1 #LyX 2.2 created this file. For more info see http://www.lyx.org/
5 \origin /systemlyxdir/doc/
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 \addto\extrasenglish{%
38 \renewcommand*{\equationautorefname}[1]{}%
39 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
40 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
41 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
44 % don't load packages twice
45 % see first footnote in sec. 9.3
46 \@ifundefined{textcolor}{\usepackage{color}}{}
48 % the pages of the TOC are numbered roman
49 % and a PDF-bookmark for the TOC is added
51 \let\myTOC\tableofcontents
52 \renewcommand{\tableofcontents}{%
54 \pdfbookmark[1]{\contentsname}{}
57 \pagenumbering{arabic}}
59 % insert additional vertical space of 1.5 mm between footnotes,
61 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
63 % provides caption formatting
64 \setkomafont{captionlabel}{\bfseries}
66 % enables calculation of values
69 % for multiple columns used in sec. 24.7
75 % for the Fourier transformation symbol
78 % define a color, used in sec.9.3
79 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
81 % declare operators (see sec. 10.4 and sec. 15.2)
82 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
83 \DeclareMathOperator{\sgn}{sgn}
85 % example definitions for sec. 20.1
86 \newcommand{\gr}{\Longrightarrow}
87 \newcommand{\us}[1]{\underline{#1}}
88 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
89 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
90 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
92 % example macro from sec. 19.4
93 %\def\tagform@#1{\maketag@@@{|#1|}}
96 % ------------------------------------
97 % used to check for needed LaTeX packages
100 % check for package undertilde
101 % used for the command \utilde
102 \newboolean{undertilde}
103 \IfFileExists{undertilde.sty}
104 {\usepackage{undertilde}
105 \setboolean{undertilde}{true}}
106 {\setboolean{undertilde}{false}}
108 % check for package eurosym
109 % used for the Euro symbol
111 \IfFileExists{eurosym.sty}
112 {\usepackage[gennarrow]{eurosym}
113 \setboolean{eurosym}{true}}
114 {\setboolean{eurosym}{false}}
116 % check for package braket
117 % used for physical vectors
119 \IfFileExists{braket.sty}
121 \setboolean{braket}{true}}
122 {\setboolean{braket}{false}}
124 % check for package cancel
126 \IfFileExists{cancel.sty}
128 \setboolean{cancel}{true}}
129 {\setboolean{cancel}{false}}
131 % check for package upgreek
133 \IfFileExists{upgreek.sty}
134 {\usepackage{upgreek}
135 \setboolean{upgreek}{true}}
136 {\setboolean{upgreek}{false}}
138 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
139 \use_default_options false
140 \maintain_unincluded_children false
142 \language_package default
147 \font_typewriter default
149 \font_default_family default
150 \use_non_tex_fonts false
156 \default_output_format default
158 \bibtex_command default
159 \index_command default
163 \pdf_title "LyX's Math Manual"
164 \pdf_author "LyX Team, Uwe Stöhr"
165 \pdf_subject "LyX-documentation about math"
166 \pdf_keywords "LyX, Mathed"
168 \pdf_bookmarksnumbered true
169 \pdf_bookmarksopen true
170 \pdf_bookmarksopenlevel 1
171 \pdf_breaklinks false
175 \pdf_pdfusetitle false
176 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
179 \use_package amsmath 2
180 \use_package amssymb 2
181 \use_package cancel 0
183 \use_package mathdots 1
184 \use_package mathtools 2
185 \use_package mhchem 1
186 \use_package stackrel 0
187 \use_package stmaryrd 0
188 \use_package undertilde 0
190 \cite_engine_type default
194 \paperorientation portrait
198 \notefontcolor #0000ff
205 \paragraph_separation skip
207 \quotes_language english
210 \paperpagestyle plain
214 \tracking_changes false
215 \output_changes false
218 \html_be_strict false
225 's detailed Math manual
229 by the \SpecialChar LyX
234 \begin_layout Plain Layout
236 If you have comments or error corrections, please send them to the \SpecialChar LyX
241 \begin_inset CommandInset href
243 name "lyx-docs@lists.lyx.org"
244 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
255 \begin_inset Note Note
258 \begin_layout Plain Layout
265 \begin_inset Newline newline
269 \begin_inset Newline newline
277 \begin_layout Standard
278 \begin_inset CommandInset toc
279 LatexCommand tableofcontents
286 \begin_layout Standard
287 \begin_inset Note Note
290 \begin_layout Plain Layout
291 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
294 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
301 If they are not installed the document can be exported anyway but the sections
302 where the packages are required will not appear in the output.
307 ; if it is not installed, this file cannot be exported.
310 \begin_layout Plain Layout
311 The latest PDF-version of this document can be found here:
312 \begin_inset Newline newline
317 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
325 \begin_layout Standard
326 \begin_inset Newpage newpage
332 \begin_layout Section
336 \begin_layout Standard
337 This document explains \SpecialChar LyX
338 's math features and is furthermore a collection
339 of \SpecialChar LaTeX
340 -commands used for mathematical characters and constructs.
341 The explanations are designed for the usage of commands.
342 It is therefore required that you have read the section
353 \begin_layout Standard
354 Most of the characters and many constructs explained in this manual are
355 also accessible via the menu
359 \SpecialChar menuseparator
375 But everybody who has to write lots of formulas will notice that it is
376 much faster to use commands instead of the math toolbar.
377 Therefore this manual is focused on commands but also mentions the correspondin
378 g toolbar buttons when available.
381 \begin_layout Standard
382 If not specially mentioned the commands are only available within formulas.
383 To be able to use all commands explained in this document, the option
387 must be checked in the document settings (menu
389 Document\SpecialChar menuseparator
390 Settings\SpecialChar menuseparator
401 \begin_layout Plain Layout
404 Use AMS math package automatically
410 \begin_layout Plain Layout
419 -math when math constructs are found that are supported by \SpecialChar LyX
428 \begin_layout Standard
429 This document doesn't list all
433 \begin_layout Plain Layout
446 \begin_layout Plain Layout
451 \begin_layout Plain Layout
460 -math commands is in the file
463 \begin_inset CommandInset href
466 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
472 , which is part of every \SpecialChar LaTeX
473 standard installation.
478 for lucidity reasons.
481 \begin_layout Section
485 \begin_layout Standard
486 To create an inline formula
487 \begin_inset Index idx
490 \begin_layout Plain Layout
496 that is embedded into a text line, use one of the shortcuts
502 or the toolbar button
509 \begin_inset Newline newline
512 To create a display style formula
513 \begin_inset Index idx
516 \begin_layout Plain Layout
517 Formula ! display style
522 which will appear bigger, has a different format, and will be in a separate
523 paragraph, use one of these shortcuts:
532 \begin_layout Standard
533 To change a display style formula to an inline formula, set the cursor into
534 the formula and use one of the shortcuts
542 Edit\SpecialChar menuseparator
543 Math\SpecialChar menuseparator
547 The same way is used to change an inline formula to a display style formula.
550 \begin_layout Standard
551 To display parts of an inline formula in the size of a display style formula,
559 \begin_inset Index idx
562 \begin_layout Plain Layout
571 Then a new blue box appears in which the desired formula part is inserted.
574 \begin_layout Standard
575 Only inline formulas are allowed inside tables.
578 \begin_layout Standard
583 can be turned on in the menu
585 View\SpecialChar menuseparator
589 When you click there on
590 \begin_inset Quotes eld
594 \begin_inset Quotes erd
597 the toolbar will be shown permanently at the bottom; this state is visualized
602 menu with a checkmark.
603 When you click in this state again on
604 \begin_inset Quotes eld
608 \begin_inset Quotes erd
619 is only shown when the cursor is within a formula; this state is visualized
620 by the renaming of the menu entry from
621 \begin_inset Quotes eld
625 \begin_inset Quotes erd
629 \begin_inset Quotes eld
637 \begin_inset Quotes erd
643 \begin_layout Standard
646 \begin_inset Index idx
649 \begin_layout Plain Layout
656 is invoked by pressing the toolbar button
664 Insert\SpecialChar menuseparator
676 \begin_layout Standard
677 To change the \SpecialChar LaTeX
679 \begin_inset Index idx
682 \begin_layout Plain Layout
691 Document\SpecialChar menuseparator
692 Settings\SpecialChar menuseparator
702 \begin_layout Standard
703 To edit matrices, case differentiations and multiline formulas subsequently,
706 Edit\SpecialChar menuseparator
711 Edit\SpecialChar menuseparator
713 \begin_inset space \thinspace{}
717 \begin_inset space \thinspace{}
727 When lines and columns are swapped via the menu, the column or line where
728 the cursor is in is exchanged with the column to the right or the line
730 Is the cursor in the last column or row, the exchange is done with the
731 column to the left or the line above.
734 \begin_layout Standard
735 To write text in formulas
739 \begin_layout Plain Layout
740 For multiline formulas the command
747 \begin_inset CommandInset ref
749 reference "subsec:Text-in-multiline"
763 \begin_inset Index idx
766 \begin_layout Plain Layout
773 \begin_inset Index idx
776 \begin_layout Plain Layout
783 This mode is invoked with the shortcut
789 or by the insertion of the command
796 \begin_inset Index idx
799 \begin_layout Plain Layout
808 The text appears black in \SpecialChar LyX
809 and can therefore be distinguished from the
810 other formula parts which appear blue.
811 In the output mathematical text is set upright, in contrary to other formula
815 \begin_layout Subsection*
819 \begin_layout Standard
820 Most of the \SpecialChar LaTeX
821 -commands for math constructs have the following scheme:
824 \begin_layout Standard
840 \begin_layout Standard
841 A command always starts with a backslash
842 \begin_inset Quotes gld
852 \begin_inset Quotes grd
856 To omit optional arguments, also omit the associated brackets.
857 The braces around the required arguments are named in this document as
860 \begin_inset Index idx
863 \begin_layout Plain Layout
871 If you add in a formula a left brace to a command name, \SpecialChar LyX
873 creates a \SpecialChar TeX
875 In all other cases \SpecialChar TeX
876 braces are created in formulas with the command
884 braces appear red in \SpecialChar LyX
885 , in contrary to normal braces which appear blue.
887 mode no command is needed to get \SpecialChar TeX
890 braces don't appear in the output.
893 \begin_layout Standard
894 When commands without arguments, like commands for symbols are entered in
896 mode, a space character must
900 be behind the command to end it.
901 This space doesn't appear in the output.
902 When the space should appear in the output, the space must be followed
903 by a protected space in normal text.
906 \begin_layout Standard
907 A protected space is inserted with
910 arg "command-alternatives space-insert protected ; math-space"
916 \begin_layout Subsection*
917 \begin_inset Newpage newpage
923 \begin_layout Itemize
925 \begin_inset space \textvisiblespace{}
928 denotes a space character to be input.
931 \begin_layout Itemize
933 \begin_inset Formula $\to$
936 denotes the usage of the corresponding arrow key on the keyboard.
941 key can often be used instead of
942 \begin_inset Formula $\to$
946 \begin_inset Formula $\downarrow$
954 \begin_inset Formula $\leftarrow$
958 \begin_inset Formula $\uparrow$
964 \begin_layout Subsection*
968 \begin_layout Standard
970 \begin_inset Float table
976 \begin_layout Plain Layout
978 \begin_inset Caption Standard
980 \begin_layout Plain Layout
981 \begin_inset CommandInset label
983 name "tab:Available-units"
995 \begin_layout Plain Layout
998 <lyxtabular version="3" rows="13" columns="2">
999 <features tabularvalignment="middle">
1000 <column alignment="center" valignment="top">
1001 <column alignment="center" valignment="top">
1003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1006 \begin_layout Plain Layout
1012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1015 \begin_layout Plain Layout
1023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1026 \begin_layout Plain Layout
1032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1035 \begin_layout Plain Layout
1043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1046 \begin_layout Plain Layout
1052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1055 \begin_layout Plain Layout
1063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1066 \begin_layout Plain Layout
1072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1075 \begin_layout Plain Layout
1077 \begin_inset space \thinspace{}
1081 \begin_inset space \thinspace{}
1091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1094 \begin_layout Plain Layout
1100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1103 \begin_layout Plain Layout
1105 \begin_inset space \thinspace{}
1109 \begin_inset space \thinspace{}
1119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1122 \begin_layout Plain Layout
1128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1131 \begin_layout Plain Layout
1133 \begin_inset space \thinspace{}
1137 \begin_inset space \thinspace{}
1147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1150 \begin_layout Plain Layout
1156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1159 \begin_layout Plain Layout
1161 \begin_inset space \thinspace{}
1165 \begin_inset space \thinspace{}
1175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1178 \begin_layout Plain Layout
1184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1187 \begin_layout Plain Layout
1189 \begin_inset space \thinspace{}
1193 \begin_inset space \thinspace{}
1203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1206 \begin_layout Plain Layout
1212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1215 \begin_layout Plain Layout
1217 \begin_inset space \thinspace{}
1221 \begin_inset Formula $\approx$
1225 \begin_inset space \thinspace{}
1235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1238 \begin_layout Plain Layout
1244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1247 \begin_layout Plain Layout
1249 \begin_inset space \thinspace{}
1253 \begin_inset space \thinspace{}
1263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1266 \begin_layout Plain Layout
1272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1275 \begin_layout Plain Layout
1279 \begin_inset Quotes eld
1285 \begin_inset Quotes erd
1295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1298 \begin_layout Plain Layout
1304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1307 \begin_layout Plain Layout
1309 \begin_inset Quotes eld
1317 \begin_inset Quotes erd
1327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1330 \begin_layout Plain Layout
1336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1339 \begin_layout Plain Layout
1341 \begin_inset space \thinspace{}
1345 \begin_inset Formula $\nicefrac{1}{18}$
1349 \begin_inset space \thinspace{}
1370 \begin_layout Standard
1371 \begin_inset Newpage newpage
1377 \begin_layout Section
1381 \begin_layout Subsection
1383 \begin_inset Index idx
1386 \begin_layout Plain Layout
1393 \begin_inset Index idx
1396 \begin_layout Plain Layout
1403 \begin_inset Index idx
1406 \begin_layout Plain Layout
1411 \begin_layout Plain Layout
1422 \begin_layout Plain Layout
1435 \begin_inset Index idx
1438 \begin_layout Plain Layout
1443 \begin_layout Plain Layout
1454 \begin_layout Plain Layout
1469 \begin_layout Standard
1470 Indices are created with an underscore
1471 \begin_inset Quotes eld
1475 \begin_inset Quotes erd
1478 or via the math toolbar button
1481 arg "math-subscript"
1484 , exponents with a caret
1485 \begin_inset Quotes eld
1489 \begin_inset Quotes erd
1492 or via the math toolbar button
1495 arg "math-superscript"
1499 \begin_inset Separator parbreak
1505 \begin_layout Standard
1507 \begin_inset Tabular
1508 <lyxtabular version="3" rows="4" columns="2">
1509 <features tabularvalignment="middle">
1510 <column alignment="center" valignment="top" width="0pt">
1511 <column alignment="center" valignment="top" width="0pt">
1513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1516 \begin_layout Plain Layout
1522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1525 \begin_layout Plain Layout
1527 \begin_inset Note Note
1530 \begin_layout Plain Layout
1537 is only used as spacer.
1549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1552 \begin_layout Plain Layout
1558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1561 \begin_layout Plain Layout
1562 \begin_inset Formula $B_{V}$
1572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1575 \begin_layout Plain Layout
1581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1584 \begin_layout Plain Layout
1585 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1598 \begin_layout Plain Layout
1600 \begin_inset space \textvisiblespace{}
1608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1611 \begin_layout Plain Layout
1612 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1628 \begin_layout Standard
1629 As the caret is in some languages an accent, vowels will be accentuated
1630 in this case and not set as exponents
1634 \begin_layout Plain Layout
1635 Depending on the used keyboard settings this can also happen for characters
1642 To get exponents in this case, press
1646 after the caret as in the last example.
1649 \begin_layout Subsection
1651 \begin_inset CommandInset label
1653 name "subsec:Fractions"
1658 \begin_inset Index idx
1661 \begin_layout Plain Layout
1670 \begin_layout Standard
1671 Fractions are generated with the command
1678 \begin_inset Index idx
1681 \begin_layout Plain Layout
1689 or via the math toolbar button
1692 arg "math-insert \\frac"
1696 The font size is adjusted automatically, depending on whether the fraction
1697 is in an inline or display style formula.
1698 With the math toolbar button
1701 arg "math-insert \\frac-square"
1704 you can select different fraction types.
1707 \begin_layout Standard
1715 \begin_inset Index idx
1718 \begin_layout Plain Layout
1726 a fraction can be created that always has the size of a display style formula.
1734 \begin_inset Index idx
1737 \begin_layout Plain Layout
1745 the fraction appears always with the size of an inline formula.
1749 \begin_layout Standard
1750 A line with the fraction
1751 \begin_inset Formula $\frac{1}{2}$
1754 that was created with the command
1763 \begin_layout Standard
1764 A line with the fraction
1765 \begin_inset Formula $\dfrac{1}{2}$
1768 that was created with the command
1775 \begin_inset Separator parbreak
1781 \begin_layout Standard
1783 \begin_inset Tabular
1784 <lyxtabular version="3" rows="4" columns="2">
1785 <features tabularvalignment="middle">
1786 <column alignment="center" valignment="top" width="0pt">
1787 <column alignment="center" valignment="top" width="0pt">
1789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1792 \begin_layout Plain Layout
1798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1801 \begin_layout Plain Layout
1803 \begin_inset Note Note
1806 \begin_layout Plain Layout
1813 is only used as spacer.
1825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1828 \begin_layout Plain Layout
1832 \begin_inset space \textvisiblespace{}
1836 \begin_inset Formula $\downarrow$
1844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1847 \begin_layout Plain Layout
1848 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1861 \begin_layout Plain Layout
1865 \begin_inset space \textvisiblespace{}
1869 \begin_inset Formula $\downarrow$
1877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1880 \begin_layout Plain Layout
1881 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1894 \begin_layout Plain Layout
1898 \begin_inset space \textvisiblespace{}
1904 \begin_inset space \textvisiblespace{}
1908 \begin_inset Formula $\downarrow$
1912 \begin_inset Formula $\downarrow\downarrow$
1920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1923 \begin_layout Plain Layout
1924 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
1940 \begin_layout Standard
1941 \begin_inset VSpace bigskip
1945 \begin_inset Newpage newpage
1948 For nested fractions the command
1955 \begin_inset Index idx
1958 \begin_layout Plain Layout
1968 \begin_inset VSpace -3mm
1974 \begin_layout Standard
1975 \begin_inset Formula
1977 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1978 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1986 \begin_layout Standard
1987 The command for the example above is:
1990 \begin_layout Standard
1996 \begin_inset space \textvisiblespace{}
2000 \begin_inset Formula $\downarrow$
2006 \begin_inset space \textvisiblespace{}
2012 \begin_inset space \textvisiblespace{}
2016 \begin_inset Formula $\downarrow$
2020 \begin_inset Formula $\downarrow$
2026 \begin_layout Standard
2027 \begin_inset VSpace medskip
2033 \begin_layout Standard
2040 sets the fraction always in the size of a displayed formula, also when
2041 it is part of another fraction.
2044 \begin_layout Standard
2045 It is possible to specify the alignment of the numerator.
2052 is used to left align it, the command
2065 centers the numerator.
2066 These fractions demonstrate the different alignments:
2069 \begin_layout Standard
2072 \begin_inset Formula
2074 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2082 \begin_layout Standard
2083 \begin_inset Note Greyedout
2086 \begin_layout Plain Layout
2103 are no real \SpecialChar LaTeX
2104 commands but represent the command
2108 cfrac[alignment]{numerator}{denominator}
2111 Therefore you cannot use them in \SpecialChar TeX
2120 \begin_layout Standard
2121 \begin_inset VSpace medskip
2124 It is often advantageous to combine
2137 \begin_inset Formula
2139 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2147 \begin_layout Standard
2148 For inline fractions with a sloped fraction stroke you can use the command
2156 \begin_inset Index idx
2159 \begin_layout Plain Layout
2168 \begin_inset Formula $\nicefrac{5}{31}$
2178 \begin_inset Index idx
2181 \begin_layout Plain Layout
2190 \begin_inset Formula $\unitfrac{5}{31}$
2193 There is furthermore the command
2199 that offers to write a fraction in combination with a number:
2200 \begin_inset Formula $\unitfrac[2]{1}{3}$
2206 \begin_layout Standard
2207 \begin_inset Note Greyedout
2210 \begin_layout Plain Layout
2221 is not a real \SpecialChar LaTeX
2222 command but the command
2223 \begin_inset Newline newline
2230 unitfrac[number]{numerator}{denominator}
2233 Therefore you cannot use it in \SpecialChar TeX
2242 \begin_layout Standard
2243 How to define own fractions where the fraction stroke can be changed, is
2245 \begin_inset CommandInset ref
2247 reference "subsec:Self-defined-Fractions"
2254 \begin_layout Standard
2255 Multiline fractions are explained in
2256 \begin_inset CommandInset ref
2258 reference "subsec:Multiline-Fractions"
2265 \begin_layout Subsection
2267 \begin_inset Index idx
2270 \begin_layout Plain Layout
2279 \begin_layout Standard
2280 Square roots are created with
2287 \begin_inset Index idx
2290 \begin_layout Plain Layout
2298 or the math toolbar button
2301 arg "math-insert \\sqrt"
2304 , all other roots with the command
2311 \begin_inset Index idx
2314 \begin_layout Plain Layout
2322 or with the math toolbar button
2325 arg "math-insert \\root"
2329 \begin_inset Separator parbreak
2335 \begin_layout Standard
2337 \begin_inset Tabular
2338 <lyxtabular version="3" rows="3" columns="2">
2339 <features tabularvalignment="middle">
2340 <column alignment="center" valignment="top" width="0pt">
2341 <column alignment="center" valignment="top" width="0pt">
2343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2346 \begin_layout Plain Layout
2352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2355 \begin_layout Plain Layout
2357 \begin_inset Note Note
2360 \begin_layout Plain Layout
2367 is only used as spacer.
2379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2382 \begin_layout Plain Layout
2386 \begin_inset space \textvisiblespace{}
2394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2397 \begin_layout Plain Layout
2398 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2408 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2411 \begin_layout Plain Layout
2415 \begin_inset space \textvisiblespace{}
2419 \begin_inset Formula $\downarrow$
2427 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2430 \begin_layout Plain Layout
2431 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2447 \begin_layout Standard
2448 A square root can also be created with
2454 when the root index field is left empty.
2457 \begin_layout Standard
2458 With certain indices the distance to the root is too small, like in this
2460 \begin_inset Formula $\sqrt[\beta]{B}$
2464 \begin_inset Newline newline
2468 \begin_inset Formula $\beta$
2472 To avoid this, the commands
2479 \begin_inset Index idx
2482 \begin_layout Plain Layout
2497 \begin_inset Index idx
2500 \begin_layout Plain Layout
2508 are used with the following scheme:
2511 \begin_layout Standard
2525 \begin_layout Standard
2526 Distance is the number of Big Points (unit bp;
2527 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2530 ), that the index should be moved to the left or top, resp..
2531 The commands are written to the index.
2532 This way the command
2533 \begin_inset Newline newline
2543 \begin_inset Formula $\to$
2549 \begin_inset Formula $\to$
2555 \begin_inset space \textvisiblespace{}
2559 \begin_inset Formula $\to$
2563 \begin_inset Newline newline
2568 produces a correct typeset formula:
2569 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2575 \begin_layout Subsection
2576 Binomial Coefficients
2577 \begin_inset Index idx
2580 \begin_layout Plain Layout
2581 Binomial coefficients
2589 \begin_layout Standard
2590 Binomial coefficients are inserted with the command
2597 \begin_inset Index idx
2600 \begin_layout Plain Layout
2608 or with the submenu of the math toolbar button
2611 arg "math-insert \\frac-square"
2627 there are the commands
2634 \begin_inset Index idx
2637 \begin_layout Plain Layout
2652 \begin_inset Index idx
2655 \begin_layout Plain Layout
2664 For other brackets around binomial coeficients there are the commands
2671 \begin_inset Index idx
2674 \begin_layout Plain Layout
2689 \begin_inset Index idx
2692 \begin_layout Plain Layout
2701 \begin_inset Separator parbreak
2707 \begin_layout Standard
2709 \begin_inset Tabular
2710 <lyxtabular version="3" rows="6" columns="2">
2711 <features tabularvalignment="middle">
2712 <column alignment="center" valignment="top" width="0pt">
2713 <column alignment="center" valignment="top" width="0pt">
2715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2718 \begin_layout Plain Layout
2724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2727 \begin_layout Plain Layout
2729 \begin_inset Note Note
2732 \begin_layout Plain Layout
2739 is only used as spacer.
2751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2754 \begin_layout Plain Layout
2758 \begin_inset space \textvisiblespace{}
2762 \begin_inset Formula $\downarrow$
2770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2773 \begin_layout Plain Layout
2774 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2787 \begin_layout Plain Layout
2791 \begin_inset space \textvisiblespace{}
2795 \begin_inset Formula $\downarrow$
2803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2806 \begin_layout Plain Layout
2807 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2820 \begin_layout Plain Layout
2824 \begin_inset space \textvisiblespace{}
2828 \begin_inset Formula $\downarrow$
2836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2839 \begin_layout Plain Layout
2840 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2853 \begin_layout Plain Layout
2857 \begin_inset space \textvisiblespace{}
2861 \begin_inset Formula $\downarrow$
2869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2872 \begin_layout Plain Layout
2873 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2886 \begin_layout Plain Layout
2890 \begin_inset space \textvisiblespace{}
2894 \begin_inset Formula $\downarrow$
2902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2905 \begin_layout Plain Layout
2906 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
2922 \begin_layout Subsection
2923 Case Differentiations
2924 \begin_inset Index idx
2927 \begin_layout Plain Layout
2928 Case differentiations
2936 \begin_layout Standard
2938 \begin_inset Tabular
2939 <lyxtabular version="3" rows="3" columns="2">
2940 <features tabularvalignment="middle">
2941 <column alignment="center" valignment="top" width="0pt">
2942 <column alignment="center" valignment="top" width="0pt">
2944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2947 \begin_layout Plain Layout
2953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2956 \begin_layout Plain Layout
2964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2967 \begin_layout Plain Layout
2971 \begin_inset space \textvisiblespace{}
2975 \begin_inset Formula $\to$
2979 \begin_inset Index idx
2982 \begin_layout Plain Layout
2995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2998 \begin_layout Plain Layout
2999 \begin_inset Formula $\begin{cases}
3010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3013 \begin_layout Plain Layout
3017 \begin_inset space \textvisiblespace{}
3023 arg "newline-insert newline"
3031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3034 \begin_layout Plain Layout
3035 \begin_inset Formula $\begin{cases}
3036 A & \textrm{for }x>0\\
3037 B & \textrm{for }x=0
3054 \begin_layout Standard
3061 or pressing the math toolbar button
3064 arg "math-insert \\cases"
3067 you can create new lines with the shortcut
3070 arg "newline-insert newline"
3073 or the table toolbar button
3076 arg "inset-modify tabular append-row"
3082 \begin_layout Standard
3089 is also available via the menu
3091 Insert\SpecialChar menuseparator
3092 Math\SpecialChar menuseparator
3098 \begin_layout Subsection
3100 \begin_inset Index idx
3103 \begin_layout Plain Layout
3112 \begin_layout Standard
3120 \begin_inset Index idx
3123 \begin_layout Plain Layout
3131 every character can be displayed canceled.
3132 The characters are quasi accentuated by a slash.
3133 \begin_inset Separator parbreak
3139 \begin_layout Standard
3141 \begin_inset Tabular
3142 <lyxtabular version="3" rows="4" columns="2">
3143 <features tabularvalignment="middle">
3144 <column alignment="center" valignment="top" width="0pt">
3145 <column alignment="center" valignment="top" width="0pt">
3147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3150 \begin_layout Plain Layout
3156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3159 \begin_layout Plain Layout
3167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3170 \begin_layout Plain Layout
3178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3181 \begin_layout Plain Layout
3182 \begin_inset Formula $\not=$
3192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3195 \begin_layout Plain Layout
3205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3208 \begin_layout Plain Layout
3209 \begin_inset Formula $\not\le$
3219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3222 \begin_layout Plain Layout
3232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3235 \begin_layout Plain Layout
3236 \begin_inset Formula $\not\parallel$
3252 \begin_layout Standard
3253 The last example shows that not all negations look good.
3254 Therefore there are special commands for some negations (see
3255 \begin_inset CommandInset ref
3257 reference "subsec:Mathematical-Symbols"
3262 \begin_inset CommandInset ref
3264 reference "sec:Relations"
3271 \begin_layout Subsection
3273 \begin_inset CommandInset label
3275 name "subsec:Placeholders"
3280 \begin_inset Index idx
3283 \begin_layout Plain Layout
3290 \begin_inset Index idx
3293 \begin_layout Plain Layout
3294 Chemical characters ! Isotopes
3300 \begin_inset Index idx
3303 \begin_layout Plain Layout
3308 \begin_layout Plain Layout
3319 \begin_layout Plain Layout
3334 \begin_layout Standard
3336 \begin_inset space \thinspace{}
3340 \begin_inset space \space{}
3347 \begin_layout Plain Layout
3348 Typesetting isotopes and chemical symbols is described in
3349 \begin_inset CommandInset ref
3351 reference "subsec:Chemical-Symbols-and"
3360 the following problem occurs:
3361 \begin_inset Separator parbreak
3367 \begin_layout Standard
3369 \begin_inset Tabular
3370 <lyxtabular version="3" rows="2" columns="2">
3371 <features tabularvalignment="middle">
3372 <column alignment="center" valignment="top" width="0pt">
3373 <column alignment="center" valignment="top" width="0pt">
3375 <cell alignment="center" valignment="top" usebox="none">
3378 \begin_layout Plain Layout
3379 Indices created with sub- and superscripts:
3384 <cell alignment="center" valignment="top" usebox="none">
3387 \begin_layout Plain Layout
3388 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3398 <cell alignment="center" valignment="top" usebox="none">
3401 \begin_layout Plain Layout
3407 <cell alignment="center" valignment="top" usebox="none">
3410 \begin_layout Plain Layout
3411 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3425 \begin_inset Note Note
3428 \begin_layout Plain Layout
3435 is only used as spacer.
3443 \begin_layout Standard
3444 The shorter index is by default placed below or above the first character
3445 of the longer index.
3446 To avoid this there is the command
3453 \begin_inset Index idx
3456 \begin_layout Plain Layout
3464 or the math toolbar button
3465 \begin_inset space \thinspace{}
3472 \begin_layout Plain Layout
3473 can be found in the submenu of the toolbar button
3476 arg "math-insert \\space"
3485 \begin_inset Graphics
3486 filename ../images/math/phantom.png
3491 that creates one or more phantom characters.
3498 a small blue box appears that is superposed with two red arrows.
3499 The arrows indicate that the complete width and height of the box content
3500 will be created as placeholder.
3501 Phantom characters are accordingly placeholders with the size of the characters.
3502 \begin_inset Separator parbreak
3508 \begin_layout Standard
3510 \begin_inset Tabular
3511 <lyxtabular version="3" rows="4" columns="2">
3512 <features tabularvalignment="middle">
3513 <column alignment="center" valignment="top">
3514 <column alignment="center" valignment="top">
3516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3519 \begin_layout Plain Layout
3525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3528 \begin_layout Plain Layout
3530 \begin_inset Note Note
3533 \begin_layout Plain Layout
3540 is only used as spacer.
3552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3555 \begin_layout Plain Layout
3557 \begin_inset space \textvisiblespace{}
3563 \begin_inset space \textvisiblespace{}
3567 \begin_inset Formula $\to$
3571 \begin_inset space \textvisiblespace{}
3579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3582 \begin_layout Plain Layout
3583 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3596 \begin_layout Plain Layout
3598 \begin_inset space \textvisiblespace{}
3604 \begin_inset space \textvisiblespace{}
3608 \begin_inset Formula $\to$
3612 \begin_inset space \textvisiblespace{}
3620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3623 \begin_layout Plain Layout
3624 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3637 \begin_layout Plain Layout
3641 \begin_inset space \textvisiblespace{}
3647 \begin_inset space \textvisiblespace{}
3651 \begin_inset Formula $\to$
3655 \begin_inset space \textvisiblespace{}
3663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3666 \begin_layout Plain Layout
3667 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3683 \begin_layout Standard
3684 Furthermore there are the commands
3691 \begin_inset Index idx
3694 \begin_layout Plain Layout
3703 \begin_inset space ~
3707 \begin_inset Graphics
3708 filename ../images/math/vphantom.png
3720 \begin_inset Index idx
3723 \begin_layout Plain Layout
3732 \begin_inset space ~
3736 \begin_inset Graphics
3737 filename ../images/math/hphantom.png
3749 creates only space for the maximal height of the characters in the box
3750 but not for its width.
