1 #LyX 2.2 created this file. For more info see http://www.lyx.org/
8 % DO NOT ALTER THIS PREAMBLE!!!
10 % This preamble is designed to ensure that the file prints
11 % out as advertised. If you mess with this preamble,
12 % parts of this document may not print out as expected. If you
13 % have problems LaTeXing this file, please contact
14 % the documentation team
15 % email: lyx-docs@lists.lyx.org
21 % set fonts for nicer pdf view
22 \IfFileExists{lmodern.sty}
23 {\usepackage{lmodern}}{}
25 \fi % end if pdflatex is used
27 % solves the following problem:
28 % If the dection number consits of too many numerals the section heading
29 % will be printed in the TOC without a space between it and the section number.
30 % As solution more space between the number and the heading is inserted:
31 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
32 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
34 % increase link area for cross-references and autoname them,
35 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
36 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
37 \@ifpackageloaded{babel}{
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41 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
42 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
46 % don't load packages twice
47 % see first footnote in sec. 9.3
48 \@ifundefined{textcolor}{\usepackage{color}}{}
50 % the pages of the TOC are numbered roman
51 % and a PDF-bookmark for the TOC is added
53 \let\myTOC\tableofcontents
54 \renewcommand{\tableofcontents}{%
56 \pdfbookmark[1]{\contentsname}{}
59 \pagenumbering{arabic}}
61 % add 0.5 mm vertical space for table rows
62 \@ifundefined{extrarowheight} {\usepackage{array}}{}
63 \setlength{\extrarowheight}{0.5mm}
65 % insert additional vertical space of 1.5 mm between footnotes,
67 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
69 % makes caption labels bold
70 \setkomafont{captionlabel}{\bfseries}
72 % enables calculation of values
75 % for multiple columns used in sec. 24.7
81 % for the Fourier transformation symbol
84 % define a color, used in sec.9.3
85 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
87 % declare operators (see sec. 10.4 and sec. 15.2)
88 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
89 \DeclareMathOperator{\sgn}{sgn}
91 % example definitions for sec. 20.1
92 \newcommand{\gr}{\Longrightarrow}
93 \newcommand{\us}[1]{\underline{#1}}
94 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
95 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
96 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
98 % example macro from sec. 19.4
99 %\def\tagform@#1{\maketag@@@{|#1|}}
102 % ------------------------------------
103 % used to check for needed LaTeX packages
106 % check for package undertilde
107 % used for the command \utilde
108 \newboolean{undertilde}
109 \IfFileExists{undertilde.sty}
110 {\usepackage{undertilde}
111 \setboolean{undertilde}{true}}
112 {\setboolean{undertilde}{false}}
114 % check for package eurosym
115 % used for the Euro symbol
117 \IfFileExists{eurosym.sty}
118 {\usepackage[gennarrow]{eurosym}
119 \setboolean{eurosym}{true}}
120 {\setboolean{eurosym}{false}}
122 % check for package braket
123 % used for physical vectors
125 \IfFileExists{braket.sty}
127 \setboolean{braket}{true}}
128 {\setboolean{braket}{false}}
130 % check for package cancel
132 \IfFileExists{cancel.sty}
134 \setboolean{cancel}{true}}
135 {\setboolean{cancel}{false}}
137 % check for package upgreek
139 \IfFileExists{upgreek.sty}
140 {\usepackage{upgreek}
141 \setboolean{upgreek}{true}}
142 {\setboolean{upgreek}{false}}
144 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
145 \use_default_options false
146 \maintain_unincluded_children false
148 \language_package default
153 \font_typewriter default
155 \font_default_family default
156 \use_non_tex_fonts false
162 \default_output_format default
164 \bibtex_command default
165 \index_command default
169 \pdf_title "LyX's Math Manual"
170 \pdf_author "LyX Team, Uwe Stöhr"
171 \pdf_subject "LyX-documentation about math"
172 \pdf_keywords "LyX, Mathed"
174 \pdf_bookmarksnumbered true
175 \pdf_bookmarksopen true
176 \pdf_bookmarksopenlevel 1
177 \pdf_breaklinks false
181 \pdf_pdfusetitle false
182 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
185 \use_package amsmath 2
186 \use_package amssymb 2
187 \use_package cancel 0
189 \use_package mathdots 1
190 \use_package mathtools 2
191 \use_package mhchem 1
192 \use_package stackrel 0
193 \use_package stmaryrd 0
194 \use_package undertilde 0
196 \cite_engine_type default
200 \paperorientation portrait
204 \notefontcolor #0000ff
211 \paragraph_separation skip
213 \quotes_language english
216 \paperpagestyle plain
220 \tracking_changes false
221 \output_changes false
224 \html_be_strict false
231 's detailed Math manual
235 by the \SpecialChar LyX
240 \begin_layout Plain Layout
242 If you have comments or error corrections, please send them to the \SpecialChar LyX
247 \begin_inset CommandInset href
249 name "lyx-docs@lists.lyx.org"
250 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
261 \begin_inset Note Note
264 \begin_layout Plain Layout
271 \begin_inset Newline newline
275 \begin_inset Newline newline
283 \begin_layout Standard
284 \begin_inset CommandInset toc
285 LatexCommand tableofcontents
292 \begin_layout Standard
293 \begin_inset Note Note
296 \begin_layout Plain Layout
297 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
300 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
307 If they are not installed the document can be exported anyway but the sections
308 where the packages are required will not appear in the output.
313 ; if it is not installed, this file cannot be exported.
316 \begin_layout Plain Layout
317 The latest PDF-version of this document can be found here:
318 \begin_inset Newline newline
323 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
331 \begin_layout Standard
332 \begin_inset Newpage newpage
338 \begin_layout Section
342 \begin_layout Standard
343 This document explains \SpecialChar LyX
344 's math features and is furthermore a collection
345 of \SpecialChar LaTeX
346 -commands used for mathematical characters and constructs.
347 The explanations are designed for the usage of commands.
348 It is therefore required that you have read the section
359 \begin_layout Standard
360 Most of the characters and many constructs explained in this manual are
361 also accessible via the menu
365 \SpecialChar menuseparator
381 But everybody who has to write lots of formulas will notice that it is
382 much faster to use commands instead of the math toolbar.
383 Therefore this manual is focused on commands but also mentions the correspondin
384 g toolbar buttons when available.
387 \begin_layout Standard
388 If not specially mentioned the commands are only available within formulas.
389 To be able to use all commands explained in this document, the option
393 must be checked in the document settings (menu
395 Document\SpecialChar menuseparator
396 Settings\SpecialChar menuseparator
407 \begin_layout Plain Layout
410 Use AMS math package automatically
416 \begin_layout Plain Layout
425 -math when math constructs are found that are supported by \SpecialChar LyX
434 \begin_layout Standard
435 This document doesn't list all
439 \begin_layout Plain Layout
452 \begin_layout Plain Layout
457 \begin_layout Plain Layout
466 -math commands is in the file
469 \begin_inset CommandInset href
472 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
478 , which is part of every \SpecialChar LaTeX
479 standard installation.
484 for lucidity reasons.
487 \begin_layout Section
491 \begin_layout Standard
492 To create an inline formula
493 \begin_inset Index idx
496 \begin_layout Plain Layout
502 that is embedded into a text line, use one of the shortcuts
508 or the toolbar button
515 \begin_inset Newline newline
518 To create a display style formula
519 \begin_inset Index idx
522 \begin_layout Plain Layout
523 Formula ! display style
528 which will appear bigger, has a different format, and will be in a separate
529 paragraph, use one of these shortcuts:
538 \begin_layout Standard
539 To change a display style formula to an inline formula, set the cursor into
540 the formula and use one of the shortcuts
548 Edit\SpecialChar menuseparator
549 Math\SpecialChar menuseparator
553 The same way is used to change an inline formula to a display style formula.
556 \begin_layout Standard
557 To display parts of an inline formula in the size of a display style formula,
565 \begin_inset Index idx
568 \begin_layout Plain Layout
577 Then a new blue box appears in which the desired formula part is inserted.
580 \begin_layout Standard
581 Only inline formulas are allowed inside tables.
584 \begin_layout Standard
589 can be turned on in the menu
591 View\SpecialChar menuseparator
595 When you click there on
596 \begin_inset Quotes eld
600 \begin_inset Quotes erd
603 the toolbar will be shown permanently at the bottom; this state is visualized
608 menu with a checkmark.
609 When you click in this state again on
610 \begin_inset Quotes eld
614 \begin_inset Quotes erd
625 is only shown when the cursor is within a formula; this state is visualized
626 by the renaming of the menu entry from
627 \begin_inset Quotes eld
631 \begin_inset Quotes erd
635 \begin_inset Quotes eld
643 \begin_inset Quotes erd
649 \begin_layout Standard
652 \begin_inset Index idx
655 \begin_layout Plain Layout
662 is invoked by pressing the toolbar button
670 Insert\SpecialChar menuseparator
682 \begin_layout Standard
683 To change the \SpecialChar LaTeX
685 \begin_inset Index idx
688 \begin_layout Plain Layout
697 Document\SpecialChar menuseparator
698 Settings\SpecialChar menuseparator
708 \begin_layout Standard
709 To edit matrices, case differentiations and multiline formulas subsequently,
712 Edit\SpecialChar menuseparator
717 Edit\SpecialChar menuseparator
719 \begin_inset space \thinspace{}
723 \begin_inset space \thinspace{}
733 When lines and columns are swapped via the menu, the column or line where
734 the cursor is in is exchanged with the column to the right or the line
736 Is the cursor in the last column or row, the exchange is done with the
737 column to the left or the line above.
740 \begin_layout Standard
741 To write text in formulas
745 \begin_layout Plain Layout
746 For multiline formulas the command
753 \begin_inset CommandInset ref
755 reference "subsec:Text-in-multiline"
769 \begin_inset Index idx
772 \begin_layout Plain Layout
779 \begin_inset Index idx
782 \begin_layout Plain Layout
789 This mode is invoked with the shortcut
795 or by the insertion of the command
802 \begin_inset Index idx
805 \begin_layout Plain Layout
814 The text appears black in \SpecialChar LyX
815 and can therefore be distinguished from the
816 other formula parts which appear blue.
817 In the output mathematical text is set upright, in contrary to other formula
821 \begin_layout Subsection*
825 \begin_layout Standard
826 Most of the \SpecialChar LaTeX
827 -commands for math constructs have the following scheme:
830 \begin_layout Standard
846 \begin_layout Standard
847 A command always starts with a backslash
848 \begin_inset Quotes gld
858 \begin_inset Quotes grd
862 To omit optional arguments, also omit the associated brackets.
863 The braces around the required arguments are named in this document as
866 \begin_inset Index idx
869 \begin_layout Plain Layout
877 If you add in a formula a left brace to a command name, \SpecialChar LyX
879 creates a \SpecialChar TeX
881 In all other cases \SpecialChar TeX
882 braces are created in formulas with the command
890 braces appear red in \SpecialChar LyX
891 , in contrary to normal braces which appear blue.
893 mode no command is needed to get \SpecialChar TeX
896 braces don't appear in the output.
899 \begin_layout Standard
900 When commands without arguments, like commands for symbols are entered in
902 mode, a space character must
906 be behind the command to end it.
907 This space doesn't appear in the output.
908 When the space should appear in the output, the space must be followed
909 by a protected space in normal text.
912 \begin_layout Standard
913 A protected space is inserted with
916 arg "command-alternatives space-insert protected ; math-space"
922 \begin_layout Subsection*
923 \begin_inset Newpage newpage
929 \begin_layout Itemize
931 \begin_inset space \textvisiblespace{}
934 denotes a space character to be input.
937 \begin_layout Itemize
939 \begin_inset Formula $\to$
942 denotes the usage of the corresponding arrow key on the keyboard.
947 key can often be used instead of
948 \begin_inset Formula $\to$
952 \begin_inset Formula $\downarrow$
960 \begin_inset Formula $\leftarrow$
964 \begin_inset Formula $\uparrow$
970 \begin_layout Subsection*
974 \begin_layout Standard
976 \begin_inset Float table
982 \begin_layout Plain Layout
984 \begin_inset Caption Standard
986 \begin_layout Plain Layout
987 \begin_inset CommandInset label
989 name "tab:Available-units"
1001 \begin_layout Plain Layout
1003 \begin_inset Tabular
1004 <lyxtabular version="3" rows="13" columns="2">
1005 <features booktabs="true" tabularvalignment="middle">
1006 <column alignment="center" valignment="top">
1007 <column alignment="center" valignment="top" width="0pt">
1009 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1012 \begin_layout Plain Layout
1018 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1021 \begin_layout Plain Layout
1029 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1032 \begin_layout Plain Layout
1038 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1041 \begin_layout Plain Layout
1049 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1052 \begin_layout Plain Layout
1058 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1061 \begin_layout Plain Layout
1069 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1072 \begin_layout Plain Layout
1078 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1081 \begin_layout Plain Layout
1083 \begin_inset space \thinspace{}
1087 \begin_inset space \thinspace{}
1097 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1100 \begin_layout Plain Layout
1106 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1109 \begin_layout Plain Layout
1111 \begin_inset space \thinspace{}
1115 \begin_inset space \thinspace{}
1125 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1128 \begin_layout Plain Layout
1134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1137 \begin_layout Plain Layout
1139 \begin_inset space \thinspace{}
1143 \begin_inset space \thinspace{}
1153 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1156 \begin_layout Plain Layout
1162 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1165 \begin_layout Plain Layout
1167 \begin_inset space \thinspace{}
1171 \begin_inset space \thinspace{}
1181 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1184 \begin_layout Plain Layout
1190 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1193 \begin_layout Plain Layout
1195 \begin_inset space \thinspace{}
1199 \begin_inset space \thinspace{}
1209 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1212 \begin_layout Plain Layout
1218 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1221 \begin_layout Plain Layout
1223 \begin_inset space \thinspace{}
1227 \begin_inset Formula $\approx$
1231 \begin_inset space \thinspace{}
1241 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1244 \begin_layout Plain Layout
1250 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1253 \begin_layout Plain Layout
1255 \begin_inset space \thinspace{}
1259 \begin_inset space \thinspace{}
1269 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1272 \begin_layout Plain Layout
1278 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1281 \begin_layout Plain Layout
1285 \begin_inset Quotes eld
1291 \begin_inset Quotes erd
1301 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1304 \begin_layout Plain Layout
1310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1313 \begin_layout Plain Layout
1315 \begin_inset Quotes eld
1323 \begin_inset Quotes erd
1333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1336 \begin_layout Plain Layout
1342 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1345 \begin_layout Plain Layout
1347 \begin_inset space \thinspace{}
1351 \begin_inset Formula $\nicefrac{1}{18}$
1355 \begin_inset space \thinspace{}
1376 \begin_layout Standard
1377 \begin_inset Newpage newpage
1383 \begin_layout Section
1387 \begin_layout Subsection
1389 \begin_inset Index idx
1392 \begin_layout Plain Layout
1399 \begin_inset Index idx
1402 \begin_layout Plain Layout
1409 \begin_inset Index idx
1412 \begin_layout Plain Layout
1417 \begin_layout Plain Layout
1428 \begin_layout Plain Layout
1441 \begin_inset Index idx
1444 \begin_layout Plain Layout
1449 \begin_layout Plain Layout
1460 \begin_layout Plain Layout
1475 \begin_layout Standard
1476 Indices are created with an underscore
1477 \begin_inset Quotes eld
1481 \begin_inset Quotes erd
1484 or via the math toolbar button
1487 arg "math-subscript"
1490 , exponents with a caret
1491 \begin_inset Quotes eld
1495 \begin_inset Quotes erd
1498 or via the math toolbar button
1501 arg "math-superscript"
1505 \begin_inset Separator parbreak
1511 \begin_layout Standard
1513 \begin_inset Tabular
1514 <lyxtabular version="3" rows="4" columns="2">
1515 <features booktabs="true" tabularvalignment="middle">
1516 <column alignment="center" valignment="top" width="0pt">
1517 <column alignment="center" valignment="top" width="0pt">
1519 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1522 \begin_layout Plain Layout
1528 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1531 \begin_layout Plain Layout
1539 <cell alignment="center" valignment="top" usebox="none">
1542 \begin_layout Plain Layout
1548 <cell alignment="center" valignment="top" usebox="none">
1551 \begin_layout Plain Layout
1552 \begin_inset Formula $B_{V}$
1561 <row topspace="1.5mm">
1562 <cell alignment="center" valignment="top" usebox="none">
1565 \begin_layout Plain Layout
1571 <cell alignment="center" valignment="top" usebox="none">
1574 \begin_layout Plain Layout
1575 \begin_inset Formula $B^{V}$
1584 <row topspace="1.5mm">
1585 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1588 \begin_layout Plain Layout
1590 \begin_inset space \textvisiblespace{}
1598 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1601 \begin_layout Plain Layout
1602 \begin_inset Formula $B^{A}$
1618 \begin_layout Standard
1619 As the caret is in some languages an accent, vowels will be accentuated
1620 in this case and not set as exponents
1624 \begin_layout Plain Layout
1625 Depending on the used keyboard settings this can also happen for characters
1632 To get exponents in this case, press
1636 after the caret as in the last example.
1639 \begin_layout Subsection
1641 \begin_inset CommandInset label
1643 name "subsec:Fractions"
1648 \begin_inset Index idx
1651 \begin_layout Plain Layout
1660 \begin_layout Standard
1661 Fractions are generated with the command
1668 \begin_inset Index idx
1671 \begin_layout Plain Layout
1679 or via the math toolbar button
1682 arg "math-insert \\frac"
1686 The font size is adjusted automatically, depending on whether the fraction
1687 is in an inline or display style formula.
1688 With the math toolbar button
1691 arg "math-insert \\frac-square"
1694 you can select different fraction types.
1697 \begin_layout Standard
1705 \begin_inset Index idx
1708 \begin_layout Plain Layout
1716 a fraction can be created that always has the size of a display style formula.
1724 \begin_inset Index idx
1727 \begin_layout Plain Layout
1735 the fraction appears always with the size of an inline formula.
1739 \begin_layout Standard
1740 A line with the fraction
1741 \begin_inset Formula $\frac{1}{2}$
1744 that was created with the command
1753 \begin_layout Standard
1754 A line with the fraction
1755 \begin_inset Formula $\dfrac{1}{2}$
1758 that was created with the command
1765 \begin_inset Separator parbreak
1771 \begin_layout Standard
1773 \begin_inset Tabular
1774 <lyxtabular version="3" rows="4" columns="2">
1775 <features booktabs="true" tabularvalignment="middle">
1776 <column alignment="center" valignment="top" width="0pt">
1777 <column alignment="center" valignment="top" width="0pt">
1779 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1782 \begin_layout Plain Layout
1788 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1791 \begin_layout Plain Layout
1798 <row topspace="1.5mm">
1799 <cell alignment="center" valignment="top" usebox="none">
1802 \begin_layout Plain Layout
1806 \begin_inset space \textvisiblespace{}
1810 \begin_inset Formula $\downarrow$
1818 <cell alignment="center" valignment="top" usebox="none">
1821 \begin_layout Plain Layout
1822 \begin_inset Formula $\frac{A}{B}$
1831 <row topspace="2mm">
1832 <cell alignment="center" valignment="top" usebox="none">
1835 \begin_layout Plain Layout
1839 \begin_inset space \textvisiblespace{}
1843 \begin_inset Formula $\downarrow$
1851 <cell alignment="center" valignment="top" usebox="none">
1854 \begin_layout Plain Layout
1855 \begin_inset Formula $\dfrac{A}{B}$
1864 <row topspace="2mm" bottomspace="1mm">
1865 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1868 \begin_layout Plain Layout
1872 \begin_inset space \textvisiblespace{}
1878 \begin_inset space \textvisiblespace{}
1882 \begin_inset Formula $\downarrow$
1886 \begin_inset Formula $\downarrow\downarrow$
1894 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1897 \begin_layout Plain Layout
1898 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1914 \begin_layout Standard
1915 \begin_inset VSpace bigskip
1919 \begin_inset Newpage newpage
1922 For nested fractions the command
1929 \begin_inset Index idx
1932 \begin_layout Plain Layout
1942 \begin_inset VSpace -3mm
1948 \begin_layout Standard
1949 \begin_inset Formula
1951 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1952 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1960 \begin_layout Standard
1961 The command for the example above is:
1964 \begin_layout Standard
1970 \begin_inset space \textvisiblespace{}
1974 \begin_inset Formula $\downarrow$
1980 \begin_inset space \textvisiblespace{}
1986 \begin_inset space \textvisiblespace{}
1990 \begin_inset Formula $\downarrow$
1994 \begin_inset Formula $\downarrow$
2000 \begin_layout Standard
2001 \begin_inset VSpace medskip
2007 \begin_layout Standard
2014 sets the fraction always in the size of a displayed formula, also when
2015 it is part of another fraction.
2018 \begin_layout Standard
2019 It is possible to specify the alignment of the numerator.
2026 is used to left align it, the command
2039 centers the numerator.
2040 These fractions demonstrate the different alignments:
2043 \begin_layout Standard
2046 \begin_inset Formula
2048 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2056 \begin_layout Standard
2057 \begin_inset Note Greyedout
2060 \begin_layout Plain Layout
2077 are no real \SpecialChar LaTeX
2078 commands but represent the command
2082 cfrac[alignment]{numerator}{denominator}
2085 Therefore you cannot use them in \SpecialChar TeX
2094 \begin_layout Standard
2095 \begin_inset VSpace medskip
2098 It is often advantageous to combine
2111 \begin_inset Formula
2113 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2121 \begin_layout Standard
2122 For inline fractions with a sloped fraction stroke you can use the command
2130 \begin_inset Index idx
2133 \begin_layout Plain Layout
2142 \begin_inset Formula $\nicefrac{5}{31}$
2152 \begin_inset Index idx
2155 \begin_layout Plain Layout
2164 \begin_inset Formula $\unitfrac{5}{31}$
2167 There is furthermore the command
2173 that offers to write a fraction in combination with a number:
2174 \begin_inset Formula $\unitfrac[2]{1}{3}$
2180 \begin_layout Standard
2181 \begin_inset Note Greyedout
2184 \begin_layout Plain Layout
2195 is not a real \SpecialChar LaTeX
2196 command but the command
2197 \begin_inset Newline newline
2204 unitfrac[number]{numerator}{denominator}
2207 Therefore you cannot use it in \SpecialChar TeX
2216 \begin_layout Standard
2217 How to define own fractions where the fraction stroke can be changed, is
2219 \begin_inset CommandInset ref
2221 reference "subsec:Self-defined-Fractions"
2228 \begin_layout Standard
2229 Multiline fractions are explained in
2230 \begin_inset CommandInset ref
2232 reference "subsec:Multiline-Fractions"
2239 \begin_layout Subsection
2241 \begin_inset Index idx
2244 \begin_layout Plain Layout
2253 \begin_layout Standard
2254 Square roots are created with
2261 \begin_inset Index idx
2264 \begin_layout Plain Layout
2272 or the math toolbar button
2275 arg "math-insert \\sqrt"
2278 , all other roots with the command
2285 \begin_inset Index idx
2288 \begin_layout Plain Layout
2296 or with the math toolbar button
2299 arg "math-insert \\root"
2303 \begin_inset Separator parbreak
2309 \begin_layout Standard
2311 \begin_inset Tabular
2312 <lyxtabular version="3" rows="3" columns="2">
2313 <features booktabs="true" tabularvalignment="middle">
2314 <column alignment="center" valignment="top" width="0pt">
2315 <column alignment="center" valignment="top" width="0pt">
2317 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2320 \begin_layout Plain Layout
2326 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2329 \begin_layout Plain Layout
2336 <row topspace="1mm">
2337 <cell alignment="center" valignment="top" usebox="none">
2340 \begin_layout Plain Layout
2344 \begin_inset space \textvisiblespace{}
2352 <cell alignment="center" valignment="top" usebox="none">
2355 \begin_layout Plain Layout
2356 \begin_inset Formula $\sqrt{A-B}$
2365 <row topspace="1mm">
2366 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2369 \begin_layout Plain Layout
2373 \begin_inset space \textvisiblespace{}
2377 \begin_inset Formula $\downarrow$
2385 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2388 \begin_layout Plain Layout
2389 \begin_inset Formula $\sqrt[3]{A-B}$
2405 \begin_layout Standard
2406 A square root can also be created with
2412 when the root index field is left empty.
2415 \begin_layout Standard
2416 With certain indices the distance to the root is too small, like in this
2418 \begin_inset Formula $\sqrt[\beta]{B}$
2422 \begin_inset Newline newline
2426 \begin_inset Formula $\beta$
2430 To avoid this, the commands
2437 \begin_inset Index idx
2440 \begin_layout Plain Layout
2455 \begin_inset Index idx
2458 \begin_layout Plain Layout
2466 are used with the following scheme:
2469 \begin_layout Standard
2483 \begin_layout Standard
2484 Distance is the number of Big Points (unit bp;
2485 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2488 ), that the index should be moved to the left or top, resp..
2489 The commands are written to the index.
2490 This way the command
2491 \begin_inset Newline newline
2501 \begin_inset Formula $\to$
2507 \begin_inset Formula $\to$
2513 \begin_inset space \textvisiblespace{}
2517 \begin_inset Formula $\to$
2521 \begin_inset Newline newline
2526 produces a correct typeset formula:
2527 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2533 \begin_layout Subsection
2534 Binomial Coefficients
2535 \begin_inset Index idx
2538 \begin_layout Plain Layout
2539 Binomial coefficients
2547 \begin_layout Standard
2548 Binomial coefficients are inserted with the command
2555 \begin_inset Index idx
2558 \begin_layout Plain Layout
2566 or with the submenu of the math toolbar button
2569 arg "math-insert \\frac-square"
2585 there are the commands
2592 \begin_inset Index idx
2595 \begin_layout Plain Layout
2610 \begin_inset Index idx
2613 \begin_layout Plain Layout
2622 For other brackets around binomial coeficients there are the commands
2629 \begin_inset Index idx
2632 \begin_layout Plain Layout
2647 \begin_inset Index idx
2650 \begin_layout Plain Layout
2659 \begin_inset Separator parbreak
2665 \begin_layout Standard
2667 \begin_inset Tabular
2668 <lyxtabular version="3" rows="6" columns="2">
2669 <features booktabs="true" tabularvalignment="middle">
2670 <column alignment="center" valignment="top" width="0pt">
2671 <column alignment="center" valignment="top" width="0pt">
2673 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2676 \begin_layout Plain Layout
2682 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2685 \begin_layout Plain Layout
2692 <row topspace="1mm">
2693 <cell alignment="center" valignment="top" usebox="none">
2696 \begin_layout Plain Layout
2700 \begin_inset space \textvisiblespace{}
2704 \begin_inset Formula $\downarrow$
2712 <cell alignment="center" valignment="top" usebox="none">
2715 \begin_layout Plain Layout
2716 \begin_inset Formula $\binom{A}{B}$
2725 <row topspace="2mm">
2726 <cell alignment="center" valignment="top" usebox="none">
2729 \begin_layout Plain Layout
2733 \begin_inset space \textvisiblespace{}
2737 \begin_inset Formula $\downarrow$
2745 <cell alignment="center" valignment="top" usebox="none">
2748 \begin_layout Plain Layout
2749 \begin_inset Formula $\dbinom{A}{B}$
2758 <row topspace="2mm" bottomspace="0.5mm">
2759 <cell alignment="center" valignment="top" usebox="none">
2762 \begin_layout Plain Layout
2766 \begin_inset space \textvisiblespace{}
2770 \begin_inset Formula $\downarrow$
2778 <cell alignment="center" valignment="top" usebox="none">
2781 \begin_layout Plain Layout
2782 \begin_inset Formula $\tbinom{A}{B}$
2791 <row topspace="1mm">
2792 <cell alignment="center" valignment="top" topline="true" usebox="none">
2795 \begin_layout Plain Layout
2799 \begin_inset space \textvisiblespace{}
2803 \begin_inset Formula $\downarrow$
2811 <cell alignment="center" valignment="top" topline="true" usebox="none">
2814 \begin_layout Plain Layout
2815 \begin_inset Formula ${A \brack B}$
2824 <row topspace="2mm" bottomspace="0.5mm">
2825 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2828 \begin_layout Plain Layout
2832 \begin_inset space \textvisiblespace{}
2836 \begin_inset Formula $\downarrow$
2844 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2847 \begin_layout Plain Layout
2848 \begin_inset Formula ${A \brace B}$
2864 \begin_layout Subsection
2865 Case Differentiations
2866 \begin_inset Index idx
2869 \begin_layout Plain Layout
2870 Case differentiations
2878 \begin_layout Standard
2880 \begin_inset Tabular
2881 <lyxtabular version="3" rows="3" columns="2">
2882 <features booktabs="true" tabularvalignment="middle">
2883 <column alignment="center" valignment="top" width="0pt">
2884 <column alignment="center" valignment="top" width="0pt">
2886 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2889 \begin_layout Plain Layout
2895 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2898 \begin_layout Plain Layout
2906 <cell alignment="center" valignment="top" usebox="none">
2909 \begin_layout Plain Layout
2913 \begin_inset space \textvisiblespace{}
2917 \begin_inset Formula $\to$
2921 \begin_inset Index idx
2924 \begin_layout Plain Layout
2937 <cell alignment="center" valignment="top" usebox="none">
2940 \begin_layout Plain Layout
2941 \begin_inset Formula $\begin{cases}
2951 <row topspace="1.5mm">
2952 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2955 \begin_layout Plain Layout
2959 \begin_inset space \textvisiblespace{}
2965 arg "newline-insert newline"
2973 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2976 \begin_layout Plain Layout
2977 \begin_inset Formula $\begin{cases}
2978 A & \textrm{for }x>0\\
2979 B & \textrm{for }x=0
2996 \begin_layout Standard
3003 or pressing the math toolbar button
3006 arg "math-insert \\cases"
3009 you can create new lines with the shortcut
3012 arg "newline-insert newline"
3015 or the table toolbar button
3018 arg "inset-modify tabular append-row"
3024 \begin_layout Standard
3031 is also available via the menu
3033 Insert\SpecialChar menuseparator
3034 Math\SpecialChar menuseparator
3040 \begin_layout Subsection
3042 \begin_inset Index idx
3045 \begin_layout Plain Layout
3054 \begin_layout Standard
3062 \begin_inset Index idx
3065 \begin_layout Plain Layout
3073 every character can be displayed canceled.
3074 The characters are quasi accentuated by a slash.
3075 \begin_inset Separator parbreak
3081 \begin_layout Standard
3083 \begin_inset Tabular
3084 <lyxtabular version="3" rows="4" columns="2">
3085 <features booktabs="true" tabularvalignment="middle">
3086 <column alignment="center" valignment="top" width="0pt">
3087 <column alignment="center" valignment="top" width="0pt">
3089 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3092 \begin_layout Plain Layout
3098 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3101 \begin_layout Plain Layout
3109 <cell alignment="center" valignment="top" usebox="none">
3112 \begin_layout Plain Layout
3120 <cell alignment="center" valignment="top" usebox="none">
3123 \begin_layout Plain Layout
3124 \begin_inset Formula $\not=$
3134 <cell alignment="center" valignment="top" usebox="none">
3137 \begin_layout Plain Layout
3147 <cell alignment="center" valignment="top" usebox="none">
3150 \begin_layout Plain Layout
3151 \begin_inset Formula $\not\le$
3161 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3164 \begin_layout Plain Layout
3174 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3177 \begin_layout Plain Layout
3178 \begin_inset Formula $\not\parallel$
3194 \begin_layout Standard
3195 The last example shows that not all negations look good.
3196 Therefore there are special commands for some negations (see
3197 \begin_inset CommandInset ref
3199 reference "subsec:Mathematical-Symbols"
3204 \begin_inset CommandInset ref
3206 reference "sec:Relations"
3213 \begin_layout Subsection
3215 \begin_inset CommandInset label
3217 name "subsec:Placeholders"
3222 \begin_inset Index idx
3225 \begin_layout Plain Layout
3232 \begin_inset Index idx
3235 \begin_layout Plain Layout
3236 Chemical characters ! Isotopes
3242 \begin_inset Index idx
3245 \begin_layout Plain Layout
3250 \begin_layout Plain Layout
3261 \begin_layout Plain Layout
3276 \begin_layout Standard
3278 \begin_inset space \thinspace{}
3282 \begin_inset space \space{}
3289 \begin_layout Plain Layout
3290 Typesetting isotopes and chemical symbols is described in
3291 \begin_inset CommandInset ref
3293 reference "subsec:Chemical-Symbols-and"
3302 the following problem occurs:
3303 \begin_inset Separator parbreak
3309 \begin_layout Standard
3311 \begin_inset Tabular
3312 <lyxtabular version="3" rows="2" columns="2">
3313 <features booktabs="true" tabularvalignment="middle">
3314 <column alignment="center" valignment="top" width="0pt">
3315 <column alignment="center" valignment="top" width="0pt">
3317 <cell alignment="center" valignment="top" usebox="none">
3320 \begin_layout Plain Layout
3321 Indices created with sub- and superscripts:
3326 <cell alignment="center" valignment="top" usebox="none">
3329 \begin_layout Plain Layout
3330 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3339 <row topspace="1.5mm">
3340 <cell alignment="center" valignment="top" usebox="none">
3343 \begin_layout Plain Layout
3349 <cell alignment="center" valignment="top" usebox="none">
3352 \begin_layout Plain Layout
3353 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3369 \begin_layout Standard
3370 The shorter index is by default placed below or above the first character
3371 of the longer index.
3372 To avoid this there is the command
3379 \begin_inset Index idx
3382 \begin_layout Plain Layout
3390 or the math toolbar button
3391 \begin_inset space \thinspace{}
3398 \begin_layout Plain Layout
3399 can be found in the submenu of the toolbar button
3402 arg "math-insert \\space"
3411 \begin_inset Graphics
3412 filename ../images/math/phantom.png
3417 that creates one or more phantom characters.
3424 a small blue box appears that is superposed with two red arrows.
3425 The arrows indicate that the complete width and height of the box content
3426 will be created as placeholder.
3427 Phantom characters are accordingly placeholders with the size of the characters.
3428 \begin_inset Separator parbreak
3434 \begin_layout Standard
3436 \begin_inset Tabular
3437 <lyxtabular version="3" rows="4" columns="2">
3438 <features booktabs="true" tabularvalignment="middle">
3439 <column alignment="center" valignment="top" width="0pt">
3440 <column alignment="center" valignment="top" width="0pt">
3442 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3445 \begin_layout Plain Layout
3451 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3454 \begin_layout Plain Layout
3461 <row topspace="1.5mm">
3462 <cell alignment="center" valignment="top" usebox="none">
3465 \begin_layout Plain Layout
3467 \begin_inset space \textvisiblespace{}
3473 \begin_inset space \textvisiblespace{}
3477 \begin_inset Formula $\to$
3481 \begin_inset space \textvisiblespace{}
3489 <cell alignment="center" valignment="top" usebox="none">
3492 \begin_layout Plain Layout
3493 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3502 <row topspace="1.5mm" bottomspace="0.5mm">
3503 <cell alignment="center" valignment="top" usebox="none">
3506 \begin_layout Plain Layout
3508 \begin_inset space \textvisiblespace{}
3514 \begin_inset space \textvisiblespace{}
3518 \begin_inset Formula $\to$
3522 \begin_inset space \textvisiblespace{}
3530 <cell alignment="center" valignment="top" usebox="none">
3533 \begin_layout Plain Layout
3534 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3543 <row topspace="1.5mm" bottomspace="0.5mm">
3544 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3547 \begin_layout Plain Layout
3551 \begin_inset space \textvisiblespace{}
3557 \begin_inset space \textvisiblespace{}
3561 \begin_inset Formula $\to$
3565 \begin_inset space \textvisiblespace{}
3573 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3576 \begin_layout Plain Layout
3577 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3593 \begin_layout Standard
3594 Furthermore there are the commands
3601 \begin_inset Index idx
3604 \begin_layout Plain Layout
3613 \begin_inset space ~
3617 \begin_inset Graphics
3618 filename ../images/math/vphantom.png
3630 \begin_inset Index idx
3633 \begin_layout Plain Layout
3642 \begin_inset space ~
3646 \begin_inset Graphics
3647 filename ../images/math/hphantom.png
3659 creates only space for the maximal height of the characters in the box
3660 but not for its width.
3667 creates only space for the width of the box content.
3668 Therefore the boxes of both commands have only one red arrow.
3671 \begin_layout Standard
3672 For example the command
3677 \begin_inset space \textvisiblespace{}
3684 creates space for the height of the integral sign,
3688 \begin_layout Plain Layout
3695 creates an integral sign, see
3696 \begin_inset CommandInset ref
3698 reference "subsec:Big-Operators"
3707 because this is the larger character.
3708 An example application is in
3709 \begin_inset CommandInset ref
3711 reference "subsec:Multiline-Brackets"
3718 \begin_layout Standard
3719 Placeholders can also be used for text when they are inserted via the menu
3722 Insert\SpecialChar menuseparator
3723 Formatting\SpecialChar menuseparator
3729 \begin_layout Standard
3731 \begin_inset Newline newline
3735 \begin_inset Phantom Phantom
3738 \begin_layout Plain Layout
3747 \begin_layout Subsection
3749 \begin_inset Index idx
3752 \begin_layout Plain Layout
3759 \begin_inset Index idx
3762 \begin_layout Plain Layout
3763 Formula ! underlined
3771 \begin_layout Standard
3773 \begin_inset Tabular
3774 <lyxtabular version="3" rows="4" columns="2">
3775 <features booktabs="true" tabularvalignment="middle">
3776 <column alignment="center" valignment="top" width="0pt">
3777 <column alignment="center" valignment="top" width="0pt">
3779 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3782 \begin_layout Plain Layout
3788 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3791 \begin_layout Plain Layout
3798 <row topspace="2mm">
3799 <cell alignment="center" valignment="top" usebox="none">
3802 \begin_layout Plain Layout
3806 \begin_inset space \textvisiblespace{}
3810 \begin_inset Index idx
3813 \begin_layout Plain Layout
3826 <cell alignment="center" valignment="top" usebox="none">
3829 \begin_layout Plain Layout
3830 \begin_inset Formula $\overline{A+B}$
3839 <row bottomspace="1mm">
3840 <cell alignment="center" valignment="top" usebox="none">
3843 \begin_layout Plain Layout
3847 \begin_inset space \textvisiblespace{}
3851 \begin_inset Index idx
3854 \begin_layout Plain Layout
3867 <cell alignment="center" valignment="top" usebox="none">
3870 \begin_layout Plain Layout
3871 \begin_inset Formula $\underline{A+B}$
3880 <row topspace="2mm" bottomspace="1mm">
3881 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3884 \begin_layout Plain Layout
3888 \begin_inset space \textvisiblespace{}
3894 \begin_inset space \textvisiblespace{}
3902 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3905 \begin_layout Plain Layout
3906 \begin_inset Formula $\overline{\underline{A+B}}$
3922 \begin_layout Standard
3923 In the last example it doesn't matter if first
3938 \begin_layout Standard
3939 To double underline use
3948 \begin_layout Standard
3949 It is possible to place up to 6 lines above or below characters.
3952 \begin_layout Standard
3953 \begin_inset VSpace bigskip
3956 Custom lines can be created using the command
3963 \begin_inset Index idx
3966 \begin_layout Plain Layout
3974 which has the following scheme:
3977 \begin_layout Standard
3982 rule[vertical offset]{length}{thickness}
3985 \begin_layout Standard
3986 The optional vertical offset shifts the line upwards (or downwards, when
3987 the value is negative).
3989 \begin_inset CommandInset ref
3991 reference "tab:Available-units"
3995 can be used for the values.
3996 Here are two example lines created with the commands
3997 \begin_inset Newline newline
4004 rule[-2ex]{3cm}{2pt}
4015 \begin_layout Standard
4017 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4023 \begin_layout Standard
4030 can also be used for text when a line is inserted via the menu
4032 Insert\SpecialChar menuseparator
4033 Formatting\SpecialChar menuseparator
4035 \begin_inset space ~
4043 \begin_layout Standard
4045 \begin_inset CommandInset line
4056 \begin_layout Subsection
4058 \begin_inset CommandInset label
4060 name "subsec:Ellipses"
4065 \begin_inset Index idx
4068 \begin_layout Plain Layout
4077 \begin_layout Standard
4078 There are different types of ellipses available.
4082 \begin_layout Plain Layout
4083 In the math toolbar in the submenu of the button
4086 arg "math-insert \\ldots"
4094 For listings dots at the baseline are used (
4101 \begin_inset Index idx
4104 \begin_layout Plain Layout
4112 ), while for operations dots are needed that are on the same height as the
4120 \begin_inset Index idx
4123 \begin_layout Plain Layout
4132 When using the command
4139 \begin_inset Index idx
4142 \begin_layout Plain Layout
4150 , \SpecialChar LaTeX
4151 decides on the basis of the next character what type is used.
