
157 \default_output_format default
159 \bibtex_command default
160 \index_command default
164 \pdf_title "LyX's Math Manual"
165 \pdf_author "LyX Team, Uwe Stöhr"
166 \pdf_subject "LyX-documentation about math"
167 \pdf_keywords "LyX, Mathed"
169 \pdf_bookmarksnumbered true
170 \pdf_bookmarksopen true
171 \pdf_bookmarksopenlevel 1
172 \pdf_breaklinks false
176 \pdf_pdfusetitle false
177 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
180 \use_package amsmath 2
181 \use_package amssymb 2
182 \use_package cancel 0
184 \use_package mathdots 1
185 \use_package mathtools 0
186 \use_package mhchem 1
187 \use_package stackrel 0
188 \use_package stmaryrd 0
189 \use_package undertilde 0
191 \cite_engine_type default
195 \paperorientation portrait
199 \notefontcolor #0000ff
206 \paragraph_separation skip
208 \quotes_language english
211 \paperpagestyle plain
215 \tracking_changes false
216 \output_changes false
219 \html_be_strict false
225 LyX's detailed Math manual
233 \begin_layout Plain Layout
235 If you have comments or error corrections, please send them to the LyX Documenta
239 \begin_inset CommandInset href
241 name "lyx-docs@lists.lyx.org"
242 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
253 \begin_inset Note Note
256 \begin_layout Plain Layout
263 \begin_inset Newline newline
267 \begin_inset Newline newline
275 \begin_layout Standard
276 \begin_inset CommandInset toc
277 LatexCommand tableofcontents
284 \begin_layout Standard
285 \begin_inset Note Note
288 \begin_layout Plain Layout
289 To export this document to PDF, PS or DVI the LaTeX-packages
291 braket, cancel, eurosym, mathdots, mhchem
298 If they are not installed the document can be exported anyway but the sections
299 where the packages are required will not appear in the output.
304 ; if it is not installed, this file cannot be exported.
307 \begin_layout Plain Layout
308 The latest PDF-version of this document can be found here:
309 \begin_inset Newline newline
314 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
322 \begin_layout Standard
323 \begin_inset Newpage newpage
329 \begin_layout Section
333 \begin_layout Standard
334 This document explains LyX's math features and is furthermore a collection
335 of LaTeX-commands used for mathematical characters and constructs.
336 The explanations are designed for the usage of commands.
337 It is therefore required that you have read the section
348 \begin_layout Standard
349 Most of the characters and many constructs explained in this manual are
350 also accessible via the menu
354 \SpecialChar \menuseparator
370 But everybody who has to write lots of formulas will notice that it is
371 much faster to use commands instead of the math toolbar.
372 Therefore this manual is focused on commands but also mentions the correspondin
373 g toolbar buttons when available.
376 \begin_layout Standard
377 If not specially mentioned the commands are only available within formulas.
378 To be able to use all commands explained in this document, the option
382 must be checked in the document settings (menu
384 Document\SpecialChar \menuseparator
385 Settings\SpecialChar \menuseparator
396 \begin_layout Plain Layout
399 Use AMS math package automatically
405 \begin_layout Plain Layout
414 -math when math constructs are found that are supported by LyX.
422 \begin_layout Standard
423 This document doesn't list all
427 \begin_layout Plain Layout
440 \begin_layout Plain Layout
445 \begin_layout Plain Layout
454 -math commands is in the file
457 \begin_inset CommandInset href
460 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
466 , which is part of every LaTeX standard installation.
471 for lucidity reasons.
474 \begin_layout Section
478 \begin_layout Standard
479 To create an inline formula
480 \begin_inset Index idx
483 \begin_layout Plain Layout
489 that is embedded into a text line, use one of the shortcuts
495 or the toolbar button
496 \begin_inset Graphics
497 filename ../images/math-mode.png
503 \begin_inset Newline newline
506 To create a display style formula
507 \begin_inset Index idx
510 \begin_layout Plain Layout
511 Formula ! display style
516 which will appear bigger, has a different format, and will be in a separate
517 paragraph, use one of these shortcuts:
526 \begin_layout Standard
527 To change a display style formula to an inline formula, set the cursor into
528 the formula and use one of the shortcuts
536 Edit\SpecialChar \menuseparator
537 Math\SpecialChar \menuseparator
541 The same way is used to change an inline formula to a display style formula.
544 \begin_layout Standard
545 To display parts of an inline formula in the size of a display style formula,
553 \begin_inset Index idx
556 \begin_layout Plain Layout
565 Then a new blue box appears in which the desired formula part is inserted.
568 \begin_layout Standard
569 Only inline formulas are allowed inside tables.
572 \begin_layout Standard
577 can be turned on in the menu
579 View\SpecialChar \menuseparator
583 When you click there on
584 \begin_inset Quotes eld
588 \begin_inset Quotes erd
591 the toolbar will be shown permanently at the bottom; this state is visualized
596 menu with a checkmark.
597 When you click in this state again on
598 \begin_inset Quotes eld
602 \begin_inset Quotes erd
613 is only shown when the cursor is within a formula; this state is visualized
614 by the renaming of the menu entry from
615 \begin_inset Quotes eld
619 \begin_inset Quotes erd
623 \begin_inset Quotes eld
631 \begin_inset Quotes erd
637 \begin_layout Standard
639 \begin_inset Index idx
642 \begin_layout Plain Layout
648 is invoked by pressing the toolbar button
649 \begin_inset Graphics
650 filename ../images/ert-insert.png
657 Insert\SpecialChar \menuseparator
662 \begin_layout Plain Layout
678 \begin_inset Note Note
681 \begin_layout Plain Layout
682 In LyX there are three
683 \begin_inset Quotes eld
687 \begin_inset Quotes erd
690 that appear in the output with sub- and superscript letters: TeX, LaTeX
694 \begin_layout Plain Layout
695 To avoid that these names are recognized as proper names, a TeX-brace pair
704 \begin_layout Standard
705 To change the LaTeX-preamble
706 \begin_inset Index idx
709 \begin_layout Plain Layout
717 Document\SpecialChar \menuseparator
718 Settings\SpecialChar \menuseparator
723 \begin_layout Plain Layout
739 \begin_layout Standard
740 To edit matrices, case differentiations and multiline formulas subsequently,
743 Edit\SpecialChar \menuseparator
748 Edit\SpecialChar \menuseparator
750 \begin_inset space \thinspace{}
754 \begin_inset space \thinspace{}
764 When lines and columns are swapped via the menu, the column or line where
765 the cursor is in is exchanged with the column to the right or the line
767 Is the cursor in the last column or row, the exchange is done with the
768 column to the left or the line above.
771 \begin_layout Standard
772 To write text in formulas
776 \begin_layout Plain Layout
777 For multiline formulas the command
784 \begin_inset CommandInset ref
786 reference "sub:Text-in-multiline"
800 \begin_inset Index idx
803 \begin_layout Plain Layout
810 \begin_inset Index idx
813 \begin_layout Plain Layout
820 This mode is invoked with the shortcut
826 or by the insertion of the command
833 \begin_inset Index idx
836 \begin_layout Plain Layout
845 The text appears black in LyX and can therefore be distinguished from the
846 other formula parts which appear blue.
847 In the output mathematical text is set upright, in contrary to other formula
851 \begin_layout Subsection*
855 \begin_layout Standard
856 Most of the LaTeX-commands for math constructs have the following scheme:
859 \begin_layout Standard
875 \begin_layout Standard
876 A command always starts with a backslash
877 \begin_inset Quotes gld
887 \begin_inset Quotes grd
891 To omit optional arguments, also omit the associated brackets.
892 The braces around the required arguments are named in this document as
894 \begin_inset Index idx
897 \begin_layout Plain Layout
904 If you add in a formula a left brace to a command name, LyX automatically
906 In all other cases TeX-braces are created in formulas with the command
914 TeX-braces appear red in LyX, in contrary to normal braces which appear
916 In TeX-mode no command is needed to get TeX-braces.
917 TeX-braces don't appear in the output.
920 \begin_layout Standard
921 When commands without arguments, like commands for symbols are entered in
922 TeX-mode, a space character must
926 be behind the command to end it.
927 This space doesn't appear in the output.
928 When the space should appear in the output, the space must be followed
929 by a protected space in normal text.
932 \begin_layout Standard
933 A protected space is inserted with
936 arg "command-alternatives space-insert protected ; math-space"
942 \begin_layout Subsection*
943 \begin_inset Newpage newpage
949 \begin_layout Itemize
954 \begin_layout Plain Layout
955 This visible space character can be created with the command
962 \begin_inset Index idx
965 \begin_layout Plain Layout
973 , inserted in TeX-mode.
982 \begin_layout Plain Layout
995 denotes a space character to be input.
998 \begin_layout Itemize
1000 \begin_inset Formula $\to$
1003 denotes the usage of the corresponding arrow key on the keyboard.
1008 key can often be used instead of
1009 \begin_inset Formula $\to$
1013 \begin_inset Formula $\downarrow$
1021 \begin_inset Formula $\leftarrow$
1025 \begin_inset Formula $\uparrow$
1031 \begin_layout Subsection*
1035 \begin_layout Standard
1037 \begin_inset Float table
1043 \begin_layout Plain Layout
1045 \begin_inset Caption Standard
1047 \begin_layout Plain Layout
1048 \begin_inset CommandInset label
1050 name "tab:Available-units"
1062 \begin_layout Plain Layout
1064 \begin_inset Tabular
1065 <lyxtabular version="3" rows="13" columns="2">
1066 <features rotate="0" tabularvalignment="middle">
1067 <column alignment="center" valignment="top">
1068 <column alignment="center" valignment="top">
1070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1073 \begin_layout Plain Layout
1079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1082 \begin_layout Plain Layout
1090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1093 \begin_layout Plain Layout
1099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1102 \begin_layout Plain Layout
1110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1113 \begin_layout Plain Layout
1119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1122 \begin_layout Plain Layout
1130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1133 \begin_layout Plain Layout
1139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1142 \begin_layout Plain Layout
1144 \begin_inset space \thinspace{}
1148 \begin_inset space \thinspace{}
1158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1161 \begin_layout Plain Layout
1167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1170 \begin_layout Plain Layout
1172 \begin_inset space \thinspace{}
1176 \begin_inset space \thinspace{}
1186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1189 \begin_layout Plain Layout
1195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1198 \begin_layout Plain Layout
1200 \begin_inset space \thinspace{}
1204 \begin_inset space \thinspace{}
1214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1217 \begin_layout Plain Layout
1223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1226 \begin_layout Plain Layout
1228 \begin_inset space \thinspace{}
1232 \begin_inset space \thinspace{}
1242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1245 \begin_layout Plain Layout
1251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1254 \begin_layout Plain Layout
1256 \begin_inset space \thinspace{}
1260 \begin_inset space \thinspace{}
1270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1273 \begin_layout Plain Layout
1279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1282 \begin_layout Plain Layout
1284 \begin_inset space \thinspace{}
1288 \begin_inset Formula $\approx$
1292 \begin_inset space \thinspace{}
1302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1305 \begin_layout Plain Layout
1311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1314 \begin_layout Plain Layout
1316 \begin_inset space \thinspace{}
1320 \begin_inset space \thinspace{}
1330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1333 \begin_layout Plain Layout
1339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1342 \begin_layout Plain Layout
1346 \begin_inset Quotes eld
1352 \begin_inset Quotes erd
1362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1365 \begin_layout Plain Layout
1371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1374 \begin_layout Plain Layout
1376 \begin_inset Quotes eld
1384 \begin_inset Quotes erd
1394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1397 \begin_layout Plain Layout
1403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1406 \begin_layout Plain Layout
1408 \begin_inset space \thinspace{}
1412 \begin_inset Formula $\nicefrac{1}{18}$
1416 \begin_inset space \thinspace{}
1437 \begin_layout Standard
1438 \begin_inset Newpage newpage
1444 \begin_layout Section
1448 \begin_layout Subsection
1450 \begin_inset Index idx
1453 \begin_layout Plain Layout
1460 \begin_inset Index idx
1463 \begin_layout Plain Layout
1470 \begin_inset Index idx
1473 \begin_layout Plain Layout
1478 \begin_layout Plain Layout
1489 \begin_layout Plain Layout
1502 \begin_inset Index idx
1505 \begin_layout Plain Layout
1510 \begin_layout Plain Layout
1521 \begin_layout Plain Layout
1536 \begin_layout Standard
1537 Indices are created with an underscore
1538 \begin_inset Quotes eld
1542 \begin_inset Quotes erd
1545 or via the math toolbar button
1546 \begin_inset Graphics
1547 filename ../images/math-subscript.png
1552 , exponents with a caret
1553 \begin_inset Quotes eld
1557 \begin_inset Quotes erd
1560 or via the math toolbar button
1561 \begin_inset Graphics
1562 filename ../images/math-superscript.png
1570 \begin_layout Standard
1572 \begin_inset Tabular
1573 <lyxtabular version="3" rows="4" columns="2">
1574 <features rotate="0" tabularvalignment="middle">
1575 <column alignment="center" valignment="top" width="0pt">
1576 <column alignment="center" valignment="top" width="0pt">
1578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1581 \begin_layout Plain Layout
1587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1590 \begin_layout Plain Layout
1592 \begin_inset Note Note
1595 \begin_layout Plain Layout
1602 is only used as spacer.
1614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1617 \begin_layout Plain Layout
1623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1626 \begin_layout Plain Layout
1627 \begin_inset Formula $B_{V}$
1637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1640 \begin_layout Plain Layout
1646 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1649 \begin_layout Plain Layout
1650 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1663 \begin_layout Plain Layout
1668 \begin_layout Plain Layout
1682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1685 \begin_layout Plain Layout
1686 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1702 \begin_layout Standard
1703 As the caret is in some languages an accent, vowels will be accentuated
1704 in this case and not set as exponents
1708 \begin_layout Plain Layout
1709 Depending on the used keyboard settings this can also happen for characters
1716 To get exponents in this case, press
1720 after the caret as in the last example.
1723 \begin_layout Subsection
1725 \begin_inset CommandInset label
1727 name "sub:Fractions"
1732 \begin_inset Index idx
1735 \begin_layout Plain Layout
1744 \begin_layout Standard
1745 Fractions are generated with the command
1752 \begin_inset Index idx
1755 \begin_layout Plain Layout
1763 or via the math toolbar button
1764 \begin_inset Graphics
1765 filename ../images/math/frac.png
1771 The font size is adjusted automatically, depending on whether the fraction
1772 is in an inline or display style formula.
1773 With the math toolbar button
1774 \begin_inset Graphics
1775 filename ../images/math/frac-square.png
1780 you can select different fraction types.
1783 \begin_layout Standard
1791 \begin_inset Index idx
1794 \begin_layout Plain Layout
1802 a fraction can be created that always has the size of a display style formula.
1810 \begin_inset Index idx
1813 \begin_layout Plain Layout
1821 the fraction appears always with the size of an inline formula.
1825 \begin_layout Standard
1826 A line with the fraction
1827 \begin_inset Formula $\frac{1}{2}$
1830 that was created with the command
1839 \begin_layout Standard
1840 A line with the fraction
1841 \begin_inset Formula $\dfrac{1}{2}$
1844 that was created with the command
1853 \begin_layout Standard
1855 \begin_inset Tabular
1856 <lyxtabular version="3" rows="4" columns="2">
1857 <features rotate="0" tabularvalignment="middle">
1858 <column alignment="center" valignment="top" width="0pt">
1859 <column alignment="center" valignment="top" width="0pt">
1861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1864 \begin_layout Plain Layout
1870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1873 \begin_layout Plain Layout
1875 \begin_inset Note Note
1878 \begin_layout Plain Layout
1885 is only used as spacer.
1897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1900 \begin_layout Plain Layout
1907 \begin_layout Plain Layout
1917 \begin_inset Formula $\downarrow$
1925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1928 \begin_layout Plain Layout
1929 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1942 \begin_layout Plain Layout
1949 \begin_layout Plain Layout
1959 \begin_inset Formula $\downarrow$
1967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1970 \begin_layout Plain Layout
1971 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1984 \begin_layout Plain Layout
1991 \begin_layout Plain Layout
2006 \begin_layout Plain Layout
2016 \begin_inset Formula $\downarrow$
2020 \begin_inset Formula $\downarrow\downarrow$
2028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2031 \begin_layout Plain Layout
2032 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2048 \begin_layout Standard
2049 \begin_inset VSpace bigskip
2053 \begin_inset Newpage newpage
2056 For nested fractions the command
2063 \begin_inset Index idx
2066 \begin_layout Plain Layout
2076 \begin_inset VSpace -3mm
2082 \begin_layout Standard
2083 \begin_inset Formula
2085 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2086 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2094 \begin_layout Standard
2095 The command for the example above is:
2098 \begin_layout Standard
2107 \begin_layout Plain Layout
2117 \begin_inset Formula $\downarrow$
2126 \begin_layout Plain Layout
2141 \begin_layout Plain Layout
2151 \begin_inset Formula $\downarrow$
2155 \begin_inset Formula $\downarrow$
2161 \begin_layout Standard
2162 \begin_inset VSpace medskip
2168 \begin_layout Standard
2175 sets the fraction always in the size of a displayed formula, also when
2176 it is part of another fraction.
2179 \begin_layout Standard
2180 It is possible to specify the alignment of the numerator.
2187 is used to left align it, the command
2200 centers the numerator.
2201 These fractions demonstrate the different alignments:
2204 \begin_layout Standard
2207 \begin_inset Formula
2209 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2217 \begin_layout Standard
2218 \begin_inset Note Greyedout
2221 \begin_layout Plain Layout
2238 are no real LaTeX commands but represent the command
2242 cfrac[alignment]{numerator}{denominator}
2245 Therefore you cannot use them in TeX code.
2253 \begin_layout Standard
2254 \begin_inset VSpace medskip
2257 It is often advantageous to combine
2270 \begin_inset Formula
2272 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2280 \begin_layout Standard
2281 For inline fractions with a sloped fraction stroke you can use the command
2289 \begin_inset Index idx
2292 \begin_layout Plain Layout
2301 \begin_inset Formula $\nicefrac{5}{31}$
2311 \begin_inset Index idx
2314 \begin_layout Plain Layout
2323 \begin_inset Formula $\unitfrac{5}{31}$
2326 There is furthermore the command
2332 that offers to write a fraction in combination with a number:
2333 \begin_inset Formula $\unitfrac[2]{1}{3}$
2339 \begin_layout Standard
2340 \begin_inset Note Greyedout
2343 \begin_layout Plain Layout
2354 is not a real LaTeX command but the command
2355 \begin_inset Newline newline
2362 unitfrac[number]{numerator}{denominator}
2365 Therefore you cannot use it in TeX code.
2373 \begin_layout Standard
2374 How to define own fractions where the fraction stroke can be changed, is
2376 \begin_inset CommandInset ref
2378 reference "sub:Self-defined-Fractions"
2385 \begin_layout Standard
2386 \begin_inset Newpage newpage
2392 \begin_layout Subsection
2394 \begin_inset Index idx
2397 \begin_layout Plain Layout
2406 \begin_layout Standard
2407 Square roots are created with
2414 \begin_inset Index idx
2417 \begin_layout Plain Layout
2425 or the math toolbar button
2426 \begin_inset Graphics
2427 filename ../images/math/sqrt.png
2432 , all other roots with the command
2439 \begin_inset Index idx
2442 \begin_layout Plain Layout
2450 or with the math toolbar button
2451 \begin_inset Graphics
2452 filename ../images/math/root.png
2460 \begin_layout Standard
2462 \begin_inset Tabular
2463 <lyxtabular version="3" rows="3" columns="2">
2464 <features rotate="0" tabularvalignment="middle">
2465 <column alignment="center" valignment="top" width="0pt">
2466 <column alignment="center" valignment="top" width="0pt">
2468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2471 \begin_layout Plain Layout
2477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2480 \begin_layout Plain Layout
2482 \begin_inset Note Note
2485 \begin_layout Plain Layout
2492 is only used as spacer.
2504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2507 \begin_layout Plain Layout
2514 \begin_layout Plain Layout
2528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2531 \begin_layout Plain Layout
2532 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2542 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2545 \begin_layout Plain Layout
2552 \begin_layout Plain Layout
2562 \begin_inset Formula $\downarrow$
2570 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2573 \begin_layout Plain Layout
2574 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2590 \begin_layout Standard
2591 A square root can also be created with
2597 when the root index field is left empty.
2600 \begin_layout Standard
2601 With certain indices the distance to the root is too small, like in this
2603 \begin_inset Formula $\sqrt[\beta]{B}$
2607 \begin_inset Newline newline
2611 \begin_inset Formula $\beta$
2615 To avoid this, the commands
2622 \begin_inset Index idx
2625 \begin_layout Plain Layout
2640 \begin_inset Index idx
2643 \begin_layout Plain Layout
2651 are used with the following scheme:
2654 \begin_layout Standard
2668 \begin_layout Standard
2669 Distance is the number of Big Points (unit bp;
2670 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2673 ), that the index should be moved to the left or top, resp..
2674 The commands are written to the index.
2675 This way the command
2676 \begin_inset Newline newline
2686 \begin_inset Formula $\to$
2692 \begin_inset Formula $\to$
2701 \begin_layout Plain Layout
2711 \begin_inset Formula $\to$
2715 \begin_inset Newline newline
2720 produces a correct typeset formula:
2721 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2727 \begin_layout Subsection
2728 Binomial Coefficients
2729 \begin_inset Index idx
2732 \begin_layout Plain Layout
2733 Binomial coefficients
2741 \begin_layout Standard
2742 Binomial coefficients are inserted with the command
2749 \begin_inset Index idx
2752 \begin_layout Plain Layout
2760 or with the submenu of the math toolbar button
2761 \begin_inset Graphics
2762 filename ../images/math/frac-square.png
2780 there are the commands
2787 \begin_inset Index idx
2790 \begin_layout Plain Layout
2805 \begin_inset Index idx
2808 \begin_layout Plain Layout
2817 For other brackets around binomial coeficients there are the commands
2824 \begin_inset Index idx
2827 \begin_layout Plain Layout
2842 \begin_inset Index idx
2845 \begin_layout Plain Layout
2856 \begin_layout Standard
2858 \begin_inset Tabular
2859 <lyxtabular version="3" rows="6" columns="2">
2860 <features rotate="0" tabularvalignment="middle">
2861 <column alignment="center" valignment="top" width="0pt">
2862 <column alignment="center" valignment="top" width="0pt">
2864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2867 \begin_layout Plain Layout
2873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2876 \begin_layout Plain Layout
2878 \begin_inset Note Note
2881 \begin_layout Plain Layout
2888 is only used as spacer.
2900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2903 \begin_layout Plain Layout
2910 \begin_layout Plain Layout
2920 \begin_inset Formula $\downarrow$
2928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2931 \begin_layout Plain Layout
2932 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2945 \begin_layout Plain Layout
2952 \begin_layout Plain Layout
2962 \begin_inset Formula $\downarrow$
2970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2973 \begin_layout Plain Layout
2974 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2987 \begin_layout Plain Layout
2994 \begin_layout Plain Layout
3004 \begin_inset Formula $\downarrow$
3012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3015 \begin_layout Plain Layout
3016 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3029 \begin_layout Plain Layout
3036 \begin_layout Plain Layout
3046 \begin_inset Formula $\downarrow$
3054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3057 \begin_layout Plain Layout
3058 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3071 \begin_layout Plain Layout
3078 \begin_layout Plain Layout
3088 \begin_inset Formula $\downarrow$
3096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3099 \begin_layout Plain Layout
3100 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3116 \begin_layout Subsection
3117 Case Differentiations
3118 \begin_inset Index idx
3121 \begin_layout Plain Layout
3122 Case differentiations
3130 \begin_layout Standard
3132 \begin_inset Tabular
3133 <lyxtabular version="3" rows="3" columns="2">
3134 <features rotate="0" tabularvalignment="middle">
3135 <column alignment="center" valignment="top" width="0pt">
3136 <column alignment="center" valignment="top" width="0pt">
3138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3141 \begin_layout Plain Layout
3147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3150 \begin_layout Plain Layout
3158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3161 \begin_layout Plain Layout
3168 \begin_layout Plain Layout
3178 \begin_inset Formula $\to$
3182 \begin_inset Index idx
3185 \begin_layout Plain Layout
3198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3201 \begin_layout Plain Layout
3202 \begin_inset Formula $\begin{cases}
3213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3216 \begin_layout Plain Layout
3223 \begin_layout Plain Layout
3235 arg "newline-insert newline"
3243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3246 \begin_layout Plain Layout
3247 \begin_inset Formula $\begin{cases}
3248 A & \textrm{for }x>0\\
3249 B & \textrm{for }x=0
3266 \begin_layout Standard
3273 or pressing the math toolbar button
3274 \begin_inset Graphics
3275 filename ../images/math/cases.png
3280 you can create new lines with the shortcut
3283 arg "newline-insert newline"
3286 or the table toolbar button
3287 \begin_inset Graphics
3288 filename ../images/tabular-feature_append-row.png
3296 \begin_layout Standard
3303 is also available via the menu
3305 Insert\SpecialChar \menuseparator
3306 Math\SpecialChar \menuseparator
3312 \begin_layout Subsection
3314 \begin_inset Index idx
3317 \begin_layout Plain Layout
3326 \begin_layout Standard
3334 \begin_inset Index idx
3337 \begin_layout Plain Layout
3345 every character can be displayed canceled.
3346 The characters are quasi accentuated by a slash.
3349 \begin_layout Standard
3351 \begin_inset Tabular
3352 <lyxtabular version="3" rows="4" columns="2">
3353 <features rotate="0" tabularvalignment="middle">
3354 <column alignment="center" valignment="top" width="0pt">
3355 <column alignment="center" valignment="top" width="0pt">
3357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3360 \begin_layout Plain Layout
3366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3369 \begin_layout Plain Layout
3377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3380 \begin_layout Plain Layout
3388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3391 \begin_layout Plain Layout
3392 \begin_inset Formula $\not=$
3402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3405 \begin_layout Plain Layout
3415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3418 \begin_layout Plain Layout
3419 \begin_inset Formula $\not\le$
3429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3432 \begin_layout Plain Layout
3442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3445 \begin_layout Plain Layout
3446 \begin_inset Formula $\not\parallel$
3462 \begin_layout Standard
3463 The last example shows that not all negations look good.
3464 Therefore there are special commands for some negations (see
3465 \begin_inset CommandInset ref
3467 reference "sub:Mathematical-Symbols"
3472 \begin_inset CommandInset ref
3474 reference "sec:Relations"
3481 \begin_layout Subsection
3483 \begin_inset CommandInset label
3485 name "sub:Placeholders"
3490 \begin_inset Index idx
3493 \begin_layout Plain Layout
3500 \begin_inset Index idx
3503 \begin_layout Plain Layout
3504 Chemical characters ! Isotopes
3510 \begin_inset Index idx
3513 \begin_layout Plain Layout
3518 \begin_layout Plain Layout
3529 \begin_layout Plain Layout
3544 \begin_layout Standard
3546 \begin_inset space \thinspace{}
3550 \begin_inset space \space{}
3557 \begin_layout Plain Layout
3558 Typesetting isotopes and chemical symbols is described in
3559 \begin_inset CommandInset ref
3561 reference "sub:Chemical-Symbols-and"
3570 the following problem occurs:
3573 \begin_layout Standard
3575 \begin_inset Tabular
3576 <lyxtabular version="3" rows="2" columns="2">
3577 <features rotate="0" tabularvalignment="middle">
3578 <column alignment="center" valignment="top" width="0pt">
3579 <column alignment="center" valignment="top" width="0pt">
3581 <cell alignment="center" valignment="top" usebox="none">
3584 \begin_layout Plain Layout
3585 Indices created with sub- and superscripts:
3590 <cell alignment="center" valignment="top" usebox="none">
3593 \begin_layout Plain Layout
3594 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3604 <cell alignment="center" valignment="top" usebox="none">
3607 \begin_layout Plain Layout
3613 <cell alignment="center" valignment="top" usebox="none">
3616 \begin_layout Plain Layout
3617 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3631 \begin_inset Note Note
3634 \begin_layout Plain Layout
3641 is only used as spacer.
3649 \begin_layout Standard
3650 The shorter index is by default placed below or above the first character
3651 of the longer index.
3652 To avoid this there is the command
3659 \begin_inset Index idx
3662 \begin_layout Plain Layout
3670 or the math toolbar button
3671 \begin_inset space \thinspace{}
3678 \begin_layout Plain Layout
3679 can be found in the submenu of the toolbar button
3680 \begin_inset Graphics
3681 filename ../images/math/space.png
3692 \begin_inset Graphics
3693 filename ../images/math/phantom.png
3698 that creates one or more phantom characters.
3705 a small blue box appears that is superposed with two red arrows.
3706 The arrows indicate that the complete width and height of the box content
3707 will be created as placeholder.
3708 Phantom characters are accordingly placeholders with the size of the characters.
3711 \begin_layout Standard
3713 \begin_inset Tabular
3714 <lyxtabular version="3" rows="4" columns="2">
3715 <features rotate="0" tabularvalignment="middle">
3716 <column alignment="center" valignment="top">
3717 <column alignment="center" valignment="top">
3719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3722 \begin_layout Plain Layout
3728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3731 \begin_layout Plain Layout
3733 \begin_inset Note Note
3736 \begin_layout Plain Layout
3743 is only used as spacer.
3755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3758 \begin_layout Plain Layout
3763 \begin_layout Plain Layout
3778 \begin_layout Plain Layout
3788 \begin_inset Formula $\to$
3795 \begin_layout Plain Layout
3809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3812 \begin_layout Plain Layout
3813 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3826 \begin_layout Plain Layout
3831 \begin_layout Plain Layout
3846 \begin_layout Plain Layout
3856 \begin_inset Formula $\to$
3863 \begin_layout Plain Layout
3877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3880 \begin_layout Plain Layout
3881 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3894 \begin_layout Plain Layout
3901 \begin_layout Plain Layout
3916 \begin_layout Plain Layout
3926 \begin_inset Formula $\to$
3933 \begin_layout Plain Layout
3947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3950 \begin_layout Plain Layout
3951 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3967 \begin_layout Standard
3968 Furthermore there are the commands
3975 \begin_inset Index idx
3978 \begin_layout Plain Layout
3987 \begin_inset space ~
3991 \begin_inset Graphics
3992 filename ../images/math/vphantom.png
4004 \begin_inset Index idx
4007 \begin_layout Plain Layout
4016 \begin_inset space ~
4020 \begin_inset Graphics
4021 filename ../images/math/hphantom.png
4033 creates only space for the maximal height of the characters in the box
4034 but not for its width.
4041 creates only space for the width of the box content.
4042 Therefore the boxes of both commands have only one red arrow.
4045 \begin_layout Standard
4046 For example the command
4056 \begin_layout Plain Layout
4071 creates space for the height of the integral sign,
4075 \begin_layout Plain Layout
4082 creates an integral sign, see
4083 \begin_inset CommandInset ref
4085 reference "sub:Big-Operators"
4094 because this is the larger character.
4095 An example application is in
4096 \begin_inset CommandInset ref
4098 reference "sub:Multiline-Brackets"
4105 \begin_layout Standard
4106 Placeholders can also be used for text when they are inserted via the menu
4109 Insert\SpecialChar \menuseparator
4110 Formatting\SpecialChar \menuseparator
4116 \begin_layout Standard
4118 \begin_inset Newline newline
4122 \begin_inset Phantom Phantom
4125 \begin_layout Plain Layout
4134 \begin_layout Subsection
4136 \begin_inset Index idx
4139 \begin_layout Plain Layout
4146 \begin_inset Index idx
4149 \begin_layout Plain Layout
4150 Formula ! underlined
4158 \begin_layout Standard
4160 \begin_inset Tabular
4161 <lyxtabular version="3" rows="4" columns="2">
4162 <features rotate="0" tabularvalignment="middle">
4163 <column alignment="center" valignment="top" width="0pt">
4164 <column alignment="center" valignment="top" width="0pt">
4166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4169 \begin_layout Plain Layout
4175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4178 \begin_layout Plain Layout
4180 \begin_inset Note Note
4183 \begin_layout Plain Layout
4190 is only used as spacer.
4202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4205 \begin_layout Plain Layout
4212 \begin_layout Plain Layout
4222 \begin_inset Index idx
4225 \begin_layout Plain Layout
4238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4241 \begin_layout Plain Layout
4242 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4252 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4255 \begin_layout Plain Layout
4262 \begin_layout Plain Layout
4272 \begin_inset Index idx
4275 \begin_layout Plain Layout
4288 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4291 \begin_layout Plain Layout
4292 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4305 \begin_layout Plain Layout
4312 \begin_layout Plain Layout
4327 \begin_layout Plain Layout
4341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4344 \begin_layout Plain Layout
4345 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4361 \begin_layout Standard
4362 In the last example it doesn't matter if first
4377 \begin_layout Standard
4378 To double underline use
4387 \begin_layout Standard
4388 It is possible to place up to 6 lines above or below characters.
4391 \begin_layout Standard
4392 \begin_inset VSpace bigskip
4395 Custom lines can be created using the command
4402 \begin_inset Index idx
4405 \begin_layout Plain Layout
4413 which has the following scheme:
4416 \begin_layout Standard
4421 rule[vertical offset]{length}{thickness}
4424 \begin_layout Standard
4425 The optional vertical offset shifts the line upwards (or downwards, when
4426 the value is negative).
4428 \begin_inset CommandInset ref
4430 reference "tab:Available-units"
4434 can be used for the values.
4435 Here are two example lines created with the commands
4436 \begin_inset Newline newline
4443 rule[-2ex]{3cm}{2pt}
4454 \begin_layout Standard
4456 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4462 \begin_layout Standard
4469 can also be used for text when a line is inserted via the menu
4471 Insert\SpecialChar \menuseparator
4472 Formatting\SpecialChar \menuseparator
4474 \begin_inset space ~
4482 \begin_layout Standard
4484 \begin_inset CommandInset line
4495 \begin_layout Subsection
4497 \begin_inset CommandInset label
4504 \begin_inset Index idx
4507 \begin_layout Plain Layout
4516 \begin_layout Standard
4517 There are different types of ellipses available.
4521 \begin_layout Plain Layout
4522 In the math toolbar in the submenu of the button
4523 \begin_inset Graphics
4524 filename ../images/math/ldots.png
4534 For listings dots at the baseline are used (
4541 \begin_inset Index idx
4544 \begin_layout Plain Layout
4552 ), while for operations dots are needed that are on the same height as the
4560 \begin_inset Index idx
4563 \begin_layout Plain Layout
4572 When using the command
4579 \begin_inset Index idx
4582 \begin_layout Plain Layout
4590 , LaTeX decides on the basis of the next character what type is used.
4593 \begin_layout Standard
4595 \begin_inset Tabular
4596 <lyxtabular version="3" rows="9" columns="2">
4597 <features rotate="0" tabularvalignment="middle">
4598 <column alignment="center" valignment="top" width="0pt">
4599 <column alignment="center" valignment="top" width="0pt">
4601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4604 \begin_layout Plain Layout
4610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4613 \begin_layout Plain Layout
4621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4624 \begin_layout Plain Layout
4629 \begin_layout Plain Layout
4644 \begin_layout Plain Layout
4658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4661 \begin_layout Plain Layout
4662 \begin_inset Formula $A_{1},\dots,A_{n}$
4672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4675 \begin_layout Plain Layout
4680 \begin_layout Plain Layout
4695 \begin_layout Plain Layout
4709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4712 \begin_layout Plain Layout
4713 \begin_inset Formula $A_{1}+\dots+A_{n}$
4723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4726 \begin_layout Plain Layout
4731 \begin_layout Plain Layout
4746 \begin_layout Plain Layout
4760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4763 \begin_layout Plain Layout
4764 \begin_inset Formula $A_{1},\ldots,A_{n}$
4774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4777 \begin_layout Plain Layout
4782 \begin_layout Plain Layout
4797 \begin_layout Plain Layout
4811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4814 \begin_layout Plain Layout
4815 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4828 \begin_layout Plain Layout
4836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4839 \begin_layout Plain Layout
4840 \begin_inset Formula $\vdots$
4850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4853 \begin_layout Plain Layout
4861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4864 \begin_layout Plain Layout
4865 \begin_inset Formula $\ddots$
4875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4878 \begin_layout Plain Layout
4886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4889 \begin_layout Plain Layout
4890 \begin_inset Formula $\iddots$
4900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4903 \begin_layout Plain Layout
4905 \begin_inset space \thinspace{}
4908 matrix with the different dots
4913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4916 \begin_layout Plain Layout
4917 \begin_inset Formula $\begin{array}{ccc}
4918 A_{11} & \cdots & A_{1m}\\
4919 \vdots & \ddots & \vdots\\
4920 A_{n1} & \cdots & A_{nm}
4937 \begin_layout Standard
4938 The ellipses available in menu
4940 Insert\SpecialChar \menuseparator
4942 \begin_inset space ~
4956 \begin_layout Standard
4957 \begin_inset VSpace medskip
4966 , one of the options
4968 Use mathdots package (automatically)
4970 must be set in the document settings under
4973 \begin_inset space ~
4979 \begin_inset Newline newline
4984 Use mathdots package
4986 will improve the appearance of all dots in the documents if their font
4987 style or size is not the default.