3757 creates only space for the width of the box content.
3758 Therefore the boxes of both commands have only one red arrow.
3761 \begin_layout Standard
3762 For example the command
3767 \begin_inset space \textvisiblespace{}
3774 creates space for the height of the integral sign,
3778 \begin_layout Plain Layout
3785 creates an integral sign, see
3786 \begin_inset CommandInset ref
3788 reference "subsec:Big-Operators"
3797 because this is the larger character.
3798 An example application is in
3799 \begin_inset CommandInset ref
3801 reference "subsec:Multiline-Brackets"
3808 \begin_layout Standard
3809 Placeholders can also be used for text when they are inserted via the menu
3812 Insert\SpecialChar menuseparator
3813 Formatting\SpecialChar menuseparator
3819 \begin_layout Standard
3821 \begin_inset Newline newline
3825 \begin_inset Phantom Phantom
3828 \begin_layout Plain Layout
3837 \begin_layout Subsection
3839 \begin_inset Index idx
3842 \begin_layout Plain Layout
3849 \begin_inset Index idx
3852 \begin_layout Plain Layout
3853 Formula ! underlined
3861 \begin_layout Standard
3863 \begin_inset Tabular
3864 <lyxtabular version="3" rows="4" columns="2">
3865 <features tabularvalignment="middle">
3866 <column alignment="center" valignment="top" width="0pt">
3867 <column alignment="center" valignment="top" width="0pt">
3869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3872 \begin_layout Plain Layout
3878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3881 \begin_layout Plain Layout
3883 \begin_inset Note Note
3886 \begin_layout Plain Layout
3893 is only used as spacer.
3905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3908 \begin_layout Plain Layout
3912 \begin_inset space \textvisiblespace{}
3916 \begin_inset Index idx
3919 \begin_layout Plain Layout
3932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3935 \begin_layout Plain Layout
3936 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3946 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
3949 \begin_layout Plain Layout
3953 \begin_inset space \textvisiblespace{}
3957 \begin_inset Index idx
3960 \begin_layout Plain Layout
3973 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
3976 \begin_layout Plain Layout
3977 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3990 \begin_layout Plain Layout
3994 \begin_inset space \textvisiblespace{}
4000 \begin_inset space \textvisiblespace{}
4008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4011 \begin_layout Plain Layout
4012 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4028 \begin_layout Standard
4029 In the last example it doesn't matter if first
4044 \begin_layout Standard
4045 To double underline use
4054 \begin_layout Standard
4055 It is possible to place up to 6 lines above or below characters.
4058 \begin_layout Standard
4059 \begin_inset VSpace bigskip
4062 Custom lines can be created using the command
4069 \begin_inset Index idx
4072 \begin_layout Plain Layout
4080 which has the following scheme:
4083 \begin_layout Standard
4088 rule[vertical offset]{length}{thickness}
4091 \begin_layout Standard
4092 The optional vertical offset shifts the line upwards (or downwards, when
4093 the value is negative).
4095 \begin_inset CommandInset ref
4097 reference "tab:Available-units"
4101 can be used for the values.
4102 Here are two example lines created with the commands
4103 \begin_inset Newline newline
4110 rule[-2ex]{3cm}{2pt}
4121 \begin_layout Standard
4123 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4129 \begin_layout Standard
4136 can also be used for text when a line is inserted via the menu
4138 Insert\SpecialChar menuseparator
4139 Formatting\SpecialChar menuseparator
4141 \begin_inset space ~
4149 \begin_layout Standard
4151 \begin_inset CommandInset line
4162 \begin_layout Subsection
4164 \begin_inset CommandInset label
4166 name "subsec:Ellipses"
4171 \begin_inset Index idx
4174 \begin_layout Plain Layout
4183 \begin_layout Standard
4184 There are different types of ellipses available.
4188 \begin_layout Plain Layout
4189 In the math toolbar in the submenu of the button
4192 arg "math-insert \\ldots"
4200 For listings dots at the baseline are used (
4207 \begin_inset Index idx
4210 \begin_layout Plain Layout
4218 ), while for operations dots are needed that are on the same height as the
4226 \begin_inset Index idx
4229 \begin_layout Plain Layout
4238 When using the command
4245 \begin_inset Index idx
4248 \begin_layout Plain Layout
4256 , \SpecialChar LaTeX
4257 decides on the basis of the next character what type is used.
4258 \begin_inset Separator parbreak
4264 \begin_layout Standard
4266 \begin_inset Tabular
4267 <lyxtabular version="3" rows="9" columns="2">
4268 <features tabularvalignment="middle">
4269 <column alignment="center" valignment="top" width="0pt">
4270 <column alignment="center" valignment="top" width="0pt">
4272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4275 \begin_layout Plain Layout
4281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4284 \begin_layout Plain Layout
4292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4295 \begin_layout Plain Layout
4297 \begin_inset space \textvisiblespace{}
4303 \begin_inset space \textvisiblespace{}
4311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4314 \begin_layout Plain Layout
4315 \begin_inset Formula $A_{1},\dots,A_{n}$
4325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4328 \begin_layout Plain Layout
4330 \begin_inset space \textvisiblespace{}
4336 \begin_inset space \textvisiblespace{}
4344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4347 \begin_layout Plain Layout
4348 \begin_inset Formula $A_{1}+\dots+A_{n}$
4358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4361 \begin_layout Plain Layout
4363 \begin_inset space \textvisiblespace{}
4369 \begin_inset space \textvisiblespace{}
4377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4380 \begin_layout Plain Layout
4381 \begin_inset Formula $A_{1},\ldots,A_{n}$
4391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4394 \begin_layout Plain Layout
4396 \begin_inset space \textvisiblespace{}
4402 \begin_inset space \textvisiblespace{}
4410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4413 \begin_layout Plain Layout
4414 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4427 \begin_layout Plain Layout
4435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4438 \begin_layout Plain Layout
4439 \begin_inset Formula $\vdots$
4449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4452 \begin_layout Plain Layout
4460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4463 \begin_layout Plain Layout
4464 \begin_inset Formula $\ddots$
4474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4477 \begin_layout Plain Layout
4485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4488 \begin_layout Plain Layout
4489 \begin_inset Formula $\iddots$
4499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4502 \begin_layout Plain Layout
4504 \begin_inset space \thinspace{}
4507 matrix with the different dots
4512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4515 \begin_layout Plain Layout
4516 \begin_inset Formula $\begin{array}{ccc}
4517 A_{11} & \cdots & A_{1m}\\
4518 \vdots & \ddots & \vdots\\
4519 A_{n1} & \cdots & A_{nm}
4536 \begin_layout Standard
4537 The ellipses available in menu
4539 Insert\SpecialChar menuseparator
4541 \begin_inset space ~
4555 \begin_layout Standard
4556 \begin_inset VSpace medskip
4565 , one of the options
4567 Use mathdots package (automatically)
4569 must be set in the document settings under
4572 \begin_inset space ~
4578 \begin_inset Newline newline
4583 Use mathdots package
4585 will improve the appearance of all dots in the documents if their font
4586 style or size is not the default.
4589 \begin_layout Standard
4590 \begin_inset VSpace medskip
4593 Specially for matrices there are ellipses that span over several columns.
4594 They are created with the command
4601 \begin_inset Index idx
4604 \begin_layout Plain Layout
4612 , that has the following scheme:
4615 \begin_layout Standard
4620 hdotsfor[distance]{number of columns}
4623 \begin_layout Standard
4624 The number of columns specifies how many columns should be spanned.
4625 Distance is a factor for the distance between the dots.
4628 \begin_layout Standard
4629 In the following matrix the command
4635 was inserted in the first box of the second line, to get an ellipsis with
4636 a dot distance twice as long as with the command
4643 \begin_inset Formula
4645 \left(\begin{array}{cccc}
4654 Note that the matrix fields that should be spanned must be empty, otherwise
4655 you get \SpecialChar LaTeX
4659 \begin_layout Standard
4660 \begin_inset VSpace bigskip
4663 Furthermore you can fill with the command
4670 \begin_inset Index idx
4673 \begin_layout Plain Layout
4681 the rest of a line with dots.
4682 The effect of these commands is the same as with
4689 \begin_inset CommandInset ref
4691 reference "subsec:Variable-Space"
4698 \begin_layout Standard
4699 For example the command
4704 \begin_inset space \textvisiblespace{}
4712 \begin_layout Standard
4713 \begin_inset Formula $A\dotfill B$
4719 \begin_layout Standard
4726 there is for a line the command
4733 \begin_inset Index idx
4736 \begin_layout Plain Layout
4747 \begin_layout Standard
4748 \begin_inset Formula $A\hrulefill B$
4754 \begin_layout Standard
4755 To use the commands for text, they have to be inserted in \SpecialChar TeX
4759 \begin_layout Section
4761 \begin_inset CommandInset label
4768 \begin_inset Index idx
4771 \begin_layout Plain Layout
4780 \begin_layout Standard
4781 Matrices can be inserted via the math toolbar button
4784 arg "dialog-show mathmatrix"
4789 Insert\SpecialChar menuseparator
4790 Math\SpecialChar menuseparator
4794 In the matrix dialog you can specify the number of columns and rows, the
4795 alignment and the decoration.
4796 The vertical alignment is only of importance for matrices in inline formulas:
4799 \begin_layout Standard
4800 The first matrix is top
4801 \begin_inset Formula $\begin{array}[t]{cccc}
4809 \begin_inset Formula $\begin{array}{cccc}
4816 and the third bottom
4817 \begin_inset Formula $\begin{array}[b]{cccc}
4827 \begin_layout Standard
4828 The horizontal alignment specifies how the column entries should be aligned.
4829 It is set by entering a letter for every column.
4834 denotes left aligned,
4843 To create for example a 4
4848 \begin_inset space ~
4851 matrix where the first column is left aligned, the second and third are
4852 centered and the last one is right aligned, one enters for the horizontal
4858 Normally in a matrix all columns are centered, therefore the default for
4866 \begin_layout Standard
4867 Horizontal alignment:
4870 \begin_layout Standard
4876 \begin_inset Formula $\begin{array}{lll}
4888 \begin_inset Formula $\begin{array}{ccc}
4900 \begin_inset Formula $\begin{array}{rrr}
4910 \begin_layout Standard
4911 To add or delete rows and columns subsequently, the math toolbar buttons
4915 arg "inset-modify tabular append-row"
4921 arg "inset-modify tabular delete-row"
4925 \begin_inset space \thinspace{}
4930 Edit\SpecialChar menuseparator
4934 New rows can also be created with
4937 arg "newline-insert newline"
4943 \begin_layout Standard
4944 \begin_inset VSpace bigskip
4951 adds parentheses in the selected style around the matrix.
4952 Alternatively, parentheses can can either be created with the commands
4960 \begin_inset Index idx
4963 \begin_layout Plain Layout
4978 \begin_inset Index idx
4981 \begin_layout Plain Layout
4992 \begin_inset space ~
4998 \begin_inset CommandInset ref
5000 reference "subsec:Automatic-Bracket-Size"
5004 , or by using the following commands:
5005 \begin_inset VSpace medskip
5011 \begin_layout Standard
5012 \begin_inset space \hfill{}
5016 \begin_inset Tabular
5017 <lyxtabular version="3" rows="4" columns="2">
5018 <features tabularvalignment="middle">
5019 <column alignment="center" valignment="top">
5020 <column alignment="center" valignment="top">
5022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5025 \begin_layout Plain Layout
5031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5034 \begin_layout Plain Layout
5036 \begin_inset Note Note
5039 \begin_layout Plain Layout
5046 is only used as spacer.
5058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5061 \begin_layout Plain Layout
5065 \begin_inset space \textvisiblespace{}
5073 \begin_inset space \thinspace{}
5081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5084 \begin_layout Plain Layout
5085 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5086 0 & \textrm{-}\mathrm{i}\\
5088 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5101 \begin_layout Plain Layout
5105 \begin_inset space \textvisiblespace{}
5113 \begin_inset space \thinspace{}
5121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5124 \begin_layout Plain Layout
5125 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5126 0 & \textrm{-}\mathrm{i}\\
5128 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5141 \begin_layout Plain Layout
5145 \begin_inset space \textvisiblespace{}
5153 \begin_inset space \thinspace{}
5161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5164 \begin_layout Plain Layout
5165 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5166 0 & \textrm{-}\mathrm{i}\\
5168 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5182 \begin_inset space \hfill{}
5186 \begin_inset Tabular
5187 <lyxtabular version="3" rows="4" columns="2">
5188 <features tabularvalignment="middle">
5189 <column alignment="center" valignment="top">
5190 <column alignment="center" valignment="top">
5192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5195 \begin_layout Plain Layout
5201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5204 \begin_layout Plain Layout
5212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5215 \begin_layout Plain Layout
5219 \begin_inset space \textvisiblespace{}
5227 \begin_inset space \thinspace{}
5235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5238 \begin_layout Plain Layout
5239 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5240 0 & \textrm{-}\mathrm{i}\\
5242 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5255 \begin_layout Plain Layout
5259 \begin_inset space \textvisiblespace{}
5267 \begin_inset space \thinspace{}
5275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5278 \begin_layout Plain Layout
5279 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5280 0 & \textrm{-}\mathrm{i}\\
5282 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5295 \begin_layout Plain Layout
5299 \begin_inset space \textvisiblespace{}
5307 \begin_inset space \thinspace{}
5315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5318 \begin_layout Plain Layout
5319 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5320 0 & \textrm{-}\mathrm{i}\\
5322 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5336 \begin_inset space \hfill{}
5342 \begin_layout Standard
5343 \begin_inset VSpace medskip
5347 \begin_inset space \thinspace{}
5351 \begin_inset space \space{}
5360 is inserted, a blue box appears between two vertical lines where the matrix
5362 \begin_inset Newline newline
5365 Note that decorated matrices ignore the vertical alignment.
5368 \begin_layout Standard
5369 \begin_inset VSpace bigskip
5372 As all multiline formulas are matrices, the length
5379 \begin_inset Index idx
5382 \begin_layout Plain Layout
5390 that is described in
5391 \begin_inset CommandInset ref
5393 reference "subsec:Column-Separation"
5397 can also be used to change the column separation of matrices.
5400 \begin_layout Standard
5401 To change the row separation, the command
5408 \begin_inset Index idx
5411 \begin_layout Plain Layout
5420 It is used as follows:
5423 \begin_layout Standard
5430 arraystretch}{stretch factor}
5431 \begin_inset Index idx
5434 \begin_layout Plain Layout
5445 \begin_layout Standard
5452 assigns the stretch factor to the predefined command
5460 \begin_inset space \thinspace{}
5464 \begin_inset space \space{}
5467 the row separation, use the factor 2.
5468 This is then used for all following matrices.
5469 To go back to the original separation, assign the factor 1 to
5478 \begin_layout Standard
5479 To set matrices into a text line, the command
5486 \begin_inset Index idx
5489 \begin_layout Plain Layout
5498 When it is inserted a blue box with two dashed lines appears.
5499 In this box the matrix is inserted.
5502 \begin_layout Standard
5504 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5506 \end{smallmatrix}\right)$
5512 \begin_layout Section
5513 Brackets and Delimiters
5514 \begin_inset Index idx
5517 \begin_layout Plain Layout
5524 \begin_inset Index idx
5527 \begin_layout Plain Layout
5536 \begin_layout Subsection
5537 Vertical Brackets and Delimiters
5538 \begin_inset Index idx
5541 \begin_layout Plain Layout
5550 \begin_layout Standard
5551 \begin_inset space \hfill{}
5555 \begin_inset Tabular
5556 <lyxtabular version="3" rows="9" columns="2">
5557 <features tabularvalignment="middle">
5558 <column alignment="center" valignment="top" width="0pt">
5559 <column alignment="center" valignment="top" width="0pt">
5561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5564 \begin_layout Plain Layout
5570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5573 \begin_layout Plain Layout
5581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5584 \begin_layout Plain Layout
5590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5593 \begin_layout Plain Layout
5594 \begin_inset Formula $($
5604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5607 \begin_layout Plain Layout
5613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5616 \begin_layout Plain Layout
5617 \begin_inset Formula $\{$
5627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5630 \begin_layout Plain Layout
5636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5639 \begin_layout Plain Layout
5640 \begin_inset Formula $[$
5650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5653 \begin_layout Plain Layout
5661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5664 \begin_layout Plain Layout
5665 \begin_inset Formula $\langle$
5675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5678 \begin_layout Plain Layout
5686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5689 \begin_layout Plain Layout
5690 \begin_inset Formula $\lceil$
5700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5703 \begin_layout Plain Layout
5711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5714 \begin_layout Plain Layout
5715 \begin_inset Formula $\lfloor$
5725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5728 \begin_layout Plain Layout
5734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5737 \begin_layout Plain Layout
5738 \begin_inset Formula $/$
5748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5751 \begin_layout Plain Layout
5757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5760 \begin_layout Plain Layout
5761 \begin_inset Formula $|$
5775 \begin_inset space \hfill{}
5779 \begin_inset Tabular
5780 <lyxtabular version="3" rows="9" columns="2">
5781 <features tabularvalignment="middle">
5782 <column alignment="center" valignment="top" width="0pt">
5783 <column alignment="center" valignment="top" width="0pt">
5785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5788 \begin_layout Plain Layout
5794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5797 \begin_layout Plain Layout
5805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5808 \begin_layout Plain Layout
5814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5817 \begin_layout Plain Layout
5818 \begin_inset Formula $)$
5828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5831 \begin_layout Plain Layout
5837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5840 \begin_layout Plain Layout
5841 \begin_inset Formula $\}$
5851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5854 \begin_layout Plain Layout
5860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5863 \begin_layout Plain Layout
5864 \begin_inset Formula $]$
5874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5877 \begin_layout Plain Layout
5885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5888 \begin_layout Plain Layout
5889 \begin_inset Formula $\rangle$
5899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5902 \begin_layout Plain Layout
5910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5913 \begin_layout Plain Layout
5914 \begin_inset Formula $\rceil$
5924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5927 \begin_layout Plain Layout
5935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5938 \begin_layout Plain Layout
5939 \begin_inset Formula $\rfloor$
5949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5952 \begin_layout Plain Layout
5962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5965 \begin_layout Plain Layout
5966 \begin_inset Formula $\backslash$
5976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5979 \begin_layout Plain Layout
5987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5990 \begin_layout Plain Layout
5991 \begin_inset Formula $\|$
6005 \begin_inset space \hfill{}
6011 \begin_layout Standard
6014 \begin_inset Note Greyedout
6017 \begin_layout Plain Layout
6030 \begin_inset Index idx
6033 \begin_layout Plain Layout
6041 must be used for the backslash, because the command
6049 produces a line break there.
6057 \begin_layout Standard
6058 For all characters listed above the size can be adjusted with the commands
6059 described in the following two subsections.
6060 When using these commands, the characters < and > can directly be used
6061 instead of the commands
6076 \begin_layout Subsubsection
6078 \begin_inset CommandInset label
6080 name "subsec:Manual-Bracket-Size"
6085 \begin_inset Index idx
6088 \begin_layout Plain Layout
6089 Bracket size ! manual
6097 \begin_layout Standard
6098 The bracket size can be specified manually by the \SpecialChar LaTeX
6106 \begin_inset Index idx
6109 \begin_layout Plain Layout
6142 denotes the smallest and
6148 the largest bracket size.
6151 \begin_layout Standard
6152 These commands are used to emphasize levels of brackets:
6153 \begin_inset Separator parbreak
6159 \begin_layout Standard
6161 \begin_inset Tabular
6162 <lyxtabular version="3" rows="2" columns="2">
6163 <features tabularvalignment="middle">
6164 <column alignment="center" valignment="top" width="0pt">
6165 <column alignment="center" valignment="top" width="0pt">
6167 <cell alignment="center" valignment="top" usebox="none">
6170 \begin_layout Plain Layout
6171 all brackets in the same size:
6176 <cell alignment="center" valignment="top" usebox="none">
6179 \begin_layout Plain Layout
6180 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6190 <cell alignment="center" valignment="top" usebox="none">
6193 \begin_layout Plain Layout
6199 <cell alignment="center" valignment="top" usebox="none">
6202 \begin_layout Plain Layout
6203 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6217 \begin_inset Note Note
6220 \begin_layout Plain Layout
6227 is only used as spacer.
6235 \begin_layout Standard
6236 For the second formula the command
6243 \begin_inset space \textvisiblespace{}
6251 \begin_layout Standard
6252 Here is an overview about all bracket sizes:
6253 \begin_inset Separator parbreak
6259 \begin_layout Standard
6276 \begin_inset space \textvisiblespace{}
6284 \begin_inset space \textvisiblespace{}
6288 \begin_inset space \textvisiblespace{}
6298 \begin_layout Standard
6300 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6306 \begin_layout Standard
6313 -commands there is the variant
6320 \begin_inset Index idx
6323 \begin_layout Plain Layout
6331 that adds a bit more space between the bracket and its content, and the
6345 \begin_inset Index idx
6348 \begin_layout Plain Layout
6358 , that don't add additional space.
6363 at the end of the command
6369 is for a left bracket; for a right bracket this will be replaced by an
6375 A left or right bracket can each be an opening or closing bracket.
6378 \begin_layout Standard
6379 In the following table is a comparison of the variants:
6380 \begin_inset Separator parbreak
6386 \begin_layout Standard
6388 \begin_inset Tabular
6389 <lyxtabular version="3" rows="5" columns="2">
6390 <features tabularvalignment="middle">
6391 <column alignment="center" valignment="middle">
6392 <column alignment="center" valignment="middle">
6394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6397 \begin_layout Plain Layout
6403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6406 \begin_layout Plain Layout
6408 \begin_inset Note Note
6411 \begin_layout Plain Layout
6418 is only used as spacer.
6430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6433 \begin_layout Plain Layout
6443 \begin_inset space \textvisiblespace{}
6453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6456 \begin_layout Plain Layout
6457 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6470 \begin_layout Plain Layout
6480 \begin_inset space \textvisiblespace{}
6490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6493 \begin_layout Plain Layout
6494 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6507 \begin_layout Plain Layout
6517 \begin_inset space \textvisiblespace{}
6527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6530 \begin_layout Plain Layout
6531 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6544 \begin_layout Plain Layout
6556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6559 \begin_layout Plain Layout
6560 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6576 \begin_layout Subsubsection
6577 Automatic Bracket Size
6578 \begin_inset CommandInset label
6580 name "subsec:Automatic-Bracket-Size"
6585 \begin_inset Index idx
6588 \begin_layout Plain Layout
6589 Bracket size ! automatic
6597 \begin_layout Standard
6598 Brackets with variable size can be inserted with the commands
6605 \begin_inset Index idx
6608 \begin_layout Plain Layout
6623 \begin_inset Index idx
6626 \begin_layout Plain Layout
6634 or via the math toolbar button
6637 arg "dialog-show mathdelimiter"
6653 the wanted bracket must be inserted.
6654 The bracket size will then automatically be calculated for the output.
6655 \begin_inset Separator parbreak
6661 \begin_layout Standard
6663 normal bracket: The command
6670 \begin_inset space \textvisiblespace{}
6674 \begin_inset Formula $\downarrow$
6678 \begin_inset space \textvisiblespace{}
6684 \begin_inset Formula
6694 \begin_layout Standard
6696 multiline bracket: The command
6705 \begin_inset space \textvisiblespace{}
6709 \begin_inset Formula $\downarrow$
6713 \begin_inset space \textvisiblespace{}
6721 \begin_inset Formula
6723 \ln\left(\frac{A}{C}\right)
6731 \begin_layout Standard
6747 \begin_inset space ~
6753 This has the advantage that you can see in \SpecialChar LyX
6754 immediately the real bracket
6755 size and that the matching right bracket will be created too.
6756 \begin_inset Newline newline
6759 The command for the last example would then be:
6770 \begin_inset space \textvisiblespace{}
6774 \begin_inset Formula $\downarrow$
6780 \begin_layout Standard
6781 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6782 For example the command
6789 \begin_inset space \textvisiblespace{}
6793 \begin_inset Formula $\downarrow$
6797 \begin_inset space \textvisiblespace{}
6807 \begin_inset Formula
6809 \left.\frac{A}{B}\right\}
6828 will be converted by \SpecialChar LyX
6829 to brackets in the right size when the document is
6830 reloaded and an omitted bracket will appear as dashed line.
6833 \begin_layout Standard
6834 \begin_inset VSpace bigskip
6837 Because all popular \SpecialChar LaTeX
6838 distributions use e\SpecialChar TeX
6839 , an extension to \SpecialChar LaTeX
6848 \begin_inset Index idx
6851 \begin_layout Plain Layout
6859 is additionally available for all brackets and limits.
6860 With this command the height of the following character is adapted to the
6861 one of the surrounding brackets, what is e.
6862 \begin_inset space \thinspace{}
6866 \begin_inset space \space{}
6869 needed for physical vectors:
6870 \begin_inset Formula
6872 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6877 For physical vectors there is a special \SpecialChar LaTeX
6878 -package, described in
6879 \begin_inset CommandInset ref
6881 reference "subsec:Physical-Vectors"
6888 \begin_layout Subsection
6890 \begin_inset Index idx
6893 \begin_layout Plain Layout
6894 Brackets ! horizontal
6902 \begin_layout Standard
6904 \begin_inset Tabular
6905 <lyxtabular version="3" rows="4" columns="2">
6906 <features tabularvalignment="middle">
6907 <column alignment="center" valignment="top" width="0pt">
6908 <column alignment="center" valignment="top" width="0pt">
6910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6913 \begin_layout Plain Layout
6915 \begin_inset Note Note
6918 \begin_layout Plain Layout
6925 is only used as spacer.
6935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6938 \begin_layout Plain Layout
6946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6949 \begin_layout Plain Layout
6953 \begin_layout Plain Layout
6965 \begin_inset space \textvisiblespace{}
6969 \begin_inset space \textvisiblespace{}
6976 \begin_layout Plain Layout
6984 \begin_inset Index idx
6987 \begin_layout Plain Layout
7000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7003 \begin_layout Plain Layout
7004 \begin_inset Formula $\overbrace{A+B}^{3}$
7014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7017 \begin_layout Plain Layout
7021 \begin_layout Plain Layout
7033 \begin_inset space \textvisiblespace{}
7037 \begin_inset space \textvisiblespace{}
7044 \begin_layout Plain Layout
7052 \begin_inset Index idx
7055 \begin_layout Plain Layout
7068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7071 \begin_layout Plain Layout
7072 \begin_inset Formula $\underbrace{A+B}_{5}$
7082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7085 \begin_layout Plain Layout
7089 \begin_inset space \textvisiblespace{}
7095 \begin_inset space \textvisiblespace{}
7099 \begin_inset space \textvisiblespace{}
7103 \begin_inset space \textvisiblespace{}
7107 \begin_inset space \textvisiblespace{}
7111 \begin_inset space \textvisiblespace{}
7115 \begin_inset space \textvisiblespace{}
7123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7126 \begin_layout Plain Layout
7127 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7143 \begin_layout Standard
7144 In the last example it doesn't matter if
7156 is inserted at first.
7159 \begin_layout Standard
7160 \begin_inset VSpace medskip
7166 \begin_layout Standard
7167 If you set in the document settings under
7170 \begin_inset space ~
7180 \begin_inset Index idx
7183 \begin_layout Plain Layout
7184 Packages ! mathtools
7192 \begin_inset space ~
7197 , you have access to square backets:
7198 \begin_inset Separator parbreak
7204 \begin_layout Standard
7206 \begin_inset Tabular
7207 <lyxtabular version="3" rows="4" columns="2">
7208 <features tabularvalignment="middle">
7209 <column alignment="center" valignment="top" width="0pt">
7210 <column alignment="center" valignment="top" width="0pt">
7212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7215 \begin_layout Plain Layout
7217 \begin_inset Note Note
7220 \begin_layout Plain Layout
7227 is only used as spacer.
7237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7240 \begin_layout Plain Layout
7248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7251 \begin_layout Plain Layout
7255 \begin_layout Plain Layout
7291 \begin_inset space \textvisiblespace{}
7298 \begin_layout Plain Layout
7306 \begin_inset Index idx
7309 \begin_layout Plain Layout
7322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7325 \begin_layout Plain Layout
7326 \begin_inset Formula $\overbracket{A+B}^{3}$
7336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7339 \begin_layout Plain Layout
7343 \begin_layout Plain Layout
7379 \begin_inset space \textvisiblespace{}
7386 \begin_layout Plain Layout
7394 \begin_inset Index idx
7397 \begin_layout Plain Layout
7422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7425 \begin_layout Plain Layout
7426 \begin_inset Formula $\underbracket{A+B}_{5}$
7436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7439 \begin_layout Plain Layout
7445 \begin_inset space \textvisiblespace{}
7449 \begin_inset space \textvisiblespace{}
7453 \begin_inset space \textvisiblespace{}
7457 \begin_inset space \textvisiblespace{}
7461 \begin_inset space \textvisiblespace{}
7469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7472 \begin_layout Plain Layout
7473 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7489 \begin_layout Standard
7502 you can change the thickness of the bracket's stroke by specifying the
7503 desired thickness in square brackets behind the command:
7504 \begin_inset Separator parbreak
7510 \begin_layout Standard
7512 \begin_inset Tabular
7513 <lyxtabular version="3" rows="3" columns="2">
7514 <features tabularvalignment="middle">
7515 <column alignment="center" valignment="top" width="0pt">
7516 <column alignment="center" valignment="top" width="0pt">
7518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7521 \begin_layout Plain Layout
7523 \begin_inset Note Note
7526 \begin_layout Plain Layout
7533 is only used as spacer.
7543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7546 \begin_layout Plain Layout
7554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7557 \begin_layout Plain Layout
7561 \begin_layout Plain Layout
7599 \begin_inset space \textvisiblespace{}
7606 \begin_layout Plain Layout
7618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7621 \begin_layout Plain Layout
7622 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7635 \begin_layout Plain Layout
7639 \begin_layout Plain Layout
7677 \begin_inset space \textvisiblespace{}
7684 \begin_layout Plain Layout
7696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7699 \begin_layout Plain Layout
7700 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7716 \begin_layout Standard
7717 \begin_inset VSpace bigskip
7720 When brackets should overlap each other, multiline formulas, as described
7722 \begin_inset CommandInset ref
7724 reference "sec:Multiline-Formulas"
7729 \begin_inset Formula
7731 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7732 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7737 In the first row the formula is inserted together with the first brace.
7738 It is hereby important that the space command
7742 \begin_layout Plain Layout
7743 Space commands are explained in
7744 \begin_inset CommandInset ref
7746 reference "subsec:Predefined-Space"
7761 is inserted before the first
7762 \begin_inset Formula $d$
7765 , because the brace that ends behind the
7766 \begin_inset Formula $q$
7769 prevents that the following
7770 \begin_inset Quotes eld
7774 \begin_inset Quotes erd
7777 is surrounded by space.
7781 \begin_layout Plain Layout
7782 because a bracket is not handled as a character, see
7783 \begin_inset CommandInset ref
7785 reference "subsec:Binary-Operators"
7794 In the second row the second brace is inserted.
7795 As it should begin before the
7796 \begin_inset Formula $b$
7811 \begin_layout Plain Layout
7819 \begin_inset CommandInset ref
7821 reference "subsec:Placeholders"
7830 This space is needed because the
7831 \begin_inset Quotes eld
7835 \begin_inset Quotes erd
7838 is also surrounded by space in the formula.
7839 The brace is placed under the command
7848 \begin_layout Standard
7849 It gets more complicated when brackets overlap each other above and under
7850 the formula, like in the following example:
7854 \begin_layout Plain Layout
7866 \begin_inset Formula
7868 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7869 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7878 \begin_layout Plain Layout
7889 The first formula row is the same as the second row of the previous example,
7890 with the difference that the brace is above.
7891 The second row contains the formula together with the second brace.
7892 To avoid that there is space between the upper brace in the first row and
7893 the formula, the row spacing needs to be reduced.
7894 This is not easily possible due to a bug in \SpecialChar LyX
7899 \begin_layout Plain Layout
7900 \begin_inset CommandInset href
7902 name "LyX-bug #1505"
7903 target "http://www.lyx.org/trac/ticket/1505"
7912 As a solution for the problem, the global formula row separation
7919 \begin_inset Index idx
7922 \begin_layout Plain Layout
7930 must be changed to -6
7931 \begin_inset space \thinspace{}
7934 pt before the formula with the command
7950 is set back after the formula to the standard value of 3
7951 \begin_inset space \thinspace{}
7954 pt using the same command.
7955 More about the row separation in formulas is explained in
7956 \begin_inset CommandInset ref
7958 reference "subsec:Line-Separation"
7965 \begin_layout Section
7967 \begin_inset Index idx
7970 \begin_layout Plain Layout
7979 \begin_layout Standard
7980 Arrows can be inserted via the math toolbar button
7983 arg "math-insert \\leftarrow"
7986 or the commands listed in the following subsections.