4152 \begin_inset Separator parbreak
4158 \begin_layout Standard
4160 \begin_inset Tabular
4161 <lyxtabular version="3" rows="9" columns="2">
4162 <features booktabs="true" 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" usebox="none">
4169 \begin_layout Plain Layout
4175 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4178 \begin_layout Plain Layout
4186 <cell alignment="center" valignment="top" usebox="none">
4189 \begin_layout Plain Layout
4191 \begin_inset space \textvisiblespace{}
4197 \begin_inset space \textvisiblespace{}
4205 <cell alignment="center" valignment="top" usebox="none">
4208 \begin_layout Plain Layout
4209 \begin_inset Formula $A_{1},\dots,A_{n}$
4219 <cell alignment="center" valignment="top" usebox="none">
4222 \begin_layout Plain Layout
4224 \begin_inset space \textvisiblespace{}
4230 \begin_inset space \textvisiblespace{}
4238 <cell alignment="center" valignment="top" usebox="none">
4241 \begin_layout Plain Layout
4242 \begin_inset Formula $A_{1}+\dots+A_{n}$
4252 <cell alignment="center" valignment="top" usebox="none">
4255 \begin_layout Plain Layout
4257 \begin_inset space \textvisiblespace{}
4263 \begin_inset space \textvisiblespace{}
4271 <cell alignment="center" valignment="top" usebox="none">
4274 \begin_layout Plain Layout
4275 \begin_inset Formula $A_{1},\ldots,A_{n}$
4285 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4288 \begin_layout Plain Layout
4290 \begin_inset space \textvisiblespace{}
4296 \begin_inset space \textvisiblespace{}
4304 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4307 \begin_layout Plain Layout
4308 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4318 <cell alignment="center" valignment="top" usebox="none">
4321 \begin_layout Plain Layout
4329 <cell alignment="center" valignment="top" usebox="none">
4332 \begin_layout Plain Layout
4333 \begin_inset Formula $\vdots$
4343 <cell alignment="center" valignment="top" usebox="none">
4346 \begin_layout Plain Layout
4354 <cell alignment="center" valignment="top" usebox="none">
4357 \begin_layout Plain Layout
4358 \begin_inset Formula $\ddots$
4368 <cell alignment="center" valignment="top" usebox="none">
4371 \begin_layout Plain Layout
4379 <cell alignment="center" valignment="top" usebox="none">
4382 \begin_layout Plain Layout
4383 \begin_inset Formula $\iddots$
4393 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4396 \begin_layout Plain Layout
4398 \begin_inset space \thinspace{}
4401 matrix with the different dots
4406 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4409 \begin_layout Plain Layout
4410 \begin_inset Formula $\begin{array}{ccc}
4411 A_{11} & \cdots & A_{1m}\\
4412 \vdots & \ddots & \vdots\\
4413 A_{n1} & \cdots & A_{nm}
4430 \begin_layout Standard
4431 The ellipses available in menu
4433 Insert\SpecialChar menuseparator
4435 \begin_inset space ~
4449 \begin_layout Standard
4450 \begin_inset VSpace medskip
4459 , one of the options
4461 Use mathdots package (automatically)
4463 must be set in the document settings under
4466 \begin_inset space ~
4472 \begin_inset Newline newline
4477 Use mathdots package
4479 will improve the appearance of all dots in the documents if their font
4480 style or size is not the default.
4483 \begin_layout Standard
4484 \begin_inset VSpace medskip
4487 Specially for matrices there are ellipses that span over several columns.
4488 They are created with the command
4495 \begin_inset Index idx
4498 \begin_layout Plain Layout
4506 , that has the following scheme:
4509 \begin_layout Standard
4514 hdotsfor[distance]{number of columns}
4517 \begin_layout Standard
4518 The number of columns specifies how many columns should be spanned.
4519 Distance is a factor for the distance between the dots.
4522 \begin_layout Standard
4523 In the following matrix the command
4529 was inserted in the first box of the second line, to get an ellipsis with
4530 a dot distance twice as long as with the command
4537 \begin_inset Formula
4539 \left(\begin{array}{cccc}
4548 Note that the matrix fields that should be spanned must be empty, otherwise
4549 you get \SpecialChar LaTeX
4553 \begin_layout Standard
4554 \begin_inset VSpace bigskip
4557 Furthermore you can fill with the command
4564 \begin_inset Index idx
4567 \begin_layout Plain Layout
4575 the rest of a line with dots.
4576 The effect of these commands is the same as with
4583 \begin_inset CommandInset ref
4585 reference "subsec:Variable-Space"
4592 \begin_layout Standard
4593 For example the command
4598 \begin_inset space \textvisiblespace{}
4606 \begin_layout Standard
4607 \begin_inset Formula $A\dotfill B$
4613 \begin_layout Standard
4620 there is for a line the command
4627 \begin_inset Index idx
4630 \begin_layout Plain Layout
4641 \begin_layout Standard
4642 \begin_inset Formula $A\hrulefill B$
4648 \begin_layout Standard
4649 To use the commands for text, they have to be inserted in \SpecialChar TeX
4653 \begin_layout Section
4655 \begin_inset CommandInset label
4662 \begin_inset Index idx
4665 \begin_layout Plain Layout
4674 \begin_layout Standard
4675 Matrices can be inserted via the math toolbar button
4678 arg "dialog-show mathmatrix"
4683 Insert\SpecialChar menuseparator
4684 Math\SpecialChar menuseparator
4688 In the matrix dialog you can specify the number of columns and rows, the
4689 alignment and the decoration.
4690 The vertical alignment is only of importance for matrices in inline formulas:
4693 \begin_layout Standard
4694 The first matrix is top
4695 \begin_inset Formula $\begin{array}[t]{cccc}
4703 \begin_inset Formula $\begin{array}{cccc}
4710 and the third bottom
4711 \begin_inset Formula $\begin{array}[b]{cccc}
4721 \begin_layout Standard
4722 The horizontal alignment specifies how the column entries should be aligned.
4723 It is set by entering a letter for every column.
4728 denotes left aligned,
4737 To create for example a 4
4742 \begin_inset space ~
4745 matrix where the first column is left aligned, the second and third are
4746 centered and the last one is right aligned, one enters for the horizontal
4752 Normally in a matrix all columns are centered, therefore the default for
4760 \begin_layout Standard
4761 Horizontal alignment:
4764 \begin_layout Standard
4770 \begin_inset Formula $\begin{array}{lll}
4782 \begin_inset Formula $\begin{array}{ccc}
4794 \begin_inset Formula $\begin{array}{rrr}
4804 \begin_layout Standard
4805 To add or delete rows and columns subsequently, the math toolbar buttons
4809 arg "inset-modify tabular append-row"
4815 arg "inset-modify tabular delete-row"
4819 \begin_inset space \thinspace{}
4824 Edit\SpecialChar menuseparator
4828 New rows can also be created with
4831 arg "newline-insert newline"
4837 \begin_layout Standard
4838 \begin_inset VSpace bigskip
4845 adds parentheses in the selected style around the matrix.
4846 Alternatively, parentheses can can either be created with the commands
4854 \begin_inset Index idx
4857 \begin_layout Plain Layout
4872 \begin_inset Index idx
4875 \begin_layout Plain Layout
4886 \begin_inset space ~
4892 \begin_inset CommandInset ref
4894 reference "subsec:Automatic-Bracket-Size"
4898 , or by using the following commands:
4899 \begin_inset VSpace medskip
4905 \begin_layout Standard
4906 \begin_inset space \hfill{}
4910 \begin_inset Tabular
4911 <lyxtabular version="3" rows="4" columns="2">
4912 <features booktabs="true" tabularvalignment="middle">
4913 <column alignment="center" valignment="top" width="0pt">
4914 <column alignment="center" valignment="top">
4916 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4919 \begin_layout Plain Layout
4925 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4928 \begin_layout Plain Layout
4935 <row topspace="1.5mm">
4936 <cell alignment="center" valignment="top" usebox="none">
4939 \begin_layout Plain Layout
4943 \begin_inset space \textvisiblespace{}
4951 \begin_inset space \thinspace{}
4959 <cell alignment="center" valignment="top" usebox="none">
4962 \begin_layout Plain Layout
4963 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4964 0 & \textrm{-}\mathrm{i}\\
4966 \end{array}\end{bmatrix}$
4975 <row topspace="1.5mm" bottomspace="0.5mm">
4976 <cell alignment="center" valignment="top" usebox="none">
4979 \begin_layout Plain Layout
4983 \begin_inset space \textvisiblespace{}
4991 \begin_inset space \thinspace{}
4999 <cell alignment="center" valignment="top" usebox="none">
5002 \begin_layout Plain Layout
5003 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
5004 0 & \textrm{-}\mathrm{i}\\
5006 \end{array}\end{Bmatrix}$
5016 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5019 \begin_layout Plain Layout
5023 \begin_inset space \textvisiblespace{}
5031 \begin_inset space \thinspace{}
5039 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5042 \begin_layout Plain Layout
5043 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5044 0 & \textrm{-}\mathrm{i}\\
5046 \end{array}\end{pmatrix}$
5060 \begin_inset space \hfill{}
5064 \begin_inset Tabular
5065 <lyxtabular version="3" rows="4" columns="2">
5066 <features booktabs="true" tabularvalignment="middle">
5067 <column alignment="center" valignment="top" width="0pt">
5068 <column alignment="center" valignment="top">
5070 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5073 \begin_layout Plain Layout
5079 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5082 \begin_layout Plain Layout
5089 <row topspace="1.5mm">
5090 <cell alignment="center" valignment="top" usebox="none">
5093 \begin_layout Plain Layout
5097 \begin_inset space \textvisiblespace{}
5105 \begin_inset space \thinspace{}
5113 <cell alignment="center" valignment="top" usebox="none">
5116 \begin_layout Plain Layout
5117 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5118 0 & \textrm{-}\mathrm{i}\\
5120 \end{array}\end{vmatrix}$
5129 <row topspace="1.5mm" bottomspace="0.5mm">
5130 <cell alignment="center" valignment="top" usebox="none">
5133 \begin_layout Plain Layout
5137 \begin_inset space \textvisiblespace{}
5145 \begin_inset space \thinspace{}
5153 <cell alignment="center" valignment="top" usebox="none">
5156 \begin_layout Plain Layout
5157 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5158 0 & \textrm{-}\mathrm{i}\\
5160 \end{array}\end{Vmatrix}$
5170 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5173 \begin_layout Plain Layout
5177 \begin_inset space \textvisiblespace{}
5185 \begin_inset space \thinspace{}
5193 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5196 \begin_layout Plain Layout
5197 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5198 0 & \textrm{-}\mathrm{i}\\
5200 \end{array}\end{matrix}$
5214 \begin_inset space \hfill{}
5220 \begin_layout Standard
5221 \begin_inset VSpace medskip
5225 \begin_inset space \thinspace{}
5229 \begin_inset space \space{}
5238 is inserted, a blue box appears between two vertical lines where the matrix
5240 \begin_inset Newline newline
5243 Note that decorated matrices ignore the vertical alignment.
5246 \begin_layout Standard
5247 \begin_inset VSpace bigskip
5250 As all multiline formulas are matrices, the length
5257 \begin_inset Index idx
5260 \begin_layout Plain Layout
5268 that is described in
5269 \begin_inset CommandInset ref
5271 reference "subsec:Column-Separation"
5275 can also be used to change the column separation of matrices.
5278 \begin_layout Standard
5279 To change the row separation, the command
5286 \begin_inset Index idx
5289 \begin_layout Plain Layout
5298 It is used as follows:
5301 \begin_layout Standard
5308 arraystretch}{stretch factor}
5309 \begin_inset Index idx
5312 \begin_layout Plain Layout
5323 \begin_layout Standard
5330 assigns the stretch factor to the predefined command
5338 \begin_inset space \thinspace{}
5342 \begin_inset space \space{}
5345 the row separation, use the factor 2.
5346 This is then used for all following matrices.
5347 To go back to the original separation, assign the factor 1 to
5356 \begin_layout Standard
5357 To set matrices into a text line, the command
5364 \begin_inset Index idx
5367 \begin_layout Plain Layout
5376 When it is inserted a blue box with two dashed lines appears.
5377 In this box the matrix is inserted.
5380 \begin_layout Standard
5382 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5384 \end{smallmatrix}\right)$
5390 \begin_layout Section
5391 Brackets and Delimiters
5392 \begin_inset Index idx
5395 \begin_layout Plain Layout
5402 \begin_inset Index idx
5405 \begin_layout Plain Layout
5414 \begin_layout Subsection
5415 Vertical Brackets and Delimiters
5416 \begin_inset Index idx
5419 \begin_layout Plain Layout
5428 \begin_layout Standard
5429 \begin_inset space \hfill{}
5433 \begin_inset Tabular
5434 <lyxtabular version="3" rows="9" columns="2">
5435 <features booktabs="true" tabularvalignment="middle">
5436 <column alignment="center" valignment="top" width="0pt">
5437 <column alignment="center" valignment="top" width="0pt">
5439 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5442 \begin_layout Plain Layout
5448 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5451 \begin_layout Plain Layout
5459 <cell alignment="center" valignment="top" usebox="none">
5462 \begin_layout Plain Layout
5468 <cell alignment="center" valignment="top" usebox="none">
5471 \begin_layout Plain Layout
5472 \begin_inset Formula $($
5482 <cell alignment="center" valignment="top" usebox="none">
5485 \begin_layout Plain Layout
5491 <cell alignment="center" valignment="top" usebox="none">
5494 \begin_layout Plain Layout
5495 \begin_inset Formula $\{$
5505 <cell alignment="center" valignment="top" usebox="none">
5508 \begin_layout Plain Layout
5514 <cell alignment="center" valignment="top" usebox="none">
5517 \begin_layout Plain Layout
5518 \begin_inset Formula $[$
5528 <cell alignment="center" valignment="top" usebox="none">
5531 \begin_layout Plain Layout
5539 <cell alignment="center" valignment="top" usebox="none">
5542 \begin_layout Plain Layout
5543 \begin_inset Formula $\langle$
5553 <cell alignment="center" valignment="top" usebox="none">
5556 \begin_layout Plain Layout
5564 <cell alignment="center" valignment="top" usebox="none">
5567 \begin_layout Plain Layout
5568 \begin_inset Formula $\lceil$
5578 <cell alignment="center" valignment="top" usebox="none">
5581 \begin_layout Plain Layout
5589 <cell alignment="center" valignment="top" usebox="none">
5592 \begin_layout Plain Layout
5593 \begin_inset Formula $\lfloor$
5603 <cell alignment="center" valignment="top" usebox="none">
5606 \begin_layout Plain Layout
5612 <cell alignment="center" valignment="top" usebox="none">
5615 \begin_layout Plain Layout
5616 \begin_inset Formula $/$
5626 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5629 \begin_layout Plain Layout
5635 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5638 \begin_layout Plain Layout
5639 \begin_inset Formula $|$
5653 \begin_inset space \hfill{}
5657 \begin_inset Tabular
5658 <lyxtabular version="3" rows="9" columns="2">
5659 <features booktabs="true" tabularvalignment="middle">
5660 <column alignment="center" valignment="top" width="0pt">
5661 <column alignment="center" valignment="top" width="0pt">
5663 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5666 \begin_layout Plain Layout
5672 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5675 \begin_layout Plain Layout
5683 <cell alignment="center" valignment="top" usebox="none">
5686 \begin_layout Plain Layout
5692 <cell alignment="center" valignment="top" usebox="none">
5695 \begin_layout Plain Layout
5696 \begin_inset Formula $)$
5706 <cell alignment="center" valignment="top" usebox="none">
5709 \begin_layout Plain Layout
5715 <cell alignment="center" valignment="top" usebox="none">
5718 \begin_layout Plain Layout
5719 \begin_inset Formula $\}$
5729 <cell alignment="center" valignment="top" usebox="none">
5732 \begin_layout Plain Layout
5738 <cell alignment="center" valignment="top" usebox="none">
5741 \begin_layout Plain Layout
5742 \begin_inset Formula $]$
5752 <cell alignment="center" valignment="top" usebox="none">
5755 \begin_layout Plain Layout
5763 <cell alignment="center" valignment="top" usebox="none">
5766 \begin_layout Plain Layout
5767 \begin_inset Formula $\rangle$
5777 <cell alignment="center" valignment="top" usebox="none">
5780 \begin_layout Plain Layout
5788 <cell alignment="center" valignment="top" usebox="none">
5791 \begin_layout Plain Layout
5792 \begin_inset Formula $\rceil$
5802 <cell alignment="center" valignment="top" usebox="none">
5805 \begin_layout Plain Layout
5813 <cell alignment="center" valignment="top" usebox="none">
5816 \begin_layout Plain Layout
5817 \begin_inset Formula $\rfloor$
5827 <cell alignment="center" valignment="top" usebox="none">
5830 \begin_layout Plain Layout
5840 <cell alignment="center" valignment="top" usebox="none">
5843 \begin_layout Plain Layout
5844 \begin_inset Formula $\backslash$
5854 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5857 \begin_layout Plain Layout
5865 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5868 \begin_layout Plain Layout
5869 \begin_inset Formula $\|$
5883 \begin_inset space \hfill{}
5889 \begin_layout Standard
5892 \begin_inset Note Greyedout
5895 \begin_layout Plain Layout
5908 \begin_inset Index idx
5911 \begin_layout Plain Layout
5919 must be used for the backslash, because the command
5927 produces a line break there.
5935 \begin_layout Standard
5936 For all characters listed above the size can be adjusted with the commands
5937 described in the following two subsections.
5938 When using these commands, the characters < and > can directly be used
5939 instead of the commands
5954 \begin_layout Subsubsection
5956 \begin_inset CommandInset label
5958 name "subsec:Manual-Bracket-Size"
5963 \begin_inset Index idx
5966 \begin_layout Plain Layout
5967 Bracket size ! manual
5975 \begin_layout Standard
5976 The bracket size can be specified manually by the \SpecialChar LaTeX
5984 \begin_inset Index idx
5987 \begin_layout Plain Layout
6020 denotes the smallest and
6026 the largest bracket size.
6029 \begin_layout Standard
6030 These commands are used to emphasize levels of brackets:
6031 \begin_inset Separator parbreak
6037 \begin_layout Standard
6039 \begin_inset Tabular
6040 <lyxtabular version="3" rows="2" columns="2">
6041 <features booktabs="true" tabularvalignment="middle">
6042 <column alignment="center" valignment="top" width="0pt">
6043 <column alignment="center" valignment="top" width="0pt">
6045 <cell alignment="center" valignment="top" usebox="none">
6048 \begin_layout Plain Layout
6049 all brackets in the same size:
6054 <cell alignment="center" valignment="top" usebox="none">
6057 \begin_layout Plain Layout
6058 \begin_inset Formula $((A+B)(A-B))^{C}$
6067 <row topspace="2mm">
6068 <cell alignment="center" valignment="top" usebox="none">
6071 \begin_layout Plain Layout
6077 <cell alignment="center" valignment="top" usebox="none">
6080 \begin_layout Plain Layout
6081 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6097 \begin_layout Standard
6098 For the second formula the command
6105 \begin_inset space \textvisiblespace{}
6113 \begin_layout Standard
6114 Here is an overview about all bracket sizes:
6115 \begin_inset Separator parbreak
6121 \begin_layout Standard
6138 \begin_inset space \textvisiblespace{}
6146 \begin_inset space \textvisiblespace{}
6150 \begin_inset space \textvisiblespace{}
6160 \begin_layout Standard
6162 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6168 \begin_layout Standard
6175 -commands there is the variant
6182 \begin_inset Index idx
6185 \begin_layout Plain Layout
6193 that adds a bit more space between the bracket and its content, and the
6207 \begin_inset Index idx
6210 \begin_layout Plain Layout
6220 , that don't add additional space.
6225 at the end of the command
6231 is for a left bracket; for a right bracket this will be replaced by an
6237 A left or right bracket can each be an opening or closing bracket.
6240 \begin_layout Standard
6241 In the following table is a comparison of the variants:
6242 \begin_inset Separator parbreak
6248 \begin_layout Standard
6250 \begin_inset Tabular
6251 <lyxtabular version="3" rows="5" columns="2">
6252 <features booktabs="true" tabularvalignment="middle">
6253 <column alignment="center" valignment="top" width="0pt">
6254 <column alignment="center" valignment="middle">
6256 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6259 \begin_layout Plain Layout
6265 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6268 \begin_layout Plain Layout
6275 <row topspace="2mm">
6276 <cell alignment="center" valignment="top" usebox="none">
6279 \begin_layout Plain Layout
6289 \begin_inset space \textvisiblespace{}
6299 <cell alignment="center" valignment="top" usebox="none">
6302 \begin_layout Plain Layout
6303 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6312 <row topspace="2mm">
6313 <cell alignment="center" valignment="top" usebox="none">
6316 \begin_layout Plain Layout
6326 \begin_inset space \textvisiblespace{}
6336 <cell alignment="center" valignment="top" usebox="none">
6339 \begin_layout Plain Layout
6340 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6349 <row topspace="2mm" bottomspace="0.5mm">
6350 <cell alignment="center" valignment="top" usebox="none">
6353 \begin_layout Plain Layout
6363 \begin_inset space \textvisiblespace{}
6373 <cell alignment="center" valignment="top" usebox="none">
6376 \begin_layout Plain Layout
6377 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6386 <row topspace="1.5mm" bottomspace="0.5mm">
6387 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6390 \begin_layout Plain Layout
6402 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6405 \begin_layout Plain Layout
6406 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6422 \begin_layout Subsubsection
6423 Automatic Bracket Size
6424 \begin_inset CommandInset label
6426 name "subsec:Automatic-Bracket-Size"
6431 \begin_inset Index idx
6434 \begin_layout Plain Layout
6435 Bracket size ! automatic
6443 \begin_layout Standard
6444 Brackets with variable size can be inserted with the commands
6451 \begin_inset Index idx
6454 \begin_layout Plain Layout
6469 \begin_inset Index idx
6472 \begin_layout Plain Layout
6480 or via the math toolbar button
6483 arg "dialog-show mathdelimiter"
6499 the wanted bracket must be inserted.
6500 The bracket size will then automatically be calculated for the output.
6501 \begin_inset Separator parbreak
6507 \begin_layout Standard
6509 normal bracket: The command
6516 \begin_inset space \textvisiblespace{}
6520 \begin_inset Formula $\downarrow$
6524 \begin_inset space \textvisiblespace{}
6530 \begin_inset Formula
6540 \begin_layout Standard
6542 multiline bracket: The command
6551 \begin_inset space \textvisiblespace{}
6555 \begin_inset Formula $\downarrow$
6559 \begin_inset space \textvisiblespace{}
6567 \begin_inset Formula
6569 \ln\left(\frac{A}{C}\right)
6577 \begin_layout Standard
6593 \begin_inset space ~
6599 This has the advantage that you can see in \SpecialChar LyX
6600 immediately the real bracket
6601 size and that the matching right bracket will be created too.
6602 \begin_inset Newline newline
6605 The command for the last example would then be:
6616 \begin_inset space \textvisiblespace{}
6620 \begin_inset Formula $\downarrow$
6626 \begin_layout Standard
6627 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6628 For example the command
6635 \begin_inset space \textvisiblespace{}
6639 \begin_inset Formula $\downarrow$
6643 \begin_inset space \textvisiblespace{}
6653 \begin_inset Formula
6655 \left.\frac{A}{B}\right\}
6674 will be converted by \SpecialChar LyX
6675 to brackets in the right size when the document is
6676 reloaded and an omitted bracket will appear as dashed line.
6679 \begin_layout Standard
6680 \begin_inset VSpace bigskip
6683 Because all popular \SpecialChar LaTeX
6684 distributions use e\SpecialChar TeX
6685 , an extension to \SpecialChar LaTeX
6694 \begin_inset Index idx
6697 \begin_layout Plain Layout
6705 is additionally available for all brackets and limits.
6706 With this command the height of the following character is adapted to the
6707 one of the surrounding brackets, what is e.
6708 \begin_inset space \thinspace{}
6712 \begin_inset space \space{}
6715 needed for physical vectors:
6716 \begin_inset Formula
6718 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6723 For physical vectors there is a special \SpecialChar LaTeX
6724 -package, described in
6725 \begin_inset CommandInset ref
6727 reference "subsec:Physical-Vectors"
6734 \begin_layout Subsection
6736 \begin_inset Index idx
6739 \begin_layout Plain Layout
6740 Brackets ! horizontal
6748 \begin_layout Standard
6750 \begin_inset Tabular
6751 <lyxtabular version="3" rows="4" columns="2">
6752 <features booktabs="true" tabularvalignment="middle">
6753 <column alignment="center" valignment="top" width="0pt">
6754 <column alignment="center" valignment="top" width="0pt">
6756 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6759 \begin_layout Plain Layout
6765 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6768 \begin_layout Plain Layout
6776 <cell alignment="center" valignment="top" usebox="none">
6779 \begin_layout Plain Layout
6783 \begin_inset space \textvisiblespace{}
6787 \begin_inset space \textvisiblespace{}
6791 \begin_inset Index idx
6794 \begin_layout Plain Layout
6807 <cell alignment="center" valignment="top" usebox="none">
6810 \begin_layout Plain Layout
6811 \begin_inset Formula $\overbrace{A+B}^{3}$
6820 <row topspace="2mm">
6821 <cell alignment="center" valignment="top" usebox="none">
6824 \begin_layout Plain Layout
6828 \begin_inset space \textvisiblespace{}
6832 \begin_inset space \textvisiblespace{}
6836 \begin_inset Index idx
6839 \begin_layout Plain Layout
6852 <cell alignment="center" valignment="top" usebox="none">
6855 \begin_layout Plain Layout
6856 \begin_inset Formula $\underbrace{A+B}_{5}$
6866 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6869 \begin_layout Plain Layout
6873 \begin_inset space \textvisiblespace{}
6879 \begin_inset space \textvisiblespace{}
6883 \begin_inset space \textvisiblespace{}
6887 \begin_inset space \textvisiblespace{}
6891 \begin_inset space \textvisiblespace{}
6895 \begin_inset space \textvisiblespace{}
6899 \begin_inset space \textvisiblespace{}
6907 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6910 \begin_layout Plain Layout
6911 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6927 \begin_layout Standard
6928 In the last example it doesn't matter if
6940 is inserted at first.
6943 \begin_layout Standard
6944 \begin_inset VSpace medskip
6950 \begin_layout Standard
6951 If you set in the document settings under
6954 \begin_inset space ~
6964 \begin_inset Index idx
6967 \begin_layout Plain Layout
6968 Packages ! mathtools
6976 \begin_inset space ~
6981 , you have access to square backets:
6982 \begin_inset Separator parbreak
6988 \begin_layout Standard
6990 \begin_inset Tabular
6991 <lyxtabular version="3" rows="4" columns="2">
6992 <features booktabs="true" tabularvalignment="middle">
6993 <column alignment="center" valignment="top" width="0pt">
6994 <column alignment="center" valignment="top" width="0pt">
6996 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6999 \begin_layout Plain Layout
7005 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7008 \begin_layout Plain Layout
7016 <cell alignment="center" valignment="top" usebox="none">
7019 \begin_layout Plain Layout
7047 \begin_inset space \textvisiblespace{}
7051 \begin_inset Index idx
7054 \begin_layout Plain Layout
7067 <cell alignment="center" valignment="top" usebox="none">
7070 \begin_layout Plain Layout
7071 \begin_inset Formula $\overbracket{A+B}^{3}$
7080 <row topspace="2mm">
7081 <cell alignment="center" valignment="top" usebox="none">
7084 \begin_layout Plain Layout
7112 \begin_inset space \textvisiblespace{}
7116 \begin_inset Index idx
7119 \begin_layout Plain Layout
7144 <cell alignment="center" valignment="top" usebox="none">
7147 \begin_layout Plain Layout
7148 \begin_inset Formula $\underbracket{A+B}_{5}$
7158 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7161 \begin_layout Plain Layout
7167 \begin_inset space \textvisiblespace{}
7171 \begin_inset space \textvisiblespace{}
7175 \begin_inset space \textvisiblespace{}
7179 \begin_inset space \textvisiblespace{}
7183 \begin_inset space \textvisiblespace{}
7191 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7194 \begin_layout Plain Layout
7195 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7211 \begin_layout Standard
7224 you can change the thickness of the bracket's stroke by specifying the
7225 desired thickness in square brackets behind the command:
7226 \begin_inset Separator parbreak
7232 \begin_layout Standard
7234 \begin_inset Tabular
7235 <lyxtabular version="3" rows="3" columns="2">
7236 <features booktabs="true" tabularvalignment="middle">
7237 <column alignment="center" valignment="top" width="0pt">
7238 <column alignment="center" valignment="top" width="0pt">
7240 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7243 \begin_layout Plain Layout
7249 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7252 \begin_layout Plain Layout
7260 <cell alignment="center" valignment="top" usebox="none">
7263 \begin_layout Plain Layout
7293 \begin_inset space \textvisiblespace{}
7301 <cell alignment="center" valignment="top" usebox="none">
7304 \begin_layout Plain Layout
7305 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7314 <row topspace="2mm">
7315 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7318 \begin_layout Plain Layout
7348 \begin_inset space \textvisiblespace{}
7356 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7359 \begin_layout Plain Layout
7360 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7376 \begin_layout Standard
7377 \begin_inset VSpace bigskip
7380 When brackets should overlap each other, multiline formulas, as described
7382 \begin_inset CommandInset ref
7384 reference "sec:Multiline-Formulas"
7389 \begin_inset Formula
7391 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7392 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7397 In the first row the formula is inserted together with the first brace.
7398 It is hereby important that the space command
7402 \begin_layout Plain Layout
7403 Space commands are explained in
7404 \begin_inset CommandInset ref
7406 reference "subsec:Predefined-Space"
7421 is inserted before the first
7422 \begin_inset Formula $d$
7425 , because the brace that ends behind the
7426 \begin_inset Formula $q$
7429 prevents that the following
7430 \begin_inset Quotes eld
7434 \begin_inset Quotes erd
7437 is surrounded by space.
7441 \begin_layout Plain Layout
7442 because a bracket is not handled as a character, see
7443 \begin_inset CommandInset ref
7445 reference "subsec:Binary-Operators"
7454 In the second row the second brace is inserted.
7455 As it should begin before the
7456 \begin_inset Formula $b$
7471 \begin_layout Plain Layout
7479 \begin_inset CommandInset ref
7481 reference "subsec:Placeholders"
7490 This space is needed because the
7491 \begin_inset Quotes eld
7495 \begin_inset Quotes erd
7498 is also surrounded by space in the formula.
7499 The brace is placed under the command
7508 \begin_layout Standard
7509 It gets more complicated when brackets overlap each other above and under
7510 the formula, like in the following example:
7514 \begin_layout Plain Layout
7526 \begin_inset Formula
7528 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7529 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7538 \begin_layout Plain Layout
7549 The first formula row is the same as the second row of the previous example,
7550 with the difference that the brace is above.
7551 The second row contains the formula together with the second brace.
7552 To avoid that there is space between the upper brace in the first row and
7553 the formula, the row spacing needs to be reduced.
7554 This is not easily possible due to a bug in \SpecialChar LyX
7559 \begin_layout Plain Layout
7560 \begin_inset CommandInset href
7562 name "LyX-bug #1505"
7563 target "http://www.lyx.org/trac/ticket/1505"
7572 As a solution for the problem, the global formula row separation
7579 \begin_inset Index idx
7582 \begin_layout Plain Layout
7590 must be changed to -6
7591 \begin_inset space \thinspace{}
7594 pt before the formula with the command
7610 is set back after the formula to the standard value of 3
7611 \begin_inset space \thinspace{}
7614 pt using the same command.
7615 More about the row separation in formulas is explained in
7616 \begin_inset CommandInset ref
7618 reference "subsec:Line-Separation"
7625 \begin_layout Section
7627 \begin_inset Index idx
7630 \begin_layout Plain Layout
7639 \begin_layout Standard
7640 Arrows can be inserted via the math toolbar button
7643 arg "math-insert \\leftarrow"
7646 or the commands listed in the following subsections.
7649 \begin_layout Subsection
7651 \begin_inset Index idx
7654 \begin_layout Plain Layout
7663 \begin_layout Standard
7664 \begin_inset space \hfill{}
7668 \begin_inset Tabular
7669 <lyxtabular version="3" rows="8" columns="2">
7670 <features booktabs="true" tabularvalignment="middle">
7671 <column alignment="center" valignment="top" width="0pt">
7672 <column alignment="center" valignment="top" width="0pt">
7674 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7677 \begin_layout Plain Layout
7683 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7686 \begin_layout Plain Layout
7694 <cell alignment="center" valignment="top" usebox="none">
7697 \begin_layout Plain Layout
7705 <cell alignment="center" valignment="top" usebox="none">
7708 \begin_layout Plain Layout
7709 \begin_inset Formula $\gets$
7719 <cell alignment="center" valignment="top" usebox="none">
7722 \begin_layout Plain Layout
7730 <cell alignment="center" valignment="top" usebox="none">
7733 \begin_layout Plain Layout
7734 \begin_inset Formula $\Leftarrow$
7744 <cell alignment="center" valignment="top" usebox="none">
7747 \begin_layout Plain Layout
7755 <cell alignment="center" valignment="top" usebox="none">
7758 \begin_layout Plain Layout
7759 \begin_inset Formula $\longleftarrow$
7769 <cell alignment="center" valignment="top" usebox="none">
7772 \begin_layout Plain Layout
7780 <cell alignment="center" valignment="top" usebox="none">
7783 \begin_layout Plain Layout
7784 \begin_inset Formula $\Longleftarrow$
7794 <cell alignment="center" valignment="top" usebox="none">
7797 \begin_layout Plain Layout
7805 <cell alignment="center" valignment="top" usebox="none">
7808 \begin_layout Plain Layout
7809 \begin_inset Formula $\leftharpoonup$
7819 <cell alignment="center" valignment="top" usebox="none">
7822 \begin_layout Plain Layout
7830 <cell alignment="center" valignment="top" usebox="none">
7833 \begin_layout Plain Layout
7834 \begin_inset Formula $\leftharpoondown$
7844 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7847 \begin_layout Plain Layout
7855 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7858 \begin_layout Plain Layout
7859 \begin_inset Formula $\hookleftarrow$
7873 \begin_inset space \hfill{}
7877 \begin_inset Tabular
7878 <lyxtabular version="3" rows="8" columns="2">
7879 <features booktabs="true" tabularvalignment="middle">
7880 <column alignment="center" valignment="top" width="0pt">
7881 <column alignment="center" valignment="top" width="0pt">
7883 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7886 \begin_layout Plain Layout
7892 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7895 \begin_layout Plain Layout
7903 <cell alignment="center" valignment="top" usebox="none">
7906 \begin_layout Plain Layout
7914 <cell alignment="center" valignment="top" usebox="none">
7917 \begin_layout Plain Layout
7918 \begin_inset Formula $\to$
7928 <cell alignment="center" valignment="top" usebox="none">
7931 \begin_layout Plain Layout
7939 <cell alignment="center" valignment="top" usebox="none">
7942 \begin_layout Plain Layout
7943 \begin_inset Formula $\Rightarrow$
7953 <cell alignment="center" valignment="top" usebox="none">
7956 \begin_layout Plain Layout
7964 <cell alignment="center" valignment="top" usebox="none">
7967 \begin_layout Plain Layout
7968 \begin_inset Formula $\longrightarrow$
7978 <cell alignment="center" valignment="top" usebox="none">
7981 \begin_layout Plain Layout
7989 <cell alignment="center" valignment="top" usebox="none">
7992 \begin_layout Plain Layout
7993 \begin_inset Formula $\Longrightarrow$
8003 <cell alignment="center" valignment="top" usebox="none">
8006 \begin_layout Plain Layout
8014 <cell alignment="center" valignment="top" usebox="none">
8017 \begin_layout Plain Layout
8018 \begin_inset Formula $\rightharpoonup$
8028 <cell alignment="center" valignment="top" usebox="none">
8031 \begin_layout Plain Layout
8039 <cell alignment="center" valignment="top" usebox="none">
8042 \begin_layout Plain Layout
8043 \begin_inset Formula $\rightharpoondown$
8053 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8056 \begin_layout Plain Layout
8064 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8067 \begin_layout Plain Layout
8068 \begin_inset Formula $\hookrightarrow$
8082 \begin_inset space \hfill{}
8088 \begin_layout Standard
8089 \begin_inset space \hfill{}
8093 \begin_inset Tabular
8094 <lyxtabular version="3" rows="6" columns="2">
8095 <features booktabs="true" tabularvalignment="middle">
8096 <column alignment="center" valignment="top" width="0pt">
8097 <column alignment="center" valignment="top" width="0pt">
8099 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8102 \begin_layout Plain Layout
8108 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8111 \begin_layout Plain Layout
8119 <cell alignment="center" valignment="top" usebox="none">
8122 \begin_layout Plain Layout
8130 <cell alignment="center" valignment="top" usebox="none">
8133 \begin_layout Plain Layout
8134 \begin_inset Formula $\leftrightarrow$
8144 <cell alignment="center" valignment="top" usebox="none">
8147 \begin_layout Plain Layout
8155 <cell alignment="center" valignment="top" usebox="none">
8158 \begin_layout Plain Layout
8159 \begin_inset Formula $\Leftrightarrow$
8169 <cell alignment="center" valignment="top" usebox="none">
8172 \begin_layout Plain Layout
8180 <cell alignment="center" valignment="top" usebox="none">
8183 \begin_layout Plain Layout
8184 \begin_inset Formula $\longleftrightarrow$
8194 <cell alignment="center" valignment="top" usebox="none">
8197 \begin_layout Plain Layout
8205 <cell alignment="center" valignment="top" usebox="none">
8208 \begin_layout Plain Layout
8209 \begin_inset Formula $\Longleftrightarrow$
8219 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8222 \begin_layout Plain Layout
8230 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8233 \begin_layout Plain Layout
8234 \begin_inset Formula $\rightleftharpoons$
8248 \begin_inset space \hspace{}
8253 \begin_inset space \hfill{}
8257 \begin_inset Tabular
8258 <lyxtabular version="3" rows="5" columns="2">
8259 <features booktabs="true" tabularvalignment="middle">
8260 <column alignment="center" valignment="top" width="0pt">
8261 <column alignment="center" valignment="top" width="0pt">
8263 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8266 \begin_layout Plain Layout
8272 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8275 \begin_layout Plain Layout
8283 <cell alignment="center" valignment="top" usebox="none">
8286 \begin_layout Plain Layout
8294 <cell alignment="center" valignment="top" usebox="none">
8297 \begin_layout Plain Layout
8298 \begin_inset Formula $\mapsto$
8308 <cell alignment="center" valignment="top" usebox="none">
8311 \begin_layout Plain Layout
8319 <cell alignment="center" valignment="top" usebox="none">
8322 \begin_layout Plain Layout
8323 \begin_inset Formula $\longmapsto$
8333 <cell alignment="center" valignment="top" usebox="none">
8336 \begin_layout Plain Layout
8344 <cell alignment="center" valignment="top" usebox="none">
8347 \begin_layout Plain Layout
8348 \begin_inset Formula $\leadsto$
8358 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8361 \begin_layout Plain Layout
8369 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8372 \begin_layout Plain Layout
8373 \begin_inset Formula $\dasharrow$
8387 \begin_inset space \hfill{}
8393 \begin_layout Standard
8394 \begin_inset VSpace medskip
8397 Arrows used as accents like e.
8398 \begin_inset space \thinspace{}
8402 \begin_inset space \space{}
8405 vector arrows are listed in
8406 \begin_inset CommandInset ref
8408 reference "sec:Accents"
8415 \begin_layout Standard
8416 \begin_inset VSpace bigskip
8419 Furthermore there are the labeled arrows
8420 \begin_inset Index idx
8423 \begin_layout Plain Layout
8436 \begin_inset Index idx
8439 \begin_layout Plain Layout
8454 \begin_inset Index idx
8457 \begin_layout Plain Layout
8464 \begin_layout Plain Layout
8479 When inserting one of these commands in a formula, an arrow with two blue
8480 boxes appear where the label can be inserted.