4990 \begin_layout Standard
4991 \begin_inset VSpace medskip
4994 Specially for matrices there are ellipses that span over several columns.
4995 They are created with the command
5002 \begin_inset Index idx
5005 \begin_layout Plain Layout
5013 , that has the following scheme:
5016 \begin_layout Standard
5021 hdotsfor[distance]{number of columns}
5024 \begin_layout Standard
5025 The number of columns specifies how many columns should be spanned.
5026 Distance is a factor for the distance between the dots.
5029 \begin_layout Standard
5030 In the following matrix the command
5036 was inserted in the first box of the second line, to get an ellipsis with
5037 a dot distance twice as long as with the command
5044 \begin_inset Formula
5046 \left(\begin{array}{cccc}
5055 Note that the matrix fields that should be spanned must be empty, otherwise
5056 you get LaTeX-errors.
5059 \begin_layout Standard
5060 \begin_inset VSpace bigskip
5063 Furthermore you can fill with the command
5070 \begin_inset Index idx
5073 \begin_layout Plain Layout
5081 the rest of a line with dots.
5082 The effect of these commands is the same as with
5089 \begin_inset CommandInset ref
5091 reference "sub:Variable-Space"
5098 \begin_layout Standard
5099 For example the command
5107 \begin_layout Plain Layout
5121 \begin_layout Standard
5122 \begin_inset Formula $A\dotfill B$
5128 \begin_layout Standard
5135 there is for a line the command
5142 \begin_inset Index idx
5145 \begin_layout Plain Layout
5156 \begin_layout Standard
5157 \begin_inset Formula $A\hrulefill B$
5163 \begin_layout Standard
5164 To use the commands for text, they have to be inserted in TeX-mode.
5167 \begin_layout Section
5169 \begin_inset CommandInset label
5176 \begin_inset Index idx
5179 \begin_layout Plain Layout
5188 \begin_layout Standard
5189 Matrices can be inserted via the math toolbar button
5190 \begin_inset Graphics
5191 filename ../images/dialog-show_mathmatrix.png
5198 Insert\SpecialChar \menuseparator
5199 Math\SpecialChar \menuseparator
5203 In the matrix dialog you can specify the number of columns and rows, the
5204 alignment and the decoration.
5205 The vertical alignment is only of importance for matrices in inline formulas:
5208 \begin_layout Standard
5209 The first matrix is top
5210 \begin_inset Formula $\begin{array}[t]{cccc}
5218 \begin_inset Formula $\begin{array}{cccc}
5225 and the third bottom
5226 \begin_inset Formula $\begin{array}[b]{cccc}
5236 \begin_layout Standard
5237 The horizontal alignment specifies how the column entries should be aligned.
5238 It is set by entering a letter for every column.
5243 denotes left aligned,
5252 To create for example a 4
5257 \begin_inset space ~
5260 matrix where the first column is left aligned, the second and third are
5261 centered and the last one is right aligned, one enters for the horizontal
5267 Normally in a matrix all columns are centered, therefore the default for
5275 \begin_layout Standard
5276 Horizontal alignment:
5279 \begin_layout Standard
5285 \begin_inset Formula $\begin{array}{lll}
5297 \begin_inset Formula $\begin{array}{ccc}
5309 \begin_inset Formula $\begin{array}{rrr}
5319 \begin_layout Standard
5320 To add or delete rows and columns subsequently, the math toolbar buttons
5322 \begin_inset Graphics
5323 filename ../images/tabular-feature_append-row.png
5329 \begin_inset Graphics
5330 filename ../images/tabular-feature_delete-row.png
5336 \begin_inset space \thinspace{}
5341 Edit\SpecialChar \menuseparator
5345 New rows can also be created with
5348 arg "newline-insert newline"
5354 \begin_layout Standard
5355 \begin_inset VSpace bigskip
5362 adds parentheses in the selected style around the matrix.
5363 Alternatively, parentheses can can either be created with the commands
5371 \begin_inset Index idx
5374 \begin_layout Plain Layout
5389 \begin_inset Index idx
5392 \begin_layout Plain Layout
5403 \begin_inset space ~
5409 \begin_inset CommandInset ref
5411 reference "sub:Automatic-Bracket-Size"
5415 , or by using the following commands:
5416 \begin_inset VSpace medskip
5422 \begin_layout Standard
5423 \begin_inset space \hfill{}
5427 \begin_inset Tabular
5428 <lyxtabular version="3" rows="4" columns="2">
5429 <features rotate="0" tabularvalignment="middle">
5430 <column alignment="center" valignment="top">
5431 <column alignment="center" valignment="top">
5433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5436 \begin_layout Plain Layout
5442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5445 \begin_layout Plain Layout
5447 \begin_inset Note Note
5450 \begin_layout Plain Layout
5457 is only used as spacer.
5469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5472 \begin_layout Plain Layout
5479 \begin_layout Plain Layout
5493 \begin_inset space \thinspace{}
5501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5504 \begin_layout Plain Layout
5505 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5506 0 & \textrm{-}\mathrm{i}\\
5508 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5521 \begin_layout Plain Layout
5528 \begin_layout Plain Layout
5542 \begin_inset space \thinspace{}
5550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5553 \begin_layout Plain Layout
5554 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5555 0 & \textrm{-}\mathrm{i}\\
5557 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5570 \begin_layout Plain Layout
5577 \begin_layout Plain Layout
5591 \begin_inset space \thinspace{}
5599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5602 \begin_layout Plain Layout
5603 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5604 0 & \textrm{-}\mathrm{i}\\
5606 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5620 \begin_inset space \hfill{}
5624 \begin_inset Tabular
5625 <lyxtabular version="3" rows="4" columns="2">
5626 <features rotate="0" tabularvalignment="middle">
5627 <column alignment="center" valignment="top">
5628 <column alignment="center" valignment="top">
5630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5633 \begin_layout Plain Layout
5639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5642 \begin_layout Plain Layout
5650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5653 \begin_layout Plain Layout
5660 \begin_layout Plain Layout
5674 \begin_inset space \thinspace{}
5682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5685 \begin_layout Plain Layout
5686 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5687 0 & \textrm{-}\mathrm{i}\\
5689 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5702 \begin_layout Plain Layout
5709 \begin_layout Plain Layout
5723 \begin_inset space \thinspace{}
5731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5734 \begin_layout Plain Layout
5735 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5736 0 & \textrm{-}\mathrm{i}\\
5738 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5751 \begin_layout Plain Layout
5758 \begin_layout Plain Layout
5772 \begin_inset space \thinspace{}
5780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5783 \begin_layout Plain Layout
5784 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5785 0 & \textrm{-}\mathrm{i}\\
5787 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5801 \begin_inset space \hfill{}
5807 \begin_layout Standard
5808 \begin_inset VSpace medskip
5812 \begin_inset space \thinspace{}
5816 \begin_inset space \space{}
5825 is inserted, a blue box appears between two vertical lines where the matrix
5827 \begin_inset Newline newline
5830 Note that decorated matrices ignore the vertical alignment.
5833 \begin_layout Standard
5834 \begin_inset VSpace bigskip
5837 As all multiline formulas are matrices, the length
5844 \begin_inset Index idx
5847 \begin_layout Plain Layout
5855 that is described in
5856 \begin_inset CommandInset ref
5858 reference "sub:Column-Separation"
5862 can also be used to change the column separation of matrices.
5865 \begin_layout Standard
5866 To change the row separation, the command
5873 \begin_inset Index idx
5876 \begin_layout Plain Layout
5885 It is used as follows:
5888 \begin_layout Standard
5895 arraystretch}{stretch factor}
5896 \begin_inset Index idx
5899 \begin_layout Plain Layout
5910 \begin_layout Standard
5917 assigns the stretch factor to the predefined command
5925 \begin_inset space \thinspace{}
5929 \begin_inset space \space{}
5932 the row separation, use the factor 2.
5933 This is then used for all following matrices.
5934 To go back to the original separation, assign the factor 1 to
5943 \begin_layout Standard
5944 To set matrices into a text line, the command
5951 \begin_inset Index idx
5954 \begin_layout Plain Layout
5963 When it is inserted a blue box with two dashed lines appears.
5964 In this box the matrix is inserted.
5967 \begin_layout Standard
5969 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5971 \end{smallmatrix}\right)$
5977 \begin_layout Section
5978 Brackets and Delimiters
5979 \begin_inset Index idx
5982 \begin_layout Plain Layout
5989 \begin_inset Index idx
5992 \begin_layout Plain Layout
6001 \begin_layout Subsection
6002 Vertical Brackets and Delimiters
6003 \begin_inset Index idx
6006 \begin_layout Plain Layout
6015 \begin_layout Standard
6016 \begin_inset space \hfill{}
6020 \begin_inset Tabular
6021 <lyxtabular version="3" rows="9" columns="2">
6022 <features rotate="0" tabularvalignment="middle">
6023 <column alignment="center" valignment="top" width="0pt">
6024 <column alignment="center" valignment="top" width="0pt">
6026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6029 \begin_layout Plain Layout
6035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6038 \begin_layout Plain Layout
6046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6049 \begin_layout Plain Layout
6055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6058 \begin_layout Plain Layout
6059 \begin_inset Formula $($
6069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6072 \begin_layout Plain Layout
6078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6081 \begin_layout Plain Layout
6082 \begin_inset Formula $\{$
6092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6095 \begin_layout Plain Layout
6101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6104 \begin_layout Plain Layout
6105 \begin_inset Formula $[$
6115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6118 \begin_layout Plain Layout
6126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6129 \begin_layout Plain Layout
6130 \begin_inset Formula $\langle$
6140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6143 \begin_layout Plain Layout
6151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6154 \begin_layout Plain Layout
6155 \begin_inset Formula $\lceil$
6165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6168 \begin_layout Plain Layout
6176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6179 \begin_layout Plain Layout
6180 \begin_inset Formula $\lfloor$
6190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6193 \begin_layout Plain Layout
6199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6202 \begin_layout Plain Layout
6203 \begin_inset Formula $/$
6213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6216 \begin_layout Plain Layout
6222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6225 \begin_layout Plain Layout
6226 \begin_inset Formula $|$
6240 \begin_inset space \hfill{}
6244 \begin_inset Tabular
6245 <lyxtabular version="3" rows="9" columns="2">
6246 <features rotate="0" tabularvalignment="middle">
6247 <column alignment="center" valignment="top" width="0pt">
6248 <column alignment="center" valignment="top" width="0pt">
6250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6253 \begin_layout Plain Layout
6259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6262 \begin_layout Plain Layout
6270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6273 \begin_layout Plain Layout
6279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6282 \begin_layout Plain Layout
6283 \begin_inset Formula $)$
6293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6296 \begin_layout Plain Layout
6302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6305 \begin_layout Plain Layout
6306 \begin_inset Formula $\}$
6316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6319 \begin_layout Plain Layout
6325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6328 \begin_layout Plain Layout
6329 \begin_inset Formula $]$
6339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6342 \begin_layout Plain Layout
6350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6353 \begin_layout Plain Layout
6354 \begin_inset Formula $\rangle$
6364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6367 \begin_layout Plain Layout
6375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6378 \begin_layout Plain Layout
6379 \begin_inset Formula $\rceil$
6389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6392 \begin_layout Plain Layout
6400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6403 \begin_layout Plain Layout
6404 \begin_inset Formula $\rfloor$
6414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6417 \begin_layout Plain Layout
6427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6430 \begin_layout Plain Layout
6431 \begin_inset Formula $\backslash$
6441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6444 \begin_layout Plain Layout
6452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6455 \begin_layout Plain Layout
6456 \begin_inset Formula $\|$
6470 \begin_inset space \hfill{}
6476 \begin_layout Standard
6479 \begin_inset Note Greyedout
6482 \begin_layout Plain Layout
6487 In TeX-mode the command
6494 \begin_inset Index idx
6497 \begin_layout Plain Layout
6505 must be used for the backslash, because the command
6513 produces a line break there.
6521 \begin_layout Standard
6522 For all characters listed above the size can be adjusted with the commands
6523 described in the following two subsections.
6524 When using these commands, the characters < and > can directly be used
6525 instead of the commands
6540 \begin_layout Subsubsection
6542 \begin_inset CommandInset label
6544 name "sub:Manual-Bracket-Size"
6549 \begin_inset Index idx
6552 \begin_layout Plain Layout
6553 Bracket size ! manual
6561 \begin_layout Standard
6562 The bracket size can be specified manually by the LaTeX-commands
6569 \begin_inset Index idx
6572 \begin_layout Plain Layout
6605 denotes the smallest and
6611 the largest bracket size.
6614 \begin_layout Standard
6615 These commands are used to emphasize levels of brackets:
6618 \begin_layout Standard
6620 \begin_inset Tabular
6621 <lyxtabular version="3" rows="2" columns="2">
6622 <features rotate="0" tabularvalignment="middle">
6623 <column alignment="center" valignment="top" width="0pt">
6624 <column alignment="center" valignment="top" width="0pt">
6626 <cell alignment="center" valignment="top" usebox="none">
6629 \begin_layout Plain Layout
6630 all brackets in the same size:
6635 <cell alignment="center" valignment="top" usebox="none">
6638 \begin_layout Plain Layout
6639 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6649 <cell alignment="center" valignment="top" usebox="none">
6652 \begin_layout Plain Layout
6658 <cell alignment="center" valignment="top" usebox="none">
6661 \begin_layout Plain Layout
6662 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6676 \begin_inset Note Note
6679 \begin_layout Plain Layout
6686 is only used as spacer.
6694 \begin_layout Standard
6695 For the second formula the command
6705 \begin_layout Plain Layout
6719 \begin_layout Standard
6720 Here is an overview about all bracket sizes:
6723 \begin_layout Standard
6743 \begin_layout Plain Layout
6760 \begin_layout Plain Layout
6773 \begin_layout Plain Layout
6789 \begin_layout Standard
6791 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6797 \begin_layout Standard
6804 -commands there is the variant
6811 \begin_inset Index idx
6814 \begin_layout Plain Layout
6822 that adds a bit more space between the bracket and its content, and the
6836 \begin_inset Index idx
6839 \begin_layout Plain Layout
6849 , that don't add additional space.
6854 at the end of the command
6860 is for a left bracket; for a right bracket this will be replaced by an
6866 A left or right bracket can each be an opening or closing bracket.
6869 \begin_layout Standard
6870 In the following table is a comparison of the variants:
6873 \begin_layout Standard
6875 \begin_inset Tabular
6876 <lyxtabular version="3" rows="5" columns="2">
6877 <features rotate="0" tabularvalignment="middle">
6878 <column alignment="center" valignment="middle">
6879 <column alignment="center" valignment="middle">
6881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6884 \begin_layout Plain Layout
6890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6893 \begin_layout Plain Layout
6895 \begin_inset Note Note
6898 \begin_layout Plain Layout
6905 is only used as spacer.
6917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6920 \begin_layout Plain Layout
6935 \begin_layout Plain Layout
6953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6956 \begin_layout Plain Layout
6957 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6970 \begin_layout Plain Layout
6985 \begin_layout Plain Layout
7003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7006 \begin_layout Plain Layout
7007 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7020 \begin_layout Plain Layout
7035 \begin_layout Plain Layout
7053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7056 \begin_layout Plain Layout
7057 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7070 \begin_layout Plain Layout
7082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7085 \begin_layout Plain Layout
7086 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7102 \begin_layout Subsubsection
7103 Automatic Bracket Size
7104 \begin_inset CommandInset label
7106 name "sub:Automatic-Bracket-Size"
7111 \begin_inset Index idx
7114 \begin_layout Plain Layout
7115 Bracket size ! automatic
7123 \begin_layout Standard
7124 Brackets with variable size can be inserted with the commands
7131 \begin_inset Index idx
7134 \begin_layout Plain Layout
7149 \begin_inset Index idx
7152 \begin_layout Plain Layout
7160 or via the math toolbar button
7161 \begin_inset Graphics
7162 filename ../images/dialog-show_mathdelimiter.png
7180 the wanted bracket must be inserted.
7181 The bracket size will then automatically be calculated for the output.
7184 \begin_layout Standard
7186 normal bracket: The command
7196 \begin_layout Plain Layout
7206 \begin_inset Formula $\downarrow$
7213 \begin_layout Plain Layout
7225 \begin_inset Formula
7235 \begin_layout Standard
7237 multiline bracket: The command
7249 \begin_layout Plain Layout
7259 \begin_inset Formula $\downarrow$
7266 \begin_layout Plain Layout
7280 \begin_inset Formula
7282 \ln\left(\frac{A}{C}\right)
7290 \begin_layout Standard
7306 \begin_inset space ~
7312 This has the advantage that you can see in LyX immediately the real bracket
7313 size and that the matching right bracket will be created too.
7314 \begin_inset Newline newline
7317 The command for the last example would then be:
7331 \begin_layout Plain Layout
7341 \begin_inset Formula $\downarrow$
7347 \begin_layout Standard
7348 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7349 For example the command
7359 \begin_layout Plain Layout
7369 \begin_inset Formula $\downarrow$
7376 \begin_layout Plain Layout
7392 \begin_inset Formula
7394 \left.\frac{A}{B}\right\}
7413 will be converted by LyX to brackets in the right size when the document
7414 is reloaded and an omitted bracket will appear as dashed line.
7417 \begin_layout Standard
7418 \begin_inset VSpace bigskip
7421 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7429 \begin_inset Index idx
7432 \begin_layout Plain Layout
7440 is additionally available for all brackets and limits.
7441 With this command the height of the following character is adapted to the
7442 one of the surrounding brackets, what is e.
7443 \begin_inset space \thinspace{}
7447 \begin_inset space \space{}
7450 needed for physical vectors:
7451 \begin_inset Formula
7453 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
7458 For physical vectors there is a special LaTeX-package, described in
7459 \begin_inset CommandInset ref
7461 reference "sub:Physical-Vectors"
7468 \begin_layout Subsection
7470 \begin_inset Index idx
7473 \begin_layout Plain Layout
7474 Brackets ! horizontal
7482 \begin_layout Standard
7484 \begin_inset Tabular
7485 <lyxtabular version="3" rows="4" columns="2">
7486 <features rotate="0" tabularvalignment="middle">
7487 <column alignment="center" valignment="top" width="0pt">
7488 <column alignment="center" valignment="top" width="0pt">
7490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7493 \begin_layout Plain Layout
7495 \begin_inset Note Note
7498 \begin_layout Plain Layout
7505 is only used as spacer.
7515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7518 \begin_layout Plain Layout
7526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7529 \begin_layout Plain Layout
7533 \begin_layout Plain Layout
7548 \begin_layout Plain Layout
7561 \begin_layout Plain Layout
7574 \begin_layout Plain Layout
7587 \begin_layout Plain Layout
7595 \begin_inset Index idx
7598 \begin_layout Plain Layout
7611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7614 \begin_layout Plain Layout
7615 \begin_inset Formula $\overbrace{A+B}^{3}$
7625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7628 \begin_layout Plain Layout
7632 \begin_layout Plain Layout
7647 \begin_layout Plain Layout
7660 \begin_layout Plain Layout
7673 \begin_layout Plain Layout
7681 \begin_inset Index idx
7684 \begin_layout Plain Layout
7697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7700 \begin_layout Plain Layout
7701 \begin_inset Formula $\underbrace{A+B}_{5}$
7711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7714 \begin_layout Plain Layout
7721 \begin_layout Plain Layout
7736 \begin_layout Plain Layout
7749 \begin_layout Plain Layout
7762 \begin_layout Plain Layout
7775 \begin_layout Plain Layout
7788 \begin_layout Plain Layout
7801 \begin_layout Plain Layout
7815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7818 \begin_layout Plain Layout
7819 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7835 \begin_layout Standard
7836 In the last example it doesn't matter if
7848 is inserted at first.
7851 \begin_layout Standard
7852 \begin_inset VSpace bigskip
7855 When brackets are needed that overlap each other, multiline formulas, as
7857 \begin_inset CommandInset ref
7859 reference "sec:Multiline-Formulas"
7864 \begin_inset Formula
7866 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7867 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7872 In the first row the formula is inserted together with the first brace.
7873 It is hereby important that the space command
7877 \begin_layout Plain Layout
7878 Space commands are explained in
7879 \begin_inset CommandInset ref
7881 reference "sub:Predefined-Space"
7896 is inserted before the first
7897 \begin_inset Formula $d$
7900 , because the brace that ends behind the
7901 \begin_inset Formula $q$
7904 prevents that the following
7905 \begin_inset Quotes eld
7909 \begin_inset Quotes erd
7912 is surrounded by space.
7916 \begin_layout Plain Layout
7917 because a bracket is not handled as a character, see
7918 \begin_inset CommandInset ref
7920 reference "sub:Binary-Operators"
7929 In the second row the second brace is inserted.
7930 As it should begin before the
7931 \begin_inset Formula $b$
7946 \begin_layout Plain Layout
7954 \begin_inset CommandInset ref
7956 reference "sub:Placeholders"
7965 This space is needed because the
7966 \begin_inset Quotes eld
7970 \begin_inset Quotes erd
7973 is also surrounded by space in the formula.
7974 The brace is placed under the command
7983 \begin_layout Standard
7984 It gets more complicated when brackets overlap each other, like in the following
7989 \begin_layout Plain Layout
8001 \begin_inset Formula
8003 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
8004 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
8013 \begin_layout Plain Layout
8024 The first formula row is the same as the second row of the previous example,
8025 with the difference that the brace is above.
8026 The second row contains the formula together with the second brace.
8027 To avoid that there is space between the upper brace in the first row and
8028 the formula, the row spacing needs to be reduced.
8029 This is not easily possible due to a bug in LyX
8033 \begin_layout Plain Layout
8034 \begin_inset CommandInset href
8036 name "LyX-bug #1505"
8037 target "http://www.lyx.org/trac/ticket/1505"
8047 As a solution for the problem, the global formula row separation
8054 \begin_inset Index idx
8057 \begin_layout Plain Layout
8065 must be changed to -6
8066 \begin_inset space \thinspace{}
8069 pt before the formula with the command
8084 is set back after the formula to the standard value of 3
8085 \begin_inset space \thinspace{}
8088 pt using the same command.
8089 More about the row separation in formulas is explained in
8090 \begin_inset CommandInset ref
8092 reference "sub:Line-Separation"
8099 \begin_layout Section
8101 \begin_inset Index idx
8104 \begin_layout Plain Layout
8113 \begin_layout Standard
8114 Arrows can be inserted via the math toolbar button
8115 \begin_inset Graphics
8116 filename ../images/math/leftarrow.png
8121 or the commands listed in the following subsections.
8124 \begin_layout Subsection
8126 \begin_inset Index idx
8129 \begin_layout Plain Layout
8138 \begin_layout Standard
8139 \begin_inset space \hfill{}
8143 \begin_inset Tabular
8144 <lyxtabular version="3" rows="8" columns="2">
8145 <features rotate="0" tabularvalignment="middle">
8146 <column alignment="center" valignment="top" width="0pt">
8147 <column alignment="center" valignment="top" width="0pt">
8149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8152 \begin_layout Plain Layout
8158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8161 \begin_layout Plain Layout
8169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8172 \begin_layout Plain Layout
8180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8183 \begin_layout Plain Layout
8184 \begin_inset Formula $\gets$
8194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8197 \begin_layout Plain Layout
8205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8208 \begin_layout Plain Layout
8209 \begin_inset Formula $\Leftarrow$
8219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8222 \begin_layout Plain Layout
8230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8233 \begin_layout Plain Layout
8234 \begin_inset Formula $\longleftarrow$
8244 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8247 \begin_layout Plain Layout
8255 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8258 \begin_layout Plain Layout
8259 \begin_inset Formula $\Longleftarrow$
8269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8272 \begin_layout Plain Layout
8280 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8283 \begin_layout Plain Layout
8284 \begin_inset Formula $\leftharpoonup$
8294 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8297 \begin_layout Plain Layout
8305 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8308 \begin_layout Plain Layout
8309 \begin_inset Formula $\leftharpoondown$
8319 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8322 \begin_layout Plain Layout
8330 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8333 \begin_layout Plain Layout
8334 \begin_inset Formula $\hookleftarrow$
8348 \begin_inset space \hfill{}
8352 \begin_inset Tabular
8353 <lyxtabular version="3" rows="8" columns="2">
8354 <features rotate="0" tabularvalignment="middle">
8355 <column alignment="center" valignment="top" width="0pt">
8356 <column alignment="center" valignment="top" width="0pt">
8358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8361 \begin_layout Plain Layout
8367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8370 \begin_layout Plain Layout
8378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8381 \begin_layout Plain Layout
8389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8392 \begin_layout Plain Layout
8393 \begin_inset Formula $\to$
8403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8406 \begin_layout Plain Layout
8414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8417 \begin_layout Plain Layout
8418 \begin_inset Formula $\Rightarrow$
8428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8431 \begin_layout Plain Layout
8439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8442 \begin_layout Plain Layout
8443 \begin_inset Formula $\longrightarrow$
8453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8456 \begin_layout Plain Layout
8464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8467 \begin_layout Plain Layout
8468 \begin_inset Formula $\Longrightarrow$
8478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8481 \begin_layout Plain Layout
8489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8492 \begin_layout Plain Layout
8493 \begin_inset Formula $\rightharpoonup$
8503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8506 \begin_layout Plain Layout
8514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8517 \begin_layout Plain Layout
8518 \begin_inset Formula $\rightharpoondown$
8528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8531 \begin_layout Plain Layout
8539 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8542 \begin_layout Plain Layout
8543 \begin_inset Formula $\hookrightarrow$
8557 \begin_inset space \hfill{}
8563 \begin_layout Standard
8564 \begin_inset space \hfill{}
8568 \begin_inset Tabular
8569 <lyxtabular version="3" rows="6" columns="2">
8570 <features rotate="0" tabularvalignment="middle">
8571 <column alignment="center" valignment="top" width="0pt">
8572 <column alignment="center" valignment="top" width="0pt">
8574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8577 \begin_layout Plain Layout
8583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8586 \begin_layout Plain Layout
8594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8597 \begin_layout Plain Layout
8605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8608 \begin_layout Plain Layout
8609 \begin_inset Formula $\leftrightarrow$
8619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8622 \begin_layout Plain Layout
8630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8633 \begin_layout Plain Layout
8634 \begin_inset Formula $\Leftrightarrow$
8644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8647 \begin_layout Plain Layout
8655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8658 \begin_layout Plain Layout
8659 \begin_inset Formula $\longleftrightarrow$
8669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8672 \begin_layout Plain Layout
8680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8683 \begin_layout Plain Layout
8684 \begin_inset Formula $\Longleftrightarrow$
8694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8697 \begin_layout Plain Layout
8705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8708 \begin_layout Plain Layout
8709 \begin_inset Formula $\rightleftharpoons$
8723 \begin_inset space \hspace{}
8728 \begin_inset space \hfill{}
8732 \begin_inset Tabular
8733 <lyxtabular version="3" rows="5" columns="2">
8734 <features rotate="0" tabularvalignment="middle">
8735 <column alignment="center" valignment="top" width="0pt">
8736 <column alignment="center" valignment="top" width="0pt">
8738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8741 \begin_layout Plain Layout
8747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8750 \begin_layout Plain Layout
8758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8761 \begin_layout Plain Layout
8769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8772 \begin_layout Plain Layout
8773 \begin_inset Formula $\mapsto$
8783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8786 \begin_layout Plain Layout
8794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8797 \begin_layout Plain Layout
8798 \begin_inset Formula $\longmapsto$
8808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8811 \begin_layout Plain Layout
8819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8822 \begin_layout Plain Layout
8823 \begin_inset Formula $\leadsto$
8833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8836 \begin_layout Plain Layout
8844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8847 \begin_layout Plain Layout
8848 \begin_inset Formula $\dasharrow$
8862 \begin_inset space \hfill{}
8868 \begin_layout Standard
8869 \begin_inset VSpace medskip
8872 Arrows used as accents like e.
8873 \begin_inset space \thinspace{}
8877 \begin_inset space \space{}
8880 vector arrows are listed in
8881 \begin_inset CommandInset ref
8883 reference "sec:Accents"
8890 \begin_layout Standard
8891 \begin_inset VSpace bigskip
8894 Furthermore there are the labeled arrows
8895 \begin_inset Index idx
8898 \begin_layout Plain Layout
8911 \begin_inset Index idx
8914 \begin_layout Plain Layout
8929 \begin_inset Index idx
8932 \begin_layout Plain Layout
8939 \begin_layout Plain Layout
8954 When inserting one of these commands in a formula, an arrow with two blue
8955 boxes appear where the label can be inserted.
8956 The length of the arrow adapts to the label width.
8959 \begin_layout Standard
8961 \begin_inset Tabular
8962 <lyxtabular version="3" rows="3" columns="2">
8963 <features rotate="0" tabularvalignment="middle">
8964 <column alignment="center" valignment="top" width="0pt">
8965 <column alignment="center" valignment="top" width="0pt">
8967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8970 \begin_layout Plain Layout
8976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8979 \begin_layout Plain Layout
8981 \begin_inset Note Note
8984 \begin_layout Plain Layout
8991 is only used as spacer.
9003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9006 \begin_layout Plain Layout
9013 \begin_layout Plain Layout
9023 \begin_inset Formula $\downarrow$
9027 \begin_inset Formula $\to$
9035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9038 \begin_layout Plain Layout
9039 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9052 \begin_layout Plain Layout
9059 \begin_layout Plain Layout
9069 \begin_inset Formula $\downarrow$
9073 \begin_inset Formula $\to$
9081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9084 \begin_layout Plain Layout
9085 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9101 \begin_layout Subsection
9102 Vertical and diagonal Arrows
9103 \begin_inset Index idx
9106 \begin_layout Plain Layout
9113 \begin_inset Index idx
9116 \begin_layout Plain Layout
9125 \begin_layout Standard
9126 \begin_inset space \hfill{}
9130 \begin_inset Tabular
9131 <lyxtabular version="3" rows="7" columns="2">
9132 <features rotate="0" tabularvalignment="middle">
9133 <column alignment="center" valignment="top" width="0pt">
9134 <column alignment="center" valignment="top" width="0pt">
9136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9139 \begin_layout Plain Layout
9145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9148 \begin_layout Plain Layout
9156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9159 \begin_layout Plain Layout
9167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9170 \begin_layout Plain Layout
9171 \begin_inset Formula $\uparrow$
9181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9184 \begin_layout Plain Layout
9192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9195 \begin_layout Plain Layout
9196 \begin_inset Formula $\Uparrow$
9206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9209 \begin_layout Plain Layout
9217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9220 \begin_layout Plain Layout
9221 \begin_inset Formula $\updownarrow$
9231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9234 \begin_layout Plain Layout
9242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9245 \begin_layout Plain Layout
9246 \begin_inset Formula $\Updownarrow$
9256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9259 \begin_layout Plain Layout
9267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9270 \begin_layout Plain Layout
9271 \begin_inset Formula $\Downarrow$
9281 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9284 \begin_layout Plain Layout
9292 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9295 \begin_layout Plain Layout
9296 \begin_inset Formula $\downarrow$
9310 \begin_inset space \hfill{}
9314 \begin_inset Tabular
9315 <lyxtabular version="3" rows="5" columns="2">
9316 <features rotate="0" tabularvalignment="middle">
9317 <column alignment="center" valignment="top" width="0pt">
9318 <column alignment="center" valignment="top" width="0pt">
9320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9323 \begin_layout Plain Layout
9329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9332 \begin_layout Plain Layout
9340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9343 \begin_layout Plain Layout
9351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9354 \begin_layout Plain Layout
9355 \begin_inset Formula $\nearrow$
9365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9368 \begin_layout Plain Layout
9376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9379 \begin_layout Plain Layout
9380 \begin_inset Formula $\searrow$
9390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9393 \begin_layout Plain Layout
9401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9404 \begin_layout Plain Layout
9405 \begin_inset Formula $\swarrow$
9415 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9418 \begin_layout Plain Layout
9426 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9429 \begin_layout Plain Layout
9430 \begin_inset Formula $\nwarrow$
9444 \begin_inset space \hfill{}
9450 \begin_layout Standard
9451 \begin_inset VSpace medskip
9454 Vertical arrows can be used also as delimiters together with the commands
9456 \begin_inset CommandInset ref
9458 reference "sub:Manual-Bracket-Size"
9463 \begin_inset CommandInset ref
9465 reference "sub:Automatic-Bracket-Size"
9472 \begin_layout Section
9474 \begin_inset CommandInset label
9481 \begin_inset Index idx
9484 \begin_layout Plain Layout
9493 \begin_layout Standard
9494 Accents can be inserted via the math toolbar button
9495 \begin_inset Graphics
9496 filename ../images/math/hat.png
9501 or the commands listed in the following subsections.
9504 \begin_layout Subsection
9505 Accents for one Character
9509 \begin_layout Plain Layout
9522 \begin_layout Plain Layout
9524 \begin_inset CommandInset ref
9526 reference "sub:Accents-in-Text"
9539 \begin_layout Plain Layout
9547 \begin_inset Note Note
9550 \begin_layout Plain Layout
9557 is used to avoid that the footnote appears in the PDF-bookmark.
9560 \begin_layout Plain Layout
9568 \begin_inset CommandInset ref
9570 reference "sub:Formulas-in-Section"
9580 \begin_inset CommandInset label
9582 name "sub:Accents-for-one"
9587 \begin_inset Index idx
9590 \begin_layout Plain Layout
9591 Accents ! for one character
9599 \begin_layout Standard
9600 \begin_inset space \hfill{}
9604 \begin_inset Tabular
9605 <lyxtabular version="3" rows="8" columns="2">
9606 <features rotate="0" tabularvalignment="middle">
9607 <column alignment="center" valignment="top" width="0pt">
9608 <column alignment="center" valignment="top" width="0pt">
9610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9613 \begin_layout Plain Layout
9619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9622 \begin_layout Plain Layout
9624 \begin_inset Note Note
9627 \begin_layout Plain Layout
9634 is only used as spacer.