7989 \begin_layout Subsection
7991 \begin_inset Index idx
7994 \begin_layout Plain Layout
8003 \begin_layout Standard
8004 \begin_inset space \hfill{}
8008 \begin_inset Tabular
8009 <lyxtabular version="3" rows="8" columns="2">
8010 <features tabularvalignment="middle">
8011 <column alignment="center" valignment="top" width="0pt">
8012 <column alignment="center" valignment="top" width="0pt">
8014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8017 \begin_layout Plain Layout
8023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8026 \begin_layout Plain Layout
8034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8037 \begin_layout Plain Layout
8045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8048 \begin_layout Plain Layout
8049 \begin_inset Formula $\gets$
8059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8062 \begin_layout Plain Layout
8070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8073 \begin_layout Plain Layout
8074 \begin_inset Formula $\Leftarrow$
8084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8087 \begin_layout Plain Layout
8095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8098 \begin_layout Plain Layout
8099 \begin_inset Formula $\longleftarrow$
8109 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8112 \begin_layout Plain Layout
8120 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8123 \begin_layout Plain Layout
8124 \begin_inset Formula $\Longleftarrow$
8134 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8137 \begin_layout Plain Layout
8145 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8148 \begin_layout Plain Layout
8149 \begin_inset Formula $\leftharpoonup$
8159 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8162 \begin_layout Plain Layout
8170 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8173 \begin_layout Plain Layout
8174 \begin_inset Formula $\leftharpoondown$
8184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8187 \begin_layout Plain Layout
8195 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8198 \begin_layout Plain Layout
8199 \begin_inset Formula $\hookleftarrow$
8213 \begin_inset space \hfill{}
8217 \begin_inset Tabular
8218 <lyxtabular version="3" rows="8" columns="2">
8219 <features tabularvalignment="middle">
8220 <column alignment="center" valignment="top" width="0pt">
8221 <column alignment="center" valignment="top" width="0pt">
8223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8226 \begin_layout Plain Layout
8232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8235 \begin_layout Plain Layout
8243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8246 \begin_layout Plain Layout
8254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8257 \begin_layout Plain Layout
8258 \begin_inset Formula $\to$
8268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8271 \begin_layout Plain Layout
8279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8282 \begin_layout Plain Layout
8283 \begin_inset Formula $\Rightarrow$
8293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8296 \begin_layout Plain Layout
8304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8307 \begin_layout Plain Layout
8308 \begin_inset Formula $\longrightarrow$
8318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8321 \begin_layout Plain Layout
8329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8332 \begin_layout Plain Layout
8333 \begin_inset Formula $\Longrightarrow$
8343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8346 \begin_layout Plain Layout
8354 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8357 \begin_layout Plain Layout
8358 \begin_inset Formula $\rightharpoonup$
8368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8371 \begin_layout Plain Layout
8379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8382 \begin_layout Plain Layout
8383 \begin_inset Formula $\rightharpoondown$
8393 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8396 \begin_layout Plain Layout
8404 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8407 \begin_layout Plain Layout
8408 \begin_inset Formula $\hookrightarrow$
8422 \begin_inset space \hfill{}
8428 \begin_layout Standard
8429 \begin_inset space \hfill{}
8433 \begin_inset Tabular
8434 <lyxtabular version="3" rows="6" columns="2">
8435 <features tabularvalignment="middle">
8436 <column alignment="center" valignment="top" width="0pt">
8437 <column alignment="center" valignment="top" width="0pt">
8439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8442 \begin_layout Plain Layout
8448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8451 \begin_layout Plain Layout
8459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8462 \begin_layout Plain Layout
8470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8473 \begin_layout Plain Layout
8474 \begin_inset Formula $\leftrightarrow$
8484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8487 \begin_layout Plain Layout
8495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8498 \begin_layout Plain Layout
8499 \begin_inset Formula $\Leftrightarrow$
8509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8512 \begin_layout Plain Layout
8520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8523 \begin_layout Plain Layout
8524 \begin_inset Formula $\longleftrightarrow$
8534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8537 \begin_layout Plain Layout
8545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8548 \begin_layout Plain Layout
8549 \begin_inset Formula $\Longleftrightarrow$
8559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8562 \begin_layout Plain Layout
8570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8573 \begin_layout Plain Layout
8574 \begin_inset Formula $\rightleftharpoons$
8588 \begin_inset space \hspace{}
8593 \begin_inset space \hfill{}
8597 \begin_inset Tabular
8598 <lyxtabular version="3" rows="5" columns="2">
8599 <features tabularvalignment="middle">
8600 <column alignment="center" valignment="top" width="0pt">
8601 <column alignment="center" valignment="top" width="0pt">
8603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8606 \begin_layout Plain Layout
8612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8615 \begin_layout Plain Layout
8623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8626 \begin_layout Plain Layout
8634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8637 \begin_layout Plain Layout
8638 \begin_inset Formula $\mapsto$
8648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8651 \begin_layout Plain Layout
8659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8662 \begin_layout Plain Layout
8663 \begin_inset Formula $\longmapsto$
8673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8676 \begin_layout Plain Layout
8684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8687 \begin_layout Plain Layout
8688 \begin_inset Formula $\leadsto$
8698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8701 \begin_layout Plain Layout
8709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8712 \begin_layout Plain Layout
8713 \begin_inset Formula $\dasharrow$
8727 \begin_inset space \hfill{}
8733 \begin_layout Standard
8734 \begin_inset VSpace medskip
8737 Arrows used as accents like e.
8738 \begin_inset space \thinspace{}
8742 \begin_inset space \space{}
8745 vector arrows are listed in
8746 \begin_inset CommandInset ref
8748 reference "sec:Accents"
8755 \begin_layout Standard
8756 \begin_inset VSpace bigskip
8759 Furthermore there are the labeled arrows
8760 \begin_inset Index idx
8763 \begin_layout Plain Layout
8776 \begin_inset Index idx
8779 \begin_layout Plain Layout
8794 \begin_inset Index idx
8797 \begin_layout Plain Layout
8804 \begin_layout Plain Layout
8819 When inserting one of these commands in a formula, an arrow with two blue
8820 boxes appear where the label can be inserted.
8821 The length of the arrow adapts to the label width.
8824 \begin_layout Standard
8826 \begin_inset Tabular
8827 <lyxtabular version="3" rows="3" columns="2">
8828 <features tabularvalignment="middle">
8829 <column alignment="center" valignment="top" width="0pt">
8830 <column alignment="center" valignment="top" width="0pt">
8832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8835 \begin_layout Plain Layout
8841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8844 \begin_layout Plain Layout
8846 \begin_inset Note Note
8849 \begin_layout Plain Layout
8856 is only used as spacer.
8868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8871 \begin_layout Plain Layout
8875 \begin_inset space \textvisiblespace{}
8879 \begin_inset Formula $\downarrow$
8883 \begin_inset Formula $\to$
8891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8894 \begin_layout Plain Layout
8895 \begin_inset Formula $\raisebox{5.5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8908 \begin_layout Plain Layout
8912 \begin_inset space \textvisiblespace{}
8916 \begin_inset Formula $\downarrow$
8920 \begin_inset Formula $\to$
8928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8931 \begin_layout Plain Layout
8932 \begin_inset Formula $\raisebox{5.5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8948 \begin_layout Standard
8949 \begin_inset VSpace medskip
8955 \begin_layout Standard
8956 If you set in the document settings under
8959 \begin_inset space ~
8969 \begin_inset Index idx
8972 \begin_layout Plain Layout
8973 Packages ! mathtools
8981 \begin_inset space ~
8986 , you have access to the following labeled arrows:
8989 \begin_layout Standard
8990 \begin_inset Newpage newpage
8994 \begin_inset Separator parbreak
9000 \begin_layout Standard
9002 \begin_inset space \hspace*{\fill}
9006 \begin_inset Tabular
9007 <lyxtabular version="3" rows="7" columns="2">
9008 <features tabularvalignment="middle">
9009 <column alignment="center" valignment="top" width="0pt">
9010 <column alignment="center" valignment="top" width="0pt">
9012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9015 \begin_layout Plain Layout
9021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9024 \begin_layout Plain Layout
9026 \begin_inset Note Note
9029 \begin_layout Plain Layout
9036 is only used as spacer.
9048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9051 \begin_layout Plain Layout
9071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9074 \begin_layout Plain Layout
9075 \begin_inset Formula $\raisebox{6mm}{}\xleftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9088 \begin_layout Plain Layout
9108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9111 \begin_layout Plain Layout
9112 \begin_inset Formula $\raisebox{6mm}{}\xLeftarrow[x=a]{x>0}\raisebox{-4mm}{}$
9122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9125 \begin_layout Plain Layout
9145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9148 \begin_layout Plain Layout
9149 \begin_inset Formula $\raisebox{6mm}{}\xRightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9162 \begin_layout Plain Layout
9182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9185 \begin_layout Plain Layout
9186 \begin_inset Formula $\raisebox{6mm}{}\xLeftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9199 \begin_layout Plain Layout
9219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9222 \begin_layout Plain Layout
9223 \begin_inset Formula $\raisebox{6mm}{}\xhookleftarrow[x=a]{x>0}\raisebox{-4mm}{}$
9233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9236 \begin_layout Plain Layout
9256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9259 \begin_layout Plain Layout
9260 \begin_inset Formula $\raisebox{6mm}{}\xhookrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9274 \begin_inset space \hspace*{\fill}
9278 \begin_inset Tabular
9279 <lyxtabular version="3" rows="7" columns="2">
9280 <features tabularvalignment="middle">
9281 <column alignment="center" valignment="top" width="0pt">
9282 <column alignment="center" valignment="top" width="0pt">
9284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9287 \begin_layout Plain Layout
9293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9296 \begin_layout Plain Layout
9298 \begin_inset Note Note
9301 \begin_layout Plain Layout
9308 is only used as spacer.
9320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9323 \begin_layout Plain Layout
9343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9346 \begin_layout Plain Layout
9347 \begin_inset Formula $\raisebox{6mm}{}\xleftharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
9357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9360 \begin_layout Plain Layout
9380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9383 \begin_layout Plain Layout
9384 \begin_inset Formula $\raisebox{6mm}{}\xleftharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
9394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9397 \begin_layout Plain Layout
9417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9420 \begin_layout Plain Layout
9421 \begin_inset Formula $\raisebox{6mm}{}\xrightharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
9431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9434 \begin_layout Plain Layout
9454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9457 \begin_layout Plain Layout
9458 \begin_inset Formula $\raisebox{6mm}{}\xrightharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
9468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9471 \begin_layout Plain Layout
9491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9494 \begin_layout Plain Layout
9495 \begin_inset Formula $\raisebox{6mm}{}\xleftrightharpoons[x=a]{x>0}\raisebox{-4mm}{}$
9505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9508 \begin_layout Plain Layout
9528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9531 \begin_layout Plain Layout
9532 \begin_inset Formula $\raisebox{6mm}{}\xrightleftharpoons[x=a]{x>0}\raisebox{-4mm}{}$
9546 \begin_inset space \hspace*{\fill}
9552 \begin_layout Standard
9553 The command scheme is for all these arrows:
9554 \begin_inset Separator parbreak
9560 \begin_layout Standard
9562 \begin_inset Tabular
9563 <lyxtabular version="3" rows="2" columns="2">
9564 <features tabularvalignment="middle">
9565 <column alignment="center" valignment="top" width="0pt">
9566 <column alignment="center" valignment="top" width="0pt">
9568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9571 \begin_layout Plain Layout
9577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9580 \begin_layout Plain Layout
9582 \begin_inset Note Note
9585 \begin_layout Plain Layout
9592 is only used as spacer.
9604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9607 \begin_layout Plain Layout
9610 xleftrightarrow[x=a]
9613 \begin_inset Formula $\to$
9621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9624 \begin_layout Plain Layout
9625 \begin_inset Formula $\raisebox{6mm}{}F(a)\xleftrightarrow[x=a]{x>0}F(x)\raisebox{-4mm}{}$
9641 \begin_layout Subsection
9642 Vertical and diagonal Arrows
9643 \begin_inset Index idx
9646 \begin_layout Plain Layout
9653 \begin_inset Index idx
9656 \begin_layout Plain Layout
9665 \begin_layout Standard
9666 \begin_inset space \hfill{}
9670 \begin_inset Tabular
9671 <lyxtabular version="3" rows="7" columns="2">
9672 <features tabularvalignment="middle">
9673 <column alignment="center" valignment="top" width="0pt">
9674 <column alignment="center" valignment="top" width="0pt">
9676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9679 \begin_layout Plain Layout
9685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9688 \begin_layout Plain Layout
9696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9699 \begin_layout Plain Layout
9707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9710 \begin_layout Plain Layout
9711 \begin_inset Formula $\uparrow$
9721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9724 \begin_layout Plain Layout
9732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9735 \begin_layout Plain Layout
9736 \begin_inset Formula $\Uparrow$
9746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9749 \begin_layout Plain Layout
9757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9760 \begin_layout Plain Layout
9761 \begin_inset Formula $\updownarrow$
9771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9774 \begin_layout Plain Layout
9782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9785 \begin_layout Plain Layout
9786 \begin_inset Formula $\Updownarrow$
9796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9799 \begin_layout Plain Layout
9807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9810 \begin_layout Plain Layout
9811 \begin_inset Formula $\Downarrow$
9821 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9824 \begin_layout Plain Layout
9832 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9835 \begin_layout Plain Layout
9836 \begin_inset Formula $\downarrow$
9850 \begin_inset space \hfill{}
9854 \begin_inset Tabular
9855 <lyxtabular version="3" rows="5" columns="2">
9856 <features tabularvalignment="middle">
9857 <column alignment="center" valignment="top" width="0pt">
9858 <column alignment="center" valignment="top" width="0pt">
9860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9863 \begin_layout Plain Layout
9869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9872 \begin_layout Plain Layout
9880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9883 \begin_layout Plain Layout
9891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9894 \begin_layout Plain Layout
9895 \begin_inset Formula $\nearrow$
9905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9908 \begin_layout Plain Layout
9916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9919 \begin_layout Plain Layout
9920 \begin_inset Formula $\searrow$
9930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9933 \begin_layout Plain Layout
9941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9944 \begin_layout Plain Layout
9945 \begin_inset Formula $\swarrow$
9955 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9958 \begin_layout Plain Layout
9966 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9969 \begin_layout Plain Layout
9970 \begin_inset Formula $\nwarrow$
9984 \begin_inset space \hfill{}
9990 \begin_layout Standard
9991 \begin_inset VSpace medskip
9994 Vertical arrows can be used also as delimiters together with the commands
9996 \begin_inset CommandInset ref
9998 reference "subsec:Manual-Bracket-Size"
10003 \begin_inset CommandInset ref
10005 reference "subsec:Automatic-Bracket-Size"
10012 \begin_layout Section
10014 \begin_inset CommandInset label
10021 \begin_inset Index idx
10024 \begin_layout Plain Layout
10033 \begin_layout Standard
10034 Accents can be inserted via the math toolbar button
10037 arg "math-insert \\hat"
10040 or the commands listed in the following subsections.
10043 \begin_layout Subsection
10044 Accents for one Character
10048 \begin_layout Plain Layout
10061 \begin_layout Plain Layout
10062 accents in text see
10063 \begin_inset CommandInset ref
10065 reference "subsec:Accents-in-Text"
10078 \begin_layout Plain Layout
10086 \begin_inset Note Note
10089 \begin_layout Plain Layout
10096 is used to avoid that the footnote appears in the PDF-bookmark.
10099 \begin_layout Plain Layout
10107 \begin_inset CommandInset ref
10109 reference "subsec:Formulas-in-Section"
10119 \begin_inset CommandInset label
10121 name "subsec:Accents-for-one"
10126 \begin_inset Index idx
10129 \begin_layout Plain Layout
10130 Accents ! for one character
10138 \begin_layout Standard
10139 \begin_inset space \hfill{}
10143 \begin_inset Tabular
10144 <lyxtabular version="3" rows="8" columns="2">
10145 <features tabularvalignment="middle">
10146 <column alignment="center" valignment="top" width="0pt">
10147 <column alignment="center" valignment="top" width="0pt">
10149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10152 \begin_layout Plain Layout
10158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10161 \begin_layout Plain Layout
10163 \begin_inset Note Note
10166 \begin_layout Plain Layout
10173 is only used as spacer.
10185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10188 \begin_layout Plain Layout
10192 \begin_inset space \textvisiblespace{}
10200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10203 \begin_layout Plain Layout
10204 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
10214 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10217 \begin_layout Plain Layout
10221 \begin_inset space \textvisiblespace{}
10229 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10232 \begin_layout Plain Layout
10233 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
10243 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10246 \begin_layout Plain Layout
10250 \begin_inset space \textvisiblespace{}
10258 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10261 \begin_layout Plain Layout
10262 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
10272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10275 \begin_layout Plain Layout
10279 \begin_inset space \textvisiblespace{}
10287 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10290 \begin_layout Plain Layout
10291 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
10301 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10304 \begin_layout Plain Layout
10308 \begin_inset space \textvisiblespace{}
10312 \begin_inset Index idx
10315 \begin_layout Plain Layout
10326 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10329 \begin_layout Plain Layout
10330 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
10340 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10343 \begin_layout Plain Layout
10347 \begin_inset space \textvisiblespace{}
10355 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10358 \begin_layout Plain Layout
10359 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
10369 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10372 \begin_layout Plain Layout
10376 \begin_inset space \textvisiblespace{}
10384 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10387 \begin_layout Plain Layout
10388 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
10402 \begin_inset space \hfill{}
10406 \begin_inset Tabular
10407 <lyxtabular version="3" rows="7" columns="2">
10408 <features tabularvalignment="middle">
10409 <column alignment="center" valignment="top" width="0pt">
10410 <column alignment="center" valignment="top" width="0pt">
10412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10415 \begin_layout Plain Layout
10421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10424 \begin_layout Plain Layout
10432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10435 \begin_layout Plain Layout
10439 \begin_inset space \textvisiblespace{}
10447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10450 \begin_layout Plain Layout
10451 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
10461 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10464 \begin_layout Plain Layout
10468 \begin_inset space \textvisiblespace{}
10476 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10479 \begin_layout Plain Layout
10480 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10490 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10493 \begin_layout Plain Layout
10497 \begin_inset space \textvisiblespace{}
10505 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10508 \begin_layout Plain Layout
10509 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10519 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10522 \begin_layout Plain Layout
10526 \begin_inset space \textvisiblespace{}
10534 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10537 \begin_layout Plain Layout
10538 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10548 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10551 \begin_layout Plain Layout
10555 \begin_inset space \textvisiblespace{}
10563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10566 \begin_layout Plain Layout
10567 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10577 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10580 \begin_layout Plain Layout
10584 \begin_inset space \textvisiblespace{}
10592 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10595 \begin_layout Plain Layout
10596 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10610 \begin_inset space \hfill{}
10616 \begin_layout Standard
10617 \begin_inset VSpace bigskip
10623 \begin_layout Standard
10624 You can directly insert accents like é to formulas.
10626 will transform them to the corresponding accent command.
10628 \begin_inset Index idx
10631 \begin_layout Plain Layout
10637 it is better to insert a quotation mark before the vowel.
10638 These two characters are then treated by \SpecialChar LaTeX
10643 character when the formula part with the umlaut is marked as German.
10651 \begin_inset Quotes eld
10655 \begin_inset Quotes erd
10658 umlauts are created as demonstrated in the following example:
10661 \begin_layout Standard
10662 \begin_inset VSpace -2mm
10668 \begin_layout Standard
10670 \begin_inset Tabular
10671 <lyxtabular version="3" rows="3" columns="2">
10672 <features tabularvalignment="middle">
10673 <column alignment="center" valignment="top">
10674 <column alignment="center" valignment="top">
10676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10679 \begin_layout Plain Layout
10685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10688 \begin_layout Plain Layout
10690 \begin_inset Note Note
10693 \begin_layout Plain Layout
10701 \begin_inset space \thinspace{}
10704 pt space are only used as spacer.
10716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10719 \begin_layout Plain Layout
10722 \begin_inset Quotes grd
10730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10733 \begin_layout Plain Layout
10734 \begin_inset space \hspace{}
10741 \begin_inset Formula $"i$
10751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10754 \begin_layout Plain Layout
10758 \begin_inset space \textvisiblespace{}
10766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10769 \begin_layout Plain Layout
10770 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10786 \begin_layout Standard
10787 Another advantage to
10793 is that umlauts can directly be converted to mathematical text because
10794 the accent commands above are
10800 in mathematical text
10803 To convert an accented character to mathematical text, only the character
10804 under the accent may be converted.
10805 This applies also for all other conversions, e.
10806 \begin_inset space \thinspace{}
10810 \begin_inset space \space{}
10816 \begin_layout Standard
10817 In mathematical text, umlauts and other accented characters can directly
10821 \begin_layout Standard
10822 \begin_inset VSpace bigskip
10828 \begin_layout Standard
10830 also supports a tilde under the character if the \SpecialChar LaTeX
10836 \begin_inset Index idx
10839 \begin_layout Plain Layout
10840 Packages ! undertilde
10845 is installed on your system:
10848 \begin_layout Standard
10852 \begin_layout Plain Layout
10862 \begin_inset Note Note
10865 \begin_layout Plain Layout
10866 The following table will only be displayed when the \SpecialChar LaTeX
10877 \begin_inset Separator parbreak
10883 \begin_layout Standard
10886 \begin_inset Tabular
10887 <lyxtabular version="3" rows="2" columns="2">
10888 <features tabularvalignment="middle">
10889 <column alignment="center" valignment="top" width="0pt">
10890 <column alignment="center" valignment="top" width="0pt">
10892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10895 \begin_layout Plain Layout
10901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10904 \begin_layout Plain Layout
10912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10915 \begin_layout Plain Layout
10919 \begin_inset space \textvisiblespace{}
10927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10930 \begin_layout Plain Layout
10931 \begin_inset Formula $\raisebox{5mm}{}\utilde{A}$
10947 \begin_layout Standard
10951 \begin_layout Plain Layout
10961 \begin_inset Note Note
10964 \begin_layout Plain Layout
10965 The following will be displayed when the \SpecialChar LaTeX
10978 \begin_layout Standard
10979 You need to install the \SpecialChar LaTeX
10984 to see the rest of this subsection in the output.
10987 \begin_layout Standard
10991 \begin_layout Plain Layout
11003 \begin_layout Standard
11004 \begin_inset Newpage newpage
11010 \begin_layout Subsection
11011 Accents for several Characters
11012 \begin_inset Index idx
11015 \begin_layout Plain Layout
11016 Accents ! for several characters
11024 \begin_layout Standard
11025 \begin_inset space \hfill{}
11029 \begin_inset Tabular
11030 <lyxtabular version="3" rows="5" columns="2">
11031 <features tabularvalignment="middle">
11032 <column alignment="center" valignment="top" width="0pt">
11033 <column alignment="center" valignment="top" width="0pt">
11035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11038 \begin_layout Plain Layout
11044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11047 \begin_layout Plain Layout
11049 \begin_inset Note Note
11052 \begin_layout Plain Layout
11059 is only used as spacer.
11071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11074 \begin_layout Plain Layout
11078 \begin_inset space \textvisiblespace{}
11086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11089 \begin_layout Plain Layout
11090 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
11100 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11103 \begin_layout Plain Layout
11107 \begin_inset space \textvisiblespace{}
11115 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11118 \begin_layout Plain Layout
11119 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
11129 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11132 \begin_layout Plain Layout
11136 \begin_inset space \textvisiblespace{}
11144 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11147 \begin_layout Plain Layout
11148 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
11158 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11161 \begin_layout Plain Layout
11164 underleftrightarrow
11165 \begin_inset space \textvisiblespace{}
11173 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11176 \begin_layout Plain Layout
11177 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
11191 \begin_inset space \hfill{}
11195 \begin_inset Tabular
11196 <lyxtabular version="3" rows="5" columns="2">
11197 <features tabularvalignment="middle">
11198 <column alignment="center" valignment="top" width="0pt">
11199 <column alignment="center" valignment="top" width="0pt">
11201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11204 \begin_layout Plain Layout
11210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11213 \begin_layout Plain Layout
11221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11224 \begin_layout Plain Layout
11228 \begin_inset space \textvisiblespace{}
11236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11239 \begin_layout Plain Layout
11240 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
11250 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11253 \begin_layout Plain Layout
11257 \begin_inset space \textvisiblespace{}
11265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11268 \begin_layout Plain Layout
11269 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
11279 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11282 \begin_layout Plain Layout
11286 \begin_inset space \textvisiblespace{}
11294 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11297 \begin_layout Plain Layout
11298 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
11308 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11311 \begin_layout Plain Layout
11315 \begin_inset space \textvisiblespace{}
11323 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11326 \begin_layout Plain Layout
11327 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11341 \begin_inset space \hfill{}
11347 \begin_layout Standard
11348 \begin_inset VSpace medskip
11351 With these commands as many characters as you like can be accented.
11364 will only be set in the output with a length of three characters, as shown
11365 in the following example:
11366 \begin_inset Formula
11368 \widetilde{A+B=C-D}
11376 \begin_layout Standard
11384 \begin_inset Index idx
11387 \begin_layout Plain Layout
11402 \begin_inset Index idx
11405 \begin_layout Plain Layout
11413 described in the previous subsection it is also possible to accent several
11420 \begin_inset space \textvisiblespace{}
11424 \begin_inset Formula $\downarrow$
11430 \begin_inset Formula
11432 \underset{***}{A=B}
11440 \begin_layout Section
11442 \begin_inset CommandInset label
11444 name "subsec:Space"
11449 \begin_inset Index idx
11452 \begin_layout Plain Layout
11461 \begin_layout Subsection
11463 \begin_inset CommandInset label
11465 name "subsec:Predefined-Space"
11470 \begin_inset Index idx
11473 \begin_layout Plain Layout
11474 Space ! horizontal ! predefined
11482 \begin_layout Standard
11483 Sometimes it is necessary to insert horizontal space into a formula.
11484 This is done by inserting a protected space (shortcut
11487 arg "command-alternatives space-insert protected ; math-space"
11492 \begin_inset Quotes eld
11498 \begin_inset space \textvisiblespace{}
11504 \begin_inset Quotes erd
11507 appears and by pressing
11511 several times one can select one of eight different space sizes.
11512 The spaces can also be inserted using the math toolbar button
11515 arg "math-insert \\space"
11518 or special commands.
11519 Independent from the inserted command, one can select the size again by
11525 \begin_inset Separator parbreak
11531 \begin_layout Standard
11534 \begin_inset Tabular
11535 <lyxtabular version="3" rows="6" columns="3">
11536 <features tabularvalignment="middle">
11537 <column alignment="center" valignment="top">
11538 <column alignment="center" valignment="top" width="15col%">
11539 <column alignment="center" valignment="top">
11541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11544 \begin_layout Plain Layout
11550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11553 \begin_layout Plain Layout
11563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11566 \begin_layout Plain Layout
11574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11577 \begin_layout Plain Layout
11585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11588 \begin_layout Plain Layout
11594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11597 \begin_layout Plain Layout
11598 \begin_inset Formula $A\,B$
11608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11611 \begin_layout Plain Layout
11619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11622 \begin_layout Plain Layout
11628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11631 \begin_layout Plain Layout
11632 \begin_inset Formula $A\:B$
11642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11645 \begin_layout Plain Layout
11653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11656 \begin_layout Plain Layout
11662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11665 \begin_layout Plain Layout
11666 \begin_inset Formula $A\;B$
11676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11679 \begin_layout Plain Layout
11687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11690 \begin_layout Plain Layout
11696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11699 \begin_layout Plain Layout
11700 \begin_inset Formula $A\quad B$
11710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11713 \begin_layout Plain Layout
11721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11724 \begin_layout Plain Layout
11730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11733 \begin_layout Plain Layout
11734 \begin_inset Formula $A\qquad B$
11748 \begin_inset space \hfill{}
11752 \begin_inset Tabular
11753 <lyxtabular version="3" rows="6" columns="3">
11754 <features tabularvalignment="middle">
11755 <column alignment="center" valignment="top">
11756 <column alignment="center" valignment="top" width="15col%">
11757 <column alignment="center" valignment="top">
11759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11762 \begin_layout Plain Layout
11768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11771 \begin_layout Plain Layout
11781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11784 \begin_layout Plain Layout
11792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11795 \begin_layout Plain Layout
11803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11806 \begin_layout Plain Layout
11812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11815 \begin_layout Plain Layout
11816 \begin_inset Formula $A\hfill B$
11826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11829 \begin_layout Plain Layout
11837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11840 \begin_layout Plain Layout
11846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11849 \begin_layout Plain Layout
11850 \begin_inset Formula $A\hspace*{1em}B$
11860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11863 \begin_layout Plain Layout
11871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11874 \begin_layout Plain Layout
11880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11883 \begin_layout Plain Layout
11884 \begin_inset Formula $A\hspace{1em}B$
11894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11897 \begin_layout Plain Layout
11901 \begin_inset space \textvisiblespace{}
11909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11912 \begin_layout Plain Layout
11918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11921 \begin_layout Plain Layout
11922 \begin_inset Formula $A\ B$
11932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11935 \begin_layout Plain Layout
11943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11946 \begin_layout Plain Layout
11952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11955 \begin_layout Plain Layout
11956 \begin_inset Formula $A\!B$
11972 \begin_layout Standard
11974 \begin_inset space ~
11978 \begin_inset space \thinspace{}
11982 \begin_inset space \thinspace{}
11985 7 are variable spaces which are explained in
11986 \begin_inset CommandInset ref
11988 reference "subsec:Variable-Space"
11994 \begin_inset space ~
11997 9 seems to produce no space.
11998 It is displayed red in \SpecialChar LyX
11999 contrary to the other sizes, because it is a negative
12001 There are two more negative spaces:
12002 \begin_inset Separator parbreak
12008 \begin_layout Standard
12010 \begin_inset Tabular
12011 <lyxtabular version="3" rows="3" columns="3">
12012 <features tabularvalignment="middle">
12013 <column alignment="center" valignment="middle" width="6.8cm">
12014 <column alignment="center" valignment="top" width="0pt">
12015 <column alignment="center" valignment="top" width="0pt">
12017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12020 \begin_layout Plain Layout
12026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12029 \begin_layout Plain Layout
12037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12040 \begin_layout Plain Layout
12050 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
12053 \begin_layout Plain Layout
12058 keystrokes after inserting the protected space
12063 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
12066 \begin_layout Plain Layout
12072 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12075 \begin_layout Plain Layout
12083 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
12086 \begin_layout Plain Layout
12092 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
12095 \begin_layout Plain Layout
12096 \begin_inset Formula $A\negmedspace B$
12104 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12107 \begin_layout Plain Layout
12108 \begin_inset Formula $A\negthickspace B$
12124 \begin_layout Standard
12125 Negative spaces can lead to characters overlapping each other.
12126 Thus they can be used to enforce ligatures, which are e.
12127 \begin_inset space \thinspace{}
12131 \begin_inset space \space{}
12134 useful for summation operators:
12135 \begin_inset Separator parbreak
12141 \begin_layout Standard
12143 \begin_inset Tabular
12144 <lyxtabular version="3" rows="3" columns="2">
12145 <features tabularvalignment="middle">
12146 <column alignment="center" valignment="top">
12147 <column alignment="center" valignment="top">
12149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12152 \begin_layout Plain Layout
12158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12161 \begin_layout Plain Layout
12163 \begin_inset Note Note
12166 \begin_layout Plain Layout
12173 is only used as spacer.
12185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12188 \begin_layout Plain Layout
12194 \begin_inset space \textvisiblespace{}
12202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12205 \begin_layout Plain Layout
12206 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
12216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12219 \begin_layout Plain Layout
12227 \begin_inset space \textvisiblespace{}
12235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12238 \begin_layout Plain Layout
12239 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
12255 \begin_layout Standard
12257 \begin_inset VSpace medskip
12263 \begin_layout Standard
12265 Relations like for example equal signs, are always surrounded by space.
12266 To suppress this, the equal sign is placed into a \SpecialChar TeX
12268 The following example demonstrates this:
12269 \begin_inset Separator parbreak
12275 \begin_layout Standard
12277 \begin_inset Tabular
12278 <lyxtabular version="3" rows="2" columns="2">
12279 <features tabularvalignment="middle">
12280 <column alignment="center" valignment="top" width="0pt">
12281 <column alignment="center" valignment="top" width="0pt">
12283 <cell alignment="center" valignment="top" usebox="none">
12286 \begin_layout Plain Layout
12292 <cell alignment="center" valignment="top" usebox="none">
12295 \begin_layout Plain Layout
12296 \begin_inset Formula $A=B$
12306 <cell alignment="center" valignment="top" usebox="none">
12309 \begin_layout Plain Layout
12310 \begin_inset Note Note
12313 \begin_layout Plain Layout
12320 is only used as spacer.