8481 The length of the arrow adapts to the label width.
8484 \begin_layout Standard
8486 \begin_inset Tabular
8487 <lyxtabular version="3" rows="3" columns="2">
8488 <features booktabs="true" tabularvalignment="middle">
8489 <column alignment="center" valignment="top" width="0pt">
8490 <column alignment="center" valignment="top" width="0pt">
8492 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8495 \begin_layout Plain Layout
8501 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8504 \begin_layout Plain Layout
8512 <cell alignment="center" valignment="top" usebox="none">
8515 \begin_layout Plain Layout
8519 \begin_inset space \textvisiblespace{}
8523 \begin_inset Formula $\downarrow$
8527 \begin_inset Formula $\to$
8535 <cell alignment="center" valignment="top" usebox="none">
8538 \begin_layout Plain Layout
8539 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8548 <row topspace="2mm">
8549 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8552 \begin_layout Plain Layout
8556 \begin_inset space \textvisiblespace{}
8560 \begin_inset Formula $\downarrow$
8564 \begin_inset Formula $\to$
8572 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8575 \begin_layout Plain Layout
8576 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8592 \begin_layout Standard
8593 \begin_inset VSpace medskip
8599 \begin_layout Standard
8600 If you set in the document settings under
8603 \begin_inset space ~
8613 \begin_inset Index idx
8616 \begin_layout Plain Layout
8617 Packages ! mathtools
8625 \begin_inset space ~
8630 , you have access to the following labeled arrows:
8633 \begin_layout Standard
8634 \begin_inset Newpage newpage
8638 \begin_inset Separator parbreak
8644 \begin_layout Standard
8646 \begin_inset space \hspace*{\fill}
8650 \begin_inset Tabular
8651 <lyxtabular version="3" rows="7" columns="2">
8652 <features booktabs="true" tabularvalignment="middle">
8653 <column alignment="center" valignment="top" width="0pt">
8654 <column alignment="center" valignment="top" width="0pt">
8656 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8659 \begin_layout Plain Layout
8665 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8668 \begin_layout Plain Layout
8676 <cell alignment="center" valignment="top" usebox="none">
8679 \begin_layout Plain Layout
8699 <cell alignment="center" valignment="top" usebox="none">
8702 \begin_layout Plain Layout
8703 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8712 <row topspace="2mm">
8713 <cell alignment="center" valignment="top" usebox="none">
8716 \begin_layout Plain Layout
8736 <cell alignment="center" valignment="top" usebox="none">
8739 \begin_layout Plain Layout
8740 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8749 <row topspace="2mm">
8750 <cell alignment="center" valignment="top" usebox="none">
8753 \begin_layout Plain Layout
8773 <cell alignment="center" valignment="top" usebox="none">
8776 \begin_layout Plain Layout
8777 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8786 <row topspace="2mm">
8787 <cell alignment="center" valignment="top" usebox="none">
8790 \begin_layout Plain Layout
8810 <cell alignment="center" valignment="top" usebox="none">
8813 \begin_layout Plain Layout
8814 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8823 <row topspace="2mm">
8824 <cell alignment="center" valignment="top" usebox="none">
8827 \begin_layout Plain Layout
8847 <cell alignment="center" valignment="top" usebox="none">
8850 \begin_layout Plain Layout
8851 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8860 <row topspace="2mm">
8861 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8864 \begin_layout Plain Layout
8884 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8887 \begin_layout Plain Layout
8888 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8902 \begin_inset space \hspace*{\fill}
8906 \begin_inset Tabular
8907 <lyxtabular version="3" rows="7" columns="2">
8908 <features booktabs="true" tabularvalignment="middle">
8909 <column alignment="center" valignment="top" width="0pt">
8910 <column alignment="center" valignment="top" width="0pt">
8912 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8915 \begin_layout Plain Layout
8921 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8924 \begin_layout Plain Layout
8932 <cell alignment="center" valignment="top" usebox="none">
8935 \begin_layout Plain Layout
8955 <cell alignment="center" valignment="top" usebox="none">
8958 \begin_layout Plain Layout
8959 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8968 <row topspace="2mm">
8969 <cell alignment="center" valignment="top" usebox="none">
8972 \begin_layout Plain Layout
8992 <cell alignment="center" valignment="top" usebox="none">
8995 \begin_layout Plain Layout
8996 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
9005 <row topspace="2mm">
9006 <cell alignment="center" valignment="top" usebox="none">
9009 \begin_layout Plain Layout
9029 <cell alignment="center" valignment="top" usebox="none">
9032 \begin_layout Plain Layout
9033 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
9042 <row topspace="2mm">
9043 <cell alignment="center" valignment="top" usebox="none">
9046 \begin_layout Plain Layout
9066 <cell alignment="center" valignment="top" usebox="none">
9069 \begin_layout Plain Layout
9070 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9079 <row topspace="2mm">
9080 <cell alignment="center" valignment="top" usebox="none">
9083 \begin_layout Plain Layout
9103 <cell alignment="center" valignment="top" usebox="none">
9106 \begin_layout Plain Layout
9107 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9116 <row topspace="2mm">
9117 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9120 \begin_layout Plain Layout
9140 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9143 \begin_layout Plain Layout
9144 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9158 \begin_inset space \hspace*{\fill}
9164 \begin_layout Standard
9165 The command scheme is for all these arrows:
9166 \begin_inset Separator parbreak
9172 \begin_layout Standard
9174 \begin_inset Tabular
9175 <lyxtabular version="3" rows="2" columns="2">
9176 <features booktabs="true" tabularvalignment="middle">
9177 <column alignment="center" valignment="top" width="0pt">
9178 <column alignment="center" valignment="top" width="0pt">
9180 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9183 \begin_layout Plain Layout
9189 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9192 \begin_layout Plain Layout
9199 <row bottomspace="0.5mm">
9200 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9203 \begin_layout Plain Layout
9206 xleftrightarrow[x=a]
9209 \begin_inset Formula $\to$
9217 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9220 \begin_layout Plain Layout
9221 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9237 \begin_layout Subsection
9238 Vertical and diagonal Arrows
9239 \begin_inset Index idx
9242 \begin_layout Plain Layout
9249 \begin_inset Index idx
9252 \begin_layout Plain Layout
9261 \begin_layout Standard
9262 \begin_inset space \hfill{}
9266 \begin_inset Tabular
9267 <lyxtabular version="3" rows="7" columns="2">
9268 <features booktabs="true" tabularvalignment="middle">
9269 <column alignment="center" valignment="top" width="0pt">
9270 <column alignment="center" valignment="top" width="0pt">
9272 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9275 \begin_layout Plain Layout
9281 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9284 \begin_layout Plain Layout
9292 <cell alignment="center" valignment="top" usebox="none">
9295 \begin_layout Plain Layout
9303 <cell alignment="center" valignment="top" usebox="none">
9306 \begin_layout Plain Layout
9307 \begin_inset Formula $\uparrow$
9317 <cell alignment="center" valignment="top" usebox="none">
9320 \begin_layout Plain Layout
9328 <cell alignment="center" valignment="top" usebox="none">
9331 \begin_layout Plain Layout
9332 \begin_inset Formula $\Uparrow$
9342 <cell alignment="center" valignment="top" usebox="none">
9345 \begin_layout Plain Layout
9353 <cell alignment="center" valignment="top" usebox="none">
9356 \begin_layout Plain Layout
9357 \begin_inset Formula $\updownarrow$
9367 <cell alignment="center" valignment="top" usebox="none">
9370 \begin_layout Plain Layout
9378 <cell alignment="center" valignment="top" usebox="none">
9381 \begin_layout Plain Layout
9382 \begin_inset Formula $\Updownarrow$
9392 <cell alignment="center" valignment="top" usebox="none">
9395 \begin_layout Plain Layout
9403 <cell alignment="center" valignment="top" usebox="none">
9406 \begin_layout Plain Layout
9407 \begin_inset Formula $\Downarrow$
9417 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9420 \begin_layout Plain Layout
9428 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9431 \begin_layout Plain Layout
9432 \begin_inset Formula $\downarrow$
9446 \begin_inset space \hfill{}
9450 \begin_inset Tabular
9451 <lyxtabular version="3" rows="5" columns="2">
9452 <features booktabs="true" tabularvalignment="middle">
9453 <column alignment="center" valignment="top" width="0pt">
9454 <column alignment="center" valignment="top" width="0pt">
9456 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9459 \begin_layout Plain Layout
9465 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9468 \begin_layout Plain Layout
9476 <cell alignment="center" valignment="top" usebox="none">
9479 \begin_layout Plain Layout
9487 <cell alignment="center" valignment="top" usebox="none">
9490 \begin_layout Plain Layout
9491 \begin_inset Formula $\nearrow$
9501 <cell alignment="center" valignment="top" usebox="none">
9504 \begin_layout Plain Layout
9512 <cell alignment="center" valignment="top" usebox="none">
9515 \begin_layout Plain Layout
9516 \begin_inset Formula $\searrow$
9526 <cell alignment="center" valignment="top" usebox="none">
9529 \begin_layout Plain Layout
9537 <cell alignment="center" valignment="top" usebox="none">
9540 \begin_layout Plain Layout
9541 \begin_inset Formula $\swarrow$
9551 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9554 \begin_layout Plain Layout
9562 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9565 \begin_layout Plain Layout
9566 \begin_inset Formula $\nwarrow$
9580 \begin_inset space \hfill{}
9586 \begin_layout Standard
9587 \begin_inset VSpace medskip
9590 Vertical arrows can be used also as delimiters together with the commands
9592 \begin_inset CommandInset ref
9594 reference "subsec:Manual-Bracket-Size"
9599 \begin_inset CommandInset ref
9601 reference "subsec:Automatic-Bracket-Size"
9608 \begin_layout Section
9610 \begin_inset CommandInset label
9617 \begin_inset Index idx
9620 \begin_layout Plain Layout
9629 \begin_layout Standard
9630 Accents can be inserted via the math toolbar button
9633 arg "math-insert \\hat"
9636 or the commands listed in the following subsections.
9639 \begin_layout Subsection
9640 Accents for one Character
9644 \begin_layout Plain Layout
9657 \begin_layout Plain Layout
9659 \begin_inset CommandInset ref
9661 reference "subsec:Accents-in-Text"
9674 \begin_layout Plain Layout
9682 \begin_inset Note Note
9685 \begin_layout Plain Layout
9692 is used to avoid that the footnote appears in the PDF-bookmark.
9695 \begin_layout Plain Layout
9703 \begin_inset CommandInset ref
9705 reference "subsec:Formulas-in-Section"
9715 \begin_inset CommandInset label
9717 name "subsec:Accents-for-one"
9722 \begin_inset Index idx
9725 \begin_layout Plain Layout
9726 Accents ! for one character
9734 \begin_layout Standard
9735 \begin_inset space \hfill{}
9739 \begin_inset Tabular
9740 <lyxtabular version="3" rows="8" columns="2">
9741 <features booktabs="true" tabularvalignment="middle">
9742 <column alignment="center" valignment="top" width="0pt">
9743 <column alignment="center" valignment="top" width="0pt">
9745 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9748 \begin_layout Plain Layout
9754 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9757 \begin_layout Plain Layout
9764 <row topspace="1.5mm">
9765 <cell alignment="center" valignment="top" usebox="none">
9768 \begin_layout Plain Layout
9772 \begin_inset space \textvisiblespace{}
9780 <cell alignment="center" valignment="top" usebox="none">
9783 \begin_layout Plain Layout
9784 \begin_inset Formula $\dot{A}$
9793 <row topspace="1.5mm">
9794 <cell alignment="center" valignment="top" usebox="none">
9797 \begin_layout Plain Layout
9801 \begin_inset space \textvisiblespace{}
9809 <cell alignment="center" valignment="top" usebox="none">
9812 \begin_layout Plain Layout
9813 \begin_inset Formula $\ddot{A}$
9822 <row topspace="1.5mm">
9823 <cell alignment="center" valignment="top" usebox="none">
9826 \begin_layout Plain Layout
9830 \begin_inset space \textvisiblespace{}
9838 <cell alignment="center" valignment="top" usebox="none">
9841 \begin_layout Plain Layout
9842 \begin_inset Formula $\dddot{A}$
9851 <row topspace="1.5mm">
9852 <cell alignment="center" valignment="top" usebox="none">
9855 \begin_layout Plain Layout
9859 \begin_inset space \textvisiblespace{}
9867 <cell alignment="center" valignment="top" usebox="none">
9870 \begin_layout Plain Layout
9871 \begin_inset Formula $\ddddot{A}$
9880 <row topspace="1.5mm">
9881 <cell alignment="center" valignment="top" usebox="none">
9884 \begin_layout Plain Layout
9888 \begin_inset space \textvisiblespace{}
9892 \begin_inset Index idx
9895 \begin_layout Plain Layout
9906 <cell alignment="center" valignment="top" usebox="none">
9909 \begin_layout Plain Layout
9910 \begin_inset Formula $\vec{A}$
9919 <row topspace="1.5mm">
9920 <cell alignment="center" valignment="top" usebox="none">
9923 \begin_layout Plain Layout
9927 \begin_inset space \textvisiblespace{}
9935 <cell alignment="center" valignment="top" usebox="none">
9938 \begin_layout Plain Layout
9939 \begin_inset Formula $\bar{A}$
9948 <row topspace="1.5mm">
9949 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9952 \begin_layout Plain Layout
9956 \begin_inset space \textvisiblespace{}
9964 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9967 \begin_layout Plain Layout
9968 \begin_inset Formula $\mathring{A}$
9982 \begin_inset space \hfill{}
9986 \begin_inset Tabular
9987 <lyxtabular version="3" rows="7" columns="2">
9988 <features booktabs="true" tabularvalignment="middle">
9989 <column alignment="center" valignment="top" width="0pt">
9990 <column alignment="center" valignment="top" width="0pt">
9992 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9995 \begin_layout Plain Layout
10001 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10004 \begin_layout Plain Layout
10011 <row topspace="1.5mm">
10012 <cell alignment="center" valignment="top" usebox="none">
10015 \begin_layout Plain Layout
10019 \begin_inset space \textvisiblespace{}
10027 <cell alignment="center" valignment="top" usebox="none">
10030 \begin_layout Plain Layout
10031 \begin_inset Formula $\tilde{A}$
10040 <row topspace="1.5mm">
10041 <cell alignment="center" valignment="top" usebox="none">
10044 \begin_layout Plain Layout
10048 \begin_inset space \textvisiblespace{}
10056 <cell alignment="center" valignment="top" usebox="none">
10059 \begin_layout Plain Layout
10060 \begin_inset Formula $\hat{A}$
10069 <row topspace="1.5mm">
10070 <cell alignment="center" valignment="top" usebox="none">
10073 \begin_layout Plain Layout
10077 \begin_inset space \textvisiblespace{}
10085 <cell alignment="center" valignment="top" usebox="none">
10088 \begin_layout Plain Layout
10089 \begin_inset Formula $\check{A}$
10098 <row topspace="1.5mm">
10099 <cell alignment="center" valignment="top" usebox="none">
10102 \begin_layout Plain Layout
10106 \begin_inset space \textvisiblespace{}
10114 <cell alignment="center" valignment="top" usebox="none">
10117 \begin_layout Plain Layout
10118 \begin_inset Formula $\acute{A}$
10127 <row topspace="1.5mm">
10128 <cell alignment="center" valignment="top" usebox="none">
10131 \begin_layout Plain Layout
10135 \begin_inset space \textvisiblespace{}
10143 <cell alignment="center" valignment="top" usebox="none">
10146 \begin_layout Plain Layout
10147 \begin_inset Formula $\grave{A}$
10156 <row topspace="1.5mm">
10157 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10160 \begin_layout Plain Layout
10164 \begin_inset space \textvisiblespace{}
10172 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10175 \begin_layout Plain Layout
10176 \begin_inset Formula $\breve{A}$
10190 \begin_inset space \hfill{}
10196 \begin_layout Standard
10197 \begin_inset VSpace bigskip
10203 \begin_layout Standard
10204 You can directly insert accents like é to formulas.
10206 will transform them to the corresponding accent command.
10208 \begin_inset Index idx
10211 \begin_layout Plain Layout
10217 it is better to insert a quotation mark before the vowel.
10218 These two characters are then treated by \SpecialChar LaTeX
10223 character when the formula part with the umlaut is marked as German.
10231 \begin_inset Quotes eld
10235 \begin_inset Quotes erd
10238 umlauts are created as demonstrated in the following example:
10241 \begin_layout Standard
10242 \begin_inset VSpace -2mm
10248 \begin_layout Standard
10250 \begin_inset Tabular
10251 <lyxtabular version="3" rows="3" columns="2">
10252 <features booktabs="true" tabularvalignment="middle">
10253 <column alignment="center" valignment="top" width="0pt">
10254 <column alignment="center" valignment="top">
10256 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10259 \begin_layout Plain Layout
10265 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10268 \begin_layout Plain Layout
10276 <cell alignment="center" valignment="top" usebox="none">
10279 \begin_layout Plain Layout
10280 \begin_inset Quotes grd
10288 <cell alignment="center" valignment="top" usebox="none">
10291 \begin_layout Plain Layout
10292 \begin_inset space \hspace{}
10299 \begin_inset Formula $"i$
10308 <row topspace="1.5mm">
10309 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10312 \begin_layout Plain Layout
10316 \begin_inset space \textvisiblespace{}
10324 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10327 \begin_layout Plain Layout
10328 \begin_inset Formula $\ddot{i}$
10344 \begin_layout Standard
10345 Another advantage to
10351 is that umlauts can directly be converted to mathematical text because
10352 the accent commands above are
10358 in mathematical text
10361 To convert an accented character to mathematical text, only the character
10362 under the accent may be converted.
10363 This applies also for all other conversions, e.
10364 \begin_inset space \thinspace{}
10368 \begin_inset space \space{}
10374 \begin_layout Standard
10375 In mathematical text, umlauts and other accented characters can directly
10379 \begin_layout Standard
10380 \begin_inset VSpace bigskip
10386 \begin_layout Standard
10388 also supports a tilde under the character if the \SpecialChar LaTeX
10394 \begin_inset Index idx
10397 \begin_layout Plain Layout
10398 Packages ! undertilde
10403 is installed on your system:
10406 \begin_layout Standard
10410 \begin_layout Plain Layout
10420 \begin_inset Note Note
10423 \begin_layout Plain Layout
10424 The following table will only be displayed when the \SpecialChar LaTeX
10435 \begin_inset Separator parbreak
10441 \begin_layout Standard
10444 \begin_inset Tabular
10445 <lyxtabular version="3" rows="2" columns="2">
10446 <features booktabs="true" tabularvalignment="middle">
10447 <column alignment="center" valignment="top" width="0pt">
10448 <column alignment="center" valignment="top" width="0pt">
10450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10453 \begin_layout Plain Layout
10459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10462 \begin_layout Plain Layout
10470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10473 \begin_layout Plain Layout
10477 \begin_inset space \textvisiblespace{}
10485 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10488 \begin_layout Plain Layout
10489 \begin_inset Formula $\utilde{A}$
10505 \begin_layout Standard
10509 \begin_layout Plain Layout
10519 \begin_inset Note Note
10522 \begin_layout Plain Layout
10523 The following will be displayed when the \SpecialChar LaTeX
10536 \begin_layout Standard
10537 You need to install the \SpecialChar LaTeX
10542 to see the rest of this subsection in the output.
10545 \begin_layout Standard
10549 \begin_layout Plain Layout
10561 \begin_layout Standard
10562 \begin_inset Newpage newpage
10568 \begin_layout Subsection
10569 Accents for several Characters
10570 \begin_inset Index idx
10573 \begin_layout Plain Layout
10574 Accents ! for several characters
10582 \begin_layout Standard
10583 \begin_inset space \hfill{}
10587 \begin_inset Tabular
10588 <lyxtabular version="3" rows="5" columns="2">
10589 <features booktabs="true" tabularvalignment="middle">
10590 <column alignment="center" valignment="top" width="0pt">
10591 <column alignment="center" valignment="top" width="0pt">
10593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10596 \begin_layout Plain Layout
10602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10605 \begin_layout Plain Layout
10612 <row topspace="1.5mm">
10613 <cell alignment="center" valignment="top" usebox="none">
10616 \begin_layout Plain Layout
10620 \begin_inset space \textvisiblespace{}
10628 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10631 \begin_layout Plain Layout
10632 \begin_inset Formula $\overleftarrow{A=B}$
10641 <row topspace="1.5mm">
10642 <cell alignment="center" valignment="top" usebox="none">
10645 \begin_layout Plain Layout
10649 \begin_inset space \textvisiblespace{}
10657 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10660 \begin_layout Plain Layout
10661 \begin_inset Formula $\underleftarrow{A=B}$
10670 <row topspace="1.5mm">
10671 <cell alignment="center" valignment="top" usebox="none">
10674 \begin_layout Plain Layout
10678 \begin_inset space \textvisiblespace{}
10686 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10689 \begin_layout Plain Layout
10690 \begin_inset Formula $\overleftrightarrow{A=B}$
10699 <row topspace="1.5mm" bottomspace="1mm">
10700 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10703 \begin_layout Plain Layout
10706 underleftrightarrow
10707 \begin_inset space \textvisiblespace{}
10715 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10718 \begin_layout Plain Layout
10719 \begin_inset Formula $\underleftrightarrow{A=B}$
10733 \begin_inset space \hfill{}
10737 \begin_inset Tabular
10738 <lyxtabular version="3" rows="5" columns="2">
10739 <features booktabs="true" tabularvalignment="middle">
10740 <column alignment="center" valignment="top" width="0pt">
10741 <column alignment="center" valignment="top" width="0pt">
10743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10746 \begin_layout Plain Layout
10752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10755 \begin_layout Plain Layout
10762 <row topspace="1.5mm">
10763 <cell alignment="center" valignment="top" usebox="none">
10766 \begin_layout Plain Layout
10770 \begin_inset space \textvisiblespace{}
10778 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10781 \begin_layout Plain Layout
10782 \begin_inset Formula $\overrightarrow{A=B}$
10791 <row topspace="1.5mm">
10792 <cell alignment="center" valignment="top" usebox="none">
10795 \begin_layout Plain Layout
10799 \begin_inset space \textvisiblespace{}
10807 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10810 \begin_layout Plain Layout
10811 \begin_inset Formula $\underrightarrow{A=B}$
10820 <row topspace="1.5mm">
10821 <cell alignment="center" valignment="top" usebox="none">
10824 \begin_layout Plain Layout
10828 \begin_inset space \textvisiblespace{}
10836 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10839 \begin_layout Plain Layout
10840 \begin_inset Formula $\widetilde{A=B}$
10849 <row topspace="1.5mm" bottomspace="1mm">
10850 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10853 \begin_layout Plain Layout
10857 \begin_inset space \textvisiblespace{}
10865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10868 \begin_layout Plain Layout
10869 \begin_inset Formula $\widehat{A=B}$
10883 \begin_inset space \hfill{}
10889 \begin_layout Standard
10890 \begin_inset VSpace medskip
10893 With these commands as many characters as you like can be accented.
10906 will only be set in the output with a length of three characters, as shown
10907 in the following example:
10908 \begin_inset Formula
10910 \widetilde{A+B=C-D}
10918 \begin_layout Standard
10926 \begin_inset Index idx
10929 \begin_layout Plain Layout
10944 \begin_inset Index idx
10947 \begin_layout Plain Layout
10955 described in the previous subsection it is also possible to accent several
10962 \begin_inset space \textvisiblespace{}
10966 \begin_inset Formula $\downarrow$
10972 \begin_inset Formula
10974 \underset{***}{A=B}
10982 \begin_layout Section
10984 \begin_inset CommandInset label
10986 name "subsec:Space"
10991 \begin_inset Index idx
10994 \begin_layout Plain Layout
11003 \begin_layout Subsection
11005 \begin_inset CommandInset label
11007 name "subsec:Predefined-Space"
11012 \begin_inset Index idx
11015 \begin_layout Plain Layout
11016 Space ! horizontal ! predefined
11024 \begin_layout Standard
11025 Sometimes it is necessary to insert horizontal space into a formula.
11026 This is done by inserting a protected space (shortcut
11029 arg "command-alternatives space-insert protected ; math-space"
11034 \begin_inset Quotes eld
11040 \begin_inset space \textvisiblespace{}
11046 \begin_inset Quotes erd
11049 appears and by pressing
11053 several times one can select one of eight different space sizes.
11054 The spaces can also be inserted using the math toolbar button
11057 arg "math-insert \\space"
11060 or special commands.
11061 Independent from the inserted command, one can select the size again by
11067 \begin_inset Separator parbreak
11073 \begin_layout Standard
11076 \begin_inset Tabular
11077 <lyxtabular version="3" rows="6" columns="3">
11078 <features booktabs="true" tabularvalignment="middle">
11079 <column alignment="center" valignment="top">
11080 <column alignment="center" valignment="top" width="15col%">
11081 <column alignment="center" valignment="top">
11083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11086 \begin_layout Plain Layout
11092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11095 \begin_layout Plain Layout
11105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11108 \begin_layout Plain Layout
11116 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11119 \begin_layout Plain Layout
11127 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11130 \begin_layout Plain Layout
11136 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11139 \begin_layout Plain Layout
11140 \begin_inset Formula $A\,B$
11150 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11153 \begin_layout Plain Layout
11161 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11164 \begin_layout Plain Layout
11170 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11173 \begin_layout Plain Layout
11174 \begin_inset Formula $A\:B$
11184 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11187 \begin_layout Plain Layout
11195 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11198 \begin_layout Plain Layout
11204 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11207 \begin_layout Plain Layout
11208 \begin_inset Formula $A\;B$
11218 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11221 \begin_layout Plain Layout
11229 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11232 \begin_layout Plain Layout
11238 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11241 \begin_layout Plain Layout
11242 \begin_inset Formula $A\quad B$
11252 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11255 \begin_layout Plain Layout
11263 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11266 \begin_layout Plain Layout
11272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11275 \begin_layout Plain Layout
11276 \begin_inset Formula $A\qquad B$
11290 \begin_inset space \hfill{}
11294 \begin_inset Tabular
11295 <lyxtabular version="3" rows="6" columns="3">
11296 <features booktabs="true" tabularvalignment="middle">
11297 <column alignment="center" valignment="top">
11298 <column alignment="center" valignment="top" width="15col%">
11299 <column alignment="center" valignment="top">
11301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11304 \begin_layout Plain Layout
11310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11313 \begin_layout Plain Layout
11323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11326 \begin_layout Plain Layout
11334 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11337 \begin_layout Plain Layout
11345 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11348 \begin_layout Plain Layout
11354 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11357 \begin_layout Plain Layout
11358 \begin_inset Formula $A\hfill B$
11368 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11371 \begin_layout Plain Layout
11379 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11382 \begin_layout Plain Layout
11388 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11391 \begin_layout Plain Layout
11392 \begin_inset Formula $A\hspace*{1em}B$
11402 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11405 \begin_layout Plain Layout
11413 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11416 \begin_layout Plain Layout
11422 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11425 \begin_layout Plain Layout
11426 \begin_inset Formula $A\hspace{1em}B$
11436 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11439 \begin_layout Plain Layout
11443 \begin_inset space \textvisiblespace{}
11451 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11454 \begin_layout Plain Layout
11460 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11463 \begin_layout Plain Layout
11464 \begin_inset Formula $A\ B$
11474 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11477 \begin_layout Plain Layout
11485 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11488 \begin_layout Plain Layout
11494 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11497 \begin_layout Plain Layout
11498 \begin_inset Formula $A\!B$
11514 \begin_layout Standard
11516 \begin_inset space ~
11520 \begin_inset space \thinspace{}
11524 \begin_inset space \thinspace{}
11527 7 are variable spaces which are explained in
11528 \begin_inset CommandInset ref
11530 reference "subsec:Variable-Space"
11536 \begin_inset space ~
11539 9 seems to produce no space.
11540 It is displayed red in \SpecialChar LyX
11541 contrary to the other sizes, because it is a negative
11543 There are two more negative spaces:
11544 \begin_inset Separator parbreak
11550 \begin_layout Standard
11552 \begin_inset Tabular
11553 <lyxtabular version="3" rows="3" columns="3">
11554 <features booktabs="true" tabularvalignment="middle">
11555 <column alignment="center" valignment="middle" width="6.8cm">
11556 <column alignment="center" valignment="top" width="0pt">
11557 <column alignment="center" valignment="top" width="0pt">
11559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11562 \begin_layout Plain Layout
11568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11571 \begin_layout Plain Layout
11579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11582 \begin_layout Plain Layout
11592 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11595 \begin_layout Plain Layout
11600 keystrokes after inserting the protected space
11605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11608 \begin_layout Plain Layout
11614 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11617 \begin_layout Plain Layout
11625 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11628 \begin_layout Plain Layout
11634 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11637 \begin_layout Plain Layout
11638 \begin_inset Formula $A\negmedspace B$
11646 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11649 \begin_layout Plain Layout
11650 \begin_inset Formula $A\negthickspace B$
11666 \begin_layout Standard
11667 Negative spaces can lead to characters overlapping each other.
11668 Thus they can be used to enforce ligatures, which are e.
11669 \begin_inset space \thinspace{}
11673 \begin_inset space \space{}
11676 useful for summation operators:
11677 \begin_inset Separator parbreak
11683 \begin_layout Standard
11685 \begin_inset Tabular
11686 <lyxtabular version="3" rows="3" columns="2">
11687 <features booktabs="true" tabularvalignment="middle">
11688 <column alignment="center" valignment="top" width="0pt">
11689 <column alignment="center" valignment="top">
11691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11694 \begin_layout Plain Layout
11700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11703 \begin_layout Plain Layout
11711 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11714 \begin_layout Plain Layout
11720 \begin_inset space \textvisiblespace{}
11728 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11731 \begin_layout Plain Layout
11732 \begin_inset Formula $\sum\sum f_{kl}$
11742 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11745 \begin_layout Plain Layout
11753 \begin_inset space \textvisiblespace{}
11761 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11764 \begin_layout Plain Layout
11765 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11781 \begin_layout Standard
11783 \begin_inset VSpace medskip
11789 \begin_layout Standard
11791 Relations like for example equal signs, are always surrounded by space.
11792 To suppress this, the equal sign is placed into a \SpecialChar TeX
11794 The following example demonstrates this:
11795 \begin_inset Separator parbreak
11801 \begin_layout Standard
11803 \begin_inset Tabular
11804 <lyxtabular version="3" rows="2" columns="2">
11805 <features tabularvalignment="middle">
11806 <column alignment="center" valignment="top" width="0pt">
11807 <column alignment="center" valignment="top" width="0pt">
11809 <cell alignment="center" valignment="top" usebox="none">
11812 \begin_layout Plain Layout
11818 <cell alignment="center" valignment="top" usebox="none">
11821 \begin_layout Plain Layout
11822 \begin_inset Formula $A=B$
11832 <cell alignment="center" valignment="top" usebox="none">
11835 \begin_layout Plain Layout
11836 equation without space
11841 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11844 \begin_layout Plain Layout
11845 \begin_inset Formula $A{=}B$
11861 \begin_layout Standard
11863 The command for the last formula is:
11868 \begin_inset Formula $\to$
11874 \begin_layout Standard
11875 \begin_inset VSpace bigskip
11881 \begin_layout Standard
11882 Spaces are needed for physical units, because the space between the value
11883 and the unit is the smallest one and not a normal space.
11884 For units in text, the smallest space is inserted via the menu
11886 Insert\SpecialChar menuseparator
11887 Formatting\SpecialChar menuseparator
11889 \begin_inset space ~
11897 arg "space-insert thin"
11903 \begin_layout Standard
11904 An example to visualize the difference:
11907 \begin_layout Standard
11908 \begin_inset Tabular
11909 <lyxtabular version="3" rows="2" columns="2">
11910 <features tabularvalignment="middle">
11911 <column alignment="left" valignment="top">
11912 <column alignment="left" valignment="top">
11914 <cell alignment="center" valignment="top" usebox="none">
11917 \begin_layout Plain Layout
11919 \begin_inset Formula $\cdot$
11927 <cell alignment="center" valignment="top" usebox="none">
11930 \begin_layout Plain Layout
11931 space between value and unit
11938 <cell alignment="center" valignment="top" usebox="none">
11941 \begin_layout Plain Layout
11943 \begin_inset space \thinspace{}
11947 \begin_inset Formula $\cdot$
11955 <cell alignment="center" valignment="top" usebox="none">
11958 \begin_layout Plain Layout
11959 smallest space between value and unit
11972 \begin_layout Subsection
11977 \begin_layout Plain Layout
11990 \begin_layout Plain Layout
11991 for vertical space in formulas see
11992 \begin_inset CommandInset ref
11994 reference "subsec:Line-Separation"
12007 \begin_layout Plain Layout
12015 \begin_inset Note Note
12018 \begin_layout Plain Layout
12021 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12024 \begin_layout Plain Layout
12027 texorpdfstring is in section
12028 \begin_inset CommandInset ref
12030 reference "subsec:Formulas-in-Section"
12040 \begin_inset CommandInset label
12042 name "subsec:Variable-Space"
12047 \begin_inset Index idx
12050 \begin_layout Plain Layout
12051 Space ! horizontal ! variable
12059 \begin_layout Standard
12060 Space with a defined length can be inserted with the command
12067 \begin_inset Index idx
12070 \begin_layout Plain Layout
12080 \begin_inset Quotes eld
12086 \begin_inset space \textvisiblespace{}
12092 \begin_inset Quotes erd
12096 The length can be specified by left-clicking on the
12097 \begin_inset Quotes eld
12103 \begin_inset space \textvisiblespace{}
12109 \begin_inset Quotes erd
12113 The length may also be negative.
12114 When a space would be the first character in a line it would be omitted.
12115 To force its output use the command
12127 or left-click on the
12128 \begin_inset Quotes eld
12134 \begin_inset space \textvisiblespace{}
12140 \begin_inset Quotes erd
12143 and check the option
12148 \begin_inset Newline newline
12151 To insert as much space as is available, the command
12158 \begin_inset Index idx
12161 \begin_layout Plain Layout
12172 \begin_layout Standard
12174 \begin_inset Tabular
12175 <lyxtabular version="3" rows="4" columns="2">
12176 <features booktabs="true" tabularvalignment="middle">
12177 <column alignment="center" valignment="top" width="0pt">
12178 <column alignment="center" valignment="top">
12180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12183 \begin_layout Plain Layout
12191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12194 \begin_layout Plain Layout
12202 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12205 \begin_layout Plain Layout
12209 \begin_inset space \textvisiblespace{}
12215 \begin_inset space \thinspace{}
12223 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12226 \begin_layout Plain Layout
12227 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12237 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12240 \begin_layout Plain Layout
12244 \begin_inset space \textvisiblespace{}
12250 \begin_inset space \thinspace{}
12258 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12261 \begin_layout Plain Layout
12262 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12275 \begin_layout Plain Layout
12279 \begin_inset space \textvisiblespace{}
12287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12290 \begin_layout Plain Layout
12291 \begin_inset Formula $A=A\hfill B=B$
12307 \begin_layout Standard
12308 In the last example the available space is given by the longest column entry
12310 In an inline formula the space depends on the length of the line in which
12318 Thus, when the line uses the full width, no space will be created.
12325 only has an effect on displayed formulas when the formula style
12330 (Formula styles are explained in
12331 \begin_inset CommandInset ref
12333 reference "sec:Formula-Styles"
12340 \begin_layout Standard
12347 , there are the commands
12359 that fill the space with a pattern, see
12360 \begin_inset CommandInset ref
12362 reference "subsec:Ellipses"
12369 \begin_layout Standard
12370 For text, variable space can be inserted via the menu
12372 Insert\SpecialChar menuseparator
12373 Formatting\SpecialChar menuseparator
12375 \begin_inset space ~
12383 \begin_layout Standard
12384 This is a line with
12385 \begin_inset space \hspace{}
12390 \begin_inset space \thinspace{}
12396 \begin_layout Standard
12397 This is a line with
12398 \begin_inset space \hfill{}
12404 \begin_layout Subsection
12405 Space besides inline Formulas
12406 \begin_inset Index idx
12409 \begin_layout Plain Layout
12410 Space ! besides inline formulas
12418 \begin_layout Standard
12419 The space that surrounds inline formulas can be adjusted with the length
12427 \begin_inset Index idx
12430 \begin_layout Plain Layout
12439 The value of a length is set with the command
12446 \begin_inset Index idx
12449 \begin_layout Plain Layout
12457 which has the following scheme:
12460 \begin_layout Standard
12465 setlength{length name}{value}
12468 \begin_layout Standard
12476 \begin_inset space \thinspace{}
12482 \begin_layout Standard
12492 \begin_layout Standard
12493 is inserted in \SpecialChar TeX
12496 \begin_inset space \thinspace{}
12499 mm space will now be set around all inline formulas:
12503 \begin_layout Plain Layout
12517 \begin_layout Standard
12518 This is a line with an inline formula
12519 \begin_inset Formula $A=B$
12523 \begin_inset space \thinspace{}
12526 mm surrounding space.
12530 \begin_layout Plain Layout
12544 \begin_layout Standard
12545 To return to the predefined value,
12551 is set to the value 0
12552 \begin_inset space \thinspace{}
12558 \begin_layout Standard
12559 \begin_inset Newpage newpage
12565 \begin_layout Section
12567 \begin_inset Index idx
12570 \begin_layout Plain Layout
12577 \begin_inset Index idx
12580 \begin_layout Plain Layout
12585 \begin_layout Plain Layout
12596 \begin_layout Plain Layout
12611 \begin_layout Standard
12612 Boxes for text are described in chapter
12619 \begin_inset space ~
12627 \begin_layout Subsection
12629 \begin_inset CommandInset label
12631 name "subsec:Boxes-with-Frame"
12636 \begin_inset Index idx
12639 \begin_layout Plain Layout
12648 \begin_layout Standard
12649 It is possible to frame a formula or part of one with the commands
12656 \begin_inset Index idx
12659 \begin_layout Plain Layout
12674 \begin_inset Index idx
12677 \begin_layout Plain Layout
12688 \begin_layout Standard
12689 When one of these commands is inserted in a formula, a blue box appears
12690 within a frame to enter formula parts.
12697 an additional formula has to be created by
12701 within this box, because the box content will otherwise be treated as mathemati
12709 is used, a new formula is automatically created inside the frame.
12712 \begin_layout Standard
12719 is not suitable to frame displayed formulas because the formula will always
12720 be set in the size of the text.
12727 is in contrary not suitable to frame inline formulas, because the formula
12728 will always be set in the size of a displayed formula.
12731 \begin_layout Standard
12745 \begin_inset Index idx
12748 \begin_layout Plain Layout
12756 where additionally the frame width and the alignment can be specified.
12763 is used in the following scheme:
12766 \begin_layout Standard
12771 framebox[frame width][position]{box content}
12774 \begin_layout Standard
12775 The position can either be
12792 right aligns the formula in the box.
12793 When no position is given, the formula will be centered.
12794 \begin_inset Newline newline
12797 If no width is given, also no position can be given.
12798 In this case the frame width is adjusted to the box content like for
12807 \begin_layout Standard
12814 is inserted, a box appears containing three blue boxes.
12815 The first two boxes are surrounded by brackets and denote the two optional
12817 The third box is for formula parts like for
12824 \begin_inset Separator parbreak
12830 \begin_layout Standard
12832 \begin_inset Tabular
12833 <lyxtabular version="3" rows="5" columns="2">
12834 <features tabularvalignment="middle">
12835 <column alignment="center" valignment="top">
12836 <column alignment="center" valignment="top">
12838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12841 \begin_layout Plain Layout
12847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12850 \begin_layout Plain Layout
12852 \begin_inset Note Note
12855 \begin_layout Plain Layout
12862 is only used as spacer.
12874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12877 \begin_layout Plain Layout
12881 \begin_inset space \textvisiblespace{}
12891 \begin_inset space \textvisiblespace{}
12899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12902 \begin_layout Plain Layout
12903 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12916 \begin_layout Plain Layout
12920 \begin_inset space \textvisiblespace{}
12926 \begin_inset space \textvisiblespace{}
12934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12937 \begin_layout Plain Layout
12938 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12951 \begin_layout Plain Layout
12955 \begin_inset space \textvisiblespace{}
12963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12966 \begin_layout Plain Layout
12967 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12980 \begin_layout Plain Layout
12984 \begin_inset space \textvisiblespace{}
12988 \begin_inset Formula $\to$
12992 \begin_inset Formula $\to$
13002 \begin_inset space \textvisiblespace{}
13006 \begin_inset Formula $\downarrow$
13014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13017 \begin_layout Plain Layout
13018 \begin_inset Formula $\raisebox{6mm}{}$
13022 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13026 \begin_inset Formula $\raisebox{-4mm}{}$
13042 \begin_layout Standard
13043 The frame thickness can also be adjusted.
13044 To do this the following commands have to be inserted in \SpecialChar TeX
13049 \begin_layout Standard
13059 \begin_inset Quotes eld
13063 \begin_inset Quotes erd
13077 \begin_inset Quotes eld
13081 \begin_inset Quotes erd
13087 \begin_layout Standard
13088 \begin_inset Quotes eld
13092 \begin_inset Quotes erd
13095 specifies the minimal distance between the frame and the first character
13097 An example for this is the following framed formula:
13101 \begin_layout Plain Layout
13113 \begin_inset Formula
13120 Before this formula the commands
13123 \begin_layout Standard
13145 \begin_layout Standard
13146 were inserted in \SpecialChar TeX
13148 The given values are used for all following boxes.
13151 \begin_layout Standard
13152 To return to the standard frame size, the command
13155 \begin_layout Standard
13180 \begin_layout Plain Layout
13194 \begin_layout Standard
13195 is inserted in \SpecialChar TeX
13196 mode before the next formula.
13199 \begin_layout Subsection
13200 Boxes without Frame
13201 \begin_inset CommandInset label
13203 name "subsec:Boxes-without-Frame"
13208 \begin_inset Index idx
13211 \begin_layout Plain Layout
13212 Boxes ! without frame
13220 \begin_layout Standard
13221 For boxes without a frame there are the following box commands:
13228 \begin_inset Index idx
13231 \begin_layout Plain Layout
13246 \begin_inset Index idx
13249 \begin_layout Plain Layout
13264 \begin_inset Index idx
13267 \begin_layout Plain Layout
13278 \begin_layout Standard
13285 a box can be super- or subscripted.