9646 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9649 \begin_layout Plain Layout
9656 \begin_layout Plain Layout
9670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9673 \begin_layout Plain Layout
9674 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9684 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9687 \begin_layout Plain Layout
9694 \begin_layout Plain Layout
9708 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9711 \begin_layout Plain Layout
9712 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9722 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9725 \begin_layout Plain Layout
9732 \begin_layout Plain Layout
9746 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9749 \begin_layout Plain Layout
9750 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9760 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9763 \begin_layout Plain Layout
9770 \begin_layout Plain Layout
9784 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9787 \begin_layout Plain Layout
9788 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9798 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9801 \begin_layout Plain Layout
9808 \begin_layout Plain Layout
9818 \begin_inset Index idx
9821 \begin_layout Plain Layout
9832 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9835 \begin_layout Plain Layout
9836 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9846 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9849 \begin_layout Plain Layout
9856 \begin_layout Plain Layout
9870 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9873 \begin_layout Plain Layout
9874 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9884 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9887 \begin_layout Plain Layout
9894 \begin_layout Plain Layout
9908 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9911 \begin_layout Plain Layout
9912 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9926 \begin_inset space \hfill{}
9930 \begin_inset Tabular
9931 <lyxtabular version="3" rows="7" columns="2">
9932 <features rotate="0" tabularvalignment="middle">
9933 <column alignment="center" valignment="top" width="0pt">
9934 <column alignment="center" valignment="top" width="0pt">
9936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9939 \begin_layout Plain Layout
9945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9948 \begin_layout Plain Layout
9956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9959 \begin_layout Plain Layout
9966 \begin_layout Plain Layout
9980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9983 \begin_layout Plain Layout
9984 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9994 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9997 \begin_layout Plain Layout
10004 \begin_layout Plain Layout
10018 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10021 \begin_layout Plain Layout
10022 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10032 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10035 \begin_layout Plain Layout
10042 \begin_layout Plain Layout
10056 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10059 \begin_layout Plain Layout
10060 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10070 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10073 \begin_layout Plain Layout
10080 \begin_layout Plain Layout
10094 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10097 \begin_layout Plain Layout
10098 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10108 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10111 \begin_layout Plain Layout
10118 \begin_layout Plain Layout
10132 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10135 \begin_layout Plain Layout
10136 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10146 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10149 \begin_layout Plain Layout
10156 \begin_layout Plain Layout
10170 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10173 \begin_layout Plain Layout
10174 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10188 \begin_inset space \hfill{}
10194 \begin_layout Standard
10195 \begin_inset VSpace bigskip
10201 \begin_layout Standard
10202 You can directly insert accents like é to formulas.
10203 LyX will transform them to the corresponding accent command.
10205 \begin_inset Index idx
10208 \begin_layout Plain Layout
10214 it is better to insert a quotation mark before the vowel.
10215 These two characters are then treated by LaTeX as
10219 character when the formula part with the umlaut is marked as German.
10227 \begin_inset Quotes eld
10231 \begin_inset Quotes erd
10234 umlauts are created as demonstrated in the following example:
10237 \begin_layout Standard
10238 \begin_inset VSpace -2mm
10244 \begin_layout Standard
10246 \begin_inset Tabular
10247 <lyxtabular version="3" rows="3" columns="2">
10248 <features rotate="0" tabularvalignment="middle">
10249 <column alignment="center" valignment="top">
10250 <column alignment="center" valignment="top">
10252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10255 \begin_layout Plain Layout
10261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10264 \begin_layout Plain Layout
10266 \begin_inset Note Note
10269 \begin_layout Plain Layout
10277 \begin_inset space \thinspace{}
10280 pt space are only used as spacer.
10292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10295 \begin_layout Plain Layout
10298 \begin_inset Quotes grd
10306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10309 \begin_layout Plain Layout
10310 \begin_inset space \hspace{}
10317 \begin_inset Formula $"i$
10327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10330 \begin_layout Plain Layout
10337 \begin_layout Plain Layout
10351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10354 \begin_layout Plain Layout
10355 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10371 \begin_layout Standard
10372 Another advantage to
10378 is that umlauts can directly be converted to mathematical text because
10379 the accent commands above are
10385 in mathematical text
10388 To convert an accented character to mathematical text, only the character
10389 under the accent may be converted.
10390 This applies also for all other conversions, e.
10391 \begin_inset space \thinspace{}
10395 \begin_inset space \space{}
10401 \begin_layout Standard
10402 In mathematical text, umlauts and other accented characters can directly
10406 \begin_layout Subsection
10407 Accents for several Characters
10408 \begin_inset Index idx
10411 \begin_layout Plain Layout
10412 Accents ! for several characters
10420 \begin_layout Standard
10421 \begin_inset space \hfill{}
10425 \begin_inset Tabular
10426 <lyxtabular version="3" rows="5" columns="2">
10427 <features rotate="0" tabularvalignment="middle">
10428 <column alignment="center" valignment="top" width="0pt">
10429 <column alignment="center" valignment="top" width="0pt">
10431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10434 \begin_layout Plain Layout
10440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10443 \begin_layout Plain Layout
10445 \begin_inset Note Note
10448 \begin_layout Plain Layout
10455 is only used as spacer.
10467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10470 \begin_layout Plain Layout
10477 \begin_layout Plain Layout
10491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10494 \begin_layout Plain Layout
10495 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10505 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10508 \begin_layout Plain Layout
10515 \begin_layout Plain Layout
10529 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10532 \begin_layout Plain Layout
10533 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10543 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10546 \begin_layout Plain Layout
10553 \begin_layout Plain Layout
10567 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10570 \begin_layout Plain Layout
10571 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10581 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10584 \begin_layout Plain Layout
10587 underleftrightarrow
10591 \begin_layout Plain Layout
10605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10608 \begin_layout Plain Layout
10609 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10623 \begin_inset space \hfill{}
10627 \begin_inset Tabular
10628 <lyxtabular version="3" rows="5" columns="2">
10629 <features rotate="0" tabularvalignment="middle">
10630 <column alignment="center" valignment="top" width="0pt">
10631 <column alignment="center" valignment="top" width="0pt">
10633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10636 \begin_layout Plain Layout
10642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10645 \begin_layout Plain Layout
10653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10656 \begin_layout Plain Layout
10663 \begin_layout Plain Layout
10677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10680 \begin_layout Plain Layout
10681 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10694 \begin_layout Plain Layout
10701 \begin_layout Plain Layout
10715 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10718 \begin_layout Plain Layout
10719 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10729 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10732 \begin_layout Plain Layout
10739 \begin_layout Plain Layout
10753 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10756 \begin_layout Plain Layout
10757 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10767 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10770 \begin_layout Plain Layout
10777 \begin_layout Plain Layout
10791 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10794 \begin_layout Plain Layout
10795 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10809 \begin_inset space \hfill{}
10815 \begin_layout Standard
10816 \begin_inset VSpace medskip
10819 With these commands as many characters as you like can be accented.
10832 will only be set in the output with a length of three characters, as shown
10833 in the following example:
10834 \begin_inset Formula
10836 \widetilde{A+B=C-D}
10844 \begin_layout Standard
10852 \begin_inset Index idx
10855 \begin_layout Plain Layout
10870 \begin_inset Index idx
10873 \begin_layout Plain Layout
10881 described in the previous subsection it is also possible to accent several
10891 \begin_layout Plain Layout
10901 \begin_inset Formula $\downarrow$
10907 \begin_inset Formula
10909 \underset{***}{A=B}
10917 \begin_layout Standard
10918 \begin_inset Newpage newpage
10924 \begin_layout Section
10926 \begin_inset CommandInset label
10933 \begin_inset Index idx
10936 \begin_layout Plain Layout
10945 \begin_layout Subsection
10947 \begin_inset CommandInset label
10949 name "sub:Predefined-Space"
10954 \begin_inset Index idx
10957 \begin_layout Plain Layout
10958 Space ! horizontal ! predefined
10966 \begin_layout Standard
10967 Sometimes it is necessary to insert horizontal space into a formula.
10968 This is done by inserting a protected space (shortcut
10971 arg "command-alternatives space-insert protected ; math-space"
10976 \begin_inset Quotes eld
10985 \begin_layout Plain Layout
10997 \begin_inset Quotes erd
11000 appears and by pressing
11004 several times one can select one of eight different space sizes.
11005 The spaces can also be inserted using the math toolbar button
11006 \begin_inset Graphics
11007 filename ../images/math/space.png
11012 or special commands.
11013 Independent from the inserted command, one can select the size again by
11021 \begin_layout Standard
11024 \begin_inset VSpace -5mm
11028 \begin_inset Tabular
11029 <lyxtabular version="3" rows="3" columns="7">
11030 <features rotate="0" tabularvalignment="middle">
11031 <column alignment="center" valignment="middle" width="6.8cm">
11032 <column alignment="center" valignment="top">
11033 <column alignment="center" valignment="top">
11034 <column alignment="center" valignment="top">
11035 <column alignment="center" valignment="top">
11036 <column alignment="center" valignment="top">
11037 <column alignment="center" valignment="top">
11039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11042 \begin_layout Plain Layout
11048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11051 \begin_layout Plain Layout
11059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11062 \begin_layout Plain Layout
11070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11073 \begin_layout Plain Layout
11081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11084 \begin_layout Plain Layout
11092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11095 \begin_layout Plain Layout
11103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11106 \begin_layout Plain Layout
11116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11119 \begin_layout Plain Layout
11124 keystrokes after inserting the protected space
11129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11132 \begin_layout Plain Layout
11138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11141 \begin_layout Plain Layout
11147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11150 \begin_layout Plain Layout
11156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11159 \begin_layout Plain Layout
11165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11168 \begin_layout Plain Layout
11174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11177 \begin_layout Plain Layout
11185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11188 \begin_layout Plain Layout
11194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11197 \begin_layout Plain Layout
11198 \begin_inset Formula $A\, B$
11206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11209 \begin_layout Plain Layout
11210 \begin_inset Formula $A\: B$
11218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11221 \begin_layout Plain Layout
11222 \begin_inset Formula $A\; B$
11230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11233 \begin_layout Plain Layout
11234 \begin_inset Formula $A\quad B$
11242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11245 \begin_layout Plain Layout
11246 \begin_inset Formula $A\qquad B$
11254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11257 \begin_layout Plain Layout
11258 \begin_inset Formula $A\! B$
11274 \begin_layout Standard
11275 The last size seem to produce no space.
11276 It is displayed red in LyX contrary to the other sizes, because it is a
11278 There are two more negative spaces:
11281 \begin_layout Standard
11283 \begin_inset Tabular
11284 <lyxtabular version="3" rows="3" columns="3">
11285 <features rotate="0" tabularvalignment="middle">
11286 <column alignment="center" valignment="middle" width="6.8cm">
11287 <column alignment="center" valignment="top" width="0pt">
11288 <column alignment="center" valignment="top" width="0pt">
11290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11293 \begin_layout Plain Layout
11299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11302 \begin_layout Plain Layout
11310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11313 \begin_layout Plain Layout
11323 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11326 \begin_layout Plain Layout
11331 keystrokes after inserting the protected space
11336 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11339 \begin_layout Plain Layout
11345 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11348 \begin_layout Plain Layout
11356 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11359 \begin_layout Plain Layout
11365 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11368 \begin_layout Plain Layout
11369 \begin_inset Formula $A\negmedspace B$
11377 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11380 \begin_layout Plain Layout
11381 \begin_inset Formula $A\negthickspace B$
11397 \begin_layout Standard
11398 Negative spaces can lead to characters overlapping each other.
11399 Thus they can be used to enforce ligatures, which are e.
11400 \begin_inset space \thinspace{}
11404 \begin_inset space \space{}
11407 useful for summation operators:
11410 \begin_layout Standard
11412 \begin_inset Tabular
11413 <lyxtabular version="3" rows="3" columns="2">
11414 <features rotate="0" tabularvalignment="middle">
11415 <column alignment="center" valignment="top">
11416 <column alignment="center" valignment="top">
11418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11421 \begin_layout Plain Layout
11427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11430 \begin_layout Plain Layout
11432 \begin_inset Note Note
11435 \begin_layout Plain Layout
11442 is only used as spacer.
11454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11457 \begin_layout Plain Layout
11466 \begin_layout Plain Layout
11480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11483 \begin_layout Plain Layout
11484 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11497 \begin_layout Plain Layout
11508 \begin_layout Plain Layout
11522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11525 \begin_layout Plain Layout
11526 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11542 \begin_layout Standard
11543 Relations like for example equal signs, are always surrounded by space.
11544 To suppress this, the equal sign is placed into a TeX-brace.
11545 The following example demonstrates this:
11548 \begin_layout Standard
11550 \begin_inset Tabular
11551 <lyxtabular version="3" rows="2" columns="2">
11552 <features rotate="0" tabularvalignment="middle">
11553 <column alignment="center" valignment="top" width="0pt">
11554 <column alignment="center" valignment="top" width="0pt">
11556 <cell alignment="center" valignment="top" usebox="none">
11559 \begin_layout Plain Layout
11565 <cell alignment="center" valignment="top" usebox="none">
11568 \begin_layout Plain Layout
11569 \begin_inset Formula $A=B$
11579 <cell alignment="center" valignment="top" usebox="none">
11582 \begin_layout Plain Layout
11583 \begin_inset Note Note
11586 \begin_layout Plain Layout
11593 is only used as spacer.
11599 \begin_inset Formula $\raisebox{5mm}{}$
11602 equation without space
11607 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11610 \begin_layout Plain Layout
11611 \begin_inset Formula $A{=}B$
11627 \begin_layout Standard
11629 The command for the last formula is:
11634 \begin_inset Formula $\to$
11640 \begin_layout Standard
11641 \begin_inset VSpace bigskip
11644 Spaces are needed for physical units, because the space between the value
11645 and the unit is the smallest one and not a normal space.
11646 For units in text, the smallest space is inserted via the menu
11648 Insert\SpecialChar \menuseparator
11649 Formatting\SpecialChar \menuseparator
11651 \begin_inset space ~
11659 arg "space-insert thin"
11665 \begin_layout Standard
11666 An example to visualize the difference:
11669 \begin_layout Standard
11670 \begin_inset Tabular
11671 <lyxtabular version="3" rows="2" columns="2">
11672 <features rotate="0" tabularvalignment="middle">
11673 <column alignment="left" valignment="top">
11674 <column alignment="left" valignment="top">
11676 <cell alignment="center" valignment="top" usebox="none">
11679 \begin_layout Plain Layout
11681 \begin_inset Formula $\cdot$
11689 <cell alignment="center" valignment="top" usebox="none">
11692 \begin_layout Plain Layout
11693 space between value and unit
11700 <cell alignment="center" valignment="top" usebox="none">
11703 \begin_layout Plain Layout
11705 \begin_inset space \thinspace{}
11709 \begin_inset Formula $\cdot$
11717 <cell alignment="center" valignment="top" usebox="none">
11720 \begin_layout Plain Layout
11721 smallest space between value and unit
11734 \begin_layout Subsection
11739 \begin_layout Plain Layout
11752 \begin_layout Plain Layout
11753 for vertical space in formulas see
11754 \begin_inset CommandInset ref
11756 reference "sub:Line-Separation"
11769 \begin_layout Plain Layout
11777 \begin_inset Note Note
11780 \begin_layout Plain Layout
11783 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11786 \begin_layout Plain Layout
11789 texorpdfstring is in section
11790 \begin_inset CommandInset ref
11792 reference "sub:Formulas-in-Section"
11802 \begin_inset CommandInset label
11804 name "sub:Variable-Space"
11809 \begin_inset Index idx
11812 \begin_layout Plain Layout
11813 Space ! horizontal ! variable
11821 \begin_layout Standard
11822 Space with a defined length can be inserted with the command
11829 \begin_inset Index idx
11832 \begin_layout Plain Layout
11842 \begin_inset Quotes eld
11851 \begin_layout Plain Layout
11863 \begin_inset Quotes erd
11867 The length can be specified by left-clicking on the
11868 \begin_inset Quotes eld
11877 \begin_layout Plain Layout
11889 \begin_inset Quotes erd
11893 The length may also be negative.
11894 To insert as much space as is available, the command
11901 \begin_inset Index idx
11904 \begin_layout Plain Layout
11915 \begin_layout Standard
11916 \begin_inset VSpace -1mm
11922 \begin_layout Standard
11924 \begin_inset Tabular
11925 <lyxtabular version="3" rows="4" columns="2">
11926 <features rotate="0" tabularvalignment="middle">
11927 <column alignment="center" valignment="top">
11928 <column alignment="center" valignment="top">
11930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11933 \begin_layout Plain Layout
11941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11944 \begin_layout Plain Layout
11952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11955 \begin_layout Plain Layout
11962 \begin_layout Plain Layout
11972 \begin_inset Formula $\to$
11978 \begin_inset space \thinspace{}
11986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11989 \begin_layout Plain Layout
11990 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12003 \begin_layout Plain Layout
12010 \begin_layout Plain Layout
12020 \begin_inset Formula $\to$
12026 \begin_inset space \thinspace{}
12034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12037 \begin_layout Plain Layout
12038 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12051 \begin_layout Plain Layout
12058 \begin_layout Plain Layout
12072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12075 \begin_layout Plain Layout
12076 \begin_inset Formula $A=A\hfill B=B$
12092 \begin_layout Standard
12093 In the last example the available space is given by the longest column entry
12095 In an inline formula the space depends on the length of the line in which
12103 Thus, when the line uses the full width, no space will be created.
12110 only has an effect on displayed formulas when the formula style
12115 (Formula styles are explained in
12116 \begin_inset CommandInset ref
12118 reference "sec:Formula-Styles"
12125 \begin_layout Standard
12132 , there are the commands
12144 that fill the space with a pattern, see
12145 \begin_inset CommandInset ref
12147 reference "sub:Ellipses"
12154 \begin_layout Standard
12155 For text, variable space can be inserted via the menu
12157 Insert\SpecialChar \menuseparator
12158 Formatting\SpecialChar \menuseparator
12160 \begin_inset space ~
12168 \begin_layout Standard
12169 This is a line with
12170 \begin_inset space \hspace{}
12175 \begin_inset space \thinspace{}
12181 \begin_layout Standard
12182 This is a line with
12183 \begin_inset space \hfill{}
12189 \begin_layout Subsection
12190 Space besides inline Formulas
12191 \begin_inset Index idx
12194 \begin_layout Plain Layout
12195 Space ! besides inline formulas
12203 \begin_layout Standard
12204 The space that surrounds inline formulas can be adjusted with the length
12212 \begin_inset Index idx
12215 \begin_layout Plain Layout
12224 The value of a length is set with the command
12231 \begin_inset Index idx
12234 \begin_layout Plain Layout
12242 which has the following scheme:
12245 \begin_layout Standard
12250 setlength{length name}{value}
12253 \begin_layout Standard
12261 \begin_inset space \thinspace{}
12267 \begin_layout Standard
12277 \begin_layout Standard
12278 is inserted in TeX-mode.
12280 \begin_inset space \thinspace{}
12283 mm space will now be set around all inline formulas:
12287 \begin_layout Plain Layout
12301 \begin_layout Standard
12302 This is a line with an inline formula
12303 \begin_inset Formula $A=B$
12307 \begin_inset space \thinspace{}
12310 mm surrounding space.
12314 \begin_layout Plain Layout
12328 \begin_layout Standard
12329 To return to the predefined value,
12335 is set to the value 0
12336 \begin_inset space \thinspace{}
12342 \begin_layout Section
12344 \begin_inset Index idx
12347 \begin_layout Plain Layout
12354 \begin_inset Index idx
12357 \begin_layout Plain Layout
12362 \begin_layout Plain Layout
12373 \begin_layout Plain Layout
12388 \begin_layout Standard
12389 Boxes for text are described in chapter
12396 \begin_inset space ~
12404 \begin_layout Subsection
12406 \begin_inset CommandInset label
12408 name "sub:Boxes-with-Frame"
12413 \begin_inset Index idx
12416 \begin_layout Plain Layout
12425 \begin_layout Standard
12426 It is possible to frame a formula or part of one with the commands
12433 \begin_inset Index idx
12436 \begin_layout Plain Layout
12451 \begin_inset Index idx
12454 \begin_layout Plain Layout
12465 \begin_layout Standard
12466 When one of these commands is inserted in a formula, a blue box appears
12467 within a frame to enter formula parts.
12474 an additional formula has to be created by
12478 within this box, because the box content will otherwise be treated as mathemati
12486 is used, a new formula is automatically created inside the frame.
12489 \begin_layout Standard
12496 is not suitable to frame displayed formulas because the formula will always
12497 be set in the size of the text.
12504 is in contrary not suitable to frame inline formulas, because the formula
12505 will always be set in the size of a displayed formula.
12508 \begin_layout Standard
12522 \begin_inset Index idx
12525 \begin_layout Plain Layout
12533 where additionally the frame width and the alignment can be specified.
12540 is used in the following scheme:
12543 \begin_layout Standard
12548 framebox[frame width][position]{box content}
12551 \begin_layout Standard
12552 The position can either be
12569 right aligns the formula in the box.
12570 When no position is given, the formula will be centered.
12571 \begin_inset Newline newline
12574 If no width is given, also no position can be given.
12575 In this case the frame width is adjusted to the box content like for
12584 \begin_layout Standard
12591 is inserted, a box appears containing three blue boxes.
12592 The first two boxes are surrounded by brackets and denote the two optional
12594 The third box is for formula parts like for
12603 \begin_layout Standard
12604 \begin_inset Newpage newpage
12610 \begin_layout Standard
12612 \begin_inset Tabular
12613 <lyxtabular version="3" rows="5" columns="2">
12614 <features rotate="0" tabularvalignment="middle">
12615 <column alignment="center" valignment="top">
12616 <column alignment="center" valignment="top">
12618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12621 \begin_layout Plain Layout
12627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12630 \begin_layout Plain Layout
12632 \begin_inset Note Note
12635 \begin_layout Plain Layout
12642 is only used as spacer.
12654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12657 \begin_layout Plain Layout
12664 \begin_layout Plain Layout
12683 \begin_layout Plain Layout
12697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12700 \begin_layout Plain Layout
12701 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12714 \begin_layout Plain Layout
12721 \begin_layout Plain Layout
12736 \begin_layout Plain Layout
12750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12753 \begin_layout Plain Layout
12754 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12767 \begin_layout Plain Layout
12774 \begin_layout Plain Layout
12788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12791 \begin_layout Plain Layout
12792 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12805 \begin_layout Plain Layout
12812 \begin_layout Plain Layout
12822 \begin_inset Formula $\to$
12826 \begin_inset Formula $\to$
12839 \begin_layout Plain Layout
12849 \begin_inset Formula $\downarrow$
12857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12860 \begin_layout Plain Layout
12861 \begin_inset Formula $\raisebox{6mm}{}$
12865 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12869 \begin_inset Formula $\raisebox{-4mm}{}$
12885 \begin_layout Standard
12886 The frame thickness can also be adjusted.
12887 To do this the following commands have to be inserted in TeX-mode before
12891 \begin_layout Standard
12901 \begin_inset Quotes eld
12905 \begin_inset Quotes erd
12919 \begin_inset Quotes eld
12923 \begin_inset Quotes erd
12929 \begin_layout Standard
12930 \begin_inset Quotes eld
12934 \begin_inset Quotes erd
12937 specifies the minimal distance between the frame and the first character
12939 An example for this is the following framed formula:
12943 \begin_layout Plain Layout
12955 \begin_inset Formula
12962 Before this formula the commands
12965 \begin_layout Standard
12987 \begin_layout Standard
12988 were inserted in TeX-mode.
12989 The given values are used for all following boxes.
12992 \begin_layout Standard
12993 To return to the standard frame size, the command
12996 \begin_layout Standard
13021 \begin_layout Plain Layout
13035 \begin_layout Standard
13036 is inserted in TeX-mode before the next formula.
13039 \begin_layout Subsection
13040 Boxes without Frame
13041 \begin_inset CommandInset label
13043 name "sub:Boxes-without-Frame"
13048 \begin_inset Index idx
13051 \begin_layout Plain Layout
13052 Boxes ! without frame
13060 \begin_layout Standard
13061 For boxes without a frame there are the following box commands:
13068 \begin_inset Index idx
13071 \begin_layout Plain Layout
13086 \begin_inset Index idx
13089 \begin_layout Plain Layout
13104 \begin_inset Index idx
13107 \begin_layout Plain Layout
13118 \begin_layout Standard
13125 a box can be super- or subscripted.
13126 But in contrary to normal super- and subscripting, the characters in the
13127 box keep their font size.
13134 is used in the following scheme:
13137 \begin_layout Standard
13142 raisebox{height}{box content}
13145 \begin_layout Standard
13146 When the box should contain a formula, an extra formula is needed like for
13157 \begin_inset Note Greyedout
13160 \begin_layout Plain Layout
13171 this extra formula is created by pressing
13175 twice instead of once because LyX doesn't yet support
13189 \begin_layout Standard
13191 \begin_inset Tabular
13192 <lyxtabular version="3" rows="4" columns="2">
13193 <features rotate="0" tabularvalignment="middle">
13194 <column alignment="center" valignment="top">
13195 <column alignment="center" valignment="top">
13197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13200 \begin_layout Plain Layout
13206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13209 \begin_layout Plain Layout
13217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13220 \begin_layout Plain Layout
13224 \begin_inset Formula $\to$
13230 \begin_inset Formula $\to$
13238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13241 \begin_layout Plain Layout
13242 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13255 \begin_layout Plain Layout
13259 \begin_inset Formula $\to$
13265 \begin_inset Formula $\to$
13273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13276 \begin_layout Plain Layout
13277 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13290 \begin_layout Plain Layout
13294 \begin_inset Formula $\to$
13313 \begin_layout Plain Layout
13327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13330 \begin_layout Plain Layout
13331 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13347 \begin_layout Standard
13372 , with the difference that there is no frame.
13375 \begin_layout Subsection
13377 \begin_inset CommandInset label
13379 name "sub:Colored-Boxes"
13384 \begin_inset Index idx
13387 \begin_layout Plain Layout
13396 \begin_layout Standard
13397 To be able to use all commands explained in this section, the LaTeX-package
13406 \begin_layout Plain Layout
13411 is part of every LaTeX standard installation.
13417 \begin_inset Index idx
13420 \begin_layout Plain Layout
13426 has to be loaded in the LaTeX-preamble with the line
13430 \begin_layout Plain Layout
13431 When text is colored somewhere in the document with a predefined color,
13432 LyX loads the LaTeX-package
13437 Thus it is possible that the package is loaded twice, but this does not
13444 \begin_inset Note Note
13447 \begin_layout Plain Layout
13448 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13457 \begin_layout Standard
13465 \begin_layout Standard
13466 \begin_inset VSpace medskip
13469 To color boxes, the command
13476 \begin_inset Index idx
13479 \begin_layout Plain Layout
13487 is used in the following scheme:
13490 \begin_layout Standard
13495 colorbox{color}{box content}
13498 \begin_layout Standard
13499 The box content can also be a box and a
13505 can also be part of another box (see the 2nd and 3rd example).
13506 When the box should contain a formula, an extra formula has to be created,
13507 the same way as for
13517 \begin_layout Plain Layout
13518 This also applies for the command
13532 \begin_layout Standard
13533 One of the following predefined colors can be chosen:
13536 \begin_layout Standard
13570 \begin_layout Standard
13572 \begin_inset Tabular
13573 <lyxtabular version="3" rows="4" columns="2">
13574 <features rotate="0" tabularvalignment="middle">
13575 <column alignment="center" valignment="top">
13576 <column alignment="center" valignment="top">
13578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13581 \begin_layout Plain Layout
13587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13590 \begin_layout Plain Layout
13592 \begin_inset Note Note
13595 \begin_layout Plain Layout
13602 is only used as spacer.
13614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13617 \begin_layout Plain Layout
13621 \begin_inset Formula $\to$
13631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13634 \begin_layout Plain Layout
13635 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13648 \begin_layout Plain Layout
13652 \begin_inset Formula $\to$
13663 \begin_layout Plain Layout
13677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13680 \begin_layout Plain Layout
13681 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13694 \begin_layout Plain Layout
13701 \begin_layout Plain Layout
13713 \begin_inset Formula $\to$
13732 \begin_layout Plain Layout
13746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13749 \begin_layout Plain Layout
13750 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13766 \begin_layout Standard
13773 only colors the box but not the characters in the box.
13774 To color all characters, the whole formula is highlighted and the desired
13775 color is chosen in the
13778 \begin_inset space ~
13784 The dialog can be called with the toolbar button
13785 \begin_inset Graphics
13786 filename ../images/dialog-show_character.png
13793 Edit\SpecialChar \menuseparator
13795 \begin_inset space ~
13798 Style\SpecialChar \menuseparator
13802 The formula number then has the same color as the formula.
13803 When the formula number should get another color than the formula characters,
13804 the color must be changed within the formula.
13807 \begin_layout Standard
13811 \begin_layout Standard
13814 \begin_inset Formula
13816 \int A=B\label{eq:red}
13824 \begin_inset Formula
13826 \textcolor{red}{\int A=B}\label{eq:redgreen}
13834 \begin_layout Standard
13836 \begin_inset CommandInset ref
13842 is completely colored red.
13843 \begin_inset Newline newline
13847 \begin_inset CommandInset ref
13849 reference "eq:redgreen"
13853 was first completely colored green to set the color for the formula number.
13854 Subsequently the formula characters were colored red.
13857 \begin_layout Standard
13858 \begin_inset VSpace bigskip
13861 To color the frame different than the rest of the box, the command
13868 \begin_inset Index idx
13871 \begin_layout Plain Layout
13879 is used in the following scheme:
13882 \begin_layout Standard
13887 fcolorbox{frame color}{color}{box content}
13890 \begin_layout Standard
13897 is an extension of the command
13904 The frame width is set, like for
13927 \begin_layout Plain Layout
13939 \begin_inset Formula
13941 \fcolorbox{cyan}{magenta}{A=B}
13950 \begin_layout Plain Layout
13964 \begin_layout Standard
13965 This formula was created with the command
13966 \begin_inset Newline newline
13974 \begin_inset Formula $\to$
13980 \begin_inset Formula $\to$
13990 \begin_layout Standard
13991 \begin_inset VSpace bigskip
13994 To use other colors than the predefined ones, they have to be defined first.
13997 \begin_layout Standard
13998 One can for example define the color
13999 \begin_inset Quotes eld
14007 \begin_inset Quotes erd
14010 with the LaTeX-preamble line:
14013 \begin_layout Standard
14018 definecolor{darkgreen}{cmyk}{0.5,
14033 \begin_inset Index idx
14036 \begin_layout Plain Layout
14047 \begin_layout Standard
14052 is the color space that denotes the colors
14069 The four comma separated numbers are the portion factor for the corresponding
14070 colors of the color space.
14071 The factors can be in the range of 0
14072 \begin_inset space \thinspace{}
14076 \begin_inset space \thinspace{}
14084 also the color space
14088 can be used for definitions.
14105 , so that there are in this case three portion factors for the corresponding
14107 Furthermore there is the color space
14111 with one portion factor for the gray value.
14114 \begin_layout Standard
14115 As example a framed box with the new defined color
14119 where the characters have been colored
14124 \begin_inset Formula
14126 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14134 \begin_layout Standard
14135 Self-defined colors can also be used for text with the help of the command
14143 \begin_inset Index idx
14146 \begin_layout Plain Layout
14155 \begin_layout Standard
14159 \begin_layout Plain Layout
14163 textcolor{darkgreen}{
14169 \begin_inset Quotes eld
14173 \begin_inset Quotes erd
14180 \begin_layout Plain Layout
14190 \begin_layout Standard
14198 \begin_inset Index idx
14201 \begin_layout Plain Layout
14209 is used in the scheme
14213 textcolor{color}{characters to color}
14218 \begin_layout Subsection
14220 \begin_inset CommandInset label
14222 name "sub:Paragraph-Boxes"
14227 \begin_inset Index idx
14230 \begin_layout Plain Layout
14231 Boxes ! as paragraph
14239 \begin_layout Standard
14240 A box that can contain several lines and paragraphs, a so-called paragraph
14241 box (parbox), can be created with the menu
14243 Insert\SpecialChar \menuseparator
14246 or the toolbar button
14247 \begin_inset Graphics
14248 filename ../images/box-insert.png
14256 \begin_layout Standard
14257 The following example shows a framed parbox in a line:
14260 \begin_layout Standard
14261 \begin_inset VSpace medskip
14265 \begin_inset Box Boxed
14275 height_special "totalheight"
14278 \begin_layout Plain Layout
14279 This is a paragraph box.
14281 \begin_inset space \thinspace{}
14284 cm long and can also contain formulas:
14285 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14296 \begin_layout Standard
14297 \begin_inset VSpace medskip
14303 \begin_layout Standard
14304 Such a box is created by right-clicking on the gray box inset.
14305 A dialog pops up showing the box properties.
14319 \begin_inset space \thinspace{}
14324 Vertical Box Alignment
14329 \begin_layout Standard
14330 \begin_inset VSpace medskip
14333 In LaTeX a parbox is created with the command
14340 \begin_inset Index idx
14343 \begin_layout Plain Layout
14351 which has the following scheme:
14354 \begin_layout Standard
14359 parbox[position]{width}{box content}
14362 \begin_layout Standard
14377 \begin_inset Quotes eld
14381 \begin_inset Quotes erd
14384 means that the box is aligned within the surrounding text with its last
14391 \begin_inset Quotes eld
14395 \begin_inset Quotes erd
14398 this is done with the first line.
14399 When no position is given, the box will be vertically centered, see section
14407 \begin_inset space ~
14412 manual for examples.
14415 \begin_layout Standard
14416 \begin_inset VSpace bigskip
14419 To frame formulas completely, including the formula number, the formula
14420 must be set into a parbox.
14421 To do this, the command
14435 is inserted in TeX-mode before the formula.
14443 \begin_inset Index idx
14446 \begin_layout Plain Layout
14454 is hereby the line width set for the document.
14455 Because the frame is outside the parbox, 2
14456 \begin_inset space \thinspace{}
14459 times the frame separation and the frame thickness must be subtracted from
14461 As this is not automatically done by LyX due to a bug
14465 \begin_layout Plain Layout
14466 \begin_inset CommandInset href
14468 name "LyX-bug #4483"
14469 target "http://www.lyx.org/trac/ticket/4483"
14478 , TeX-mode has to be used.
14479 To be able to multiply and subtract in arguments, the LaTeX-package
14487 \begin_layout Plain Layout
14492 is part of every LaTeX standard installation.
14498 \begin_inset Index idx
14501 \begin_layout Plain Layout
14507 must be loaded in the LaTeX-preamble with the line
14510 \begin_layout Standard
14518 \begin_layout Standard
14519 Behind the formula both boxes are closed by entering
14524 Here is an example:
14528 \begin_layout Plain Layout
14542 \begin_layout Standard
14546 \begin_layout Plain Layout
14564 \begin_inset Formula
14566 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14575 \begin_layout Plain Layout
14586 \begin_layout Plain Layout
14600 \begin_layout Standard
14601 \begin_inset VSpace medskip
14604 As a parbox is used as the argument of
14610 , there is in this case no difference between
14625 \begin_layout Standard
14626 \begin_inset VSpace bigskip
14629 Paragraph boxes are very useful to comment formulas directly.
14636 is used in combination with the command
14650 \begin_inset CommandInset ref
14652 reference "sub:User-defined-Numbering"
14659 \begin_layout Standard
14660 An example of a formula commented with
14669 \begin_layout Standard
14673 \begin_layout Plain Layout
14686 This is a description.
14687 It is distinctly separated from the formula and multiline.
14691 \begin_layout Plain Layout
14703 \begin_layout Standard
14704 Such a formula must be inserted completely in TeX-mode because LyX does
14705 not yet support the command
14712 The formula is created with the following command sequence:
14715 \begin_layout Standard
14728 is inserted in TeX-mode.
14732 \begin_layout Plain Layout
14733 When the formula style
14745 can also be replaced by
14752 (formula styles see
14753 \begin_inset CommandInset ref
14755 reference "sec:Formula-Styles"
14764 Then the description follows as normal text and finally
14770 is inserted in TeX-mode.
14783 hereby create a displayed formula.