12326 \begin_inset Formula $\raisebox{5mm}{}$
12329 equation without space
12334 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
12337 \begin_layout Plain Layout
12338 \begin_inset Formula $A{=}B$
12354 \begin_layout Standard
12356 The command for the last formula is:
12361 \begin_inset Formula $\to$
12367 \begin_layout Standard
12368 \begin_inset VSpace bigskip
12374 \begin_layout Standard
12375 Spaces are needed for physical units, because the space between the value
12376 and the unit is the smallest one and not a normal space.
12377 For units in text, the smallest space is inserted via the menu
12379 Insert\SpecialChar menuseparator
12380 Formatting\SpecialChar menuseparator
12382 \begin_inset space ~
12390 arg "space-insert thin"
12396 \begin_layout Standard
12397 An example to visualize the difference:
12400 \begin_layout Standard
12401 \begin_inset Tabular
12402 <lyxtabular version="3" rows="2" columns="2">
12403 <features tabularvalignment="middle">
12404 <column alignment="left" valignment="top">
12405 <column alignment="left" valignment="top">
12407 <cell alignment="center" valignment="top" usebox="none">
12410 \begin_layout Plain Layout
12412 \begin_inset Formula $\cdot$
12420 <cell alignment="center" valignment="top" usebox="none">
12423 \begin_layout Plain Layout
12424 space between value and unit
12431 <cell alignment="center" valignment="top" usebox="none">
12434 \begin_layout Plain Layout
12436 \begin_inset space \thinspace{}
12440 \begin_inset Formula $\cdot$
12448 <cell alignment="center" valignment="top" usebox="none">
12451 \begin_layout Plain Layout
12452 smallest space between value and unit
12465 \begin_layout Subsection
12470 \begin_layout Plain Layout
12483 \begin_layout Plain Layout
12484 for vertical space in formulas see
12485 \begin_inset CommandInset ref
12487 reference "subsec:Line-Separation"
12500 \begin_layout Plain Layout
12508 \begin_inset Note Note
12511 \begin_layout Plain Layout
12514 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12517 \begin_layout Plain Layout
12520 texorpdfstring is in section
12521 \begin_inset CommandInset ref
12523 reference "subsec:Formulas-in-Section"
12533 \begin_inset CommandInset label
12535 name "subsec:Variable-Space"
12540 \begin_inset Index idx
12543 \begin_layout Plain Layout
12544 Space ! horizontal ! variable
12552 \begin_layout Standard
12553 Space with a defined length can be inserted with the command
12560 \begin_inset Index idx
12563 \begin_layout Plain Layout
12573 \begin_inset Quotes eld
12579 \begin_inset space \textvisiblespace{}
12585 \begin_inset Quotes erd
12589 The length can be specified by left-clicking on the
12590 \begin_inset Quotes eld
12596 \begin_inset space \textvisiblespace{}
12602 \begin_inset Quotes erd
12606 The length may also be negative.
12607 When a space would be the first character in a line it would be omitted.
12608 To force its output use the command
12620 or left-click on the
12621 \begin_inset Quotes eld
12627 \begin_inset space \textvisiblespace{}
12633 \begin_inset Quotes erd
12636 and check the option
12641 \begin_inset Newline newline
12644 To insert as much space as is available, the command
12651 \begin_inset Index idx
12654 \begin_layout Plain Layout
12665 \begin_layout Standard
12666 \begin_inset VSpace -1mm
12672 \begin_layout Standard
12674 \begin_inset Tabular
12675 <lyxtabular version="3" rows="4" columns="2">
12676 <features tabularvalignment="middle">
12677 <column alignment="center" valignment="top">
12678 <column alignment="center" valignment="top">
12680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12683 \begin_layout Plain Layout
12691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12694 \begin_layout Plain Layout
12702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12705 \begin_layout Plain Layout
12709 \begin_inset space \textvisiblespace{}
12715 \begin_inset space \thinspace{}
12723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12726 \begin_layout Plain Layout
12727 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12740 \begin_layout Plain Layout
12744 \begin_inset space \textvisiblespace{}
12750 \begin_inset space \thinspace{}
12758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12761 \begin_layout Plain Layout
12762 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12775 \begin_layout Plain Layout
12779 \begin_inset space \textvisiblespace{}
12787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12790 \begin_layout Plain Layout
12791 \begin_inset Formula $A=A\hfill B=B$
12807 \begin_layout Standard
12808 In the last example the available space is given by the longest column entry
12810 In an inline formula the space depends on the length of the line in which
12818 Thus, when the line uses the full width, no space will be created.
12825 only has an effect on displayed formulas when the formula style
12830 (Formula styles are explained in
12831 \begin_inset CommandInset ref
12833 reference "sec:Formula-Styles"
12840 \begin_layout Standard
12847 , there are the commands
12859 that fill the space with a pattern, see
12860 \begin_inset CommandInset ref
12862 reference "subsec:Ellipses"
12869 \begin_layout Standard
12870 For text, variable space can be inserted via the menu
12872 Insert\SpecialChar menuseparator
12873 Formatting\SpecialChar menuseparator
12875 \begin_inset space ~
12883 \begin_layout Standard
12884 This is a line with
12885 \begin_inset space \hspace{}
12890 \begin_inset space \thinspace{}
12896 \begin_layout Standard
12897 This is a line with
12898 \begin_inset space \hfill{}
12904 \begin_layout Subsection
12905 Space besides inline Formulas
12906 \begin_inset Index idx
12909 \begin_layout Plain Layout
12910 Space ! besides inline formulas
12918 \begin_layout Standard
12919 The space that surrounds inline formulas can be adjusted with the length
12927 \begin_inset Index idx
12930 \begin_layout Plain Layout
12939 The value of a length is set with the command
12946 \begin_inset Index idx
12949 \begin_layout Plain Layout
12957 which has the following scheme:
12960 \begin_layout Standard
12965 setlength{length name}{value}
12968 \begin_layout Standard
12976 \begin_inset space \thinspace{}
12982 \begin_layout Standard
12992 \begin_layout Standard
12993 is inserted in \SpecialChar TeX
12996 \begin_inset space \thinspace{}
12999 mm space will now be set around all inline formulas:
13003 \begin_layout Plain Layout
13017 \begin_layout Standard
13018 This is a line with an inline formula
13019 \begin_inset Formula $A=B$
13023 \begin_inset space \thinspace{}
13026 mm surrounding space.
13030 \begin_layout Plain Layout
13044 \begin_layout Standard
13045 To return to the predefined value,
13051 is set to the value 0
13052 \begin_inset space \thinspace{}
13058 \begin_layout Section
13060 \begin_inset Index idx
13063 \begin_layout Plain Layout
13070 \begin_inset Index idx
13073 \begin_layout Plain Layout
13078 \begin_layout Plain Layout
13089 \begin_layout Plain Layout
13104 \begin_layout Standard
13105 Boxes for text are described in chapter
13112 \begin_inset space ~
13120 \begin_layout Subsection
13122 \begin_inset CommandInset label
13124 name "subsec:Boxes-with-Frame"
13129 \begin_inset Index idx
13132 \begin_layout Plain Layout
13141 \begin_layout Standard
13142 It is possible to frame a formula or part of one with the commands
13149 \begin_inset Index idx
13152 \begin_layout Plain Layout
13167 \begin_inset Index idx
13170 \begin_layout Plain Layout
13181 \begin_layout Standard
13182 When one of these commands is inserted in a formula, a blue box appears
13183 within a frame to enter formula parts.
13190 an additional formula has to be created by
13194 within this box, because the box content will otherwise be treated as mathemati
13202 is used, a new formula is automatically created inside the frame.
13205 \begin_layout Standard
13212 is not suitable to frame displayed formulas because the formula will always
13213 be set in the size of the text.
13220 is in contrary not suitable to frame inline formulas, because the formula
13221 will always be set in the size of a displayed formula.
13224 \begin_layout Standard
13238 \begin_inset Index idx
13241 \begin_layout Plain Layout
13249 where additionally the frame width and the alignment can be specified.
13256 is used in the following scheme:
13259 \begin_layout Standard
13264 framebox[frame width][position]{box content}
13267 \begin_layout Standard
13268 The position can either be
13285 right aligns the formula in the box.
13286 When no position is given, the formula will be centered.
13287 \begin_inset Newline newline
13290 If no width is given, also no position can be given.
13291 In this case the frame width is adjusted to the box content like for
13300 \begin_layout Standard
13307 is inserted, a box appears containing three blue boxes.
13308 The first two boxes are surrounded by brackets and denote the two optional
13310 The third box is for formula parts like for
13317 \begin_inset Separator parbreak
13323 \begin_layout Standard
13325 \begin_inset Tabular
13326 <lyxtabular version="3" rows="5" columns="2">
13327 <features tabularvalignment="middle">
13328 <column alignment="center" valignment="top">
13329 <column alignment="center" valignment="top">
13331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13334 \begin_layout Plain Layout
13340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13343 \begin_layout Plain Layout
13345 \begin_inset Note Note
13348 \begin_layout Plain Layout
13355 is only used as spacer.
13367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13370 \begin_layout Plain Layout
13374 \begin_inset space \textvisiblespace{}
13384 \begin_inset space \textvisiblespace{}
13392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13395 \begin_layout Plain Layout
13396 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
13406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13409 \begin_layout Plain Layout
13413 \begin_inset space \textvisiblespace{}
13419 \begin_inset space \textvisiblespace{}
13427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13430 \begin_layout Plain Layout
13431 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
13441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13444 \begin_layout Plain Layout
13448 \begin_inset space \textvisiblespace{}
13456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13459 \begin_layout Plain Layout
13460 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13473 \begin_layout Plain Layout
13477 \begin_inset space \textvisiblespace{}
13481 \begin_inset Formula $\to$
13485 \begin_inset Formula $\to$
13495 \begin_inset space \textvisiblespace{}
13499 \begin_inset Formula $\downarrow$
13507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13510 \begin_layout Plain Layout
13511 \begin_inset Formula $\raisebox{6mm}{}$
13515 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13519 \begin_inset Formula $\raisebox{-4mm}{}$
13535 \begin_layout Standard
13536 The frame thickness can also be adjusted.
13537 To do this the following commands have to be inserted in \SpecialChar TeX
13542 \begin_layout Standard
13552 \begin_inset Quotes eld
13556 \begin_inset Quotes erd
13570 \begin_inset Quotes eld
13574 \begin_inset Quotes erd
13580 \begin_layout Standard
13581 \begin_inset Quotes eld
13585 \begin_inset Quotes erd
13588 specifies the minimal distance between the frame and the first character
13590 An example for this is the following framed formula:
13594 \begin_layout Plain Layout
13606 \begin_inset Formula
13613 Before this formula the commands
13616 \begin_layout Standard
13638 \begin_layout Standard
13639 were inserted in \SpecialChar TeX
13641 The given values are used for all following boxes.
13644 \begin_layout Standard
13645 To return to the standard frame size, the command
13648 \begin_layout Standard
13673 \begin_layout Plain Layout
13687 \begin_layout Standard
13688 is inserted in \SpecialChar TeX
13689 mode before the next formula.
13692 \begin_layout Subsection
13693 Boxes without Frame
13694 \begin_inset CommandInset label
13696 name "subsec:Boxes-without-Frame"
13701 \begin_inset Index idx
13704 \begin_layout Plain Layout
13705 Boxes ! without frame
13713 \begin_layout Standard
13714 For boxes without a frame there are the following box commands:
13721 \begin_inset Index idx
13724 \begin_layout Plain Layout
13739 \begin_inset Index idx
13742 \begin_layout Plain Layout
13757 \begin_inset Index idx
13760 \begin_layout Plain Layout
13771 \begin_layout Standard
13778 a box can be super- or subscripted.
13779 But in contrary to normal super- and subscripting, the characters in the
13780 box keep their font size.
13787 is used in the following scheme:
13790 \begin_layout Standard
13795 raisebox{height}{box content}
13798 \begin_layout Standard
13799 When the box should contain a formula, an extra formula is needed like for
13810 \begin_inset Note Greyedout
13813 \begin_layout Plain Layout
13824 this extra formula is created by pressing
13828 twice instead of once because \SpecialChar LyX
13829 doesn't yet support
13843 \begin_inset Separator parbreak
13849 \begin_layout Standard
13851 \begin_inset Tabular
13852 <lyxtabular version="3" rows="4" columns="2">
13853 <features tabularvalignment="middle">
13854 <column alignment="center" valignment="top">
13855 <column alignment="center" valignment="top">
13857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13860 \begin_layout Plain Layout
13866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13869 \begin_layout Plain Layout
13877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13880 \begin_layout Plain Layout
13884 \begin_inset Formula $\to$
13890 \begin_inset Formula $\to$
13898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13901 \begin_layout Plain Layout
13902 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13915 \begin_layout Plain Layout
13919 \begin_inset Formula $\to$
13925 \begin_inset Formula $\to$
13933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13936 \begin_layout Plain Layout
13937 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13950 \begin_layout Plain Layout
13954 \begin_inset Formula $\to$
13970 \begin_inset space \textvisiblespace{}
13978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13981 \begin_layout Plain Layout
13982 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13998 \begin_layout Standard
14023 , with the difference that there is no frame.
14026 \begin_layout Subsection
14028 \begin_inset CommandInset label
14030 name "subsec:Colored-Boxes"
14035 \begin_inset Index idx
14038 \begin_layout Plain Layout
14047 \begin_layout Standard
14048 To be able to use all commands explained in this section, the \SpecialChar LaTeX
14057 \begin_layout Plain Layout
14058 The \SpecialChar LaTeX
14063 is part of every \SpecialChar LaTeX
14064 standard installation.
14070 \begin_inset Index idx
14073 \begin_layout Plain Layout
14079 has to be loaded in the \SpecialChar LaTeX
14080 -preamble with the line
14084 \begin_layout Plain Layout
14085 When text is colored somewhere in the document with a predefined color,
14087 loads the \SpecialChar LaTeX
14093 Thus it is possible that the package is loaded twice, but this does not
14100 \begin_inset Note Note
14103 \begin_layout Plain Layout
14104 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
14113 \begin_layout Standard
14121 \begin_layout Standard
14122 \begin_inset VSpace medskip
14125 To color boxes, the command
14132 \begin_inset Index idx
14135 \begin_layout Plain Layout
14143 is used in the following scheme:
14146 \begin_layout Standard
14151 colorbox{color}{box content}
14154 \begin_layout Standard
14155 The box content can also be a box and a
14161 can also be part of another box (see the 2nd and 3rd example).
14162 When the box should contain a formula, an extra formula has to be created,
14163 the same way as for
14173 \begin_layout Plain Layout
14174 This also applies for the command
14188 \begin_layout Standard
14189 One of the following predefined colors can be chosen:
14192 \begin_layout Standard
14226 \begin_inset Separator parbreak
14232 \begin_layout Standard
14234 \begin_inset Tabular
14235 <lyxtabular version="3" rows="4" columns="2">
14236 <features tabularvalignment="middle">
14237 <column alignment="center" valignment="top">
14238 <column alignment="center" valignment="top">
14240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14243 \begin_layout Plain Layout
14249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14252 \begin_layout Plain Layout
14254 \begin_inset Note Note
14257 \begin_layout Plain Layout
14264 is only used as spacer.
14276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14279 \begin_layout Plain Layout
14283 \begin_inset Formula $\to$
14293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14296 \begin_layout Plain Layout
14297 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
14307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14310 \begin_layout Plain Layout
14314 \begin_inset Formula $\to$
14322 \begin_inset space \textvisiblespace{}
14330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14333 \begin_layout Plain Layout
14334 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
14344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14347 \begin_layout Plain Layout
14351 \begin_inset space \textvisiblespace{}
14357 \begin_inset Formula $\to$
14373 \begin_inset space \textvisiblespace{}
14381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14384 \begin_layout Plain Layout
14385 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
14401 \begin_layout Standard
14408 only colors the box but not the characters in the box.
14409 To color all characters, the whole formula is highlighted and the desired
14410 color is chosen in the
14413 \begin_inset space ~
14419 The dialog can be called with the toolbar button
14422 arg "dialog-show character"
14427 Edit\SpecialChar menuseparator
14429 \begin_inset space ~
14432 Style\SpecialChar menuseparator
14436 The formula number then has the same color as the formula.
14437 When the formula number should get another color than the formula characters,
14438 the color must be changed within the formula.
14441 \begin_layout Standard
14445 \begin_layout Standard
14448 \begin_inset Formula
14450 \int A=B\label{eq:red}
14458 \begin_inset Formula
14460 \textcolor{red}{\int A=B}\label{eq:redgreen}
14468 \begin_layout Standard
14470 \begin_inset CommandInset ref
14476 is completely colored red.
14477 \begin_inset Newline newline
14481 \begin_inset CommandInset ref
14483 reference "eq:redgreen"
14487 was first completely colored green to set the color for the formula number.
14488 Subsequently the formula characters were colored red.
14491 \begin_layout Standard
14492 \begin_inset VSpace bigskip
14495 To color the frame different than the rest of the box, the command
14502 \begin_inset Index idx
14505 \begin_layout Plain Layout
14513 is used in the following scheme:
14516 \begin_layout Standard
14521 fcolorbox{frame color}{color}{box content}
14524 \begin_layout Standard
14531 is an extension of the command
14538 The frame width is set, like for
14561 \begin_layout Plain Layout
14573 \begin_inset Formula
14575 \fcolorbox{cyan}{magenta}{A=B}
14584 \begin_layout Plain Layout
14598 \begin_layout Standard
14599 This formula was created with the command
14600 \begin_inset Newline newline
14608 \begin_inset Formula $\to$
14614 \begin_inset Formula $\to$
14624 \begin_layout Standard
14625 \begin_inset VSpace bigskip
14628 To use other colors than the predefined ones, they have to be defined first.
14631 \begin_layout Standard
14632 One can for example define the color
14633 \begin_inset Quotes eld
14641 \begin_inset Quotes erd
14644 with the \SpecialChar LaTeX
14648 \begin_layout Standard
14653 definecolor{darkgreen}{cmyk}{0.5,
14668 \begin_inset Index idx
14671 \begin_layout Plain Layout
14682 \begin_layout Standard
14687 is the color space that denotes the colors
14704 The four comma separated numbers are the portion factor for the corresponding
14705 colors of the color space.
14706 The factors can be in the range of 0
14707 \begin_inset space \thinspace{}
14711 \begin_inset space \thinspace{}
14719 also the color space
14723 can be used for definitions.
14740 , so that there are in this case three portion factors for the corresponding
14742 Furthermore there is the color space
14746 with one portion factor for the gray value.
14749 \begin_layout Standard
14750 As example a framed box with the new defined color
14754 where the characters have been colored
14759 \begin_inset Formula
14761 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14769 \begin_layout Standard
14770 Self-defined colors can also be used for text with the help of the command
14778 \begin_inset Index idx
14781 \begin_layout Plain Layout
14790 \begin_layout Standard
14794 \begin_layout Plain Layout
14798 textcolor{darkgreen}{
14804 \begin_inset Quotes eld
14808 \begin_inset Quotes erd
14815 \begin_layout Plain Layout
14825 \begin_layout Standard
14833 \begin_inset Index idx
14836 \begin_layout Plain Layout
14844 is used in the scheme
14848 textcolor{color}{characters to color}
14853 \begin_layout Subsection
14855 \begin_inset CommandInset label
14857 name "subsec:Paragraph-Boxes"
14862 \begin_inset Index idx
14865 \begin_layout Plain Layout
14866 Boxes ! as paragraph
14874 \begin_layout Standard
14875 A box that can contain several lines and paragraphs, a so-called paragraph
14876 box (parbox), can be created with the menu
14878 Insert\SpecialChar menuseparator
14881 or the toolbar button
14890 \begin_layout Standard
14891 The following example shows a framed parbox in a line:
14894 \begin_layout Standard
14895 \begin_inset VSpace medskip
14899 \begin_inset Box Boxed
14909 height_special "totalheight"
14914 backgroundcolor "none"
14917 \begin_layout Plain Layout
14918 This is a paragraph box.
14920 \begin_inset space \thinspace{}
14923 cm long and can also contain formulas:
14924 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14935 \begin_layout Standard
14936 \begin_inset VSpace medskip
14942 \begin_layout Standard
14943 Such a box is created by right-clicking on the gray box inset.
14944 A dialog pops up showing the box properties.
14958 \begin_inset space \thinspace{}
14963 Vertical Box Alignment
14968 \begin_layout Standard
14969 \begin_inset VSpace medskip
14972 In \SpecialChar LaTeX
14973 a parbox is created with the command
14980 \begin_inset Index idx
14983 \begin_layout Plain Layout
14991 which has the following scheme:
14994 \begin_layout Standard
14999 parbox[position]{width}{box content}
15002 \begin_layout Standard
15017 \begin_inset Quotes eld
15021 \begin_inset Quotes erd
15024 means that the box is aligned within the surrounding text with its last
15031 \begin_inset Quotes eld
15035 \begin_inset Quotes erd
15038 this is done with the first line.
15039 When no position is given, the box will be vertically centered, see section
15047 \begin_inset space ~
15052 manual for examples.
15055 \begin_layout Standard
15056 \begin_inset VSpace bigskip
15059 To frame formulas completely, including the formula number, the formula
15060 must be set into a parbox.
15061 To do this, the command
15075 is inserted in \SpecialChar TeX
15076 mode before the formula.
15084 \begin_inset Index idx
15087 \begin_layout Plain Layout
15095 is hereby the line width set for the document.
15096 Because the frame is outside the parbox, 2
15097 \begin_inset space \thinspace{}
15100 times the frame separation and the frame thickness must be subtracted from
15102 As this is not automatically done by \SpecialChar LyX
15107 \begin_layout Plain Layout
15108 \begin_inset CommandInset href
15110 name "LyX-bug #4483"
15111 target "http://www.lyx.org/trac/ticket/4483"
15121 mode has to be used.
15122 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
15131 \begin_layout Plain Layout
15136 is part of every \SpecialChar LaTeX
15137 standard installation.
15143 \begin_inset Index idx
15146 \begin_layout Plain Layout
15152 must be loaded in the \SpecialChar LaTeX
15153 -preamble with the line
15156 \begin_layout Standard
15164 \begin_layout Standard
15165 Behind the formula both boxes are closed by entering
15169 in \SpecialChar TeX
15171 Here is an example:
15175 \begin_layout Plain Layout
15189 \begin_layout Standard
15193 \begin_layout Plain Layout
15211 \begin_inset Formula
15213 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
15222 \begin_layout Plain Layout
15233 \begin_layout Plain Layout
15247 \begin_layout Standard
15248 \begin_inset VSpace medskip
15251 As a parbox is used as the argument of
15257 , there is in this case no difference between
15272 \begin_layout Standard
15273 \begin_inset VSpace bigskip
15276 Paragraph boxes are very useful to comment formulas directly.
15283 is used in combination with the command
15297 \begin_inset CommandInset ref
15299 reference "subsec:User-defined-Numbering"
15306 \begin_layout Standard
15307 An example of a formula commented with
15316 \begin_layout Standard
15320 \begin_layout Plain Layout
15333 This is a description.
15334 It is distinctly separated from the formula and multiline.
15338 \begin_layout Plain Layout
15350 \begin_layout Standard
15351 Such a formula must be inserted completely in \SpecialChar TeX
15352 mode because \SpecialChar LyX
15354 support the command
15361 The formula is created with the following command sequence:
15364 \begin_layout Standard
15377 is inserted in \SpecialChar TeX
15382 \begin_layout Plain Layout
15383 When the formula style
15395 can also be replaced by
15402 (formula styles see
15403 \begin_inset CommandInset ref
15405 reference "sec:Formula-Styles"
15414 Then the description follows as normal text and finally
15420 is inserted in \SpecialChar TeX
15434 hereby create a displayed formula.
15437 \begin_layout Standard
15444 can be seen in this example that was
15445 \begin_inset Quotes eld
15449 \begin_inset Quotes erd
15452 using the mathematical textmode:
15453 \begin_inset Formula
15455 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15463 \begin_layout Section
15465 \begin_inset Index idx
15468 \begin_layout Plain Layout
15477 \begin_layout Subsection
15479 \begin_inset CommandInset label
15481 name "subsec:Big-Operators"
15486 \begin_inset Index idx
15489 \begin_layout Plain Layout
15496 \begin_inset Index idx
15499 \begin_layout Plain Layout
15506 \begin_inset Index idx
15509 \begin_layout Plain Layout
15518 \begin_layout Standard
15519 To be able to use all integral operators listed here, the option
15521 Use esint package automatically
15523 must be set in the document settings under
15526 \begin_inset space ~
15534 \begin_layout Standard
15535 \begin_inset space \hfill{}
15539 \begin_inset Tabular
15540 <lyxtabular version="3" rows="11" columns="2">
15541 <features tabularvalignment="middle">
15542 <column alignment="center" valignment="top" width="0pt">
15543 <column alignment="center" valignment="top" width="0pt">
15545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15548 \begin_layout Plain Layout
15554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15557 \begin_layout Plain Layout
15565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15568 \begin_layout Plain Layout
15572 \begin_inset Index idx
15575 \begin_layout Plain Layout
15588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15591 \begin_layout Plain Layout
15592 \begin_inset Formula $\int$
15602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15605 \begin_layout Plain Layout
15613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15616 \begin_layout Plain Layout
15617 \begin_inset Formula $\oint$
15627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15630 \begin_layout Plain Layout
15638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15641 \begin_layout Plain Layout
15642 \begin_inset Formula $\ointctrclockwise$
15652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15655 \begin_layout Plain Layout
15663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15666 \begin_layout Plain Layout
15667 \begin_inset Formula $\ointclockwise$
15677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15680 \begin_layout Plain Layout
15688 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15691 \begin_layout Plain Layout
15692 \begin_inset Formula $\sqint$
15702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15705 \begin_layout Plain Layout
15713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15716 \begin_layout Plain Layout
15718 \begin_inset Formula $\fint$
15728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15731 \begin_layout Plain Layout
15739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15742 \begin_layout Plain Layout
15744 \begin_inset Formula $\landupint$
15754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15757 \begin_layout Plain Layout
15765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15768 \begin_layout Plain Layout
15770 \begin_inset Formula $\landdownint$
15780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15783 \begin_layout Plain Layout
15791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15794 \begin_layout Plain Layout
15795 \begin_inset Formula $\bigcap$
15805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15808 \begin_layout Plain Layout
15816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15819 \begin_layout Plain Layout
15820 \begin_inset Formula $\bigcup$
15834 \begin_inset space \hfill{}
15838 \begin_inset Tabular
15839 <lyxtabular version="3" rows="11" columns="2">
15840 <features tabularvalignment="middle">
15841 <column alignment="center" valignment="top" width="0pt">
15842 <column alignment="center" valignment="top" width="0pt">
15844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15847 \begin_layout Plain Layout
15853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15856 \begin_layout Plain Layout
15864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15867 \begin_layout Plain Layout
15871 \begin_inset Index idx
15874 \begin_layout Plain Layout
15887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15890 \begin_layout Plain Layout
15891 \begin_inset Formula $\sum$
15901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15904 \begin_layout Plain Layout
15908 \begin_inset Index idx
15911 \begin_layout Plain Layout
15918 \begin_layout Plain Layout
15937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15940 \begin_layout Plain Layout
15941 \begin_inset Formula $\prod$
15951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15954 \begin_layout Plain Layout
15962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15965 \begin_layout Plain Layout
15966 \begin_inset Formula $\coprod$
15976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15979 \begin_layout Plain Layout
15987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15990 \begin_layout Plain Layout
15991 \begin_inset Formula $\bigodot$
16001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16004 \begin_layout Plain Layout
16012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16015 \begin_layout Plain Layout
16016 \begin_inset Formula $\bigotimes$
16026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16029 \begin_layout Plain Layout
16037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16040 \begin_layout Plain Layout
16041 \begin_inset Formula $\bigoplus$
16051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16054 \begin_layout Plain Layout
16062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16065 \begin_layout Plain Layout
16066 \begin_inset Formula $\bigwedge$
16076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16079 \begin_layout Plain Layout
16087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16090 \begin_layout Plain Layout
16091 \begin_inset Formula $\bigvee$
16101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16104 \begin_layout Plain Layout
16112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16115 \begin_layout Plain Layout
16116 \begin_inset Formula $\bigsqcup$
16126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16129 \begin_layout Plain Layout
16137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16140 \begin_layout Plain Layout
16141 \begin_inset Formula $\biguplus$
16155 \begin_inset space \hfill{}
16161 \begin_layout Standard
16162 All big operators can also be inserted via the math toolbar button
16165 arg "math-insert \\intop"
16171 \begin_layout Standard
16172 The operators are called big because they are bigger than the sometimes
16173 equal looking binary operators.
16174 All big operators can have limits as described in the next subsection.
16177 \begin_layout Standard
16178 For all integral operators there is a second version available, ending in
16196 These operators are different from
16203 \begin_inset space \space{}
16206 in the style the operator limits are displayed, see
16207 \begin_inset CommandInset ref
16209 reference "subsec:Operator-Limits"
16217 \begin_layout Subsubsection*
16218 Advice for Integrals
16221 \begin_layout Standard
16226 in an integral is an operator, that therefore has to be set upright.
16227 This is done by highlighting the
16231 and using the keyboard shortcut
16241 \begin_layout Plain Layout
16247 \begin_inset CommandInset ref
16249 reference "subsec:Font-Styles"
16259 Finally the smallest space is inserted before the
16263 , as this is usual for operators.
16267 \begin_layout Standard
16269 \begin_inset Formula $\int A(x)dx$
16273 \begin_inset Newline newline
16277 \begin_inset Phantom HPhantom
16280 \begin_layout Plain Layout
16287 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
16293 \begin_layout Standard
16294 For multiple integrals there are the following commands:
16295 \begin_inset VSpace medskip
16301 \begin_layout Standard
16302 \begin_inset space \hfill{}
16306 \begin_inset Tabular
16307 <lyxtabular version="3" rows="4" columns="2">
16308 <features tabularvalignment="middle">
16309 <column alignment="center" valignment="top">
16310 <column alignment="center" valignment="top">
16312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16315 \begin_layout Plain Layout
16321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16324 \begin_layout Plain Layout
16326 \begin_inset Note Note
16329 \begin_layout Plain Layout
16336 is only used as spacer.
16348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16351 \begin_layout Plain Layout
16359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16362 \begin_layout Plain Layout
16363 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
16373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16376 \begin_layout Plain Layout
16384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16387 \begin_layout Plain Layout
16388 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
16398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16401 \begin_layout Plain Layout
16409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16412 \begin_layout Plain Layout
16413 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
16427 \begin_inset space \hfill{}
16431 \begin_inset Tabular
16432 <lyxtabular version="3" rows="4" columns="2">
16433 <features tabularvalignment="middle">
16434 <column alignment="center" valignment="top">
16435 <column alignment="center" valignment="top">
16437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16440 \begin_layout Plain Layout
16446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16449 \begin_layout Plain Layout
16457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16460 \begin_layout Plain Layout
16468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16471 \begin_layout Plain Layout
16472 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16485 \begin_layout Plain Layout
16493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16496 \begin_layout Plain Layout
16497 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16510 \begin_layout Plain Layout
16518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16521 \begin_layout Plain Layout
16522 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16536 \begin_inset space \hfill{}
16542 \begin_layout Subsection
16544 \begin_inset CommandInset label
16546 name "subsec:Operator-Limits"
16551 \begin_inset Index idx
16554 \begin_layout Plain Layout
16563 \begin_layout Standard
16564 Limits are created by super- and subscripts:
16565 \begin_inset Separator parbreak
16571 \begin_layout Standard
16573 \begin_inset Tabular
16574 <lyxtabular version="3" rows="2" columns="2">
16575 <features tabularvalignment="middle">
16576 <column alignment="center" valignment="top" width="0pt">
16577 <column alignment="center" valignment="top" width="0pt">
16579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16582 \begin_layout Plain Layout
16588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16591 \begin_layout Plain Layout
16593 \begin_inset Note Note
16596 \begin_layout Plain Layout
16603 is only used as spacer.
16615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16618 \begin_layout Plain Layout
16624 \begin_inset space \textvisiblespace{}
16628 \begin_inset Formula $\to$
16632 \begin_inset Formula $\to$
16640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16643 \begin_layout Plain Layout
16644 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16660 \begin_layout Standard
16661 Limits of inline formulas are set right beside the operator.
16662 Limits in displayed formulas are set above or below the operator, except
16663 for integral limits.
16666 \begin_layout Standard
16667 To force that the limits are set beside the operator, the cursor is set
16668 directly behind the operator and the limits type is changed with the menu
16671 Edit\SpecialChar menuseparator
16672 Math\SpecialChar menuseparator
16691 \begin_layout Standard
16692 The default limits type is this:
16693 \begin_inset Formula
16695 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16700 This is how it looks when the limits type was changed to
16707 \begin_inset Formula
16709 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16714 For integrals, except those ending with
16730 etc., the limits are by default set beside the operator.