13286 But in contrary to normal super- and subscripting, the characters in the
13287 box keep their font size.
13294 is used in the following scheme:
13297 \begin_layout Standard
13302 raisebox{height}{box content}
13305 \begin_layout Standard
13306 When the box should contain a formula, an extra formula is needed like for
13317 \begin_inset Note Greyedout
13320 \begin_layout Plain Layout
13331 this extra formula is created by pressing
13335 twice instead of once because \SpecialChar LyX
13336 doesn't yet support
13350 \begin_inset Separator parbreak
13356 \begin_layout Standard
13358 \begin_inset Tabular
13359 <lyxtabular version="3" rows="4" columns="2">
13360 <features tabularvalignment="middle">
13361 <column alignment="center" valignment="top">
13362 <column alignment="center" valignment="top">
13364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13367 \begin_layout Plain Layout
13373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13376 \begin_layout Plain Layout
13384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13387 \begin_layout Plain Layout
13391 \begin_inset Formula $\to$
13397 \begin_inset Formula $\to$
13405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13408 \begin_layout Plain Layout
13409 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13422 \begin_layout Plain Layout
13426 \begin_inset Formula $\to$
13432 \begin_inset Formula $\to$
13440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13443 \begin_layout Plain Layout
13444 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13457 \begin_layout Plain Layout
13461 \begin_inset Formula $\to$
13477 \begin_inset space \textvisiblespace{}
13485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13488 \begin_layout Plain Layout
13489 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13505 \begin_layout Standard
13530 , with the difference that there is no frame.
13533 \begin_layout Subsection
13535 \begin_inset CommandInset label
13537 name "subsec:Colored-Boxes"
13542 \begin_inset Index idx
13545 \begin_layout Plain Layout
13554 \begin_layout Standard
13555 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13564 \begin_layout Plain Layout
13565 The \SpecialChar LaTeX
13570 is part of every \SpecialChar LaTeX
13571 standard installation.
13577 \begin_inset Index idx
13580 \begin_layout Plain Layout
13586 has to be loaded in the \SpecialChar LaTeX
13587 -preamble with the line
13591 \begin_layout Plain Layout
13592 When text is colored somewhere in the document with a predefined color,
13594 loads the \SpecialChar LaTeX
13600 Thus it is possible that the package is loaded twice, but this does not
13607 \begin_inset Note Note
13610 \begin_layout Plain Layout
13611 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13620 \begin_layout Standard
13628 \begin_layout Standard
13629 \begin_inset VSpace medskip
13632 To color boxes, the command
13639 \begin_inset Index idx
13642 \begin_layout Plain Layout
13650 is used in the following scheme:
13653 \begin_layout Standard
13658 colorbox{color}{box content}
13661 \begin_layout Standard
13662 The box content can also be a box and a
13668 can also be part of another box (see the 2nd and 3rd example).
13669 When the box should contain a formula, an extra formula has to be created,
13670 the same way as for
13680 \begin_layout Plain Layout
13681 This also applies for the command
13695 \begin_layout Standard
13696 One of the following predefined colors can be chosen:
13699 \begin_layout Standard
13733 \begin_inset Separator parbreak
13739 \begin_layout Standard
13741 \begin_inset Tabular
13742 <lyxtabular version="3" rows="4" columns="2">
13743 <features tabularvalignment="middle">
13744 <column alignment="center" valignment="top">
13745 <column alignment="center" valignment="top">
13747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13750 \begin_layout Plain Layout
13756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13759 \begin_layout Plain Layout
13761 \begin_inset Note Note
13764 \begin_layout Plain Layout
13771 is only used as spacer.
13783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13786 \begin_layout Plain Layout
13790 \begin_inset Formula $\to$
13800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13803 \begin_layout Plain Layout
13804 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13817 \begin_layout Plain Layout
13821 \begin_inset Formula $\to$
13829 \begin_inset space \textvisiblespace{}
13837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13840 \begin_layout Plain Layout
13841 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13854 \begin_layout Plain Layout
13858 \begin_inset space \textvisiblespace{}
13864 \begin_inset Formula $\to$
13880 \begin_inset space \textvisiblespace{}
13888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13891 \begin_layout Plain Layout
13892 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13908 \begin_layout Standard
13915 only colors the box but not the characters in the box.
13916 To color all characters, the whole formula is highlighted and the desired
13917 color is chosen in the
13920 \begin_inset space ~
13926 The dialog can be called with the toolbar button
13929 arg "dialog-show character"
13934 Edit\SpecialChar menuseparator
13936 \begin_inset space ~
13939 Style\SpecialChar menuseparator
13943 The formula number then has the same color as the formula.
13944 When the formula number should get another color than the formula characters,
13945 the color must be changed within the formula.
13948 \begin_layout Standard
13952 \begin_layout Standard
13955 \begin_inset Formula
13957 \int A=B\label{eq:red}
13965 \begin_inset Formula
13967 \textcolor{red}{\int A=B}\label{eq:redgreen}
13975 \begin_layout Standard
13977 \begin_inset CommandInset ref
13983 is completely colored red.
13984 \begin_inset Newline newline
13988 \begin_inset CommandInset ref
13990 reference "eq:redgreen"
13994 was first completely colored green to set the color for the formula number.
13995 Subsequently the formula characters were colored red.
13998 \begin_layout Standard
13999 \begin_inset VSpace bigskip
14002 To color the frame different than the rest of the box, the command
14009 \begin_inset Index idx
14012 \begin_layout Plain Layout
14020 is used in the following scheme:
14023 \begin_layout Standard
14028 fcolorbox{frame color}{color}{box content}
14031 \begin_layout Standard
14038 is an extension of the command
14045 The frame width is set, like for
14068 \begin_layout Plain Layout
14080 \begin_inset Formula
14082 \fcolorbox{cyan}{magenta}{A=B}
14091 \begin_layout Plain Layout
14105 \begin_layout Standard
14106 This formula was created with the command
14107 \begin_inset Newline newline
14115 \begin_inset Formula $\to$
14121 \begin_inset Formula $\to$
14131 \begin_layout Standard
14132 \begin_inset VSpace bigskip
14135 To use other colors than the predefined ones, they have to be defined first.
14138 \begin_layout Standard
14139 One can for example define the color
14140 \begin_inset Quotes eld
14148 \begin_inset Quotes erd
14151 with the \SpecialChar LaTeX
14155 \begin_layout Standard
14160 definecolor{darkgreen}{cmyk}{0.5,
14175 \begin_inset Index idx
14178 \begin_layout Plain Layout
14189 \begin_layout Standard
14194 is the color space that denotes the colors
14211 The four comma separated numbers are the portion factor for the corresponding
14212 colors of the color space.
14213 The factors can be in the range of 0
14214 \begin_inset space \thinspace{}
14218 \begin_inset space \thinspace{}
14226 also the color space
14230 can be used for definitions.
14247 , so that there are in this case three portion factors for the corresponding
14249 Furthermore there is the color space
14253 with one portion factor for the gray value.
14256 \begin_layout Standard
14257 As example a framed box with the new defined color
14261 where the characters have been colored
14266 \begin_inset Formula
14268 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14276 \begin_layout Standard
14277 Self-defined colors can also be used for text with the help of the command
14285 \begin_inset Index idx
14288 \begin_layout Plain Layout
14297 \begin_layout Standard
14301 \begin_layout Plain Layout
14305 textcolor{darkgreen}{
14311 \begin_inset Quotes eld
14315 \begin_inset Quotes erd
14322 \begin_layout Plain Layout
14332 \begin_layout Standard
14340 \begin_inset Index idx
14343 \begin_layout Plain Layout
14351 is used in the scheme
14355 textcolor{color}{characters to color}
14360 \begin_layout Subsection
14362 \begin_inset CommandInset label
14364 name "subsec:Paragraph-Boxes"
14369 \begin_inset Index idx
14372 \begin_layout Plain Layout
14373 Boxes ! as paragraph
14381 \begin_layout Standard
14382 A box that can contain several lines and paragraphs, a so-called paragraph
14383 box (parbox), can be created with the menu
14385 Insert\SpecialChar menuseparator
14388 or the toolbar button
14397 \begin_layout Standard
14398 The following example shows a framed parbox in a line:
14401 \begin_layout Standard
14402 \begin_inset VSpace medskip
14406 \begin_inset Box Boxed
14416 height_special "totalheight"
14421 backgroundcolor "none"
14424 \begin_layout Plain Layout
14425 This is a paragraph box.
14427 \begin_inset space \thinspace{}
14430 cm long and can also contain formulas:
14431 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14442 \begin_layout Standard
14443 \begin_inset VSpace medskip
14449 \begin_layout Standard
14450 Such a box is created by right-clicking on the gray box inset.
14451 A dialog pops up showing the box properties.
14465 \begin_inset space \thinspace{}
14470 Vertical Box Alignment
14475 \begin_layout Standard
14476 \begin_inset VSpace medskip
14479 In \SpecialChar LaTeX
14480 a parbox is created with the command
14487 \begin_inset Index idx
14490 \begin_layout Plain Layout
14498 which has the following scheme:
14501 \begin_layout Standard
14506 parbox[position]{width}{box content}
14509 \begin_layout Standard
14524 \begin_inset Quotes eld
14528 \begin_inset Quotes erd
14531 means that the box is aligned within the surrounding text with its last
14538 \begin_inset Quotes eld
14542 \begin_inset Quotes erd
14545 this is done with the first line.
14546 When no position is given, the box will be vertically centered, see section
14554 \begin_inset space ~
14559 manual for examples.
14562 \begin_layout Standard
14563 \begin_inset VSpace bigskip
14566 To frame formulas completely, including the formula number, the formula
14567 must be set into a parbox.
14568 To do this, the command
14582 is inserted in \SpecialChar TeX
14583 mode before the formula.
14591 \begin_inset Index idx
14594 \begin_layout Plain Layout
14602 is hereby the line width set for the document.
14603 Because the frame is outside the parbox, 2
14604 \begin_inset space \thinspace{}
14607 times the frame separation and the frame thickness must be subtracted from
14609 As this is not automatically done by \SpecialChar LyX
14614 \begin_layout Plain Layout
14615 \begin_inset CommandInset href
14617 name "LyX-bug #4483"
14618 target "http://www.lyx.org/trac/ticket/4483"
14628 mode has to be used.
14629 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14638 \begin_layout Plain Layout
14643 is part of every \SpecialChar LaTeX
14644 standard installation.
14650 \begin_inset Index idx
14653 \begin_layout Plain Layout
14659 must be loaded in the \SpecialChar LaTeX
14660 -preamble with the line
14663 \begin_layout Standard
14671 \begin_layout Standard
14672 Behind the formula both boxes are closed by entering
14676 in \SpecialChar TeX
14678 Here is an example:
14682 \begin_layout Plain Layout
14696 \begin_layout Standard
14700 \begin_layout Plain Layout
14718 \begin_inset Formula
14720 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14729 \begin_layout Plain Layout
14740 \begin_layout Plain Layout
14754 \begin_layout Standard
14755 \begin_inset VSpace medskip
14758 As a parbox is used as the argument of
14764 , there is in this case no difference between
14779 \begin_layout Standard
14780 \begin_inset VSpace bigskip
14783 Paragraph boxes are very useful to comment formulas directly.
14790 is used in combination with the command
14804 \begin_inset CommandInset ref
14806 reference "subsec:User-defined-Numbering"
14813 \begin_layout Standard
14814 An example of a formula commented with
14823 \begin_layout Standard
14827 \begin_layout Plain Layout
14840 This is a description.
14841 It is distinctly separated from the formula and multiline.
14845 \begin_layout Plain Layout
14857 \begin_layout Standard
14858 Such a formula must be inserted completely in \SpecialChar TeX
14859 mode because \SpecialChar LyX
14861 support the command
14868 The formula is created with the following command sequence:
14871 \begin_layout Standard
14884 is inserted in \SpecialChar TeX
14889 \begin_layout Plain Layout
14890 When the formula style
14902 can also be replaced by
14909 (formula styles see
14910 \begin_inset CommandInset ref
14912 reference "sec:Formula-Styles"
14921 Then the description follows as normal text and finally
14927 is inserted in \SpecialChar TeX
14941 hereby create a displayed formula.
14944 \begin_layout Standard
14951 can be seen in this example that was
14952 \begin_inset Quotes eld
14956 \begin_inset Quotes erd
14959 using the mathematical textmode:
14960 \begin_inset Formula
14962 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14970 \begin_layout Section
14972 \begin_inset Index idx
14975 \begin_layout Plain Layout
14984 \begin_layout Subsection
14986 \begin_inset CommandInset label
14988 name "subsec:Big-Operators"
14993 \begin_inset Index idx
14996 \begin_layout Plain Layout
15003 \begin_inset Index idx
15006 \begin_layout Plain Layout
15013 \begin_inset Index idx
15016 \begin_layout Plain Layout
15025 \begin_layout Standard
15026 To be able to use all integral operators listed here, the option
15028 Use esint package automatically
15030 must be set in the document settings under
15033 \begin_inset space ~
15041 \begin_layout Standard
15042 \begin_inset space \hfill{}
15046 \begin_inset Tabular
15047 <lyxtabular version="3" rows="11" columns="2">
15048 <features booktabs="true" tabularvalignment="middle">
15049 <column alignment="center" valignment="top" width="0pt">
15050 <column alignment="center" valignment="top" width="0pt">
15052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15055 \begin_layout Plain Layout
15061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15064 \begin_layout Plain Layout
15072 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15075 \begin_layout Plain Layout
15079 \begin_inset Index idx
15082 \begin_layout Plain Layout
15095 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15098 \begin_layout Plain Layout
15099 \begin_inset Formula $\int$
15109 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15112 \begin_layout Plain Layout
15120 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15123 \begin_layout Plain Layout
15124 \begin_inset Formula $\oint$
15134 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15137 \begin_layout Plain Layout
15145 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15148 \begin_layout Plain Layout
15149 \begin_inset Formula $\ointctrclockwise$
15159 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15162 \begin_layout Plain Layout
15170 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15173 \begin_layout Plain Layout
15174 \begin_inset Formula $\ointclockwise$
15184 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15187 \begin_layout Plain Layout
15195 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15198 \begin_layout Plain Layout
15199 \begin_inset Formula $\sqint$
15209 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15212 \begin_layout Plain Layout
15220 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15223 \begin_layout Plain Layout
15225 \begin_inset Formula $\fint$
15235 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15238 \begin_layout Plain Layout
15246 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15249 \begin_layout Plain Layout
15251 \begin_inset Formula $\landupint$
15261 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15264 \begin_layout Plain Layout
15272 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15275 \begin_layout Plain Layout
15277 \begin_inset Formula $\landdownint$
15287 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15290 \begin_layout Plain Layout
15298 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15301 \begin_layout Plain Layout
15302 \begin_inset Formula $\bigcap$
15312 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15315 \begin_layout Plain Layout
15323 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15326 \begin_layout Plain Layout
15327 \begin_inset Formula $\bigcup$
15341 \begin_inset space \hfill{}
15345 \begin_inset Tabular
15346 <lyxtabular version="3" rows="11" columns="2">
15347 <features booktabs="true" tabularvalignment="middle">
15348 <column alignment="center" valignment="top" width="0pt">
15349 <column alignment="center" valignment="top" width="0pt">
15351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15354 \begin_layout Plain Layout
15360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15363 \begin_layout Plain Layout
15371 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15374 \begin_layout Plain Layout
15378 \begin_inset Index idx
15381 \begin_layout Plain Layout
15394 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15397 \begin_layout Plain Layout
15398 \begin_inset Formula $\sum$
15408 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15411 \begin_layout Plain Layout
15415 \begin_inset Index idx
15418 \begin_layout Plain Layout
15425 \begin_layout Plain Layout
15444 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15447 \begin_layout Plain Layout
15448 \begin_inset Formula $\prod$
15458 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15461 \begin_layout Plain Layout
15469 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15472 \begin_layout Plain Layout
15473 \begin_inset Formula $\coprod$
15483 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15486 \begin_layout Plain Layout
15494 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15497 \begin_layout Plain Layout
15498 \begin_inset Formula $\bigodot$
15508 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15511 \begin_layout Plain Layout
15519 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15522 \begin_layout Plain Layout
15523 \begin_inset Formula $\bigotimes$
15533 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15536 \begin_layout Plain Layout
15544 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15547 \begin_layout Plain Layout
15548 \begin_inset Formula $\bigoplus$
15558 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15561 \begin_layout Plain Layout
15569 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15572 \begin_layout Plain Layout
15573 \begin_inset Formula $\bigwedge$
15583 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15586 \begin_layout Plain Layout
15594 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15597 \begin_layout Plain Layout
15598 \begin_inset Formula $\bigvee$
15608 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15611 \begin_layout Plain Layout
15619 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15622 \begin_layout Plain Layout
15623 \begin_inset Formula $\bigsqcup$
15633 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15636 \begin_layout Plain Layout
15644 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15647 \begin_layout Plain Layout
15648 \begin_inset Formula $\biguplus$
15662 \begin_inset space \hfill{}
15668 \begin_layout Standard
15669 All big operators can also be inserted via the math toolbar button
15672 arg "math-insert \\intop"
15678 \begin_layout Standard
15679 The operators are called big because they are bigger than the sometimes
15680 equal looking binary operators.
15681 All big operators can have limits as described in the next subsection.
15684 \begin_layout Standard
15685 For all integral operators there is a second version available, ending in
15703 These operators are different from
15710 \begin_inset space \space{}
15713 in the style the operator limits are displayed, see
15714 \begin_inset CommandInset ref
15716 reference "subsec:Operator-Limits"
15724 \begin_layout Subsubsection*
15725 Advice for Integrals
15728 \begin_layout Standard
15733 in an integral is an operator, that therefore has to be set upright.
15734 This is done by highlighting the
15738 and using the keyboard shortcut
15748 \begin_layout Plain Layout
15754 \begin_inset CommandInset ref
15756 reference "subsec:Font-Styles"
15766 Finally the smallest space is inserted before the
15770 , as this is usual for operators.
15774 \begin_layout Standard
15776 \begin_inset Formula $\int A(x)dx$
15780 \begin_inset Newline newline
15784 \begin_inset Phantom HPhantom
15787 \begin_layout Plain Layout
15794 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15800 \begin_layout Standard
15801 For multiple integrals there are the following commands:
15802 \begin_inset VSpace medskip
15808 \begin_layout Standard
15809 \begin_inset space \hfill{}
15813 \begin_inset Tabular
15814 <lyxtabular version="3" rows="4" columns="2">
15815 <features booktabs="true" tabularvalignment="middle">
15816 <column alignment="center" valignment="top" width="0pt">
15817 <column alignment="center" valignment="top" width="0pt">
15819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15822 \begin_layout Plain Layout
15828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15831 \begin_layout Plain Layout
15838 <row bottomspace="1mm">
15839 <cell alignment="center" valignment="top" usebox="none">
15842 \begin_layout Plain Layout
15850 <cell alignment="center" valignment="top" usebox="none">
15853 \begin_layout Plain Layout
15854 \begin_inset Formula $\iint$
15863 <row bottomspace="1mm">
15864 <cell alignment="center" valignment="top" usebox="none">
15867 \begin_layout Plain Layout
15875 <cell alignment="center" valignment="top" usebox="none">
15878 \begin_layout Plain Layout
15879 \begin_inset Formula $\oiint$
15888 <row bottomspace="1mm">
15889 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15892 \begin_layout Plain Layout
15900 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15903 \begin_layout Plain Layout
15904 \begin_inset Formula $\sqiint$
15918 \begin_inset space \hfill{}
15922 \begin_inset Tabular
15923 <lyxtabular version="3" rows="4" columns="2">
15924 <features booktabs="true" tabularvalignment="middle">
15925 <column alignment="center" valignment="top" width="0pt">
15926 <column alignment="center" valignment="top" width="0pt">
15928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15931 \begin_layout Plain Layout
15937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15940 \begin_layout Plain Layout
15947 <row bottomspace="1mm">
15948 <cell alignment="center" valignment="top" usebox="none">
15951 \begin_layout Plain Layout
15959 <cell alignment="center" valignment="top" usebox="none">
15962 \begin_layout Plain Layout
15963 \begin_inset Formula $\iiint$
15972 <row bottomspace="1mm">
15973 <cell alignment="center" valignment="top" usebox="none">
15976 \begin_layout Plain Layout
15984 <cell alignment="center" valignment="top" usebox="none">
15987 \begin_layout Plain Layout
15988 \begin_inset Formula $\iiiint$
15997 <row bottomspace="1mm">
15998 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16001 \begin_layout Plain Layout
16009 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16012 \begin_layout Plain Layout
16013 \begin_inset Formula $\dotsint$
16027 \begin_inset space \hfill{}
16033 \begin_layout Subsection
16035 \begin_inset CommandInset label
16037 name "subsec:Operator-Limits"
16042 \begin_inset Index idx
16045 \begin_layout Plain Layout
16054 \begin_layout Standard
16055 Limits are created by super- and subscripts:
16056 \begin_inset Separator parbreak
16062 \begin_layout Standard
16064 \begin_inset Tabular
16065 <lyxtabular version="3" rows="2" columns="2">
16066 <features booktabs="true" tabularvalignment="middle">
16067 <column alignment="center" valignment="top" width="0pt">
16068 <column alignment="center" valignment="top" width="0pt">
16070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16073 \begin_layout Plain Layout
16079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16082 \begin_layout Plain Layout
16090 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16093 \begin_layout Plain Layout
16099 \begin_inset space \textvisiblespace{}
16103 \begin_inset Formula $\to$
16107 \begin_inset Formula $\to$
16115 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16118 \begin_layout Plain Layout
16119 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
16135 \begin_layout Standard
16136 Limits of inline formulas are set right beside the operator.
16137 Limits in displayed formulas are set above or below the operator, except
16138 for integral limits.
16141 \begin_layout Standard
16142 To force that the limits are set beside the operator, the cursor is set
16143 directly behind the operator and the limits type is changed with the menu
16146 Edit\SpecialChar menuseparator
16147 Math\SpecialChar menuseparator
16166 \begin_layout Standard
16167 The default limits type is this:
16168 \begin_inset Formula
16170 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16175 This is how it looks when the limits type was changed to
16182 \begin_inset Formula
16184 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16189 For integrals, except those ending with
16205 etc., the limits are by default set beside the operator.
16206 But for multiple integrals the limits are often set below the operator.
16207 In the following example the limits type was therefore set to
16211 and so set below the integrals:
16212 \begin_inset Formula
16214 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16222 \begin_layout Standard
16223 \begin_inset VSpace medskip
16226 To specify conditions for limits, the commands
16233 \begin_inset Index idx
16236 \begin_layout Plain Layout
16251 \begin_inset Index idx
16254 \begin_layout Plain Layout
16263 To create for example this expression
16264 \begin_inset Formula
16266 \sum_{\begin{subarray}{c}
16270 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16278 \begin_layout Standard
16279 the following has to be done:
16280 \begin_inset Newline newline
16292 \begin_inset space \textvisiblespace{}
16298 One is now in a blue box under the summation operator and insert there
16304 \begin_inset space \textvisiblespace{}
16310 The blue box is now within a purple box and now several lines can be written
16312 A new line is created by inserting a line break (
16315 arg "newline-insert newline"
16320 \begin_inset Newline newline
16325 0<k<1000 Ctrl+Return
16326 \begin_inset Newline newline
16331 is typed in, a new box appears below for the new line.
16334 \begin_layout Standard
16335 The alignment of the lines can be changed to left aligned with the
16345 Edit\SpecialChar menuseparator
16349 To get right alignment,
16354 \begin_inset space \textvisiblespace{}
16359 is inserted at the beginning of the line.
16362 \begin_layout Standard
16375 with the difference that the lines are always centered.
16378 \begin_layout Standard
16379 \begin_inset VSpace bigskip
16383 \begin_inset CommandInset ref
16385 reference "eq:substack"
16389 there can be too much space beside an operator, because the characters
16390 following the operator are set beside the limits.
16391 To avoid this the command
16398 \begin_inset Index idx
16401 \begin_layout Plain Layout
16410 To activate it, set in the document settings under
16413 \begin_inset space ~
16423 \begin_inset Index idx
16426 \begin_layout Plain Layout
16427 Packages ! mathtools
16435 \begin_inset space ~
16447 sets the space besides the operator to 0
16448 \begin_inset space \thinspace{}
16452 \begin_inset Newline newline
16456 \begin_inset CommandInset ref
16458 reference "eq:substack"
16462 , one uses the command
16465 \begin_layout Standard
16473 \begin_layout Standard
16474 and inserts the operator with its limits into the braces.
16475 Behind the brace one continues the formula:
16476 \begin_inset Formula
16478 \smashoperator{\sum_{\begin{subarray}{c}
16482 \end{subarray}}^{n}}k^{-2}
16490 \begin_layout Standard
16491 It is possible to set the space of only one side of the operator to 0
16492 \begin_inset space \thinspace{}
16496 To do this write either
16515 stands for the left and
16519 for the right side of the operator.
16520 Here is an example of the possible
16529 \begin_layout Standard
16530 \begin_inset Formula
16532 Y\smashoperator{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[l]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[r]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}
16540 \begin_layout Standard
16541 \begin_inset VSpace bigskip
16547 \begin_layout Standard
16548 When several consecutive operators have limits the typesetting of the limits
16549 looks often imperfect in the output, see this example:
16550 \begin_inset Formula
16552 \text{a)}\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\limsup_{n\to\infty}\max_{p\ge n}
16557 To improve the typesetting set in the document settings under
16560 \begin_inset space ~
16570 \begin_inset Index idx
16573 \begin_layout Plain Layout
16574 Packages ! mathtools
16582 \begin_inset space ~
16588 Then insert into your formula the command
16595 \begin_inset Index idx
16598 \begin_layout Plain Layout
16606 directly before the first operator.
16607 The example will then look like this:
16608 \begin_inset Formula
16610 \text{a)}\adjustlimits\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\adjustlimits\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\adjustlimits\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\adjustlimits\limsup_{n\to\infty}\max_{p\ge n}
16618 \begin_layout Standard
16619 \begin_inset VSpace bigskip
16622 How to use one limit for several operators is described in
16623 \begin_inset CommandInset ref
16625 reference "subsec:Self-defined-Operators"
16632 \begin_layout Subsection
16633 Decoration for Operators
16634 \begin_inset Index idx
16637 \begin_layout Plain Layout
16638 Operators ! Decoration
16646 \begin_layout Standard
16654 \begin_inset Index idx
16657 \begin_layout Plain Layout
16672 \begin_inset Index idx
16675 \begin_layout Plain Layout
16683 characters can be placed above or below an operator, respectively.
16691 \begin_inset Index idx
16694 \begin_layout Plain Layout
16702 characters can be set before and behind a big operator.
16705 \begin_layout Standard
16707 \begin_inset space ~
16719 \begin_layout Itemize
16726 is used to set characters at the corners of the operator
16729 \begin_layout Itemize
16736 is used to set characters before and/or behind the operator (this variant
16737 represents \SpecialChar LaTeX
16747 \begin_layout Itemize
16754 is used to set characters at the left corners and/or behind the operator
16757 \begin_layout Itemize
16764 is used to set characters at the right corners and/or before the operator
16767 \begin_layout Standard
16768 For example the command
16773 \begin_inset space \textvisiblespace{}
16779 \begin_inset space \textvisiblespace{}
16783 \begin_inset Formula $\to$
16787 \begin_inset Formula $\to$
16791 \begin_inset space \textvisiblespace{}
16801 \begin_inset Formula
16803 \sideset{}{'}\sum_{k=1}^{n}
16811 \begin_layout Standard
16812 \begin_inset Note Greyedout
16815 \begin_layout Plain Layout
16822 can only be used to decorate big operators, binary operators are not allowed.
16830 \begin_layout Standard
16843 can also be used to decorate symbols and characters.
16844 For example, the command
16849 \begin_inset space \textvisiblespace{}
16855 \begin_inset space \textvisiblespace{}
16861 \begin_inset Formula $\uparrow$
16869 \begin_inset Formula
16871 \overset{a}{\maltese}
16879 \begin_layout Subsection
16881 \begin_inset CommandInset label
16883 name "subsec:Binary-Operators"
16888 \begin_inset Index idx
16891 \begin_layout Plain Layout
16900 \begin_layout Standard
16901 Binary operators are surrounded by space when there is a character before
16903 \begin_inset VSpace medskip
16909 \begin_layout Standard
16910 \begin_inset Tabular
16911 <lyxtabular version="3" rows="13" columns="2">
16912 <features booktabs="true" tabularvalignment="middle">
16913 <column alignment="center" valignment="top" width="0pt">
16914 <column alignment="center" valignment="top" width="0pt">
16916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16919 \begin_layout Plain Layout
16921 \begin_inset Note Note
16924 \begin_layout Plain Layout
16931 is only used as spacer.
16941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16944 \begin_layout Plain Layout
16952 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16955 \begin_layout Plain Layout
16961 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16964 \begin_layout Plain Layout
16965 \begin_inset Formula $+$
16975 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16978 \begin_layout Plain Layout
16984 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16987 \begin_layout Plain Layout
16988 \begin_inset Formula $-$
16998 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17001 \begin_layout Plain Layout
17009 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17012 \begin_layout Plain Layout
17013 \begin_inset Formula $\pm$
17023 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17026 \begin_layout Plain Layout
17034 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17037 \begin_layout Plain Layout
17038 \begin_inset Formula $\mp$
17048 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17051 \begin_layout Plain Layout
17059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17062 \begin_layout Plain Layout
17063 \begin_inset Formula $\cdot$
17073 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17076 \begin_layout Plain Layout
17084 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17087 \begin_layout Plain Layout
17088 \begin_inset Formula $\times$
17098 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17101 \begin_layout Plain Layout
17109 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17112 \begin_layout Plain Layout
17113 \begin_inset Formula $\div$
17123 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17126 \begin_layout Plain Layout
17130 \begin_layout Plain Layout
17143 \begin_layout Plain Layout
17155 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17158 \begin_layout Plain Layout
17159 \begin_inset Formula $*$
17169 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17172 \begin_layout Plain Layout
17180 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17183 \begin_layout Plain Layout
17184 \begin_inset Formula $\star$
17194 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17197 \begin_layout Plain Layout
17205 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17208 \begin_layout Plain Layout
17209 \begin_inset Formula $\circ$
17219 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17222 \begin_layout Plain Layout
17230 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17233 \begin_layout Plain Layout
17234 \begin_inset Formula $\diamond$
17244 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17247 \begin_layout Plain Layout
17255 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17258 \begin_layout Plain Layout
17259 \begin_inset Formula $\bullet$
17273 \begin_inset space \hfill{}
17277 \begin_inset Tabular
17278 <lyxtabular version="3" rows="13" columns="2">
17279 <features booktabs="true" tabularvalignment="middle">
17280 <column alignment="center" valignment="top" width="0pt">
17281 <column alignment="center" valignment="top" width="0pt">
17283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17286 \begin_layout Plain Layout
17292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17295 \begin_layout Plain Layout
17303 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17306 \begin_layout Plain Layout
17314 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17317 \begin_layout Plain Layout
17318 \begin_inset Formula $\nabla$
17328 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17331 \begin_layout Plain Layout
17339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17342 \begin_layout Plain Layout
17343 \begin_inset Formula $\bigtriangledown$
17353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17356 \begin_layout Plain Layout
17364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17367 \begin_layout Plain Layout
17368 \begin_inset Formula $\bigtriangleup$
17378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17381 \begin_layout Plain Layout
17389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17392 \begin_layout Plain Layout
17393 \begin_inset Formula $\Box$
17403 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17406 \begin_layout Plain Layout
17414 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17417 \begin_layout Plain Layout
17418 \begin_inset Formula $\cap$
17428 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17431 \begin_layout Plain Layout
17439 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17442 \begin_layout Plain Layout
17443 \begin_inset Formula $\cup$
17453 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17456 \begin_layout Plain Layout
17464 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17467 \begin_layout Plain Layout
17468 \begin_inset Formula $\dagger$
17478 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17481 \begin_layout Plain Layout
17489 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17492 \begin_layout Plain Layout
17493 \begin_inset Formula $\ddagger$
17503 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17506 \begin_layout Plain Layout
17514 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17517 \begin_layout Plain Layout
17518 \begin_inset Formula $\wr$
17528 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17531 \begin_layout Plain Layout
17539 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17542 \begin_layout Plain Layout
17543 \begin_inset Formula $\bigcirc$
17553 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17556 \begin_layout Plain Layout
17564 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17567 \begin_layout Plain Layout
17568 \begin_inset Formula $\wedge$
17578 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17581 \begin_layout Plain Layout
17589 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17592 \begin_layout Plain Layout
17593 \begin_inset Formula $\vee$
17607 \begin_inset space \hfill{}
17611 \begin_inset Tabular
17612 <lyxtabular version="3" rows="13" columns="2">
17613 <features booktabs="true" tabularvalignment="middle">
17614 <column alignment="center" valignment="top" width="0pt">
17615 <column alignment="center" valignment="top" width="0pt">
17617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17620 \begin_layout Plain Layout
17626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17629 \begin_layout Plain Layout
17637 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17640 \begin_layout Plain Layout
17648 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17651 \begin_layout Plain Layout
17652 \begin_inset Formula $\oplus$
17662 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17665 \begin_layout Plain Layout
17673 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17676 \begin_layout Plain Layout
17677 \begin_inset Formula $\ominus$
17687 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17690 \begin_layout Plain Layout
17698 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17701 \begin_layout Plain Layout
17702 \begin_inset Formula $\otimes$
17712 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17715 \begin_layout Plain Layout
17723 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17726 \begin_layout Plain Layout
17727 \begin_inset Formula $\oslash$
17737 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17740 \begin_layout Plain Layout
17748 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17751 \begin_layout Plain Layout
17752 \begin_inset Formula $\odot$
17762 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17765 \begin_layout Plain Layout
17773 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17776 \begin_layout Plain Layout
17777 \begin_inset Formula $\amalg$
17787 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17790 \begin_layout Plain Layout
17798 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17801 \begin_layout Plain Layout
17802 \begin_inset Formula $\uplus$
17812 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17815 \begin_layout Plain Layout
17823 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17826 \begin_layout Plain Layout
17827 \begin_inset Formula $\setminus$
17837 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17840 \begin_layout Plain Layout
17848 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17851 \begin_layout Plain Layout
17852 \begin_inset Formula $\sqcap$
17862 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17865 \begin_layout Plain Layout
17873 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17876 \begin_layout Plain Layout
17877 \begin_inset Formula $\sqcup$
17887 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17890 \begin_layout Plain Layout
17898 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17901 \begin_layout Plain Layout
17902 \begin_inset Formula $\triangleleft$
17912 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17915 \begin_layout Plain Layout
17923 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17926 \begin_layout Plain Layout
17927 \begin_inset Formula $\triangleright$
17943 \begin_layout Standard
17944 All binary operators can also be inserted via the math toolbar button
17947 arg "math-insert \\pm"
17953 \begin_layout Standard
17954 To typeset the Laplace operator also
17971 \begin_inset Formula $\nabla^{2}$
17974 ) can be used instead of
17983 \begin_layout Standard
17990 Insert\SpecialChar menuseparator
18002 \begin_layout Subsection
18003 Self-defined Operators
18004 \begin_inset CommandInset label
18006 name "subsec:Self-defined-Operators"
18011 \begin_inset Index idx
18014 \begin_layout Plain Layout
18015 Operators ! self-defined
18023 \begin_layout Standard
18024 With the help of the command
18028 DeclareMathOperator
18031 \begin_inset Index idx
18034 \begin_layout Plain Layout
18039 DeclareMathOperator
18044 custom operators can be defined in the \SpecialChar LaTeX
18046 Its command scheme is:
18049 \begin_layout Standard
18054 DeclareMathOperator{new command}{display}
18057 \begin_layout Standard
18058 Display can be characters or symbols that define how the operator looks
18060 To define a big operator a * is set behind the command.
18061 All self-defined big operators can have limits as described in
18062 \begin_inset CommandInset ref
18064 reference "subsec:Operator-Limits"
18071 \begin_layout Standard
18072 For example the \SpecialChar LaTeX
18076 \begin_layout Standard
18081 DeclareMathOperator*{
18088 \begin_layout Standard
18089 defines the command
18095 , that inserts a big operator consisting of the lozenge symbol from
18096 \begin_inset CommandInset ref
18098 reference "subsec:Miscellaneous-Symbols"
18103 \begin_inset Formula
18105 \Lozenge_{n=1}^{\infty}
18110 The command for this formula is:
18121 \begin_inset Formula $\to$
18127 \begin_layout Standard
18128 \begin_inset VSpace bigskip
18131 When self-defined operators are not used several times in the document,
18132 they can also be defined with the commands
18139 \begin_inset Index idx
18142 \begin_layout Plain Layout
18157 \begin_inset Index idx
18160 \begin_layout Plain Layout
18168 , which have the following scheme:
18171 \begin_layout Standard
18185 \begin_layout Standard
18192 defines big operators,
18201 \begin_layout Standard
18209 \begin_inset space \thinspace{}
18213 \begin_inset space \space{}
18216 be used to use one limit for several operators:
18219 \begin_layout Standard
18220 \begin_inset Formula
18222 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18230 \begin_layout Standard
18231 The command for the formula above is:
18232 \begin_inset Newline newline
18248 \begin_inset space \textvisiblespace{}
18254 \begin_inset Formula $\to$
18260 \begin_inset space \textvisiblespace{}
18268 \begin_layout Section
18270 \begin_inset Index idx
18273 \begin_layout Plain Layout
18282 \begin_layout Subsection
18284 \begin_inset CommandInset label
18286 name "subsec:Font-Styles"
18291 \begin_inset Index idx
18294 \begin_layout Plain Layout
18303 \begin_layout Standard
18304 Latin letters in formulas can be set in one of the following font styles:
18307 \begin_layout Standard
18309 \begin_inset space \hfill{}
18313 \begin_inset Tabular
18314 <lyxtabular version="3" rows="6" columns="2">
18315 <features booktabs="true" tabularvalignment="middle">
18316 <column alignment="center" valignment="top" width="0pt">
18317 <column alignment="center" valignment="top">
18319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18322 \begin_layout Plain Layout
18328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18331 \begin_layout Plain Layout
18339 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18342 \begin_layout Plain Layout
18348 \begin_inset space \textvisiblespace{}
18358 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18361 \begin_layout Plain Layout
18362 \begin_inset Formula $\mathbb{ABC}$
18372 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18375 \begin_layout Plain Layout
18381 \begin_inset space \textvisiblespace{}
18391 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18394 \begin_layout Plain Layout
18395 \begin_inset Formula $\mathbf{AbC}$
18405 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18408 \begin_layout Plain Layout
18414 \begin_inset space \textvisiblespace{}
18424 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18427 \begin_layout Plain Layout
18428 \begin_inset Formula $\boldsymbol{AbC}$
18438 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18441 \begin_layout Plain Layout
18447 \begin_inset space \textvisiblespace{}
18457 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18460 \begin_layout Plain Layout
18461 \begin_inset Formula $\mathcal{ABC}$
18471 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18474 \begin_layout Plain Layout
18480 \begin_inset space \textvisiblespace{}
18490 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18493 \begin_layout Plain Layout
18494 \begin_inset Formula $\mathfrak{AbC}$
18508 \begin_inset space \hfill{}
18512 \begin_inset Tabular
18513 <lyxtabular version="3" rows="6" columns="2">
18514 <features booktabs="true" tabularvalignment="middle">
18515 <column alignment="center" valignment="top" width="0pt">
18516 <column alignment="center" valignment="top">
18518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18521 \begin_layout Plain Layout
18527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18530 \begin_layout Plain Layout
18538 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18541 \begin_layout Plain Layout
18547 \begin_inset space \textvisiblespace{}
18557 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18560 \begin_layout Plain Layout
18561 \begin_inset Formula $\mathit{AbC}$
18571 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18574 \begin_layout Plain Layout
18580 \begin_inset space \textvisiblespace{}
18590 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18593 \begin_layout Plain Layout
18594 \begin_inset Formula $\mathrm{AbC}$
18604 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18607 \begin_layout Plain Layout
18613 \begin_inset space \textvisiblespace{}
18623 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18626 \begin_layout Plain Layout
18627 \begin_inset Formula $\mathsf{AbC}$
18637 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18640 \begin_layout Plain Layout
18646 \begin_inset space \textvisiblespace{}
18656 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18659 \begin_layout Plain Layout
18660 \begin_inset Formula $\mathtt{AbC}$
18670 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18673 \begin_layout Plain Layout
18679 \begin_inset space \textvisiblespace{}
18689 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18692 \begin_layout Plain Layout
18693 \begin_inset Formula $\mathscr{ABC}$
18707 \begin_inset space \hfill{}
18713 \begin_layout Standard
18714 \begin_inset Note Greyedout
18717 \begin_layout Plain Layout
18740 can only be used for big letters.