14786 \begin_layout Standard
14793 can be seen in this example that was
14794 \begin_inset Quotes eld
14798 \begin_inset Quotes erd
14801 using the mathematical textmode:
14802 \begin_inset Formula
14804 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14812 \begin_layout Section
14814 \begin_inset Index idx
14817 \begin_layout Plain Layout
14826 \begin_layout Subsection
14828 \begin_inset CommandInset label
14830 name "sub:Big-Operators"
14835 \begin_inset Index idx
14838 \begin_layout Plain Layout
14845 \begin_inset Index idx
14848 \begin_layout Plain Layout
14855 \begin_inset Index idx
14858 \begin_layout Plain Layout
14867 \begin_layout Standard
14868 To be able to use all integral operators listed here, the option
14870 Use esint package automatically
14872 must be set in the document settings under
14875 \begin_inset space ~
14883 \begin_layout Standard
14884 \begin_inset space \hfill{}
14888 \begin_inset Tabular
14889 <lyxtabular version="3" rows="11" columns="2">
14890 <features rotate="0" tabularvalignment="middle">
14891 <column alignment="center" valignment="top" width="0pt">
14892 <column alignment="center" valignment="top" width="0pt">
14894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14897 \begin_layout Plain Layout
14903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14906 \begin_layout Plain Layout
14914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14917 \begin_layout Plain Layout
14921 \begin_inset Index idx
14924 \begin_layout Plain Layout
14937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14940 \begin_layout Plain Layout
14941 \begin_inset Formula $\int$
14951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14954 \begin_layout Plain Layout
14962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14965 \begin_layout Plain Layout
14966 \begin_inset Formula $\oint$
14976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14979 \begin_layout Plain Layout
14987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14990 \begin_layout Plain Layout
14991 \begin_inset Formula $\ointctrclockwise$
15001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15004 \begin_layout Plain Layout
15012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15015 \begin_layout Plain Layout
15016 \begin_inset Formula $\ointclockwise$
15026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15029 \begin_layout Plain Layout
15037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15040 \begin_layout Plain Layout
15041 \begin_inset Formula $\sqint$
15051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15054 \begin_layout Plain Layout
15062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15065 \begin_layout Plain Layout
15067 \begin_inset Formula $\fint$
15077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15080 \begin_layout Plain Layout
15088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15091 \begin_layout Plain Layout
15093 \begin_inset Formula $\landupint$
15103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15106 \begin_layout Plain Layout
15114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15117 \begin_layout Plain Layout
15119 \begin_inset Formula $\landdownint$
15129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15132 \begin_layout Plain Layout
15140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15143 \begin_layout Plain Layout
15144 \begin_inset Formula $\bigcap$
15154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15157 \begin_layout Plain Layout
15165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15168 \begin_layout Plain Layout
15169 \begin_inset Formula $\bigcup$
15183 \begin_inset space \hfill{}
15187 \begin_inset Tabular
15188 <lyxtabular version="3" rows="11" columns="2">
15189 <features rotate="0" tabularvalignment="middle">
15190 <column alignment="center" valignment="top" width="0pt">
15191 <column alignment="center" valignment="top" width="0pt">
15193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15196 \begin_layout Plain Layout
15202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15205 \begin_layout Plain Layout
15213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15216 \begin_layout Plain Layout
15220 \begin_inset Index idx
15223 \begin_layout Plain Layout
15236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15239 \begin_layout Plain Layout
15240 \begin_inset Formula $\sum$
15250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15253 \begin_layout Plain Layout
15257 \begin_inset Index idx
15260 \begin_layout Plain Layout
15267 \begin_layout Plain Layout
15286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15289 \begin_layout Plain Layout
15290 \begin_inset Formula $\prod$
15300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15303 \begin_layout Plain Layout
15311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15314 \begin_layout Plain Layout
15315 \begin_inset Formula $\coprod$
15325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15328 \begin_layout Plain Layout
15336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15339 \begin_layout Plain Layout
15340 \begin_inset Formula $\bigodot$
15350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15353 \begin_layout Plain Layout
15361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15364 \begin_layout Plain Layout
15365 \begin_inset Formula $\bigotimes$
15375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15378 \begin_layout Plain Layout
15386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15389 \begin_layout Plain Layout
15390 \begin_inset Formula $\bigoplus$
15400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15403 \begin_layout Plain Layout
15411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15414 \begin_layout Plain Layout
15415 \begin_inset Formula $\bigwedge$
15425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15428 \begin_layout Plain Layout
15436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15439 \begin_layout Plain Layout
15440 \begin_inset Formula $\bigvee$
15450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15453 \begin_layout Plain Layout
15461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15464 \begin_layout Plain Layout
15465 \begin_inset Formula $\bigsqcup$
15475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15478 \begin_layout Plain Layout
15486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15489 \begin_layout Plain Layout
15490 \begin_inset Formula $\biguplus$
15504 \begin_inset space \hfill{}
15510 \begin_layout Standard
15511 All big operators can also be inserted via the math toolbar button
15512 \begin_inset Graphics
15513 filename ../images/math/intop.png
15521 \begin_layout Standard
15522 The operators are called big because they are bigger than the sometimes
15523 equal looking binary operators.
15524 All big operators can have limits as described in the next subsection.
15527 \begin_layout Standard
15528 For all integral operators there is a second version available, ending in
15546 These operators are different from
15553 \begin_inset space \space{}
15556 in the style the operator limits are displayed, see
15557 \begin_inset CommandInset ref
15559 reference "sub:Operator-Limits"
15567 \begin_layout Subsubsection*
15568 Advice for Integrals
15571 \begin_layout Standard
15576 in an integral is an operator, that therefore has to be set upright.
15577 This is done by highlighting the
15581 and using the keyboard shortcut
15591 \begin_layout Plain Layout
15597 \begin_inset CommandInset ref
15599 reference "sub:Font-Styles"
15609 Finally the smallest space is inserted before the
15613 , as this is usual for operators.
15617 \begin_layout Standard
15619 \begin_inset Formula $\int A(x)dx$
15623 \begin_inset Newline newline
15627 \begin_inset Phantom HPhantom
15630 \begin_layout Plain Layout
15637 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15643 \begin_layout Standard
15644 For multiple integrals there are the following commands:
15645 \begin_inset VSpace medskip
15651 \begin_layout Standard
15652 \begin_inset space \hfill{}
15656 \begin_inset Tabular
15657 <lyxtabular version="3" rows="4" columns="2">
15658 <features rotate="0" tabularvalignment="middle">
15659 <column alignment="center" valignment="top">
15660 <column alignment="center" valignment="top">
15662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15665 \begin_layout Plain Layout
15671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15674 \begin_layout Plain Layout
15676 \begin_inset Note Note
15679 \begin_layout Plain Layout
15686 is only used as spacer.
15698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15701 \begin_layout Plain Layout
15709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15712 \begin_layout Plain Layout
15713 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15726 \begin_layout Plain Layout
15734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15737 \begin_layout Plain Layout
15738 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15751 \begin_layout Plain Layout
15759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15762 \begin_layout Plain Layout
15763 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15777 \begin_inset space \hfill{}
15781 \begin_inset Tabular
15782 <lyxtabular version="3" rows="4" columns="2">
15783 <features rotate="0" tabularvalignment="middle">
15784 <column alignment="center" valignment="top">
15785 <column alignment="center" valignment="top">
15787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15790 \begin_layout Plain Layout
15796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15799 \begin_layout Plain Layout
15807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15810 \begin_layout Plain Layout
15818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15821 \begin_layout Plain Layout
15822 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15835 \begin_layout Plain Layout
15843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15846 \begin_layout Plain Layout
15847 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15860 \begin_layout Plain Layout
15868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15871 \begin_layout Plain Layout
15872 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15886 \begin_inset space \hfill{}
15892 \begin_layout Standard
15893 \begin_inset Newpage newpage
15899 \begin_layout Subsection
15901 \begin_inset CommandInset label
15903 name "sub:Operator-Limits"
15908 \begin_inset Index idx
15911 \begin_layout Plain Layout
15920 \begin_layout Standard
15921 Limits are created by super- and subscripts:
15924 \begin_layout Standard
15926 \begin_inset Tabular
15927 <lyxtabular version="3" rows="2" columns="2">
15928 <features rotate="0" tabularvalignment="middle">
15929 <column alignment="center" valignment="top" width="0pt">
15930 <column alignment="center" valignment="top" width="0pt">
15932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15935 \begin_layout Plain Layout
15941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15944 \begin_layout Plain Layout
15946 \begin_inset Note Note
15949 \begin_layout Plain Layout
15956 is only used as spacer.
15968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15971 \begin_layout Plain Layout
15980 \begin_layout Plain Layout
15990 \begin_inset Formula $\to$
15994 \begin_inset Formula $\to$
16002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16005 \begin_layout Plain Layout
16006 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16022 \begin_layout Standard
16023 Limits of inline formulas are set right beside the operator.
16024 Limits in displayed formulas are set above or below the operator, except
16025 for integral limits.
16028 \begin_layout Standard
16029 To force that the limits are set beside the operator, the cursor is set
16030 directly behind the operator and the limits type is changed with the menu
16033 Edit\SpecialChar \menuseparator
16034 Math\SpecialChar \menuseparator
16053 \begin_layout Standard
16054 The default limits type is this:
16055 \begin_inset Formula
16057 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16062 This is how it looks when the limits type was changed to
16069 \begin_inset Formula
16071 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16076 For integrals, except those ending with
16092 etc., the limits are by default set beside the operator.
16093 But for multiple integrals the limits are often set below the operator.
16094 In the following example the limits type was therefore set to
16098 and so set below the integrals:
16099 \begin_inset Formula
16101 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16109 \begin_layout Standard
16110 \begin_inset VSpace medskip
16113 To specify conditions for limits, the commands
16120 \begin_inset Index idx
16123 \begin_layout Plain Layout
16138 \begin_inset Index idx
16141 \begin_layout Plain Layout
16150 To create for example this expression
16151 \begin_inset Formula
16153 \sum_{\begin{subarray}{c}
16157 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16165 \begin_layout Standard
16166 the following has to be done:
16167 \begin_inset Newline newline
16182 \begin_layout Plain Layout
16194 One is now in a blue box under the summation operator and insert there
16203 \begin_layout Plain Layout
16215 The blue box is now within a purple box and now several lines can be written
16217 A new line is created by inserting a line break (
16220 arg "newline-insert newline"
16225 \begin_inset Newline newline
16230 0<k<1000 Ctrl+Return
16231 \begin_inset Newline newline
16236 is typed in, a new box appears below for the new line.
16239 \begin_layout Standard
16240 The alignment of the lines can be changed to left aligned with the
16250 Edit\SpecialChar \menuseparator
16254 To get right alignment,
16262 \begin_layout Plain Layout
16273 is inserted at the beginning of the line.
16276 \begin_layout Standard
16289 with the difference that the lines are always centered.
16292 \begin_layout Standard
16293 \begin_inset VSpace bigskip
16297 \begin_inset CommandInset ref
16299 reference "eq:substack"
16303 there can be too much space beside an operator, because the characters
16304 following the operator are set beside the limits.
16307 \begin_layout Standard
16308 To avoid this, the following macro can be used in the LaTeX-preamble:
16311 \begin_layout Standard
16325 \begin_inset Newline newline
16337 \begin_inset Newline newline
16344 mathclapinternal #1#2{
16348 mathsurround =0pt #1{#2}$}}
16351 \begin_layout Standard
16352 This defines the command
16359 \begin_inset Index idx
16362 \begin_layout Plain Layout
16370 that sets the width of the limit to 0
16371 \begin_inset space \thinspace{}
16375 The command scheme is
16378 \begin_layout Standard
16386 \begin_layout Standard
16387 where the limit can consist of several conditions.
16390 \begin_layout Standard
16392 \begin_inset CommandInset ref
16394 reference "eq:substack"
16398 , one uses the command
16401 \begin_layout Standard
16414 \begin_layout Plain Layout
16423 0<k<1000 Ctrl+Return
16426 \begin_layout Standard
16427 to create the lower limit.
16428 The summand is now directly behind the summation operator:
16429 \begin_inset Formula
16431 \sum_{\mathclap{\substack{0<k<1000\\
16443 \begin_layout Standard
16444 \begin_inset VSpace bigskip
16447 How to use one limit for several operators is described in
16448 \begin_inset CommandInset ref
16450 reference "sub:Self-defined-Operators"
16457 \begin_layout Subsection
16458 Decoration for Operators
16459 \begin_inset Index idx
16462 \begin_layout Plain Layout
16463 Operators ! Decoration
16471 \begin_layout Standard
16479 \begin_inset Index idx
16482 \begin_layout Plain Layout
16497 \begin_inset Index idx
16500 \begin_layout Plain Layout
16508 characters can be placed above or below an operator, respectively.
16516 \begin_inset Index idx
16519 \begin_layout Plain Layout
16527 characters can be set before and behind a big operator.
16528 The command scheme is:
16531 \begin_layout Standard
16547 \begin_layout Standard
16554 must always be before the operator.
16555 You can decorate with several characters and even with other operators
16557 To place for example only characters behind a big operator, write nothing
16558 between the first braces but don't omit the braces.
16561 \begin_layout Standard
16562 For example the command
16567 \begin_inset Formula $\to$
16577 \begin_inset Formula $\to$
16586 \begin_layout Plain Layout
16602 \begin_inset Formula
16604 \sideset{}{'}\sum_{k=1}^{n}
16612 \begin_layout Standard
16613 \begin_inset Note Greyedout
16616 \begin_layout Plain Layout
16623 can only be used to decorate big operators, binary operators are not allowed.
16631 \begin_layout Standard
16644 can also be used to decorate symbols and characters.
16645 For example, the command
16653 \begin_layout Plain Layout
16668 \begin_layout Plain Layout
16680 \begin_inset Formula $\uparrow$
16688 \begin_inset Formula
16690 \overset{a}{\maltese}
16698 \begin_layout Subsection
16700 \begin_inset CommandInset label
16702 name "sub:Binary-Operators"
16707 \begin_inset Index idx
16710 \begin_layout Plain Layout
16719 \begin_layout Standard
16720 Binary operators are surrounded by space when there is a character before
16722 \begin_inset VSpace medskip
16728 \begin_layout Standard
16729 \begin_inset space \hfill{}
16733 \begin_inset Tabular
16734 <lyxtabular version="3" rows="13" columns="2">
16735 <features rotate="0" tabularvalignment="middle">
16736 <column alignment="center" valignment="top" width="0pt">
16737 <column alignment="center" valignment="top" width="0pt">
16739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16742 \begin_layout Plain Layout
16744 \begin_inset Note Note
16747 \begin_layout Plain Layout
16754 is only used as spacer.
16764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16767 \begin_layout Plain Layout
16775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16778 \begin_layout Plain Layout
16784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16787 \begin_layout Plain Layout
16788 \begin_inset Formula $+$
16798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16801 \begin_layout Plain Layout
16807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16810 \begin_layout Plain Layout
16811 \begin_inset Formula $-$
16821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16824 \begin_layout Plain Layout
16832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16835 \begin_layout Plain Layout
16836 \begin_inset Formula $\pm$
16846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16849 \begin_layout Plain Layout
16857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16860 \begin_layout Plain Layout
16861 \begin_inset Formula $\mp$
16871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16874 \begin_layout Plain Layout
16882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16885 \begin_layout Plain Layout
16886 \begin_inset Formula $\cdot$
16896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16899 \begin_layout Plain Layout
16907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16910 \begin_layout Plain Layout
16911 \begin_inset Formula $\times$
16921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16924 \begin_layout Plain Layout
16932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16935 \begin_layout Plain Layout
16936 \begin_inset Formula $\div$
16946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16949 \begin_layout Plain Layout
16953 \begin_layout Plain Layout
16966 \begin_layout Plain Layout
16978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16981 \begin_layout Plain Layout
16982 \begin_inset Formula $*$
16992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16995 \begin_layout Plain Layout
17003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17006 \begin_layout Plain Layout
17007 \begin_inset Formula $\star$
17017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17020 \begin_layout Plain Layout
17028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17031 \begin_layout Plain Layout
17032 \begin_inset Formula $\circ$
17042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17045 \begin_layout Plain Layout
17053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17056 \begin_layout Plain Layout
17057 \begin_inset Formula $\diamond$
17067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17070 \begin_layout Plain Layout
17078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17081 \begin_layout Plain Layout
17082 \begin_inset Formula $\bullet$
17096 \begin_inset space \hfill{}
17100 \begin_inset Tabular
17101 <lyxtabular version="3" rows="13" columns="2">
17102 <features rotate="0" tabularvalignment="middle">
17103 <column alignment="center" valignment="top" width="0pt">
17104 <column alignment="center" valignment="top" width="0pt">
17106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17109 \begin_layout Plain Layout
17115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17118 \begin_layout Plain Layout
17126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17129 \begin_layout Plain Layout
17137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17140 \begin_layout Plain Layout
17141 \begin_inset Formula $\nabla$
17151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17154 \begin_layout Plain Layout
17162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17165 \begin_layout Plain Layout
17166 \begin_inset Formula $\bigtriangledown$
17176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17179 \begin_layout Plain Layout
17187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17190 \begin_layout Plain Layout
17191 \begin_inset Formula $\bigtriangleup$
17201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17204 \begin_layout Plain Layout
17212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17215 \begin_layout Plain Layout
17216 \begin_inset Formula $\Box$
17226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17229 \begin_layout Plain Layout
17237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17240 \begin_layout Plain Layout
17241 \begin_inset Formula $\cap$
17251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17254 \begin_layout Plain Layout
17262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17265 \begin_layout Plain Layout
17266 \begin_inset Formula $\cup$
17276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17279 \begin_layout Plain Layout
17287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17290 \begin_layout Plain Layout
17291 \begin_inset Formula $\dagger$
17301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17304 \begin_layout Plain Layout
17312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17315 \begin_layout Plain Layout
17316 \begin_inset Formula $\ddagger$
17326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17329 \begin_layout Plain Layout
17337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17340 \begin_layout Plain Layout
17341 \begin_inset Formula $\wr$
17351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17354 \begin_layout Plain Layout
17362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17365 \begin_layout Plain Layout
17366 \begin_inset Formula $\bigcirc$
17376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17379 \begin_layout Plain Layout
17387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17390 \begin_layout Plain Layout
17391 \begin_inset Formula $\wedge$
17401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17404 \begin_layout Plain Layout
17412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17415 \begin_layout Plain Layout
17416 \begin_inset Formula $\vee$
17430 \begin_inset space \hfill{}
17434 \begin_inset Tabular
17435 <lyxtabular version="3" rows="13" columns="2">
17436 <features rotate="0" tabularvalignment="middle">
17437 <column alignment="center" valignment="top" width="0pt">
17438 <column alignment="center" valignment="top" width="0pt">
17440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17443 \begin_layout Plain Layout
17449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17452 \begin_layout Plain Layout
17460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17463 \begin_layout Plain Layout
17471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17474 \begin_layout Plain Layout
17475 \begin_inset Formula $\oplus$
17485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17488 \begin_layout Plain Layout
17496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17499 \begin_layout Plain Layout
17500 \begin_inset Formula $\ominus$
17510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17513 \begin_layout Plain Layout
17521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17524 \begin_layout Plain Layout
17525 \begin_inset Formula $\otimes$
17535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17538 \begin_layout Plain Layout
17546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17549 \begin_layout Plain Layout
17550 \begin_inset Formula $\oslash$
17560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17563 \begin_layout Plain Layout
17571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17574 \begin_layout Plain Layout
17575 \begin_inset Formula $\odot$
17585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17588 \begin_layout Plain Layout
17596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17599 \begin_layout Plain Layout
17600 \begin_inset Formula $\amalg$
17610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17613 \begin_layout Plain Layout
17621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17624 \begin_layout Plain Layout
17625 \begin_inset Formula $\uplus$
17635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17638 \begin_layout Plain Layout
17646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17649 \begin_layout Plain Layout
17650 \begin_inset Formula $\setminus$
17660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17663 \begin_layout Plain Layout
17671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17674 \begin_layout Plain Layout
17675 \begin_inset Formula $\sqcap$
17685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17688 \begin_layout Plain Layout
17696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17699 \begin_layout Plain Layout
17700 \begin_inset Formula $\sqcup$
17710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17713 \begin_layout Plain Layout
17721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17724 \begin_layout Plain Layout
17725 \begin_inset Formula $\triangleleft$
17735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17738 \begin_layout Plain Layout
17746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17749 \begin_layout Plain Layout
17750 \begin_inset Formula $\triangleright$
17764 \begin_inset space \hfill{}
17770 \begin_layout Standard
17771 All binary operators can also be inserted via the math toolbar button
17772 \begin_inset Graphics
17773 filename ../images/math/pm.png
17781 \begin_layout Standard
17782 To typeset the Laplace operator also
17799 \begin_inset Formula $\nabla^{2}$
17802 ) can be used instead of
17811 \begin_layout Standard
17818 Insert\SpecialChar \menuseparator
17830 \begin_layout Subsection
17831 Self-defined Operators
17832 \begin_inset CommandInset label
17834 name "sub:Self-defined-Operators"
17839 \begin_inset Index idx
17842 \begin_layout Plain Layout
17843 Operators ! self-defined
17851 \begin_layout Standard
17852 With the help of the command
17856 DeclareMathOperator
17859 \begin_inset Index idx
17862 \begin_layout Plain Layout
17867 DeclareMathOperator
17872 custom operators can be defined in the LaTeX-preamble.
17873 Its command scheme is:
17876 \begin_layout Standard
17881 DeclareMathOperator{new command}{display}
17884 \begin_layout Standard
17885 Display can be characters or symbols that define how the operator looks
17887 To define a big operator a * is set behind the command.
17888 All self-defined big operators can have limits as described in
17889 \begin_inset CommandInset ref
17891 reference "sub:Operator-Limits"
17898 \begin_layout Standard
17899 For example the LaTeX-preamble line
17902 \begin_layout Standard
17907 DeclareMathOperator*{
17914 \begin_layout Standard
17915 defines the command
17921 , that inserts a big operator consisting of the lozenge symbol from
17922 \begin_inset CommandInset ref
17924 reference "sub:Miscellaneous-Symbols"
17929 \begin_inset Formula
17931 \Lozenge_{n=1}^{\infty}
17936 The command for this formula is:
17947 \begin_inset Formula $\to$
17953 \begin_layout Standard
17954 \begin_inset VSpace bigskip
17957 When self-defined operators are not used several times in the document,
17958 they can also be defined with the commands
17965 \begin_inset Index idx
17968 \begin_layout Plain Layout
17983 \begin_inset Index idx
17986 \begin_layout Plain Layout
17994 , which have the following scheme:
17997 \begin_layout Standard
18011 \begin_layout Standard
18018 defines big operators,
18027 \begin_layout Standard
18035 \begin_inset space \thinspace{}
18039 \begin_inset space \space{}
18042 be used to use one limit for several operators:
18045 \begin_layout Standard
18046 \begin_inset Formula
18048 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18056 \begin_layout Standard
18057 The command for the formula above is:
18058 \begin_inset Newline newline
18077 \begin_layout Plain Layout
18089 \begin_inset Formula $\to$
18098 \begin_layout Plain Layout
18112 \begin_layout Section
18114 \begin_inset Index idx
18117 \begin_layout Plain Layout
18126 \begin_layout Subsection
18128 \begin_inset CommandInset label
18130 name "sub:Font-Styles"
18135 \begin_inset Index idx
18138 \begin_layout Plain Layout
18147 \begin_layout Standard
18148 Latin letters in formulas can be set in one of the following font styles:
18149 \begin_inset VSpace -2mm
18155 \begin_layout Standard
18157 \begin_inset Tabular
18158 <lyxtabular version="3" rows="7" columns="3">
18159 <features rotate="0" tabularvalignment="middle">
18160 <column alignment="center" valignment="top">
18161 <column alignment="center" valignment="top">
18162 <column alignment="center" valignment="top">
18164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18167 \begin_layout Plain Layout
18173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18176 \begin_layout Plain Layout
18182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18185 \begin_layout Plain Layout
18193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18196 \begin_layout Plain Layout
18205 \begin_layout Plain Layout
18221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18224 \begin_layout Plain Layout
18225 \begin_inset Formula $\mathbb{ABC}$
18233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18236 \begin_layout Plain Layout
18249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18252 \begin_layout Plain Layout
18261 \begin_layout Plain Layout
18277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18280 \begin_layout Plain Layout
18281 \begin_inset Formula $\mathbf{AbC}$
18289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18292 \begin_layout Plain Layout
18305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18308 \begin_layout Plain Layout
18317 \begin_layout Plain Layout
18333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18336 \begin_layout Plain Layout
18337 \begin_inset Formula $\boldsymbol{AbC}$
18345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18348 \begin_layout Plain Layout
18351 arg "font-boldsymbol"
18361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18364 \begin_layout Plain Layout
18373 \begin_layout Plain Layout
18389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18392 \begin_layout Plain Layout
18393 \begin_inset Formula $\mathcal{ABC}$
18401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18404 \begin_layout Plain Layout
18417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18420 \begin_layout Plain Layout
18429 \begin_layout Plain Layout
18445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18448 \begin_layout Plain Layout
18449 \begin_inset Formula $\mathfrak{AbC}$
18457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18460 \begin_layout Plain Layout
18468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18471 \begin_layout Plain Layout
18480 \begin_layout Plain Layout
18496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18499 \begin_layout Plain Layout
18500 \begin_inset Formula $\mathscr{AbC}$
18508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18511 \begin_layout Plain Layout
18525 \begin_layout Standard
18527 \begin_inset Tabular
18528 <lyxtabular version="3" rows="5" columns="3">
18529 <features rotate="0" tabularvalignment="middle">
18530 <column alignment="center" valignment="top">
18531 <column alignment="center" valignment="top">
18532 <column alignment="center" valignment="top">
18534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18537 \begin_layout Plain Layout
18543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18546 \begin_layout Plain Layout
18552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18555 \begin_layout Plain Layout
18563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18566 \begin_layout Plain Layout
18575 \begin_layout Plain Layout
18591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18594 \begin_layout Plain Layout
18595 \begin_inset Formula $\mathit{AbC}$
18603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18606 \begin_layout Plain Layout
18614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18617 \begin_layout Plain Layout
18626 \begin_layout Plain Layout
18642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18645 \begin_layout Plain Layout
18646 \begin_inset Formula $\mathrm{AbC}$
18654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18657 \begin_layout Plain Layout
18670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18673 \begin_layout Plain Layout
18682 \begin_layout Plain Layout
18698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18701 \begin_layout Plain Layout
18702 \begin_inset Formula $\mathsf{AbC}$
18710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18713 \begin_layout Plain Layout
18726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18729 \begin_layout Plain Layout
18738 \begin_layout Plain Layout
18754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18757 \begin_layout Plain Layout
18758 \begin_inset Formula $\mathtt{AbC}$
18766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18769 \begin_layout Plain Layout
18772 arg "font-typewriter"
18788 \begin_layout Standard
18789 \begin_inset Note Greyedout
18792 \begin_layout Plain Layout
18809 can only be used for big letters.
18817 \begin_layout Standard
18818 Predefined is the style
18827 \begin_layout Standard
18828 The style commands work also for letters in mathematical constructs:
18829 \begin_inset Formula
18831 \mathfrak{A=\frac{b}{C}}
18839 \begin_layout Standard
18840 Characters in mathematical text don't appear in a math font style but in
18841 the text font style
18848 That their style can't be set correctly via the text style dialog is a
18853 \begin_layout Plain Layout
18854 \begin_inset CommandInset href
18856 name "LyX-bug #4629"
18857 target "http://www.lyx.org/trac/ticket/4629"
18869 \begin_layout Standard
18870 Instead of the style commands the dialog
18872 Edit\SpecialChar \menuseparator
18873 Math\SpecialChar \menuseparator
18876 or the toolbar button
18877 \begin_inset Graphics
18878 filename ../images/math/font.png
18886 \begin_layout Subsection
18888 \begin_inset CommandInset label
18890 name "sub:Bold-Formulas"
18895 \begin_inset Index idx
18898 \begin_layout Plain Layout
18907 \begin_layout Standard
18908 To make a complete formula bold, the command
18914 from the previous subsection cannot be used, because it doesn't work for
18915 small Greek letters.
18916 Furthermore it prints Latin letters always upright, like in the following
18920 \begin_layout Standard
18921 \begin_inset Formula
18923 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18931 \begin_layout Standard
18932 To display the formula correctly, the command
18939 \begin_inset Formula
18941 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18946 It is also possible to set the formula in a
18948 boldmath environment
18951 This environment is created by inserting the command
18958 \begin_inset Index idx
18961 \begin_layout Plain Layout
18970 To end the environment, the command
18977 \begin_inset Index idx
18980 \begin_layout Plain Layout
18988 is inserted in TeX-mode.
18992 \begin_layout Plain Layout
19002 \begin_inset Formula
19004 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19013 \begin_layout Plain Layout
19025 \begin_layout Subsection
19027 \begin_inset Index idx
19030 \begin_layout Plain Layout
19039 \begin_layout Standard
19040 Formulas can be colored like normal text: Highlight a formula or a formula
19046 Here is a formula in magenta:
19047 \begin_inset Formula
19049 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19057 \begin_layout Standard
19058 You can also define your own colors as described in
19059 \begin_inset CommandInset ref
19061 reference "sub:Colored-Boxes"
19066 They can be used with the TeX code command
19073 \begin_inset Index idx
19076 \begin_layout Plain Layout
19087 \begin_layout Standard
19092 textcolor{color}{characters or formula}
19095 \begin_layout Standard
19096 The following example was colored completely dark green and partly red:
19099 \begin_layout Standard
19103 \begin_layout Plain Layout
19107 textcolor{darkgreen}{
19113 \begin_inset Formula
19115 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19124 \begin_layout Plain Layout
19134 \begin_layout Standard
19135 Due to a bug in LyX only complete formulas can be colored with self-defined
19140 \begin_layout Plain Layout
19141 \begin_inset CommandInset href
19143 name "LyX-bug #5269"
19144 target "http://www.lyx.org/trac/ticket/5269"
19156 \begin_layout Subsection
19158 \begin_inset CommandInset label
19160 name "sub:Font-Sizes"
19165 \begin_inset Index idx
19168 \begin_layout Plain Layout
19177 \begin_layout Standard
19178 For characters in formulas there are, analog to characters in text, the
19179 following size commands:
19182 \begin_layout Standard
19226 \begin_inset Newline newline
19248 \begin_layout Standard
19249 The size produced by the commands depends on the document font size, which
19250 corresponds to the command
19257 The other commands produce smaller or larger sizes than
19264 The font size can however not exceed a certain value.
19265 Is for example the document font size 12
19266 \begin_inset space \thinspace{}
19275 switches to the same size as
19285 \begin_layout Standard
19286 A size command is inserted in TeX-mode before the formula and sets the size
19287 for all following formula and text characters.
19288 To switch back to the initial size, the command
19294 is inserted behind the formula in TeX-mode.
19297 \begin_layout Standard
19298 Within a formula the size can be changed using the following size commands:
19301 \begin_layout Standard
19304 \begin_inset Tabular
19305 <lyxtabular version="3" rows="5" columns="2">
19306 <features rotate="0" tabularvalignment="middle">
19307 <column alignment="center" valignment="top">
19308 <column alignment="center" valignment="top">
19310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19313 \begin_layout Plain Layout
19319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19322 \begin_layout Plain Layout
19324 \begin_inset Note Note
19327 \begin_layout Plain Layout
19334 is only used as spacer.
19346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19349 \begin_layout Plain Layout
19353 \begin_inset Index idx
19356 \begin_layout Plain Layout
19369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19372 \begin_layout Plain Layout
19373 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19386 \begin_layout Plain Layout
19394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19397 \begin_layout Plain Layout
19398 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19411 \begin_layout Plain Layout
19419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19422 \begin_layout Plain Layout
19423 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19436 \begin_layout Plain Layout
19444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19447 \begin_layout Plain Layout
19448 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19464 \begin_layout Standard
19465 After entering these commands, a blue box appears in which the formula parts
19469 \begin_layout Standard
19470 There is a further method to change the font size, that though only works
19471 for symbols or letters in mathematical text.
19472 To use it, one of the above text size commands is inserted in mathematical
19474 All following characters until the end of the mathematical text or until
19475 another size command will have the selected size.
19477 \begin_inset VSpace -2mm
19483 \begin_layout Standard
19487 \begin_layout Plain Layout
19497 \begin_inset Formula
19499 A=\frac{B}{c}\cdot\maltese
19505 \begin_inset Formula
19507 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19516 \begin_layout Plain Layout
19528 \begin_layout Standard
19529 \begin_inset VSpace medskip
19532 Before both formulas the command
19539 The command for the second formula is:
19540 \begin_inset Newline newline
19551 \begin_layout Plain Layout
19566 \begin_layout Plain Layout
19581 \begin_layout Plain Layout
19596 \begin_layout Plain Layout
19606 \begin_inset Formula $\to$
19610 \begin_inset Formula $\to$
19614 \begin_inset Newline newline
19618 \begin_inset space \hspace*{}
19632 \begin_layout Plain Layout
19647 \begin_layout Plain Layout
19662 \begin_layout Plain Layout
19674 \begin_layout Standard
19675 If a symbol cannot be displayed in different sizes, it will always be displayed
19676 in the default size.
19679 \begin_layout Section
19681 \begin_inset Index idx
19684 \begin_layout Plain Layout
19693 \begin_layout Standard
19694 Greek letters can also be inserted via the toolbar button
19695 \begin_inset Graphics
19696 filename ../images/math/alpha.png
19702 All international typesetting norms purport that Greek letters in math
19703 have to be typeset italic/slanted.