16731 But for multiple integrals the limits are often set below the operator.
16732 In the following example the limits type was therefore set to
16736 and so set below the integrals:
16737 \begin_inset Formula
16739 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16747 \begin_layout Standard
16748 \begin_inset VSpace medskip
16751 To specify conditions for limits, the commands
16758 \begin_inset Index idx
16761 \begin_layout Plain Layout
16776 \begin_inset Index idx
16779 \begin_layout Plain Layout
16788 To create for example this expression
16789 \begin_inset Formula
16791 \sum_{\begin{subarray}{c}
16795 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16803 \begin_layout Standard
16804 the following has to be done:
16805 \begin_inset Newline newline
16817 \begin_inset space \textvisiblespace{}
16823 One is now in a blue box under the summation operator and insert there
16829 \begin_inset space \textvisiblespace{}
16835 The blue box is now within a purple box and now several lines can be written
16837 A new line is created by inserting a line break (
16840 arg "newline-insert newline"
16845 \begin_inset Newline newline
16850 0<k<1000 Ctrl+Return
16851 \begin_inset Newline newline
16856 is typed in, a new box appears below for the new line.
16859 \begin_layout Standard
16860 The alignment of the lines can be changed to left aligned with the
16870 Edit\SpecialChar menuseparator
16874 To get right alignment,
16879 \begin_inset space \textvisiblespace{}
16884 is inserted at the beginning of the line.
16887 \begin_layout Standard
16900 with the difference that the lines are always centered.
16903 \begin_layout Standard
16904 \begin_inset VSpace bigskip
16908 \begin_inset CommandInset ref
16910 reference "eq:substack"
16914 there can be too much space beside an operator, because the characters
16915 following the operator are set beside the limits.
16916 To avoid this the command
16923 \begin_inset Index idx
16926 \begin_layout Plain Layout
16935 To activate it, set in the document settings under
16938 \begin_inset space ~
16948 \begin_inset Index idx
16951 \begin_layout Plain Layout
16952 Packages ! mathtools
16960 \begin_inset space ~
16972 sets the space besides the operator to 0
16973 \begin_inset space \thinspace{}
16977 \begin_inset Newline newline
16981 \begin_inset CommandInset ref
16983 reference "eq:substack"
16987 , one uses the command
16990 \begin_layout Standard
16998 \begin_layout Standard
16999 and inserts the operator with its limits into the braces.
17000 Behind the brace one continues the formula:
17001 \begin_inset Formula
17003 \smashoperator{\sum_{\begin{subarray}{c}
17007 \end{subarray}}^{n}}k^{-2}
17015 \begin_layout Standard
17016 It is possible to set the space of only one side of the operator to 0
17017 \begin_inset space \thinspace{}
17021 To do this write either
17040 stands for the left and
17044 for the right side of the operator.
17045 Here is an example of the possible
17054 \begin_layout Standard
17055 \begin_inset Formula
17057 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}
17065 \begin_layout Standard
17066 \begin_inset VSpace bigskip
17072 \begin_layout Standard
17073 When several consecutive operators have limits the typesetting of the limits
17074 looks often imperfect in the output, see this example:
17075 \begin_inset Formula
17077 \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}
17082 To improve the typesetting set in the document settings under
17085 \begin_inset space ~
17095 \begin_inset Index idx
17098 \begin_layout Plain Layout
17099 Packages ! mathtools
17107 \begin_inset space ~
17113 Then insert into your formula the command
17120 \begin_inset Index idx
17123 \begin_layout Plain Layout
17131 directly before the first operator.
17132 The example will then look like this:
17133 \begin_inset Formula
17135 \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}
17143 \begin_layout Standard
17144 \begin_inset VSpace bigskip
17147 How to use one limit for several operators is described in
17148 \begin_inset CommandInset ref
17150 reference "subsec:Self-defined-Operators"
17157 \begin_layout Subsection
17158 Decoration for Operators
17159 \begin_inset Index idx
17162 \begin_layout Plain Layout
17163 Operators ! Decoration
17171 \begin_layout Standard
17179 \begin_inset Index idx
17182 \begin_layout Plain Layout
17197 \begin_inset Index idx
17200 \begin_layout Plain Layout
17208 characters can be placed above or below an operator, respectively.
17216 \begin_inset Index idx
17219 \begin_layout Plain Layout
17227 characters can be set before and behind a big operator.
17230 \begin_layout Standard
17232 \begin_inset space ~
17244 \begin_layout Itemize
17251 is used to set characters at the corners of the operator
17254 \begin_layout Itemize
17261 is used to set characters before and/or behind the operator (this variant
17262 represents \SpecialChar LaTeX
17272 \begin_layout Itemize
17279 is used to set characters at the left corners and/or behind the operator
17282 \begin_layout Itemize
17289 is used to set characters at the right corners and/or before the operator
17292 \begin_layout Standard
17293 For example the command
17298 \begin_inset space \textvisiblespace{}
17304 \begin_inset space \textvisiblespace{}
17308 \begin_inset Formula $\to$
17312 \begin_inset Formula $\to$
17316 \begin_inset space \textvisiblespace{}
17326 \begin_inset Formula
17328 \sideset{}{'}\sum_{k=1}^{n}
17336 \begin_layout Standard
17337 \begin_inset Note Greyedout
17340 \begin_layout Plain Layout
17347 can only be used to decorate big operators, binary operators are not allowed.
17355 \begin_layout Standard
17368 can also be used to decorate symbols and characters.
17369 For example, the command
17374 \begin_inset space \textvisiblespace{}
17380 \begin_inset space \textvisiblespace{}
17386 \begin_inset Formula $\uparrow$
17394 \begin_inset Formula
17396 \overset{a}{\maltese}
17404 \begin_layout Subsection
17406 \begin_inset CommandInset label
17408 name "subsec:Binary-Operators"
17413 \begin_inset Index idx
17416 \begin_layout Plain Layout
17425 \begin_layout Standard
17426 Binary operators are surrounded by space when there is a character before
17428 \begin_inset VSpace medskip
17434 \begin_layout Standard
17435 \begin_inset space \hfill{}
17439 \begin_inset Tabular
17440 <lyxtabular version="3" rows="13" columns="2">
17441 <features tabularvalignment="middle">
17442 <column alignment="center" valignment="top" width="0pt">
17443 <column alignment="center" valignment="top" width="0pt">
17445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17448 \begin_layout Plain Layout
17450 \begin_inset Note Note
17453 \begin_layout Plain Layout
17460 is only used as spacer.
17470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17473 \begin_layout Plain Layout
17481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17484 \begin_layout Plain Layout
17490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17493 \begin_layout Plain Layout
17494 \begin_inset Formula $+$
17504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17507 \begin_layout Plain Layout
17513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17516 \begin_layout Plain Layout
17517 \begin_inset Formula $-$
17527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17530 \begin_layout Plain Layout
17538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17541 \begin_layout Plain Layout
17542 \begin_inset Formula $\pm$
17552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17555 \begin_layout Plain Layout
17563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17566 \begin_layout Plain Layout
17567 \begin_inset Formula $\mp$
17577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17580 \begin_layout Plain Layout
17588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17591 \begin_layout Plain Layout
17592 \begin_inset Formula $\cdot$
17602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17605 \begin_layout Plain Layout
17613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17616 \begin_layout Plain Layout
17617 \begin_inset Formula $\times$
17627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17630 \begin_layout Plain Layout
17638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17641 \begin_layout Plain Layout
17642 \begin_inset Formula $\div$
17652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17655 \begin_layout Plain Layout
17659 \begin_layout Plain Layout
17672 \begin_layout Plain Layout
17684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17687 \begin_layout Plain Layout
17688 \begin_inset Formula $*$
17698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17701 \begin_layout Plain Layout
17709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17712 \begin_layout Plain Layout
17713 \begin_inset Formula $\star$
17723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17726 \begin_layout Plain Layout
17734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17737 \begin_layout Plain Layout
17738 \begin_inset Formula $\circ$
17748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17751 \begin_layout Plain Layout
17759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17762 \begin_layout Plain Layout
17763 \begin_inset Formula $\diamond$
17773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17776 \begin_layout Plain Layout
17784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17787 \begin_layout Plain Layout
17788 \begin_inset Formula $\bullet$
17802 \begin_inset space \hfill{}
17806 \begin_inset Tabular
17807 <lyxtabular version="3" rows="13" columns="2">
17808 <features tabularvalignment="middle">
17809 <column alignment="center" valignment="top" width="0pt">
17810 <column alignment="center" valignment="top" width="0pt">
17812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17815 \begin_layout Plain Layout
17821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17824 \begin_layout Plain Layout
17832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17835 \begin_layout Plain Layout
17843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17846 \begin_layout Plain Layout
17847 \begin_inset Formula $\nabla$
17857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17860 \begin_layout Plain Layout
17868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17871 \begin_layout Plain Layout
17872 \begin_inset Formula $\bigtriangledown$
17882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17885 \begin_layout Plain Layout
17893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17896 \begin_layout Plain Layout
17897 \begin_inset Formula $\bigtriangleup$
17907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17910 \begin_layout Plain Layout
17918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17921 \begin_layout Plain Layout
17922 \begin_inset Formula $\Box$
17932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17935 \begin_layout Plain Layout
17943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17946 \begin_layout Plain Layout
17947 \begin_inset Formula $\cap$
17957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17960 \begin_layout Plain Layout
17968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17971 \begin_layout Plain Layout
17972 \begin_inset Formula $\cup$
17982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17985 \begin_layout Plain Layout
17993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17996 \begin_layout Plain Layout
17997 \begin_inset Formula $\dagger$
18007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18010 \begin_layout Plain Layout
18018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18021 \begin_layout Plain Layout
18022 \begin_inset Formula $\ddagger$
18032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18035 \begin_layout Plain Layout
18043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18046 \begin_layout Plain Layout
18047 \begin_inset Formula $\wr$
18057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18060 \begin_layout Plain Layout
18068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18071 \begin_layout Plain Layout
18072 \begin_inset Formula $\bigcirc$
18082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18085 \begin_layout Plain Layout
18093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18096 \begin_layout Plain Layout
18097 \begin_inset Formula $\wedge$
18107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18110 \begin_layout Plain Layout
18118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18121 \begin_layout Plain Layout
18122 \begin_inset Formula $\vee$
18136 \begin_inset space \hfill{}
18140 \begin_inset Tabular
18141 <lyxtabular version="3" rows="13" columns="2">
18142 <features tabularvalignment="middle">
18143 <column alignment="center" valignment="top" width="0pt">
18144 <column alignment="center" valignment="top" width="0pt">
18146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18149 \begin_layout Plain Layout
18155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18158 \begin_layout Plain Layout
18166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18169 \begin_layout Plain Layout
18177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18180 \begin_layout Plain Layout
18181 \begin_inset Formula $\oplus$
18191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18194 \begin_layout Plain Layout
18202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18205 \begin_layout Plain Layout
18206 \begin_inset Formula $\ominus$
18216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18219 \begin_layout Plain Layout
18227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18230 \begin_layout Plain Layout
18231 \begin_inset Formula $\otimes$
18241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18244 \begin_layout Plain Layout
18252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18255 \begin_layout Plain Layout
18256 \begin_inset Formula $\oslash$
18266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18269 \begin_layout Plain Layout
18277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18280 \begin_layout Plain Layout
18281 \begin_inset Formula $\odot$
18291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18294 \begin_layout Plain Layout
18302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18305 \begin_layout Plain Layout
18306 \begin_inset Formula $\amalg$
18316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18319 \begin_layout Plain Layout
18327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18330 \begin_layout Plain Layout
18331 \begin_inset Formula $\uplus$
18341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18344 \begin_layout Plain Layout
18352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18355 \begin_layout Plain Layout
18356 \begin_inset Formula $\setminus$
18366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18369 \begin_layout Plain Layout
18377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18380 \begin_layout Plain Layout
18381 \begin_inset Formula $\sqcap$
18391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18394 \begin_layout Plain Layout
18402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18405 \begin_layout Plain Layout
18406 \begin_inset Formula $\sqcup$
18416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18419 \begin_layout Plain Layout
18427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18430 \begin_layout Plain Layout
18431 \begin_inset Formula $\triangleleft$
18441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18444 \begin_layout Plain Layout
18452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18455 \begin_layout Plain Layout
18456 \begin_inset Formula $\triangleright$
18470 \begin_inset space \hfill{}
18476 \begin_layout Standard
18477 All binary operators can also be inserted via the math toolbar button
18480 arg "math-insert \\pm"
18486 \begin_layout Standard
18487 To typeset the Laplace operator also
18504 \begin_inset Formula $\nabla^{2}$
18507 ) can be used instead of
18516 \begin_layout Standard
18523 Insert\SpecialChar menuseparator
18535 \begin_layout Subsection
18536 Self-defined Operators
18537 \begin_inset CommandInset label
18539 name "subsec:Self-defined-Operators"
18544 \begin_inset Index idx
18547 \begin_layout Plain Layout
18548 Operators ! self-defined
18556 \begin_layout Standard
18557 With the help of the command
18561 DeclareMathOperator
18564 \begin_inset Index idx
18567 \begin_layout Plain Layout
18572 DeclareMathOperator
18577 custom operators can be defined in the \SpecialChar LaTeX
18579 Its command scheme is:
18582 \begin_layout Standard
18587 DeclareMathOperator{new command}{display}
18590 \begin_layout Standard
18591 Display can be characters or symbols that define how the operator looks
18593 To define a big operator a * is set behind the command.
18594 All self-defined big operators can have limits as described in
18595 \begin_inset CommandInset ref
18597 reference "subsec:Operator-Limits"
18604 \begin_layout Standard
18605 For example the \SpecialChar LaTeX
18609 \begin_layout Standard
18614 DeclareMathOperator*{
18621 \begin_layout Standard
18622 defines the command
18628 , that inserts a big operator consisting of the lozenge symbol from
18629 \begin_inset CommandInset ref
18631 reference "subsec:Miscellaneous-Symbols"
18636 \begin_inset Formula
18638 \Lozenge_{n=1}^{\infty}
18643 The command for this formula is:
18654 \begin_inset Formula $\to$
18660 \begin_layout Standard
18661 \begin_inset VSpace bigskip
18664 When self-defined operators are not used several times in the document,
18665 they can also be defined with the commands
18672 \begin_inset Index idx
18675 \begin_layout Plain Layout
18690 \begin_inset Index idx
18693 \begin_layout Plain Layout
18701 , which have the following scheme:
18704 \begin_layout Standard
18718 \begin_layout Standard
18725 defines big operators,
18734 \begin_layout Standard
18742 \begin_inset space \thinspace{}
18746 \begin_inset space \space{}
18749 be used to use one limit for several operators:
18752 \begin_layout Standard
18753 \begin_inset Formula
18755 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18763 \begin_layout Standard
18764 The command for the formula above is:
18765 \begin_inset Newline newline
18781 \begin_inset space \textvisiblespace{}
18787 \begin_inset Formula $\to$
18793 \begin_inset space \textvisiblespace{}
18801 \begin_layout Section
18803 \begin_inset Index idx
18806 \begin_layout Plain Layout
18815 \begin_layout Subsection
18817 \begin_inset CommandInset label
18819 name "subsec:Font-Styles"
18824 \begin_inset Index idx
18827 \begin_layout Plain Layout
18836 \begin_layout Standard
18837 Latin letters in formulas can be set in one of the following font styles:
18840 \begin_layout Standard
18842 \begin_inset space \hfill{}
18846 \begin_inset Tabular
18847 <lyxtabular version="3" rows="6" columns="2">
18848 <features tabularvalignment="middle">
18849 <column alignment="center" valignment="top">
18850 <column alignment="center" valignment="top">
18852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18855 \begin_layout Plain Layout
18861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18864 \begin_layout Plain Layout
18872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18875 \begin_layout Plain Layout
18881 \begin_inset space \textvisiblespace{}
18891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18894 \begin_layout Plain Layout
18895 \begin_inset Formula $\mathbb{ABC}$
18905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18908 \begin_layout Plain Layout
18914 \begin_inset space \textvisiblespace{}
18924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18927 \begin_layout Plain Layout
18928 \begin_inset Formula $\mathbf{AbC}$
18938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18941 \begin_layout Plain Layout
18947 \begin_inset space \textvisiblespace{}
18957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18960 \begin_layout Plain Layout
18961 \begin_inset Formula $\boldsymbol{AbC}$
18971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18974 \begin_layout Plain Layout
18980 \begin_inset space \textvisiblespace{}
18990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18993 \begin_layout Plain Layout
18994 \begin_inset Formula $\mathcal{ABC}$
19004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19007 \begin_layout Plain Layout
19013 \begin_inset space \textvisiblespace{}
19023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19026 \begin_layout Plain Layout
19027 \begin_inset Formula $\mathfrak{AbC}$
19041 \begin_inset space \hfill{}
19045 \begin_inset Tabular
19046 <lyxtabular version="3" rows="6" columns="2">
19047 <features tabularvalignment="middle">
19048 <column alignment="center" valignment="top">
19049 <column alignment="center" valignment="top">
19051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19054 \begin_layout Plain Layout
19060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19063 \begin_layout Plain Layout
19071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19074 \begin_layout Plain Layout
19080 \begin_inset space \textvisiblespace{}
19090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19093 \begin_layout Plain Layout
19094 \begin_inset Formula $\mathit{AbC}$
19104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19107 \begin_layout Plain Layout
19113 \begin_inset space \textvisiblespace{}
19123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19126 \begin_layout Plain Layout
19127 \begin_inset Formula $\mathrm{AbC}$
19137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19140 \begin_layout Plain Layout
19146 \begin_inset space \textvisiblespace{}
19156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19159 \begin_layout Plain Layout
19160 \begin_inset Formula $\mathsf{AbC}$
19170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19173 \begin_layout Plain Layout
19179 \begin_inset space \textvisiblespace{}
19189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19192 \begin_layout Plain Layout
19193 \begin_inset Formula $\mathtt{AbC}$
19203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19206 \begin_layout Plain Layout
19212 \begin_inset space \textvisiblespace{}
19222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19225 \begin_layout Plain Layout
19226 \begin_inset Formula $\mathscr{ABC}$
19240 \begin_inset space \hfill{}
19246 \begin_layout Standard
19247 \begin_inset Note Greyedout
19250 \begin_layout Plain Layout
19273 can only be used for big letters.
19281 \begin_layout Standard
19282 Predefined is the style
19291 \begin_layout Standard
19292 The style commands work also for letters in mathematical constructs:
19293 \begin_inset Formula
19295 \mathfrak{A=\frac{b}{C}}
19303 \begin_layout Standard
19304 Characters in mathematical text don't appear in a math font style but in
19305 the text font style
19312 That their style can't be set correctly via the text style dialog is a
19313 bug in \SpecialChar LyX
19318 \begin_layout Plain Layout
19319 \begin_inset CommandInset href
19321 name "LyX-bug #4629"
19322 target "http://www.lyx.org/trac/ticket/4629"
19334 \begin_layout Standard
19335 Instead of the style commands the dialog
19337 Edit\SpecialChar menuseparator
19338 Math\SpecialChar menuseparator
19341 or the toolbar button
19344 arg "math-insert \\font"
19350 \begin_layout Subsection
19352 \begin_inset CommandInset label
19354 name "subsec:Bold-Formulas"
19359 \begin_inset Index idx
19362 \begin_layout Plain Layout
19371 \begin_layout Standard
19372 To make a complete formula bold, the command
19378 from the previous subsection cannot be used, because it doesn't work for
19379 small Greek letters.
19380 Furthermore it prints Latin letters always upright, like in the following
19384 \begin_layout Standard
19385 \begin_inset Formula
19387 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
19395 \begin_layout Standard
19396 To display the formula correctly, the command
19403 \begin_inset Formula
19405 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
19410 It is also possible to set the formula in a
19412 boldmath environment
19415 This environment is created by inserting the command
19422 \begin_inset Index idx
19425 \begin_layout Plain Layout
19433 in \SpecialChar TeX
19435 To end the environment, the command
19442 \begin_inset Index idx
19445 \begin_layout Plain Layout
19453 is inserted in \SpecialChar TeX
19458 \begin_layout Plain Layout
19468 \begin_inset Formula
19470 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19479 \begin_layout Plain Layout
19491 \begin_layout Subsection
19493 \begin_inset Index idx
19496 \begin_layout Plain Layout
19505 \begin_layout Standard
19506 Formulas can be colored like normal text: Highlight a formula or a formula
19512 Here is a formula in magenta:
19513 \begin_inset Formula
19515 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19523 \begin_layout Standard
19524 You can also define your own colors as described in
19525 \begin_inset CommandInset ref
19527 reference "subsec:Colored-Boxes"
19532 They can be used with the \SpecialChar TeX
19540 \begin_inset Index idx
19543 \begin_layout Plain Layout
19554 \begin_layout Standard
19559 textcolor{color}{characters or formula}
19562 \begin_layout Standard
19563 The following example was colored completely dark green and partly red:
19566 \begin_layout Standard
19570 \begin_layout Plain Layout
19574 textcolor{darkgreen}{
19580 \begin_inset Formula
19582 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19591 \begin_layout Plain Layout
19601 \begin_layout Standard
19602 Due to a bug in \SpecialChar LyX
19603 only complete formulas can be colored with self-defined
19608 \begin_layout Plain Layout
19609 \begin_inset CommandInset href
19611 name "LyX-bug #5269"
19612 target "http://www.lyx.org/trac/ticket/5269"
19624 \begin_layout Subsection
19626 \begin_inset CommandInset label
19628 name "subsec:Font-Sizes"
19633 \begin_inset Index idx
19636 \begin_layout Plain Layout
19645 \begin_layout Standard
19646 For characters in formulas there are, analog to characters in text, the
19647 following size commands:
19650 \begin_layout Standard
19694 \begin_inset Newline newline
19716 \begin_layout Standard
19717 The size produced by the commands depends on the document font size, which
19718 corresponds to the command
19725 The other commands produce smaller or larger sizes than
19732 The font size can however not exceed a certain value.
19733 Is for example the document font size 12
19734 \begin_inset space \thinspace{}
19743 switches to the same size as
19753 \begin_layout Standard
19754 A size command is inserted in \SpecialChar TeX
19755 mode before the formula and sets the size
19756 for all following formula and text characters.
19757 To switch back to the initial size, the command
19763 is inserted behind the formula in \SpecialChar TeX
19767 \begin_layout Standard
19768 Within a formula the size can be changed using the following size commands
19769 or the toolbar button
19772 arg "math-insert \\style"
19776 \begin_inset Separator parbreak
19782 \begin_layout Standard
19785 \begin_inset Tabular
19786 <lyxtabular version="3" rows="5" columns="2">
19787 <features tabularvalignment="middle">
19788 <column alignment="center" valignment="top">
19789 <column alignment="center" valignment="top">
19791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19794 \begin_layout Plain Layout
19800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19803 \begin_layout Plain Layout
19805 \begin_inset Note Note
19808 \begin_layout Plain Layout
19815 is only used as spacer.
19827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19830 \begin_layout Plain Layout
19834 \begin_inset Index idx
19837 \begin_layout Plain Layout
19850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19853 \begin_layout Plain Layout
19854 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19867 \begin_layout Plain Layout
19875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19878 \begin_layout Plain Layout
19879 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19892 \begin_layout Plain Layout
19900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19903 \begin_layout Plain Layout
19904 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19917 \begin_layout Plain Layout
19925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19928 \begin_layout Plain Layout
19929 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19945 \begin_layout Standard
19946 After entering these commands, a blue box appears in which the formula parts
19950 \begin_layout Standard
19951 There is a further method to change the font size, that though only works
19952 for symbols or letters in mathematical text.
19953 To use it, one of the above text size commands is inserted in mathematical
19955 All following characters until the end of the mathematical text or until
19956 another size command will have the selected size.
19958 \begin_inset VSpace -2mm
19964 \begin_layout Standard
19968 \begin_layout Plain Layout
19978 \begin_inset Formula
19980 A=\frac{B}{c}\cdot\maltese
19986 \begin_inset Formula
19988 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19997 \begin_layout Plain Layout
20009 \begin_layout Standard
20010 \begin_inset VSpace medskip
20013 Before both formulas the command
20020 The command for the second formula is:
20021 \begin_inset Newline newline
20029 \begin_inset space \textvisiblespace{}
20035 \begin_inset space \textvisiblespace{}
20041 \begin_inset space \textvisiblespace{}
20047 \begin_inset space \textvisiblespace{}
20051 \begin_inset Formula $\to$
20055 \begin_inset Formula $\to$
20059 \begin_inset Newline newline
20063 \begin_inset space \hspace*{}
20074 \begin_inset space \textvisiblespace{}
20080 \begin_inset space \textvisiblespace{}
20086 \begin_inset space \textvisiblespace{}
20092 \begin_layout Standard
20093 If a symbol cannot be displayed in different sizes, it will always be displayed
20094 in the default size.
20097 \begin_layout Section
20099 \begin_inset Index idx
20102 \begin_layout Plain Layout
20111 \begin_layout Standard
20112 Greek letters can also be inserted via the toolbar button
20115 arg "math-insert \\alpha"
20119 All international typesetting norms purport that Greek letters in math
20120 have to be typeset italic/slanted.
20121 In some languages, like French or Russian, they are nevertheless sometimes
20125 \begin_layout Subsection
20127 \begin_inset Index idx
20130 \begin_layout Plain Layout
20131 Greek letters ! small
20139 \begin_layout Standard
20140 \begin_inset space \hfill{}
20144 \begin_inset Tabular
20145 <lyxtabular version="3" rows="11" columns="2">
20146 <features tabularvalignment="middle">
20147 <column alignment="center" valignment="top" width="0pt">
20148 <column alignment="center" valignment="top" width="0pt">
20150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20153 \begin_layout Plain Layout
20159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20162 \begin_layout Plain Layout
20170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20173 \begin_layout Plain Layout
20181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20184 \begin_layout Plain Layout
20185 \begin_inset Formula $\alpha$
20195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20198 \begin_layout Plain Layout
20206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20209 \begin_layout Plain Layout
20210 \begin_inset Formula $\beta$
20220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20223 \begin_layout Plain Layout
20231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20234 \begin_layout Plain Layout
20235 \begin_inset Formula $\gamma$
20245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20248 \begin_layout Plain Layout
20256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20259 \begin_layout Plain Layout
20260 \begin_inset Formula $\delta$
20270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20273 \begin_layout Plain Layout
20281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20284 \begin_layout Plain Layout
20285 \begin_inset Formula $\epsilon$
20295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20298 \begin_layout Plain Layout
20306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20309 \begin_layout Plain Layout
20310 \begin_inset Formula $\varepsilon$
20320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20323 \begin_layout Plain Layout
20331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20334 \begin_layout Plain Layout
20335 \begin_inset Formula $\zeta$
20345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20348 \begin_layout Plain Layout
20356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20359 \begin_layout Plain Layout
20360 \begin_inset Formula $\eta$
20370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20373 \begin_layout Plain Layout
20381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20384 \begin_layout Plain Layout
20385 \begin_inset Formula $\theta$
20395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20398 \begin_layout Plain Layout
20406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20409 \begin_layout Plain Layout
20410 \begin_inset Formula $\vartheta$
20424 \begin_inset space \hfill{}
20428 \begin_inset Tabular
20429 <lyxtabular version="3" rows="12" columns="2">
20430 <features tabularvalignment="middle">
20431 <column alignment="center" valignment="top" width="0pt">
20432 <column alignment="center" valignment="top" width="0pt">
20434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20437 \begin_layout Plain Layout
20443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20446 \begin_layout Plain Layout
20454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20457 \begin_layout Plain Layout
20465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20468 \begin_layout Plain Layout
20469 \begin_inset Formula $\iota$
20479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20482 \begin_layout Plain Layout
20490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20493 \begin_layout Plain Layout
20494 \begin_inset Formula $\kappa$
20504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20507 \begin_layout Plain Layout
20515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20518 \begin_layout Plain Layout
20519 \begin_inset Formula $\varkappa$
20529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20532 \begin_layout Plain Layout
20540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20543 \begin_layout Plain Layout
20544 \begin_inset Formula $\lambda$
20554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20557 \begin_layout Plain Layout
20565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20568 \begin_layout Plain Layout
20569 \begin_inset Formula $\mu$
20579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20582 \begin_layout Plain Layout
20590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20593 \begin_layout Plain Layout
20594 \begin_inset Formula $\nu$
20604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20607 \begin_layout Plain Layout
20615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20618 \begin_layout Plain Layout
20619 \begin_inset Formula $\xi$
20629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20632 \begin_layout Plain Layout
20638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20641 \begin_layout Plain Layout
20642 \begin_inset Formula $o$
20652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20655 \begin_layout Plain Layout
20663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20666 \begin_layout Plain Layout
20667 \begin_inset Formula $\pi$
20677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20680 \begin_layout Plain Layout
20688 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20691 \begin_layout Plain Layout
20692 \begin_inset Formula $\varpi$
20702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20705 \begin_layout Plain Layout
20713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20716 \begin_layout Plain Layout
20717 \begin_inset Formula $\rho$
20731 \begin_inset space \hfill{}
20735 \begin_inset Tabular
20736 <lyxtabular version="3" rows="11" columns="2">
20737 <features tabularvalignment="middle">
20738 <column alignment="center" valignment="top" width="0pt">
20739 <column alignment="center" valignment="top" width="0pt">
20741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20744 \begin_layout Plain Layout
20750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20753 \begin_layout Plain Layout
20761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20764 \begin_layout Plain Layout
20772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20775 \begin_layout Plain Layout
20776 \begin_inset Formula $\varrho$
20786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20789 \begin_layout Plain Layout
20797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20800 \begin_layout Plain Layout
20801 \begin_inset Formula $\sigma$
20811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20814 \begin_layout Plain Layout
20822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20825 \begin_layout Plain Layout
20826 \begin_inset Formula $\varsigma$
20836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20839 \begin_layout Plain Layout
20847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20850 \begin_layout Plain Layout
20851 \begin_inset Formula $\tau$
20861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20864 \begin_layout Plain Layout
20872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20875 \begin_layout Plain Layout
20876 \begin_inset Formula $\upsilon$
20886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20889 \begin_layout Plain Layout
20897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20900 \begin_layout Plain Layout
20901 \begin_inset Formula $\phi$
20911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20914 \begin_layout Plain Layout
20922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20925 \begin_layout Plain Layout
20926 \begin_inset Formula $\varphi$
20936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20939 \begin_layout Plain Layout
20947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20950 \begin_layout Plain Layout
20951 \begin_inset Formula $\chi$
20961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20964 \begin_layout Plain Layout
20972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20975 \begin_layout Plain Layout
20976 \begin_inset Formula $\psi$
20986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20989 \begin_layout Plain Layout
20997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21000 \begin_layout Plain Layout
21001 \begin_inset Formula $\omega$
21015 \begin_inset space \hfill{}
21021 \begin_layout Standard
21022 \begin_inset VSpace medskip
21028 \begin_layout Standard
21029 How to create special upright Greek letters is explained in
21030 \begin_inset CommandInset ref
21032 reference "subsec:Upright-small-Greek"
21039 \begin_layout Subsection
21041 \begin_inset Index idx
21044 \begin_layout Plain Layout
21045 Greek letters ! big
21053 \begin_layout Standard
21054 \begin_inset space \hfill{}
21058 \begin_inset Tabular
21059 <lyxtabular version="3" rows="7" columns="2">
21060 <features tabularvalignment="middle">
21061 <column alignment="center" valignment="top" width="0pt">
21062 <column alignment="center" valignment="top" width="0pt">
21064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21067 \begin_layout Plain Layout
21073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21076 \begin_layout Plain Layout
21084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21087 \begin_layout Plain Layout
21095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21098 \begin_layout Plain Layout
21099 \begin_inset Formula $\Gamma$
21109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21112 \begin_layout Plain Layout
21120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21123 \begin_layout Plain Layout
21124 \begin_inset Formula $\Delta$
21134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21137 \begin_layout Plain Layout
21145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21148 \begin_layout Plain Layout
21149 \begin_inset Formula $\Theta$
21159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21162 \begin_layout Plain Layout
21170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21173 \begin_layout Plain Layout
21174 \begin_inset Formula $\Lambda$
21184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21187 \begin_layout Plain Layout
21195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21198 \begin_layout Plain Layout
21199 \begin_inset Formula $\Xi$
21209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21212 \begin_layout Plain Layout
21220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21223 \begin_layout Plain Layout
21224 \begin_inset Formula $\Pi$
21238 \begin_inset space \hfill{}
21242 \begin_inset Tabular
21243 <lyxtabular version="3" rows="6" columns="2">
21244 <features tabularvalignment="middle">
21245 <column alignment="center" valignment="top" width="0pt">
21246 <column alignment="center" valignment="top" width="0pt">
21248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21251 \begin_layout Plain Layout
21257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21260 \begin_layout Plain Layout
21268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21271 \begin_layout Plain Layout
21279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21282 \begin_layout Plain Layout
21283 \begin_inset Formula $\Sigma$
21293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21296 \begin_layout Plain Layout
21304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21307 \begin_layout Plain Layout
21308 \begin_inset Formula $\Upsilon$
21318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21321 \begin_layout Plain Layout
21329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21332 \begin_layout Plain Layout
21333 \begin_inset Formula $\Phi$
21343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21346 \begin_layout Plain Layout
21354 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21357 \begin_layout Plain Layout
21358 \begin_inset Formula $\Psi$
21368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21371 \begin_layout Plain Layout
21379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21382 \begin_layout Plain Layout