18748 \begin_layout Standard
18749 Predefined is the style
18758 \begin_layout Standard
18759 The style commands work also for letters in mathematical constructs:
18760 \begin_inset Formula
18762 \mathfrak{A=\frac{b}{C}}
18770 \begin_layout Standard
18771 Characters in mathematical text don't appear in a math font style but in
18772 the text font style
18779 That their style can't be set correctly via the text style dialog is a
18780 bug in \SpecialChar LyX
18785 \begin_layout Plain Layout
18786 \begin_inset CommandInset href
18788 name "LyX-bug #4629"
18789 target "http://www.lyx.org/trac/ticket/4629"
18801 \begin_layout Standard
18802 Instead of the style commands the dialog
18804 Edit\SpecialChar menuseparator
18805 Math\SpecialChar menuseparator
18808 or the toolbar button
18811 arg "math-insert \\font"
18817 \begin_layout Subsection
18819 \begin_inset CommandInset label
18821 name "subsec:Bold-Formulas"
18826 \begin_inset Index idx
18829 \begin_layout Plain Layout
18838 \begin_layout Standard
18839 To make a complete formula bold, the command
18845 from the previous subsection cannot be used, because it doesn't work for
18846 small Greek letters.
18847 Furthermore it prints Latin letters always upright, like in the following
18851 \begin_layout Standard
18852 \begin_inset Formula
18854 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18862 \begin_layout Standard
18863 To display the formula correctly, the command
18870 \begin_inset Formula
18872 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18877 It is also possible to set the formula in a
18879 boldmath environment
18882 This environment is created by inserting the command
18889 \begin_inset Index idx
18892 \begin_layout Plain Layout
18900 in \SpecialChar TeX
18902 To end the environment, the command
18909 \begin_inset Index idx
18912 \begin_layout Plain Layout
18920 is inserted in \SpecialChar TeX
18925 \begin_layout Plain Layout
18935 \begin_inset Formula
18937 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18946 \begin_layout Plain Layout
18958 \begin_layout Subsection
18960 \begin_inset Index idx
18963 \begin_layout Plain Layout
18972 \begin_layout Standard
18973 Formulas can be colored like normal text: Highlight a formula or a formula
18979 Here is a formula in magenta:
18980 \begin_inset Formula
18982 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18990 \begin_layout Standard
18991 You can also define your own colors as described in
18992 \begin_inset CommandInset ref
18994 reference "subsec:Colored-Boxes"
18999 They can be used with the \SpecialChar TeX
19007 \begin_inset Index idx
19010 \begin_layout Plain Layout
19021 \begin_layout Standard
19026 textcolor{color}{characters or formula}
19029 \begin_layout Standard
19030 The following example was colored completely dark green and partly red:
19033 \begin_layout Standard
19037 \begin_layout Plain Layout
19041 textcolor{darkgreen}{
19047 \begin_inset Formula
19049 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19058 \begin_layout Plain Layout
19068 \begin_layout Standard
19069 Due to a bug in \SpecialChar LyX
19070 only complete formulas can be colored with self-defined
19075 \begin_layout Plain Layout
19076 \begin_inset CommandInset href
19078 name "LyX-bug #5269"
19079 target "http://www.lyx.org/trac/ticket/5269"
19091 \begin_layout Subsection
19093 \begin_inset CommandInset label
19095 name "subsec:Font-Sizes"
19100 \begin_inset Index idx
19103 \begin_layout Plain Layout
19112 \begin_layout Standard
19113 For characters in formulas there are, analog to characters in text, the
19114 following size commands:
19117 \begin_layout Standard
19161 \begin_inset Newline newline
19183 \begin_layout Standard
19184 The size produced by the commands depends on the document font size, which
19185 corresponds to the command
19192 The other commands produce smaller or larger sizes than
19199 The font size can however not exceed a certain value.
19200 Is for example the document font size 12
19201 \begin_inset space \thinspace{}
19210 switches to the same size as
19220 \begin_layout Standard
19221 A size command is inserted in \SpecialChar TeX
19222 mode before the formula and sets the size
19223 for all following formula and text characters.
19224 To switch back to the initial size, the command
19230 is inserted behind the formula in \SpecialChar TeX
19234 \begin_layout Standard
19235 Within a formula the size can be changed using the following size commands
19236 or the toolbar button
19239 arg "math-insert \\style"
19243 \begin_inset Separator parbreak
19249 \begin_layout Standard
19252 \begin_inset Tabular
19253 <lyxtabular version="3" rows="5" columns="2">
19254 <features booktabs="true" tabularvalignment="middle">
19255 <column alignment="center" valignment="top" width="0pt">
19256 <column alignment="center" valignment="top">
19258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19261 \begin_layout Plain Layout
19267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19270 \begin_layout Plain Layout
19278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19281 \begin_layout Plain Layout
19285 \begin_inset Index idx
19288 \begin_layout Plain Layout
19301 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19304 \begin_layout Plain Layout
19305 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19314 <row topspace="1mm">
19315 <cell alignment="center" valignment="top" usebox="none">
19318 \begin_layout Plain Layout
19326 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19329 \begin_layout Plain Layout
19330 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19340 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19343 \begin_layout Plain Layout
19351 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19354 \begin_layout Plain Layout
19355 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19365 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19368 \begin_layout Plain Layout
19376 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19379 \begin_layout Plain Layout
19380 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19396 \begin_layout Standard
19397 After entering these commands, a blue box appears in which the formula parts
19401 \begin_layout Standard
19402 There is a further method to change the font size, that though only works
19403 for symbols or letters in mathematical text.
19404 To use it, one of the above text size commands is inserted in mathematical
19406 All following characters until the end of the mathematical text or until
19407 another size command will have the selected size.
19409 \begin_inset VSpace -2mm
19415 \begin_layout Standard
19419 \begin_layout Plain Layout
19429 \begin_inset Formula
19431 A=\frac{B}{c}\cdot\maltese
19437 \begin_inset Formula
19439 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19448 \begin_layout Plain Layout
19460 \begin_layout Standard
19461 \begin_inset VSpace medskip
19464 Before both formulas the command
19471 The command for the second formula is:
19472 \begin_inset Newline newline
19480 \begin_inset space \textvisiblespace{}
19486 \begin_inset space \textvisiblespace{}
19492 \begin_inset space \textvisiblespace{}
19498 \begin_inset space \textvisiblespace{}
19502 \begin_inset Formula $\to$
19506 \begin_inset Formula $\to$
19510 \begin_inset Newline newline
19514 \begin_inset space \hspace*{}
19525 \begin_inset space \textvisiblespace{}
19531 \begin_inset space \textvisiblespace{}
19537 \begin_inset space \textvisiblespace{}
19543 \begin_layout Standard
19544 If a symbol cannot be displayed in different sizes, it will always be displayed
19545 in the default size.
19548 \begin_layout Section
19550 \begin_inset Index idx
19553 \begin_layout Plain Layout
19562 \begin_layout Standard
19563 Greek letters can also be inserted via the toolbar button
19566 arg "math-insert \\alpha"
19570 All international typesetting norms purport that Greek letters in math
19571 have to be typeset italic/slanted.
19572 In some languages, like French or Russian, they are nevertheless sometimes
19576 \begin_layout Subsection
19578 \begin_inset Index idx
19581 \begin_layout Plain Layout
19582 Greek letters ! small
19590 \begin_layout Standard
19591 \begin_inset space \hfill{}
19595 \begin_inset Tabular
19596 <lyxtabular version="3" rows="11" columns="2">
19597 <features booktabs="true" tabularvalignment="middle">
19598 <column alignment="center" valignment="top" width="0pt">
19599 <column alignment="center" valignment="top" width="0pt">
19601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19604 \begin_layout Plain Layout
19610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19613 \begin_layout Plain Layout
19621 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19624 \begin_layout Plain Layout
19632 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19635 \begin_layout Plain Layout
19636 \begin_inset Formula $\alpha$
19646 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19649 \begin_layout Plain Layout
19657 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19660 \begin_layout Plain Layout
19661 \begin_inset Formula $\beta$
19671 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19674 \begin_layout Plain Layout
19682 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19685 \begin_layout Plain Layout
19686 \begin_inset Formula $\gamma$
19696 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19699 \begin_layout Plain Layout
19707 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19710 \begin_layout Plain Layout
19711 \begin_inset Formula $\delta$
19721 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19724 \begin_layout Plain Layout
19732 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19735 \begin_layout Plain Layout
19736 \begin_inset Formula $\epsilon$
19746 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19749 \begin_layout Plain Layout
19757 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19760 \begin_layout Plain Layout
19761 \begin_inset Formula $\varepsilon$
19771 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19774 \begin_layout Plain Layout
19782 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19785 \begin_layout Plain Layout
19786 \begin_inset Formula $\zeta$
19796 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19799 \begin_layout Plain Layout
19807 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19810 \begin_layout Plain Layout
19811 \begin_inset Formula $\eta$
19821 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19824 \begin_layout Plain Layout
19832 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19835 \begin_layout Plain Layout
19836 \begin_inset Formula $\theta$
19846 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19849 \begin_layout Plain Layout
19857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19860 \begin_layout Plain Layout
19861 \begin_inset Formula $\vartheta$
19875 \begin_inset space \hfill{}
19879 \begin_inset Tabular
19880 <lyxtabular version="3" rows="12" columns="2">
19881 <features booktabs="true" tabularvalignment="middle">
19882 <column alignment="center" valignment="top" width="0pt">
19883 <column alignment="center" valignment="top" width="0pt">
19885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19888 \begin_layout Plain Layout
19894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19897 \begin_layout Plain Layout
19905 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19908 \begin_layout Plain Layout
19916 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19919 \begin_layout Plain Layout
19920 \begin_inset Formula $\iota$
19930 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19933 \begin_layout Plain Layout
19941 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19944 \begin_layout Plain Layout
19945 \begin_inset Formula $\kappa$
19955 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19958 \begin_layout Plain Layout
19966 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19969 \begin_layout Plain Layout
19970 \begin_inset Formula $\varkappa$
19980 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19983 \begin_layout Plain Layout
19991 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19994 \begin_layout Plain Layout
19995 \begin_inset Formula $\lambda$
20005 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20008 \begin_layout Plain Layout
20016 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20019 \begin_layout Plain Layout
20020 \begin_inset Formula $\mu$
20030 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20033 \begin_layout Plain Layout
20041 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20044 \begin_layout Plain Layout
20045 \begin_inset Formula $\nu$
20055 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20058 \begin_layout Plain Layout
20066 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20069 \begin_layout Plain Layout
20070 \begin_inset Formula $\xi$
20080 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20083 \begin_layout Plain Layout
20089 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20092 \begin_layout Plain Layout
20093 \begin_inset Formula $o$
20103 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20106 \begin_layout Plain Layout
20114 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20117 \begin_layout Plain Layout
20118 \begin_inset Formula $\pi$
20128 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20131 \begin_layout Plain Layout
20139 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20142 \begin_layout Plain Layout
20143 \begin_inset Formula $\varpi$
20153 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20156 \begin_layout Plain Layout
20164 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20167 \begin_layout Plain Layout
20168 \begin_inset Formula $\rho$
20182 \begin_inset space \hfill{}
20186 \begin_inset Tabular
20187 <lyxtabular version="3" rows="11" columns="2">
20188 <features booktabs="true" tabularvalignment="middle">
20189 <column alignment="center" valignment="top" width="0pt">
20190 <column alignment="center" valignment="top" width="0pt">
20192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20195 \begin_layout Plain Layout
20201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20204 \begin_layout Plain Layout
20212 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20215 \begin_layout Plain Layout
20223 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20226 \begin_layout Plain Layout
20227 \begin_inset Formula $\varrho$
20237 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20240 \begin_layout Plain Layout
20248 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20251 \begin_layout Plain Layout
20252 \begin_inset Formula $\sigma$
20262 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20265 \begin_layout Plain Layout
20273 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20276 \begin_layout Plain Layout
20277 \begin_inset Formula $\varsigma$
20287 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20290 \begin_layout Plain Layout
20298 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20301 \begin_layout Plain Layout
20302 \begin_inset Formula $\tau$
20312 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20315 \begin_layout Plain Layout
20323 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20326 \begin_layout Plain Layout
20327 \begin_inset Formula $\upsilon$
20337 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20340 \begin_layout Plain Layout
20348 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20351 \begin_layout Plain Layout
20352 \begin_inset Formula $\phi$
20362 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20365 \begin_layout Plain Layout
20373 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20376 \begin_layout Plain Layout
20377 \begin_inset Formula $\varphi$
20387 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20390 \begin_layout Plain Layout
20398 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20401 \begin_layout Plain Layout
20402 \begin_inset Formula $\chi$
20412 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20415 \begin_layout Plain Layout
20423 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20426 \begin_layout Plain Layout
20427 \begin_inset Formula $\psi$
20437 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20440 \begin_layout Plain Layout
20448 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20451 \begin_layout Plain Layout
20452 \begin_inset Formula $\omega$
20466 \begin_inset space \hfill{}
20472 \begin_layout Standard
20473 \begin_inset VSpace medskip
20479 \begin_layout Standard
20480 How to create special upright Greek letters is explained in
20481 \begin_inset CommandInset ref
20483 reference "subsec:Upright-small-Greek"
20490 \begin_layout Subsection
20492 \begin_inset Index idx
20495 \begin_layout Plain Layout
20496 Greek letters ! big
20504 \begin_layout Standard
20505 \begin_inset space \hfill{}
20509 \begin_inset Tabular
20510 <lyxtabular version="3" rows="7" columns="2">
20511 <features booktabs="true" tabularvalignment="middle">
20512 <column alignment="center" valignment="top" width="0pt">
20513 <column alignment="center" valignment="top" width="0pt">
20515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20518 \begin_layout Plain Layout
20524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20527 \begin_layout Plain Layout
20535 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20538 \begin_layout Plain Layout
20546 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20549 \begin_layout Plain Layout
20550 \begin_inset Formula $\Gamma$
20560 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20563 \begin_layout Plain Layout
20571 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20574 \begin_layout Plain Layout
20575 \begin_inset Formula $\Delta$
20585 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20588 \begin_layout Plain Layout
20596 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20599 \begin_layout Plain Layout
20600 \begin_inset Formula $\Theta$
20610 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20613 \begin_layout Plain Layout
20621 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20624 \begin_layout Plain Layout
20625 \begin_inset Formula $\Lambda$
20635 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20638 \begin_layout Plain Layout
20646 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20649 \begin_layout Plain Layout
20650 \begin_inset Formula $\Xi$
20660 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20663 \begin_layout Plain Layout
20671 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20674 \begin_layout Plain Layout
20675 \begin_inset Formula $\Pi$
20689 \begin_inset space \hfill{}
20693 \begin_inset Tabular
20694 <lyxtabular version="3" rows="6" columns="2">
20695 <features booktabs="true" tabularvalignment="middle">
20696 <column alignment="center" valignment="top" width="0pt">
20697 <column alignment="center" valignment="top" width="0pt">
20699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20702 \begin_layout Plain Layout
20708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20711 \begin_layout Plain Layout
20719 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20722 \begin_layout Plain Layout
20730 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20733 \begin_layout Plain Layout
20734 \begin_inset Formula $\Sigma$
20744 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20747 \begin_layout Plain Layout
20755 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20758 \begin_layout Plain Layout
20759 \begin_inset Formula $\Upsilon$
20769 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20772 \begin_layout Plain Layout
20780 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20783 \begin_layout Plain Layout
20784 \begin_inset Formula $\Phi$
20794 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20797 \begin_layout Plain Layout
20805 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20808 \begin_layout Plain Layout
20809 \begin_inset Formula $\Psi$
20819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20822 \begin_layout Plain Layout
20830 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20833 \begin_layout Plain Layout
20834 \begin_inset Formula $\Omega$
20848 \begin_inset space \hfill{}
20854 \begin_layout Standard
20855 \begin_inset VSpace medskip
20858 That the big Greek letters appear upright is caused by a design bug when
20861 To get correct italic big letters, begin every command with
20866 For example the command
20873 \begin_inset Formula $\varGamma$
20877 Another way is to load the package
20885 \begin_layout Plain Layout
20890 is part of the \SpecialChar LaTeX
20896 \begin_inset Index idx
20899 \begin_layout Plain Layout
20904 \begin_layout Plain Layout
20924 \begin_inset Index idx
20927 \begin_layout Plain Layout
20933 with the \SpecialChar LaTeX
20937 \begin_layout Standard
20942 usepackage{fixmath}
20945 \begin_layout Standard
20946 Then all big Greek letters in a document will automatically be typeset italic.
20949 \begin_layout Subsection
20951 \begin_inset Index idx
20954 \begin_layout Plain Layout
20955 Greek letters ! bold
20963 \begin_layout Standard
20964 Greek letters cannot be set with different font styles like Latin letters.
20965 They can only be made bold with the command
20972 \begin_inset Index idx
20975 \begin_layout Plain Layout
20984 \begin_inset Separator parbreak
20990 \begin_layout Standard
20992 \begin_inset Tabular
20993 <lyxtabular version="3" rows="3" columns="2">
20994 <features booktabs="true" tabularvalignment="middle">
20995 <column alignment="center" valignment="top" width="0pt">
20996 <column alignment="center" valignment="top">
20998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21001 \begin_layout Plain Layout
21007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21010 \begin_layout Plain Layout
21018 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21021 \begin_layout Plain Layout
21033 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21036 \begin_layout Plain Layout
21037 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21047 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21050 \begin_layout Plain Layout
21062 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21065 \begin_layout Plain Layout
21066 \begin_inset Formula $\theta\boldsymbol{\theta}$
21082 \begin_layout Section
21087 \begin_layout Plain Layout
21100 \begin_layout Plain Layout
21101 A list with all symbols of most of the \SpecialChar LaTeX
21102 -packages can be found in
21103 \begin_inset CommandInset citation
21118 \begin_layout Plain Layout
21126 \begin_inset Note Note
21129 \begin_layout Plain Layout
21132 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21135 \begin_layout Plain Layout
21138 texorpdfstring is in section
21139 \begin_inset CommandInset ref
21141 reference "subsec:Formulas-in-Section"
21151 \begin_inset Index idx
21154 \begin_layout Plain Layout
21163 \begin_layout Standard
21164 Many of the symbols listed in this section can also be inserted via the
21168 arg "math-insert \\nabla"
21174 arg "math-insert \\digamma"
21180 \begin_layout Subsection
21181 Mathematical Symbols
21182 \begin_inset CommandInset label
21184 name "subsec:Mathematical-Symbols"
21189 \begin_inset Index idx
21192 \begin_layout Plain Layout
21193 Symbols ! mathematical
21201 \begin_layout Standard
21202 \begin_inset Tabular
21203 <lyxtabular version="3" rows="10" columns="2">
21204 <features booktabs="true" tabularvalignment="middle">
21205 <column alignment="center" valignment="top" width="0pt">
21206 <column alignment="center" valignment="top" width="0pt">
21208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21211 \begin_layout Plain Layout
21217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21220 \begin_layout Plain Layout
21228 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21231 \begin_layout Plain Layout
21239 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21242 \begin_layout Plain Layout
21243 \begin_inset Formula $\neg$
21253 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21256 \begin_layout Plain Layout
21264 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21267 \begin_layout Plain Layout
21268 \begin_inset Formula $\Im$
21278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21281 \begin_layout Plain Layout
21289 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21292 \begin_layout Plain Layout
21293 \begin_inset Formula $\Re$
21303 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21306 \begin_layout Plain Layout
21314 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21317 \begin_layout Plain Layout
21318 \begin_inset Formula $\aleph$
21328 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21331 \begin_layout Plain Layout
21339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21342 \begin_layout Plain Layout
21343 \begin_inset Formula $\partial$
21353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21356 \begin_layout Plain Layout
21364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21367 \begin_layout Plain Layout
21368 \begin_inset Formula $\infty$
21378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21381 \begin_layout Plain Layout
21389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21392 \begin_layout Plain Layout
21393 \begin_inset Formula $\wp$
21403 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21406 \begin_layout Plain Layout
21414 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21417 \begin_layout Plain Layout
21418 \begin_inset Formula $\imath$
21428 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21431 \begin_layout Plain Layout
21439 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21442 \begin_layout Plain Layout
21443 \begin_inset Formula $\jmath$
21457 \begin_inset space \hfill{}
21461 \begin_inset Tabular
21462 <lyxtabular version="3" rows="10" columns="2">
21463 <features booktabs="true" tabularvalignment="middle">
21464 <column alignment="center" valignment="top" width="0pt">
21465 <column alignment="center" valignment="top" width="0pt">
21467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21470 \begin_layout Plain Layout
21476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21479 \begin_layout Plain Layout
21481 \begin_inset Note Note
21484 \begin_layout Plain Layout
21491 is only used as spacer.
21503 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21506 \begin_layout Plain Layout
21514 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21517 \begin_layout Plain Layout
21518 \begin_inset Formula $\forall$
21528 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21531 \begin_layout Plain Layout
21539 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21542 \begin_layout Plain Layout
21543 \begin_inset Formula $\exists$
21553 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21556 \begin_layout Plain Layout
21564 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21567 \begin_layout Plain Layout
21568 \begin_inset Formula $\nexists$
21578 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21581 \begin_layout Plain Layout
21589 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21592 \begin_layout Plain Layout
21593 \begin_inset Formula $\emptyset$
21603 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21606 \begin_layout Plain Layout
21614 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21617 \begin_layout Plain Layout
21618 \begin_inset Formula $\varnothing$
21628 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21631 \begin_layout Plain Layout
21639 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21642 \begin_layout Plain Layout
21643 \begin_inset Formula $\dag$
21653 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21656 \begin_layout Plain Layout
21664 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21667 \begin_layout Plain Layout
21668 \begin_inset Formula $\ddag$
21678 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21681 \begin_layout Plain Layout
21689 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21692 \begin_layout Plain Layout
21696 \begin_layout Plain Layout
21706 \begin_inset Formula $\complement$
21713 \begin_layout Plain Layout
21727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21730 \begin_layout Plain Layout
21738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21741 \begin_layout Plain Layout
21742 \begin_inset Formula $\Bbbk$
21756 \begin_inset space \hfill{}
21760 \begin_inset Tabular
21761 <lyxtabular version="3" rows="10" columns="2">
21762 <features booktabs="true" tabularvalignment="middle">
21763 <column alignment="center" valignment="top" width="0pt">
21764 <column alignment="center" valignment="top" width="0pt">
21766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21769 \begin_layout Plain Layout
21775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21778 \begin_layout Plain Layout
21786 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21789 \begin_layout Plain Layout
21797 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21800 \begin_layout Plain Layout
21801 \begin_inset Formula $\prime$
21811 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21814 \begin_layout Plain Layout
21822 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21825 \begin_layout Plain Layout
21826 \begin_inset Formula $\backprime$
21836 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21839 \begin_layout Plain Layout
21847 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21850 \begin_layout Plain Layout
21851 \begin_inset Formula $\mho$
21861 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21864 \begin_layout Plain Layout
21872 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21875 \begin_layout Plain Layout
21876 \begin_inset Formula $\triangle$
21886 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21889 \begin_layout Plain Layout
21897 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21900 \begin_layout Plain Layout
21901 \begin_inset Formula $\angle$
21911 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21914 \begin_layout Plain Layout
21922 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21925 \begin_layout Plain Layout
21926 \begin_inset Formula $\measuredangle$
21936 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21939 \begin_layout Plain Layout
21947 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21950 \begin_layout Plain Layout
21951 \begin_inset Formula $\sphericalangle$
21961 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21964 \begin_layout Plain Layout
21972 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21975 \begin_layout Plain Layout
21976 \begin_inset Formula $\top$
21986 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21989 \begin_layout Plain Layout
21997 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22000 \begin_layout Plain Layout
22001 \begin_inset Formula $\bot$
22017 \begin_layout Standard
22018 \begin_inset Newpage newpage
22024 \begin_layout Subsection
22025 Miscellaneous Symbols
22026 \begin_inset CommandInset label
22028 name "subsec:Miscellaneous-Symbols"
22033 \begin_inset Index idx
22036 \begin_layout Plain Layout
22037 Symbols ! miscellaneous
22045 \begin_layout Standard
22048 \begin_inset Tabular
22049 <lyxtabular version="3" rows="10" columns="2">
22050 <features booktabs="true" tabularvalignment="middle">
22051 <column alignment="center" valignment="top" width="0pt">
22052 <column alignment="center" valignment="top" width="0pt">
22054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22057 \begin_layout Plain Layout
22063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22066 \begin_layout Plain Layout
22074 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22077 \begin_layout Plain Layout
22085 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22088 \begin_layout Plain Layout
22089 \begin_inset Formula $\flat$
22099 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22102 \begin_layout Plain Layout
22110 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22113 \begin_layout Plain Layout
22114 \begin_inset Formula $\natural$
22124 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22127 \begin_layout Plain Layout
22135 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22138 \begin_layout Plain Layout
22139 \begin_inset Formula $\sharp$
22149 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22152 \begin_layout Plain Layout
22160 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22163 \begin_layout Plain Layout
22164 \begin_inset Formula $\surd$
22174 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22177 \begin_layout Plain Layout
22185 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22188 \begin_layout Plain Layout
22189 \begin_inset Formula $\checkmark$
22199 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22202 \begin_layout Plain Layout
22210 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22213 \begin_layout Plain Layout
22214 \begin_inset Formula $\yen$
22224 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22227 \begin_layout Plain Layout
22235 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22238 \begin_layout Plain Layout
22239 \begin_inset Formula $\pounds$
22249 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22252 \begin_layout Plain Layout
22258 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22261 \begin_layout Plain Layout
22262 \begin_inset Formula $\$$
22272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22275 \begin_layout Plain Layout
22281 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22284 \begin_layout Plain Layout
22285 \begin_inset Formula $§$
22299 \begin_inset space \hfill{}
22303 \begin_inset Tabular
22304 <lyxtabular version="3" rows="10" columns="2">
22305 <features booktabs="true" tabularvalignment="middle">
22306 <column alignment="center" valignment="top" width="0pt">
22307 <column alignment="center" valignment="top">
22309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22312 \begin_layout Plain Layout
22318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22321 \begin_layout Plain Layout
22329 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22332 \begin_layout Plain Layout
22340 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22343 \begin_layout Plain Layout
22344 \begin_inset Formula $\hbar$
22354 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22357 \begin_layout Plain Layout
22365 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22368 \begin_layout Plain Layout
22369 \begin_inset Formula $\hslash$
22379 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22382 \begin_layout Plain Layout
22390 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22393 \begin_layout Plain Layout
22394 \begin_inset Formula $\clubsuit$
22404 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22407 \begin_layout Plain Layout
22415 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22418 \begin_layout Plain Layout
22419 \begin_inset Formula $\spadesuit$
22429 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22432 \begin_layout Plain Layout
22440 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22443 \begin_layout Plain Layout
22444 \begin_inset Formula $\bigstar$
22454 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22457 \begin_layout Plain Layout
22465 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22468 \begin_layout Plain Layout
22469 \begin_inset Formula $\blacklozenge$
22479 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22482 \begin_layout Plain Layout
22490 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22493 \begin_layout Plain Layout
22494 \begin_inset Formula $\blacktriangle$
22504 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22507 \begin_layout Plain Layout
22515 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22518 \begin_layout Plain Layout
22519 \begin_inset Formula $\blacktriangledown$
22529 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22532 \begin_layout Plain Layout
22540 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22543 \begin_layout Plain Layout
22544 \begin_inset Formula $\bullet$
22558 \begin_inset space \hfill{}
22562 \begin_inset Tabular
22563 <lyxtabular version="3" rows="10" columns="2">
22564 <features booktabs="true" tabularvalignment="middle">
22565 <column alignment="center" valignment="top" width="0pt">
22566 <column alignment="center" valignment="top" width="0pt">
22568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22571 \begin_layout Plain Layout
22577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22580 \begin_layout Plain Layout
22588 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22591 \begin_layout Plain Layout
22599 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22602 \begin_layout Plain Layout
22603 \begin_inset Formula $\diamondsuit$
22613 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22616 \begin_layout Plain Layout
22624 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22627 \begin_layout Plain Layout
22628 \begin_inset Formula $\Diamond$
22638 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22641 \begin_layout Plain Layout
22649 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22652 \begin_layout Plain Layout
22653 \begin_inset Formula $\heartsuit$
22663 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22666 \begin_layout Plain Layout
22674 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22677 \begin_layout Plain Layout
22678 \begin_inset Formula $\P$
22688 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22691 \begin_layout Plain Layout
22699 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22702 \begin_layout Plain Layout
22703 \begin_inset Formula $\copyright$
22713 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22716 \begin_layout Plain Layout
22724 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22727 \begin_layout Plain Layout
22728 \begin_inset Formula $\circledR$
22738 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22741 \begin_layout Plain Layout
22749 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22752 \begin_layout Plain Layout
22753 \begin_inset Formula $\maltese$
22763 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22766 \begin_layout Plain Layout
22774 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22777 \begin_layout Plain Layout
22778 \begin_inset Formula $\diagup$
22788 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22791 \begin_layout Plain Layout
22799 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22802 \begin_layout Plain Layout
22803 \begin_inset Formula $\diagdown$
22819 \begin_layout Standard
22820 \begin_inset VSpace medskip
22826 \begin_layout Standard
22827 Some symbols can be displayed in different sizes, see
22828 \begin_inset CommandInset ref
22830 reference "subsec:Font-Sizes"
22837 \begin_layout Subsection
22839 \begin_inset Index idx
22842 \begin_layout Plain Layout
22843 Symbols ! Euro-symbol
22849 \begin_inset Index idx
22852 \begin_layout Plain Layout
22859 \begin_layout Plain Layout
22876 \begin_layout Standard
22877 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22883 \begin_inset Index idx
22886 \begin_layout Plain Layout
22892 must be installed and loaded with the \SpecialChar LaTeX
22896 \begin_layout Standard
22901 usepackage[gennarrow]{eurosym}
22904 \begin_layout Standard
22905 The Euro symbol can now be inserted with the command
22912 \begin_inset Index idx
22915 \begin_layout Plain Layout
22926 \begin_layout Standard
22927 The Euro symbol can directly be inserted with the € key in mathematical
22928 text, without having
22943 can also be inserted in \SpecialChar TeX
22945 The official currency symbol can then be inserted with the command
22952 \begin_inset Index idx
22955 \begin_layout Plain Layout
22963 , that is only available in \SpecialChar TeX
22967 \begin_layout Standard
22971 \begin_layout Plain Layout
22981 \begin_inset Note Note
22984 \begin_layout Plain Layout
22985 The following table will only be displayed when the \SpecialChar LaTeX
22998 \begin_layout Standard
22999 An overview about the different Euro symbols:
23000 \begin_inset Separator parbreak
23006 \begin_layout Standard
23008 \begin_inset Tabular
23009 <lyxtabular version="3" rows="4" columns="3">
23010 <features booktabs="true" tabularvalignment="middle">
23011 <column alignment="center" valignment="top" width="0pt">
23012 <column alignment="center" valignment="top" width="0pt">
23013 <column alignment="center" valignment="top" width="0pt">
23015 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
23018 \begin_layout Plain Layout
23022 \begin_layout Plain Layout
23026 cmidrule[0.08em]{2-3}
23036 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23039 \begin_layout Plain Layout
23045 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23048 \begin_layout Plain Layout
23056 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23059 \begin_layout Plain Layout
23065 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23068 \begin_layout Plain Layout
23076 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23079 \begin_layout Plain Layout
23080 \begin_inset Formula $\euro$
23090 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23093 \begin_layout Plain Layout
23099 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23102 \begin_layout Plain Layout
23108 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23111 \begin_layout Plain Layout
23112 \begin_inset Formula $\mbox{€}$
23122 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23125 \begin_layout Plain Layout
23132 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23135 \begin_layout Plain Layout
23143 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23146 \begin_layout Plain Layout
23150 \begin_layout Plain Layout
23170 \begin_inset Note Note
23173 \begin_layout Plain Layout
23180 is used here only for table borders.
23190 manual for details.
23198 \begin_layout Standard
23202 \begin_layout Plain Layout
23212 \begin_inset Note Note
23215 \begin_layout Plain Layout
23216 The following will be displayed when the \SpecialChar LaTeX
23229 \begin_layout Standard
23230 You need to install the \SpecialChar LaTeX
23235 to see the rest of this subsection in the output.
23238 \begin_layout Standard
23242 \begin_layout Plain Layout
23254 \begin_layout Standard
23255 \begin_inset Newpage newpage
23261 \begin_layout Section
23263 \begin_inset CommandInset label
23265 name "sec:Relations"
23270 \begin_inset Index idx
23273 \begin_layout Plain Layout
23280 \begin_inset Index idx
23283 \begin_layout Plain Layout
23288 \begin_layout Plain Layout
23299 \begin_layout Plain Layout
23314 \begin_layout Standard
23315 All following relations can also be inserted via the toolbar button
23318 arg "math-insert \\leq"
23324 \begin_layout Standard
23325 \begin_inset Tabular
23326 <lyxtabular version="3" rows="17" columns="2">
23327 <features booktabs="true" tabularvalignment="middle">
23328 <column alignment="center" valignment="top" width="0pt">
23329 <column alignment="center" valignment="top" width="0pt">
23331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23334 \begin_layout Plain Layout
23340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23343 \begin_layout Plain Layout
23351 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23354 \begin_layout Plain Layout
23360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23363 \begin_layout Plain Layout
23364 \begin_inset Formula $<$
23374 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23377 \begin_layout Plain Layout
23385 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23388 \begin_layout Plain Layout
23389 \begin_inset Formula $\le$
23399 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23402 \begin_layout Plain Layout
23410 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23413 \begin_layout Plain Layout
23414 \begin_inset Formula $\ll$
23424 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23427 \begin_layout Plain Layout
23435 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23438 \begin_layout Plain Layout
23439 \begin_inset Formula $\prec$
23449 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23452 \begin_layout Plain Layout
23460 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23463 \begin_layout Plain Layout
23464 \begin_inset Formula $\preceq$
23474 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23477 \begin_layout Plain Layout
23485 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23488 \begin_layout Plain Layout
23489 \begin_inset Formula $\subset$
23499 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23502 \begin_layout Plain Layout
23510 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23513 \begin_layout Plain Layout
23514 \begin_inset Formula $\subseteq$
23524 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23527 \begin_layout Plain Layout
23535 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23538 \begin_layout Plain Layout
23539 \begin_inset Formula $\sqsubseteq$
23549 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23552 \begin_layout Plain Layout
23560 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23563 \begin_layout Plain Layout
23564 \begin_inset Formula $\in$
23574 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23577 \begin_layout Plain Layout
23585 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23588 \begin_layout Plain Layout
23589 \begin_inset Formula $\vdash$
23599 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23602 \begin_layout Plain Layout
23610 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23613 \begin_layout Plain Layout
23614 \begin_inset Formula $\smile$
23624 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23627 \begin_layout Plain Layout
23635 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23638 \begin_layout Plain Layout
23639 \begin_inset Formula $\lhd$
23649 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23652 \begin_layout Plain Layout
23660 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23663 \begin_layout Plain Layout
23664 \begin_inset Formula $\unlhd$
23674 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23677 \begin_layout Plain Layout
23685 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23688 \begin_layout Plain Layout
23689 \begin_inset Formula $\gtrless$
23699 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23702 \begin_layout Plain Layout
23710 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23713 \begin_layout Plain Layout
23714 \begin_inset Formula $\mid$
23724 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23727 \begin_layout Plain Layout
23735 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23738 \begin_layout Plain Layout
23739 \begin_inset Formula $\nmid$
23753 \begin_inset space \hfill{}
23757 \begin_inset Tabular
23758 <lyxtabular version="3" rows="17" columns="2">
23759 <features booktabs="true" tabularvalignment="middle">
23760 <column alignment="center" valignment="top" width="0pt">
23761 <column alignment="center" valignment="top" width="0pt">
23763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23766 \begin_layout Plain Layout
23772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23775 \begin_layout Plain Layout
23783 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23786 \begin_layout Plain Layout
23792 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23795 \begin_layout Plain Layout
23796 \begin_inset Formula $=$
23806 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23809 \begin_layout Plain Layout
23817 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23820 \begin_layout Plain Layout
23821 \begin_inset Formula $\not=$
23831 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23834 \begin_layout Plain Layout
23842 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23845 \begin_layout Plain Layout
23846 \begin_inset Formula $\equiv$
23856 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23859 \begin_layout Plain Layout
23867 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23870 \begin_layout Plain Layout
23871 \begin_inset Formula $\sim$
23881 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23884 \begin_layout Plain Layout
23892 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23895 \begin_layout Plain Layout
23896 \begin_inset Formula $\simeq$
23906 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23909 \begin_layout Plain Layout
23917 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23920 \begin_layout Plain Layout
23921 \begin_inset Formula $\approx$
23931 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23934 \begin_layout Plain Layout
23942 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23945 \begin_layout Plain Layout
23946 \begin_inset Formula $\cong$
23956 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23959 \begin_layout Plain Layout
23967 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23970 \begin_layout Plain Layout
23971 \begin_inset Formula $\bowtie$
23981 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23984 \begin_layout Plain Layout
23992 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23995 \begin_layout Plain Layout
23996 \begin_inset Formula $\notin$
24006 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24009 \begin_layout Plain Layout
24017 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24020 \begin_layout Plain Layout
24021 \begin_inset Formula $\perp$
24031 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24034 \begin_layout Plain Layout
24042 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24045 \begin_layout Plain Layout
24046 \begin_inset Formula $\propto$
24056 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24059 \begin_layout Plain Layout
24067 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24070 \begin_layout Plain Layout
24071 \begin_inset Formula $\asymp$
24081 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24084 \begin_layout Plain Layout
24092 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24095 \begin_layout Plain Layout
24096 \begin_inset Formula $\doteq$
24106 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24109 \begin_layout Plain Layout
24117 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24120 \begin_layout Plain Layout
24121 \begin_inset Formula $\circeq$
24131 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24134 \begin_layout Plain Layout
24142 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24145 \begin_layout Plain Layout
24146 \begin_inset Formula $\models$
24156 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24159 \begin_layout Plain Layout
24167 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24170 \begin_layout Plain Layout
24171 \begin_inset Formula $\widehat{=}$
24185 \begin_inset space \hfill{}
24189 \begin_inset Tabular
24190 <lyxtabular version="3" rows="17" columns="2">
24191 <features booktabs="true" tabularvalignment="middle">
24192 <column alignment="center" valignment="top" width="0pt">
24193 <column alignment="center" valignment="top" width="0pt">
24195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24198 \begin_layout Plain Layout
24204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24207 \begin_layout Plain Layout
24215 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24218 \begin_layout Plain Layout
24224 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24227 \begin_layout Plain Layout
24228 \begin_inset Formula $>$
24238 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24241 \begin_layout Plain Layout
24249 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24252 \begin_layout Plain Layout
24253 \begin_inset Formula $\ge$
24263 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24266 \begin_layout Plain Layout
24274 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24277 \begin_layout Plain Layout
24278 \begin_inset Formula $\gg$
24288 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24291 \begin_layout Plain Layout
24299 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24302 \begin_layout Plain Layout
24303 \begin_inset Formula $\succ$
24313 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24316 \begin_layout Plain Layout
24324 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24327 \begin_layout Plain Layout
24328 \begin_inset Formula $\succeq$
24338 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24341 \begin_layout Plain Layout
24349 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24352 \begin_layout Plain Layout
24353 \begin_inset Formula $\supset$
24363 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24366 \begin_layout Plain Layout
24374 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24377 \begin_layout Plain Layout
24378 \begin_inset Formula $\supseteq$
24388 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24391 \begin_layout Plain Layout
24399 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24402 \begin_layout Plain Layout
24403 \begin_inset Formula $\sqsupseteq$
24413 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24416 \begin_layout Plain Layout
24424 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24427 \begin_layout Plain Layout
24428 \begin_inset Formula $\ni$
24438 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24441 \begin_layout Plain Layout
24449 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24452 \begin_layout Plain Layout
24453 \begin_inset Formula $\dashv$
24463 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24466 \begin_layout Plain Layout
24474 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24477 \begin_layout Plain Layout
24478 \begin_inset Formula $\frown$
24488 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24491 \begin_layout Plain Layout
24499 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24502 \begin_layout Plain Layout
24503 \begin_inset Formula $\rhd$
24513 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24516 \begin_layout Plain Layout
24524 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24527 \begin_layout Plain Layout
24528 \begin_inset Formula $\unrhd$
24538 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24541 \begin_layout Plain Layout
24549 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24552 \begin_layout Plain Layout
24553 \begin_inset Formula $\lessgtr$
24563 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24566 \begin_layout Plain Layout
24574 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24577 \begin_layout Plain Layout
24578 \begin_inset Formula $\parallel$
24588 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24591 \begin_layout Plain Layout
24599 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24602 \begin_layout Plain Layout
24603 \begin_inset Formula $\nparallel$
24619 \begin_layout Standard
24620 \begin_inset VSpace medskip
24635 are bigger than the equal looking operators
24650 \begin_layout Standard
24652 supports also many special relations.