19704 In some languages, like French or Russian, they are nevertheless sometimes
19708 \begin_layout Subsection
19710 \begin_inset Index idx
19713 \begin_layout Plain Layout
19714 Greek letters ! small
19722 \begin_layout Standard
19723 \begin_inset space \hfill{}
19727 \begin_inset Tabular
19728 <lyxtabular version="3" rows="11" columns="2">
19729 <features rotate="0" tabularvalignment="middle">
19730 <column alignment="center" valignment="top" width="0pt">
19731 <column alignment="center" valignment="top" width="0pt">
19733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19736 \begin_layout Plain Layout
19742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19745 \begin_layout Plain Layout
19753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19756 \begin_layout Plain Layout
19764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19767 \begin_layout Plain Layout
19768 \begin_inset Formula $\alpha$
19778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19781 \begin_layout Plain Layout
19789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19792 \begin_layout Plain Layout
19793 \begin_inset Formula $\beta$
19803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19806 \begin_layout Plain Layout
19814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19817 \begin_layout Plain Layout
19818 \begin_inset Formula $\gamma$
19828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19831 \begin_layout Plain Layout
19839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19842 \begin_layout Plain Layout
19843 \begin_inset Formula $\delta$
19853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19856 \begin_layout Plain Layout
19864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19867 \begin_layout Plain Layout
19868 \begin_inset Formula $\epsilon$
19878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19881 \begin_layout Plain Layout
19889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19892 \begin_layout Plain Layout
19893 \begin_inset Formula $\varepsilon$
19903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19906 \begin_layout Plain Layout
19914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19917 \begin_layout Plain Layout
19918 \begin_inset Formula $\zeta$
19928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19931 \begin_layout Plain Layout
19939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19942 \begin_layout Plain Layout
19943 \begin_inset Formula $\eta$
19953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19956 \begin_layout Plain Layout
19964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19967 \begin_layout Plain Layout
19968 \begin_inset Formula $\theta$
19978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19981 \begin_layout Plain Layout
19989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19992 \begin_layout Plain Layout
19993 \begin_inset Formula $\vartheta$
20007 \begin_inset space \hfill{}
20011 \begin_inset Tabular
20012 <lyxtabular version="3" rows="12" columns="2">
20013 <features rotate="0" tabularvalignment="middle">
20014 <column alignment="center" valignment="top" width="0pt">
20015 <column alignment="center" valignment="top" width="0pt">
20017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20020 \begin_layout Plain Layout
20026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20029 \begin_layout Plain Layout
20037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20040 \begin_layout Plain Layout
20048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20051 \begin_layout Plain Layout
20052 \begin_inset Formula $\iota$
20062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20065 \begin_layout Plain Layout
20073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20076 \begin_layout Plain Layout
20077 \begin_inset Formula $\kappa$
20087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20090 \begin_layout Plain Layout
20098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20101 \begin_layout Plain Layout
20102 \begin_inset Formula $\varkappa$
20112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20115 \begin_layout Plain Layout
20123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20126 \begin_layout Plain Layout
20127 \begin_inset Formula $\lambda$
20137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20140 \begin_layout Plain Layout
20148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20151 \begin_layout Plain Layout
20152 \begin_inset Formula $\mu$
20162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20165 \begin_layout Plain Layout
20173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20176 \begin_layout Plain Layout
20177 \begin_inset Formula $\nu$
20187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20190 \begin_layout Plain Layout
20198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20201 \begin_layout Plain Layout
20202 \begin_inset Formula $\xi$
20212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20215 \begin_layout Plain Layout
20221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20224 \begin_layout Plain Layout
20225 \begin_inset Formula $o$
20235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20238 \begin_layout Plain Layout
20246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20249 \begin_layout Plain Layout
20250 \begin_inset Formula $\pi$
20260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20263 \begin_layout Plain Layout
20271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20274 \begin_layout Plain Layout
20275 \begin_inset Formula $\varpi$
20285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20288 \begin_layout Plain Layout
20296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20299 \begin_layout Plain Layout
20300 \begin_inset Formula $\rho$
20314 \begin_inset space \hfill{}
20318 \begin_inset Tabular
20319 <lyxtabular version="3" rows="11" columns="2">
20320 <features rotate="0" tabularvalignment="middle">
20321 <column alignment="center" valignment="top" width="0pt">
20322 <column alignment="center" valignment="top" width="0pt">
20324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20327 \begin_layout Plain Layout
20333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20336 \begin_layout Plain Layout
20344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20347 \begin_layout Plain Layout
20355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20358 \begin_layout Plain Layout
20359 \begin_inset Formula $\varrho$
20369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20372 \begin_layout Plain Layout
20380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20383 \begin_layout Plain Layout
20384 \begin_inset Formula $\sigma$
20394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20397 \begin_layout Plain Layout
20405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20408 \begin_layout Plain Layout
20409 \begin_inset Formula $\varsigma$
20419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20422 \begin_layout Plain Layout
20430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20433 \begin_layout Plain Layout
20434 \begin_inset Formula $\tau$
20444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20447 \begin_layout Plain Layout
20455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20458 \begin_layout Plain Layout
20459 \begin_inset Formula $\upsilon$
20469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20472 \begin_layout Plain Layout
20480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20483 \begin_layout Plain Layout
20484 \begin_inset Formula $\phi$
20494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20497 \begin_layout Plain Layout
20505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20508 \begin_layout Plain Layout
20509 \begin_inset Formula $\varphi$
20519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20522 \begin_layout Plain Layout
20530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20533 \begin_layout Plain Layout
20534 \begin_inset Formula $\chi$
20544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20547 \begin_layout Plain Layout
20555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20558 \begin_layout Plain Layout
20559 \begin_inset Formula $\psi$
20569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20572 \begin_layout Plain Layout
20580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20583 \begin_layout Plain Layout
20584 \begin_inset Formula $\omega$
20598 \begin_inset space \hfill{}
20604 \begin_layout Standard
20605 \begin_inset VSpace medskip
20611 \begin_layout Standard
20612 How to create special upright Greek letters is explained in
20613 \begin_inset CommandInset ref
20615 reference "sub:Upright-small-Greek"
20622 \begin_layout Subsection
20624 \begin_inset Index idx
20627 \begin_layout Plain Layout
20628 Greek letters ! big
20636 \begin_layout Standard
20637 \begin_inset space \hfill{}
20641 \begin_inset Tabular
20642 <lyxtabular version="3" rows="7" columns="2">
20643 <features rotate="0" tabularvalignment="middle">
20644 <column alignment="center" valignment="top" width="0pt">
20645 <column alignment="center" valignment="top" width="0pt">
20647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20650 \begin_layout Plain Layout
20656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20659 \begin_layout Plain Layout
20667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20670 \begin_layout Plain Layout
20678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20681 \begin_layout Plain Layout
20682 \begin_inset Formula $\Gamma$
20692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20695 \begin_layout Plain Layout
20703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20706 \begin_layout Plain Layout
20707 \begin_inset Formula $\Delta$
20717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20720 \begin_layout Plain Layout
20728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20731 \begin_layout Plain Layout
20732 \begin_inset Formula $\Theta$
20742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20745 \begin_layout Plain Layout
20753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20756 \begin_layout Plain Layout
20757 \begin_inset Formula $\Lambda$
20767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20770 \begin_layout Plain Layout
20778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20781 \begin_layout Plain Layout
20782 \begin_inset Formula $\Xi$
20792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20795 \begin_layout Plain Layout
20803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20806 \begin_layout Plain Layout
20807 \begin_inset Formula $\Pi$
20821 \begin_inset space \hfill{}
20825 \begin_inset Tabular
20826 <lyxtabular version="3" rows="6" columns="2">
20827 <features rotate="0" tabularvalignment="middle">
20828 <column alignment="center" valignment="top" width="0pt">
20829 <column alignment="center" valignment="top" width="0pt">
20831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20834 \begin_layout Plain Layout
20840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20843 \begin_layout Plain Layout
20851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20854 \begin_layout Plain Layout
20862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20865 \begin_layout Plain Layout
20866 \begin_inset Formula $\Sigma$
20876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20879 \begin_layout Plain Layout
20887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20890 \begin_layout Plain Layout
20891 \begin_inset Formula $\Upsilon$
20901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20904 \begin_layout Plain Layout
20912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20915 \begin_layout Plain Layout
20916 \begin_inset Formula $\Phi$
20926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20929 \begin_layout Plain Layout
20937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20940 \begin_layout Plain Layout
20941 \begin_inset Formula $\Psi$
20951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20954 \begin_layout Plain Layout
20962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20965 \begin_layout Plain Layout
20966 \begin_inset Formula $\Omega$
20980 \begin_inset space \hfill{}
20986 \begin_layout Standard
20987 \begin_inset VSpace medskip
20990 That the big Greek letters appear upright is caused by a design bug when
20992 To get correct italic big letters, begin every command with
20997 For example the command
21004 \begin_inset Formula $\varGamma$
21008 Another way is to load the package
21016 \begin_layout Plain Layout
21021 is part of the LaTeX-package
21026 \begin_inset Index idx
21029 \begin_layout Plain Layout
21034 \begin_layout Plain Layout
21054 \begin_inset Index idx
21057 \begin_layout Plain Layout
21063 with the LaTeX-preamble line
21066 \begin_layout Standard
21071 usepackage{fixmath}
21074 \begin_layout Standard
21075 Then all big Greek letters in a document will automatically be typeset italic.
21078 \begin_layout Subsection
21080 \begin_inset Index idx
21083 \begin_layout Plain Layout
21084 Greek letters ! bold
21092 \begin_layout Standard
21093 Greek letters cannot be set with different font styles like Latin letters.
21094 They can only be made bold with the command
21101 \begin_inset Index idx
21104 \begin_layout Plain Layout
21115 \begin_layout Standard
21117 \begin_inset Tabular
21118 <lyxtabular version="3" rows="3" columns="2">
21119 <features rotate="0" tabularvalignment="middle">
21120 <column alignment="center" valignment="top">
21121 <column alignment="center" valignment="top">
21123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21126 \begin_layout Plain Layout
21132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21135 \begin_layout Plain Layout
21143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21146 \begin_layout Plain Layout
21158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21161 \begin_layout Plain Layout
21162 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21175 \begin_layout Plain Layout
21187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21190 \begin_layout Plain Layout
21191 \begin_inset Formula $\theta\boldsymbol{\theta}$
21207 \begin_layout Section
21212 \begin_layout Plain Layout
21225 \begin_layout Plain Layout
21226 A list with all symbols of most of the LaTeX-packages can be found in
21227 \begin_inset CommandInset citation
21242 \begin_layout Plain Layout
21250 \begin_inset Note Note
21253 \begin_layout Plain Layout
21256 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21259 \begin_layout Plain Layout
21262 texorpdfstring is in section
21263 \begin_inset CommandInset ref
21265 reference "sub:Formulas-in-Section"
21275 \begin_inset Index idx
21278 \begin_layout Plain Layout
21287 \begin_layout Standard
21288 Many of the symbols listed in this section can also be inserted via the
21290 \begin_inset Graphics
21291 filename ../images/math/nabla.png
21297 \begin_inset Graphics
21298 filename ../images/math/digamma.png
21306 \begin_layout Subsection
21307 Mathematical Symbols
21308 \begin_inset CommandInset label
21310 name "sub:Mathematical-Symbols"
21315 \begin_inset Index idx
21318 \begin_layout Plain Layout
21319 Symbols ! mathematical
21327 \begin_layout Standard
21328 \begin_inset space \hfill{}
21332 \begin_inset Tabular
21333 <lyxtabular version="3" rows="10" columns="2">
21334 <features rotate="0" tabularvalignment="middle">
21335 <column alignment="center" valignment="top" width="0pt">
21336 <column alignment="center" valignment="top" width="0pt">
21338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21341 \begin_layout Plain Layout
21347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21350 \begin_layout Plain Layout
21358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21361 \begin_layout Plain Layout
21369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21372 \begin_layout Plain Layout
21373 \begin_inset Formula $\neg$
21383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21386 \begin_layout Plain Layout
21394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21397 \begin_layout Plain Layout
21398 \begin_inset Formula $\Im$
21408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21411 \begin_layout Plain Layout
21419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21422 \begin_layout Plain Layout
21423 \begin_inset Formula $\Re$
21433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21436 \begin_layout Plain Layout
21444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21447 \begin_layout Plain Layout
21448 \begin_inset Formula $\aleph$
21458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21461 \begin_layout Plain Layout
21469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21472 \begin_layout Plain Layout
21473 \begin_inset Formula $\partial$
21483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21486 \begin_layout Plain Layout
21494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21497 \begin_layout Plain Layout
21498 \begin_inset Formula $\infty$
21508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21511 \begin_layout Plain Layout
21519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21522 \begin_layout Plain Layout
21523 \begin_inset Formula $\wp$
21533 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21536 \begin_layout Plain Layout
21544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21547 \begin_layout Plain Layout
21548 \begin_inset Formula $\imath$
21558 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21561 \begin_layout Plain Layout
21569 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21572 \begin_layout Plain Layout
21573 \begin_inset Formula $\jmath$
21587 \begin_inset space \hfill{}
21591 \begin_inset Tabular
21592 <lyxtabular version="3" rows="10" columns="2">
21593 <features rotate="0" tabularvalignment="middle">
21594 <column alignment="center" valignment="top" width="0pt">
21595 <column alignment="center" valignment="top" width="0pt">
21597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21600 \begin_layout Plain Layout
21606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21609 \begin_layout Plain Layout
21611 \begin_inset Note Note
21614 \begin_layout Plain Layout
21621 is only used as spacer.
21633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21636 \begin_layout Plain Layout
21644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21647 \begin_layout Plain Layout
21648 \begin_inset Formula $\forall$
21658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21661 \begin_layout Plain Layout
21669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21672 \begin_layout Plain Layout
21673 \begin_inset Formula $\exists$
21683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21686 \begin_layout Plain Layout
21694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21697 \begin_layout Plain Layout
21698 \begin_inset Formula $\nexists$
21708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21711 \begin_layout Plain Layout
21719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21722 \begin_layout Plain Layout
21723 \begin_inset Formula $\emptyset$
21733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21736 \begin_layout Plain Layout
21744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21747 \begin_layout Plain Layout
21748 \begin_inset Formula $\varnothing$
21758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21761 \begin_layout Plain Layout
21769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21772 \begin_layout Plain Layout
21773 \begin_inset Formula $\dag$
21783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21786 \begin_layout Plain Layout
21794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21797 \begin_layout Plain Layout
21798 \begin_inset Formula $\ddag$
21808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21811 \begin_layout Plain Layout
21819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21822 \begin_layout Plain Layout
21826 \begin_layout Plain Layout
21836 \begin_inset Formula $\complement$
21843 \begin_layout Plain Layout
21857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21860 \begin_layout Plain Layout
21868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21871 \begin_layout Plain Layout
21872 \begin_inset Formula $\Bbbk$
21886 \begin_inset space \hfill{}
21890 \begin_inset Tabular
21891 <lyxtabular version="3" rows="10" columns="2">
21892 <features rotate="0" tabularvalignment="middle">
21893 <column alignment="center" valignment="top" width="0pt">
21894 <column alignment="center" valignment="top" width="0pt">
21896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21899 \begin_layout Plain Layout
21905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21908 \begin_layout Plain Layout
21916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21919 \begin_layout Plain Layout
21927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21930 \begin_layout Plain Layout
21931 \begin_inset Formula $\prime$
21941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21944 \begin_layout Plain Layout
21952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21955 \begin_layout Plain Layout
21956 \begin_inset Formula $\backprime$
21966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21969 \begin_layout Plain Layout
21977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21980 \begin_layout Plain Layout
21981 \begin_inset Formula $\mho$
21991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21994 \begin_layout Plain Layout
22002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22005 \begin_layout Plain Layout
22006 \begin_inset Formula $\triangle$
22016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22019 \begin_layout Plain Layout
22027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22030 \begin_layout Plain Layout
22031 \begin_inset Formula $\angle$
22041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22044 \begin_layout Plain Layout
22052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22055 \begin_layout Plain Layout
22056 \begin_inset Formula $\measuredangle$
22066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22069 \begin_layout Plain Layout
22077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22080 \begin_layout Plain Layout
22081 \begin_inset Formula $\sphericalangle$
22091 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22094 \begin_layout Plain Layout
22102 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22105 \begin_layout Plain Layout
22106 \begin_inset Formula $\top$
22116 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22119 \begin_layout Plain Layout
22127 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22130 \begin_layout Plain Layout
22131 \begin_inset Formula $\bot$
22145 \begin_inset space \hfill{}
22151 \begin_layout Subsection
22152 Miscellaneous Symbols
22153 \begin_inset CommandInset label
22155 name "sub:Miscellaneous-Symbols"
22160 \begin_inset Index idx
22163 \begin_layout Plain Layout
22164 Symbols ! miscellaneous
22172 \begin_layout Standard
22175 \begin_inset Tabular
22176 <lyxtabular version="3" rows="10" columns="2">
22177 <features rotate="0" tabularvalignment="middle">
22178 <column alignment="center" valignment="top" width="0pt">
22179 <column alignment="center" valignment="top" width="0pt">
22181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22184 \begin_layout Plain Layout
22190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22193 \begin_layout Plain Layout
22201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22204 \begin_layout Plain Layout
22212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22215 \begin_layout Plain Layout
22216 \begin_inset Formula $\flat$
22226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22229 \begin_layout Plain Layout
22237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22240 \begin_layout Plain Layout
22241 \begin_inset Formula $\natural$
22251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22254 \begin_layout Plain Layout
22262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22265 \begin_layout Plain Layout
22266 \begin_inset Formula $\sharp$
22276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22279 \begin_layout Plain Layout
22287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22290 \begin_layout Plain Layout
22291 \begin_inset Formula $\surd$
22301 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22304 \begin_layout Plain Layout
22312 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22315 \begin_layout Plain Layout
22316 \begin_inset Formula $\checkmark$
22326 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22329 \begin_layout Plain Layout
22337 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22340 \begin_layout Plain Layout
22341 \begin_inset Formula $\yen$
22351 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22354 \begin_layout Plain Layout
22362 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22365 \begin_layout Plain Layout
22366 \begin_inset Formula $\pounds$
22376 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22379 \begin_layout Plain Layout
22385 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22388 \begin_layout Plain Layout
22389 \begin_inset Formula $\$$
22399 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22402 \begin_layout Plain Layout
22408 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22411 \begin_layout Plain Layout
22412 \begin_inset Formula $§$
22426 \begin_inset Tabular
22427 <lyxtabular version="3" rows="10" columns="2">
22428 <features rotate="0" tabularvalignment="middle">
22429 <column alignment="center" valignment="top">
22430 <column alignment="center" valignment="top">
22432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22435 \begin_layout Plain Layout
22441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22444 \begin_layout Plain Layout
22452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22455 \begin_layout Plain Layout
22463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22466 \begin_layout Plain Layout
22467 \begin_inset Formula $\hbar$
22477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22480 \begin_layout Plain Layout
22488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22491 \begin_layout Plain Layout
22492 \begin_inset Formula $\hslash$
22502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22505 \begin_layout Plain Layout
22513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22516 \begin_layout Plain Layout
22517 \begin_inset Formula $\clubsuit$
22527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22530 \begin_layout Plain Layout
22538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22541 \begin_layout Plain Layout
22542 \begin_inset Formula $\spadesuit$
22552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22555 \begin_layout Plain Layout
22563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22566 \begin_layout Plain Layout
22567 \begin_inset Formula $\bigstar$
22577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22580 \begin_layout Plain Layout
22588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22591 \begin_layout Plain Layout
22592 \begin_inset Formula $\blacklozenge$
22602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22605 \begin_layout Plain Layout
22613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22616 \begin_layout Plain Layout
22617 \begin_inset Formula $\blacktriangle$
22627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22630 \begin_layout Plain Layout
22638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22641 \begin_layout Plain Layout
22642 \begin_inset Formula $\blacktriangledown$
22652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22655 \begin_layout Plain Layout
22663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22666 \begin_layout Plain Layout
22667 \begin_inset Formula $\bullet$
22681 \begin_inset Tabular
22682 <lyxtabular version="3" rows="10" columns="2">
22683 <features rotate="0" tabularvalignment="middle">
22684 <column alignment="center" valignment="top" width="0pt">
22685 <column alignment="center" valignment="top" width="0pt">
22687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22690 \begin_layout Plain Layout
22696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22699 \begin_layout Plain Layout
22707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22710 \begin_layout Plain Layout
22718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22721 \begin_layout Plain Layout
22722 \begin_inset Formula $\diamondsuit$
22732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22735 \begin_layout Plain Layout
22743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22746 \begin_layout Plain Layout
22747 \begin_inset Formula $\Diamond$
22757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22760 \begin_layout Plain Layout
22768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22771 \begin_layout Plain Layout
22772 \begin_inset Formula $\heartsuit$
22782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22785 \begin_layout Plain Layout
22793 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22796 \begin_layout Plain Layout
22797 \begin_inset Formula $\P$
22807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22810 \begin_layout Plain Layout
22818 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22821 \begin_layout Plain Layout
22822 \begin_inset Formula $\copyright$
22832 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22835 \begin_layout Plain Layout
22843 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22846 \begin_layout Plain Layout
22847 \begin_inset Formula $\circledR$
22857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22860 \begin_layout Plain Layout
22868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22871 \begin_layout Plain Layout
22872 \begin_inset Formula $\maltese$
22882 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22885 \begin_layout Plain Layout
22893 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22896 \begin_layout Plain Layout
22897 \begin_inset Formula $\diagup$
22907 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22910 \begin_layout Plain Layout
22918 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22921 \begin_layout Plain Layout
22922 \begin_inset Formula $\diagdown$
22938 \begin_layout Standard
22939 \begin_inset VSpace medskip
22944 \begin_layout Standard
22945 Some symbols can be displayed in different sizes, see
22946 \begin_inset CommandInset ref
22948 reference "sub:Font-Sizes"
22955 \begin_layout Subsection
22957 \begin_inset Index idx
22960 \begin_layout Plain Layout
22961 Symbols ! Euro-symbol
22967 \begin_inset Index idx
22970 \begin_layout Plain Layout
22977 \begin_layout Plain Layout
22994 \begin_layout Standard
22995 To use the Euro symbol in formulas, the LaTeX-package
23000 \begin_inset Index idx
23003 \begin_layout Plain Layout
23009 must be installed and loaded with the LaTeX-preamble line
23012 \begin_layout Standard
23017 usepackage[gennarrow]{eurosym}
23020 \begin_layout Standard
23021 The Euro symbol can now be inserted with the command
23028 \begin_inset Index idx
23031 \begin_layout Plain Layout
23042 \begin_layout Standard
23043 The Euro symbol can directly be inserted with the € key in mathematical
23044 text, without having
23059 can also be inserted in TeX-mode.
23060 The official currency symbol can then be inserted with the command
23067 \begin_inset Index idx
23070 \begin_layout Plain Layout
23078 , that is only available in TeX-mode.
23081 \begin_layout Standard
23085 \begin_layout Plain Layout
23095 \begin_inset Note Note
23098 \begin_layout Plain Layout
23099 The following table will only be displayed when the LaTeX-package
23111 \begin_layout Standard
23112 An overview about the different Euro symbols:
23115 \begin_layout Standard
23117 \begin_inset Tabular
23118 <lyxtabular version="3" rows="4" columns="3">
23119 <features rotate="0" tabularvalignment="middle">
23120 <column alignment="center" valignment="top" width="0pt">
23121 <column alignment="center" valignment="top" width="0pt">
23122 <column alignment="center" valignment="top" width="0pt">
23124 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23127 \begin_layout Plain Layout
23133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23136 \begin_layout Plain Layout
23142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23145 \begin_layout Plain Layout
23153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23156 \begin_layout Plain Layout
23162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23165 \begin_layout Plain Layout
23173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23176 \begin_layout Plain Layout
23177 \begin_inset Formula $\euro$
23187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23190 \begin_layout Plain Layout
23196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23199 \begin_layout Plain Layout
23205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23208 \begin_layout Plain Layout
23209 \begin_inset Formula $\mbox{€}$
23219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23222 \begin_layout Plain Layout
23228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23231 \begin_layout Plain Layout
23239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23242 \begin_layout Plain Layout
23246 \begin_layout Plain Layout
23268 \begin_layout Standard
23272 \begin_layout Plain Layout
23282 \begin_inset Note Note
23285 \begin_layout Plain Layout
23286 The following will be displayed when the LaTeX-package
23298 \begin_layout Standard
23299 You need to install the LaTeX-package
23303 to see the rest of this subsection in the output.
23306 \begin_layout Standard
23310 \begin_layout Plain Layout
23322 \begin_layout Section
23324 \begin_inset CommandInset label
23326 name "sec:Relations"
23331 \begin_inset Index idx
23334 \begin_layout Plain Layout
23341 \begin_inset Index idx
23344 \begin_layout Plain Layout
23349 \begin_layout Plain Layout
23360 \begin_layout Plain Layout
23375 \begin_layout Standard
23376 All relations can also be inserted via the toolbar button
23377 \begin_inset Graphics
23378 filename ../images/math/leq.png
23386 \begin_layout Standard
23387 \begin_inset space \hfill{}
23391 \begin_inset Tabular
23392 <lyxtabular version="3" rows="17" columns="2">
23393 <features rotate="0" tabularvalignment="middle">
23394 <column alignment="center" valignment="top" width="0pt">
23395 <column alignment="center" valignment="top" width="0pt">
23397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23400 \begin_layout Plain Layout
23406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23409 \begin_layout Plain Layout
23417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23420 \begin_layout Plain Layout
23426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23429 \begin_layout Plain Layout
23430 \begin_inset Formula $<$
23440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23443 \begin_layout Plain Layout
23451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23454 \begin_layout Plain Layout
23455 \begin_inset Formula $\le$
23465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23468 \begin_layout Plain Layout
23476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23479 \begin_layout Plain Layout
23480 \begin_inset Formula $\ll$
23490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23493 \begin_layout Plain Layout
23501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23504 \begin_layout Plain Layout
23505 \begin_inset Formula $\prec$
23515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23518 \begin_layout Plain Layout
23526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23529 \begin_layout Plain Layout
23530 \begin_inset Formula $\preceq$
23540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23543 \begin_layout Plain Layout
23551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23554 \begin_layout Plain Layout
23555 \begin_inset Formula $\subset$
23565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23568 \begin_layout Plain Layout
23576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23579 \begin_layout Plain Layout
23580 \begin_inset Formula $\subseteq$
23590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23593 \begin_layout Plain Layout
23601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23604 \begin_layout Plain Layout
23605 \begin_inset Formula $\sqsubseteq$
23615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23618 \begin_layout Plain Layout
23626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23629 \begin_layout Plain Layout
23630 \begin_inset Formula $\in$
23640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23643 \begin_layout Plain Layout
23651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23654 \begin_layout Plain Layout
23655 \begin_inset Formula $\vdash$
23665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23668 \begin_layout Plain Layout
23676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23679 \begin_layout Plain Layout
23680 \begin_inset Formula $\smile$
23690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23693 \begin_layout Plain Layout
23701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23704 \begin_layout Plain Layout
23705 \begin_inset Formula $\lhd$
23715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23718 \begin_layout Plain Layout
23726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23729 \begin_layout Plain Layout
23730 \begin_inset Formula $\unlhd$
23740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23743 \begin_layout Plain Layout
23751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23754 \begin_layout Plain Layout
23755 \begin_inset Formula $\gtrless$
23765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23768 \begin_layout Plain Layout
23776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23779 \begin_layout Plain Layout
23780 \begin_inset Formula $\mid$
23790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23793 \begin_layout Plain Layout
23801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23804 \begin_layout Plain Layout
23805 \begin_inset Formula $\nmid$
23819 \begin_inset space \hfill{}
23823 \begin_inset Tabular
23824 <lyxtabular version="3" rows="17" columns="2">
23825 <features rotate="0" tabularvalignment="middle">
23826 <column alignment="center" valignment="top" width="0pt">
23827 <column alignment="center" valignment="top" width="0pt">
23829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23832 \begin_layout Plain Layout
23838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23841 \begin_layout Plain Layout
23849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23852 \begin_layout Plain Layout
23858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23861 \begin_layout Plain Layout
23862 \begin_inset Formula $=$
23872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23875 \begin_layout Plain Layout
23883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23886 \begin_layout Plain Layout
23887 \begin_inset Formula $\not=$
23897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23900 \begin_layout Plain Layout
23908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23911 \begin_layout Plain Layout
23912 \begin_inset Formula $\equiv$
23922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23925 \begin_layout Plain Layout
23933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23936 \begin_layout Plain Layout
23937 \begin_inset Formula $\sim$
23947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23950 \begin_layout Plain Layout
23958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23961 \begin_layout Plain Layout
23962 \begin_inset Formula $\simeq$
23972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23975 \begin_layout Plain Layout
23983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23986 \begin_layout Plain Layout
23987 \begin_inset Formula $\approx$
23997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24000 \begin_layout Plain Layout
24008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24011 \begin_layout Plain Layout
24012 \begin_inset Formula $\cong$
24022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24025 \begin_layout Plain Layout
24033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24036 \begin_layout Plain Layout
24037 \begin_inset Formula $\bowtie$
24047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24050 \begin_layout Plain Layout
24058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24061 \begin_layout Plain Layout
24062 \begin_inset Formula $\notin$
24072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24075 \begin_layout Plain Layout
24083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24086 \begin_layout Plain Layout
24087 \begin_inset Formula $\perp$
24097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24100 \begin_layout Plain Layout
24108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24111 \begin_layout Plain Layout
24112 \begin_inset Formula $\propto$
24122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24125 \begin_layout Plain Layout
24133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24136 \begin_layout Plain Layout
24137 \begin_inset Formula $\asymp$
24147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24150 \begin_layout Plain Layout
24158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24161 \begin_layout Plain Layout
24162 \begin_inset Formula $\doteq$
24172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24175 \begin_layout Plain Layout
24183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24186 \begin_layout Plain Layout
24187 \begin_inset Formula $\circeq$
24197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24200 \begin_layout Plain Layout
24208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24211 \begin_layout Plain Layout
24212 \begin_inset Formula $\models$
24222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24225 \begin_layout Plain Layout
24233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24236 \begin_layout Plain Layout
24237 \begin_inset Formula $\widehat{=}$
24251 \begin_inset space \hfill{}
24255 \begin_inset Tabular
24256 <lyxtabular version="3" rows="17" columns="2">
24257 <features rotate="0" tabularvalignment="middle">
24258 <column alignment="center" valignment="top" width="0pt">
24259 <column alignment="center" valignment="top" width="0pt">
24261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24264 \begin_layout Plain Layout
24270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24273 \begin_layout Plain Layout
24281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24284 \begin_layout Plain Layout
24290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24293 \begin_layout Plain Layout
24294 \begin_inset Formula $>$
24304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24307 \begin_layout Plain Layout
24315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24318 \begin_layout Plain Layout
24319 \begin_inset Formula $\ge$
24329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24332 \begin_layout Plain Layout
24340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24343 \begin_layout Plain Layout
24344 \begin_inset Formula $\gg$
24354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24357 \begin_layout Plain Layout
24365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24368 \begin_layout Plain Layout
24369 \begin_inset Formula $\succ$
24379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24382 \begin_layout Plain Layout
24390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24393 \begin_layout Plain Layout
24394 \begin_inset Formula $\succeq$
24404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24407 \begin_layout Plain Layout
24415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24418 \begin_layout Plain Layout
24419 \begin_inset Formula $\supset$
24429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24432 \begin_layout Plain Layout
24440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24443 \begin_layout Plain Layout
24444 \begin_inset Formula $\supseteq$
24454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24457 \begin_layout Plain Layout
24465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24468 \begin_layout Plain Layout
24469 \begin_inset Formula $\sqsupseteq$
24479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24482 \begin_layout Plain Layout
24490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24493 \begin_layout Plain Layout
24494 \begin_inset Formula $\ni$
24504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24507 \begin_layout Plain Layout
24515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24518 \begin_layout Plain Layout
24519 \begin_inset Formula $\dashv$
24529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24532 \begin_layout Plain Layout
24540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24543 \begin_layout Plain Layout
24544 \begin_inset Formula $\frown$
24554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24557 \begin_layout Plain Layout
24565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24568 \begin_layout Plain Layout
24569 \begin_inset Formula $\rhd$
24579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24582 \begin_layout Plain Layout
24590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24593 \begin_layout Plain Layout
24594 \begin_inset Formula $\unrhd$
24604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24607 \begin_layout Plain Layout
24615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24618 \begin_layout Plain Layout
24619 \begin_inset Formula $\lessgtr$
24629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24632 \begin_layout Plain Layout
24640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24643 \begin_layout Plain Layout
24644 \begin_inset Formula $\parallel$
24654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24657 \begin_layout Plain Layout
24665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24668 \begin_layout Plain Layout
24669 \begin_inset Formula $\nparallel$
24683 \begin_inset space \hfill{}
24689 \begin_layout Standard
24690 \begin_inset VSpace medskip
24705 are bigger than the equal looking operators
24720 \begin_layout Standard
24721 Relations are, in contrary to symbols, always surrounded by space.
24724 \begin_layout Standard
24725 Relations with labels can be created with the command
24732 \begin_inset Index idx
24735 \begin_layout Plain Layout
24746 \begin_layout Standard
24748 \begin_inset Tabular
24749 <lyxtabular version="3" rows="2" columns="2">
24750 <features rotate="0" tabularvalignment="middle">
24751 <column alignment="center" valignment="top">
24752 <column alignment="center" valignment="top">
24754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24757 \begin_layout Plain Layout
24763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24766 \begin_layout Plain Layout
24768 \begin_inset Note Note
24771 \begin_layout Plain Layout
24778 is only used as spacer.
24790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24793 \begin_layout Plain Layout
24800 \begin_layout Plain Layout
24817 \begin_layout Plain Layout
24827 \begin_inset Formula $\downarrow$
24836 \begin_layout Plain Layout
24849 \begin_layout Plain Layout
24863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24866 \begin_layout Plain Layout
24867 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24883 \begin_layout Section
24887 \begin_layout Subsection
24888 Predefined Functions
24889 \begin_inset CommandInset label
24891 name "sub:Predefined-Functions"
24896 \begin_inset Index idx
24899 \begin_layout Plain Layout
24900 Functions ! predefined
24908 \begin_layout Standard
24909 In general, variables are set
24913 in mathematical expressions, but not function names, because
24914 \begin_inset Formula $sin$
24917 could be misunderstood as
24918 \begin_inset Formula $s\cdot i\cdot n$
24922 Therefore there are predefined functionswhich are additionally a bit separated
24924 They are inserted as commands starting with a backslash before their name.
24927 \begin_layout Standard
24929 \begin_inset Tabular
24930 <lyxtabular version="3" rows="2" columns="4">
24931 <features rotate="0" tabularvalignment="middle">
24932 <column alignment="center" valignment="top" width="0pt">
24933 <column alignment="center" valignment="top" width="0pt">
24934 <column alignment="center" valignment="top" width="0pt">
24935 <column alignment="center" valignment="top" width="0pt">
24937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24940 \begin_layout Plain Layout
24946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24949 \begin_layout Plain Layout
24955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24958 \begin_layout Plain Layout
24964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24967 \begin_layout Plain Layout
24975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24978 \begin_layout Plain Layout
24984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24987 \begin_layout Plain Layout
24988 \begin_inset Formula $Asin(x)+B$
24996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24999 \begin_layout Plain Layout
25007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25010 \begin_layout Plain Layout
25011 \begin_inset Formula $A\sin(x)+B$
25027 \begin_layout Standard
25028 The following functions are predefined:
25031 \begin_layout Standard
25032 \begin_inset VSpace -2mm
25038 \begin_layout Standard
25040 \begin_inset Tabular
25041 <lyxtabular version="3" rows="9" columns="4">
25042 <features rotate="0" tabularvalignment="middle">
25043 <column alignment="center" valignment="top" width="0pt">
25044 <column alignment="center" valignment="top" width="0pt">
25045 <column alignment="center" valignment="top" width="0pt">
25046 <column alignment="center" valignment="top" width="0pt">
25048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25051 \begin_layout Plain Layout
25057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25060 \begin_layout Plain Layout
25066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25069 \begin_layout Plain Layout
25075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25078 \begin_layout Plain Layout
25086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25089 \begin_layout Plain Layout
25097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25100 \begin_layout Plain Layout
25108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25111 \begin_layout Plain Layout
25119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25122 \begin_layout Plain Layout
25132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25135 \begin_layout Plain Layout
25143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25146 \begin_layout Plain Layout
25154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25157 \begin_layout Plain Layout
25165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25168 \begin_layout Plain Layout
25178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25181 \begin_layout Plain Layout
25189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25192 \begin_layout Plain Layout
25200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25203 \begin_layout Plain Layout
25211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25214 \begin_layout Plain Layout
25224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25227 \begin_layout Plain Layout
25235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25238 \begin_layout Plain Layout
25246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25249 \begin_layout Plain Layout
25257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25260 \begin_layout Plain Layout
25270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25273 \begin_layout Plain Layout
25281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25284 \begin_layout Plain Layout
25292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25295 \begin_layout Plain Layout
25303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25306 \begin_layout Plain Layout
25316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25319 \begin_layout Plain Layout
25327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25330 \begin_layout Plain Layout
25338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25341 \begin_layout Plain Layout
25349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25352 \begin_layout Plain Layout
25362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25365 \begin_layout Plain Layout
25373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25376 \begin_layout Plain Layout
25384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25387 \begin_layout Plain Layout
25395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25398 \begin_layout Plain Layout
25408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25411 \begin_layout Plain Layout
25419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25422 \begin_layout Plain Layout
25430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25433 \begin_layout Plain Layout
25441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25444 \begin_layout Plain Layout
25460 \begin_layout Standard
25461 They can also be inserted with the math toolbar button
25462 \begin_inset Graphics
25463 filename ../images/math/functions.png
25471 \begin_layout Subsection
25472 Self-defined Functions
25473 \begin_inset Index idx
25476 \begin_layout Plain Layout
25477 Functions ! self-defined
25485 \begin_layout Standard
25486 To use a function that is not predefined, like for example the sign function
25487 sgn(x), there are two possibilities:
25490 \begin_layout Itemize
25491 Define the function by inserting the following line to the LaTeX-preamble
25495 \begin_layout Plain Layout
25500 DeclareMathOperator
25503 \begin_inset CommandInset ref
25505 reference "sub:Self-defined-Operators"
25515 \begin_inset Newline newline
25519 \begin_inset VSpace -3mm
25523 \begin_inset Newline newline
25530 DeclareMathOperator{
25535 \begin_inset Index idx
25538 \begin_layout Plain Layout
25543 DeclareMathOperator
25549 \begin_inset Newline newline
25553 \begin_inset VSpace -2mm
25557 \begin_inset Newline newline
25560 Now the new defined function can be called with the command
25569 \begin_layout Itemize
25570 Write the formula as usual, mark the formula name, in our example the letters
25575 , and change it to mathematical text.
25576 Finally, a space is inserted between prefactor and function.
25579 \begin_layout Standard
25580 The result is the same with both methods as with a predefined function
25584 \begin_layout Plain Layout
25585 In LyX self-defined functions are displayed red, predefined ones black.
25593 \begin_layout Standard
25595 \begin_inset Tabular
25596 <lyxtabular version="3" rows="3" columns="2">
25597 <features rotate="0" tabularvalignment="middle">
25598 <column alignment="center" valignment="top" width="0pt">
25599 <column alignment="center" valignment="top" width="0pt">
25601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25604 \begin_layout Plain Layout
25610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25613 \begin_layout Plain Layout
25621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25624 \begin_layout Plain Layout
25632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25635 \begin_layout Plain Layout
25636 \begin_inset Formula $A\sgn(x)+B$
25646 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25649 \begin_layout Plain Layout
25653 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25664 \begin_layout Plain Layout
25665 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25681 \begin_layout Standard
25682 The first method is more suitable when the self-defined function should
25683 be used several times.