21383 \begin_inset Formula $\Omega$
21397 \begin_inset space \hfill{}
21403 \begin_layout Standard
21404 \begin_inset VSpace medskip
21407 That the big Greek letters appear upright is caused by a design bug when
21410 To get correct italic big letters, begin every command with
21415 For example the command
21422 \begin_inset Formula $\varGamma$
21426 Another way is to load the package
21434 \begin_layout Plain Layout
21439 is part of the \SpecialChar LaTeX
21445 \begin_inset Index idx
21448 \begin_layout Plain Layout
21453 \begin_layout Plain Layout
21473 \begin_inset Index idx
21476 \begin_layout Plain Layout
21482 with the \SpecialChar LaTeX
21486 \begin_layout Standard
21491 usepackage{fixmath}
21494 \begin_layout Standard
21495 Then all big Greek letters in a document will automatically be typeset italic.
21498 \begin_layout Subsection
21500 \begin_inset Index idx
21503 \begin_layout Plain Layout
21504 Greek letters ! bold
21512 \begin_layout Standard
21513 Greek letters cannot be set with different font styles like Latin letters.
21514 They can only be made bold with the command
21521 \begin_inset Index idx
21524 \begin_layout Plain Layout
21533 \begin_inset Separator parbreak
21539 \begin_layout Standard
21541 \begin_inset Tabular
21542 <lyxtabular version="3" rows="3" columns="2">
21543 <features tabularvalignment="middle">
21544 <column alignment="center" valignment="top">
21545 <column alignment="center" valignment="top">
21547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21550 \begin_layout Plain Layout
21556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21559 \begin_layout Plain Layout
21567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21570 \begin_layout Plain Layout
21582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21585 \begin_layout Plain Layout
21586 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21599 \begin_layout Plain Layout
21611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21614 \begin_layout Plain Layout
21615 \begin_inset Formula $\theta\boldsymbol{\theta}$
21631 \begin_layout Section
21636 \begin_layout Plain Layout
21649 \begin_layout Plain Layout
21650 A list with all symbols of most of the \SpecialChar LaTeX
21651 -packages can be found in
21652 \begin_inset CommandInset citation
21667 \begin_layout Plain Layout
21675 \begin_inset Note Note
21678 \begin_layout Plain Layout
21681 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21684 \begin_layout Plain Layout
21687 texorpdfstring is in section
21688 \begin_inset CommandInset ref
21690 reference "subsec:Formulas-in-Section"
21700 \begin_inset Index idx
21703 \begin_layout Plain Layout
21712 \begin_layout Standard
21713 Many of the symbols listed in this section can also be inserted via the
21717 arg "math-insert \\nabla"
21723 arg "math-insert \\digamma"
21729 \begin_layout Subsection
21730 Mathematical Symbols
21731 \begin_inset CommandInset label
21733 name "subsec:Mathematical-Symbols"
21738 \begin_inset Index idx
21741 \begin_layout Plain Layout
21742 Symbols ! mathematical
21750 \begin_layout Standard
21751 \begin_inset space \hfill{}
21755 \begin_inset Tabular
21756 <lyxtabular version="3" rows="10" columns="2">
21757 <features tabularvalignment="middle">
21758 <column alignment="center" valignment="top" width="0pt">
21759 <column alignment="center" valignment="top" width="0pt">
21761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21764 \begin_layout Plain Layout
21770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21773 \begin_layout Plain Layout
21781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21784 \begin_layout Plain Layout
21792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21795 \begin_layout Plain Layout
21796 \begin_inset Formula $\neg$
21806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21809 \begin_layout Plain Layout
21817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21820 \begin_layout Plain Layout
21821 \begin_inset Formula $\Im$
21831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21834 \begin_layout Plain Layout
21842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21845 \begin_layout Plain Layout
21846 \begin_inset Formula $\Re$
21856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21859 \begin_layout Plain Layout
21867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21870 \begin_layout Plain Layout
21871 \begin_inset Formula $\aleph$
21881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21884 \begin_layout Plain Layout
21892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21895 \begin_layout Plain Layout
21896 \begin_inset Formula $\partial$
21906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21909 \begin_layout Plain Layout
21917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21920 \begin_layout Plain Layout
21921 \begin_inset Formula $\infty$
21931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21934 \begin_layout Plain Layout
21942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21945 \begin_layout Plain Layout
21946 \begin_inset Formula $\wp$
21956 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21959 \begin_layout Plain Layout
21967 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21970 \begin_layout Plain Layout
21971 \begin_inset Formula $\imath$
21981 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21984 \begin_layout Plain Layout
21992 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21995 \begin_layout Plain Layout
21996 \begin_inset Formula $\jmath$
22010 \begin_inset space \hfill{}
22014 \begin_inset Tabular
22015 <lyxtabular version="3" rows="10" columns="2">
22016 <features tabularvalignment="middle">
22017 <column alignment="center" valignment="top" width="0pt">
22018 <column alignment="center" valignment="top" width="0pt">
22020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22023 \begin_layout Plain Layout
22029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22032 \begin_layout Plain Layout
22034 \begin_inset Note Note
22037 \begin_layout Plain Layout
22044 is only used as spacer.
22056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22059 \begin_layout Plain Layout
22067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22070 \begin_layout Plain Layout
22071 \begin_inset Formula $\forall$
22081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22084 \begin_layout Plain Layout
22092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22095 \begin_layout Plain Layout
22096 \begin_inset Formula $\exists$
22106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22109 \begin_layout Plain Layout
22117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22120 \begin_layout Plain Layout
22121 \begin_inset Formula $\nexists$
22131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22134 \begin_layout Plain Layout
22142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22145 \begin_layout Plain Layout
22146 \begin_inset Formula $\emptyset$
22156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22159 \begin_layout Plain Layout
22167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22170 \begin_layout Plain Layout
22171 \begin_inset Formula $\varnothing$
22181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22184 \begin_layout Plain Layout
22192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22195 \begin_layout Plain Layout
22196 \begin_inset Formula $\dag$
22206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22209 \begin_layout Plain Layout
22217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22220 \begin_layout Plain Layout
22221 \begin_inset Formula $\ddag$
22231 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22234 \begin_layout Plain Layout
22242 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22245 \begin_layout Plain Layout
22249 \begin_layout Plain Layout
22259 \begin_inset Formula $\complement$
22266 \begin_layout Plain Layout
22280 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22283 \begin_layout Plain Layout
22291 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22294 \begin_layout Plain Layout
22295 \begin_inset Formula $\Bbbk$
22309 \begin_inset space \hfill{}
22313 \begin_inset Tabular
22314 <lyxtabular version="3" rows="10" columns="2">
22315 <features tabularvalignment="middle">
22316 <column alignment="center" valignment="top" width="0pt">
22317 <column alignment="center" valignment="top" width="0pt">
22319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22322 \begin_layout Plain Layout
22328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22331 \begin_layout Plain Layout
22339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22342 \begin_layout Plain Layout
22350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22353 \begin_layout Plain Layout
22354 \begin_inset Formula $\prime$
22364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22367 \begin_layout Plain Layout
22375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22378 \begin_layout Plain Layout
22379 \begin_inset Formula $\backprime$
22389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22392 \begin_layout Plain Layout
22400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22403 \begin_layout Plain Layout
22404 \begin_inset Formula $\mho$
22414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22417 \begin_layout Plain Layout
22425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22428 \begin_layout Plain Layout
22429 \begin_inset Formula $\triangle$
22439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22442 \begin_layout Plain Layout
22450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22453 \begin_layout Plain Layout
22454 \begin_inset Formula $\angle$
22464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22467 \begin_layout Plain Layout
22475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22478 \begin_layout Plain Layout
22479 \begin_inset Formula $\measuredangle$
22489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22492 \begin_layout Plain Layout
22500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22503 \begin_layout Plain Layout
22504 \begin_inset Formula $\sphericalangle$
22514 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22517 \begin_layout Plain Layout
22525 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22528 \begin_layout Plain Layout
22529 \begin_inset Formula $\top$
22539 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22542 \begin_layout Plain Layout
22550 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22553 \begin_layout Plain Layout
22554 \begin_inset Formula $\bot$
22568 \begin_inset space \hfill{}
22574 \begin_layout Standard
22575 \begin_inset Newpage newpage
22581 \begin_layout Subsection
22582 Miscellaneous Symbols
22583 \begin_inset CommandInset label
22585 name "subsec:Miscellaneous-Symbols"
22590 \begin_inset Index idx
22593 \begin_layout Plain Layout
22594 Symbols ! miscellaneous
22602 \begin_layout Standard
22605 \begin_inset Tabular
22606 <lyxtabular version="3" rows="10" columns="2">
22607 <features tabularvalignment="middle">
22608 <column alignment="center" valignment="top" width="0pt">
22609 <column alignment="center" valignment="top" width="0pt">
22611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22614 \begin_layout Plain Layout
22620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22623 \begin_layout Plain Layout
22631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22634 \begin_layout Plain Layout
22642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22645 \begin_layout Plain Layout
22646 \begin_inset Formula $\flat$
22656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22659 \begin_layout Plain Layout
22667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22670 \begin_layout Plain Layout
22671 \begin_inset Formula $\natural$
22681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22684 \begin_layout Plain Layout
22692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22695 \begin_layout Plain Layout
22696 \begin_inset Formula $\sharp$
22706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22709 \begin_layout Plain Layout
22717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22720 \begin_layout Plain Layout
22721 \begin_inset Formula $\surd$
22731 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22734 \begin_layout Plain Layout
22742 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22745 \begin_layout Plain Layout
22746 \begin_inset Formula $\checkmark$
22756 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22759 \begin_layout Plain Layout
22767 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22770 \begin_layout Plain Layout
22771 \begin_inset Formula $\yen$
22781 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22784 \begin_layout Plain Layout
22792 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22795 \begin_layout Plain Layout
22796 \begin_inset Formula $\pounds$
22806 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22809 \begin_layout Plain Layout
22815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22818 \begin_layout Plain Layout
22819 \begin_inset Formula $\$$
22829 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22832 \begin_layout Plain Layout
22838 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22841 \begin_layout Plain Layout
22842 \begin_inset Formula $§$
22856 \begin_inset Tabular
22857 <lyxtabular version="3" rows="10" columns="2">
22858 <features tabularvalignment="middle">
22859 <column alignment="center" valignment="top">
22860 <column alignment="center" valignment="top">
22862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22865 \begin_layout Plain Layout
22871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22874 \begin_layout Plain Layout
22882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22885 \begin_layout Plain Layout
22893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22896 \begin_layout Plain Layout
22897 \begin_inset Formula $\hbar$
22907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22910 \begin_layout Plain Layout
22918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22921 \begin_layout Plain Layout
22922 \begin_inset Formula $\hslash$
22932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22935 \begin_layout Plain Layout
22943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22946 \begin_layout Plain Layout
22947 \begin_inset Formula $\clubsuit$
22957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22960 \begin_layout Plain Layout
22968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22971 \begin_layout Plain Layout
22972 \begin_inset Formula $\spadesuit$
22982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22985 \begin_layout Plain Layout
22993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22996 \begin_layout Plain Layout
22997 \begin_inset Formula $\bigstar$
23007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23010 \begin_layout Plain Layout
23018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23021 \begin_layout Plain Layout
23022 \begin_inset Formula $\blacklozenge$
23032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23035 \begin_layout Plain Layout
23043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23046 \begin_layout Plain Layout
23047 \begin_inset Formula $\blacktriangle$
23057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23060 \begin_layout Plain Layout
23068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23071 \begin_layout Plain Layout
23072 \begin_inset Formula $\blacktriangledown$
23082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23085 \begin_layout Plain Layout
23093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23096 \begin_layout Plain Layout
23097 \begin_inset Formula $\bullet$
23111 \begin_inset Tabular
23112 <lyxtabular version="3" rows="10" columns="2">
23113 <features tabularvalignment="middle">
23114 <column alignment="center" valignment="top" width="0pt">
23115 <column alignment="center" valignment="top" width="0pt">
23117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23120 \begin_layout Plain Layout
23126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23129 \begin_layout Plain Layout
23137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23140 \begin_layout Plain Layout
23148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23151 \begin_layout Plain Layout
23152 \begin_inset Formula $\diamondsuit$
23162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23165 \begin_layout Plain Layout
23173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23176 \begin_layout Plain Layout
23177 \begin_inset Formula $\Diamond$
23187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23190 \begin_layout Plain Layout
23198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23201 \begin_layout Plain Layout
23202 \begin_inset Formula $\heartsuit$
23212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23215 \begin_layout Plain Layout
23223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23226 \begin_layout Plain Layout
23227 \begin_inset Formula $\P$
23237 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23240 \begin_layout Plain Layout
23248 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23251 \begin_layout Plain Layout
23252 \begin_inset Formula $\copyright$
23262 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23265 \begin_layout Plain Layout
23273 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23276 \begin_layout Plain Layout
23277 \begin_inset Formula $\circledR$
23287 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23290 \begin_layout Plain Layout
23298 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23301 \begin_layout Plain Layout
23302 \begin_inset Formula $\maltese$
23312 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23315 \begin_layout Plain Layout
23323 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23326 \begin_layout Plain Layout
23327 \begin_inset Formula $\diagup$
23337 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23340 \begin_layout Plain Layout
23348 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23351 \begin_layout Plain Layout
23352 \begin_inset Formula $\diagdown$
23368 \begin_layout Standard
23369 \begin_inset VSpace medskip
23375 \begin_layout Standard
23376 Some symbols can be displayed in different sizes, see
23377 \begin_inset CommandInset ref
23379 reference "subsec:Font-Sizes"
23386 \begin_layout Subsection
23388 \begin_inset Index idx
23391 \begin_layout Plain Layout
23392 Symbols ! Euro-symbol
23398 \begin_inset Index idx
23401 \begin_layout Plain Layout
23408 \begin_layout Plain Layout
23425 \begin_layout Standard
23426 To use the Euro symbol in formulas, the \SpecialChar LaTeX
23432 \begin_inset Index idx
23435 \begin_layout Plain Layout
23441 must be installed and loaded with the \SpecialChar LaTeX
23445 \begin_layout Standard
23450 usepackage[gennarrow]{eurosym}
23453 \begin_layout Standard
23454 The Euro symbol can now be inserted with the command
23461 \begin_inset Index idx
23464 \begin_layout Plain Layout
23475 \begin_layout Standard
23476 The Euro symbol can directly be inserted with the € key in mathematical
23477 text, without having
23492 can also be inserted in \SpecialChar TeX
23494 The official currency symbol can then be inserted with the command
23501 \begin_inset Index idx
23504 \begin_layout Plain Layout
23512 , that is only available in \SpecialChar TeX
23516 \begin_layout Standard
23520 \begin_layout Plain Layout
23530 \begin_inset Note Note
23533 \begin_layout Plain Layout
23534 The following table will only be displayed when the \SpecialChar LaTeX
23547 \begin_layout Standard
23548 An overview about the different Euro symbols:
23549 \begin_inset Separator parbreak
23555 \begin_layout Standard
23557 \begin_inset Tabular
23558 <lyxtabular version="3" rows="4" columns="3">
23559 <features tabularvalignment="middle">
23560 <column alignment="center" valignment="top" width="0pt">
23561 <column alignment="center" valignment="top" width="0pt">
23562 <column alignment="center" valignment="top" width="0pt">
23564 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23567 \begin_layout Plain Layout
23573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23576 \begin_layout Plain Layout
23582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23585 \begin_layout Plain Layout
23593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23596 \begin_layout Plain Layout
23602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23605 \begin_layout Plain Layout
23613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23616 \begin_layout Plain Layout
23617 \begin_inset Formula $\euro$
23627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23630 \begin_layout Plain Layout
23636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23639 \begin_layout Plain Layout
23645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23648 \begin_layout Plain Layout
23649 \begin_inset Formula $\mbox{€}$
23659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23662 \begin_layout Plain Layout
23669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23672 \begin_layout Plain Layout
23680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23683 \begin_layout Plain Layout
23687 \begin_layout Plain Layout
23709 \begin_layout Standard
23713 \begin_layout Plain Layout
23723 \begin_inset Note Note
23726 \begin_layout Plain Layout
23727 The following will be displayed when the \SpecialChar LaTeX
23740 \begin_layout Standard
23741 You need to install the \SpecialChar LaTeX
23746 to see the rest of this subsection in the output.
23749 \begin_layout Standard
23753 \begin_layout Plain Layout
23765 \begin_layout Standard
23766 \begin_inset Newpage newpage
23772 \begin_layout Section
23774 \begin_inset CommandInset label
23776 name "sec:Relations"
23781 \begin_inset Index idx
23784 \begin_layout Plain Layout
23791 \begin_inset Index idx
23794 \begin_layout Plain Layout
23799 \begin_layout Plain Layout
23810 \begin_layout Plain Layout
23825 \begin_layout Standard
23826 All following relations can also be inserted via the toolbar button
23829 arg "math-insert \\leq"
23835 \begin_layout Standard
23836 \begin_inset space \hfill{}
23840 \begin_inset Tabular
23841 <lyxtabular version="3" rows="17" columns="2">
23842 <features tabularvalignment="middle">
23843 <column alignment="center" valignment="top" width="0pt">
23844 <column alignment="center" valignment="top" width="0pt">
23846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23849 \begin_layout Plain Layout
23855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23858 \begin_layout Plain Layout
23866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23869 \begin_layout Plain Layout
23875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23878 \begin_layout Plain Layout
23879 \begin_inset Formula $<$
23889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23892 \begin_layout Plain Layout
23900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23903 \begin_layout Plain Layout
23904 \begin_inset Formula $\le$
23914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23917 \begin_layout Plain Layout
23925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23928 \begin_layout Plain Layout
23929 \begin_inset Formula $\ll$
23939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23942 \begin_layout Plain Layout
23950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23953 \begin_layout Plain Layout
23954 \begin_inset Formula $\prec$
23964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23967 \begin_layout Plain Layout
23975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23978 \begin_layout Plain Layout
23979 \begin_inset Formula $\preceq$
23989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23992 \begin_layout Plain Layout
24000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24003 \begin_layout Plain Layout
24004 \begin_inset Formula $\subset$
24014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24017 \begin_layout Plain Layout
24025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24028 \begin_layout Plain Layout
24029 \begin_inset Formula $\subseteq$
24039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24042 \begin_layout Plain Layout
24050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24053 \begin_layout Plain Layout
24054 \begin_inset Formula $\sqsubseteq$
24064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24067 \begin_layout Plain Layout
24075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24078 \begin_layout Plain Layout
24079 \begin_inset Formula $\in$
24089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24092 \begin_layout Plain Layout
24100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24103 \begin_layout Plain Layout
24104 \begin_inset Formula $\vdash$
24114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24117 \begin_layout Plain Layout
24125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24128 \begin_layout Plain Layout
24129 \begin_inset Formula $\smile$
24139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24142 \begin_layout Plain Layout
24150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24153 \begin_layout Plain Layout
24154 \begin_inset Formula $\lhd$
24164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24167 \begin_layout Plain Layout
24175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24178 \begin_layout Plain Layout
24179 \begin_inset Formula $\unlhd$
24189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24192 \begin_layout Plain Layout
24200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24203 \begin_layout Plain Layout
24204 \begin_inset Formula $\gtrless$
24214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24217 \begin_layout Plain Layout
24225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24228 \begin_layout Plain Layout
24229 \begin_inset Formula $\mid$
24239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24242 \begin_layout Plain Layout
24250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24253 \begin_layout Plain Layout
24254 \begin_inset Formula $\nmid$
24268 \begin_inset space \hfill{}
24272 \begin_inset Tabular
24273 <lyxtabular version="3" rows="17" columns="2">
24274 <features tabularvalignment="middle">
24275 <column alignment="center" valignment="top" width="0pt">
24276 <column alignment="center" valignment="top" width="0pt">
24278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24281 \begin_layout Plain Layout
24287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24290 \begin_layout Plain Layout
24298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24301 \begin_layout Plain Layout
24307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24310 \begin_layout Plain Layout
24311 \begin_inset Formula $=$
24321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24324 \begin_layout Plain Layout
24332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24335 \begin_layout Plain Layout
24336 \begin_inset Formula $\not=$
24346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24349 \begin_layout Plain Layout
24357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24360 \begin_layout Plain Layout
24361 \begin_inset Formula $\equiv$
24371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24374 \begin_layout Plain Layout
24382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24385 \begin_layout Plain Layout
24386 \begin_inset Formula $\sim$
24396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24399 \begin_layout Plain Layout
24407 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24410 \begin_layout Plain Layout
24411 \begin_inset Formula $\simeq$
24421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24424 \begin_layout Plain Layout
24432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24435 \begin_layout Plain Layout
24436 \begin_inset Formula $\approx$
24446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24449 \begin_layout Plain Layout
24457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24460 \begin_layout Plain Layout
24461 \begin_inset Formula $\cong$
24471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24474 \begin_layout Plain Layout
24482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24485 \begin_layout Plain Layout
24486 \begin_inset Formula $\bowtie$
24496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24499 \begin_layout Plain Layout
24507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24510 \begin_layout Plain Layout
24511 \begin_inset Formula $\notin$
24521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24524 \begin_layout Plain Layout
24532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24535 \begin_layout Plain Layout
24536 \begin_inset Formula $\perp$
24546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24549 \begin_layout Plain Layout
24557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24560 \begin_layout Plain Layout
24561 \begin_inset Formula $\propto$
24571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24574 \begin_layout Plain Layout
24582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24585 \begin_layout Plain Layout
24586 \begin_inset Formula $\asymp$
24596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24599 \begin_layout Plain Layout
24607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24610 \begin_layout Plain Layout
24611 \begin_inset Formula $\doteq$
24621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24624 \begin_layout Plain Layout
24632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24635 \begin_layout Plain Layout
24636 \begin_inset Formula $\circeq$
24646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24649 \begin_layout Plain Layout
24657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24660 \begin_layout Plain Layout
24661 \begin_inset Formula $\models$
24671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24674 \begin_layout Plain Layout
24682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24685 \begin_layout Plain Layout
24686 \begin_inset Formula $\widehat{=}$
24700 \begin_inset space \hfill{}
24704 \begin_inset Tabular
24705 <lyxtabular version="3" rows="17" columns="2">
24706 <features tabularvalignment="middle">
24707 <column alignment="center" valignment="top" width="0pt">
24708 <column alignment="center" valignment="top" width="0pt">
24710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24713 \begin_layout Plain Layout
24719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24722 \begin_layout Plain Layout
24730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24733 \begin_layout Plain Layout
24739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24742 \begin_layout Plain Layout
24743 \begin_inset Formula $>$
24753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24756 \begin_layout Plain Layout
24764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24767 \begin_layout Plain Layout
24768 \begin_inset Formula $\ge$
24778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24781 \begin_layout Plain Layout
24789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24792 \begin_layout Plain Layout
24793 \begin_inset Formula $\gg$
24803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24806 \begin_layout Plain Layout
24814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24817 \begin_layout Plain Layout
24818 \begin_inset Formula $\succ$
24828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24831 \begin_layout Plain Layout
24839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24842 \begin_layout Plain Layout
24843 \begin_inset Formula $\succeq$
24853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24856 \begin_layout Plain Layout
24864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24867 \begin_layout Plain Layout
24868 \begin_inset Formula $\supset$
24878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24881 \begin_layout Plain Layout
24889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24892 \begin_layout Plain Layout
24893 \begin_inset Formula $\supseteq$
24903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24906 \begin_layout Plain Layout
24914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24917 \begin_layout Plain Layout
24918 \begin_inset Formula $\sqsupseteq$
24928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24931 \begin_layout Plain Layout
24939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24942 \begin_layout Plain Layout
24943 \begin_inset Formula $\ni$
24953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24956 \begin_layout Plain Layout
24964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24967 \begin_layout Plain Layout
24968 \begin_inset Formula $\dashv$
24978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24981 \begin_layout Plain Layout
24989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24992 \begin_layout Plain Layout
24993 \begin_inset Formula $\frown$
25003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25006 \begin_layout Plain Layout
25014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25017 \begin_layout Plain Layout
25018 \begin_inset Formula $\rhd$
25028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25031 \begin_layout Plain Layout
25039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25042 \begin_layout Plain Layout
25043 \begin_inset Formula $\unrhd$
25053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25056 \begin_layout Plain Layout
25064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25067 \begin_layout Plain Layout
25068 \begin_inset Formula $\lessgtr$
25078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25081 \begin_layout Plain Layout
25089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25092 \begin_layout Plain Layout
25093 \begin_inset Formula $\parallel$
25103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25106 \begin_layout Plain Layout
25114 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25117 \begin_layout Plain Layout
25118 \begin_inset Formula $\nparallel$
25132 \begin_inset space \hfill{}
25138 \begin_layout Standard
25139 \begin_inset VSpace medskip
25154 are bigger than the equal looking operators
25169 \begin_layout Standard
25171 supports also many special relations.
25172 Use the toolbar button
25175 arg "math-insert \\leqq"
25178 to see a list of these relations.
25181 \begin_layout Standard
25182 Relations are, in contrary to symbols, always surrounded by space.
25185 \begin_layout Standard
25186 Relations with labels can be created with the command
25193 \begin_inset Index idx
25196 \begin_layout Plain Layout
25205 \begin_inset Separator parbreak
25211 \begin_layout Standard
25213 \begin_inset Tabular
25214 <lyxtabular version="3" rows="2" columns="2">
25215 <features tabularvalignment="middle">
25216 <column alignment="center" valignment="top">
25217 <column alignment="center" valignment="top">
25219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25222 \begin_layout Plain Layout
25228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25231 \begin_layout Plain Layout
25233 \begin_inset Note Note
25236 \begin_layout Plain Layout
25243 is only used as spacer.
25255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25258 \begin_layout Plain Layout
25262 \begin_inset space \textvisiblespace{}
25270 \begin_inset space \textvisiblespace{}
25274 \begin_inset Formula $\downarrow$
25280 \begin_inset space \textvisiblespace{}
25284 \begin_inset space \textvisiblespace{}
25292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25295 \begin_layout Plain Layout
25296 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
25312 \begin_layout Section
25316 \begin_layout Subsection
25317 Predefined Functions
25318 \begin_inset CommandInset label
25320 name "subsec:Predefined-Functions"
25325 \begin_inset Index idx
25328 \begin_layout Plain Layout
25329 Functions ! predefined
25337 \begin_layout Standard
25338 In general, variables are set
25342 in mathematical expressions, but not function names, because
25343 \begin_inset Formula $sin$
25346 could be misunderstood as
25347 \begin_inset Formula $s\cdot i\cdot n$
25351 Therefore there are predefined functionswhich are additionally a bit separated
25353 They are inserted as commands starting with a backslash before their name.
25354 \begin_inset Separator parbreak
25360 \begin_layout Standard
25362 \begin_inset Tabular
25363 <lyxtabular version="3" rows="2" columns="4">
25364 <features tabularvalignment="middle">
25365 <column alignment="center" valignment="top" width="0pt">
25366 <column alignment="center" valignment="top" width="0pt">
25367 <column alignment="center" valignment="top" width="0pt">
25368 <column alignment="center" valignment="top" width="0pt">
25370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25373 \begin_layout Plain Layout
25379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25382 \begin_layout Plain Layout
25388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25391 \begin_layout Plain Layout
25397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25400 \begin_layout Plain Layout
25408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25411 \begin_layout Plain Layout
25417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25420 \begin_layout Plain Layout
25421 \begin_inset Formula $Asin(x)+B$
25429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25432 \begin_layout Plain Layout
25440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25443 \begin_layout Plain Layout
25444 \begin_inset Formula $A\sin(x)+B$
25460 \begin_layout Standard
25461 The following functions are predefined:
25464 \begin_layout Standard
25465 \begin_inset VSpace -2mm
25471 \begin_layout Standard
25473 \begin_inset Tabular
25474 <lyxtabular version="3" rows="9" columns="4">
25475 <features tabularvalignment="middle">
25476 <column alignment="center" valignment="top" width="0pt">
25477 <column alignment="center" valignment="top" width="0pt">
25478 <column alignment="center" valignment="top" width="0pt">
25479 <column alignment="center" valignment="top" width="0pt">
25481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25484 \begin_layout Plain Layout
25490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25493 \begin_layout Plain Layout
25499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25502 \begin_layout Plain Layout
25508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25511 \begin_layout Plain Layout
25519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25522 \begin_layout Plain Layout
25530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25533 \begin_layout Plain Layout
25541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25544 \begin_layout Plain Layout
25552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25555 \begin_layout Plain Layout
25565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25568 \begin_layout Plain Layout
25576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25579 \begin_layout Plain Layout
25587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25590 \begin_layout Plain Layout
25598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25601 \begin_layout Plain Layout
25611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25614 \begin_layout Plain Layout
25622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25625 \begin_layout Plain Layout
25633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25636 \begin_layout Plain Layout
25644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25647 \begin_layout Plain Layout
25657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25660 \begin_layout Plain Layout
25668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25671 \begin_layout Plain Layout
25679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25682 \begin_layout Plain Layout
25690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25693 \begin_layout Plain Layout
25703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25706 \begin_layout Plain Layout
25714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25717 \begin_layout Plain Layout
25725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25728 \begin_layout Plain Layout
25736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25739 \begin_layout Plain Layout
25749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25752 \begin_layout Plain Layout
25760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25763 \begin_layout Plain Layout
25771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25774 \begin_layout Plain Layout
25782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25785 \begin_layout Plain Layout
25795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25798 \begin_layout Plain Layout
25806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25809 \begin_layout Plain Layout
25817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25820 \begin_layout Plain Layout
25828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25831 \begin_layout Plain Layout
25841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25844 \begin_layout Plain Layout
25852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25855 \begin_layout Plain Layout
25863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25866 \begin_layout Plain Layout
25874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25877 \begin_layout Plain Layout
25893 \begin_layout Standard
25894 They can also be inserted with the math toolbar button
25897 arg "math-insert \\functions"
25903 \begin_layout Subsection
25904 Self-defined Functions
25905 \begin_inset Index idx
25908 \begin_layout Plain Layout
25909 Functions ! self-defined
25917 \begin_layout Standard
25918 To use a function that is not predefined, like for example the sign function
25919 sgn(x), there are two possibilities:
25922 \begin_layout Itemize
25923 Define the function by inserting the following line to the \SpecialChar LaTeX
25928 \begin_layout Plain Layout
25933 DeclareMathOperator
25936 \begin_inset CommandInset ref
25938 reference "subsec:Self-defined-Operators"
25948 \begin_inset Newline newline
25952 \begin_inset VSpace -3mm
25956 \begin_inset Newline newline
25963 DeclareMathOperator{
25968 \begin_inset Index idx
25971 \begin_layout Plain Layout
25976 DeclareMathOperator
25982 \begin_inset Newline newline
25986 \begin_inset VSpace -2mm
25990 \begin_inset Newline newline
25993 Now the new defined function can be called with the command
26002 \begin_layout Itemize
26003 Write the formula as usual, mark the formula name, in our example the letters
26008 , and change it to mathematical text.
26009 Finally, a space is inserted between prefactor and function.
26012 \begin_layout Standard
26013 The result is the same with both methods as with a predefined function
26017 \begin_layout Plain Layout
26018 In \SpecialChar LyX
26019 self-defined functions are displayed red, predefined ones black.
26025 \begin_inset Separator parbreak
26031 \begin_layout Standard
26033 \begin_inset Tabular
26034 <lyxtabular version="3" rows="3" columns="2">
26035 <features tabularvalignment="middle">
26036 <column alignment="center" valignment="top" width="0pt">
26037 <column alignment="center" valignment="top" width="0pt">
26039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26042 \begin_layout Plain Layout
26048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26051 \begin_layout Plain Layout
26059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26062 \begin_layout Plain Layout
26070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26073 \begin_layout Plain Layout
26074 \begin_inset Formula $A\sgn(x)+B$
26084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26087 \begin_layout Plain Layout
26091 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
26099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26102 \begin_layout Plain Layout
26103 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
26119 \begin_layout Standard
26120 The first method is more suitable when the self-defined function should
26121 be used several times.
26124 \begin_layout Subsection
26126 \begin_inset Index idx
26129 \begin_layout Plain Layout
26138 \begin_layout Standard
26139 For limits, in addition to the commands
26146 \begin_inset Index idx
26149 \begin_layout Plain Layout
26169 the following functions are defined:
26170 \begin_inset Separator parbreak
26176 \begin_layout Standard
26178 \begin_inset Tabular
26179 <lyxtabular version="3" rows="5" columns="2">
26180 <features tabularvalignment="middle">
26181 <column alignment="center" valignment="top">
26182 <column alignment="center" valignment="top">
26184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26187 \begin_layout Plain Layout
26193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26196 \begin_layout Plain Layout
26198 \begin_inset Note Note
26201 \begin_layout Plain Layout
26208 is only used as spacer.