24653 Use the toolbar button
24656 arg "math-insert \\leqq"
24659 to see a list of these relations.
24662 \begin_layout Standard
24663 Relations are, in contrary to symbols, always surrounded by space.
24666 \begin_layout Standard
24667 Relations with labels can be created with the command
24674 \begin_inset Index idx
24677 \begin_layout Plain Layout
24686 \begin_inset Separator parbreak
24692 \begin_layout Standard
24694 \begin_inset Tabular
24695 <lyxtabular version="3" rows="2" columns="2">
24696 <features booktabs="true" tabularvalignment="middle">
24697 <column alignment="center" valignment="top" width="0pt">
24698 <column alignment="center" valignment="top">
24700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24703 \begin_layout Plain Layout
24709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24712 \begin_layout Plain Layout
24719 <row topspace="1.5mm">
24720 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24723 \begin_layout Plain Layout
24727 \begin_inset space \textvisiblespace{}
24735 \begin_inset space \textvisiblespace{}
24739 \begin_inset Formula $\downarrow$
24745 \begin_inset space \textvisiblespace{}
24749 \begin_inset space \textvisiblespace{}
24757 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24760 \begin_layout Plain Layout
24761 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24777 \begin_layout Section
24781 \begin_layout Subsection
24782 Predefined Functions
24783 \begin_inset CommandInset label
24785 name "subsec:Predefined-Functions"
24790 \begin_inset Index idx
24793 \begin_layout Plain Layout
24794 Functions ! predefined
24802 \begin_layout Standard
24803 In general, variables are set
24807 in mathematical expressions, but not function names, because
24808 \begin_inset Formula $sin$
24811 could be misunderstood as
24812 \begin_inset Formula $s\cdot i\cdot n$
24816 Therefore there are predefined functionswhich are additionally a bit separated
24818 They are inserted as commands starting with a backslash before their name.
24819 \begin_inset Separator parbreak
24825 \begin_layout Standard
24827 \begin_inset Tabular
24828 <lyxtabular version="3" rows="2" columns="2">
24829 <features booktabs="true" tabularvalignment="middle">
24830 <column alignment="center" valignment="top" width="0pt">
24831 <column alignment="center" valignment="top" width="0pt">
24833 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24836 \begin_layout Plain Layout
24842 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24845 \begin_layout Plain Layout
24853 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24856 \begin_layout Plain Layout
24862 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24865 \begin_layout Plain Layout
24866 \begin_inset Formula $Asin(x)+B$
24880 \begin_inset space \quad{}
24884 \begin_inset Tabular
24885 <lyxtabular version="3" rows="2" columns="2">
24886 <features booktabs="true" tabularvalignment="middle">
24887 <column alignment="center" valignment="top" width="0pt">
24888 <column alignment="center" valignment="top" width="0pt">
24890 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24893 \begin_layout Plain Layout
24899 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24902 \begin_layout Plain Layout
24910 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24913 \begin_layout Plain Layout
24921 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24924 \begin_layout Plain Layout
24925 \begin_inset Formula $A\sin(x)+B$
24941 \begin_layout Standard
24942 The following functions are predefined:
24945 \begin_layout Standard
24946 \begin_inset VSpace -2mm
24952 \begin_layout Standard
24954 \begin_inset Tabular
24955 <lyxtabular version="3" rows="9" columns="4">
24956 <features booktabs="true" tabularvalignment="middle">
24957 <column alignment="center" valignment="top" width="0pt">
24958 <column alignment="center" valignment="top" width="0pt">
24959 <column alignment="center" valignment="top" width="0pt">
24960 <column alignment="center" valignment="top" width="0pt">
24962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24965 \begin_layout Plain Layout
24971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24974 \begin_layout Plain Layout
24980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24983 \begin_layout Plain Layout
24989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24992 \begin_layout Plain Layout
25000 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25003 \begin_layout Plain Layout
25011 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25014 \begin_layout Plain Layout
25022 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25025 \begin_layout Plain Layout
25033 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25036 \begin_layout Plain Layout
25046 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25049 \begin_layout Plain Layout
25057 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25060 \begin_layout Plain Layout
25068 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25071 \begin_layout Plain Layout
25079 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25082 \begin_layout Plain Layout
25092 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25095 \begin_layout Plain Layout
25103 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25106 \begin_layout Plain Layout
25114 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25117 \begin_layout Plain Layout
25125 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25128 \begin_layout Plain Layout
25138 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25141 \begin_layout Plain Layout
25149 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25152 \begin_layout Plain Layout
25160 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25163 \begin_layout Plain Layout
25171 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25174 \begin_layout Plain Layout
25184 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25187 \begin_layout Plain Layout
25195 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25198 \begin_layout Plain Layout
25206 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25209 \begin_layout Plain Layout
25217 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25220 \begin_layout Plain Layout
25230 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25233 \begin_layout Plain Layout
25241 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25244 \begin_layout Plain Layout
25252 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25255 \begin_layout Plain Layout
25263 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25266 \begin_layout Plain Layout
25276 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25279 \begin_layout Plain Layout
25287 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25290 \begin_layout Plain Layout
25298 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25301 \begin_layout Plain Layout
25309 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25312 \begin_layout Plain Layout
25322 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25325 \begin_layout Plain Layout
25333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25336 \begin_layout Plain Layout
25344 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25347 \begin_layout Plain Layout
25355 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25358 \begin_layout Plain Layout
25374 \begin_layout Standard
25375 They can also be inserted with the math toolbar button
25378 arg "math-insert \\functions"
25384 \begin_layout Subsection
25385 Self-defined Functions
25386 \begin_inset Index idx
25389 \begin_layout Plain Layout
25390 Functions ! self-defined
25398 \begin_layout Standard
25399 To use a function that is not predefined, like for example the sign function
25400 sgn(x), there are two possibilities:
25403 \begin_layout Itemize
25404 Define the function by inserting the following line to the \SpecialChar LaTeX
25409 \begin_layout Plain Layout
25414 DeclareMathOperator
25417 \begin_inset CommandInset ref
25419 reference "subsec:Self-defined-Operators"
25429 \begin_inset Newline newline
25433 \begin_inset VSpace -3mm
25437 \begin_inset Newline newline
25444 DeclareMathOperator{
25449 \begin_inset Index idx
25452 \begin_layout Plain Layout
25457 DeclareMathOperator
25463 \begin_inset Newline newline
25467 \begin_inset VSpace -2mm
25471 \begin_inset Newline newline
25474 Now the new defined function can be called with the command
25483 \begin_layout Itemize
25484 Write the formula as usual, mark the formula name, in our example the letters
25489 , and change it to mathematical text.
25490 Finally, a space is inserted between prefactor and function.
25493 \begin_layout Standard
25494 The result is the same with both methods as with a predefined function
25498 \begin_layout Plain Layout
25499 In \SpecialChar LyX
25500 self-defined functions are displayed red, predefined ones black.
25506 \begin_inset Separator parbreak
25512 \begin_layout Standard
25514 \begin_inset Tabular
25515 <lyxtabular version="3" rows="3" columns="2">
25516 <features booktabs="true" tabularvalignment="middle">
25517 <column alignment="center" valignment="top" width="0pt">
25518 <column alignment="center" valignment="top" width="0pt">
25520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25523 \begin_layout Plain Layout
25529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25532 \begin_layout Plain Layout
25540 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25543 \begin_layout Plain Layout
25551 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25554 \begin_layout Plain Layout
25555 \begin_inset Formula $A\sgn(x)+B$
25565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25568 \begin_layout Plain Layout
25572 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25583 \begin_layout Plain Layout
25584 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25600 \begin_layout Standard
25601 The first method is more suitable when the self-defined function should
25602 be used several times.
25605 \begin_layout Subsection
25607 \begin_inset Index idx
25610 \begin_layout Plain Layout
25619 \begin_layout Standard
25620 For limits, in addition to the commands
25627 \begin_inset Index idx
25630 \begin_layout Plain Layout
25650 the following functions are defined:
25651 \begin_inset Separator parbreak
25657 \begin_layout Standard
25659 \begin_inset Tabular
25660 <lyxtabular version="3" rows="5" columns="2">
25661 <features booktabs="true" tabularvalignment="middle">
25662 <column alignment="center" valignment="top" width="0pt">
25663 <column alignment="center" valignment="top" width="0pt">
25665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25668 \begin_layout Plain Layout
25674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25677 \begin_layout Plain Layout
25685 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25688 \begin_layout Plain Layout
25696 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25699 \begin_layout Plain Layout
25700 \begin_inset Formula $\varliminf$
25709 <row topspace="1.5mm">
25710 <cell alignment="center" valignment="top" usebox="none">
25713 \begin_layout Plain Layout
25721 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25724 \begin_layout Plain Layout
25725 \begin_inset Formula $\varlimsup$
25734 <row topspace="1.5mm">
25735 <cell alignment="center" valignment="top" usebox="none">
25738 \begin_layout Plain Layout
25746 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25749 \begin_layout Plain Layout
25750 \begin_inset Formula $\varprojlim$
25759 <row topspace="1.5mm" bottomspace="1mm">
25760 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25763 \begin_layout Plain Layout
25771 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25774 \begin_layout Plain Layout
25775 \begin_inset Formula $\varinjlim$
25791 \begin_layout Standard
25792 \begin_inset VSpace medskip
25795 The limit is created by inserting a subscript.
25796 It is set right beside the function in an inline formula:
25799 \begin_layout Standard
25801 \begin_inset Tabular
25802 <lyxtabular version="3" rows="2" columns="2">
25803 <features booktabs="true" tabularvalignment="middle">
25804 <column alignment="center" valignment="top" width="0pt">
25805 <column alignment="center" valignment="top" width="0pt">
25807 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25810 \begin_layout Plain Layout
25816 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25819 \begin_layout Plain Layout
25827 <cell alignment="center" valignment="top" usebox="none">
25830 \begin_layout Plain Layout
25836 \begin_inset space \textvisiblespace{}
25840 \begin_inset space \textvisiblespace{}
25848 <cell alignment="center" valignment="top" usebox="none">
25851 \begin_layout Plain Layout
25852 \begin_inset Formula $\lim_{x\to A}x=B$
25868 \begin_layout Standard
25869 In a displayed formula the limit is set below the formula, as usual:
25870 \begin_inset Formula
25880 \begin_layout Standard
25881 \begin_inset VSpace medskip
25887 \begin_layout Standard
25888 How to adjust the typesetting of the limits see
25889 \begin_inset CommandInset ref
25891 reference "subsec:Operator-Limits"
25898 \begin_layout Subsection
25900 \begin_inset Index idx
25903 \begin_layout Plain Layout
25904 Functions ! modulo-
25912 \begin_layout Standard
25913 The modulo-function is special, because it exists in four variants.
25914 The variants in a displayed formula are:
25915 \begin_inset Formula
25917 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25918 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25919 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25920 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25921 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25929 \begin_layout Standard
25930 In an inline formula less space is set before the function names for all
25932 By default the modulo-functions take only the first following character
25934 To use more than one character, one has to put them into \SpecialChar TeX
25936 \begin_inset Formula
25938 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25939 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25940 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25948 \begin_layout Section
25950 \begin_inset Index idx
25953 \begin_layout Plain Layout
25962 \begin_layout Standard
25963 The characters ^ and _ would normally create a superscript and subscript,
25965 To get these characters you have to insert them with a leading
25968 \begin_inset Separator parbreak
25974 \begin_layout Standard
25977 \begin_inset Tabular
25978 <lyxtabular version="3" rows="3" columns="2">
25979 <features booktabs="true" tabularvalignment="middle">
25980 <column alignment="left" valignment="top" width="0pt">
25981 <column alignment="block" valignment="top">
25983 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25986 \begin_layout Plain Layout
25992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25995 \begin_layout Plain Layout
26003 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26006 \begin_layout Plain Layout
26010 \begin_inset space \textvisiblespace{}
26018 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26021 \begin_layout Plain Layout
26022 \begin_inset Formula $\mathcircumflex$
26032 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26035 \begin_layout Plain Layout
26043 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26046 \begin_layout Plain Layout
26047 \begin_inset Formula $\_$
26063 \begin_layout Subsection
26064 Special Characters in Mathematical Text
26067 \begin_layout Standard
26068 The following commands can only be used in mathematical text or in \SpecialChar TeX
26072 \begin_layout Standard
26073 \begin_inset space \hfill{}
26077 \begin_inset Tabular
26078 <lyxtabular version="3" rows="8" columns="2">
26079 <features booktabs="true" tabularvalignment="middle">
26080 <column alignment="left" valignment="top" width="0pt">
26081 <column alignment="block" valignment="top">
26083 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26086 \begin_layout Plain Layout
26092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26095 \begin_layout Plain Layout
26103 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26106 \begin_layout Plain Layout
26114 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26117 \begin_layout Plain Layout
26118 \begin_inset Formula $\textrm{œ}$
26128 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26131 \begin_layout Plain Layout
26139 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26142 \begin_layout Plain Layout
26143 \begin_inset Formula $\textrm{Œ}$
26153 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26156 \begin_layout Plain Layout
26164 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26167 \begin_layout Plain Layout
26168 \begin_inset Formula $\textrm{æ}$
26178 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26181 \begin_layout Plain Layout
26189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26192 \begin_layout Plain Layout
26193 \begin_inset Formula $\textrm{Æ}$
26203 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26206 \begin_layout Plain Layout
26214 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26217 \begin_layout Plain Layout
26218 \begin_inset Formula $\textrm{\aa}$
26228 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26231 \begin_layout Plain Layout
26235 \begin_inset Index idx
26238 \begin_layout Plain Layout
26245 \begin_layout Plain Layout
26266 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26269 \begin_layout Plain Layout
26270 \begin_inset Formula $\textrm{Å}$
26280 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26283 \begin_layout Plain Layout
26291 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26294 \begin_layout Plain Layout
26295 \begin_inset Formula $\textrm{ı}$
26309 \begin_inset space \hfill{}
26313 \begin_inset Tabular
26314 <lyxtabular version="3" rows="8" columns="2">
26315 <features booktabs="true" tabularvalignment="middle">
26316 <column alignment="left" valignment="top" width="0pt">
26317 <column alignment="center" valignment="top">
26319 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26322 \begin_layout Plain Layout
26324 \begin_inset Note Note
26327 \begin_layout Plain Layout
26329 \begin_inset space \thinspace{}
26332 mm is used for separation, because otherwise the output will be ¡ and ¿
26343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26346 \begin_layout Plain Layout
26354 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26357 \begin_layout Plain Layout
26365 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26368 \begin_layout Plain Layout
26369 \begin_inset Formula $\textrm{ø}$
26379 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26382 \begin_layout Plain Layout
26390 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26393 \begin_layout Plain Layout
26394 \begin_inset Formula $\textrm{Ø}$
26404 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26407 \begin_layout Plain Layout
26415 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26418 \begin_layout Plain Layout
26419 \begin_inset Formula $\textrm{ł}$
26429 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26432 \begin_layout Plain Layout
26440 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26443 \begin_layout Plain Layout
26444 \begin_inset Formula $\textrm{Ł}$
26454 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26457 \begin_layout Plain Layout
26459 \begin_inset space \hspace{}
26464 \begin_inset space \textvisiblespace{}
26472 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26475 \begin_layout Plain Layout
26476 \begin_inset Formula $\textrm{!`}$
26486 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26489 \begin_layout Plain Layout
26491 \begin_inset space \hspace{}
26496 \begin_inset space \textvisiblespace{}
26504 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26507 \begin_layout Plain Layout
26508 \begin_inset Formula $\textrm{?`}$
26518 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26521 \begin_layout Plain Layout
26529 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26532 \begin_layout Plain Layout
26533 \begin_inset Formula $\textrm{ȷ}$
26547 \begin_inset space \hfill{}
26553 \begin_layout Standard
26555 \begin_inset Formula $\textrm{\textrm{Å}}$
26559 \begin_inset Formula $\textrm{\textrm{Ø}}$
26562 can also be inserted via the math toolbar button
26565 arg "math-insert \\digamma"
26571 \begin_layout Standard
26572 An exception are the commands
26575 \begin_inset space \hspace{}
26584 \begin_inset space \hspace{}
26590 , because they can be inserted in \SpecialChar LyX
26594 \begin_layout Subsection
26596 \begin_inset CommandInset label
26598 name "subsec:Accents-in-Text"
26603 \begin_inset Index idx
26606 \begin_layout Plain Layout
26615 \begin_layout Standard
26616 With the following commands all letters can be accented.
26617 The commands must be inserted in \SpecialChar TeX
26621 \begin_layout Standard
26622 \begin_inset space \hfill{}
26626 \begin_inset Tabular
26627 <lyxtabular version="3" rows="8" columns="2">
26628 <features booktabs="true" tabularvalignment="middle">
26629 <column alignment="left" valignment="top" width="0pt">
26630 <column alignment="block" valignment="top">
26632 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26635 \begin_layout Plain Layout
26641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26644 \begin_layout Plain Layout
26652 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26655 \begin_layout Plain Layout
26659 \begin_inset Quotes grd
26667 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26670 \begin_layout Plain Layout
26674 \begin_layout Plain Layout
26690 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26693 \begin_layout Plain Layout
26701 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26704 \begin_layout Plain Layout
26708 \begin_layout Plain Layout
26724 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26727 \begin_layout Plain Layout
26731 \begin_inset space \textvisiblespace{}
26739 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26742 \begin_layout Plain Layout
26746 \begin_layout Plain Layout
26762 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26765 \begin_layout Plain Layout
26773 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26776 \begin_layout Plain Layout
26780 \begin_layout Plain Layout
26796 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26799 \begin_layout Plain Layout
26803 \begin_inset space \textvisiblespace{}
26811 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26814 \begin_layout Plain Layout
26818 \begin_layout Plain Layout
26834 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26837 \begin_layout Plain Layout
26841 \begin_inset space \textvisiblespace{}
26849 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26852 \begin_layout Plain Layout
26856 \begin_layout Plain Layout
26872 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26875 \begin_layout Plain Layout
26879 \begin_inset space \textvisiblespace{}
26887 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26890 \begin_layout Plain Layout
26894 \begin_layout Plain Layout
26914 \begin_inset space \hfill{}
26918 \begin_inset Tabular
26919 <lyxtabular version="3" rows="8" columns="2">
26920 <features booktabs="true" tabularvalignment="middle">
26921 <column alignment="left" valignment="top" width="0pt">
26922 <column alignment="center" valignment="top">
26924 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26927 \begin_layout Plain Layout
26933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26936 \begin_layout Plain Layout
26944 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26947 \begin_layout Plain Layout
26951 \begin_inset space \textvisiblespace{}
26959 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26962 \begin_layout Plain Layout
26966 \begin_layout Plain Layout
26982 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26985 \begin_layout Plain Layout
26993 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26996 \begin_layout Plain Layout
27000 \begin_layout Plain Layout
27016 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27019 \begin_layout Plain Layout
27023 \begin_inset Index idx
27026 \begin_layout Plain Layout
27037 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27040 \begin_layout Plain Layout
27044 \begin_layout Plain Layout
27060 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27063 \begin_layout Plain Layout
27071 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27074 \begin_layout Plain Layout
27078 \begin_layout Plain Layout
27094 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27097 \begin_layout Plain Layout
27101 \begin_inset space \textvisiblespace{}
27109 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27112 \begin_layout Plain Layout
27116 \begin_layout Plain Layout
27132 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27135 \begin_layout Plain Layout
27139 \begin_inset space \textvisiblespace{}
27147 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27150 \begin_layout Plain Layout
27154 \begin_layout Plain Layout
27170 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27173 \begin_layout Plain Layout
27177 \begin_inset space \textvisiblespace{}
27185 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27188 \begin_layout Plain Layout
27192 \begin_layout Plain Layout
27212 \begin_inset space \hfill{}
27218 \begin_layout Standard
27219 \begin_inset VSpace medskip
27228 also two different characters can be accented.
27234 \begin_inset space \textvisiblespace{}
27243 \begin_layout Plain Layout
27255 \begin_layout Standard
27268 can in combination with vowels directly be inserted with the keyboard without
27269 using \SpecialChar TeX
27271 The same applies for the tilde
27275 \begin_layout Plain Layout
27276 This only applies for keyboards where the tilde is defined as accent.
27285 in combination with
27300 \begin_layout Standard
27343 and accents that are inserted directly with the keyboard are also available
27344 in mathematical text.
27345 For the other accents there are special math commands to be used in formulas,
27347 \begin_inset CommandInset ref
27349 reference "subsec:Accents-for-one"
27356 \begin_layout Standard
27357 \begin_inset VSpace bigskip
27360 Furthermore, with the command
27367 \begin_inset Index idx
27370 \begin_layout Plain Layout
27378 all numbers and letters can be set into a circle, quasi accented with a
27379 circle, similar to the copyright symbol.
27382 \begin_layout Standard
27384 \begin_inset Tabular
27385 <lyxtabular version="3" rows="3" columns="2">
27386 <features booktabs="true" tabularvalignment="middle">
27387 <column alignment="center" valignment="top" width="0pt">
27388 <column alignment="center" valignment="top">
27390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27393 \begin_layout Plain Layout
27399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27402 \begin_layout Plain Layout
27410 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27413 \begin_layout Plain Layout
27421 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27424 \begin_layout Plain Layout
27428 \begin_layout Plain Layout
27443 <row topspace="1mm">
27444 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27447 \begin_layout Plain Layout
27458 raisebox{-1.5pt}{W}}
27463 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27466 \begin_layout Plain Layout
27470 \begin_layout Plain Layout
27500 \begin_layout Standard
27501 One has to take care that the character fits in the circle.
27512 \begin_layout Plain Layout
27514 \begin_inset CommandInset ref
27516 reference "subsec:Font-Sizes"
27525 specifies thereby the size of the circle.
27536 \begin_layout Plain Layout
27538 \begin_inset CommandInset ref
27540 reference "subsec:Boxes-without-Frame"
27549 the character can be centered.
27552 \begin_layout Subsection
27554 \begin_inset Index idx
27557 \begin_layout Plain Layout
27566 \begin_layout Standard
27567 Old-style figures (also known as old-style numerals) are created with the
27575 \begin_inset Index idx
27578 \begin_layout Plain Layout
27587 The command can be used in formulas and in \SpecialChar TeX
27589 The command scheme is:
27592 \begin_layout Standard
27597 oldstylenums{number}
27600 \begin_layout Standard
27605 oldstylenums{0123456789
27608 \begin_inset Formula $\oldstylenums{0123456789}$
27614 \begin_layout Section
27616 \begin_inset CommandInset label
27618 name "sec:Formula-Styles"
27623 \begin_inset Index idx
27626 \begin_layout Plain Layout
27635 \begin_layout Itemize
27636 There are two different alignment styles:
27637 \begin_inset Separator parbreak
27644 \begin_layout Description
27645 Centered is the predefined standard
27648 \begin_layout Description
27649 Indented for this the option
27653 must be inserted in the menu
27655 Document\SpecialChar menuseparator
27661 \begin_inset space ~
27667 \begin_layout Standard
27672 is used, the indentation can be adjusted with the length
27679 \begin_inset Index idx
27682 \begin_layout Plain Layout
27691 Should the distance be 15
27692 \begin_inset space \thinspace{}
27695 mm, the following command line is inserted in the \SpecialChar LaTeX
27699 \begin_layout Standard
27709 \begin_layout Standard
27710 When no length is specified, the predefined value of 30
27711 \begin_inset space \thinspace{}
27718 \begin_layout Itemize
27719 And two different numbering styles:
27720 \begin_inset Separator parbreak
27727 \begin_layout Description
27728 Right is the predefined standard
27731 \begin_layout Description
27732 Left for this the option
27736 must be inserted in the menu
27738 Document\SpecialChar menuseparator
27744 \begin_inset space ~
27751 \begin_layout Standard
27760 can also be used together.
27761 In this case both options are inserted, separated by a comma.
27764 \begin_layout Standard
27765 The chosen styles are used for all displayed formulas of the document.
27766 When both, centered and indented formulas should be created in a document,
27772 The indented formulas are then set in a flalign environment, see
27773 \begin_inset CommandInset ref
27775 reference "subsec:Flalign-Environment"
27782 \begin_layout Section
27784 \begin_inset CommandInset label
27786 name "sec:Multiline-Formulas"
27791 \begin_inset Index idx
27794 \begin_layout Plain Layout
27795 Formula ! multiline
27803 \begin_layout Subsection
27807 \begin_layout Standard
27808 In \SpecialChar LyX
27809 multiline formulas are created by pressing
27812 arg "newline-insert newline"
27816 This creates either an
27818 eqnarray environment
27820 that is described in
27821 \begin_inset CommandInset ref
27823 reference "subsec:Eqnarray-Environment"
27827 or, when the option
27829 Use AMS math package
27831 in the document settings is selected, an
27835 that is described in
27836 \begin_inset CommandInset ref
27838 reference "subsec:Standard-align-Environment"
27843 The align environment is recommended because it provides in any case a
27844 typographically correct output.
27847 \begin_layout Standard
27848 There are other multiline formula environments that can be created via the
27851 Insert\SpecialChar menuseparator
27855 These environments are described in the following sections.
27858 \begin_layout Standard
27859 In all multiline formula environments a new line is created by pressing
27863 arg "newline-insert newline"
27867 To add or delete lines, the math toolbar buttons
27870 arg "inset-modify tabular append-row"
27876 arg "inset-modify tabular delete-row"
27879 , respectively, or the menu
27881 Edit\SpecialChar menuseparator
27887 \begin_layout Subsubsection
27889 \begin_inset CommandInset label
27891 name "subsec:Line-Separation"
27896 \begin_inset Index idx
27899 \begin_layout Plain Layout
27900 Formula ! multiline ! Line separation
27908 \begin_layout Standard
27909 There is sometimes not enough space in multiline formulas between the lines:
27910 \begin_inset Formula
27912 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}\\
27913 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
27921 \begin_layout Standard
27922 In \SpecialChar LaTeX
27923 additional line space is specified as optional argument of the new line
27925 This is not yet possible in \SpecialChar LyX
27930 \begin_layout Plain Layout
27932 \begin_inset CommandInset href
27934 name "LyX-bug #1505"
27935 target "http://www.lyx.org/trac/ticket/1505"
27944 , therefore the whole formula must be inserted in \SpecialChar TeX
27946 To add in our example space, the command
27954 is inserted at the end of the first line.
27959 \begin_layout Plain Layout
27966 \begin_layout Plain Layout
27968 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27971 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27978 \begin_layout Plain Layout
27982 left(B^{2}+x_{0}^{2}
27990 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27995 \begin_layout Plain Layout
28007 \begin_layout Standard
28008 \begin_inset VSpace bigskip
28011 To set the line separation for all lines in a formula, the length
28018 \begin_inset Index idx
28021 \begin_layout Plain Layout
28031 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
28042 \begin_inset space \thinspace{}
28047 \begin_inset space \thinspace{}
28050 mm additional line separation as in the previous example, the command
28053 \begin_layout Standard
28063 \begin_layout Standard
28064 is inserted in \SpecialChar TeX
28065 mode before the formula.
28066 This requires that the \SpecialChar LaTeX
28075 \begin_layout Plain Layout
28080 is part of every \SpecialChar LaTeX
28081 standard installation.
28087 \begin_inset Index idx
28090 \begin_layout Plain Layout
28096 was loaded in \SpecialChar LaTeX
28097 -preamble with the line
28100 \begin_layout Standard
28108 \begin_layout Standard
28113 \begin_layout Plain Layout
28125 \begin_inset Formula
28127 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}\\
28128 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
28136 \begin_layout Standard
28140 \begin_layout Plain Layout
28151 To get back to the predefined distance,
28157 is set to the value 3
28158 \begin_inset space \thinspace{}
28164 \begin_layout Subsubsection
28166 \begin_inset CommandInset label
28168 name "subsec:Column-Separation"
28173 \begin_inset Index idx
28176 \begin_layout Plain Layout
28177 Formula ! multiline ! Column separation
28185 \begin_layout Standard
28186 Multiline formulas form a matrix.
28187 A formula in the eqnarray environment is for example a matrix with three
28189 By changing the column separation in this environment, the space beside
28190 the relation sign can be changed.
28193 \begin_layout Standard
28194 The column separation is specified with the length
28201 \begin_inset Index idx
28204 \begin_layout Plain Layout
28213 \begin_inset Newline newline
28216 column separation = 2
28217 \begin_inset space \thinspace{}
28227 \begin_inset Newline newline
28233 \begin_layout Standard
28243 \begin_layout Standard
28244 inserted in \SpecialChar TeX
28245 mode, sets for all following formulas a column separation of
28247 \begin_inset space \thinspace{}
28251 To get back to the predefined distance,
28258 \begin_inset space \thinspace{}
28264 \begin_layout Standard
28266 \begin_inset space \thinspace{}
28269 cm column separation:
28273 \begin_layout Plain Layout
28285 \begin_inset Formula
28293 A formula with the predefined column separation for matrices of 10
28294 \begin_inset space \thinspace{}
28301 \begin_layout Plain Layout
28313 \begin_inset Formula
28324 \begin_layout Subsubsection
28326 \begin_inset Index idx
28329 \begin_layout Plain Layout
28338 \begin_layout Standard
28339 Long formulas can be typeset using these methods:
28342 \begin_layout Itemize
28343 When one side of the equation is much shorter than the line width, this
28344 one is chosen for the left side and the right side is typeset over two
28346 \begin_inset Formula
28348 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 \\
28349 & & -\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}
28354 The minus sign at the beginning of the second line does normally not appear
28355 as an operator because it is the first character of the line.
28356 Thus it would not be surrounded by space and could not be distinguished
28357 from the fraction bar.
28359 \begin_inset space \thinspace{}
28362 pt space was inserted behind the minus sign with the command
28372 \begin_layout Plain Layout
28380 \begin_inset CommandInset ref
28382 reference "subsec:Variable-Space"
28392 \begin_inset Index idx
28395 \begin_layout Plain Layout
28406 \begin_layout Itemize
28407 When both sides of the equation are too long, the command
28414 \begin_inset Index idx
28417 \begin_layout Plain Layout
28426 It is inserted in the first column of the first line and causes all further
28427 insertions to overwrite the following columns:
28428 \begin_inset Formula
28430 \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 \\
28431 & & -\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 \\
28432 & & =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}
28437 After the insertion of
28443 , the cursor is in a purple box that is a bit shifted to the left from the
28445 In this the formula is inserted.
28446 \begin_inset Newline newline
28449 The content of the further lines is inserted to the second or another formula
28451 The greater the column number where it was inserted, the larger the indentation.
28452 \begin_inset VSpace medskip
28456 \begin_inset Newline newline
28460 \begin_inset Note Greyedout
28463 \begin_layout Plain Layout
28464 Note the following when using
28473 \begin_layout Itemize
28474 The formula doesn't use the full page width.
28476 \begin_inset space \thinspace{}
28480 \begin_inset space \space{}
28484 \begin_inset Formula $-B^{2}$
28487 is added to the first line in the above example, it would have been outside
28489 To better use the width, negative space can be inserted at the beginning
28493 \begin_layout Itemize
28494 Due to a bug in \SpecialChar LyX
28495 the cursor cannot be set with the mouse into the first
28500 \begin_layout Plain Layout
28501 \begin_inset CommandInset href
28503 name "LyX-bug #1429"
28504 target "http://www.lyx.org/trac/ticket/1429"
28513 One can only set the cursor at the beginning of the line and move it with
28522 \begin_layout Itemize
28523 Other methods to set long formulas are offered by the environments described
28525 \begin_inset CommandInset ref
28527 reference "subsec:Multline-Environment"
28532 \begin_inset CommandInset ref
28534 reference "subsec:Multiline-Formula-Parts"
28541 \begin_layout Subsubsection
28542 Multiline Fractions
28543 \begin_inset CommandInset label
28545 name "subsec:Multiline-Fractions"
28550 \begin_inset Index idx
28553 \begin_layout Plain Layout
28554 Fractions ! multiline
28562 \begin_layout Standard
28563 There are cases where the denominator and/or the numerator of a fraction
28564 is so long that the fraction does not fit into one line.
28565 It is then necessary to add a line break within the fraction.
28566 This can be done using the command
28573 \begin_inset Index idx
28576 \begin_layout Plain Layout
28585 To activate it, set in the document settings under
28588 \begin_inset space ~
28598 \begin_inset Index idx
28601 \begin_layout Plain Layout
28602 Packages ! mathtools
28610 \begin_inset space ~
28625 \begin_layout Standard
28630 splitfrac{first line}{second line}
28633 \begin_layout Standard
28634 and is used as denominator and/or numerator:
28637 \begin_layout Standard
28638 \begin_inset Formula
28640 a=\frac{\splitfrac{xy+xy+xy+xy+xy}{+wy+wy+wy+wy}}{z}\ne\frac{\splitdfrac{xy+\frac{xy}{z}+xy+xy+xy}{+xy+xy+xy+xy}}{z}
28645 The command for the first numerator above is:
28648 \begin_layout Standard
28653 splitfrac{xy+xy+xy+xy+xy
28654 \begin_inset space \textvisiblespace{}
28662 \begin_layout Subsubsection
28664 \begin_inset CommandInset label
28666 name "subsec: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 "subsec:Automatic-Bracket-Size"
28757 \begin_inset Index idx
28760 \begin_layout Plain Layout
28783 \begin_inset space \textvisiblespace{}
28793 \begin_inset space \textvisiblespace{}
28803 \begin_inset space \textvisiblespace{}
28809 \begin_inset Formula $\downarrow$
28815 \begin_inset Index idx
28818 \begin_layout Plain Layout
28826 is inserted, because the multiplication operator with its limits is the
28827 largest symbol in the first line and this should be the size for the bracket
28828 in the second line.
28831 \begin_layout Standard
28832 The result is this:
28833 \begin_inset Formula
28835 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28836 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28844 \begin_layout Subsection
28848 \begin_layout Standard
28849 Align environments can be used for every kind of multiline formulas.
28850 They are especially useful to set several formulas side by side.
28853 \begin_layout Standard
28854 Align environments consist of columns.
28855 The odd columns are right aligned, the even ones left aligned.
28856 Every line in an Align environment can be numbered.
28859 \begin_layout Standard
28860 Align environments are created via the menu
28862 Insert\SpecialChar menuseparator
28868 Edit\SpecialChar menuseparator
28869 Math\SpecialChar menuseparator
28870 Change Formula Type
28872 already existing formulas can be converted to Align environments.
28875 \begin_layout Standard
28876 To add or delete columns, the math toolbar buttons
28879 arg "inset-modify tabular append-column"
28885 arg "inset-modify tabular delete-column"
28888 , respectively, or the menu
28890 Edit\SpecialChar menuseparator
28896 \begin_layout Subsubsection
28897 Standard align Environment
28898 \begin_inset CommandInset label
28900 name "subsec:Standard-align-Environment"
28905 \begin_inset Index idx
28908 \begin_layout Plain Layout
28909 Formula ! multiline ! align environment
28917 \begin_layout Standard
28918 This Align environment is created by pressing
28921 arg "newline-insert newline"
28924 in a formula or by the menu
28926 Insert\SpecialChar menuseparator
28927 Math\SpecialChar menuseparator
28928 AMS align Environment
28933 \begin_layout Standard
28934 An example for two formulas set side by side, that are created with a four
28935 column align environment:
28936 \begin_inset Formula
28938 A & =\sin(B) & C & =D\\
28939 C & \ne A & B & \ne D
28944 As it can be seen, the formulas in this environment are placed so as if
28953 \begin_layout Plain Layout
28961 \begin_inset CommandInset ref
28963 reference "subsec:Variable-Space"
28974 before the first and after every even column.
28975 When the formula style
28981 \begin_layout Plain Layout
28983 \begin_inset CommandInset ref
28985 reference "sec:Formula-Styles"
28996 is used, the formula is set without the
29002 before the first column.
29005 \begin_layout Subsubsection
29006 Alignat Environment
29007 \begin_inset Index idx
29010 \begin_layout Plain Layout
29011 Formula ! multiline ! alignat environment
29019 \begin_layout Standard
29020 The alignat environment has no predefined column separation.
29021 It can be inserted manually with the spaces that are described
29022 \begin_inset CommandInset ref
29024 reference "subsec:Space"
29031 \begin_layout Standard
29032 The above example in the alignat environment where 1
29033 \begin_inset space \thinspace{}
29036 cm space was inserted at the beginning of the second formula:
29037 \begin_inset Formula
29038 \begin{alignat*}{2}
29039 A & =\sin(B) & \hspace{1cm}C & =D\\
29040 C & \ne A & B & \ne D
29045 Because the column separation can be set separately for every column, this
29046 environment is especially suitable to set three and more formulas side
29050 \begin_layout Subsubsection
29051 Flalign Environment
29052 \begin_inset CommandInset label
29054 name "subsec:Flalign-Environment"
29059 \begin_inset Index idx
29062 \begin_layout Plain Layout
29063 Formula ! multiline ! flalign environment
29071 \begin_layout Standard
29072 In this environment the first two columns are always set as much as possible
29073 to the left and the last two ones to the right.
29075 \begin_inset Formula
29077 A & =1 & B & =2 & C & =3\\
29078 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29086 \begin_layout Standard
29087 By creating a flalign environment with an odd number of columns where an
29088 empty \SpecialChar TeX
29089 brace is inserted to the last column, several formulas in a document
29090 can be set to the left, although the formula style
29095 As example the indented formula
29096 \begin_inset CommandInset ref
29098 reference "eq:VolInt"
29103 \begin_inset Formula
29105 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29110 The first two columns contain the formula.
29111 To indent it as with the formula style
29116 \begin_inset space \thinspace{}
29119 pt space was inserted at the beginning of the first column.
29122 \begin_layout Subsection
29123 Eqnarray Environment
29124 \begin_inset CommandInset label
29126 name "subsec:Eqnarray-Environment"
29131 \begin_inset Index idx
29134 \begin_layout Plain Layout
29135 Formula ! multiline ! eqnarray environment
29143 \begin_layout Standard
29144 When this environment has been created, three blue boxes appear.
29145 The content of the first box is right aligned, the content of the last
29147 The content of the middle box appears centered and a bit smaller, because
29148 it is designed to insert there only relation characters.
29149 \begin_inset Formula
29151 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29161 \begin_layout Subsection
29163 \begin_inset Index idx
29166 \begin_layout Plain Layout
29167 Formula ! multiline ! gather environment
29175 \begin_layout Standard
29176 This environment consists of only one centered column.
29177 Every line can be numbered.
29178 \begin_inset Formula
29189 \begin_layout Subsection
29190 Multline Environment
29191 \begin_inset CommandInset label
29193 name "subsec:Multline-Environment"
29198 \begin_inset Index idx
29201 \begin_layout Plain Layout
29202 Formula ! multiline ! multline environment
29210 \begin_layout Standard
29211 The multline environment consists, like the gather environment, of only
29213 But the first line is left aligned, the last one right aligned.
29214 All other lines are centered.
29215 Therefore this environment is suitable for long formulas.
29217 \begin_inset CommandInset ref
29219 reference "eq:lefteqn"
29223 in the multline environment:
29224 \begin_inset Formula
29226 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}\\
29227 -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}\\
29228 =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}}
29236 \begin_layout Standard
29237 In the output only the last (first) line of a multline environment appears
29238 numbered when the document numbering is right (left).
29242 \begin_layout Plain Layout
29243 numbering styles see
29244 \begin_inset CommandInset ref
29246 reference "sec:Formula-Styles"
29258 \begin_layout Standard
29266 \begin_inset Index idx
29269 \begin_layout Plain Layout
29284 \begin_inset Index idx
29287 \begin_layout Plain Layout
29295 a centered line can be right or left aligned, respectively.
29296 The commands are used as follows:
29299 \begin_layout Standard
29304 shoveright{line content}
29310 shoveleft{line content}
29313 \begin_layout Standard
29314 \begin_inset VSpace medskip
29324 \begin_inset Index idx
29327 \begin_layout Plain Layout
29335 specifies the distance of the first line from the left page margin.
29336 Predefined is the length 0
29337 \begin_inset space \thinspace{}
29343 \begin_layout Standard
29344 As example the above formula where the command
29347 \begin_layout Standard
29357 \begin_layout Standard
29358 was inserted in \SpecialChar TeX
29363 \begin_layout Plain Layout
29375 \begin_inset Formula
29377 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}\\
29378 \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}}\\
29379 =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}}
29388 \begin_layout Plain Layout
29399 The second line was left aligned using
29408 \begin_layout Subsection
29409 Multiline Formula Parts
29410 \begin_inset CommandInset label
29412 name "subsec:Multiline-Formula-Parts"
29417 \begin_inset Index idx
29420 \begin_layout Plain Layout
29421 Formula ! multiline ! formula parts
29429 \begin_layout Standard
29430 To display only parts of a formula with multiple lines, one of the following
29431 environments is used:
29448 They can be inserted via the menu
29450 Insert\SpecialChar menuseparator
29453 or by using the commands described in this section.