25686 \begin_layout Subsection
25688 \begin_inset Index idx
25691 \begin_layout Plain Layout
25700 \begin_layout Standard
25701 For limits, in addition to the commands
25708 \begin_inset Index idx
25711 \begin_layout Plain Layout
25731 the following functions are defined:
25734 \begin_layout Standard
25736 \begin_inset Tabular
25737 <lyxtabular version="3" rows="5" columns="2">
25738 <features rotate="0" tabularvalignment="middle">
25739 <column alignment="center" valignment="top">
25740 <column alignment="center" valignment="top">
25742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25745 \begin_layout Plain Layout
25751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25754 \begin_layout Plain Layout
25756 \begin_inset Note Note
25759 \begin_layout Plain Layout
25766 is only used as spacer.
25778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25781 \begin_layout Plain Layout
25789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25792 \begin_layout Plain Layout
25793 \begin_inset Formula $\varliminf$
25803 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25806 \begin_layout Plain Layout
25814 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25817 \begin_layout Plain Layout
25818 \begin_inset Formula $\varlimsup$
25828 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25831 \begin_layout Plain Layout
25839 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25842 \begin_layout Plain Layout
25843 \begin_inset Formula $\varprojlim$
25853 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25856 \begin_layout Plain Layout
25864 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25867 \begin_layout Plain Layout
25868 \begin_inset Formula $\varinjlim$
25872 \begin_inset Formula $\raisebox{-2.5mm}{}$
25888 \begin_layout Standard
25889 \begin_inset VSpace medskip
25892 The limit is created by inserting a subscript.
25893 It is set right beside the function in an inline formula:
25896 \begin_layout Standard
25898 \begin_inset Tabular
25899 <lyxtabular version="3" rows="2" columns="2">
25900 <features rotate="0" tabularvalignment="middle">
25901 <column alignment="center" valignment="top" width="0pt">
25902 <column alignment="center" valignment="top" width="0pt">
25904 <cell alignment="center" valignment="top" usebox="none">
25907 \begin_layout Plain Layout
25913 <cell alignment="center" valignment="top" usebox="none">
25916 \begin_layout Plain Layout
25917 \begin_inset space \hspace{}
25922 \begin_inset Note Note
25925 \begin_layout Plain Layout
25932 are used here as spacer.
25944 <cell alignment="center" valignment="top" usebox="none">
25947 \begin_layout Plain Layout
25956 \begin_layout Plain Layout
25969 \begin_layout Plain Layout
25983 <cell alignment="center" valignment="top" usebox="none">
25986 \begin_layout Plain Layout
25987 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
26003 \begin_layout Standard
26004 In a displayed formula the limit is set below the formula, as usual:
26005 \begin_inset Formula
26015 \begin_layout Subsection
26017 \begin_inset Index idx
26020 \begin_layout Plain Layout
26021 Functions ! modulo-
26029 \begin_layout Standard
26030 The modulo-function is special, because it exists in four variants.
26031 The variants in a displayed formula are:
26032 \begin_inset Formula
26034 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26035 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
26036 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
26037 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
26038 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
26046 \begin_layout Standard
26047 In an inline formula less space is set before the function names for all
26049 By default the modulo-functions take only the first following character
26051 To use more than one character, one has to put them into TeX-braces:
26052 \begin_inset Formula
26054 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26055 \mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\
26056 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26064 \begin_layout Section
26066 \begin_inset Index idx
26069 \begin_layout Plain Layout
26078 \begin_layout Subsection
26079 Special Characters in Mathematical Text
26082 \begin_layout Standard
26083 The following commands can only be used in mathematical text or in TeX-mode:
26086 \begin_layout Standard
26087 \begin_inset space \hfill{}
26091 \begin_inset Tabular
26092 <lyxtabular version="3" rows="8" columns="2">
26093 <features rotate="0" tabularvalignment="middle">
26094 <column alignment="block" valignment="top">
26095 <column alignment="block" valignment="top">
26097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26100 \begin_layout Plain Layout
26106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26109 \begin_layout Plain Layout
26117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26120 \begin_layout Plain Layout
26128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26131 \begin_layout Plain Layout
26132 \begin_inset Formula $\textrm{œ}$
26142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26145 \begin_layout Plain Layout
26153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26156 \begin_layout Plain Layout
26157 \begin_inset Formula $\textrm{Œ}$
26167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26170 \begin_layout Plain Layout
26178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26181 \begin_layout Plain Layout
26182 \begin_inset Formula $\textrm{æ}$
26192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26195 \begin_layout Plain Layout
26203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26206 \begin_layout Plain Layout
26207 \begin_inset Formula $\textrm{Æ}$
26217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26220 \begin_layout Plain Layout
26228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26231 \begin_layout Plain Layout
26232 \begin_inset Formula $\textrm{\aa}$
26242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26245 \begin_layout Plain Layout
26249 \begin_inset Index idx
26252 \begin_layout Plain Layout
26259 \begin_layout Plain Layout
26280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26283 \begin_layout Plain Layout
26284 \begin_inset Formula $\textrm{Å}$
26294 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26297 \begin_layout Plain Layout
26305 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26308 \begin_layout Plain Layout
26309 \begin_inset Formula $\textrm{ı}$
26323 \begin_inset space \hfill{}
26327 \begin_inset Tabular
26328 <lyxtabular version="3" rows="8" columns="2">
26329 <features rotate="0" tabularvalignment="middle">
26330 <column alignment="block" valignment="top">
26331 <column alignment="center" valignment="top">
26333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26336 \begin_layout Plain Layout
26338 \begin_inset Note Note
26341 \begin_layout Plain Layout
26343 \begin_inset space \thinspace{}
26346 mm is used for separation, because otherwise the output will be ¡ and ¿
26357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26360 \begin_layout Plain Layout
26368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26371 \begin_layout Plain Layout
26379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26382 \begin_layout Plain Layout
26383 \begin_inset Formula $\textrm{ø}$
26393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26396 \begin_layout Plain Layout
26404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26407 \begin_layout Plain Layout
26408 \begin_inset Formula $\textrm{Ø}$
26418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26421 \begin_layout Plain Layout
26429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26432 \begin_layout Plain Layout
26433 \begin_inset Formula $\textrm{ł}$
26443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26446 \begin_layout Plain Layout
26454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26457 \begin_layout Plain Layout
26458 \begin_inset Formula $\textrm{Ł}$
26468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26471 \begin_layout Plain Layout
26473 \begin_inset space \hspace{}
26481 \begin_layout Plain Layout
26495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26498 \begin_layout Plain Layout
26499 \begin_inset Formula $\textrm{!`}$
26509 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26512 \begin_layout Plain Layout
26514 \begin_inset space \hspace{}
26522 \begin_layout Plain Layout
26536 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26539 \begin_layout Plain Layout
26540 \begin_inset Formula $\textrm{?`}$
26550 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26553 \begin_layout Plain Layout
26561 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26564 \begin_layout Plain Layout
26565 \begin_inset Formula $\textrm{ȷ}$
26579 \begin_inset space \hfill{}
26585 \begin_layout Standard
26587 \begin_inset Formula $\textrm{\textrm{Å}}$
26591 \begin_inset Formula $\textrm{\textrm{Ø}}$
26594 can also be inserted via the math toolbar button
26595 \begin_inset Graphics
26596 filename ../images/math/digamma.png
26604 \begin_layout Standard
26605 An exception are the commands
26608 \begin_inset space \hspace{}
26617 \begin_inset space \hspace{}
26623 , because they can be inserted in LyX directly to text.
26626 \begin_layout Subsection
26628 \begin_inset CommandInset label
26630 name "sub:Accents-in-Text"
26635 \begin_inset Index idx
26638 \begin_layout Plain Layout
26647 \begin_layout Standard
26648 With the following commands all letters can be accented.
26649 The commands must be inserted in TeX-mode.
26652 \begin_layout Standard
26653 \begin_inset space \hfill{}
26657 \begin_inset Tabular
26658 <lyxtabular version="3" rows="8" columns="2">
26659 <features rotate="0" tabularvalignment="middle">
26660 <column alignment="block" valignment="top">
26661 <column alignment="block" valignment="top">
26663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26666 \begin_layout Plain Layout
26672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26675 \begin_layout Plain Layout
26683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26686 \begin_layout Plain Layout
26690 \begin_inset Quotes grd
26698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26701 \begin_layout Plain Layout
26705 \begin_layout Plain Layout
26721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26724 \begin_layout Plain Layout
26732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26735 \begin_layout Plain Layout
26739 \begin_layout Plain Layout
26755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26758 \begin_layout Plain Layout
26765 \begin_layout Plain Layout
26779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26782 \begin_layout Plain Layout
26786 \begin_layout Plain Layout
26802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26805 \begin_layout Plain Layout
26813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26816 \begin_layout Plain Layout
26820 \begin_layout Plain Layout
26836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26839 \begin_layout Plain Layout
26846 \begin_layout Plain Layout
26860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26863 \begin_layout Plain Layout
26867 \begin_layout Plain Layout
26883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26886 \begin_layout Plain Layout
26893 \begin_layout Plain Layout
26907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26910 \begin_layout Plain Layout
26914 \begin_layout Plain Layout
26930 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26933 \begin_layout Plain Layout
26940 \begin_layout Plain Layout
26954 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26957 \begin_layout Plain Layout
26961 \begin_layout Plain Layout
26981 \begin_inset space \hfill{}
26985 \begin_inset Tabular
26986 <lyxtabular version="3" rows="8" columns="2">
26987 <features rotate="0" tabularvalignment="middle">
26988 <column alignment="block" valignment="top">
26989 <column alignment="center" valignment="top">
26991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26994 \begin_layout Plain Layout
27000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27003 \begin_layout Plain Layout
27011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27014 \begin_layout Plain Layout
27021 \begin_layout Plain Layout
27035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27038 \begin_layout Plain Layout
27042 \begin_layout Plain Layout
27058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27061 \begin_layout Plain Layout
27069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27072 \begin_layout Plain Layout
27076 \begin_layout Plain Layout
27092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27095 \begin_layout Plain Layout
27099 \begin_inset Index idx
27102 \begin_layout Plain Layout
27113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27116 \begin_layout Plain Layout
27120 \begin_layout Plain Layout
27136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27139 \begin_layout Plain Layout
27147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27150 \begin_layout Plain Layout
27154 \begin_layout Plain Layout
27170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27173 \begin_layout Plain Layout
27180 \begin_layout Plain Layout
27194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27197 \begin_layout Plain Layout
27201 \begin_layout Plain Layout
27217 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27220 \begin_layout Plain Layout
27227 \begin_layout Plain Layout
27241 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27244 \begin_layout Plain Layout
27248 \begin_layout Plain Layout
27264 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27267 \begin_layout Plain Layout
27274 \begin_layout Plain Layout
27288 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27291 \begin_layout Plain Layout
27295 \begin_layout Plain Layout
27315 \begin_inset space \hfill{}
27321 \begin_layout Standard
27322 \begin_inset VSpace medskip
27331 also two different characters can be accented.
27340 \begin_layout Plain Layout
27355 \begin_layout Plain Layout
27367 \begin_layout Standard
27380 can in combination with vowels directly be inserted with the keyboard without
27382 The same applies for the tilde
27386 \begin_layout Plain Layout
27387 This only applies for keyboards where the tilde is defined as accent.
27396 in combination with
27411 \begin_layout Standard
27454 and accents that are inserted directly with the keyboard are also available
27455 in mathematical text.
27456 For the other accents there are special math commands to be used in formulas,
27458 \begin_inset CommandInset ref
27460 reference "sub:Accents-for-one"
27467 \begin_layout Standard
27468 \begin_inset VSpace bigskip
27471 Furthermore, with the command
27478 \begin_inset Index idx
27481 \begin_layout Plain Layout
27489 all numbers and letters can be set into a circle, quasi accented with a
27490 circle, similar to the copyright symbol.
27493 \begin_layout Standard
27495 \begin_inset Tabular
27496 <lyxtabular version="3" rows="3" columns="2">
27497 <features rotate="0" tabularvalignment="middle">
27498 <column alignment="center" valignment="top">
27499 <column alignment="center" valignment="top">
27501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27504 \begin_layout Plain Layout
27510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27513 \begin_layout Plain Layout
27515 \begin_inset Note Note
27518 \begin_layout Plain Layout
27525 is only used as spacer.
27537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27540 \begin_layout Plain Layout
27548 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27551 \begin_layout Plain Layout
27555 \begin_layout Plain Layout
27571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27574 \begin_layout Plain Layout
27585 raisebox{-1.5pt}{W}}
27590 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27593 \begin_layout Plain Layout
27594 \begin_inset Formula $\raisebox{4.5mm}{}$
27601 \begin_layout Plain Layout
27619 \begin_inset Formula $\raisebox{-2mm}{}$
27635 \begin_layout Standard
27636 One has to take care that the character fits in the circle.
27647 \begin_layout Plain Layout
27649 \begin_inset CommandInset ref
27651 reference "sub:Font-Sizes"
27660 specifies thereby the size of the circle.
27671 \begin_layout Plain Layout
27673 \begin_inset CommandInset ref
27675 reference "sub:Boxes-without-Frame"
27684 the character can be centered.
27687 \begin_layout Subsection
27689 \begin_inset Index idx
27692 \begin_layout Plain Layout
27701 \begin_layout Standard
27702 Old-style figures (also known as old-style numerals) are created with the
27710 \begin_inset Index idx
27713 \begin_layout Plain Layout
27722 The command can be used in formulas and in TeX-mode.
27723 The command scheme is:
27726 \begin_layout Standard
27731 oldstylenums{number}
27734 \begin_layout Standard
27739 oldstylenums{0123456789
27742 \begin_inset Formula $\oldstylenums{0123456789}$
27748 \begin_layout Section
27750 \begin_inset CommandInset label
27752 name "sec:Formula-Styles"
27757 \begin_inset Index idx
27760 \begin_layout Plain Layout
27769 \begin_layout Itemize
27770 There are two different alignment styles:
27774 \begin_layout Description
27775 Centered is the predefined standard
27778 \begin_layout Description
27779 Indented for this the option
27783 must be inserted in the menu
27785 Document\SpecialChar \menuseparator
27791 \begin_inset space ~
27797 \begin_layout Standard
27802 is used, the indentation can be adjusted with the length
27809 \begin_inset Index idx
27812 \begin_layout Plain Layout
27821 Should the distance be 15
27822 \begin_inset space \thinspace{}
27825 mm, the following command line is inserted in the LaTeX-preamble
27828 \begin_layout Standard
27838 \begin_layout Standard
27839 When no length is specified, the predefined value of 30
27840 \begin_inset space \thinspace{}
27847 \begin_layout Itemize
27848 And two different numbering styles:
27852 \begin_layout Description
27853 Right is the predefined standard
27856 \begin_layout Description
27857 Left for this the option
27861 must be inserted in the menu
27863 Document\SpecialChar \menuseparator
27869 \begin_inset space ~
27876 \begin_layout Standard
27885 can also be used together.
27886 In this case both options are inserted, separated by a comma.
27889 \begin_layout Standard
27890 The chosen styles are used for all displayed formulas of the document.
27891 When both, centered and indented formulas should be created in a document,
27897 The indented formulas are then set in a flalign environment, see
27898 \begin_inset CommandInset ref
27900 reference "sub:Flalign-Environment"
27907 \begin_layout Section
27909 \begin_inset CommandInset label
27911 name "sec:Multiline-Formulas"
27916 \begin_inset Index idx
27919 \begin_layout Plain Layout
27920 Formula ! multiline
27928 \begin_layout Subsection
27932 \begin_layout Standard
27933 In LyX multiline formulas are created by pressing
27938 arg "newline-insert newline"
27944 This creates either an
27946 eqnarray environment
27948 that is described in
27949 \begin_inset CommandInset ref
27951 reference "sub:Eqnarray-Environment"
27955 or, when the option
27957 Use AMS math package
27959 in the document settings is selected, an
27963 that is described in
27964 \begin_inset CommandInset ref
27966 reference "sub:Standard-align-Environment"
27971 The align environment is recommended because it provides in any case a
27972 typographically correct output.
27975 \begin_layout Standard
27976 There are other multiline formula environments that can be created via the
27979 Insert\SpecialChar \menuseparator
27983 These environments are described in the following sections.
27986 \begin_layout Standard
27987 In all multiline formula environments a new line is created by pressing
27991 arg "newline-insert newline"
27995 To add or delete lines, the math toolbar buttons
27996 \begin_inset Graphics
27997 filename ../images/tabular-feature_append-row.png
28003 \begin_inset Graphics
28004 filename ../images/tabular-feature_delete-row.png
28009 , respectively, or the menu
28011 Edit\SpecialChar \menuseparator
28017 \begin_layout Subsubsection
28019 \begin_inset CommandInset label
28021 name "sub:Line-Separation"
28026 \begin_inset Index idx
28029 \begin_layout Plain Layout
28030 Formula ! multiline ! Line separation
28038 \begin_layout Standard
28039 There is sometimes not enough space in multiline formulas between the lines:
28040 \begin_inset Formula
28042 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}\\
28043 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
28051 \begin_layout Standard
28052 In LaTeX additional line space is specified as optional argument of the
28054 This is not yet possible in LyX
28058 \begin_layout Plain Layout
28060 \begin_inset CommandInset href
28062 name "LyX-bug #1505"
28063 target "http://www.lyx.org/trac/ticket/1505"
28072 , therefore the whole formula must be inserted in TeX-mode.
28073 To add in our example space, the command
28081 is inserted at the end of the first line.
28086 \begin_layout Plain Layout
28093 \begin_layout Plain Layout
28095 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28098 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28105 \begin_layout Plain Layout
28109 left(B^{2}+x_{0}^{2}
28117 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28122 \begin_layout Plain Layout
28134 \begin_layout Standard
28135 \begin_inset VSpace bigskip
28138 To set the line separation for all lines in a formula, the length
28145 \begin_inset Index idx
28148 \begin_layout Plain Layout
28158 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28169 \begin_inset space \thinspace{}
28174 \begin_inset space \thinspace{}
28177 mm additional line separation as in the previous example, the command
28180 \begin_layout Standard
28190 \begin_layout Standard
28191 is inserted in TeX-mode before the formula.
28192 This requires that the LaTeX-package
28200 \begin_layout Plain Layout
28205 is part of every LaTeX standard installation.
28211 \begin_inset Index idx
28214 \begin_layout Plain Layout
28220 was loaded in LaTeX-preamble with the line
28223 \begin_layout Standard
28231 \begin_layout Standard
28236 \begin_layout Plain Layout
28248 \begin_inset Formula
28250 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}\\
28251 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
28259 \begin_layout Standard
28263 \begin_layout Plain Layout
28274 To get back to the predefined distance,
28280 is set to the value 3
28281 \begin_inset space \thinspace{}
28287 \begin_layout Subsubsection
28289 \begin_inset CommandInset label
28291 name "sub:Column-Separation"
28296 \begin_inset Index idx
28299 \begin_layout Plain Layout
28300 Formula ! multiline ! Column separation
28308 \begin_layout Standard
28309 Multiline formulas form a matrix.
28310 A formula in the eqnarray environment is for example a matrix with three
28312 By changing the column separation in this environment, the space beside
28313 the relation sign can be changed.
28316 \begin_layout Standard
28317 The column separation is specified with the length
28324 \begin_inset Index idx
28327 \begin_layout Plain Layout
28336 \begin_inset Newline newline
28339 column separation = 2
28340 \begin_inset space \thinspace{}
28350 \begin_inset Newline newline
28356 \begin_layout Standard
28366 \begin_layout Standard
28367 inserted in TeX-mode, sets for all following formulas a column separation
28369 \begin_inset space \thinspace{}
28373 To get back to the predefined distance,
28380 \begin_inset space \thinspace{}
28386 \begin_layout Standard
28388 \begin_inset space \thinspace{}
28391 cm column separation:
28395 \begin_layout Plain Layout
28407 \begin_inset Formula
28415 A formula with the predefined column separation for matrices of 10
28416 \begin_inset space \thinspace{}
28423 \begin_layout Plain Layout
28435 \begin_inset Formula
28446 \begin_layout Subsubsection
28448 \begin_inset Index idx
28451 \begin_layout Plain Layout
28460 \begin_layout Standard
28461 Long formulas can be typeset using these methods:
28464 \begin_layout Itemize
28465 When one side of the equation is much shorter than the line width, this
28466 one is chosen for the left side and the right side is typeset over two
28468 \begin_inset Formula
28470 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 \\
28471 & & -\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}
28476 The minus sign at the beginning of the second line does normally not appear
28477 as an operator because it is the first character of the line.
28478 Thus it would not be surrounded by space and could not be distinguished
28479 from the fraction bar.
28481 \begin_inset space \thinspace{}
28484 pt space was inserted behind the minus sign with the command
28494 \begin_layout Plain Layout
28502 \begin_inset CommandInset ref
28504 reference "sub:Variable-Space"
28514 \begin_inset Index idx
28517 \begin_layout Plain Layout
28528 \begin_layout Itemize
28529 When both sides of the equation are too long, the command
28536 \begin_inset Index idx
28539 \begin_layout Plain Layout
28548 It is inserted in the first column of the first line and causes all further
28549 insertions to overwrite the following columns:
28550 \begin_inset Formula
28552 \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 \\
28553 & & -\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 \\
28554 & & =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}
28559 After the insertion of
28565 , the cursor is in a purple box that is a bit shifted to the left from the
28567 In this the formula is inserted.
28568 \begin_inset Newline newline
28571 The content of the further lines is inserted to the second or another formula
28573 The greater the column number where it was inserted, the larger the indentation.
28574 \begin_inset VSpace medskip
28578 \begin_inset Newline newline
28582 \begin_inset Note Greyedout
28585 \begin_layout Plain Layout
28586 Note the following when using
28595 \begin_layout Itemize
28596 The formula doesn't use the full page width.
28598 \begin_inset space \thinspace{}
28602 \begin_inset space \space{}
28606 \begin_inset Formula $-B^{2}$
28609 is added to the first line in the above example, it would have been outside
28611 To better use the width, negative space can be inserted at the beginning
28615 \begin_layout Itemize
28616 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28621 \begin_layout Plain Layout
28622 \begin_inset CommandInset href
28624 name "LyX-bug #1429"
28625 target "http://www.lyx.org/trac/ticket/1429"
28634 One can only set the cursor at the beginning of the line and move it with
28643 \begin_layout Itemize
28644 Other methods to set long formulas are offered by the environments described
28646 \begin_inset CommandInset ref
28648 reference "sub:Multline-Environment"
28653 \begin_inset CommandInset ref
28655 reference "sub:Multiline-Formula-Parts"
28662 \begin_layout Subsubsection
28664 \begin_inset CommandInset label
28666 name "sub:Multiline-Brackets"
28671 \begin_inset Index idx
28674 \begin_layout Plain Layout
28675 Brackets ! for multiline expressions
28683 \begin_layout Standard
28684 For brackets spanning multiple lines the following problem occurs:
28685 \begin_inset Formula
28687 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28688 & & \left.\cdots+B-D\right]
28696 \begin_layout Standard
28697 The closing bracket is smaller than the opening bracket because brackets
28698 with variable size may not span multiple lines.
28701 \begin_layout Standard
28702 To set the bracket size for the second line correctly, the first line is
28710 \begin_inset Index idx
28713 \begin_layout Plain Layout
28721 and the second line with
28729 \begin_layout Plain Layout
28743 \begin_inset CommandInset ref
28745 reference "sub:Automatic-Bracket-Size"
28757 \begin_inset Index idx
28760 \begin_layout Plain Layout
28786 \begin_layout Plain Layout
28805 \begin_layout Plain Layout
28824 \begin_layout Plain Layout
28836 \begin_inset Formula $\downarrow$
28842 \begin_inset Index idx
28845 \begin_layout Plain Layout
28853 is inserted, because the multiplication operator with its limits is the
28854 largest symbol in the first line and this should be the size for the bracket
28855 in the second line.
28858 \begin_layout Standard
28859 The result is this:
28860 \begin_inset Formula
28862 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28863 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28871 \begin_layout Subsection
28875 \begin_layout Standard
28876 Align environments can be used for every kind of multiline formulas.
28877 They are especially useful to set several formulas side by side.
28880 \begin_layout Standard
28881 Align environments consist of columns.
28882 The odd columns are right aligned, the even ones left aligned.
28883 Every line in an Align environment can be numbered.
28886 \begin_layout Standard
28887 Align environments are created via the menu
28889 Insert\SpecialChar \menuseparator
28895 Edit\SpecialChar \menuseparator
28896 Math\SpecialChar \menuseparator
28897 Change Formula Type
28899 already existing formulas can be converted to Align environments.
28902 \begin_layout Standard
28903 To add or delete columns, the math toolbar buttons
28904 \begin_inset Graphics
28905 filename ../images/tabular-feature_append-column.png
28911 \begin_inset Graphics
28912 filename ../images/tabular-feature_delete-column.png
28917 , respectively, or the menu
28919 Edit\SpecialChar \menuseparator
28925 \begin_layout Subsubsection
28926 Standard align Environment
28927 \begin_inset CommandInset label
28929 name "sub:Standard-align-Environment"
28934 \begin_inset Index idx
28937 \begin_layout Plain Layout
28938 Formula ! multiline ! align environment
28946 \begin_layout Standard
28947 This Align environment is created by pressing
28950 arg "newline-insert newline"
28953 in a formula or by the menu
28955 Insert\SpecialChar \menuseparator
28956 Math\SpecialChar \menuseparator
28957 AMS align Environment
28962 \begin_layout Standard
28963 An example for two formulas set side by side, that are created with a four
28964 column align environment:
28965 \begin_inset Formula
28967 A & =\sin(B) & C & =D\\
28968 C & \ne A & B & \ne D
28973 As it can be seen, the formulas in this environment are placed so as if
28982 \begin_layout Plain Layout
28990 \begin_inset CommandInset ref
28992 reference "sub:Variable-Space"
29003 before the first and after every even column.
29004 When the formula style
29010 \begin_layout Plain Layout
29012 \begin_inset CommandInset ref
29014 reference "sec:Formula-Styles"
29025 is used, the formula is set without the
29031 before the first column.
29034 \begin_layout Subsubsection
29035 Alignat Environment
29036 \begin_inset Index idx
29039 \begin_layout Plain Layout
29040 Formula ! multiline ! alignat environment
29048 \begin_layout Standard
29049 The alignat environment has no predefined column separation.
29050 It can be inserted manually with the spaces that are described
29051 \begin_inset CommandInset ref
29053 reference "sub:Space"
29060 \begin_layout Standard
29061 The above example in the alignat environment where 1
29062 \begin_inset space \thinspace{}
29065 cm space was inserted at the beginning of the second formula:
29066 \begin_inset Formula
29067 \begin{alignat*}{2}
29068 A & =\sin(B) & \hspace{1cm}C & =D\\
29069 C & \ne A & B & \ne D
29074 Because the column separation can be set separately for every column, this
29075 environment is especially suitable to set three and more formulas side
29079 \begin_layout Subsubsection
29080 Flalign Environment
29081 \begin_inset CommandInset label
29083 name "sub:Flalign-Environment"
29088 \begin_inset Index idx
29091 \begin_layout Plain Layout
29092 Formula ! multiline ! flalign environment
29100 \begin_layout Standard
29101 In this environment the first two columns are always set as much as possible
29102 to the left and the last two ones to the right.
29104 \begin_inset Formula
29106 A & =1 & B & =2 & C & =3\\
29107 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29115 \begin_layout Standard
29116 By creating a flalign environment with an odd number of columns where an
29117 empty TeX-brace is inserted to the last column, several formulas in a document
29118 can be set to the left, although the formula style
29123 As example the indented formula
29124 \begin_inset CommandInset ref
29126 reference "eq:VolInt"
29131 \begin_inset Formula
29133 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29138 The first two columns contain the formula.
29139 To indent it as with the formula style
29144 \begin_inset space \thinspace{}
29147 pt space was inserted at the beginning of the first column.
29150 \begin_layout Subsection
29151 Eqnarray Environment
29152 \begin_inset CommandInset label
29154 name "sub:Eqnarray-Environment"
29159 \begin_inset Index idx
29162 \begin_layout Plain Layout
29163 Formula ! multiline ! eqnarray environment
29171 \begin_layout Standard
29172 When this environment has been created, three blue boxes appear.
29173 The content of the first box is right aligned, the content of the last
29175 The content of the middle box appears centered and a bit smaller, because
29176 it is designed to insert there only relation characters.
29177 \begin_inset Formula
29179 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29189 \begin_layout Subsection
29191 \begin_inset Index idx
29194 \begin_layout Plain Layout
29195 Formula ! multiline ! gather environment
29203 \begin_layout Standard
29204 This environment consists of only one centered column.
29205 Every line can be numbered.
29206 \begin_inset Formula
29217 \begin_layout Subsection
29218 Multline Environment
29219 \begin_inset CommandInset label
29221 name "sub:Multline-Environment"
29226 \begin_inset Index idx
29229 \begin_layout Plain Layout
29230 Formula ! multiline ! multline environment
29238 \begin_layout Standard
29239 The multline environment consists, like the gather environment, of only
29241 But the first line is left aligned, the last one right aligned.
29242 All other lines are centered.
29243 Therefore this environment is suitable for long formulas.
29245 \begin_inset CommandInset ref
29247 reference "eq:lefteqn"
29251 in the multline environment:
29252 \begin_inset Formula
29254 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}\\
29255 -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}\\
29256 =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}}
29264 \begin_layout Standard
29265 In the output only the last (first) line of a multline environment appears
29266 numbered when the document numbering is right (left).
29270 \begin_layout Plain Layout
29271 numbering styles see
29272 \begin_inset CommandInset ref
29274 reference "sec:Formula-Styles"
29286 \begin_layout Standard
29294 \begin_inset Index idx
29297 \begin_layout Plain Layout
29312 \begin_inset Index idx
29315 \begin_layout Plain Layout
29323 a centered line can be right or left aligned, respectively.
29324 The commands are used as follows:
29327 \begin_layout Standard
29332 shoveright{line content}
29338 shoveleft{line content}
29341 \begin_layout Standard
29342 \begin_inset VSpace medskip
29352 \begin_inset Index idx
29355 \begin_layout Plain Layout
29363 specifies the distance of the first line from the left page margin.
29364 Predefined is the length 0
29365 \begin_inset space \thinspace{}
29371 \begin_layout Standard
29372 As example the above formula where the command
29375 \begin_layout Standard
29385 \begin_layout Standard
29386 was inserted in TeX-mode before:
29390 \begin_layout Plain Layout
29402 \begin_inset Formula
29404 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}\\
29405 \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}}\\
29406 =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}}
29415 \begin_layout Plain Layout
29426 The second line was left aligned using
29435 \begin_layout Subsection
29436 Multiline Formula Parts
29437 \begin_inset CommandInset label
29439 name "sub:Multiline-Formula-Parts"
29444 \begin_inset Index idx
29447 \begin_layout Plain Layout
29448 Formula ! multiline ! formula parts
29456 \begin_layout Standard
29457 To display only parts of a formula with multiple lines, one of the following
29458 environments is used:
29475 They can be inserted via the menu
29477 Insert\SpecialChar \menuseparator
29480 or by using the commands described in this section.
29483 \begin_layout Standard
29484 The first three have the same properties as the corresponding multiline
29485 formula environments, but it is possible to set further formula parts beside
29488 \begin_inset Formula
29490 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29491 \Delta E\Delta t & \ge\frac{\hbar}{2}
29493 \right\} \textrm{Uncertainty relations}
29501 \begin_layout Standard
29502 To get this formula, a displayed formula is created where the command
29509 \begin_inset Index idx
29512 \begin_layout Plain Layout
29521 A purple box appears around the blue formula box where now columns and
29522 lines can be added.
29523 Outside the multiline environment other formula parts can be set, like
29527 \begin_layout Standard
29528 The aligned environment is also suitable for long formulas whose lines are
29529 horizontally aligned.
29530 Using aligned in a displayed formula has the advantage that the formula
29531 number is vertically centered behind the lines.
29533 \begin_inset CommandInset ref
29535 reference "eq:shortlong"
29539 in the aligned environment:
29540 \begin_inset Formula
29542 \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}|}\\
29543 & -\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}|}
29552 \begin_layout Standard
29553 To use the environments
29572 \begin_inset Index idx
29575 \begin_layout Plain Layout
29590 \begin_inset Index idx
29593 \begin_layout Plain Layout
29608 \begin_inset Index idx
29611 \begin_layout Plain Layout
29619 are inserted, respectively.
29620 The split environment has the same properties as the aligned environment
29621 but it can only have two columns.
29624 \begin_layout Subsection
29625 Text in multiline Formulas
29626 \begin_inset CommandInset label
29628 name "sub:Text-in-multiline"
29633 \begin_inset Index idx
29636 \begin_layout Plain Layout
29643 \begin_inset Index idx
29646 \begin_layout Plain Layout
29647 Formula ! multiline ! text
29655 \begin_layout Standard
29656 In the Align environments, and the multline and gather environment, text
29657 can be inserted that will appear in a separate line and doesn't affect
29658 the column alignment.
29659 To do this, the command
29666 \begin_inset Index idx
29669 \begin_layout Plain Layout
29677 is used in the following scheme:
29680 \begin_layout Standard
29688 \begin_layout Standard
29689 The text should not be longer than a line because it cannot be hyphenated.
29690 As LyX doesn't yet support
29696 directly, the text is written as mathematical text.
29703 must hereby be at the beginning of a line and appears in the output above
29705 An example where the text was inserted at the beginning of the second line:
29706 \begin_inset Formula
29708 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29709 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29717 \begin_layout Section
29719 \begin_inset Index idx
29722 \begin_layout Plain Layout
29729 \begin_inset Index idx
29732 \begin_layout Plain Layout
29733 Formula ! numbering|see
29737 \begin_layout Plain Layout
29748 \begin_layout Plain Layout
29763 \begin_layout Subsection
29767 \begin_layout Standard
29768 Numbered formulas can be created with the menu
29770 Insert\SpecialChar \menuseparator
29771 Math\SpecialChar \menuseparator
29773 \begin_inset space ~
29781 \begin_inset space ~
29787 Existing formulas can be numbered with the menu
29789 Edit\SpecialChar \menuseparator
29790 Math\SpecialChar \menuseparator
29792 \begin_inset space ~
29800 arg "math-number-toggle"
29804 The formula number is displayed in LyX behind the formula as a number sign
29806 The number sign is replaced in the output by the formula number.
29809 \begin_layout Standard
29810 When numbering is turned on in multiline formulas, all lines will be numbered.
29811 But the numbering can be controlled with the menu
29813 Edit\SpecialChar \menuseparator
29814 Math\SpecialChar \menuseparator
29816 \begin_inset space ~
29820 \begin_inset space ~
29824 \begin_inset space ~
29832 arg "math-number-line-toggle"
29838 \begin_layout Standard
29839 Except for inline formulas, all formulas can be numbered with two different
29841 \begin_inset CommandInset ref
29843 reference "sec:Formula-Styles"
29850 \begin_layout Subsection
29852 \begin_inset Index idx
29855 \begin_layout Plain Layout
29856 Cross-references ! to formulas
29864 \begin_layout Standard
29865 All labeled formulas can be cross-referenced.
29866 A label is added by the menu
29868 Insert\SpecialChar \menuseparator
29871 or the toolbar button
29872 \begin_inset Graphics
29873 filename ../images/label-insert.png
29879 The cursor must hereby be inside a displayed formula.
29880 Alternatively you can right-click on the formula and choose
29885 A dialog pops up displaying the prefix
29890 The label is inserted there behind the prefix.
29891 The predefined prefix means
29892 \begin_inset Quotes eld
29896 \begin_inset Quotes erd
29899 and makes it easier to find labels in large documents because it marks
29900 it as formula label to divide it from e.