26220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26223 \begin_layout Plain Layout
26231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26234 \begin_layout Plain Layout
26235 \begin_inset Formula $\varliminf$
26245 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26248 \begin_layout Plain Layout
26256 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26259 \begin_layout Plain Layout
26260 \begin_inset Formula $\varlimsup$
26270 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26273 \begin_layout Plain Layout
26281 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26284 \begin_layout Plain Layout
26285 \begin_inset Formula $\varprojlim$
26295 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26298 \begin_layout Plain Layout
26306 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26309 \begin_layout Plain Layout
26310 \begin_inset Formula $\varinjlim$
26314 \begin_inset Formula $\raisebox{-2.5mm}{}$
26330 \begin_layout Standard
26331 \begin_inset VSpace medskip
26334 The limit is created by inserting a subscript.
26335 It is set right beside the function in an inline formula:
26338 \begin_layout Standard
26340 \begin_inset Tabular
26341 <lyxtabular version="3" rows="2" columns="2">
26342 <features tabularvalignment="middle">
26343 <column alignment="center" valignment="top" width="0pt">
26344 <column alignment="center" valignment="top" width="0pt">
26346 <cell alignment="center" valignment="top" usebox="none">
26349 \begin_layout Plain Layout
26355 <cell alignment="center" valignment="top" usebox="none">
26358 \begin_layout Plain Layout
26359 \begin_inset space \hspace{}
26364 \begin_inset Note Note
26367 \begin_layout Plain Layout
26374 are used here as spacer.
26386 <cell alignment="center" valignment="top" usebox="none">
26389 \begin_layout Plain Layout
26395 \begin_inset space \textvisiblespace{}
26399 \begin_inset space \textvisiblespace{}
26407 <cell alignment="center" valignment="top" usebox="none">
26410 \begin_layout Plain Layout
26411 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
26427 \begin_layout Standard
26428 In a displayed formula the limit is set below the formula, as usual:
26429 \begin_inset Formula
26439 \begin_layout Standard
26440 \begin_inset VSpace medskip
26446 \begin_layout Standard
26447 How to adjust the typesetting of the limits see
26448 \begin_inset CommandInset ref
26450 reference "subsec:Operator-Limits"
26457 \begin_layout Subsection
26459 \begin_inset Index idx
26462 \begin_layout Plain Layout
26463 Functions ! modulo-
26471 \begin_layout Standard
26472 The modulo-function is special, because it exists in four variants.
26473 The variants in a displayed formula are:
26474 \begin_inset Formula
26476 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26477 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
26478 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
26479 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
26480 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
26488 \begin_layout Standard
26489 In an inline formula less space is set before the function names for all
26491 By default the modulo-functions take only the first following character
26493 To use more than one character, one has to put them into \SpecialChar TeX
26495 \begin_inset Formula
26497 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26498 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
26499 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26507 \begin_layout Section
26509 \begin_inset Index idx
26512 \begin_layout Plain Layout
26521 \begin_layout Standard
26522 The characters ^ and _ would normally create a superscript and subscript,
26524 To get these characters you have to insert them with a leading
26527 \begin_inset Separator parbreak
26533 \begin_layout Standard
26536 \begin_inset Tabular
26537 <lyxtabular version="3" rows="3" columns="2">
26538 <features tabularvalignment="middle">
26539 <column alignment="block" valignment="top">
26540 <column alignment="block" valignment="top">
26542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26545 \begin_layout Plain Layout
26551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26554 \begin_layout Plain Layout
26562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26565 \begin_layout Plain Layout
26569 \begin_inset space \textvisiblespace{}
26577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26580 \begin_layout Plain Layout
26581 \begin_inset Formula $\mathcircumflex$
26591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26594 \begin_layout Plain Layout
26602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26605 \begin_layout Plain Layout
26606 \begin_inset Formula $\_$
26622 \begin_layout Subsection
26623 Special Characters in Mathematical Text
26626 \begin_layout Standard
26627 The following commands can only be used in mathematical text or in \SpecialChar TeX
26631 \begin_layout Standard
26632 \begin_inset space \hfill{}
26636 \begin_inset Tabular
26637 <lyxtabular version="3" rows="8" columns="2">
26638 <features tabularvalignment="middle">
26639 <column alignment="block" valignment="top">
26640 <column alignment="block" valignment="top">
26642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26645 \begin_layout Plain Layout
26651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26654 \begin_layout Plain Layout
26662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26665 \begin_layout Plain Layout
26673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26676 \begin_layout Plain Layout
26677 \begin_inset Formula $\textrm{œ}$
26687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26690 \begin_layout Plain Layout
26698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26701 \begin_layout Plain Layout
26702 \begin_inset Formula $\textrm{Œ}$
26712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26715 \begin_layout Plain Layout
26723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26726 \begin_layout Plain Layout
26727 \begin_inset Formula $\textrm{æ}$
26737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26740 \begin_layout Plain Layout
26748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26751 \begin_layout Plain Layout
26752 \begin_inset Formula $\textrm{Æ}$
26762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26765 \begin_layout Plain Layout
26773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26776 \begin_layout Plain Layout
26777 \begin_inset Formula $\textrm{\aa}$
26787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26790 \begin_layout Plain Layout
26794 \begin_inset Index idx
26797 \begin_layout Plain Layout
26804 \begin_layout Plain Layout
26825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26828 \begin_layout Plain Layout
26829 \begin_inset Formula $\textrm{Å}$
26839 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26842 \begin_layout Plain Layout
26850 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26853 \begin_layout Plain Layout
26854 \begin_inset Formula $\textrm{ı}$
26868 \begin_inset space \hfill{}
26872 \begin_inset Tabular
26873 <lyxtabular version="3" rows="8" columns="2">
26874 <features tabularvalignment="middle">
26875 <column alignment="block" valignment="top">
26876 <column alignment="center" valignment="top">
26878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26881 \begin_layout Plain Layout
26883 \begin_inset Note Note
26886 \begin_layout Plain Layout
26888 \begin_inset space \thinspace{}
26891 mm is used for separation, because otherwise the output will be ¡ and ¿
26902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26905 \begin_layout Plain Layout
26913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26916 \begin_layout Plain Layout
26924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26927 \begin_layout Plain Layout
26928 \begin_inset Formula $\textrm{ø}$
26938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26941 \begin_layout Plain Layout
26949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26952 \begin_layout Plain Layout
26953 \begin_inset Formula $\textrm{Ø}$
26963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26966 \begin_layout Plain Layout
26974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26977 \begin_layout Plain Layout
26978 \begin_inset Formula $\textrm{ł}$
26988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26991 \begin_layout Plain Layout
26999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27002 \begin_layout Plain Layout
27003 \begin_inset Formula $\textrm{Ł}$
27013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27016 \begin_layout Plain Layout
27018 \begin_inset space \hspace{}
27023 \begin_inset space \textvisiblespace{}
27031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27034 \begin_layout Plain Layout
27035 \begin_inset Formula $\textrm{!`}$
27045 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27048 \begin_layout Plain Layout
27050 \begin_inset space \hspace{}
27055 \begin_inset space \textvisiblespace{}
27063 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27066 \begin_layout Plain Layout
27067 \begin_inset Formula $\textrm{?`}$
27077 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27080 \begin_layout Plain Layout
27088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27091 \begin_layout Plain Layout
27092 \begin_inset Formula $\textrm{ȷ}$
27106 \begin_inset space \hfill{}
27112 \begin_layout Standard
27114 \begin_inset Formula $\textrm{\textrm{Å}}$
27118 \begin_inset Formula $\textrm{\textrm{Ø}}$
27121 can also be inserted via the math toolbar button
27124 arg "math-insert \\digamma"
27130 \begin_layout Standard
27131 An exception are the commands
27134 \begin_inset space \hspace{}
27143 \begin_inset space \hspace{}
27149 , because they can be inserted in \SpecialChar LyX
27153 \begin_layout Subsection
27155 \begin_inset CommandInset label
27157 name "subsec:Accents-in-Text"
27162 \begin_inset Index idx
27165 \begin_layout Plain Layout
27174 \begin_layout Standard
27175 With the following commands all letters can be accented.
27176 The commands must be inserted in \SpecialChar TeX
27180 \begin_layout Standard
27181 \begin_inset space \hfill{}
27185 \begin_inset Tabular
27186 <lyxtabular version="3" rows="8" columns="2">
27187 <features tabularvalignment="middle">
27188 <column alignment="block" valignment="top">
27189 <column alignment="block" valignment="top">
27191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27194 \begin_layout Plain Layout
27200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27203 \begin_layout Plain Layout
27211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27214 \begin_layout Plain Layout
27218 \begin_inset Quotes grd
27226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27229 \begin_layout Plain Layout
27233 \begin_layout Plain Layout
27249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27252 \begin_layout Plain Layout
27260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27263 \begin_layout Plain Layout
27267 \begin_layout Plain Layout
27283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27286 \begin_layout Plain Layout
27290 \begin_inset space \textvisiblespace{}
27298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27301 \begin_layout Plain Layout
27305 \begin_layout Plain Layout
27321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27324 \begin_layout Plain Layout
27332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27335 \begin_layout Plain Layout
27339 \begin_layout Plain Layout
27355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27358 \begin_layout Plain Layout
27362 \begin_inset space \textvisiblespace{}
27370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27373 \begin_layout Plain Layout
27377 \begin_layout Plain Layout
27393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27396 \begin_layout Plain Layout
27400 \begin_inset space \textvisiblespace{}
27408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27411 \begin_layout Plain Layout
27415 \begin_layout Plain Layout
27431 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27434 \begin_layout Plain Layout
27438 \begin_inset space \textvisiblespace{}
27446 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27449 \begin_layout Plain Layout
27453 \begin_layout Plain Layout
27473 \begin_inset space \hfill{}
27477 \begin_inset Tabular
27478 <lyxtabular version="3" rows="8" columns="2">
27479 <features tabularvalignment="middle">
27480 <column alignment="block" valignment="top">
27481 <column alignment="center" valignment="top">
27483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27486 \begin_layout Plain Layout
27492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27495 \begin_layout Plain Layout
27503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27506 \begin_layout Plain Layout
27510 \begin_inset space \textvisiblespace{}
27518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27521 \begin_layout Plain Layout
27525 \begin_layout Plain Layout
27541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27544 \begin_layout Plain Layout
27552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27555 \begin_layout Plain Layout
27559 \begin_layout Plain Layout
27575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27578 \begin_layout Plain Layout
27582 \begin_inset Index idx
27585 \begin_layout Plain Layout
27596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27599 \begin_layout Plain Layout
27603 \begin_layout Plain Layout
27619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27622 \begin_layout Plain Layout
27630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27633 \begin_layout Plain Layout
27637 \begin_layout Plain Layout
27653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27656 \begin_layout Plain Layout
27660 \begin_inset space \textvisiblespace{}
27668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27671 \begin_layout Plain Layout
27675 \begin_layout Plain Layout
27691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27694 \begin_layout Plain Layout
27698 \begin_inset space \textvisiblespace{}
27706 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27709 \begin_layout Plain Layout
27713 \begin_layout Plain Layout
27729 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27732 \begin_layout Plain Layout
27736 \begin_inset space \textvisiblespace{}
27744 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27747 \begin_layout Plain Layout
27751 \begin_layout Plain Layout
27771 \begin_inset space \hfill{}
27777 \begin_layout Standard
27778 \begin_inset VSpace medskip
27787 also two different characters can be accented.
27793 \begin_inset space \textvisiblespace{}
27802 \begin_layout Plain Layout
27814 \begin_layout Standard
27827 can in combination with vowels directly be inserted with the keyboard without
27828 using \SpecialChar TeX
27830 The same applies for the tilde
27834 \begin_layout Plain Layout
27835 This only applies for keyboards where the tilde is defined as accent.
27844 in combination with
27859 \begin_layout Standard
27902 and accents that are inserted directly with the keyboard are also available
27903 in mathematical text.
27904 For the other accents there are special math commands to be used in formulas,
27906 \begin_inset CommandInset ref
27908 reference "subsec:Accents-for-one"
27915 \begin_layout Standard
27916 \begin_inset VSpace bigskip
27919 Furthermore, with the command
27926 \begin_inset Index idx
27929 \begin_layout Plain Layout
27937 all numbers and letters can be set into a circle, quasi accented with a
27938 circle, similar to the copyright symbol.
27941 \begin_layout Standard
27943 \begin_inset Tabular
27944 <lyxtabular version="3" rows="3" columns="2">
27945 <features tabularvalignment="middle">
27946 <column alignment="center" valignment="top">
27947 <column alignment="center" valignment="top">
27949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27952 \begin_layout Plain Layout
27958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27961 \begin_layout Plain Layout
27963 \begin_inset Note Note
27966 \begin_layout Plain Layout
27973 is only used as spacer.
27985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27988 \begin_layout Plain Layout
27996 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27999 \begin_layout Plain Layout
28003 \begin_layout Plain Layout
28019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28022 \begin_layout Plain Layout
28033 raisebox{-1.5pt}{W}}
28038 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
28041 \begin_layout Plain Layout
28042 \begin_inset Formula $\raisebox{4.5mm}{}$
28049 \begin_layout Plain Layout
28067 \begin_inset Formula $\raisebox{-2mm}{}$
28083 \begin_layout Standard
28084 One has to take care that the character fits in the circle.
28095 \begin_layout Plain Layout
28097 \begin_inset CommandInset ref
28099 reference "subsec:Font-Sizes"
28108 specifies thereby the size of the circle.
28119 \begin_layout Plain Layout
28121 \begin_inset CommandInset ref
28123 reference "subsec:Boxes-without-Frame"
28132 the character can be centered.
28135 \begin_layout Subsection
28137 \begin_inset Index idx
28140 \begin_layout Plain Layout
28149 \begin_layout Standard
28150 Old-style figures (also known as old-style numerals) are created with the
28158 \begin_inset Index idx
28161 \begin_layout Plain Layout
28170 The command can be used in formulas and in \SpecialChar TeX
28172 The command scheme is:
28175 \begin_layout Standard
28180 oldstylenums{number}
28183 \begin_layout Standard
28188 oldstylenums{0123456789
28191 \begin_inset Formula $\oldstylenums{0123456789}$
28197 \begin_layout Section
28199 \begin_inset CommandInset label
28201 name "sec:Formula-Styles"
28206 \begin_inset Index idx
28209 \begin_layout Plain Layout
28218 \begin_layout Itemize
28219 There are two different alignment styles:
28220 \begin_inset Separator parbreak
28227 \begin_layout Description
28228 Centered is the predefined standard
28231 \begin_layout Description
28232 Indented for this the option
28236 must be inserted in the menu
28238 Document\SpecialChar menuseparator
28244 \begin_inset space ~
28250 \begin_layout Standard
28255 is used, the indentation can be adjusted with the length
28262 \begin_inset Index idx
28265 \begin_layout Plain Layout
28274 Should the distance be 15
28275 \begin_inset space \thinspace{}
28278 mm, the following command line is inserted in the \SpecialChar LaTeX
28282 \begin_layout Standard
28292 \begin_layout Standard
28293 When no length is specified, the predefined value of 30
28294 \begin_inset space \thinspace{}
28301 \begin_layout Itemize
28302 And two different numbering styles:
28303 \begin_inset Separator parbreak
28310 \begin_layout Description
28311 Right is the predefined standard
28314 \begin_layout Description
28315 Left for this the option
28319 must be inserted in the menu
28321 Document\SpecialChar menuseparator
28327 \begin_inset space ~
28334 \begin_layout Standard
28343 can also be used together.
28344 In this case both options are inserted, separated by a comma.
28347 \begin_layout Standard
28348 The chosen styles are used for all displayed formulas of the document.
28349 When both, centered and indented formulas should be created in a document,
28355 The indented formulas are then set in a flalign environment, see
28356 \begin_inset CommandInset ref
28358 reference "subsec:Flalign-Environment"
28365 \begin_layout Section
28367 \begin_inset CommandInset label
28369 name "sec:Multiline-Formulas"
28374 \begin_inset Index idx
28377 \begin_layout Plain Layout
28378 Formula ! multiline
28386 \begin_layout Subsection
28390 \begin_layout Standard
28391 In \SpecialChar LyX
28392 multiline formulas are created by pressing
28395 arg "newline-insert newline"
28399 This creates either an
28401 eqnarray environment
28403 that is described in
28404 \begin_inset CommandInset ref
28406 reference "subsec:Eqnarray-Environment"
28410 or, when the option
28412 Use AMS math package
28414 in the document settings is selected, an
28418 that is described in
28419 \begin_inset CommandInset ref
28421 reference "subsec:Standard-align-Environment"
28426 The align environment is recommended because it provides in any case a
28427 typographically correct output.
28430 \begin_layout Standard
28431 There are other multiline formula environments that can be created via the
28434 Insert\SpecialChar menuseparator
28438 These environments are described in the following sections.
28441 \begin_layout Standard
28442 In all multiline formula environments a new line is created by pressing
28446 arg "newline-insert newline"
28450 To add or delete lines, the math toolbar buttons
28453 arg "inset-modify tabular append-row"
28459 arg "inset-modify tabular delete-row"
28462 , respectively, or the menu
28464 Edit\SpecialChar menuseparator
28470 \begin_layout Subsubsection
28472 \begin_inset CommandInset label
28474 name "subsec:Line-Separation"
28479 \begin_inset Index idx
28482 \begin_layout Plain Layout
28483 Formula ! multiline ! Line separation
28491 \begin_layout Standard
28492 There is sometimes not enough space in multiline formulas between the lines:
28493 \begin_inset Formula
28495 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}\\
28496 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
28504 \begin_layout Standard
28505 In \SpecialChar LaTeX
28506 additional line space is specified as optional argument of the new line
28508 This is not yet possible in \SpecialChar LyX
28513 \begin_layout Plain Layout
28515 \begin_inset CommandInset href
28517 name "LyX-bug #1505"
28518 target "http://www.lyx.org/trac/ticket/1505"
28527 , therefore the whole formula must be inserted in \SpecialChar TeX
28529 To add in our example space, the command
28537 is inserted at the end of the first line.
28542 \begin_layout Plain Layout
28549 \begin_layout Plain Layout
28551 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28554 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28561 \begin_layout Plain Layout
28565 left(B^{2}+x_{0}^{2}
28573 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28578 \begin_layout Plain Layout
28590 \begin_layout Standard
28591 \begin_inset VSpace bigskip
28594 To set the line separation for all lines in a formula, the length
28601 \begin_inset Index idx
28604 \begin_layout Plain Layout
28614 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
28625 \begin_inset space \thinspace{}
28630 \begin_inset space \thinspace{}
28633 mm additional line separation as in the previous example, the command
28636 \begin_layout Standard
28646 \begin_layout Standard
28647 is inserted in \SpecialChar TeX
28648 mode before the formula.
28649 This requires that the \SpecialChar LaTeX
28658 \begin_layout Plain Layout
28663 is part of every \SpecialChar LaTeX
28664 standard installation.
28670 \begin_inset Index idx
28673 \begin_layout Plain Layout
28679 was loaded in \SpecialChar LaTeX
28680 -preamble with the line
28683 \begin_layout Standard
28691 \begin_layout Standard
28696 \begin_layout Plain Layout
28708 \begin_inset Formula
28710 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}\\
28711 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
28719 \begin_layout Standard
28723 \begin_layout Plain Layout
28734 To get back to the predefined distance,
28740 is set to the value 3
28741 \begin_inset space \thinspace{}
28747 \begin_layout Subsubsection
28749 \begin_inset CommandInset label
28751 name "subsec:Column-Separation"
28756 \begin_inset Index idx
28759 \begin_layout Plain Layout
28760 Formula ! multiline ! Column separation
28768 \begin_layout Standard
28769 Multiline formulas form a matrix.
28770 A formula in the eqnarray environment is for example a matrix with three
28772 By changing the column separation in this environment, the space beside
28773 the relation sign can be changed.
28776 \begin_layout Standard
28777 The column separation is specified with the length
28784 \begin_inset Index idx
28787 \begin_layout Plain Layout
28796 \begin_inset Newline newline
28799 column separation = 2
28800 \begin_inset space \thinspace{}
28810 \begin_inset Newline newline
28816 \begin_layout Standard
28826 \begin_layout Standard
28827 inserted in \SpecialChar TeX
28828 mode, sets for all following formulas a column separation of
28830 \begin_inset space \thinspace{}
28834 To get back to the predefined distance,
28841 \begin_inset space \thinspace{}
28847 \begin_layout Standard
28849 \begin_inset space \thinspace{}
28852 cm column separation:
28856 \begin_layout Plain Layout
28868 \begin_inset Formula
28876 A formula with the predefined column separation for matrices of 10
28877 \begin_inset space \thinspace{}
28884 \begin_layout Plain Layout
28896 \begin_inset Formula
28907 \begin_layout Subsubsection
28909 \begin_inset Index idx
28912 \begin_layout Plain Layout
28921 \begin_layout Standard
28922 Long formulas can be typeset using these methods:
28925 \begin_layout Itemize
28926 When one side of the equation is much shorter than the line width, this
28927 one is chosen for the left side and the right side is typeset over two
28929 \begin_inset Formula
28931 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 \\
28932 & & -\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}
28937 The minus sign at the beginning of the second line does normally not appear
28938 as an operator because it is the first character of the line.
28939 Thus it would not be surrounded by space and could not be distinguished
28940 from the fraction bar.
28942 \begin_inset space \thinspace{}
28945 pt space was inserted behind the minus sign with the command
28955 \begin_layout Plain Layout
28963 \begin_inset CommandInset ref
28965 reference "subsec:Variable-Space"
28975 \begin_inset Index idx
28978 \begin_layout Plain Layout
28989 \begin_layout Itemize
28990 When both sides of the equation are too long, the command
28997 \begin_inset Index idx
29000 \begin_layout Plain Layout
29009 It is inserted in the first column of the first line and causes all further
29010 insertions to overwrite the following columns:
29011 \begin_inset Formula
29013 \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 \\
29014 & & -\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 \\
29015 & & =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}
29020 After the insertion of
29026 , the cursor is in a purple box that is a bit shifted to the left from the
29028 In this the formula is inserted.
29029 \begin_inset Newline newline
29032 The content of the further lines is inserted to the second or another formula
29034 The greater the column number where it was inserted, the larger the indentation.
29035 \begin_inset VSpace medskip
29039 \begin_inset Newline newline
29043 \begin_inset Note Greyedout
29046 \begin_layout Plain Layout
29047 Note the following when using
29056 \begin_layout Itemize
29057 The formula doesn't use the full page width.
29059 \begin_inset space \thinspace{}
29063 \begin_inset space \space{}
29067 \begin_inset Formula $-B^{2}$
29070 is added to the first line in the above example, it would have been outside
29072 To better use the width, negative space can be inserted at the beginning
29076 \begin_layout Itemize
29077 Due to a bug in \SpecialChar LyX
29078 the cursor cannot be set with the mouse into the first
29083 \begin_layout Plain Layout
29084 \begin_inset CommandInset href
29086 name "LyX-bug #1429"
29087 target "http://www.lyx.org/trac/ticket/1429"
29096 One can only set the cursor at the beginning of the line and move it with
29105 \begin_layout Itemize
29106 Other methods to set long formulas are offered by the environments described
29108 \begin_inset CommandInset ref
29110 reference "subsec:Multline-Environment"
29115 \begin_inset CommandInset ref
29117 reference "subsec:Multiline-Formula-Parts"
29124 \begin_layout Subsubsection
29125 Multiline Fractions
29126 \begin_inset CommandInset label
29128 name "subsec:Multiline-Fractions"
29133 \begin_inset Index idx
29136 \begin_layout Plain Layout
29137 Fractions ! multiline
29145 \begin_layout Standard
29146 There are cases where the denominator and/or the numerator of a fraction
29147 is so long that the fraction does not fit into one line.
29148 It is then necessary to add a line break within the fraction.
29149 This can be done using the command
29156 \begin_inset Index idx
29159 \begin_layout Plain Layout
29168 To activate it, set in the document settings under
29171 \begin_inset space ~
29181 \begin_inset Index idx
29184 \begin_layout Plain Layout
29185 Packages ! mathtools
29193 \begin_inset space ~
29208 \begin_layout Standard
29213 splitfrac{first line}{second line}
29216 \begin_layout Standard
29217 and is used as denominator and/or numerator:
29220 \begin_layout Standard
29221 \begin_inset Formula
29223 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}
29228 The command for the first numerator above is:
29231 \begin_layout Standard
29236 splitfrac{xy+xy+xy+xy+xy
29237 \begin_inset space \textvisiblespace{}
29245 \begin_layout Subsubsection
29247 \begin_inset CommandInset label
29249 name "subsec:Multiline-Brackets"
29254 \begin_inset Index idx
29257 \begin_layout Plain Layout
29258 Brackets ! for multiline expressions
29266 \begin_layout Standard
29267 For brackets spanning multiple lines the following problem occurs:
29268 \begin_inset Formula
29270 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29271 & & \left.\cdots+B-D\right]
29279 \begin_layout Standard
29280 The closing bracket is smaller than the opening bracket because brackets
29281 with variable size may not span multiple lines.
29284 \begin_layout Standard
29285 To set the bracket size for the second line correctly, the first line is
29293 \begin_inset Index idx
29296 \begin_layout Plain Layout
29304 and the second line with
29312 \begin_layout Plain Layout
29326 \begin_inset CommandInset ref
29328 reference "subsec:Automatic-Bracket-Size"
29340 \begin_inset Index idx
29343 \begin_layout Plain Layout
29366 \begin_inset space \textvisiblespace{}
29376 \begin_inset space \textvisiblespace{}
29386 \begin_inset space \textvisiblespace{}
29392 \begin_inset Formula $\downarrow$
29398 \begin_inset Index idx
29401 \begin_layout Plain Layout
29409 is inserted, because the multiplication operator with its limits is the
29410 largest symbol in the first line and this should be the size for the bracket
29411 in the second line.
29414 \begin_layout Standard
29415 The result is this:
29416 \begin_inset Formula
29418 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29419 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29427 \begin_layout Subsection
29431 \begin_layout Standard
29432 Align environments can be used for every kind of multiline formulas.
29433 They are especially useful to set several formulas side by side.
29436 \begin_layout Standard
29437 Align environments consist of columns.
29438 The odd columns are right aligned, the even ones left aligned.
29439 Every line in an Align environment can be numbered.
29442 \begin_layout Standard
29443 Align environments are created via the menu
29445 Insert\SpecialChar menuseparator
29451 Edit\SpecialChar menuseparator
29452 Math\SpecialChar menuseparator
29453 Change Formula Type
29455 already existing formulas can be converted to Align environments.
29458 \begin_layout Standard
29459 To add or delete columns, the math toolbar buttons
29462 arg "inset-modify tabular append-column"
29468 arg "inset-modify tabular delete-column"
29471 , respectively, or the menu
29473 Edit\SpecialChar menuseparator
29479 \begin_layout Subsubsection
29480 Standard align Environment
29481 \begin_inset CommandInset label
29483 name "subsec:Standard-align-Environment"
29488 \begin_inset Index idx
29491 \begin_layout Plain Layout
29492 Formula ! multiline ! align environment
29500 \begin_layout Standard
29501 This Align environment is created by pressing
29504 arg "newline-insert newline"
29507 in a formula or by the menu
29509 Insert\SpecialChar menuseparator
29510 Math\SpecialChar menuseparator
29511 AMS align Environment
29516 \begin_layout Standard
29517 An example for two formulas set side by side, that are created with a four
29518 column align environment:
29519 \begin_inset Formula
29521 A & =\sin(B) & C & =D\\
29522 C & \ne A & B & \ne D
29527 As it can be seen, the formulas in this environment are placed so as if
29536 \begin_layout Plain Layout
29544 \begin_inset CommandInset ref
29546 reference "subsec:Variable-Space"
29557 before the first and after every even column.
29558 When the formula style
29564 \begin_layout Plain Layout
29566 \begin_inset CommandInset ref
29568 reference "sec:Formula-Styles"
29579 is used, the formula is set without the
29585 before the first column.
29588 \begin_layout Subsubsection
29589 Alignat Environment
29590 \begin_inset Index idx
29593 \begin_layout Plain Layout
29594 Formula ! multiline ! alignat environment
29602 \begin_layout Standard
29603 The alignat environment has no predefined column separation.
29604 It can be inserted manually with the spaces that are described
29605 \begin_inset CommandInset ref
29607 reference "subsec:Space"
29614 \begin_layout Standard
29615 The above example in the alignat environment where 1
29616 \begin_inset space \thinspace{}
29619 cm space was inserted at the beginning of the second formula:
29620 \begin_inset Formula
29621 \begin{alignat*}{2}
29622 A & =\sin(B) & \hspace{1cm}C & =D\\
29623 C & \ne A & B & \ne D
29628 Because the column separation can be set separately for every column, this
29629 environment is especially suitable to set three and more formulas side
29633 \begin_layout Subsubsection
29634 Flalign Environment
29635 \begin_inset CommandInset label
29637 name "subsec:Flalign-Environment"
29642 \begin_inset Index idx
29645 \begin_layout Plain Layout
29646 Formula ! multiline ! flalign environment
29654 \begin_layout Standard
29655 In this environment the first two columns are always set as much as possible
29656 to the left and the last two ones to the right.
29658 \begin_inset Formula
29660 A & =1 & B & =2 & C & =3\\
29661 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29669 \begin_layout Standard
29670 By creating a flalign environment with an odd number of columns where an
29671 empty \SpecialChar TeX
29672 brace is inserted to the last column, several formulas in a document
29673 can be set to the left, although the formula style
29678 As example the indented formula
29679 \begin_inset CommandInset ref
29681 reference "eq:VolInt"
29686 \begin_inset Formula
29688 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29693 The first two columns contain the formula.
29694 To indent it as with the formula style
29699 \begin_inset space \thinspace{}
29702 pt space was inserted at the beginning of the first column.
29705 \begin_layout Subsection
29706 Eqnarray Environment
29707 \begin_inset CommandInset label
29709 name "subsec:Eqnarray-Environment"
29714 \begin_inset Index idx
29717 \begin_layout Plain Layout
29718 Formula ! multiline ! eqnarray environment
29726 \begin_layout Standard
29727 When this environment has been created, three blue boxes appear.
29728 The content of the first box is right aligned, the content of the last
29730 The content of the middle box appears centered and a bit smaller, because
29731 it is designed to insert there only relation characters.
29732 \begin_inset Formula
29734 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29744 \begin_layout Subsection
29746 \begin_inset Index idx
29749 \begin_layout Plain Layout
29750 Formula ! multiline ! gather environment
29758 \begin_layout Standard
29759 This environment consists of only one centered column.
29760 Every line can be numbered.
29761 \begin_inset Formula
29772 \begin_layout Subsection
29773 Multline Environment
29774 \begin_inset CommandInset label
29776 name "subsec:Multline-Environment"
29781 \begin_inset Index idx
29784 \begin_layout Plain Layout
29785 Formula ! multiline ! multline environment
29793 \begin_layout Standard
29794 The multline environment consists, like the gather environment, of only
29796 But the first line is left aligned, the last one right aligned.
29797 All other lines are centered.
29798 Therefore this environment is suitable for long formulas.
29800 \begin_inset CommandInset ref
29802 reference "eq:lefteqn"
29806 in the multline environment:
29807 \begin_inset Formula
29809 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}\\
29810 -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}\\
29811 =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}}
29819 \begin_layout Standard
29820 In the output only the last (first) line of a multline environment appears
29821 numbered when the document numbering is right (left).
29825 \begin_layout Plain Layout
29826 numbering styles see
29827 \begin_inset CommandInset ref
29829 reference "sec:Formula-Styles"
29841 \begin_layout Standard
29849 \begin_inset Index idx
29852 \begin_layout Plain Layout
29867 \begin_inset Index idx
29870 \begin_layout Plain Layout
29878 a centered line can be right or left aligned, respectively.
29879 The commands are used as follows:
29882 \begin_layout Standard
29887 shoveright{line content}
29893 shoveleft{line content}
29896 \begin_layout Standard
29897 \begin_inset VSpace medskip
29907 \begin_inset Index idx
29910 \begin_layout Plain Layout
29918 specifies the distance of the first line from the left page margin.
29919 Predefined is the length 0
29920 \begin_inset space \thinspace{}
29926 \begin_layout Standard
29927 As example the above formula where the command
29930 \begin_layout Standard
29940 \begin_layout Standard
29941 was inserted in \SpecialChar TeX
29946 \begin_layout Plain Layout
29958 \begin_inset Formula
29960 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}\\
29961 \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}}\\
29962 =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}}
29971 \begin_layout Plain Layout
29982 The second line was left aligned using
29991 \begin_layout Subsection
29992 Multiline Formula Parts
29993 \begin_inset CommandInset label
29995 name "subsec:Multiline-Formula-Parts"
30000 \begin_inset Index idx
30003 \begin_layout Plain Layout
30004 Formula ! multiline ! formula parts
30012 \begin_layout Standard
30013 To display only parts of a formula with multiple lines, one of the following
30014 environments is used:
30031 They can be inserted via the menu
30033 Insert\SpecialChar menuseparator
30036 or by using the commands described in this section.