29456 \begin_layout Standard
29457 The first three have the same properties as the corresponding multiline
29458 formula environments, but it is possible to set further formula parts beside
29461 \begin_inset Formula
29463 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29464 \Delta E\Delta t & \ge\frac{\hbar}{2}
29466 \right\} \textrm{Uncertainty relations}
29474 \begin_layout Standard
29475 To get this formula, a displayed formula is created where the command
29482 \begin_inset Index idx
29485 \begin_layout Plain Layout
29494 A purple box appears around the blue formula box where now columns and
29495 lines can be added.
29496 Outside the multiline environment other formula parts can be set, like
29500 \begin_layout Standard
29501 The aligned environment is also suitable for long formulas whose lines are
29502 horizontally aligned.
29503 Using aligned in a displayed formula has the advantage that the formula
29504 number is vertically centered behind the lines.
29506 \begin_inset CommandInset ref
29508 reference "eq:shortlong"
29512 in the aligned environment:
29513 \begin_inset Formula
29515 \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}|}\\
29516 & -\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}|}
29525 \begin_layout Standard
29526 To use the environments
29545 \begin_inset Index idx
29548 \begin_layout Plain Layout
29563 \begin_inset Index idx
29566 \begin_layout Plain Layout
29581 \begin_inset Index idx
29584 \begin_layout Plain Layout
29592 are inserted, respectively.
29593 The split environment has the same properties as the aligned environment
29594 but it can only have two columns.
29597 \begin_layout Subsection
29598 Text in multiline Formulas
29599 \begin_inset CommandInset label
29601 name "subsec:Text-in-multiline"
29606 \begin_inset Index idx
29609 \begin_layout Plain Layout
29616 \begin_inset Index idx
29619 \begin_layout Plain Layout
29620 Formula ! multiline ! text
29628 \begin_layout Standard
29629 In the Align environments, and the multline and gather environment, text
29630 can be inserted that will appear in a separate line and doesn't affect
29631 the column alignment.
29632 To do this, the command
29639 \begin_inset Index idx
29642 \begin_layout Plain Layout
29650 is used in the following scheme:
29653 \begin_layout Standard
29661 \begin_layout Standard
29662 The text should not be longer than a line because it cannot be hyphenated.
29663 As \SpecialChar LyX
29664 doesn't yet support
29670 directly, the text is written as mathematical text.
29677 must hereby be at the beginning of a line and appears in the output above
29679 An example where the text was inserted at the beginning of the second line:
29680 \begin_inset Formula
29682 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29683 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29691 \begin_layout Standard
29698 always creates some vertical space between the text and the formula lines.
29699 To avoid this space, set in the document settings under
29702 \begin_inset space ~
29712 \begin_inset Index idx
29715 \begin_layout Plain Layout
29716 Packages ! mathtools
29724 \begin_inset space ~
29730 Then you can use the command
29737 \begin_inset Index idx
29740 \begin_layout Plain Layout
29757 \begin_layout Standard
29758 \begin_inset Formula
29760 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29761 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29769 \begin_layout Section
29771 \begin_inset Index idx
29774 \begin_layout Plain Layout
29781 \begin_inset Index idx
29784 \begin_layout Plain Layout
29785 Formula ! numbering|see
29789 \begin_layout Plain Layout
29800 \begin_layout Plain Layout
29815 \begin_layout Subsection
29819 \begin_layout Standard
29820 Numbered formulas can be created with the menu
29822 Insert\SpecialChar menuseparator
29823 Math\SpecialChar menuseparator
29825 \begin_inset space ~
29833 \begin_inset space ~
29839 Existing formulas can be numbered with the menu
29841 Edit\SpecialChar menuseparator
29842 Math\SpecialChar menuseparator
29844 \begin_inset space ~
29852 arg "math-number-toggle"
29856 The formula number is displayed in \SpecialChar LyX
29857 behind the formula as a number sign
29859 The number sign is replaced in the output by the formula number.
29862 \begin_layout Standard
29863 When numbering is turned on in multiline formulas, all lines will be numbered.
29864 But the numbering can be controlled with the menu
29866 Edit\SpecialChar menuseparator
29867 Math\SpecialChar menuseparator
29869 \begin_inset space ~
29873 \begin_inset space ~
29877 \begin_inset space ~
29885 arg "math-number-line-toggle"
29891 \begin_layout Standard
29892 Except for inline formulas, all formulas can be numbered with two different
29894 \begin_inset CommandInset ref
29896 reference "sec:Formula-Styles"
29903 \begin_layout Subsection
29905 \begin_inset Index idx
29908 \begin_layout Plain Layout
29909 Cross-references ! to formulas
29917 \begin_layout Standard
29918 All labeled formulas can be cross-referenced.
29919 A label is added by the menu
29921 Insert\SpecialChar menuseparator
29924 or the toolbar button
29931 The cursor must hereby be inside a displayed formula.
29932 Alternatively you can right-click on the formula and choose
29937 A dialog pops up displaying the prefix
29942 The label is inserted there behind the prefix.
29943 The predefined prefix means
29944 \begin_inset Quotes eld
29948 \begin_inset Quotes erd
29951 and makes it easier to find labels in large documents because it marks
29952 it as formula label to divide it from e.
29953 \begin_inset space \thinspace{}
29957 \begin_inset space \space{}
29961 To change a label, the menu
29963 Insert\SpecialChar menuseparator
29966 is used again or you right-click on a formula and then on
29973 \begin_layout Standard
29974 The name of the label is displayed in \SpecialChar LyX
29975 within two parentheses behind formula.
29976 A formula with a label is always numbered.
29979 \begin_layout Standard
29980 Cross-references are inserted via the menu
29982 Insert\SpecialChar menuseparator
29985 or with the toolbar button
29988 arg "dialog-show-new-inset ref"
29992 A formula cross-reference appears in the output as formula number.
29993 When in the cross-reference dialog window the format
29997 is chosen, the cross-reference appears in the output as formula number
29999 \begin_inset Newline newline
30002 By right-clicking on a cross-reference in \SpecialChar LyX
30003 , one jumps to the formula that
30007 \begin_layout Standard
30008 Here are as examples cross-references to formulas of the following subsections:
30009 \begin_inset Note Note
30012 \begin_layout Plain Layout
30013 Note the different cross-reference types.
30021 \begin_layout Standard
30023 \begin_inset CommandInset ref
30030 \begin_inset CommandInset ref
30038 \begin_inset CommandInset ref
30044 ) big Latin letters are used for the numbering in contrary to (
30045 \begin_inset CommandInset ref
30054 \begin_layout Standard
30055 \begin_inset VSpace medskip
30058 When the argument of
30066 \begin_layout Plain Layout
30074 \begin_inset CommandInset ref
30076 reference "subsec:User-defined-Numbering"
30087 contains a box like in
30088 \begin_inset CommandInset ref
30090 reference "subsec:Paragraph-Boxes"
30094 , the formula cannot be referenced.
30097 \begin_layout Subsection
30099 \begin_inset Index idx
30102 \begin_layout Plain Layout
30103 Formula numbering ! subnumbering
30111 \begin_layout Standard
30112 With the help of the commands
30116 begin{subequations}
30124 formulas can be subnumbered.
30125 Both commands are inserted in \SpecialChar TeX
30129 \begin_layout Standard
30131 \begin_inset Formula
30142 \begin_layout Plain Layout
30146 addtocounter{equation}{-1}
30155 \begin_layout Plain Layout
30159 begin{subequations}
30165 \begin_inset VSpace -5mm
30169 \begin_inset Formula
30177 \begin_inset Formula
30187 \begin_layout Standard
30191 \begin_layout Plain Layout
30203 \begin_layout Standard
30204 To create the example, the following is done:
30207 \begin_layout Enumerate
30208 first formula is inserted
30211 \begin_layout Enumerate
30216 addtocounter{equation}{-1}
30218 begin{subequations}
30219 \begin_inset Index idx
30222 \begin_layout Plain Layout
30231 \begin_inset Newline newline
30236 is inserted after the first formula
30239 \begin_layout Enumerate
30240 second formula is inserted
30243 \begin_layout Enumerate
30244 third formula is inserted
30247 \begin_layout Enumerate
30254 is inserted after the third formula
30257 \begin_layout Standard
30258 Every formula between the commands
30270 is subnumbered as a, b,
30271 \begin_inset Newline linebreak
30274 c, \SpecialChar ldots
30275 For multiline formulas every line will be subnumbered.
30276 All subnumbered formulas are treated as
30281 But as every numbered formula increases the counter
30285 by one, the command
30291 is needed to decrease it.
30292 Otherwise the formulas
30293 \begin_inset CommandInset ref
30300 \begin_inset CommandInset ref
30307 \begin_inset CommandInset ref
30313 would be numbered as
30314 \begin_inset CommandInset ref
30321 \begin_inset CommandInset ref
30328 \begin_inset CommandInset ref
30337 \begin_layout Standard
30338 By inserting the commands in \SpecialChar TeX
30339 mode, a space is created between the first
30342 \begin_inset space \thinspace{}
30345 mm vertical space is inserted after the command
30349 begin{subequations}
30352 When the formula style
30358 \begin_layout Plain Layout
30360 \begin_inset CommandInset ref
30362 reference "sec:Formula-Styles"
30374 \begin_inset space \thinspace{}
30377 mm space is inserted instead.
30380 \begin_layout Standard
30381 Here is an example for a multiline formula where the numbering was turned
30382 off for the second line:
30386 \begin_layout Plain Layout
30390 begin{subequations}
30396 \begin_inset Formula
30398 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30399 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30400 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30409 \begin_layout Plain Layout
30421 \begin_layout Subsection
30422 User-defined Numbering
30423 \begin_inset CommandInset label
30425 name "subsec:User-defined-Numbering"
30430 \begin_inset Index idx
30433 \begin_layout Plain Layout
30434 Formula numbering ! user-defined
30442 \begin_layout Standard
30443 \begin_inset Index idx
30446 \begin_layout Plain Layout
30447 Formula numbering ! self-defined delimiters
30452 With the standard numbering parentheses are set around the formula number.
30453 To replace the parentheses for example by vertical bars, the following
30454 line is added to the \SpecialChar LaTeX
30458 \begin_layout Standard
30470 \begin_inset Note Note
30473 \begin_layout Plain Layout
30474 This macro is already declared in the \SpecialChar LaTeX
30475 -preamble for testing.
30476 To activate it, remove the percent sign at the beginning.
30484 \begin_layout Standard
30485 To use other characters, the vertical bars besides the
30489 are replaced by one ore more characters.
30490 To get only the formula number the vertical bars are omitted.
30493 \begin_layout Standard
30494 \begin_inset VSpace bigskip
30497 When there should be an expression of your choice instead of the consecutive
30498 formula number in parentheses behind the formula, the command
30505 \begin_inset Index idx
30508 \begin_layout Plain Layout
30517 \begin_inset Formula
30519 A+B=C\tag{something}\label{eq:tag}
30524 In this example the command
30529 \begin_inset space \textvisiblespace{}
30534 was inserted in the formula.
30537 \begin_layout Standard
30543 \begin_inset space \textvisiblespace{}
30548 is inserted instead, the star prevents the parentheses around the expression:
30549 \begin_inset Formula
30551 A+B=C\tag*{something}
30559 \begin_layout Standard
30560 \begin_inset VSpace bigskip
30563 To restart the formula numbering with new document parts or sections, the
30564 following command is used:
30567 \begin_layout Standard
30572 @addtoreset{equation}{part}
30575 \begin_inset Index idx
30578 \begin_layout Plain Layout
30583 \begin_layout Plain Layout
30594 \begin_layout Plain Layout
30607 \begin_layout Plain Layout
30618 \begin_layout Plain Layout
30631 \begin_inset Newline newline
30635 \begin_inset Newline newline
30642 @addtoreset{equation}{section}
30645 \begin_layout Standard
30646 To be able to use these commands in \SpecialChar TeX
30648 \begin_inset Quotes eld
30652 \begin_inset Quotes erd
30655 character has to be made
30656 \begin_inset Quotes eld
30660 \begin_inset Quotes erd
30663 for \SpecialChar LaTeX
30678 So the command sequence in \SpecialChar TeX
30682 \begin_layout Standard
30688 \begin_inset Newline newline
30693 @addtoreset{equation}{section}
30694 \begin_inset Newline newline
30702 \begin_layout Standard
30703 In the \SpecialChar LaTeX
30716 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30720 \begin_layout Standard
30735 \begin_layout Plain Layout
30740 is part of the \SpecialChar LaTeX
30746 \begin_inset Index idx
30749 \begin_layout Plain Layout
30750 Packages ! carlisle
30755 that is part of every \SpecialChar LaTeX
30756 standard installation.
30762 \begin_inset Index idx
30765 \begin_layout Plain Layout
30766 Packages ! remreset
30771 has to be loaded in the \SpecialChar LaTeX
30772 -preamble with the line
30775 \begin_layout Standard
30780 usepackage{remreset}
30783 \begin_layout Standard
30791 \begin_inset Index idx
30794 \begin_layout Plain Layout
30799 \begin_layout Plain Layout
30810 \begin_layout Plain Layout
30823 \begin_layout Plain Layout
30834 \begin_layout Plain Layout
30846 can be used with the same scheme as
30855 \begin_layout Standard
30856 \begin_inset VSpace bigskip
30859 Sometimes formulas should be numbered in the following form:
30862 \begin_layout Standard
30865 (section number.formula number)
30868 \begin_layout Standard
30869 The formula number should start with every section with
30870 \begin_inset Quotes eld
30874 \begin_inset Quotes erd
30880 \begin_layout Standard
30881 For this case there is the command
30888 \begin_inset Index idx
30891 \begin_layout Plain Layout
30899 , which is used with the following scheme:
30902 \begin_layout Standard
30907 numberwithin{counter}{sectioning}
30910 \begin_layout Standard
30911 Counter denotes what kind of numbering is affected, sectioning denotes what
30912 number is before the dot.
30915 \begin_layout Standard
30916 Thus in our case the following \SpecialChar LaTeX
30917 preamble or \SpecialChar TeX
30921 \begin_layout Standard
30926 numberwithin{equation}{section}
30929 \begin_layout Standard
30930 This is the result:
30934 \begin_layout Plain Layout
30938 numberwithin{equation}{section}
30944 \begin_inset Formula
30954 \begin_layout Standard
30956 \begin_inset space \thinspace{}
30960 \begin_inset space \space{}
30963 tables so that the number of the part is the sectioning,
30964 \begin_inset Newline newline
30971 numberwithin{table}{part}
30976 \begin_layout Standard
30977 To go back to the standard numbering or to prevent this kind of numbering
30978 when it is defined by the document class, the following command is inserted
30979 as \SpecialChar TeX
30980 code or to the \SpecialChar LaTeX
30984 \begin_layout Standard
30994 \begin_inset Index idx
30997 \begin_layout Plain Layout
31011 \begin_layout Plain Layout
31027 \begin_inset Newline newline
31035 \begin_inset Newline newline
31047 \begin_layout Standard
31054 uses internally the command
31060 , described above, that also needs to be reverted.
31064 \begin_layout Plain Layout
31071 \begin_layout Plain Layout
31075 @removefromreset{equation}{section}
31078 \begin_layout Plain Layout
31090 \begin_layout Subsection
31091 Numbering with Roman Numbers and Letters
31092 \begin_inset Index idx
31095 \begin_layout Plain Layout
31096 Formula numbering ! with letters
31102 \begin_inset Index idx
31105 \begin_layout Plain Layout
31106 Formula numbering ! with Roman numbers
31114 \begin_layout Standard
31115 Formulas can also be numbered with Roman numbers and Latin letters.
31116 To number for example with small Roman numbers, the command
31119 \begin_layout Standard
31131 \begin_layout Standard
31132 is inserted before the formula in \SpecialChar TeX
31141 \begin_inset Index idx
31144 \begin_layout Plain Layout
31152 redefines the predefined command
31168 \begin_layout Plain Layout
31175 has the same scheme like the command
31181 that is described in
31182 \begin_inset CommandInset ref
31184 reference "subsec:The-Command-newcommand"
31197 is the formula counter.
31204 is used as prefix for a counter, the value of the counter is output as
31206 When a formula is numbered, \SpecialChar LaTeX
31207 sets internally the command
31213 behind the formula.
31219 \begin_inset Index idx
31222 \begin_layout Plain Layout
31232 outputs the counter as small Roman number.
31235 \begin_layout Standard
31236 All formulas behind the command
31246 are now numbered Roman.
31247 To switch to numbering with big Roman numbers, the command is inserted
31261 \begin_inset Index idx
31264 \begin_layout Plain Layout
31276 \begin_inset Quotes eld
31280 \begin_inset Quotes erd
31283 with small Latin letters there is the command
31290 \begin_inset Index idx
31293 \begin_layout Plain Layout
31301 , for big ones there is the command
31308 \begin_inset Index idx
31311 \begin_layout Plain Layout
31324 \begin_layout Standard
31325 \begin_inset Note Greyedout
31328 \begin_layout Plain Layout
31335 \begin_inset space ~
31338 formulas can be numbered with Latin letters in one document.
31346 \begin_layout Standard
31350 \begin_layout Plain Layout
31366 \begin_layout Standard
31367 \begin_inset Formula
31369 A=\textrm{small roman}
31378 \begin_layout Plain Layout
31392 \begin_inset Formula
31394 B=\textrm{big Roman}\label{eq:Rom}
31403 \begin_layout Plain Layout
31417 \begin_inset Formula
31419 C=\textrm{small Latin}
31428 \begin_layout Plain Layout
31442 \begin_inset Formula
31444 D=\textrm{big Latin}\label{eq:Lat}
31452 \begin_layout Standard
31453 To switch back to the default numbering, insert the command:
31456 \begin_layout Standard
31466 \begin_inset Index idx
31469 \begin_layout Plain Layout
31480 \begin_layout Standard
31484 \begin_layout Plain Layout
31498 \begin_inset Formula
31508 \begin_layout Standard
31509 \begin_inset VSpace medskip
31512 As you see, formulas are numbered serially independent from the numbering
31514 When then numbering should start with
31515 \begin_inset Quotes eld
31519 \begin_inset Quotes erd
31522 when the style is changed, new equation counters have to be defined.
31523 A description about this can be found in the file
31524 \begin_inset CommandInset href
31526 name "Formula-numbering.lyx"
31527 target "run:Formula-numbering.lyx"
31534 \begin_layout Section
31535 Chemical Symbols and Equations
31536 \begin_inset CommandInset label
31538 name "subsec:Chemical-Symbols-and"
31543 \begin_inset Index idx
31546 \begin_layout Plain Layout
31547 Chemical characters ! Symbols
31553 \begin_inset Index idx
31556 \begin_layout Plain Layout
31563 \begin_inset Index idx
31566 \begin_layout Plain Layout
31575 \begin_layout Standard
31576 An example text from chemistry:
31579 \begin_layout Quote
31581 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31584 -ion reacts with two
31585 \begin_inset Formula $\mathrm{Na^{+}}$
31588 -ions to sodium sulfate
31589 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31593 The chemical equation for this is:
31594 \begin_inset Formula
31596 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31604 \begin_layout Standard
31605 This chemical equation can directly be created as formula.
31606 To avoid that the symbols appear italic, everything is highlighted and
31607 changed by the shortcut
31613 to the upright font style.
31617 \begin_layout Plain Layout
31623 \begin_inset CommandInset ref
31625 reference "subsec:Font-Styles"
31637 \begin_layout Standard
31638 A more convenient way to typeset chemical formulas is to use the command
31646 \begin_inset Index idx
31649 \begin_layout Plain Layout
31657 that is available when the \SpecialChar LaTeX
31663 \begin_inset Index idx
31666 \begin_layout Plain Layout
31679 to a formula a new blue box appears where chemical formulas can be inserted
31680 in an intuitive way.
31681 \begin_inset Separator parbreak
31687 \begin_layout Standard
31689 \begin_inset Tabular
31690 <lyxtabular version="3" rows="10" columns="2">
31691 <features booktabs="true" tabularvalignment="middle">
31692 <column alignment="center" valignment="top" width="0pt">
31693 <column alignment="center" valignment="top">
31695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31698 \begin_layout Plain Layout
31704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31707 \begin_layout Plain Layout
31715 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31718 \begin_layout Plain Layout
31722 \begin_inset space \textvisiblespace{}
31730 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31733 \begin_layout Plain Layout
31734 \begin_inset Formula $\ce{H2CO3}$
31743 <row topspace="1.5mm">
31744 <cell alignment="center" valignment="top" usebox="none">
31747 \begin_layout Plain Layout
31751 \begin_inset space \textvisiblespace{}
31759 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31762 \begin_layout Plain Layout
31763 \begin_inset Formula $\ce{SO4^{2-}}$
31772 <row topspace="1.5mm">
31773 <cell alignment="center" valignment="top" usebox="none">
31776 \begin_layout Plain Layout
31780 \begin_inset space \textvisiblespace{}
31788 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31791 \begin_layout Plain Layout
31792 \begin_inset Formula $\ce{(NH4)2S}$
31801 <row topspace="1.5mm">
31802 <cell alignment="center" valignment="top" usebox="none">
31805 \begin_layout Plain Layout
31809 \begin_inset space \textvisiblespace{}
31817 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31820 \begin_layout Plain Layout
31821 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31830 <row topspace="1.5mm">
31831 <cell alignment="center" valignment="top" usebox="none">
31834 \begin_layout Plain Layout
31838 \begin_inset space \textvisiblespace{}
31844 \begin_inset space \textvisiblespace{}
31850 \begin_inset space \textvisiblespace{}
31858 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31861 \begin_layout Plain Layout
31862 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31871 <row topspace="1.5mm">
31872 <cell alignment="center" valignment="top" usebox="none">
31875 \begin_layout Plain Layout
31879 \begin_inset space \textvisiblespace{}
31883 \begin_inset Formula $\downarrow$
31887 \begin_inset Formula $\to$
31895 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31898 \begin_layout Plain Layout
31899 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31909 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31912 \begin_layout Plain Layout
31916 \begin_inset space \textvisiblespace{}
31922 \begin_inset space \textvisiblespace{}
31928 \begin_inset space \textvisiblespace{}
31936 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31939 \begin_layout Plain Layout
31940 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31953 \begin_layout Plain Layout
31957 \begin_inset space \textvisiblespace{}
31961 \begin_inset space \textvisiblespace{}
31965 \begin_inset space \textvisiblespace{}
31969 \begin_inset space \textvisiblespace{}
31973 \begin_inset space \textvisiblespace{}
31981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31984 \begin_layout Plain Layout
31985 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31994 <row topspace="1.5mm">
31995 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31998 \begin_layout Plain Layout
32002 \begin_inset space \textvisiblespace{}
32006 \begin_inset space \textvisiblespace{}
32010 \begin_inset space \textvisiblespace{}
32014 \begin_inset space \textvisiblespace{}
32022 \begin_inset space \textvisiblespace{}
32030 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
32033 \begin_layout Plain Layout
32034 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
32050 \begin_layout Standard
32051 \begin_inset Note Greyedout
32054 \begin_layout Plain Layout
32060 It is not possible in \SpecialChar LyX
32061 to use the character ^ to get an up-arrow as described
32067 One instead uses a negative thin space followed by the command
32074 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32085 \begin_layout Standard
32092 the command for equation
32093 \begin_inset space ~
32097 \begin_inset CommandInset ref
32099 reference "eq:chem-reaction"
32104 \begin_inset Newline newline
32112 \begin_inset space \textvisiblespace{}
32116 \begin_inset space \textvisiblespace{}
32120 \begin_inset space \textvisiblespace{}
32124 \begin_inset space \textvisiblespace{}
32128 \begin_inset space \textvisiblespace{}
32132 \begin_inset space \textvisiblespace{}
32138 \begin_layout Standard
32139 To create multiline chemical equations first a multiline formula is created
32141 \begin_inset CommandInset ref
32143 reference "sec:Multiline-Formulas"
32148 Afterwards the command
32154 is used in every small blue box of the formula.
32156 \begin_inset CommandInset ref
32158 reference "eq:TEOS-reaction-1"
32163 \begin_inset CommandInset ref
32165 reference "eq:TEOS-reaction-2"
32169 are an example of a multi-stage chemical reaction where every equation
32170 has its own number.
32171 \begin_inset Formula
32173 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32174 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32182 \begin_layout Standard
32193 package provides the command
32200 \begin_inset Index idx
32203 \begin_layout Plain Layout
32211 that has to be used for special cases.
32212 For more information about
32218 and more examples have a look at the documentation of
32223 \begin_inset CommandInset citation
32232 \begin_layout Section
32236 \begin_layout Standard
32238 supports two types of commutative diagrams:
32246 that are explained in the following.
32249 \begin_layout Subsection
32251 \begin_inset Index idx
32254 \begin_layout Plain Layout
32263 \begin_layout Standard
32264 Diagrams of this type visualize relations by vertical and horizontal lines
32266 \begin_inset Formula
32268 \begin{CD}A@>>>B@>>>C\\
32279 \begin_layout Standard
32280 To get them, the command
32285 \begin_inset Index idx
32288 \begin_layout Plain Layout
32298 is inserted to a formula.
32299 A blue box appears with two dashed lines where further commands can be
32304 arg "newline-insert newline"
32307 a new line is created.
32308 Horizontal relations are inserted in odd, vertical in even formula lines.
32311 \begin_layout Standard
32312 To create the relations there are the following commands:
32315 \begin_layout Itemize
32320 creates a left arrow,
32331 \begin_layout Itemize
32336 creates an up arrow,
32344 a vertical equal sign
32347 \begin_layout Itemize
32353 is a placeholder for non-existent relations
32356 \begin_layout Standard
32357 All arrows can be labeled as follows:
32360 \begin_layout Itemize
32361 If text inserted between the first and second < or >, resp., it is placed
32363 When it is inserted between the second and third one, it appears under
32367 \begin_layout Itemize
32368 When text for vertical arrows is inserted between the first and second A
32369 or V, resp., it is placed left beside the arrow.
32370 When it is inserted between the second and third one, it appears right
32372 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32376 \begin_layout Standard
32377 As example a diagram with all possible relations:
32380 \begin_layout Standard
32381 \begin_inset Formula
32383 \begin{CD}A@>j>>B@>>k>C@=F\\
32394 \begin_layout Standard
32395 The command for this is:
32396 \begin_inset Newline newline
32404 \begin_inset space \textvisiblespace{}
32407 A@>j>>B@>>k>C@=F Ctrl+Return
32408 \begin_inset Newline newline
32412 \begin_inset Phantom HPhantom
32415 \begin_layout Plain Layout
32421 \begin_inset space \textvisiblespace{}
32434 \begin_inset Formula $\to$
32440 \begin_inset Newline newline
32444 \begin_inset Phantom HPhantom
32447 \begin_layout Plain Layout
32453 \begin_inset space \textvisiblespace{}
32464 \begin_layout Subsection
32466 \begin_inset Index idx
32469 \begin_layout Plain Layout
32470 Diagrams ! xymatrix
32478 \begin_layout Standard
32479 To be able to use xymatrices, the \SpecialChar LaTeX
32485 A xymatrix is created by inserting the command
32492 Then you are able to add new matrix columns and rows like for normal matrices,
32494 \begin_inset CommandInset ref
32496 reference "sec:Matrices"
32503 \begin_layout Standard
32504 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32506 All possibilities to create commutative diagrams and decorations are explained
32511 that you find in the menu
32513 Help\SpecialChar menuseparator
32515 \begin_inset space ~
32523 \begin_layout Subsection
32529 \begin_inset Index idx
32532 \begin_layout Plain Layout
32541 \begin_layout Standard
32546 -diagrams, the \SpecialChar LaTeX
32556 -diagram is created by inserting the command
32563 Then you are able to add new matrix columns and rows like for normal matrices,
32565 \begin_inset CommandInset ref
32567 reference "sec:Matrices"
32574 \begin_layout Standard
32575 Examples how to create
32579 diagrams in \SpecialChar LyX
32582 Feynman-diagram manual
32584 that you find in the menu
32586 Help\SpecialChar menuseparator
32588 \begin_inset space ~
32596 \begin_layout Standard
32597 \begin_inset Newpage newpage
32603 \begin_layout Section
32604 User-defined Commands
32605 \begin_inset Index idx
32608 \begin_layout Plain Layout
32609 User-defined commands
32617 \begin_layout Standard
32618 \begin_inset Note Greyedout
32621 \begin_layout Plain Layout
32626 The names of user-defined commands and macros may only consist of Latin
32635 \begin_layout Subsection
32639 \begin_inset CommandInset label
32641 name "subsec:The-Command-newcommand"
32646 \begin_inset Index idx
32649 \begin_layout Plain Layout
32650 User-defined commands !
32658 \begin_inset Index idx
32661 \begin_layout Plain Layout
32672 \begin_layout Standard
32673 Many \SpecialChar LaTeX
32674 -commands are too long to be used frequently.
32675 But it is possible to define with the command
32681 new shorter commands.
32684 \begin_layout Standard
32685 The command scheme of
32694 \begin_layout Standard
32699 newcommand{new command name}[number of arguments][optional
32704 \begin_inset Newline newline
32708 \begin_inset Phantom HPhantom
32711 \begin_layout Plain Layout
32721 {command definition}
32724 \begin_layout Standard
32725 \begin_inset Note Greyedout
32728 \begin_layout Plain Layout
32733 Assure that the name of the new command is not already used in your document
32734 or by \SpecialChar LaTeX
32735 -packages that you use.
32736 When you for example define the command
32748 , you get an error message because
32754 is already defined as command for
32755 \begin_inset Quotes eld
32759 \begin_inset Formula $\le$
32763 \begin_inset Quotes erd
32774 \begin_layout Standard
32775 The number of arguments is an integer in the range 0
32776 \begin_inset space \thinspace{}
32780 \begin_inset space \thinspace{}
32783 9 and specifies how many arguments the new command should have.
32784 With the optional value a value for an optional argument can be predefined.
32785 When this is done, the
32793 rgument of the new command is automatically an optional one.
32796 \begin_layout Standard
32797 Here are some examples:
32800 \begin_layout Itemize
32801 To define the command
32813 , the \SpecialChar LaTeX
32815 \begin_inset VSpace medskip
32819 \begin_inset Newline newline
32833 \begin_layout Itemize
32834 To define the command
32846 , the argument (that should be underlined) must be taken into account.
32847 For this the preamble line is:
32848 \begin_inset VSpace medskip
32852 \begin_inset Newline newline
32866 \begin_inset VSpace medskip
32870 \begin_inset Newline newline
32877 acts as argument placeholder, the
32881 behind it denotes that it is the placeholder for the first argument.
32884 \begin_layout Itemize
32892 \begin_inset space \thinspace{}
32896 \begin_inset space \space{}
32906 \begin_inset VSpace medskip
32910 \begin_inset Newline newline
32921 framebox#1#2{$#3$}}
32924 \begin_inset VSpace medskip
32928 \begin_inset Newline newline
32931 The two Dollar signs creates the extra formula needed for
32938 \begin_inset CommandInset ref
32940 reference "subsec:Boxes-with-Frame"
32947 \begin_layout Itemize
32948 To create a new command for
32954 where the color for the box need not be specified, the argument for the
32955 color is defined optional:
32956 \begin_inset VSpace medskip
32960 \begin_inset Newline newline
32971 fcolorbox{#2}{#1}{$#3$}}
32974 \begin_inset VSpace medskip
32978 \begin_inset Newline newline
32981 When the color is not specified when using
32987 , the predefined color
32994 \begin_layout Standard
32995 A test of the new defined commands:
32996 \begin_inset Separator parbreak
33002 \begin_layout Standard
33004 \begin_inset Tabular
33005 <lyxtabular version="3" rows="6" columns="2">
33006 <features booktabs="true" tabularvalignment="middle">
33007 <column alignment="center" valignment="top" width="0pt">
33008 <column alignment="center" valignment="top">
33010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33013 \begin_layout Plain Layout
33019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33022 \begin_layout Plain Layout
33030 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33033 \begin_layout Plain Layout
33037 \begin_inset space \textvisiblespace{}
33045 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33048 \begin_layout Plain Layout
33049 \begin_inset Formula $A\gr B$
33059 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33062 \begin_layout Plain Layout
33070 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33073 \begin_layout Plain Layout
33074 \begin_inset Formula $\us{ABcd}$
33083 <row topspace="1mm">
33084 <cell alignment="center" valignment="top" usebox="none">
33087 \begin_layout Plain Layout
33091 \begin_inset Formula $\to$
33097 \begin_inset Formula $\to$
33105 \begin_inset space \textvisiblespace{}
33113 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33116 \begin_layout Plain Layout
33117 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33126 <row topspace="1.5mm">
33127 <cell alignment="center" valignment="top" usebox="none">
33130 \begin_layout Plain Layout
33134 \begin_inset Formula $\to$
33142 \begin_inset space \textvisiblespace{}
33150 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33153 \begin_layout Plain Layout
33154 \begin_inset Formula $\cb{red}{\int A=B}$
33163 <row topspace="1.5mm" bottomspace="1mm">
33164 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33167 \begin_layout Plain Layout
33173 \begin_inset Formula $\to$
33181 \begin_inset space \textvisiblespace{}
33189 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33192 \begin_layout Plain Layout
33193 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33209 \begin_layout Subsection
33211 \begin_inset Index idx
33214 \begin_layout Plain Layout
33215 User-defined commands! Math macros
33221 \begin_inset Index idx
33224 \begin_layout Plain Layout
33233 \begin_layout Standard
33234 User-defined commands are especially convenient for complex expressions.
33235 When you are for example dealing with a document that has quadratic equations,
33236 the same solution type occurs several times.
33237 The general form of a quadratic equation is
33238 \begin_inset Formula
33240 0=\lambda^{2}+p\lambda+q
33245 The general form of the solution is
33246 \begin_inset Formula
33248 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33256 \begin_layout Standard
33257 To define a command for the solution formula where only the three parameters
33259 \begin_inset Formula $\lambda$
33263 \begin_inset Formula $p$
33267 \begin_inset Formula $q$
33270 need to be specified and the index of
33271 \begin_inset Formula $\lambda$
33274 can be given optionally, the \SpecialChar LaTeX
33276 \begin_inset Newline newline
33292 \begin_inset Newline newline
33296 \begin_inset Phantom HPhantom
33299 \begin_layout Plain Layout
33313 frac{#3^{2}}{4}-#4}}
33316 \begin_layout Standard
33317 To create with this the solution formula, the command
33318 \begin_inset Newline newline
33328 \begin_inset Formula $\to$
33334 \begin_inset Formula $\to$
33341 is inserted to a formula
33346 \begin_layout Standard
33347 The definition of the new command is unintuitive because one has to know
33348 the schemes of all used \SpecialChar LaTeX
33350 \begin_inset space \thinspace{}
33354 \begin_inset space \space{}
33357 that a fraction is inserted in \SpecialChar LaTeX
33362 frac{numerator}{denominator}
33365 Furthermore one can easily forget a brace in the definition and cannot
33366 see in \SpecialChar LyX
33367 what the new command is doing.
33368 To avoid these problems \SpecialChar LyX
33369 offers the possibility to use math macros instead
33379 \begin_layout Standard
33380 A math macro is created by using the menu
33382 Insert\SpecialChar menuseparator
33383 Math\SpecialChar menuseparator
33386 or the toolbar button
33389 arg "math-macro newmacroname_newcommand"
33393 The math macro toolbar appears together with the following box where the
33395 \begin_inset Newline newline
33399 \begin_inset space \hspace*{\fill}
33403 \begin_inset Graphics
33404 filename clipart/macrobox.png
33410 \begin_inset space \hspace*{\fill}
33414 \begin_inset Newline newline
33418 \begin_inset FormulaMacro
33419 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33424 newmacroname is the default name of the macro that should be changed to
33425 something sensible.
33426 The wanted formula is inserted in the first blue box.
33427 An argument placeholder is inserted with the command
33434 \begin_inset space \thinspace{}
33438 \begin_inset space \space{}
33447 or by using the macro toolbar button
33450 arg "math-macro-add-param"
33454 Argument placeholders are displayed red.
33456 \begin_inset space ~
33459 arguments are possible.
33460 Optional arguments are created with the toolbar button
33463 arg "math-macro-add-optional-param"
33467 The first non-optional argument can be transformed to an optional one with
33471 arg "math-macro-make-optional"
33475 In the second blue box the appearance of the macro in \SpecialChar LyX
33477 Normally you want to see it as it is defined, so the box is kept empty.
33478 But when you have created a macro that needs lot of space on the screen,
33479 you can insert in the box for example
33480 \begin_inset Newline newline
33510 \begin_inset Newline newline
33515 For the macro only the arguments with the macro name in front of them will
33516 then be displayed in \SpecialChar LyX
33517 , leading to a better overview.
33518 The formula appears in the output as defined in the first box.
33519 \begin_inset Newline newline
33522 The appearance of macros in formulas can furthermore be changed for single
33523 macros by setting the cursor in the macro and using the menu
33525 View\SpecialChar menuseparator
33527 \begin_inset space ~
33531 \begin_inset space ~
33539 \begin_layout Standard
33540 To use a macro, the macro name is inserted as command to a formula, in our
33548 Our macro looks in \SpecialChar LyX
33550 \begin_inset Newline newline
33554 \begin_inset space \hspace*{\fill}
33558 \begin_inset Graphics
33559 filename clipart/macrouse.png
33565 \begin_inset space \hspace*{\fill}
33569 \begin_inset Newline newline
33572 Here is our macro example with the arguments
33573 \begin_inset Formula $x$
33577 \begin_inset Formula $\ln(x)$
33581 \begin_inset Formula $B$
33587 \begin_layout Standard
33588 \begin_inset Formula
33598 \begin_layout Standard
33602 Tools\SpecialChar menuseparator
33603 Preferences\SpecialChar menuseparator
33604 Editing\SpecialChar menuseparator
33607 different styles to edit macros.
33608 To find the style that suits you the most, choose a style and set the cursor
33609 in a macro formula to see the difference.
33612 \begin_layout Standard
33613 A math macro is transformed internally to a
33619 command when exporting the document.
33626 command is not placed in the \SpecialChar LaTeX
33627 -preamble, therefore macros can only be used
33628 in formulas that are in the document below the macro definition box.
33631 \begin_layout Standard
33632 Math macros can also be directly created from a
33639 When writing for example the command
33642 \begin_inset Newline newline
33651 xleftarrow[#2]{#1}}
33652 \begin_inset Newline newline
33657 in \SpecialChar LyX
33658 as normal text, highlighting it completely and using then the shortcut
33663 , the command will be transformed to a math macro.
33664 Using this method you need to be careful that the
33670 command is typed correctly, otherwise you get a faulty macro leading to
33675 \begin_layout Standard
33676 Math macros currently have the problem that further formulas in macro definition
33677 s are handled wrongly.
33678 Therefore the example
33685 \begin_inset CommandInset ref
33687 reference "subsec:The-Command-newcommand"
33691 cannot be created as macro.