29901 \begin_inset space \thinspace{}
29905 \begin_inset space \space{}
29909 To change a label, the menu
29911 Insert\SpecialChar \menuseparator
29914 is used again or you right-click on a formula and then on
29921 \begin_layout Standard
29922 The name of the label is displayed in LyX within two parentheses behind
29924 A formula with a label is always numbered.
29927 \begin_layout Standard
29928 Cross-references are inserted via the menu
29930 Insert\SpecialChar \menuseparator
29933 or with the toolbar button
29934 \begin_inset Graphics
29935 filename ../images/dialog-show-new-inset_ref.png
29941 A formula cross-reference appears in the output as formula number.
29942 When in the cross-reference dialog window the format
29946 is chosen, the cross-reference appears in the output as formula number
29948 \begin_inset Newline newline
29951 By right-clicking on a cross-reference in LyX, one jumps to the formula
29952 that is referenced.
29955 \begin_layout Standard
29956 Here are as examples cross-references to formulas of the following subsections:
29957 \begin_inset Note Note
29960 \begin_layout Plain Layout
29961 Note the different cross-reference types.
29969 \begin_layout Standard
29971 \begin_inset CommandInset ref
29978 \begin_inset CommandInset ref
29986 \begin_inset CommandInset ref
29992 ) big Latin letters are used for the numbering in contrary to (
29993 \begin_inset CommandInset ref
30002 \begin_layout Standard
30003 \begin_inset VSpace medskip
30006 When the argument of
30014 \begin_layout Plain Layout
30022 \begin_inset CommandInset ref
30024 reference "sub:User-defined-Numbering"
30035 contains a box like in
30036 \begin_inset CommandInset ref
30038 reference "sub:Paragraph-Boxes"
30042 , the formula cannot be referenced.
30045 \begin_layout Subsection
30047 \begin_inset Index idx
30050 \begin_layout Plain Layout
30051 Formula numbering ! subnumbering
30059 \begin_layout Standard
30060 With the help of the commands
30064 begin{subequations}
30072 formulas can be subnumbered.
30073 Both commands are inserted in TeX-mode.
30076 \begin_layout Standard
30078 \begin_inset Formula
30089 \begin_layout Plain Layout
30093 addtocounter{equation}{-1}
30102 \begin_layout Plain Layout
30106 begin{subequations}
30112 \begin_inset VSpace -5mm
30116 \begin_inset Formula
30124 \begin_inset Formula
30134 \begin_layout Standard
30138 \begin_layout Plain Layout
30150 \begin_layout Standard
30151 To create the example, the following is done:
30154 \begin_layout Enumerate
30155 first formula is inserted
30158 \begin_layout Enumerate
30163 addtocounter{equation}{-1}
30165 begin{subequations}
30166 \begin_inset Index idx
30169 \begin_layout Plain Layout
30178 \begin_inset Newline newline
30183 is inserted after the first formula
30186 \begin_layout Enumerate
30187 second formula is inserted
30190 \begin_layout Enumerate
30191 third formula is inserted
30194 \begin_layout Enumerate
30201 is inserted after the third formula
30204 \begin_layout Standard
30205 Every formula between the commands
30217 is subnumbered as a, b,
30218 \begin_inset Newline linebreak
30221 c, \SpecialChar \ldots{}
30222 For multiline formulas every line will be subnumbered.
30223 All subnumbered formulas are treated as
30228 But as every numbered formula increases the counter
30232 by one, the command
30238 is needed to decrease it.
30239 Otherwise the formulas
30240 \begin_inset CommandInset ref
30247 \begin_inset CommandInset ref
30254 \begin_inset CommandInset ref
30260 would be numbered as
30261 \begin_inset CommandInset ref
30268 \begin_inset CommandInset ref
30275 \begin_inset CommandInset ref
30284 \begin_layout Standard
30285 By inserting the commands in TeX-mode, a space is created between the first
30288 \begin_inset space \thinspace{}
30291 mm vertical space is inserted after the command
30295 begin{subequations}
30298 When the formula style
30304 \begin_layout Plain Layout
30306 \begin_inset CommandInset ref
30308 reference "sec:Formula-Styles"
30320 \begin_inset space \thinspace{}
30323 mm space is inserted instead.
30326 \begin_layout Standard
30327 Here is an example for a multiline formula where the numbering was turned
30328 off for the second line:
30332 \begin_layout Plain Layout
30336 begin{subequations}
30342 \begin_inset Formula
30344 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30345 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30346 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30355 \begin_layout Plain Layout
30367 \begin_layout Subsection
30368 User-defined Numbering
30369 \begin_inset CommandInset label
30371 name "sub:User-defined-Numbering"
30376 \begin_inset Index idx
30379 \begin_layout Plain Layout
30380 Formula numbering ! user-defined
30388 \begin_layout Standard
30389 \begin_inset Index idx
30392 \begin_layout Plain Layout
30393 Formula numbering ! self-defined delimiters
30398 With the standard numbering parentheses are set around the formula number.
30399 To replace the parentheses for example by vertical bars, the following
30400 line is added to the LaTeX-preamble:
30403 \begin_layout Standard
30415 \begin_inset Note Note
30418 \begin_layout Plain Layout
30419 This macro is already declared in the LaTeX-preamble for testing.
30420 To activate it, remove the percent sign at the beginning.
30428 \begin_layout Standard
30429 To use other characters, the vertical bars besides the
30433 are replaced by one ore more characters.
30434 To get only the formula number the vertical bars are omitted.
30437 \begin_layout Standard
30438 \begin_inset VSpace bigskip
30441 When there should be an expression of your choice instead of the consecutive
30442 formula number in parentheses behind the formula, the command
30449 \begin_inset Index idx
30452 \begin_layout Plain Layout
30461 \begin_inset Formula
30463 A+B=C\tag{something}\label{eq:tag}
30468 In this example the command
30476 \begin_layout Plain Layout
30487 was inserted in the formula.
30490 \begin_layout Standard
30499 \begin_layout Plain Layout
30510 is inserted instead, the star prevents the parentheses around the expression:
30511 \begin_inset Formula
30513 A+B=C\tag*{something}
30521 \begin_layout Standard
30522 \begin_inset VSpace bigskip
30525 To restart the formula numbering with new document parts or sections, the
30526 following command is used:
30529 \begin_layout Standard
30534 @addtoreset{equation}{part}
30537 \begin_inset Index idx
30540 \begin_layout Plain Layout
30545 \begin_layout Plain Layout
30556 \begin_layout Plain Layout
30569 \begin_layout Plain Layout
30580 \begin_layout Plain Layout
30593 \begin_inset Newline newline
30597 \begin_inset Newline newline
30604 @addtoreset{equation}{section}
30607 \begin_layout Standard
30608 To be able to use these commands in TeX-mode, the
30609 \begin_inset Quotes eld
30613 \begin_inset Quotes erd
30616 character has to be made
30617 \begin_inset Quotes eld
30621 \begin_inset Quotes erd
30624 for LaTeX using the command
30638 So the command sequence in TeX-mode is:
30641 \begin_layout Standard
30647 \begin_inset Newline newline
30652 @addtoreset{equation}{section}
30653 \begin_inset Newline newline
30661 \begin_layout Standard
30662 In the LaTeX-preamble
30674 can be omitted as they are automatically internally inserted by LyX.
30677 \begin_layout Standard
30692 \begin_layout Plain Layout
30697 is part of the LaTeX-package
30702 \begin_inset Index idx
30705 \begin_layout Plain Layout
30706 Packages ! carlisle
30711 that is part of every LaTeX standard installation.
30717 \begin_inset Index idx
30720 \begin_layout Plain Layout
30721 Packages ! remreset
30726 has to be loaded in the LaTeX-preamble with the line
30729 \begin_layout Standard
30734 usepackage{remreset}
30737 \begin_layout Standard
30745 \begin_inset Index idx
30748 \begin_layout Plain Layout
30753 \begin_layout Plain Layout
30764 \begin_layout Plain Layout
30777 \begin_layout Plain Layout
30788 \begin_layout Plain Layout
30800 can be used with the same scheme as
30809 \begin_layout Standard
30810 \begin_inset VSpace bigskip
30813 Sometimes formulas should be numbered in the following form:
30816 \begin_layout Standard
30819 (section number.formula number)
30822 \begin_layout Standard
30823 The formula number should start with every section with
30824 \begin_inset Quotes eld
30828 \begin_inset Quotes erd
30834 \begin_layout Standard
30835 For this case there is the command
30842 \begin_inset Index idx
30845 \begin_layout Plain Layout
30853 , which is used with the following scheme:
30856 \begin_layout Standard
30861 numberwithin{counter}{sectioning}
30864 \begin_layout Standard
30865 Counter denotes what kind of numbering is affected, sectioning denotes what
30866 number is before the dot.
30869 \begin_layout Standard
30870 Thus in our case the following LaTeX-preamble or TeX code line is used:
30873 \begin_layout Standard
30878 numberwithin{equation}{section}
30881 \begin_layout Standard
30882 This is the result:
30886 \begin_layout Plain Layout
30890 numberwithin{equation}{section}
30896 \begin_inset Formula
30906 \begin_layout Standard
30908 \begin_inset space \thinspace{}
30912 \begin_inset space \space{}
30915 tables so that the number of the part is the sectioning,
30916 \begin_inset Newline newline
30923 numberwithin{table}{part}
30928 \begin_layout Standard
30929 To go back to the standard numbering or to prevent this kind of numbering
30930 when it is defined by the document class, the following command is inserted
30931 as TeX code or to the LaTeX-preamble:
30934 \begin_layout Standard
30944 \begin_inset Index idx
30947 \begin_layout Plain Layout
30961 \begin_layout Plain Layout
30977 \begin_inset Newline newline
30985 \begin_inset Newline newline
30997 \begin_layout Standard
31004 uses internally the command
31010 , described above, that also needs to be reverted.
31014 \begin_layout Plain Layout
31021 \begin_layout Plain Layout
31025 @removefromreset{equation}{section}
31028 \begin_layout Plain Layout
31040 \begin_layout Subsection
31041 Numbering with Roman Numbers and Letters
31042 \begin_inset Index idx
31045 \begin_layout Plain Layout
31046 Formula numbering ! with letters
31052 \begin_inset Index idx
31055 \begin_layout Plain Layout
31056 Formula numbering ! with Roman numbers
31064 \begin_layout Standard
31065 Formulas can also be numbered with Roman numbers and Latin letters.
31066 To number for example with small Roman numbers, the command
31069 \begin_layout Standard
31081 \begin_layout Standard
31082 is inserted before the formula in TeX-mode.
31090 \begin_inset Index idx
31093 \begin_layout Plain Layout
31101 redefines the predefined command
31117 \begin_layout Plain Layout
31124 has the same scheme like the command
31130 that is described in
31131 \begin_inset CommandInset ref
31133 reference "sub:The-Command-newcommand"
31146 is the formula counter.
31153 is used as prefix for a counter, the value of the counter is output as
31155 When a formula is numbered, LaTeX sets internally the command
31161 behind the formula.
31167 \begin_inset Index idx
31170 \begin_layout Plain Layout
31180 outputs the counter as small Roman number.
31183 \begin_layout Standard
31184 All formulas behind the command
31194 are now numbered Roman.
31195 To switch to numbering with big Roman numbers, the command is inserted
31209 \begin_inset Index idx
31212 \begin_layout Plain Layout
31224 \begin_inset Quotes eld
31228 \begin_inset Quotes erd
31231 with small Latin letters there is the command
31238 \begin_inset Index idx
31241 \begin_layout Plain Layout
31249 , for big ones there is the command
31256 \begin_inset Index idx
31259 \begin_layout Plain Layout
31272 \begin_layout Standard
31273 \begin_inset Note Greyedout
31276 \begin_layout Plain Layout
31283 \begin_inset space ~
31286 formulas can be numbered with Latin letters in one document.
31294 \begin_layout Standard
31298 \begin_layout Plain Layout
31314 \begin_layout Standard
31315 \begin_inset Formula
31317 A=\textrm{small roman}
31326 \begin_layout Plain Layout
31340 \begin_inset Formula
31342 B=\textrm{big Roman}\label{eq:Rom}
31351 \begin_layout Plain Layout
31365 \begin_inset Formula
31367 C=\textrm{small Latin}
31376 \begin_layout Plain Layout
31390 \begin_inset Formula
31392 D=\textrm{big Latin}\label{eq:Lat}
31400 \begin_layout Standard
31401 To switch back to the default numbering, insert the command:
31404 \begin_layout Standard
31414 \begin_inset Index idx
31417 \begin_layout Plain Layout
31428 \begin_layout Standard
31432 \begin_layout Plain Layout
31446 \begin_inset Formula
31456 \begin_layout Standard
31457 \begin_inset VSpace medskip
31460 As you see, formulas are numbered serially independent from the numbering
31462 When then numbering should start with
31463 \begin_inset Quotes eld
31467 \begin_inset Quotes erd
31470 when the style is changed, new equation counters have to be defined.
31471 A description about this can be found in the file
31472 \begin_inset CommandInset href
31474 name "Formula-numbering.lyx"
31475 target "run:Formula-numbering.lyx"
31482 \begin_layout Standard
31483 \begin_inset Newpage newpage
31489 \begin_layout Section
31490 Chemical Symbols and Equations
31491 \begin_inset CommandInset label
31493 name "sub:Chemical-Symbols-and"
31498 \begin_inset Index idx
31501 \begin_layout Plain Layout
31502 Chemical characters ! Symbols
31508 \begin_inset Index idx
31511 \begin_layout Plain Layout
31518 \begin_inset Index idx
31521 \begin_layout Plain Layout
31530 \begin_layout Standard
31531 An example text from chemistry:
31534 \begin_layout Quote
31536 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31539 -ion reacts with two
31540 \begin_inset Formula $\mathrm{Na^{+}}$
31543 -ions to sodium sulfate
31544 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31548 The chemical equation for this is:
31549 \begin_inset Formula
31551 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31559 \begin_layout Standard
31560 This chemical equation can directly be created as formula.
31561 To avoid that the symbols appear italic, everything is highlighted and
31562 changed by the shortcut
31568 to the upright font style.
31572 \begin_layout Plain Layout
31578 \begin_inset CommandInset ref
31580 reference "sub:Font-Styles"
31592 \begin_layout Standard
31593 A more convenient way to typeset chemical formulas is to use the command
31601 \begin_inset Index idx
31604 \begin_layout Plain Layout
31612 that is available when the LaTeX-package
31617 \begin_inset Index idx
31620 \begin_layout Plain Layout
31633 to a formula a new blue box appears where chemical formulas can be inserted
31634 in an intuitive way.
31637 \begin_layout Standard
31639 \begin_inset Tabular
31640 <lyxtabular version="3" rows="9" columns="2">
31641 <features rotate="0" tabularvalignment="middle">
31642 <column alignment="center" valignment="top">
31643 <column alignment="center" valignment="top">
31645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31648 \begin_layout Plain Layout
31654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31657 \begin_layout Plain Layout
31659 \begin_inset Note Note
31662 \begin_layout Plain Layout
31669 is only used as spacer.
31681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31684 \begin_layout Plain Layout
31691 \begin_layout Plain Layout
31705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31708 \begin_layout Plain Layout
31709 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31722 \begin_layout Plain Layout
31729 \begin_layout Plain Layout
31743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31746 \begin_layout Plain Layout
31747 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31760 \begin_layout Plain Layout
31767 \begin_layout Plain Layout
31781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31784 \begin_layout Plain Layout
31785 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31798 \begin_layout Plain Layout
31805 \begin_layout Plain Layout
31819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31822 \begin_layout Plain Layout
31823 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31836 \begin_layout Plain Layout
31843 \begin_layout Plain Layout
31858 \begin_layout Plain Layout
31873 \begin_layout Plain Layout
31887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31890 \begin_layout Plain Layout
31891 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31904 \begin_layout Plain Layout
31911 \begin_layout Plain Layout
31921 \begin_inset Formula $\downarrow$
31925 \begin_inset Formula $\to$
31933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31936 \begin_layout Plain Layout
31937 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31950 \begin_layout Plain Layout
31957 \begin_layout Plain Layout
31970 \begin_layout Plain Layout
31983 \begin_layout Plain Layout
31996 \begin_layout Plain Layout
32009 \begin_layout Plain Layout
32023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32026 \begin_layout Plain Layout
32027 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32040 \begin_layout Plain Layout
32047 \begin_layout Plain Layout
32060 \begin_layout Plain Layout
32073 \begin_layout Plain Layout
32086 \begin_layout Plain Layout
32103 \begin_layout Plain Layout
32117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32120 \begin_layout Plain Layout
32121 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32137 \begin_layout Standard
32138 \begin_inset Note Greyedout
32141 \begin_layout Plain Layout
32147 Inserting a formula to a
32153 box will lead to LaTeX errors due to a LyX bug.
32159 \begin_layout Plain Layout
32160 \begin_inset CommandInset href
32162 name "LyX-bug #8566"
32163 target "http://www.lyx.org/trac/ticket/8566"
32174 In this case TeX code has to be used like for
32188 \begin_layout Plain Layout
32209 \begin_layout Standard
32210 \begin_inset Note Greyedout
32213 \begin_layout Plain Layout
32219 It is not possible in LyX to use the character ^ to get an up-arrow as
32225 One instead uses a negative thin space followed by the command
32232 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32243 \begin_layout Standard
32250 the command for equation
32251 \begin_inset space ~
32255 \begin_inset CommandInset ref
32257 reference "eq:chem-reaction"
32262 \begin_inset Newline newline
32273 \begin_layout Plain Layout
32286 \begin_layout Plain Layout
32299 \begin_layout Plain Layout
32312 \begin_layout Plain Layout
32325 \begin_layout Plain Layout
32338 \begin_layout Plain Layout
32350 \begin_layout Standard
32351 To create multiline chemical equations first a multiline formula is created
32353 \begin_inset CommandInset ref
32355 reference "sec:Multiline-Formulas"
32360 Afterwards the command
32366 is used in every small blue box of the formula.
32368 \begin_inset CommandInset ref
32370 reference "eq:TEOS-reaction-1"
32375 \begin_inset CommandInset ref
32377 reference "eq:TEOS-reaction-2"
32381 are an example of a multi-stage chemical reaction where every equation
32382 has its own number.
32383 \begin_inset Formula
32385 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32386 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32394 \begin_layout Standard
32405 package provides the command
32412 \begin_inset Index idx
32415 \begin_layout Plain Layout
32423 that has to be used for special cases.
32424 For more information about
32430 and more examples have a look at the documentation of
32435 \begin_inset CommandInset citation
32444 \begin_layout Section
32448 \begin_layout Standard
32449 LyX supports two types of commutative diagrams:
32457 that are explained in the following.
32460 \begin_layout Subsection
32462 \begin_inset Index idx
32465 \begin_layout Plain Layout
32474 \begin_layout Standard
32475 Diagrams of this type visualize relations by vertical and horizontal lines
32477 \begin_inset Formula
32479 \begin{CD}A@>>>B@>>>C\\
32490 \begin_layout Standard
32491 To get them, the command
32496 \begin_inset Index idx
32499 \begin_layout Plain Layout
32509 is inserted to a formula.
32510 A blue box appears with two dashed lines where further commands can be
32515 arg "newline-insert newline"
32518 a new line is created.
32519 Horizontal relations are inserted in odd, vertical in even formula lines.
32522 \begin_layout Standard
32523 To create the relations there are the following commands:
32526 \begin_layout Itemize
32531 creates a left arrow,
32542 \begin_layout Itemize
32547 creates an up arrow,
32555 a vertical equal sign
32558 \begin_layout Itemize
32564 is a placeholder for non-existent relations
32567 \begin_layout Standard
32568 All arrows can be labeled as follows:
32571 \begin_layout Itemize
32572 If text inserted between the first and second < or >, resp., it is placed
32574 When it is inserted between the second and third one, it appears under
32578 \begin_layout Itemize
32579 When text for vertical arrows is inserted between the first and second A
32580 or V, resp., it is placed left beside the arrow.
32581 When it is inserted between the second and third one, it appears right
32583 If the text contains an A or V, these letters must be set into a TeX-brace.
32586 \begin_layout Standard
32587 As example a diagram with all possible relations:
32590 \begin_layout Standard
32591 \begin_inset Formula
32593 \begin{CD}A@>j>>B@>>k>C@=F\\
32604 \begin_layout Standard
32605 The command for this is:
32606 \begin_inset Newline newline
32617 \begin_layout Plain Layout
32626 A@>j>>B@>>k>C@=F Ctrl+Return
32627 \begin_inset Newline newline
32631 \begin_inset Phantom HPhantom
32634 \begin_layout Plain Layout
32643 \begin_layout Plain Layout
32662 \begin_inset Formula $\to$
32668 \begin_inset Newline newline
32672 \begin_inset Phantom HPhantom
32675 \begin_layout Plain Layout
32684 \begin_layout Plain Layout
32701 \begin_layout Subsection
32703 \begin_inset Index idx
32706 \begin_layout Plain Layout
32707 Diagrams ! xymatrix
32715 \begin_layout Standard
32716 To be able to use xymatrices, the LaTeX-package
32721 A xymatrix is created by inserting the command
32728 Then you are able to add new matrix columns and rows like for normal matrices,
32730 \begin_inset CommandInset ref
32732 reference "sec:Matrices"
32739 \begin_layout Standard
32740 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32742 All possibilities to create commutative diagrams and decorations are explained
32747 that you find in the menu
32749 Help\SpecialChar \menuseparator
32751 \begin_inset space ~
32759 \begin_layout Subsection
32765 \begin_inset Index idx
32768 \begin_layout Plain Layout
32777 \begin_layout Standard
32782 -diagrams, the LaTeX-package
32791 -diagram is created by inserting the command
32798 Then you are able to add new matrix columns and rows like for normal matrices,
32800 \begin_inset CommandInset ref
32802 reference "sec:Matrices"
32809 \begin_layout Standard
32810 Examples how to create
32814 diagrams in LyX is given in the
32816 Feynman-diagram manual
32818 that you find in the menu
32820 Help\SpecialChar \menuseparator
32822 \begin_inset space ~
32830 \begin_layout Standard
32831 \begin_inset Newpage newpage
32837 \begin_layout Section
32838 User-defined Commands
32839 \begin_inset Index idx
32842 \begin_layout Plain Layout
32843 User-defined commands
32851 \begin_layout Standard
32852 \begin_inset Note Greyedout
32855 \begin_layout Plain Layout
32860 The names of user-defined commands and macros may only consist of Latin
32869 \begin_layout Subsection
32873 \begin_inset CommandInset label
32875 name "sub:The-Command-newcommand"
32880 \begin_inset Index idx
32883 \begin_layout Plain Layout
32884 User-defined commands !
32892 \begin_inset Index idx
32895 \begin_layout Plain Layout
32906 \begin_layout Standard
32907 Many LaTeX-commands are too long to be used frequently.
32908 But it is possible to define with the command
32914 new shorter commands.
32917 \begin_layout Standard
32918 The command scheme of
32927 \begin_layout Standard
32932 newcommand{new command name}[number of arguments][optional
32937 \begin_inset Newline newline
32941 \begin_inset Phantom HPhantom
32944 \begin_layout Plain Layout
32954 {command definition}
32957 \begin_layout Standard
32958 \begin_inset Note Greyedout
32961 \begin_layout Plain Layout
32966 Assure that the name of the new command is not already used in your document
32967 or by LaTeX-packages that you use.
32968 When you for example define the command
32980 , you get an error message because
32986 is already defined as command for
32987 \begin_inset Quotes eld
32991 \begin_inset Formula $\le$
32995 \begin_inset Quotes erd
33006 \begin_layout Standard
33007 The number of arguments is an integer in the range 0
33008 \begin_inset space \thinspace{}
33012 \begin_inset space \thinspace{}
33015 9 and specifies how many arguments the new command should have.
33016 With the optional value a value for an optional argument can be predefined.
33017 When this is done, the
33025 rgument of the new command is automatically an optional one.
33028 \begin_layout Standard
33029 Here are some examples:
33032 \begin_layout Itemize
33033 To define the command
33045 , the LaTeX-preamble line is:
33046 \begin_inset VSpace medskip
33050 \begin_inset Newline newline
33064 \begin_layout Itemize
33065 To define the command
33077 , the argument (that should be underlined) must be taken into account.
33078 For this the preamble line is:
33079 \begin_inset VSpace medskip
33083 \begin_inset Newline newline
33097 \begin_inset VSpace medskip
33101 \begin_inset Newline newline
33108 acts as argument placeholder, the
33112 behind it denotes that it is the placeholder for the first argument.
33115 \begin_layout Itemize
33123 \begin_inset space \thinspace{}
33127 \begin_inset space \space{}
33137 \begin_inset VSpace medskip
33141 \begin_inset Newline newline
33152 framebox#1#2{$#3$}}
33155 \begin_inset VSpace medskip
33159 \begin_inset Newline newline
33162 The two Dollar signs creates the extra formula needed for
33169 \begin_inset CommandInset ref
33171 reference "sub:Boxes-with-Frame"
33178 \begin_layout Itemize
33179 To create a new command for
33185 where the color for the box need not be specified, the argument for the
33186 color is defined optional:
33187 \begin_inset VSpace medskip
33191 \begin_inset Newline newline
33202 fcolorbox{#2}{#1}{$#3$}}
33205 \begin_inset VSpace medskip
33209 \begin_inset Newline newline
33212 When the color is not specified when using
33218 , the predefined color
33225 \begin_layout Standard
33226 A test of the new defined commands:
33229 \begin_layout Standard
33231 \begin_inset Tabular
33232 <lyxtabular version="3" rows="6" columns="2">
33233 <features rotate="0" tabularvalignment="middle">
33234 <column alignment="center" valignment="top">
33235 <column alignment="center" valignment="top">
33237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33240 \begin_layout Plain Layout
33246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33249 \begin_layout Plain Layout
33251 \begin_inset Note Note
33254 \begin_layout Plain Layout
33261 is only used as spacer.
33273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33276 \begin_layout Plain Layout
33283 \begin_layout Plain Layout
33297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33300 \begin_layout Plain Layout
33301 \begin_inset Formula $A\gr B$
33311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33314 \begin_layout Plain Layout
33322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33325 \begin_layout Plain Layout
33326 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33339 \begin_layout Plain Layout
33343 \begin_inset Formula $\to$
33349 \begin_inset Formula $\to$
33360 \begin_layout Plain Layout
33374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33377 \begin_layout Plain Layout
33378 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33391 \begin_layout Plain Layout
33395 \begin_inset Formula $\to$
33406 \begin_layout Plain Layout
33420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33423 \begin_layout Plain Layout
33424 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33437 \begin_layout Plain Layout
33443 \begin_inset Formula $\to$
33454 \begin_layout Plain Layout
33468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33471 \begin_layout Plain Layout
33472 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33488 \begin_layout Subsection
33490 \begin_inset Index idx
33493 \begin_layout Plain Layout
33494 User-defined commands! Math macros
33500 \begin_inset Index idx
33503 \begin_layout Plain Layout
33512 \begin_layout Standard
33513 User-defined commands are especially convenient for complex expressions.
33514 When you are for example dealing with a document that has quadratic equations,
33515 the same solution type occurs several times.
33516 The general form of a quadratic equation is
33517 \begin_inset Formula
33519 0=\lambda^{2}+p\lambda+q
33524 The general form of the solution is
33525 \begin_inset Formula
33527 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33535 \begin_layout Standard
33536 To define a command for the solution formula where only the three parameters
33538 \begin_inset Formula $\lambda$
33542 \begin_inset Formula $p$
33546 \begin_inset Formula $q$
33549 need to be specified and the index of
33550 \begin_inset Formula $\lambda$
33553 can be given optionally, the LaTeX-preamble line is
33554 \begin_inset Newline newline
33570 \begin_inset Newline newline
33574 \begin_inset Phantom HPhantom
33577 \begin_layout Plain Layout
33591 frac{#3^{2}}{4}-#4}}
33594 \begin_layout Standard
33595 To create with this the solution formula, the command
33596 \begin_inset Newline newline
33606 \begin_inset Formula $\to$
33612 \begin_inset Formula $\to$
33619 is inserted to a formula
33624 \begin_layout Standard
33625 The definition of the new command is unintuitive because one has to know
33626 the schemes of all used LaTeX commands, e.
33627 \begin_inset space \thinspace{}
33631 \begin_inset space \space{}
33634 that a fraction is inserted in LaTeX as
33638 frac{numerator}{denominator}
33641 Furthermore one can easily forget a brace in the definition and cannot
33642 see in LyX what the new command is doing.
33643 To avoid these problems LyX offers the possibility to use math macros instead
33653 \begin_layout Standard
33654 A math macro is created by using the menu
33656 Insert\SpecialChar \menuseparator
33657 Math\SpecialChar \menuseparator
33660 or the toolbar button
33661 \begin_inset Graphics
33662 filename ../images/math-macro_newmacroname_newcommand.png
33668 The math macro toolbar appears together with the following box where the
33670 \begin_inset Newline newline
33674 \begin_inset space \hspace*{\fill}
33678 \begin_inset Graphics
33679 filename clipart/macrobox.png
33684 \begin_inset space \hspace*{\fill}
33688 \begin_inset Newline newline
33692 \begin_inset FormulaMacro
33693 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33698 newmacroname is the default name of the macro that should be changed to
33699 something sensible.
33700 The wanted formula is inserted in the first blue box.
33701 An argument placeholder is inserted with the command
33708 \begin_inset space \thinspace{}
33712 \begin_inset space \space{}
33721 or by using the macro toolbar button
33722 \begin_inset Graphics
33723 filename ../images/math-macro-add-param.png
33729 Argument placeholders are displayed red.
33731 \begin_inset space ~
33734 arguments are possible.
33735 Optional arguments are created with the toolbar button
33736 \begin_inset Graphics
33737 filename ../images/math-macro-add-optional-param.png
33743 The first non-optional argument can be transformed to an optional one with
33745 \begin_inset Graphics
33746 filename ../images/math-macro-make-optional.png
33752 In the second blue box the appearance of the macro in LyX can be defined.
33753 Normally you want to see it as it is defined, so the box is kept empty.
33754 But when you have created a macro that needs lot of space on the screen,
33755 you can insert in the box for example
33756 \begin_inset Newline newline
33786 \begin_inset Newline newline
33791 For the macro only the arguments with the macro name in front of them will
33792 then be displayed in LyX, leading to a better overview.
33793 The formula appears in the output as defined in the first box.
33794 \begin_inset Newline newline
33797 The appearance of macros in formulas can furthermore be changed for single
33798 macros by setting the cursor in the macro and using the menu
33800 View\SpecialChar \menuseparator
33802 \begin_inset space ~
33806 \begin_inset space ~
33814 \begin_layout Standard
33815 To use a macro, the macro name is inserted as command to a formula, in our
33823 Our macro looks in LyX like this:
33824 \begin_inset Newline newline
33828 \begin_inset space \hspace*{\fill}
33832 \begin_inset Graphics
33833 filename clipart/macrouse.png
33838 \begin_inset space \hspace*{\fill}
33842 \begin_inset Newline newline
33845 Here is our macro example with the arguments
33846 \begin_inset Formula $x$
33850 \begin_inset Formula $\ln(x)$
33854 \begin_inset Formula $B$
33860 \begin_layout Standard
33861 \begin_inset Formula
33871 \begin_layout Standard
33872 LyX offers in the menu
33874 Tools\SpecialChar \menuseparator
33875 Preferences\SpecialChar \menuseparator
33876 Editing\SpecialChar \menuseparator
33879 different styles to edit macros.
33880 To find the style that suits you the most, choose a style and set the cursor
33881 in a macro formula to see the difference.
33884 \begin_layout Standard
33885 A math macro is transformed internally to a
33891 command when exporting the document.
33898 command is not placed in the LaTeX-preamble, therefore macros can only
33899 be used in formulas that are in the document below the macro definition
33903 \begin_layout Standard
33904 Math macros can also be directly created from a
33911 When writing for example the command
33914 \begin_inset Newline newline
33923 xleftarrow[#2]{#1}}
33924 \begin_inset Newline newline
33929 in LyX as normal text, highlighting it completely and using then the shortcut
33934 , the command will be transformed to a math macro.
33935 Using this method you need to be careful that the
33941 command is typed correctly, otherwise you get a faulty macro leading to
33945 \begin_layout Standard
33946 Math macros currently have the problem that further formulas in macro definition
33947 s are handled wrongly.
33948 Therefore the example
33955 \begin_inset CommandInset ref
33957 reference "sub:The-Command-newcommand"
33961 cannot be created as macro.
33964 \begin_layout Standard
33965 When the cursor is in a macro definition box, you will see the macro toolbar
33969 \begin_layout Standard
33970 \begin_inset VSpace defskip
33976 \begin_layout Standard
33977 \begin_inset Graphics
33978 filename clipart/MacroToolbar.png
33983 \begin_inset Index idx
33986 \begin_layout Plain Layout
33995 \begin_layout Standard
33996 \begin_inset VSpace defskip
34002 \begin_layout Standard
34003 The macro toolbar contains from left to right the following buttons:
34006 \begin_layout Standard
34007 \begin_inset VSpace defskip
34013 \begin_layout Standard
34014 \begin_inset Tabular
34015 <lyxtabular version="3" rows="9" columns="2">
34016 <features rotate="0" islongtable="true" longtabularalignment="center">
34017 <column alignment="left" valignment="top">
34018 <column alignment="left" valignment="top" width="85col%">
34019 <row interlinespace="2.5mm">
34020 <cell alignment="center" valignment="top" usebox="none">
34023 \begin_layout Plain Layout
34024 \begin_inset Graphics
34025 filename ../images/math-macro-remove-param.png
34026 rotateOrigin center
34035 <cell alignment="center" valignment="top" usebox="none">
34038 \begin_layout Plain Layout
34041 Edit\SpecialChar \menuseparator
34042 Math\SpecialChar \menuseparator
34044 \begin_inset space ~
34047 Definition\SpecialChar \menuseparator
34048 Remove Last Argument
34054 <row interlinespace="2.5mm">
34055 <cell alignment="center" valignment="top" usebox="none">
34058 \begin_layout Plain Layout
34059 \begin_inset Graphics
34060 filename ../images/math-macro-add-param.png
34061 rotateOrigin center
34070 <cell alignment="center" valignment="top" usebox="none">
34073 \begin_layout Plain Layout
34076 Edit\SpecialChar \menuseparator
34077 Math\SpecialChar \menuseparator
34079 \begin_inset space ~
34082 Definition\SpecialChar \menuseparator
34089 <row interlinespace="2.5mm">
34090 <cell alignment="center" valignment="top" usebox="none">
34093 \begin_layout Plain Layout
34094 \begin_inset Graphics
34095 filename ../images/math-macro-make-optional.png
34096 rotateOrigin center
34105 <cell alignment="center" valignment="top" usebox="none">
34108 \begin_layout Plain Layout
34111 Edit\SpecialChar \menuseparator
34112 Math\SpecialChar \menuseparator
34114 \begin_inset space ~
34117 Definition\SpecialChar \menuseparator
34118 Make First Non-Optional into
34119 \begin_inset Newline newline
34123 \begin_inset Phantom HPhantom
34126 \begin_layout Plain Layout
34129 Edit\SpecialChar \menuseparator
34130 Math\SpecialChar \menuseparator
34132 \begin_inset space ~
34135 Definition\SpecialChar \menuseparator
34147 <row interlinespace="2.5mm">
34148 <cell alignment="center" valignment="top" usebox="none">
34151 \begin_layout Plain Layout
34152 \begin_inset Graphics
34153 filename ../images/math-macro-make-nonoptional.png
34154 rotateOrigin center
34163 <cell alignment="center" valignment="top" usebox="none">
34166 \begin_layout Plain Layout
34169 Edit\SpecialChar \menuseparator
34170 Math\SpecialChar \menuseparator
34172 \begin_inset space ~
34175 Definition\SpecialChar \menuseparator
34176 Make Last Optional into
34177 \begin_inset Newline newline
34181 \begin_inset Phantom HPhantom
34184 \begin_layout Plain Layout
34187 Edit\SpecialChar \menuseparator
34188 Math\SpecialChar \menuseparator
34190 \begin_inset space ~
34193 Definition\SpecialChar \menuseparator
34199 Non-Optional Argument
34205 <row interlinespace="2.5mm">
34206 <cell alignment="center" valignment="top" usebox="none">
34209 \begin_layout Plain Layout
34210 \begin_inset Graphics
34211 filename ../images/math-macro-remove-optional-param.png
34212 rotateOrigin center
34221 <cell alignment="center" valignment="top" usebox="none">
34224 \begin_layout Plain Layout
34227 Edit\SpecialChar \menuseparator
34228 Math\SpecialChar \menuseparator
34230 \begin_inset space ~
34233 Definition\SpecialChar \menuseparator
34234 Remove Optional Argument
34240 <row interlinespace="2.5mm">
34241 <cell alignment="center" valignment="top" usebox="none">
34244 \begin_layout Plain Layout
34245 \begin_inset Graphics
34246 filename ../images/math-macro-add-optional-param.png
34247 rotateOrigin center
34256 <cell alignment="center" valignment="top" usebox="none">
34259 \begin_layout Plain Layout
34262 Edit\SpecialChar \menuseparator
34263 Math\SpecialChar \menuseparator
34265 \begin_inset space ~
34268 Definition\SpecialChar \menuseparator
34269 Insert Optional Argument
34275 <row interlinespace="2.5mm">
34276 <cell alignment="center" valignment="top" usebox="none">
34279 \begin_layout Plain Layout
34280 \begin_inset Graphics
34281 filename ../images/math-macro-remove-greedy-param.png
34282 rotateOrigin center
34291 <cell alignment="center" valignment="top" usebox="none">
34294 \begin_layout Plain Layout
34297 Edit\SpecialChar \menuseparator
34298 Math\SpecialChar \menuseparator
34300 \begin_inset space ~
34303 Definition\SpecialChar \menuseparator
34304 Remove Last Argument
34305 \begin_inset Newline newline
34309 \begin_inset Phantom HPhantom
34312 \begin_layout Plain Layout
34315 Edit\SpecialChar \menuseparator
34316 Math\SpecialChar \menuseparator
34318 \begin_inset space ~
34321 Definition\SpecialChar \menuseparator
34327 Spitting Out To The Right
34333 <row interlinespace="2.5mm">
34334 <cell alignment="center" valignment="top" usebox="none">
34337 \begin_layout Plain Layout
34338 \begin_inset Graphics
34339 filename ../images/math-macro-append-greedy-param.png
34340 rotateOrigin center
34349 <cell alignment="center" valignment="top" usebox="none">
34352 \begin_layout Plain Layout
34355 Edit\SpecialChar \menuseparator
34356 Math\SpecialChar \menuseparator
34358 \begin_inset space ~
34361 Definition\SpecialChar \menuseparator
34363 \begin_inset Newline newline
34367 \begin_inset Phantom HPhantom
34370 \begin_layout Plain Layout
34373 Edit\SpecialChar \menuseparator
34374 Math\SpecialChar \menuseparator
34376 \begin_inset space ~
34379 Definition\SpecialChar \menuseparator
34385 Eating From The Right
34391 <row interlinespace="2.5mm">
34392 <cell alignment="center" valignment="top" usebox="none">
34395 \begin_layout Plain Layout
34396 \begin_inset Graphics
34397 filename ../images/math-macro-add-greedy-optional-param.png
34398 rotateOrigin center
34407 <cell alignment="center" valignment="top" usebox="none">
34410 \begin_layout Plain Layout
34413 Edit\SpecialChar \menuseparator
34414 Math\SpecialChar \menuseparator
34416 \begin_inset space ~
34419 Definition\SpecialChar \menuseparator
34420 Append Optional Argument
34421 \begin_inset Newline newline
34425 \begin_inset Phantom HPhantom
34428 \begin_layout Plain Layout
34431 Edit\SpecialChar \menuseparator
34432 Math\SpecialChar \menuseparator
34434 \begin_inset space ~
34437 Definition\SpecialChar \menuseparator
34443 Eating From The Right
34456 \begin_layout Section
34457 Computer Algebra Systems
34460 \begin_layout Standard
34461 LyX offers the exchange between mathematical expressions written in LyX's
34462 math editor and external applications or user defined scripts.
34463 Currently supported applications are
34480 Note that the set of supported mathematical constructs is limited only
34481 to very simple cases.
34484 \begin_layout Subsection
34488 \begin_layout Standard
34489 Write some expression in a formula, go to the
34491 Edit\SpecialChar \menuseparator
34492 Math\SpecialChar \menuseparator
34493 Use Computer Algebra System
34495 menu and choose the application you have installed on the computer.
34496 After that the result of computation should show on the right side of the
34497 expression together with the
34498 \begin_inset Quotes eld
34502 \begin_inset Quotes erd
34508 \begin_layout Standard
34509 Here are few simple examples (with results from
34513 ) to show what kind of computations can be performed:
34516 \begin_layout Itemize
34517 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34523 \begin_layout Itemize
34524 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34530 \begin_layout Itemize
34531 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34537 \begin_layout Itemize
34538 \begin_inset Formula $\det\left[\begin{array}{ccc}
34542 \end{array}\right]=-56$
34548 \begin_layout Itemize
34549 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34555 \begin_layout Subsection
34559 \begin_layout Standard
34560 Currently there is no keyboard shortcut for calling the algebra applications.
34561 One can easily bind a shortcut to the
34565 LyX function (see the
34573 \begin_inset space \thinspace{}
34577 \begin_inset space \space{}
34584 key inside the math editor.
34589 one would use this shortcut definition command:
34592 \begin_layout Standard
34595 command-alternatives break-paragraph;math-extern maxima
34598 \begin_layout Section
34600 \begin_inset Index idx
34603 \begin_layout Plain Layout
34612 \begin_layout Subsection
34614 \begin_inset Index idx
34617 \begin_layout Plain Layout
34626 \begin_layout Standard
34627 Negative numbers often look ugly in formulas because the minus sign before
34628 the number is set with the same length as the minus operator sign.
34629 When writing the negative number in normal text, the minus sign appears
34633 \begin_layout Standard
34634 Thus, the problem disappears when converting the minus sign to mathematical
34638 \begin_layout Standard
34639 An example to visualize the problem:
34642 \begin_layout Standard
34644 \begin_inset Tabular
34645 <lyxtabular version="3" rows="3" columns="2">
34646 <features rotate="0" tabularvalignment="middle">
34647 <column alignment="right" valignment="top">
34648 <column alignment="left" valignment="top">
34650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34653 \begin_layout Plain Layout
34659 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34662 \begin_layout Plain Layout
34670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34673 \begin_layout Plain Layout
34679 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34682 \begin_layout Plain Layout
34683 \begin_inset Formula $x=-2$
34693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34696 \begin_layout Plain Layout
34702 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34705 \begin_layout Plain Layout
34706 \begin_inset Formula $x=\textrm{-}2$
34722 \begin_layout Subsection
34723 Comma as decimal Separator
34724 \begin_inset Index idx
34727 \begin_layout Plain Layout
34736 \begin_layout Standard
34737 In LaTeX a comma inside a formula is used, according to the English convention,
34738 as number group separator.
34739 So there will be space added behind all commas in formulas.
34742 \begin_layout Standard
34743 To avoid this, the comma is highlighted and changed to mathematical text
34753 \begin_layout Standard
34754 To use all formula commas in the document as decimal separator, the file
34763 \begin_layout Plain Layout
34768 is part of the LaTeX-package
34773 \begin_inset Index idx
34776 \begin_layout Plain Layout
34781 \begin_layout Plain Layout
34801 \begin_inset Index idx
34804 \begin_layout Plain Layout
34810 is loaded with the LaTeX-preamble line
34813 \begin_layout Standard
34821 \begin_layout Subsection
34823 \begin_inset CommandInset label
34825 name "sub:Physical-Vectors"
34830 \begin_inset Index idx
34833 \begin_layout Plain Layout
34842 \begin_layout Standard
34843 Predefined vectors are offered by the LaTeX-package
34848 \begin_inset Index idx
34851 \begin_layout Plain Layout
34857 that is loaded with the LaTeX-preamble line
34860 \begin_layout Standard
34868 \begin_layout Standard
34872 \begin_layout Plain Layout
34882 \begin_inset Note Note
34885 \begin_layout Plain Layout
34886 The following table will only be displayed when the LaTeX-package
34898 \begin_layout Standard
34899 The following commands are defined:
34902 \begin_layout Standard
34904 \begin_inset Tabular
34905 <lyxtabular version="3" rows="4" columns="2">
34906 <features rotate="0" tabularvalignment="middle">
34907 <column alignment="center" valignment="top">
34908 <column alignment="center" valignment="top">
34910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34913 \begin_layout Plain Layout
34919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34922 \begin_layout Plain Layout
34930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34933 \begin_layout Plain Layout
34943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34946 \begin_layout Plain Layout
34947 \begin_inset Formula $\Bra{\psi}$
34957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34960 \begin_layout Plain Layout
34970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34973 \begin_layout Plain Layout
34974 \begin_inset Formula $\Ket{\psi}$
34984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34987 \begin_layout Plain Layout
34999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35002 \begin_layout Plain Layout
35003 \begin_inset Formula $\Braket{\psi|\phi}$
35019 \begin_layout Standard
35026 assures that all vertical bars are set in the size of the surrounding brackets:
35027 \begin_inset Formula
35029 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
35038 \begin_layout Plain Layout
35048 \begin_inset Note Note
35051 \begin_layout Plain Layout
35052 The following will be displayed when the LaTeX-package
35064 \begin_layout Standard
35065 You need to install the LaTeX-package
35069 to see the rest of this subsection in the output.
35072 \begin_layout Standard
35076 \begin_layout Plain Layout
35088 \begin_layout Standard
35095 can also be achieved using the command
35101 , that is described in
35102 \begin_inset CommandInset ref
35104 reference "sub:Automatic-Bracket-Size"
35111 \begin_layout Subsection
35112 Self-defined Fractions
35113 \begin_inset CommandInset label
35115 name "sub:Self-defined-Fractions"
35120 \begin_inset Index idx
35123 \begin_layout Plain Layout
35124 Fractions ! self-defined
35132 \begin_layout Standard
35133 To define custom commands for fractions, the command
35140 \begin_inset Index idx
35143 \begin_layout Plain Layout
35150 \begin_layout Plain Layout
35164 is used in the following scheme:
35167 \begin_layout Standard
35180 bracket}{fraction bar thickness}{style}
35181 \begin_inset Newline newline
35185 \begin_inset Phantom HPhantom
35188 \begin_layout Plain Layout
35198 {numerator}{denominator}
35201 \begin_layout Standard
35202 The style is a number in the range of 0
35203 \begin_inset space \thinspace{}
35207 \begin_inset space \thinspace{}
35213 \begin_layout Standard
35215 \begin_inset Tabular
35216 <lyxtabular version="3" rows="5" columns="2">
35217 <features rotate="0" tabularvalignment="middle">
35218 <column alignment="center" valignment="top">
35219 <column alignment="center" valignment="top">
35221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35224 \begin_layout Plain Layout
35230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35233 \begin_layout Plain Layout
35241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35244 \begin_layout Plain Layout
35250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35253 \begin_layout Plain Layout
35254 display style formula
35261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35264 \begin_layout Plain Layout
35270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35273 \begin_layout Plain Layout
35281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35284 \begin_layout Plain Layout
35290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35293 \begin_layout Plain Layout
35301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35304 \begin_layout Plain Layout
35310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35313 \begin_layout Plain Layout
35327 \begin_layout Standard
35328 When no style is given, the size is adjusted to the surrounding environment
35329 like for the command
35338 \begin_layout Standard
35339 When no fraction bar thickness is given, the predefined value of 0.4
35340 \begin_inset space \thinspace{}
35346 \begin_layout Standard
35347 \begin_inset VSpace medskip
35350 For example, the commands
35363 \begin_inset CommandInset ref
35365 reference "sub:Fractions"
35369 are defined with the commands
35372 \begin_layout Standard
35381 genfrac{}{}{}{0}{#1}{#2}}
35384 \begin_layout Standard
35388 \begin_layout Standard
35397 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35400 \begin_layout Standard
35401 \begin_inset VSpace medskip
35404 To define a fraction where the fraction bar thickness can be given as optional
35405 argument, the following line is inserted to the LaTeX-preamble:
35408 \begin_layout Standard
35417 genfrac{}{}{#1}{}{#2}{#3}}
35420 \begin_layout Standard
35422 \begin_inset Formula
35424 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35425 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35430 As one can see, the distance of the numerator and the denominator to the
35431 fraction bar is round about three times the bar thickness.
35434 \begin_layout Subsection
35436 \begin_inset Index idx
35439 \begin_layout Plain Layout
35448 \begin_layout Standard
35449 To cancel formulas or formula parts, the LaTeX-package
35454 \begin_inset Index idx
35457 \begin_layout Plain Layout
35463 has to be loaded with the LaTeX-preamble line
35466 \begin_layout Standard
35474 \begin_layout Standard
35478 \begin_layout Plain Layout
35488 \begin_inset Note Note
35491 \begin_layout Plain Layout
35492 The following table will only be displayed when the LaTeX-package
35504 \begin_layout Standard
35505 There are four ways to cancel formulas:
35508 \begin_layout Standard
35510 \begin_inset Tabular
35511 <lyxtabular version="3" rows="5" columns="2">
35512 <features rotate="0" tabularvalignment="middle">
35513 <column alignment="center" valignment="top">
35514 <column alignment="center" valignment="top">
35516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35519 \begin_layout Plain Layout
35525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35528 \begin_layout Plain Layout
35530 \begin_inset Note Note
35533 \begin_layout Plain Layout
35540 are used here as spacer.
35552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35555 \begin_layout Plain Layout
35564 \begin_layout Plain Layout
35578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35581 \begin_layout Plain Layout
35582 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35595 \begin_layout Plain Layout
35604 \begin_layout Plain Layout
35618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35621 \begin_layout Plain Layout
35622 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35635 \begin_layout Plain Layout
35644 \begin_layout Plain Layout
35658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35661 \begin_layout Plain Layout
35662 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35675 \begin_layout Plain Layout
35679 \begin_inset Formula $\to$
35690 \begin_layout Plain Layout
35704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35707 \begin_layout Plain Layout
35708 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35724 \begin_layout Standard
35731 is especially suitable to visualize the reduction of fractions within formulas:
35732 \begin_inset Formula
35734 \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}}}
35742 \begin_layout Standard
35743 To change the size of
35750 \begin_inset Quotes eld
35754 \begin_inset Quotes erd
35757 value one can load the package
35761 with either the option
35765 which leads to the same size as for the canceled value or with the option
35770 which makes is it a bit smaller than the size one gets without using a
35776 was loaded with this line:
35779 \begin_layout Standard
35784 usepackage[samesize]{cancel}
35787 \begin_layout Standard
35788 To color the cancellation bar one adds this command as TeX code:
35791 \begin_layout Standard
35803 \begin_layout Standard
35808 can be replaced by a color of your choice.
35811 \begin_layout Standard
35815 \begin_layout Plain Layout
35831 \begin_layout Standard
35832 \begin_inset Formula
35834 \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}}}
35842 \begin_layout Standard
35846 \begin_layout Plain Layout
35860 \begin_inset Note Note
35863 \begin_layout Plain Layout
35872 \begin_layout Standard
35873 For further customizations, see the documentation of the package
35878 \begin_inset CommandInset citation
35887 \begin_layout Standard
35891 \begin_layout Plain Layout
35901 \begin_inset Note Note
35904 \begin_layout Plain Layout
35905 The following will be displayed when the LaTeX-package
35917 \begin_layout Standard
35918 You need to install the LaTeX-package
35922 to see the rest of this subsection in the output.
35925 \begin_layout Standard
35929 \begin_layout Plain Layout
35941 \begin_layout Standard
35942 \begin_inset Newpage newpage
35948 \begin_layout Subsection
35949 Formulas in Section Headings
35950 \begin_inset CommandInset label
35952 name "sub:Formulas-in-Section"
35957 \begin_inset Index idx
35960 \begin_layout Plain Layout
35961 Formula ! in section headings
35969 \begin_layout Standard
35970 When formulas are used in section headings, the following has to be taken
35974 \begin_layout Standard
35975 \begin_inset Note Greyedout
35978 \begin_layout Plain Layout
35984 \begin_inset Index idx
35987 \begin_layout Plain Layout
35988 Packages ! hyperref
35993 support is enabled in the document settings dialog under
35996 \begin_inset space ~
36001 , PDF-bookmarks are created for every section heading in the table of contents.
36002 If a section heading contains formulas, they are incorrectly displayed
36003 in the bookmark text, because formulas in bookmarks infringe the PDF convention
36012 \begin_layout Standard
36013 Both problems can be solved by inserting at the end of the section heading
36014 a short title with the menu
36016 Insert\SpecialChar \menuseparator
36018 \begin_inset space ~
36024 Short titles are used as alternative for multiline section headings to
36025 keep the table of contents clearly arranged.
36026 Only the short title appears in the table of contents and therefore also
36027 in the PDF-bookmark.
36030 \begin_layout Standard
36031 When formulas should be used in the table of contents but
36035 is used, one can use the following command in TeX-mode:
36038 \begin_layout Standard
36043 texorpdfstring{part}{alternative}
36044 \begin_inset Index idx
36047 \begin_layout Plain Layout
36058 \begin_layout Standard
36059 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36060 This can be characters, formulas, footnotes, but also cross-references.
36061 The alternative is used instead of the part for the bookmark.
36064 \begin_layout Standard
36065 Here are two example headings:
36066 \begin_inset VSpace -3mm
36073 \begin_layout Plain Layout
36085 \begin_layout Subsubsection
36086 Heading without formula in table of contents
36087 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36091 \begin_inset Argument 1
36094 \begin_layout Plain Layout
36095 Heading without formula in table of contents
36103 \begin_layout Subsubsection
36104 Heading with formula in table of contents
36108 \begin_layout Plain Layout
36118 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36125 \begin_layout Plain Layout
36135 \begin_layout Standard
36139 \begin_layout Plain Layout
36148 In the first heading a short title was used, in the second one
36157 \begin_layout Standard
36158 To get the same formatting as for the other headings, the complete heading
36167 \begin_layout Plain Layout
36169 \begin_inset CommandInset ref
36171 reference "sub:Bold-Formulas"
36183 \begin_layout Subsection
36184 Formulas in multi-column Text
36185 \begin_inset Index idx
36188 \begin_layout Plain Layout
36189 Formula ! in multi-column text
36197 \begin_layout Standard
36198 Formulas in multi-column text are often too wide to fit into a column and
36199 thus need to be set over the whole page width.
36200 This is done by using the LaTeX-package
36208 \begin_layout Plain Layout
36213 is part of every LaTeX standard installation.
36219 \begin_inset Index idx
36222 \begin_layout Plain Layout
36223 Packages ! multicol
36228 , that is loaded with the LaTeX-preamble line
36231 \begin_layout Standard
36236 usepackage{multicol}
36239 \begin_layout Standard
36240 \begin_inset Note Greyedout
36243 \begin_layout Plain Layout
36244 Note that in this case the setting
36247 \begin_inset space ~
36254 Document\SpecialChar \menuseparator
36260 \begin_inset space ~
36280 \begin_layout Standard
36281 Before the multi-column text the command
36284 \begin_layout Standard
36289 begin{multicols}{column number}
36292 \begin_layout Standard
36293 is written in TeX-mode.
36294 The column number is a number in the range of 2
36295 \begin_inset space \thinspace{}
36299 \begin_inset space \thinspace{}
36303 Before the formula the multi-column text is ended by inserting the command
36306 \begin_layout Standard
36314 \begin_layout Standard
36318 \begin_layout Standard
36319 Due to the command some space is automatically added before the formula.
36321 \begin_inset space \thinspace{}
36324 mm vertical space is inserted before the formula.
36325 When the formula style
36331 \begin_layout Plain Layout
36333 \begin_inset CommandInset ref
36335 reference "sec:Formula-Styles"
36347 \begin_inset space \thinspace{}
36350 mm space is inserted instead.
36353 \begin_layout Standard
36354 As example a multi-column text with a displayed formula:
36357 \begin_layout Standard
36363 \begin_layout Plain Layout
36367 begin{multicols}{2}
36372 Das Spektrum wird fouriertransformiert.
36373 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36374 , Lösungsmittel) zu trennen.
36375 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36376 nun das Aussehen des Ausgangssignals.
36377 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36378 über alle Phasen integrieren muss.
36380 \begin_inset Formula $S$
36383 unser normiertes Ausgangssignal und
36384 \begin_inset Formula $P$
36387 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36391 \begin_layout Plain Layout
36401 \begin_inset VSpace -6mm
36405 \begin_inset Formula
36407 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36416 \begin_layout Plain Layout
36420 begin{multicols}{2}
36426 \begin_inset Formula $S_{0}$
36429 das Signal ohne Gradient ist und die Normierungsbedingung
36430 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36434 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36436 \begin_inset Formula $\nicefrac{\pi}{2}$
36440 \begin_inset space \thinspace{}
36443 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36444 das Signal zusätzlich abschwächt.
36445 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36447 \begin_inset Formula $T_{2}$
36453 \begin_layout Standard
36459 \begin_layout Plain Layout
36471 \begin_layout Subsection
36472 Formulas with Description of Variables
36473 \begin_inset Index idx
36476 \begin_layout Plain Layout
36477 Formula ! with description of variables
36485 \begin_layout Standard
36486 To describe variables within a formula, like in formula
36487 \begin_inset CommandInset ref
36489 reference "eq:within"
36498 \begin_inset Formula $n$
36502 \begin_inset space ~
36505 matrix is used with left aligned columns for the
36506 \begin_inset Formula $n$
36513 \begin_layout Plain Layout
36515 \begin_inset CommandInset ref
36517 reference "sec:Matrices"
36526 To set the description in a smaller size, before the matrix e.
36527 \begin_inset space \thinspace{}
36531 \begin_inset space \space{}
36544 \begin_layout Plain Layout
36546 \begin_inset CommandInset ref
36548 reference "sub:Font-Sizes"
36560 \begin_layout Standard
36561 When the formula style
36567 \begin_layout Plain Layout
36569 \begin_inset CommandInset ref
36571 reference "sec:Formula-Styles"
36592 \begin_layout Plain Layout
36599 only works in formulas with the style
36604 \begin_inset CommandInset ref
36606 reference "sub:Variable-Space"
36615 is inserted before and after the matrix to have the same separation of
36616 the matrix from the equation and the side margin.
36619 \begin_layout Standard
36620 When the formula style
36624 is used, the method described in
36625 \begin_inset CommandInset ref
36627 reference "sub:Flalign-Environment"
36631 is used to indent formulas.
36633 \begin_inset CommandInset ref
36635 reference "eq:within"
36639 consists of five columns where in the first two columns contain the equation,
36640 the third the matrix and the last one an empty TeX-brace.
36641 \begin_inset Formula
36643 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36644 \rho & \textrm{density}\\
36645 V & \textrm{volume}\\
36646 g & \textrm{gravitational acceleration}
36647 \end{array} & & {}\label{eq:within}
36655 \begin_layout Subsection
36656 Upright small Greek Letters
36657 \begin_inset CommandInset label
36659 name "sub:Upright-small-Greek"
36664 \begin_inset Index idx
36667 \begin_layout Plain Layout
36668 Greek letters ! upright
36676 \begin_layout Standard
36677 Most of the math fonts only provide italic small Greek letters.
36678 But for symbols of elementary particles like pions and neutrinos, upright
36679 Greek letters are needed.
36688 \begin_layout Plain Layout
36693 is part of the LaTeX-package
36698 \begin_inset Index idx
36701 \begin_layout Plain Layout
36706 \begin_layout Plain Layout
36726 \begin_inset Index idx
36729 \begin_layout Plain Layout
36735 that is loaded with the LaTeX-preamble line
36738 \begin_layout Standard
36743 usepackage{upgreek}
36746 \begin_layout Standard
36752 \begin_layout Plain Layout
36762 \begin_inset Note Note
36765 \begin_layout Plain Layout
36766 The following table will only be displayed when the LaTeX-package
36775 They are created when the command for a small Greek letter is started with
36781 For example the command
36788 \begin_inset Formula $\uptau$
36794 \begin_layout Standard
36795 With these commands reactions of elementary particles can be typeset:
36796 \begin_inset Formula
36798 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36806 \begin_layout Standard
36807 The upright letters are more bold and wider than the italic ones.
36808 They should therefore not be used for units like
36809 \begin_inset Quotes eld
36813 \begin_inset Quotes erd
36819 \begin_layout Standard
36823 \begin_layout Plain Layout
36833 \begin_inset Note Note
36836 \begin_layout Plain Layout
36837 The following will be displayed when the LaTeX-package
36849 \begin_layout Standard
36850 You need to install the LaTeX-package
36854 to see the rest of this subsection in the output.
36857 \begin_layout Standard
36861 \begin_layout Plain Layout
36873 \begin_layout Subsection
36874 Text Characters in Formulas
36875 \begin_inset CommandInset label
36877 name "sub:Text-Characters-in"
36882 \begin_inset Index idx
36885 \begin_layout Plain Layout
36894 \begin_layout Standard
36895 In some cases you might want to insert text characters directly into formulas.
36896 When for example the centered dot · is often used in formulas like
36897 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36900 , one would have to insert the command
36910 \begin_layout Plain Layout
36912 \begin_inset CommandInset ref
36914 reference "sub:Binary-Operators"
36923 all the time, because this character is defined in all encodings as text
36925 But the encoding can be changed by this LaTeX-preamble line:
36928 \begin_layout Standard
36933 Declare Inputtext{183}{
36943 f\SpecialChar \textcompwordmark{}
36947 \begin_layout Standard
36948 The character encoding (menu
36950 Document\SpecialChar \menuseparator
36951 Settings\SpecialChar \menuseparator
36954 ) specifies what character appears when a keyboard key is pressed.
36955 When the key for the character '·' is pressed, internally the command
36962 But this command is not available in a formula so that you would get LaTeX-erro
36964 With the changed encoding the right command is chosen automatically, depending
36965 on if the character was inserted into a formula or not.
36968 \begin_layout Standard
36969 The encoding of several characters is saved in definition files.
36970 For example the encoding
36974 is defined in the file
36978 which is in the installation folder of LaTeX.
36979 Encodings should only be changed via the LaTeX-preamble and not in the
36981 Otherwise documents could not be edited by other LyX users working on other
36985 \begin_layout Standard
36986 \begin_inset VSpace medskip
36989 Besides the centered dot, in this document the degree sign ° is defined
36990 with the following LaTeX-preamble line so that it can be directly inserted
36994 \begin_layout Standard
36999 DeclareInputtext{176}{
37009 f\SpecialChar \textcompwordmark{}
37013 \begin_layout Standard
37014 \begin_inset Newpage newpage
37020 \begin_layout Section
37023 \begin_inset Index idx
37026 \begin_layout Plain Layout
37035 \begin_layout Standard
37036 This section is a summary of the most important typographic rules, listed
37041 \begin_layout Plain Layout
37042 This collection was partly taken from the German semi-official dictionary
37044 \begin_inset Quotes eld
37048 \begin_inset Quotes erd
37052 \begin_inset CommandInset citation
37058 that lists some of the ISO rules.
37059 More rules are listed in
37060 \begin_inset CommandInset citation
37074 \begin_layout Itemize
37083 \begin_layout Plain Layout
37084 done with font styles, see
37085 \begin_inset CommandInset ref
37087 reference "sub:Font-Styles"
37096 , no matter if they appear in italic text: 30
37097 \begin_inset space \thinspace{}
37101 \begin_inset Newline newline
37104 Between the value and the unit is the smallest space, see
37105 \begin_inset CommandInset ref
37107 reference "sub:Predefined-Space"
37112 \begin_inset Newline newline
37115 This convention is automatically fulfilled when the command
37122 When it is entered to a formula, two boxes appear.
37123 In the first one the value is inserted, in the second one the unit, and
37125 \begin_inset Formula $\unit[30]{km/h}$
37129 \begin_inset space \thinspace{}
37139 is not a real LaTeX command but the command
37145 , therefore you cannot use it in TeX code.
37148 \begin_layout Itemize
37149 Percent and perthousand signs are set like physical units:
37150 \begin_inset Newline newline
37154 \begin_inset space \thinspace{}
37160 \begin_layout Itemize
37161 The degree sign follows directly on the value: 15°, but not when it is used
37163 \begin_inset space \thinspace{}
37169 \begin_layout Itemize
37170 In numbers with more than four digits the smallest space is inserted before
37171 every third digit to group them:
37181 \begin_inset space \thinspace{}
37185 \begin_inset space \thinspace{}
37191 \begin_layout Itemize
37192 For dimensions like 120×90×40
37193 \begin_inset space \thinspace{}
37196 cm the multiplication sign
37197 \begin_inset Quotes eld
37201 \begin_inset Quotes erd
37205 It is available either via the command
37213 Insert\SpecialChar \menuseparator
37214 Special Character\SpecialChar \menuseparator
37220 \begin_layout Itemize
37221 Functions with names consisting of several letters are set upright to avoid
37223 \begin_inset CommandInset ref
37225 reference "sub:Predefined-Functions"
37232 \begin_layout Itemize
37233 Indices consisting of several letters, are set upright:
37234 \begin_inset Formula $E_{\mathrm{kin}}$
37238 \begin_inset Newline newline
37241 Components of matrices are set italic:
37242 \begin_inset Formula $\hat{H}_{kl}$
37248 \begin_layout Itemize
37249 The differentiation/integration operator 'd', the Euler's number 'e' and
37250 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37254 \begin_layout Itemize
37255 The character that denotes a
37259 transformation is inserted either by the command
37267 \begin_layout Plain Layout
37280 Insert\SpecialChar \menuseparator
37281 Special Character\SpecialChar \menuseparator
37282 Symbols\SpecialChar \menuseparator
37284 \begin_inset space ~
37290 \begin_inset Formula $\mathscr{F}$
37296 \begin_layout Standard
37297 \begin_inset Newpage newpage
37303 \begin_layout Section
37305 \begin_inset Index idx
37308 \begin_layout Plain Layout
37317 \begin_layout Standard
37318 Some characters and symbols can be created with several commands.
37319 Here is a list of the synonym commands:
37322 \begin_layout Standard
37323 \begin_inset VSpace bigskip
37327 \begin_inset space \hfill{}
37331 \begin_inset Tabular
37332 <lyxtabular version="3" rows="12" columns="2">
37333 <features rotate="0" tabularvalignment="middle">
37334 <column alignment="center" valignment="top" width="0pt">
37335 <column alignment="center" valignment="top" width="0pt">
37337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37340 \begin_layout Plain Layout
37346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37349 \begin_layout Plain Layout
37351 \begin_inset Note Note
37354 \begin_layout Plain Layout
37361 is only used as spacer.
37373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37376 \begin_layout Plain Layout
37384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37387 \begin_layout Plain Layout
37391 \begin_layout Plain Layout
37404 \begin_layout Plain Layout
37418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37421 \begin_layout Plain Layout
37429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37432 \begin_layout Plain Layout
37442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37445 \begin_layout Plain Layout
37453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37456 \begin_layout Plain Layout
37466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37469 \begin_layout Plain Layout
37477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37480 \begin_layout Plain Layout
37488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37491 \begin_layout Plain Layout
37499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37502 \begin_layout Plain Layout
37510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37513 \begin_layout Plain Layout
37521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37524 \begin_layout Plain Layout
37534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37537 \begin_layout Plain Layout
37545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37548 \begin_layout Plain Layout
37558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37561 \begin_layout Plain Layout
37569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37572 \begin_layout Plain Layout
37582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37585 \begin_layout Plain Layout
37593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37596 \begin_layout Plain Layout
37606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37609 \begin_layout Plain Layout
37617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37620 \begin_layout Plain Layout
37628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37631 \begin_layout Plain Layout
37639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37642 \begin_layout Plain Layout
37654 \begin_inset space \hfill{}
37658 \begin_inset Tabular
37659 <lyxtabular version="3" rows="12" columns="2">
37660 <features rotate="0" tabularvalignment="middle">
37661 <column alignment="center" valignment="top" width="0pt">
37662 <column alignment="center" valignment="top" width="0pt">
37664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37667 \begin_layout Plain Layout
37673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37676 \begin_layout Plain Layout
37684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37687 \begin_layout Plain Layout
37695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37698 \begin_layout Plain Layout
37710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37713 \begin_layout Plain Layout
37721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37724 \begin_layout Plain Layout
37734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37737 \begin_layout Plain Layout
37745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37748 \begin_layout Plain Layout
37758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37761 \begin_layout Plain Layout
37769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37772 \begin_layout Plain Layout
37780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37783 \begin_layout Plain Layout
37791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37794 \begin_layout Plain Layout
37802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37805 \begin_layout Plain Layout
37813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37816 \begin_layout Plain Layout
37826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37829 \begin_layout Plain Layout
37837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37840 \begin_layout Plain Layout
37850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37853 \begin_layout Plain Layout
37861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37864 \begin_layout Plain Layout
37874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37877 \begin_layout Plain Layout
37885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37888 \begin_layout Plain Layout
37898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37901 \begin_layout Plain Layout
37909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37912 \begin_layout Plain Layout
37922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37925 \begin_layout Plain Layout
37933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37936 \begin_layout Plain Layout
37950 \begin_inset space \hfill{}
37956 \begin_layout Standard
37957 \begin_inset Newpage newpage
37963 \begin_layout Bibliography
37964 \begin_inset CommandInset bibitem
37965 LatexCommand bibitem
37977 The LaTeX Companion
37980 Addison Wesley, 2004
37983 \begin_layout Bibliography
37984 \begin_inset CommandInset bibitem
37985 LatexCommand bibitem
37991 \begin_inset CommandInset href
37994 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37998 of LaTeX's math abilities
38001 \begin_layout Bibliography
38002 \begin_inset CommandInset bibitem
38003 LatexCommand bibitem
38009 \begin_inset CommandInset href
38012 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
38020 \begin_layout Plain Layout
38032 \begin_layout Bibliography
38033 \begin_inset CommandInset bibitem
38034 LatexCommand bibitem
38040 \begin_inset CommandInset href
38043 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38047 of all symbols available with LaTeX-packages
38050 \begin_layout Bibliography
38051 \begin_inset CommandInset bibitem
38052 LatexCommand bibitem
38058 \begin_inset CommandInset href
38060 name "Documentation"
38061 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
38065 of the LaTeX-package
38070 \begin_inset Index idx
38073 \begin_layout Plain Layout
38082 \begin_layout Bibliography
38083 \begin_inset CommandInset bibitem
38084 LatexCommand bibitem
38090 \begin_inset CommandInset href
38092 name "Documentation"
38093 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38097 of the LaTeX-package
38102 \begin_inset Index idx
38105 \begin_layout Plain Layout
38106 Packages ! hyperref
38114 \begin_layout Bibliography
38115 \begin_inset CommandInset bibitem
38116 LatexCommand bibitem
38122 \begin_inset CommandInset href
38124 name "Documentation"
38125 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38129 of the LaTeX-package
38134 \begin_inset Index idx
38137 \begin_layout Plain Layout
38146 \begin_layout Bibliography
38147 \begin_inset CommandInset bibitem
38148 LatexCommand bibitem
38154 \begin_inset CommandInset href
38157 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
38168 \begin_inset CommandInset ref
38170 reference "sub:Operator-Limits"
38175 \begin_inset Index idx
38178 \begin_layout Plain Layout
38189 \begin_layout Bibliography
38190 \begin_inset CommandInset bibitem
38191 LatexCommand bibitem
38202 Auflage, Duden 2001
38205 \begin_layout Bibliography
38206 \begin_inset CommandInset bibitem
38207 LatexCommand bibitem
38213 \begin_inset CommandInset href
38216 target "http://physics.nist.gov/Document/checklist.pdf"
38220 for reviewing manuscripts
38223 \begin_layout Standard
38224 \begin_inset CommandInset index_print
38225 LatexCommand printindex