33694 \begin_layout Standard
33695 When the cursor is in a macro definition box, you will see the macro toolbar
33696 in \SpecialChar LyX
33700 \begin_layout Standard
33701 \begin_inset VSpace defskip
33707 \begin_layout Standard
33708 \begin_inset Graphics
33709 filename clipart/MacroToolbar.png
33714 \begin_inset Index idx
33717 \begin_layout Plain Layout
33726 \begin_layout Standard
33727 \begin_inset VSpace defskip
33733 \begin_layout Standard
33734 The macro toolbar contains from left to right the following buttons:
33737 \begin_layout Standard
33738 \begin_inset VSpace defskip
33744 \begin_layout Standard
33745 \begin_inset Tabular
33746 <lyxtabular version="3" rows="9" columns="2">
33747 <features islongtable="true" longtabularalignment="center">
33748 <column alignment="left" valignment="top">
33749 <column alignment="left" valignment="top" width="85col%">
33750 <row interlinespace="2.5mm">
33751 <cell alignment="center" valignment="top" usebox="none">
33754 \begin_layout Plain Layout
33757 arg "math-macro-remove-param"
33765 <cell alignment="center" valignment="top" usebox="none">
33768 \begin_layout Plain Layout
33771 Edit\SpecialChar menuseparator
33772 Math\SpecialChar menuseparator
33774 \begin_inset space ~
33777 Definition\SpecialChar menuseparator
33778 Remove Last Argument
33784 <row interlinespace="2.5mm">
33785 <cell alignment="center" valignment="top" usebox="none">
33788 \begin_layout Plain Layout
33791 arg "math-macro-add-param"
33799 <cell alignment="center" valignment="top" usebox="none">
33802 \begin_layout Plain Layout
33805 Edit\SpecialChar menuseparator
33806 Math\SpecialChar menuseparator
33808 \begin_inset space ~
33811 Definition\SpecialChar menuseparator
33818 <row interlinespace="2.5mm">
33819 <cell alignment="center" valignment="top" usebox="none">
33822 \begin_layout Plain Layout
33825 arg "math-macro-make-optional"
33833 <cell alignment="center" valignment="top" usebox="none">
33836 \begin_layout Plain Layout
33839 Edit\SpecialChar menuseparator
33840 Math\SpecialChar menuseparator
33842 \begin_inset space ~
33845 Definition\SpecialChar menuseparator
33846 Transform First Non-Optional to
33847 \begin_inset Newline newline
33851 \begin_inset Phantom HPhantom
33854 \begin_layout Plain Layout
33857 Edit\SpecialChar menuseparator
33858 Math\SpecialChar menuseparator
33860 \begin_inset space ~
33863 Definition\SpecialChar menuseparator
33875 <row interlinespace="2.5mm">
33876 <cell alignment="center" valignment="top" usebox="none">
33879 \begin_layout Plain Layout
33882 arg "math-macro-make-nonoptional"
33890 <cell alignment="center" valignment="top" usebox="none">
33893 \begin_layout Plain Layout
33896 Edit\SpecialChar menuseparator
33897 Math\SpecialChar menuseparator
33899 \begin_inset space ~
33902 Definition\SpecialChar menuseparator
33903 Transform Last Optional to
33904 \begin_inset Newline newline
33908 \begin_inset Phantom HPhantom
33911 \begin_layout Plain Layout
33914 Edit\SpecialChar menuseparator
33915 Math\SpecialChar menuseparator
33917 \begin_inset space ~
33920 Definition\SpecialChar menuseparator
33926 Non-Optional Argument
33932 <row interlinespace="2.5mm">
33933 <cell alignment="center" valignment="top" usebox="none">
33936 \begin_layout Plain Layout
33939 arg "math-macro-remove-optional-param"
33947 <cell alignment="center" valignment="top" usebox="none">
33950 \begin_layout Plain Layout
33953 Edit\SpecialChar menuseparator
33954 Math\SpecialChar menuseparator
33956 \begin_inset space ~
33959 Definition\SpecialChar menuseparator
33960 Remove Optional Argument
33966 <row interlinespace="2.5mm">
33967 <cell alignment="center" valignment="top" usebox="none">
33970 \begin_layout Plain Layout
33973 arg "math-macro-add-optional-param"
33981 <cell alignment="center" valignment="top" usebox="none">
33984 \begin_layout Plain Layout
33987 Edit\SpecialChar menuseparator
33988 Math\SpecialChar menuseparator
33990 \begin_inset space ~
33993 Definition\SpecialChar menuseparator
33994 Insert Optional Argument
34000 <row interlinespace="2.5mm">
34001 <cell alignment="center" valignment="top" usebox="none">
34004 \begin_layout Plain Layout
34007 arg "math-macro-remove-greedy-param"
34015 <cell alignment="center" valignment="top" usebox="none">
34018 \begin_layout Plain Layout
34021 Edit\SpecialChar menuseparator
34022 Math\SpecialChar menuseparator
34024 \begin_inset space ~
34027 Definition\SpecialChar menuseparator
34028 Remove Last Argument
34029 \begin_inset Newline newline
34033 \begin_inset Phantom HPhantom
34036 \begin_layout Plain Layout
34039 Edit\SpecialChar menuseparator
34040 Math\SpecialChar menuseparator
34042 \begin_inset space ~
34045 Definition\SpecialChar menuseparator
34051 Spitting Out To The Right
34057 <row interlinespace="2.5mm">
34058 <cell alignment="center" valignment="top" usebox="none">
34061 \begin_layout Plain Layout
34064 arg "math-macro-append-greedy-param"
34072 <cell alignment="center" valignment="top" usebox="none">
34075 \begin_layout Plain Layout
34078 Edit\SpecialChar menuseparator
34079 Math\SpecialChar menuseparator
34081 \begin_inset space ~
34084 Definition\SpecialChar menuseparator
34086 \begin_inset Newline newline
34090 \begin_inset Phantom HPhantom
34093 \begin_layout Plain Layout
34096 Edit\SpecialChar menuseparator
34097 Math\SpecialChar menuseparator
34099 \begin_inset space ~
34102 Definition\SpecialChar menuseparator
34108 Eating From The Right
34114 <row interlinespace="2.5mm">
34115 <cell alignment="center" valignment="top" usebox="none">
34118 \begin_layout Plain Layout
34121 arg "math-macro-add-greedy-optional-param"
34129 <cell alignment="center" valignment="top" usebox="none">
34132 \begin_layout Plain Layout
34135 Edit\SpecialChar menuseparator
34136 Math\SpecialChar menuseparator
34138 \begin_inset space ~
34141 Definition\SpecialChar menuseparator
34142 Append Optional Argument
34143 \begin_inset Newline newline
34147 \begin_inset Phantom HPhantom
34150 \begin_layout Plain Layout
34153 Edit\SpecialChar menuseparator
34154 Math\SpecialChar menuseparator
34156 \begin_inset space ~
34159 Definition\SpecialChar menuseparator
34165 Eating From The Right
34178 \begin_layout Section
34179 Computer Algebra Systems
34182 \begin_layout Standard
34184 offers the exchange between mathematical expressions written in \SpecialChar LyX
34186 editor and external applications or user defined scripts.
34187 Currently supported applications are
34204 Note that the set of supported mathematical constructs is limited only
34205 to very simple cases.
34208 \begin_layout Subsection
34212 \begin_layout Standard
34213 Write some expression in a formula, go to the
34215 Edit\SpecialChar menuseparator
34216 Math\SpecialChar menuseparator
34217 Use Computer Algebra System
34219 menu and choose the application you have installed on the computer.
34220 After that the result of computation should show on the right side of the
34221 expression together with the
34222 \begin_inset Quotes eld
34226 \begin_inset Quotes erd
34232 \begin_layout Standard
34233 Here are few simple examples (with results from
34237 ) to show what kind of computations can be performed:
34240 \begin_layout Itemize
34241 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34247 \begin_layout Itemize
34248 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34254 \begin_layout Itemize
34255 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34261 \begin_layout Itemize
34262 \begin_inset Formula $\det\left[\begin{array}{ccc}
34266 \end{array}\right]=-56$
34272 \begin_layout Itemize
34273 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34279 \begin_layout Subsection
34283 \begin_layout Standard
34284 Currently there is no keyboard shortcut for calling the algebra applications.
34285 One can easily bind a shortcut to the
34299 \begin_inset space \thinspace{}
34303 \begin_inset space \space{}
34310 key inside the math editor.
34315 one would use this shortcut definition command:
34318 \begin_layout Standard
34321 command-alternatives paragraph-break;math-extern maxima
34324 \begin_layout Section
34326 \begin_inset Index idx
34329 \begin_layout Plain Layout
34338 \begin_layout Subsection
34340 \begin_inset Index idx
34343 \begin_layout Plain Layout
34352 \begin_layout Standard
34353 Negative numbers often look ugly in formulas because the minus sign before
34354 the number is set with the same length as the minus operator sign.
34355 When writing the negative number in normal text, the minus sign appears
34359 \begin_layout Standard
34360 Thus, the problem disappears when converting the minus sign to mathematical
34364 \begin_layout Standard
34365 An example to visualize the problem:
34366 \begin_inset Separator parbreak
34372 \begin_layout Standard
34374 \begin_inset Tabular
34375 <lyxtabular version="3" rows="3" columns="2">
34376 <features booktabs="true" tabularvalignment="middle">
34377 <column alignment="right" valignment="top" width="0pt">
34378 <column alignment="left" valignment="top">
34380 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34383 \begin_layout Plain Layout
34389 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34392 \begin_layout Plain Layout
34400 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34403 \begin_layout Plain Layout
34409 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34412 \begin_layout Plain Layout
34413 \begin_inset Formula $x=-2$
34423 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34426 \begin_layout Plain Layout
34432 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34435 \begin_layout Plain Layout
34436 \begin_inset Formula $x=\textrm{-}2$
34452 \begin_layout Subsection
34453 Comma as decimal Separator
34454 \begin_inset Index idx
34457 \begin_layout Plain Layout
34466 \begin_layout Standard
34467 In \SpecialChar LaTeX
34468 a comma inside a formula is used, according to the English convention,
34469 as number group separator.
34470 So there will be space added behind all commas in formulas.
34473 \begin_layout Standard
34474 To avoid this, the comma is highlighted and changed to mathematical text
34484 \begin_layout Standard
34485 To use all formula commas in the document as decimal separator, the file
34494 \begin_layout Plain Layout
34499 is part of the \SpecialChar LaTeX
34505 \begin_inset Index idx
34508 \begin_layout Plain Layout
34513 \begin_layout Plain Layout
34533 \begin_inset Index idx
34536 \begin_layout Plain Layout
34542 is loaded with the \SpecialChar LaTeX
34546 \begin_layout Standard
34554 \begin_layout Subsection
34556 \begin_inset CommandInset label
34558 name "subsec:Physical-Vectors"
34563 \begin_inset Index idx
34566 \begin_layout Plain Layout
34575 \begin_layout Standard
34576 Predefined vectors are offered by the \SpecialChar LaTeX
34582 \begin_inset Index idx
34585 \begin_layout Plain Layout
34591 that is loaded with the \SpecialChar LaTeX
34595 \begin_layout Standard
34603 \begin_layout Standard
34607 \begin_layout Plain Layout
34617 \begin_inset Note Note
34620 \begin_layout Plain Layout
34621 The following table will only be displayed when the \SpecialChar LaTeX
34634 \begin_layout Standard
34635 The following commands are defined:
34636 \begin_inset Separator parbreak
34642 \begin_layout Standard
34644 \begin_inset Tabular
34645 <lyxtabular version="3" rows="4" columns="2">
34646 <features booktabs="true" tabularvalignment="middle">
34647 <column alignment="center" valignment="top" width="0pt">
34648 <column alignment="center" valignment="top">
34650 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34653 \begin_layout Plain Layout
34659 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34662 \begin_layout Plain Layout
34670 <cell alignment="center" valignment="top" usebox="none">
34673 \begin_layout Plain Layout
34683 <cell alignment="center" valignment="top" usebox="none">
34686 \begin_layout Plain Layout
34687 \begin_inset Formula $\Bra{\psi}$
34697 <cell alignment="center" valignment="top" usebox="none">
34700 \begin_layout Plain Layout
34710 <cell alignment="center" valignment="top" usebox="none">
34713 \begin_layout Plain Layout
34714 \begin_inset Formula $\Ket{\psi}$
34724 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34727 \begin_layout Plain Layout
34739 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34742 \begin_layout Plain Layout
34743 \begin_inset Formula $\Braket{\psi|\phi}$
34759 \begin_layout Standard
34766 assures that all vertical bars are set in the size of the surrounding brackets:
34767 \begin_inset Formula
34769 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34778 \begin_layout Plain Layout
34788 \begin_inset Note Note
34791 \begin_layout Plain Layout
34792 The following will be displayed when the \SpecialChar LaTeX
34805 \begin_layout Standard
34806 You need to install the \SpecialChar LaTeX
34811 to see the rest of this subsection in the output.
34814 \begin_layout Standard
34818 \begin_layout Plain Layout
34830 \begin_layout Standard
34837 can also be achieved using the command
34843 , that is described in
34844 \begin_inset CommandInset ref
34846 reference "subsec:Automatic-Bracket-Size"
34853 \begin_layout Subsection
34854 Self-defined Fractions
34855 \begin_inset CommandInset label
34857 name "subsec:Self-defined-Fractions"
34862 \begin_inset Index idx
34865 \begin_layout Plain Layout
34866 Fractions ! self-defined
34874 \begin_layout Standard
34875 To define custom commands for fractions, the command
34882 \begin_inset Index idx
34885 \begin_layout Plain Layout
34892 \begin_layout Plain Layout
34906 is used in the following scheme:
34909 \begin_layout Standard
34922 bracket}{fraction bar thickness}{style}
34923 \begin_inset Newline newline
34927 \begin_inset Phantom HPhantom
34930 \begin_layout Plain Layout
34940 {numerator}{denominator}
34943 \begin_layout Standard
34944 The style is a number in the range of 0
34945 \begin_inset space \thinspace{}
34949 \begin_inset space \thinspace{}
34953 \begin_inset Separator parbreak
34959 \begin_layout Standard
34961 \begin_inset Tabular
34962 <lyxtabular version="3" rows="5" columns="2">
34963 <features booktabs="true" tabularvalignment="middle">
34964 <column alignment="center" valignment="top" width="0pt">
34965 <column alignment="center" valignment="top">
34967 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34970 \begin_layout Plain Layout
34976 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34979 \begin_layout Plain Layout
34987 <cell alignment="center" valignment="top" usebox="none">
34990 \begin_layout Plain Layout
34996 <cell alignment="center" valignment="top" usebox="none">
34999 \begin_layout Plain Layout
35000 display style formula
35007 <cell alignment="center" valignment="top" usebox="none">
35010 \begin_layout Plain Layout
35016 <cell alignment="center" valignment="top" usebox="none">
35019 \begin_layout Plain Layout
35027 <cell alignment="center" valignment="top" usebox="none">
35030 \begin_layout Plain Layout
35036 <cell alignment="center" valignment="top" usebox="none">
35039 \begin_layout Plain Layout
35047 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35050 \begin_layout Plain Layout
35056 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35059 \begin_layout Plain Layout
35073 \begin_layout Standard
35074 When no style is given, the size is adjusted to the surrounding environment
35075 like for the command
35084 \begin_layout Standard
35085 When no fraction bar thickness is given, the predefined value of 0.4
35086 \begin_inset space \thinspace{}
35092 \begin_layout Standard
35093 \begin_inset VSpace medskip
35096 For example, the commands
35109 \begin_inset CommandInset ref
35111 reference "subsec:Fractions"
35115 are defined with the commands
35118 \begin_layout Standard
35127 genfrac{}{}{}{0}{#1}{#2}}
35130 \begin_layout Standard
35134 \begin_layout Standard
35143 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35146 \begin_layout Standard
35147 \begin_inset VSpace medskip
35150 To define a fraction where the fraction bar thickness can be given as optional
35151 argument, the following line is inserted to the \SpecialChar LaTeX
35155 \begin_layout Standard
35164 genfrac{}{}{#1}{}{#2}{#3}}
35167 \begin_layout Standard
35169 \begin_inset Formula
35171 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35172 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35177 As one can see, the distance of the numerator and the denominator to the
35178 fraction bar is round about three times the bar thickness.
35181 \begin_layout Subsection
35183 \begin_inset Index idx
35186 \begin_layout Plain Layout
35195 \begin_layout Standard
35196 There are four ways to cancel formulas or parts of formulas:
35199 \begin_layout Standard
35203 \begin_layout Plain Layout
35213 \begin_inset Note Note
35216 \begin_layout Plain Layout
35217 The following table will only be displayed when the \SpecialChar LaTeX
35228 \begin_inset Separator parbreak
35234 \begin_layout Standard
35236 \begin_inset Tabular
35237 <lyxtabular version="3" rows="5" columns="2">
35238 <features booktabs="true" tabularvalignment="middle">
35239 <column alignment="center" valignment="top" width="0pt">
35240 <column alignment="center" valignment="top">
35242 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35245 \begin_layout Plain Layout
35251 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35254 \begin_layout Plain Layout
35262 <cell alignment="center" valignment="top" usebox="none">
35265 \begin_layout Plain Layout
35269 \begin_inset space \textvisiblespace{}
35275 \begin_inset space \textvisiblespace{}
35283 <cell alignment="center" valignment="top" usebox="none">
35286 \begin_layout Plain Layout
35287 \begin_inset Formula $\cancel{\int A=B}$
35296 <row topspace="1.5mm">
35297 <cell alignment="center" valignment="top" usebox="none">
35300 \begin_layout Plain Layout
35304 \begin_inset space \textvisiblespace{}
35310 \begin_inset space \textvisiblespace{}
35318 <cell alignment="center" valignment="top" usebox="none">
35321 \begin_layout Plain Layout
35322 \begin_inset Formula $\bcancel{\int A=B}$
35331 <row topspace="1.5mm">
35332 <cell alignment="center" valignment="top" usebox="none">
35335 \begin_layout Plain Layout
35339 \begin_inset space \textvisiblespace{}
35345 \begin_inset space \textvisiblespace{}
35353 <cell alignment="center" valignment="top" usebox="none">
35356 \begin_layout Plain Layout
35357 \begin_inset Formula $\xcancel{\int A=B}$
35367 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35370 \begin_layout Plain Layout
35374 \begin_inset space \textvisiblespace{}
35380 \begin_inset space \textvisiblespace{}
35384 \begin_inset Formula $\to$
35392 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35395 \begin_layout Plain Layout
35396 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35412 \begin_layout Standard
35419 is especially suitable to visualize the reduction of fractions within formulas:
35420 \begin_inset Formula
35422 \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}}}
35430 \begin_layout Standard
35431 To change the size of
35438 \begin_inset Quotes eld
35442 \begin_inset Quotes erd
35445 value one can add the \SpecialChar LaTeX
35449 \begin_layout Standard
35454 PassOptionsToPackage{option}{cancel}
35457 \begin_layout Standard
35466 which leads to the same size as for the canceled value, or
35470 which makes is it a bit smaller than normal.
35473 \begin_layout Standard
35474 To color the cancellation bar one adds this command as \SpecialChar TeX
35478 \begin_layout Standard
35490 \begin_layout Standard
35495 can be replaced by a color of your choice.
35498 \begin_layout Standard
35502 \begin_layout Plain Layout
35518 \begin_layout Standard
35519 \begin_inset Formula
35521 \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}}}
35529 \begin_layout Standard
35533 \begin_layout Plain Layout
35547 \begin_inset Note Note
35550 \begin_layout Plain Layout
35559 \begin_layout Standard
35560 For further customizations, see the documentation of the package
35565 \begin_inset CommandInset citation
35572 \begin_inset Index idx
35575 \begin_layout Plain Layout
35584 \begin_layout Standard
35588 \begin_layout Plain Layout
35598 \begin_inset Note Note
35601 \begin_layout Plain Layout
35602 The following will be displayed when the \SpecialChar LaTeX
35615 \begin_layout Standard
35616 You need to install the \SpecialChar LaTeX
35621 to see the rest of this subsection in the output.
35624 \begin_layout Standard
35628 \begin_layout Plain Layout
35640 \begin_layout Subsection
35641 Formulas in Section Headings
35642 \begin_inset CommandInset label
35644 name "subsec:Formulas-in-Section"
35649 \begin_inset Index idx
35652 \begin_layout Plain Layout
35653 Formula ! in section headings
35661 \begin_layout Standard
35662 When formulas are used in section headings, the following has to be taken
35666 \begin_layout Standard
35667 \begin_inset Note Greyedout
35670 \begin_layout Plain Layout
35676 \begin_inset Index idx
35679 \begin_layout Plain Layout
35680 Packages ! hyperref
35685 support is enabled in the document settings dialog under
35688 \begin_inset space ~
35693 , PDF-bookmarks are created for every section heading in the table of contents.
35694 If a section heading contains formulas, they are incorrectly displayed
35695 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35704 \begin_layout Standard
35705 Both problems can be solved by inserting at the end of the section heading
35706 a short title with the menu
35708 Insert\SpecialChar menuseparator
35710 \begin_inset space ~
35716 Short titles are used as alternative for multiline section headings to
35717 keep the table of contents clearly arranged.
35718 Only the short title appears in the table of contents and therefore also
35719 in the PDF-bookmark.
35722 \begin_layout Standard
35723 When formulas should be used in the table of contents but
35727 is used, one can use the following command in \SpecialChar TeX
35731 \begin_layout Standard
35736 texorpdfstring{part}{alternative}
35737 \begin_inset Index idx
35740 \begin_layout Plain Layout
35751 \begin_layout Standard
35752 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35753 This can be characters, formulas, footnotes, but also cross-references.
35754 The alternative is used instead of the part for the bookmark.
35757 \begin_layout Standard
35758 Here are two example headings:
35759 \begin_inset VSpace -3mm
35766 \begin_layout Plain Layout
35778 \begin_layout Subsubsection
35779 Heading without formula in table of contents
35780 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35784 \begin_inset Argument 1
35787 \begin_layout Plain Layout
35788 Heading without formula in table of contents
35796 \begin_layout Subsubsection
35797 Heading with formula in table of contents
35801 \begin_layout Plain Layout
35811 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35818 \begin_layout Plain Layout
35828 \begin_layout Standard
35832 \begin_layout Plain Layout
35841 In the first heading a short title was used, in the second one
35850 \begin_layout Standard
35851 To get the same formatting as for the other headings, the complete heading
35860 \begin_layout Plain Layout
35862 \begin_inset CommandInset ref
35864 reference "subsec:Bold-Formulas"
35876 \begin_layout Subsection
35877 Formulas in multi-column Text
35878 \begin_inset Index idx
35881 \begin_layout Plain Layout
35882 Formula ! in multi-column text
35890 \begin_layout Standard
35891 Formulas in multi-column text are often too wide to fit into a column and
35892 thus need to be set over the whole page width.
35893 This is done by using the \SpecialChar LaTeX
35902 \begin_layout Plain Layout
35907 is part of every \SpecialChar LaTeX
35908 standard installation.
35914 \begin_inset Index idx
35917 \begin_layout Plain Layout
35918 Packages ! multicol
35923 , that is loaded with the \SpecialChar LaTeX
35927 \begin_layout Standard
35932 usepackage{multicol}
35935 \begin_layout Standard
35936 \begin_inset Note Greyedout
35939 \begin_layout Plain Layout
35940 Note that in this case the setting
35943 \begin_inset space ~
35950 Document\SpecialChar menuseparator
35956 \begin_inset space ~
35976 \begin_layout Standard
35977 Before the multi-column text the command
35980 \begin_layout Standard
35985 begin{multicols}{column number}
35988 \begin_layout Standard
35989 is written in \SpecialChar TeX
35991 The column number is a number in the range of 2
35992 \begin_inset space \thinspace{}
35996 \begin_inset space \thinspace{}
36000 Before the formula the multi-column text is ended by inserting the command
36003 \begin_layout Standard
36011 \begin_layout Standard
36012 in \SpecialChar TeX
36016 \begin_layout Standard
36017 Due to the command some space is automatically added before the formula.
36019 \begin_inset space \thinspace{}
36022 mm vertical space is inserted before the formula.
36023 When the formula style
36029 \begin_layout Plain Layout
36031 \begin_inset CommandInset ref
36033 reference "sec:Formula-Styles"
36045 \begin_inset space \thinspace{}
36048 mm space is inserted instead.
36051 \begin_layout Standard
36052 As example a multi-column text with a displayed formula:
36055 \begin_layout Standard
36061 \begin_layout Plain Layout
36065 begin{multicols}{2}
36070 Das Spektrum wird fouriertransformiert.
36071 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36072 , Lösungsmittel) zu trennen.
36073 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36074 nun das Aussehen des Ausgangssignals.
36075 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36076 über alle Phasen integrieren muss.
36078 \begin_inset Formula $S$
36081 unser normiertes Ausgangssignal und
36082 \begin_inset Formula $P$
36085 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36089 \begin_layout Plain Layout
36099 \begin_inset VSpace -6mm
36103 \begin_inset Formula
36105 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36114 \begin_layout Plain Layout
36118 begin{multicols}{2}
36124 \begin_inset Formula $S_{0}$
36127 das Signal ohne Gradient ist und die Normierungsbedingung
36128 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36132 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36134 \begin_inset Formula $\nicefrac{\pi}{2}$
36138 \begin_inset space \thinspace{}
36141 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36142 das Signal zusätzlich abschwächt.
36143 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36145 \begin_inset Formula $T_{2}$
36151 \begin_layout Standard
36157 \begin_layout Plain Layout
36169 \begin_layout Subsection
36170 Formulas with Description of Variables
36171 \begin_inset Index idx
36174 \begin_layout Plain Layout
36175 Formula ! with description of variables
36183 \begin_layout Standard
36184 To describe variables within a formula, like in formula
36185 \begin_inset CommandInset ref
36187 reference "eq:within"
36196 \begin_inset Formula $n$
36200 \begin_inset space ~
36203 matrix is used with left aligned columns for the
36204 \begin_inset Formula $n$
36211 \begin_layout Plain Layout
36213 \begin_inset CommandInset ref
36215 reference "sec:Matrices"
36224 To set the description in a smaller size, before the matrix e.
36225 \begin_inset space \thinspace{}
36229 \begin_inset space \space{}
36242 \begin_layout Plain Layout
36244 \begin_inset CommandInset ref
36246 reference "subsec:Font-Sizes"
36258 \begin_layout Standard
36259 When the formula style
36265 \begin_layout Plain Layout
36267 \begin_inset CommandInset ref
36269 reference "sec:Formula-Styles"
36290 \begin_layout Plain Layout
36297 only works in formulas with the style
36302 \begin_inset CommandInset ref
36304 reference "subsec:Variable-Space"
36313 is inserted before and after the matrix to have the same separation of
36314 the matrix from the equation and the side margin.
36317 \begin_layout Standard
36318 When the formula style
36322 is used, the method described in
36323 \begin_inset CommandInset ref
36325 reference "subsec:Flalign-Environment"
36329 is used to indent formulas.
36331 \begin_inset CommandInset ref
36333 reference "eq:within"
36337 consists of five columns where in the first two columns contain the equation,
36338 the third the matrix and the last one an empty \SpecialChar TeX
36340 \begin_inset Formula
36342 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36343 \rho & \textrm{density}\\
36344 V & \textrm{volume}\\
36345 g & \textrm{gravitational acceleration}
36346 \end{array} & & {}\label{eq:within}
36354 \begin_layout Subsection
36355 Upright small Greek Letters
36356 \begin_inset CommandInset label
36358 name "subsec:Upright-small-Greek"
36363 \begin_inset Index idx
36366 \begin_layout Plain Layout
36367 Greek letters ! upright
36375 \begin_layout Standard
36376 Most of the math fonts only provide italic small Greek letters.
36377 But for symbols of elementary particles like pions and neutrinos, upright
36378 Greek letters are needed.
36387 \begin_layout Plain Layout
36392 is part of the \SpecialChar LaTeX
36398 \begin_inset Index idx
36401 \begin_layout Plain Layout
36406 \begin_layout Plain Layout
36426 \begin_inset Index idx
36429 \begin_layout Plain Layout
36435 that is loaded with the \SpecialChar LaTeX
36439 \begin_layout Standard
36444 usepackage{upgreek}
36447 \begin_layout Standard
36453 \begin_layout Plain Layout
36463 \begin_inset Note Note
36466 \begin_layout Plain Layout
36467 The following table will only be displayed when the \SpecialChar LaTeX
36477 They are created when the command for a small Greek letter is started with
36483 For example the command
36490 \begin_inset Formula $\uptau$
36496 \begin_layout Standard
36497 With these commands reactions of elementary particles can be typeset:
36498 \begin_inset Formula
36500 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36508 \begin_layout Standard
36509 The upright letters are more bold and wider than the italic ones.
36510 They should therefore not be used for units like
36511 \begin_inset Quotes eld
36515 \begin_inset Quotes erd
36521 \begin_layout Standard
36525 \begin_layout Plain Layout
36535 \begin_inset Note Note
36538 \begin_layout Plain Layout
36539 The following will be displayed when the \SpecialChar LaTeX
36552 \begin_layout Standard
36553 You need to install the \SpecialChar LaTeX
36558 to see the rest of this subsection in the output.
36561 \begin_layout Standard
36565 \begin_layout Plain Layout
36577 \begin_layout Subsection
36578 Text Characters in Formulas
36579 \begin_inset Index idx
36582 \begin_layout Plain Layout
36591 \begin_layout Standard
36592 In some cases you might want to insert text characters directly into formulas.
36593 When for example the centered dot · is often used in formulas like
36594 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36597 , one would have to insert the command
36607 \begin_layout Plain Layout
36609 \begin_inset CommandInset ref
36611 reference "subsec:Binary-Operators"
36620 all the time, because this character is defined in all encodings as text
36622 But the encoding can be changed by this \SpecialChar LaTeX
36626 \begin_layout Standard
36631 Declare Inputtext{183}{
36641 f\SpecialChar ligaturebreak
36645 \begin_layout Standard
36646 The character encoding (menu
36648 Document\SpecialChar menuseparator
36649 Settings\SpecialChar menuseparator
36652 ) specifies what character appears when a keyboard key is pressed.
36653 When the key for the character '·' is pressed, internally the command
36660 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36662 With the changed encoding the right command is chosen automatically, depending
36663 on if the character was inserted into a formula or not.
36666 \begin_layout Standard
36667 The encoding of several characters is saved in definition files.
36668 For example the encoding
36672 is defined in the file
36676 which is in the installation folder of \SpecialChar LaTeX
36678 Encodings should only be changed via the \SpecialChar LaTeX
36679 -preamble and not in the definition
36681 Otherwise documents could not be edited by other \SpecialChar LyX
36682 users working on other
36686 \begin_layout Standard
36687 \begin_inset VSpace medskip
36690 Besides the centered dot, in this document the degree sign ° is defined
36691 with the following \SpecialChar LaTeX
36692 -preamble line so that it can be directly inserted into
36696 \begin_layout Standard
36701 DeclareInputtext{176}{
36711 f\SpecialChar ligaturebreak
36715 \begin_layout Subsection
36717 -comments in formulas
36718 \begin_inset Index idx
36721 \begin_layout Plain Layout
36731 \begin_layout Standard
36732 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36734 code of your file with the menu
36736 Insert\SpecialChar menuseparator
36737 Note\SpecialChar menuseparator
36741 This is not possible in a formula but you can insert \SpecialChar LaTeX
36746 \begin_layout Standard
36754 \begin_layout Standard
36755 This creates a box in which you can write your comment.
36756 Due to a bug in \SpecialChar LyX
36761 \begin_layout Plain Layout
36762 \begin_inset CommandInset href
36764 name "LyX-bug #9002"
36765 target "http://www.lyx.org/trac/ticket/9002"
36774 you cannot write normal text inside the comment, even when you use mathematical
36775 text, you will see its \SpecialChar LaTeX
36776 -commands in the \SpecialChar LaTeX
36778 \begin_inset Newline newline
36781 This a formula with a \SpecialChar LaTeX
36783 \begin_inset Formula
36785 A=B%\text{This is the comment}
36793 \begin_layout Standard
36794 \begin_inset Newpage newpage
36800 \begin_layout Section
36803 \begin_inset Index idx
36806 \begin_layout Plain Layout
36815 \begin_layout Standard
36816 This section is a summary of the most important typographic rules, listed
36821 \begin_layout Plain Layout
36822 This collection was partly taken from the German semi-official dictionary
36824 \begin_inset Quotes eld
36828 \begin_inset Quotes erd
36832 \begin_inset CommandInset citation
36838 that lists some of the ISO rules.
36839 More rules are listed in
36840 \begin_inset CommandInset citation
36854 \begin_layout Itemize
36863 \begin_layout Plain Layout
36864 done with font styles, see
36865 \begin_inset CommandInset ref
36867 reference "subsec:Font-Styles"
36876 , no matter if they appear in italic text: 30
36877 \begin_inset space \thinspace{}
36881 \begin_inset Newline newline
36884 Between the value and the unit is the smallest space, see
36885 \begin_inset CommandInset ref
36887 reference "subsec:Predefined-Space"
36892 \begin_inset Newline newline
36895 This convention is automatically fulfilled when the command
36902 When it is entered to a formula, two boxes appear.
36903 In the first one the value is inserted, in the second one the unit, and
36905 \begin_inset Formula $\unit[30]{km/h}$
36909 \begin_inset space \thinspace{}
36919 is not a real \SpecialChar LaTeX
36920 command but the command
36926 , therefore you cannot use it in \SpecialChar TeX
36930 \begin_layout Itemize
36931 Percent and perthousand signs are set like physical units:
36932 \begin_inset Newline newline
36936 \begin_inset space \thinspace{}
36942 \begin_layout Itemize
36943 The degree sign follows directly on the value: 15°, but not when it is used
36945 \begin_inset space \thinspace{}
36951 \begin_layout Itemize
36952 In numbers with more than four digits the smallest space is inserted before
36953 every third digit to group them:
36963 \begin_inset space \thinspace{}
36967 \begin_inset space \thinspace{}
36973 \begin_layout Itemize
36974 For dimensions like 120×90×40
36975 \begin_inset space \thinspace{}
36978 cm the multiplication sign
36979 \begin_inset Quotes eld
36983 \begin_inset Quotes erd
36987 It is available either via the command
36995 Insert\SpecialChar menuseparator
36996 Special Character\SpecialChar menuseparator
37002 \begin_layout Itemize
37003 Functions with names consisting of several letters are set upright to avoid
37005 \begin_inset CommandInset ref
37007 reference "subsec:Predefined-Functions"
37014 \begin_layout Itemize
37015 Indices consisting of several letters, are set upright:
37016 \begin_inset Formula $E_{\mathrm{kin}}$
37020 \begin_inset Newline newline
37023 Components of matrices are set italic:
37024 \begin_inset Formula $\hat{H}_{kl}$
37030 \begin_layout Itemize
37031 The differentiation/integration operator 'd', the Euler's number 'e' and
37032 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37036 \begin_layout Itemize
37037 The character that denotes a
37041 transformation is inserted either by the command
37046 \begin_inset space \textvisiblespace{}
37053 Insert\SpecialChar menuseparator
37054 Special Character\SpecialChar menuseparator
37055 Symbols\SpecialChar menuseparator
37057 \begin_inset space ~
37063 \begin_inset Formula $\mathscr{F}$
37069 \begin_layout Standard
37070 \begin_inset Newpage newpage
37076 \begin_layout Section
37078 \begin_inset Index idx
37081 \begin_layout Plain Layout
37090 \begin_layout Standard
37091 Some characters and symbols can be created with several commands.
37092 Here is a list of the synonym commands:
37095 \begin_layout Standard
37096 \begin_inset VSpace bigskip
37100 \begin_inset space \hfill{}
37104 \begin_inset Tabular
37105 <lyxtabular version="3" rows="12" columns="2">
37106 <features booktabs="true" tabularvalignment="middle">
37107 <column alignment="center" valignment="top" width="0pt">
37108 <column alignment="center" valignment="top" width="0pt">
37110 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37113 \begin_layout Plain Layout
37119 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37122 \begin_layout Plain Layout
37130 <cell alignment="center" valignment="top" usebox="none">
37133 \begin_layout Plain Layout
37141 <cell alignment="center" valignment="top" usebox="none">
37144 \begin_layout Plain Layout
37152 <cell alignment="center" valignment="top" usebox="none">
37155 \begin_layout Plain Layout
37163 <cell alignment="center" valignment="top" usebox="none">
37166 \begin_layout Plain Layout
37176 <cell alignment="center" valignment="top" usebox="none">
37179 \begin_layout Plain Layout
37187 <cell alignment="center" valignment="top" usebox="none">
37190 \begin_layout Plain Layout
37200 <cell alignment="center" valignment="top" usebox="none">
37203 \begin_layout Plain Layout
37211 <cell alignment="center" valignment="top" usebox="none">
37214 \begin_layout Plain Layout
37222 <cell alignment="center" valignment="top" usebox="none">
37225 \begin_layout Plain Layout
37233 <cell alignment="center" valignment="top" usebox="none">
37236 \begin_layout Plain Layout
37244 <cell alignment="center" valignment="top" usebox="none">
37247 \begin_layout Plain Layout
37255 <cell alignment="center" valignment="top" usebox="none">
37258 \begin_layout Plain Layout
37268 <cell alignment="center" valignment="top" usebox="none">
37271 \begin_layout Plain Layout
37279 <cell alignment="center" valignment="top" usebox="none">
37282 \begin_layout Plain Layout
37292 <cell alignment="center" valignment="top" usebox="none">
37295 \begin_layout Plain Layout
37303 <cell alignment="center" valignment="top" usebox="none">
37306 \begin_layout Plain Layout
37316 <cell alignment="center" valignment="top" usebox="none">
37319 \begin_layout Plain Layout
37327 <cell alignment="center" valignment="top" usebox="none">
37330 \begin_layout Plain Layout
37340 <cell alignment="center" valignment="top" usebox="none">
37343 \begin_layout Plain Layout
37351 <cell alignment="center" valignment="top" usebox="none">
37354 \begin_layout Plain Layout
37362 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37365 \begin_layout Plain Layout
37373 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37376 \begin_layout Plain Layout
37388 \begin_inset space \hfill{}
37392 \begin_inset Tabular
37393 <lyxtabular version="3" rows="12" columns="2">
37394 <features booktabs="true" tabularvalignment="middle">
37395 <column alignment="center" valignment="top" width="0pt">
37396 <column alignment="center" valignment="top" width="0pt">
37398 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37401 \begin_layout Plain Layout
37407 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37410 \begin_layout Plain Layout
37418 <cell alignment="center" valignment="top" usebox="none">
37421 \begin_layout Plain Layout
37429 <cell alignment="center" valignment="top" usebox="none">
37432 \begin_layout Plain Layout
37444 <cell alignment="center" valignment="top" usebox="none">
37447 \begin_layout Plain Layout
37455 <cell alignment="center" valignment="top" usebox="none">
37458 \begin_layout Plain Layout
37468 <cell alignment="center" valignment="top" usebox="none">
37471 \begin_layout Plain Layout
37479 <cell alignment="center" valignment="top" usebox="none">
37482 \begin_layout Plain Layout
37492 <cell alignment="center" valignment="top" usebox="none">
37495 \begin_layout Plain Layout
37503 <cell alignment="center" valignment="top" usebox="none">
37506 \begin_layout Plain Layout
37514 <cell alignment="center" valignment="top" usebox="none">
37517 \begin_layout Plain Layout
37525 <cell alignment="center" valignment="top" usebox="none">
37528 \begin_layout Plain Layout
37536 <cell alignment="center" valignment="top" usebox="none">
37539 \begin_layout Plain Layout
37547 <cell alignment="center" valignment="top" usebox="none">
37550 \begin_layout Plain Layout
37560 <cell alignment="center" valignment="top" usebox="none">
37563 \begin_layout Plain Layout
37571 <cell alignment="center" valignment="top" usebox="none">
37574 \begin_layout Plain Layout
37584 <cell alignment="center" valignment="top" usebox="none">
37587 \begin_layout Plain Layout
37595 <cell alignment="center" valignment="top" usebox="none">
37598 \begin_layout Plain Layout
37608 <cell alignment="center" valignment="top" usebox="none">
37611 \begin_layout Plain Layout
37619 <cell alignment="center" valignment="top" usebox="none">
37622 \begin_layout Plain Layout
37632 <cell alignment="center" valignment="top" usebox="none">
37635 \begin_layout Plain Layout
37643 <cell alignment="center" valignment="top" usebox="none">
37646 \begin_layout Plain Layout
37656 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37659 \begin_layout Plain Layout
37667 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37670 \begin_layout Plain Layout
37684 \begin_inset space \hfill{}
37690 \begin_layout Standard
37691 \begin_inset Newpage newpage
37697 \begin_layout Bibliography
37698 \begin_inset CommandInset bibitem
37699 LatexCommand bibitem
37711 The \SpecialChar LaTeX
37715 Addison Wesley, 2004
37718 \begin_layout Bibliography
37719 \begin_inset CommandInset bibitem
37720 LatexCommand bibitem
37726 \begin_inset CommandInset href
37729 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37733 of \SpecialChar LaTeX
37737 \begin_layout Bibliography
37738 \begin_inset CommandInset bibitem
37739 LatexCommand bibitem
37745 \begin_inset CommandInset href
37748 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37756 \begin_layout Plain Layout
37765 -\SpecialChar LaTeX
37769 \begin_layout Bibliography
37770 \begin_inset CommandInset bibitem
37771 LatexCommand bibitem
37777 \begin_inset CommandInset href
37780 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37784 of all symbols available with \SpecialChar LaTeX
37788 \begin_layout Bibliography
37789 \begin_inset CommandInset bibitem
37790 LatexCommand bibitem
37796 \begin_inset CommandInset href
37798 name "Documentation"
37799 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37803 of the \SpecialChar LaTeX
37809 \begin_inset Index idx
37812 \begin_layout Plain Layout
37821 \begin_layout Bibliography
37822 \begin_inset CommandInset bibitem
37823 LatexCommand bibitem
37829 \begin_inset CommandInset href
37831 name "Documentation"
37832 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37836 of the \SpecialChar LaTeX
37842 \begin_inset Index idx
37845 \begin_layout Plain Layout
37846 Packages ! hyperref
37854 \begin_layout Bibliography
37855 \begin_inset CommandInset bibitem
37856 LatexCommand bibitem
37862 \begin_inset CommandInset href
37864 name "Documentation"
37865 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37869 of the \SpecialChar LaTeX
37875 \begin_inset Index idx
37878 \begin_layout Plain Layout
37887 \begin_layout Bibliography
37888 \begin_inset CommandInset bibitem
37889 LatexCommand bibitem
37900 Auflage, Duden 2001
37903 \begin_layout Bibliography
37904 \begin_inset CommandInset bibitem
37905 LatexCommand bibitem
37911 \begin_inset CommandInset href
37914 target "http://physics.nist.gov/Document/checklist.pdf"
37918 for reviewing manuscripts
37921 \begin_layout Standard
37922 \begin_inset CommandInset index_print
37923 LatexCommand printindex