30039 \begin_layout Standard
30040 The first three have the same properties as the corresponding multiline
30041 formula environments, but it is possible to set further formula parts beside
30044 \begin_inset Formula
30046 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
30047 \Delta E\Delta t & \ge\frac{\hbar}{2}
30049 \right\} \textrm{Uncertainty relations}
30057 \begin_layout Standard
30058 To get this formula, a displayed formula is created where the command
30065 \begin_inset Index idx
30068 \begin_layout Plain Layout
30077 A purple box appears around the blue formula box where now columns and
30078 lines can be added.
30079 Outside the multiline environment other formula parts can be set, like
30083 \begin_layout Standard
30084 The aligned environment is also suitable for long formulas whose lines are
30085 horizontally aligned.
30086 Using aligned in a displayed formula has the advantage that the formula
30087 number is vertically centered behind the lines.
30089 \begin_inset CommandInset ref
30091 reference "eq:shortlong"
30095 in the aligned environment:
30096 \begin_inset Formula
30098 \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}|}\\
30099 & -\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}|}
30108 \begin_layout Standard
30109 To use the environments
30128 \begin_inset Index idx
30131 \begin_layout Plain Layout
30146 \begin_inset Index idx
30149 \begin_layout Plain Layout
30164 \begin_inset Index idx
30167 \begin_layout Plain Layout
30175 are inserted, respectively.
30176 The split environment has the same properties as the aligned environment
30177 but it can only have two columns.
30180 \begin_layout Subsection
30181 Text in multiline Formulas
30182 \begin_inset CommandInset label
30184 name "subsec:Text-in-multiline"
30189 \begin_inset Index idx
30192 \begin_layout Plain Layout
30199 \begin_inset Index idx
30202 \begin_layout Plain Layout
30203 Formula ! multiline ! text
30211 \begin_layout Standard
30212 In the Align environments, and the multline and gather environment, text
30213 can be inserted that will appear in a separate line and doesn't affect
30214 the column alignment.
30215 To do this, the command
30222 \begin_inset Index idx
30225 \begin_layout Plain Layout
30233 is used in the following scheme:
30236 \begin_layout Standard
30244 \begin_layout Standard
30245 The text should not be longer than a line because it cannot be hyphenated.
30246 As \SpecialChar LyX
30247 doesn't yet support
30253 directly, the text is written as mathematical text.
30260 must hereby be at the beginning of a line and appears in the output above
30262 An example where the text was inserted at the beginning of the second line:
30263 \begin_inset Formula
30265 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
30266 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
30274 \begin_layout Standard
30281 always creates some vertical space between the text and the formula lines.
30282 To avoid this space, set in the document settings under
30285 \begin_inset space ~
30295 \begin_inset Index idx
30298 \begin_layout Plain Layout
30299 Packages ! mathtools
30307 \begin_inset space ~
30313 Then you can use the command
30320 \begin_inset Index idx
30323 \begin_layout Plain Layout
30340 \begin_layout Standard
30341 \begin_inset Formula
30343 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
30344 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
30352 \begin_layout Section
30354 \begin_inset Index idx
30357 \begin_layout Plain Layout
30364 \begin_inset Index idx
30367 \begin_layout Plain Layout
30368 Formula ! numbering|see
30372 \begin_layout Plain Layout
30383 \begin_layout Plain Layout
30398 \begin_layout Subsection
30402 \begin_layout Standard
30403 Numbered formulas can be created with the menu
30405 Insert\SpecialChar menuseparator
30406 Math\SpecialChar menuseparator
30408 \begin_inset space ~
30416 \begin_inset space ~
30422 Existing formulas can be numbered with the menu
30424 Edit\SpecialChar menuseparator
30425 Math\SpecialChar menuseparator
30427 \begin_inset space ~
30435 arg "math-number-toggle"
30439 The formula number is displayed in \SpecialChar LyX
30440 behind the formula as a number sign
30442 The number sign is replaced in the output by the formula number.
30445 \begin_layout Standard
30446 When numbering is turned on in multiline formulas, all lines will be numbered.
30447 But the numbering can be controlled with the menu
30449 Edit\SpecialChar menuseparator
30450 Math\SpecialChar menuseparator
30452 \begin_inset space ~
30456 \begin_inset space ~
30460 \begin_inset space ~
30468 arg "math-number-line-toggle"
30474 \begin_layout Standard
30475 Except for inline formulas, all formulas can be numbered with two different
30477 \begin_inset CommandInset ref
30479 reference "sec:Formula-Styles"
30486 \begin_layout Subsection
30488 \begin_inset Index idx
30491 \begin_layout Plain Layout
30492 Cross-references ! to formulas
30500 \begin_layout Standard
30501 All labeled formulas can be cross-referenced.
30502 A label is added by the menu
30504 Insert\SpecialChar menuseparator
30507 or the toolbar button
30514 The cursor must hereby be inside a displayed formula.
30515 Alternatively you can right-click on the formula and choose
30520 A dialog pops up displaying the prefix
30525 The label is inserted there behind the prefix.
30526 The predefined prefix means
30527 \begin_inset Quotes eld
30531 \begin_inset Quotes erd
30534 and makes it easier to find labels in large documents because it marks
30535 it as formula label to divide it from e.
30536 \begin_inset space \thinspace{}
30540 \begin_inset space \space{}
30544 To change a label, the menu
30546 Insert\SpecialChar menuseparator
30549 is used again or you right-click on a formula and then on
30556 \begin_layout Standard
30557 The name of the label is displayed in \SpecialChar LyX
30558 within two parentheses behind formula.
30559 A formula with a label is always numbered.
30562 \begin_layout Standard
30563 Cross-references are inserted via the menu
30565 Insert\SpecialChar menuseparator
30568 or with the toolbar button
30571 arg "dialog-show-new-inset ref"
30575 A formula cross-reference appears in the output as formula number.
30576 When in the cross-reference dialog window the format
30580 is chosen, the cross-reference appears in the output as formula number
30582 \begin_inset Newline newline
30585 By right-clicking on a cross-reference in \SpecialChar LyX
30586 , one jumps to the formula that
30590 \begin_layout Standard
30591 Here are as examples cross-references to formulas of the following subsections:
30592 \begin_inset Note Note
30595 \begin_layout Plain Layout
30596 Note the different cross-reference types.
30604 \begin_layout Standard
30606 \begin_inset CommandInset ref
30613 \begin_inset CommandInset ref
30621 \begin_inset CommandInset ref
30627 ) big Latin letters are used for the numbering in contrary to (
30628 \begin_inset CommandInset ref
30637 \begin_layout Standard
30638 \begin_inset VSpace medskip
30641 When the argument of
30649 \begin_layout Plain Layout
30657 \begin_inset CommandInset ref
30659 reference "subsec:User-defined-Numbering"
30670 contains a box like in
30671 \begin_inset CommandInset ref
30673 reference "subsec:Paragraph-Boxes"
30677 , the formula cannot be referenced.
30680 \begin_layout Subsection
30682 \begin_inset Index idx
30685 \begin_layout Plain Layout
30686 Formula numbering ! subnumbering
30694 \begin_layout Standard
30695 With the help of the commands
30699 begin{subequations}
30707 formulas can be subnumbered.
30708 Both commands are inserted in \SpecialChar TeX
30712 \begin_layout Standard
30714 \begin_inset Formula
30725 \begin_layout Plain Layout
30729 addtocounter{equation}{-1}
30738 \begin_layout Plain Layout
30742 begin{subequations}
30748 \begin_inset VSpace -5mm
30752 \begin_inset Formula
30760 \begin_inset Formula
30770 \begin_layout Standard
30774 \begin_layout Plain Layout
30786 \begin_layout Standard
30787 To create the example, the following is done:
30790 \begin_layout Enumerate
30791 first formula is inserted
30794 \begin_layout Enumerate
30799 addtocounter{equation}{-1}
30801 begin{subequations}
30802 \begin_inset Index idx
30805 \begin_layout Plain Layout
30814 \begin_inset Newline newline
30819 is inserted after the first formula
30822 \begin_layout Enumerate
30823 second formula is inserted
30826 \begin_layout Enumerate
30827 third formula is inserted
30830 \begin_layout Enumerate
30837 is inserted after the third formula
30840 \begin_layout Standard
30841 Every formula between the commands
30853 is subnumbered as a, b,
30854 \begin_inset Newline linebreak
30857 c, \SpecialChar ldots
30858 For multiline formulas every line will be subnumbered.
30859 All subnumbered formulas are treated as
30864 But as every numbered formula increases the counter
30868 by one, the command
30874 is needed to decrease it.
30875 Otherwise the formulas
30876 \begin_inset CommandInset ref
30883 \begin_inset CommandInset ref
30890 \begin_inset CommandInset ref
30896 would be numbered as
30897 \begin_inset CommandInset ref
30904 \begin_inset CommandInset ref
30911 \begin_inset CommandInset ref
30920 \begin_layout Standard
30921 By inserting the commands in \SpecialChar TeX
30922 mode, a space is created between the first
30925 \begin_inset space \thinspace{}
30928 mm vertical space is inserted after the command
30932 begin{subequations}
30935 When the formula style
30941 \begin_layout Plain Layout
30943 \begin_inset CommandInset ref
30945 reference "sec:Formula-Styles"
30957 \begin_inset space \thinspace{}
30960 mm space is inserted instead.
30963 \begin_layout Standard
30964 Here is an example for a multiline formula where the numbering was turned
30965 off for the second line:
30969 \begin_layout Plain Layout
30973 begin{subequations}
30979 \begin_inset Formula
30981 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30982 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30983 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30992 \begin_layout Plain Layout
31004 \begin_layout Subsection
31005 User-defined Numbering
31006 \begin_inset CommandInset label
31008 name "subsec:User-defined-Numbering"
31013 \begin_inset Index idx
31016 \begin_layout Plain Layout
31017 Formula numbering ! user-defined
31025 \begin_layout Standard
31026 \begin_inset Index idx
31029 \begin_layout Plain Layout
31030 Formula numbering ! self-defined delimiters
31035 With the standard numbering parentheses are set around the formula number.
31036 To replace the parentheses for example by vertical bars, the following
31037 line is added to the \SpecialChar LaTeX
31041 \begin_layout Standard
31053 \begin_inset Note Note
31056 \begin_layout Plain Layout
31057 This macro is already declared in the \SpecialChar LaTeX
31058 -preamble for testing.
31059 To activate it, remove the percent sign at the beginning.
31067 \begin_layout Standard
31068 To use other characters, the vertical bars besides the
31072 are replaced by one ore more characters.
31073 To get only the formula number the vertical bars are omitted.
31076 \begin_layout Standard
31077 \begin_inset VSpace bigskip
31080 When there should be an expression of your choice instead of the consecutive
31081 formula number in parentheses behind the formula, the command
31088 \begin_inset Index idx
31091 \begin_layout Plain Layout
31100 \begin_inset Formula
31102 A+B=C\tag{something}\label{eq:tag}
31107 In this example the command
31112 \begin_inset space \textvisiblespace{}
31117 was inserted in the formula.
31120 \begin_layout Standard
31126 \begin_inset space \textvisiblespace{}
31131 is inserted instead, the star prevents the parentheses around the expression:
31132 \begin_inset Formula
31134 A+B=C\tag*{something}
31142 \begin_layout Standard
31143 \begin_inset VSpace bigskip
31146 To restart the formula numbering with new document parts or sections, the
31147 following command is used:
31150 \begin_layout Standard
31155 @addtoreset{equation}{part}
31158 \begin_inset Index idx
31161 \begin_layout Plain Layout
31166 \begin_layout Plain Layout
31177 \begin_layout Plain Layout
31190 \begin_layout Plain Layout
31201 \begin_layout Plain Layout
31214 \begin_inset Newline newline
31218 \begin_inset Newline newline
31225 @addtoreset{equation}{section}
31228 \begin_layout Standard
31229 To be able to use these commands in \SpecialChar TeX
31231 \begin_inset Quotes eld
31235 \begin_inset Quotes erd
31238 character has to be made
31239 \begin_inset Quotes eld
31243 \begin_inset Quotes erd
31246 for \SpecialChar LaTeX
31261 So the command sequence in \SpecialChar TeX
31265 \begin_layout Standard
31271 \begin_inset Newline newline
31276 @addtoreset{equation}{section}
31277 \begin_inset Newline newline
31285 \begin_layout Standard
31286 In the \SpecialChar LaTeX
31299 can be omitted as they are automatically internally inserted by \SpecialChar LyX
31303 \begin_layout Standard
31318 \begin_layout Plain Layout
31323 is part of the \SpecialChar LaTeX
31329 \begin_inset Index idx
31332 \begin_layout Plain Layout
31333 Packages ! carlisle
31338 that is part of every \SpecialChar LaTeX
31339 standard installation.
31345 \begin_inset Index idx
31348 \begin_layout Plain Layout
31349 Packages ! remreset
31354 has to be loaded in the \SpecialChar LaTeX
31355 -preamble with the line
31358 \begin_layout Standard
31363 usepackage{remreset}
31366 \begin_layout Standard
31374 \begin_inset Index idx
31377 \begin_layout Plain Layout
31382 \begin_layout Plain Layout
31393 \begin_layout Plain Layout
31406 \begin_layout Plain Layout
31417 \begin_layout Plain Layout
31429 can be used with the same scheme as
31438 \begin_layout Standard
31439 \begin_inset VSpace bigskip
31442 Sometimes formulas should be numbered in the following form:
31445 \begin_layout Standard
31448 (section number.formula number)
31451 \begin_layout Standard
31452 The formula number should start with every section with
31453 \begin_inset Quotes eld
31457 \begin_inset Quotes erd
31463 \begin_layout Standard
31464 For this case there is the command
31471 \begin_inset Index idx
31474 \begin_layout Plain Layout
31482 , which is used with the following scheme:
31485 \begin_layout Standard
31490 numberwithin{counter}{sectioning}
31493 \begin_layout Standard
31494 Counter denotes what kind of numbering is affected, sectioning denotes what
31495 number is before the dot.
31498 \begin_layout Standard
31499 Thus in our case the following \SpecialChar LaTeX
31500 preamble or \SpecialChar TeX
31504 \begin_layout Standard
31509 numberwithin{equation}{section}
31512 \begin_layout Standard
31513 This is the result:
31517 \begin_layout Plain Layout
31521 numberwithin{equation}{section}
31527 \begin_inset Formula
31537 \begin_layout Standard
31539 \begin_inset space \thinspace{}
31543 \begin_inset space \space{}
31546 tables so that the number of the part is the sectioning,
31547 \begin_inset Newline newline
31554 numberwithin{table}{part}
31559 \begin_layout Standard
31560 To go back to the standard numbering or to prevent this kind of numbering
31561 when it is defined by the document class, the following command is inserted
31562 as \SpecialChar TeX
31563 code or to the \SpecialChar LaTeX
31567 \begin_layout Standard
31577 \begin_inset Index idx
31580 \begin_layout Plain Layout
31594 \begin_layout Plain Layout
31610 \begin_inset Newline newline
31618 \begin_inset Newline newline
31630 \begin_layout Standard
31637 uses internally the command
31643 , described above, that also needs to be reverted.
31647 \begin_layout Plain Layout
31654 \begin_layout Plain Layout
31658 @removefromreset{equation}{section}
31661 \begin_layout Plain Layout
31673 \begin_layout Subsection
31674 Numbering with Roman Numbers and Letters
31675 \begin_inset Index idx
31678 \begin_layout Plain Layout
31679 Formula numbering ! with letters
31685 \begin_inset Index idx
31688 \begin_layout Plain Layout
31689 Formula numbering ! with Roman numbers
31697 \begin_layout Standard
31698 Formulas can also be numbered with Roman numbers and Latin letters.
31699 To number for example with small Roman numbers, the command
31702 \begin_layout Standard
31714 \begin_layout Standard
31715 is inserted before the formula in \SpecialChar TeX
31724 \begin_inset Index idx
31727 \begin_layout Plain Layout
31735 redefines the predefined command
31751 \begin_layout Plain Layout
31758 has the same scheme like the command
31764 that is described in
31765 \begin_inset CommandInset ref
31767 reference "subsec:The-Command-newcommand"
31780 is the formula counter.
31787 is used as prefix for a counter, the value of the counter is output as
31789 When a formula is numbered, \SpecialChar LaTeX
31790 sets internally the command
31796 behind the formula.
31802 \begin_inset Index idx
31805 \begin_layout Plain Layout
31815 outputs the counter as small Roman number.
31818 \begin_layout Standard
31819 All formulas behind the command
31829 are now numbered Roman.
31830 To switch to numbering with big Roman numbers, the command is inserted
31844 \begin_inset Index idx
31847 \begin_layout Plain Layout
31859 \begin_inset Quotes eld
31863 \begin_inset Quotes erd
31866 with small Latin letters there is the command
31873 \begin_inset Index idx
31876 \begin_layout Plain Layout
31884 , for big ones there is the command
31891 \begin_inset Index idx
31894 \begin_layout Plain Layout
31907 \begin_layout Standard
31908 \begin_inset Note Greyedout
31911 \begin_layout Plain Layout
31918 \begin_inset space ~
31921 formulas can be numbered with Latin letters in one document.
31929 \begin_layout Standard
31933 \begin_layout Plain Layout
31949 \begin_layout Standard
31950 \begin_inset Formula
31952 A=\textrm{small roman}
31961 \begin_layout Plain Layout
31975 \begin_inset Formula
31977 B=\textrm{big Roman}\label{eq:Rom}
31986 \begin_layout Plain Layout
32000 \begin_inset Formula
32002 C=\textrm{small Latin}
32011 \begin_layout Plain Layout
32025 \begin_inset Formula
32027 D=\textrm{big Latin}\label{eq:Lat}
32035 \begin_layout Standard
32036 To switch back to the default numbering, insert the command:
32039 \begin_layout Standard
32049 \begin_inset Index idx
32052 \begin_layout Plain Layout
32063 \begin_layout Standard
32067 \begin_layout Plain Layout
32081 \begin_inset Formula
32091 \begin_layout Standard
32092 \begin_inset VSpace medskip
32095 As you see, formulas are numbered serially independent from the numbering
32097 When then numbering should start with
32098 \begin_inset Quotes eld
32102 \begin_inset Quotes erd
32105 when the style is changed, new equation counters have to be defined.
32106 A description about this can be found in the file
32107 \begin_inset CommandInset href
32109 name "Formula-numbering.lyx"
32110 target "run:Formula-numbering.lyx"
32117 \begin_layout Section
32118 Chemical Symbols and Equations
32119 \begin_inset CommandInset label
32121 name "subsec:Chemical-Symbols-and"
32126 \begin_inset Index idx
32129 \begin_layout Plain Layout
32130 Chemical characters ! Symbols
32136 \begin_inset Index idx
32139 \begin_layout Plain Layout
32146 \begin_inset Index idx
32149 \begin_layout Plain Layout
32158 \begin_layout Standard
32159 An example text from chemistry:
32162 \begin_layout Quote
32164 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32167 -ion reacts with two
32168 \begin_inset Formula $\mathrm{Na^{+}}$
32171 -ions to sodium sulfate
32172 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32176 The chemical equation for this is:
32177 \begin_inset Formula
32179 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
32187 \begin_layout Standard
32188 This chemical equation can directly be created as formula.
32189 To avoid that the symbols appear italic, everything is highlighted and
32190 changed by the shortcut
32196 to the upright font style.
32200 \begin_layout Plain Layout
32206 \begin_inset CommandInset ref
32208 reference "subsec:Font-Styles"
32220 \begin_layout Standard
32221 A more convenient way to typeset chemical formulas is to use the command
32229 \begin_inset Index idx
32232 \begin_layout Plain Layout
32240 that is available when the \SpecialChar LaTeX
32246 \begin_inset Index idx
32249 \begin_layout Plain Layout
32262 to a formula a new blue box appears where chemical formulas can be inserted
32263 in an intuitive way.
32264 \begin_inset Separator parbreak
32270 \begin_layout Standard
32272 \begin_inset Tabular
32273 <lyxtabular version="3" rows="10" columns="2">
32274 <features tabularvalignment="middle">
32275 <column alignment="center" valignment="top">
32276 <column alignment="center" valignment="top">
32278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32281 \begin_layout Plain Layout
32287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32290 \begin_layout Plain Layout
32292 \begin_inset Note Note
32295 \begin_layout Plain Layout
32302 is only used as spacer.
32314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32317 \begin_layout Plain Layout
32321 \begin_inset space \textvisiblespace{}
32329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32332 \begin_layout Plain Layout
32333 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
32343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32346 \begin_layout Plain Layout
32350 \begin_inset space \textvisiblespace{}
32358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32361 \begin_layout Plain Layout
32362 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
32372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32375 \begin_layout Plain Layout
32379 \begin_inset space \textvisiblespace{}
32387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32390 \begin_layout Plain Layout
32391 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
32401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32404 \begin_layout Plain Layout
32408 \begin_inset space \textvisiblespace{}
32416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32419 \begin_layout Plain Layout
32420 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32433 \begin_layout Plain Layout
32437 \begin_inset space \textvisiblespace{}
32443 \begin_inset space \textvisiblespace{}
32449 \begin_inset space \textvisiblespace{}
32457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32460 \begin_layout Plain Layout
32461 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32474 \begin_layout Plain Layout
32478 \begin_inset space \textvisiblespace{}
32482 \begin_inset Formula $\downarrow$
32486 \begin_inset Formula $\to$
32494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32497 \begin_layout Plain Layout
32498 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32511 \begin_layout Plain Layout
32515 \begin_inset space \textvisiblespace{}
32521 \begin_inset space \textvisiblespace{}
32527 \begin_inset space \textvisiblespace{}
32535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32538 \begin_layout Plain Layout
32539 \begin_inset Formula $\raisebox{4.5mm}{}\ce{\ensuremath{\mu\hyphen}Cl}\raisebox{-2mm}{}$
32549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32552 \begin_layout Plain Layout
32556 \begin_inset space \textvisiblespace{}
32560 \begin_inset space \textvisiblespace{}
32564 \begin_inset space \textvisiblespace{}
32568 \begin_inset space \textvisiblespace{}
32572 \begin_inset space \textvisiblespace{}
32580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32583 \begin_layout Plain Layout
32584 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32597 \begin_layout Plain Layout
32601 \begin_inset space \textvisiblespace{}
32605 \begin_inset space \textvisiblespace{}
32609 \begin_inset space \textvisiblespace{}
32613 \begin_inset space \textvisiblespace{}
32621 \begin_inset space \textvisiblespace{}
32629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32632 \begin_layout Plain Layout
32633 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32649 \begin_layout Standard
32650 \begin_inset Note Greyedout
32653 \begin_layout Plain Layout
32659 It is not possible in \SpecialChar LyX
32660 to use the character ^ to get an up-arrow as described
32666 One instead uses a negative thin space followed by the command
32673 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32684 \begin_layout Standard
32691 the command for equation
32692 \begin_inset space ~
32696 \begin_inset CommandInset ref
32698 reference "eq:chem-reaction"
32703 \begin_inset Newline newline
32711 \begin_inset space \textvisiblespace{}
32715 \begin_inset space \textvisiblespace{}
32719 \begin_inset space \textvisiblespace{}
32723 \begin_inset space \textvisiblespace{}
32727 \begin_inset space \textvisiblespace{}
32731 \begin_inset space \textvisiblespace{}
32737 \begin_layout Standard
32738 To create multiline chemical equations first a multiline formula is created
32740 \begin_inset CommandInset ref
32742 reference "sec:Multiline-Formulas"
32747 Afterwards the command
32753 is used in every small blue box of the formula.
32755 \begin_inset CommandInset ref
32757 reference "eq:TEOS-reaction-1"
32762 \begin_inset CommandInset ref
32764 reference "eq:TEOS-reaction-2"
32768 are an example of a multi-stage chemical reaction where every equation
32769 has its own number.
32770 \begin_inset Formula
32772 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32773 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32781 \begin_layout Standard
32792 package provides the command
32799 \begin_inset Index idx
32802 \begin_layout Plain Layout
32810 that has to be used for special cases.
32811 For more information about
32817 and more examples have a look at the documentation of
32822 \begin_inset CommandInset citation
32831 \begin_layout Section
32835 \begin_layout Standard
32837 supports two types of commutative diagrams:
32845 that are explained in the following.
32848 \begin_layout Subsection
32850 \begin_inset Index idx
32853 \begin_layout Plain Layout
32862 \begin_layout Standard
32863 Diagrams of this type visualize relations by vertical and horizontal lines
32865 \begin_inset Formula
32867 \begin{CD}A@>>>B@>>>C\\
32878 \begin_layout Standard
32879 To get them, the command
32884 \begin_inset Index idx
32887 \begin_layout Plain Layout
32897 is inserted to a formula.
32898 A blue box appears with two dashed lines where further commands can be
32903 arg "newline-insert newline"
32906 a new line is created.
32907 Horizontal relations are inserted in odd, vertical in even formula lines.
32910 \begin_layout Standard
32911 To create the relations there are the following commands:
32914 \begin_layout Itemize
32919 creates a left arrow,
32930 \begin_layout Itemize
32935 creates an up arrow,
32943 a vertical equal sign
32946 \begin_layout Itemize
32952 is a placeholder for non-existent relations
32955 \begin_layout Standard
32956 All arrows can be labeled as follows:
32959 \begin_layout Itemize
32960 If text inserted between the first and second < or >, resp., it is placed
32962 When it is inserted between the second and third one, it appears under
32966 \begin_layout Itemize
32967 When text for vertical arrows is inserted between the first and second A
32968 or V, resp., it is placed left beside the arrow.
32969 When it is inserted between the second and third one, it appears right
32971 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32975 \begin_layout Standard
32976 As example a diagram with all possible relations:
32979 \begin_layout Standard
32980 \begin_inset Formula
32982 \begin{CD}A@>j>>B@>>k>C@=F\\
32993 \begin_layout Standard
32994 The command for this is:
32995 \begin_inset Newline newline
33003 \begin_inset space \textvisiblespace{}
33006 A@>j>>B@>>k>C@=F Ctrl+Return
33007 \begin_inset Newline newline
33011 \begin_inset Phantom HPhantom
33014 \begin_layout Plain Layout
33020 \begin_inset space \textvisiblespace{}
33033 \begin_inset Formula $\to$
33039 \begin_inset Newline newline
33043 \begin_inset Phantom HPhantom
33046 \begin_layout Plain Layout
33052 \begin_inset space \textvisiblespace{}
33063 \begin_layout Subsection
33065 \begin_inset Index idx
33068 \begin_layout Plain Layout
33069 Diagrams ! xymatrix
33077 \begin_layout Standard
33078 To be able to use xymatrices, the \SpecialChar LaTeX
33084 A xymatrix is created by inserting the command
33091 Then you are able to add new matrix columns and rows like for normal matrices,
33093 \begin_inset CommandInset ref
33095 reference "sec:Matrices"
33102 \begin_layout Standard
33103 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
33105 All possibilities to create commutative diagrams and decorations are explained
33110 that you find in the menu
33112 Help\SpecialChar menuseparator
33114 \begin_inset space ~
33122 \begin_layout Subsection
33128 \begin_inset Index idx
33131 \begin_layout Plain Layout
33140 \begin_layout Standard
33145 -diagrams, the \SpecialChar LaTeX
33155 -diagram is created by inserting the command
33162 Then you are able to add new matrix columns and rows like for normal matrices,
33164 \begin_inset CommandInset ref
33166 reference "sec:Matrices"
33173 \begin_layout Standard
33174 Examples how to create
33178 diagrams in \SpecialChar LyX
33181 Feynman-diagram manual
33183 that you find in the menu
33185 Help\SpecialChar menuseparator
33187 \begin_inset space ~
33195 \begin_layout Standard
33196 \begin_inset Newpage newpage
33202 \begin_layout Section
33203 User-defined Commands
33204 \begin_inset Index idx
33207 \begin_layout Plain Layout
33208 User-defined commands
33216 \begin_layout Standard
33217 \begin_inset Note Greyedout
33220 \begin_layout Plain Layout
33225 The names of user-defined commands and macros may only consist of Latin
33234 \begin_layout Subsection
33238 \begin_inset CommandInset label
33240 name "subsec:The-Command-newcommand"
33245 \begin_inset Index idx
33248 \begin_layout Plain Layout
33249 User-defined commands !
33257 \begin_inset Index idx
33260 \begin_layout Plain Layout
33271 \begin_layout Standard
33272 Many \SpecialChar LaTeX
33273 -commands are too long to be used frequently.
33274 But it is possible to define with the command
33280 new shorter commands.
33283 \begin_layout Standard
33284 The command scheme of
33293 \begin_layout Standard
33298 newcommand{new command name}[number of arguments][optional
33303 \begin_inset Newline newline
33307 \begin_inset Phantom HPhantom
33310 \begin_layout Plain Layout
33320 {command definition}
33323 \begin_layout Standard
33324 \begin_inset Note Greyedout
33327 \begin_layout Plain Layout
33332 Assure that the name of the new command is not already used in your document
33333 or by \SpecialChar LaTeX
33334 -packages that you use.
33335 When you for example define the command
33347 , you get an error message because
33353 is already defined as command for
33354 \begin_inset Quotes eld
33358 \begin_inset Formula $\le$
33362 \begin_inset Quotes erd
33373 \begin_layout Standard
33374 The number of arguments is an integer in the range 0
33375 \begin_inset space \thinspace{}
33379 \begin_inset space \thinspace{}
33382 9 and specifies how many arguments the new command should have.
33383 With the optional value a value for an optional argument can be predefined.
33384 When this is done, the
33392 rgument of the new command is automatically an optional one.
33395 \begin_layout Standard
33396 Here are some examples:
33399 \begin_layout Itemize
33400 To define the command
33412 , the \SpecialChar LaTeX
33414 \begin_inset VSpace medskip
33418 \begin_inset Newline newline
33432 \begin_layout Itemize
33433 To define the command
33445 , the argument (that should be underlined) must be taken into account.
33446 For this the preamble line is:
33447 \begin_inset VSpace medskip
33451 \begin_inset Newline newline
33465 \begin_inset VSpace medskip
33469 \begin_inset Newline newline
33476 acts as argument placeholder, the
33480 behind it denotes that it is the placeholder for the first argument.
33483 \begin_layout Itemize
33491 \begin_inset space \thinspace{}
33495 \begin_inset space \space{}
33505 \begin_inset VSpace medskip
33509 \begin_inset Newline newline
33520 framebox#1#2{$#3$}}
33523 \begin_inset VSpace medskip
33527 \begin_inset Newline newline
33530 The two Dollar signs creates the extra formula needed for
33537 \begin_inset CommandInset ref
33539 reference "subsec:Boxes-with-Frame"
33546 \begin_layout Itemize
33547 To create a new command for
33553 where the color for the box need not be specified, the argument for the
33554 color is defined optional:
33555 \begin_inset VSpace medskip
33559 \begin_inset Newline newline
33570 fcolorbox{#2}{#1}{$#3$}}
33573 \begin_inset VSpace medskip
33577 \begin_inset Newline newline
33580 When the color is not specified when using
33586 , the predefined color
33593 \begin_layout Standard
33594 A test of the new defined commands:
33595 \begin_inset Separator parbreak
33601 \begin_layout Standard
33603 \begin_inset Tabular
33604 <lyxtabular version="3" rows="6" columns="2">
33605 <features tabularvalignment="middle">
33606 <column alignment="center" valignment="top">
33607 <column alignment="center" valignment="top">
33609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33612 \begin_layout Plain Layout
33618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33621 \begin_layout Plain Layout
33623 \begin_inset Note Note
33626 \begin_layout Plain Layout
33633 is only used as spacer.
33645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33648 \begin_layout Plain Layout
33652 \begin_inset space \textvisiblespace{}
33660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33663 \begin_layout Plain Layout
33664 \begin_inset Formula $A\gr B$
33674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33677 \begin_layout Plain Layout
33685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33688 \begin_layout Plain Layout
33689 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33702 \begin_layout Plain Layout
33706 \begin_inset Formula $\to$
33712 \begin_inset Formula $\to$
33720 \begin_inset space \textvisiblespace{}
33728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33731 \begin_layout Plain Layout
33732 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33745 \begin_layout Plain Layout
33749 \begin_inset Formula $\to$
33757 \begin_inset space \textvisiblespace{}
33765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33768 \begin_layout Plain Layout
33769 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33782 \begin_layout Plain Layout
33788 \begin_inset Formula $\to$
33796 \begin_inset space \textvisiblespace{}
33804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33807 \begin_layout Plain Layout
33808 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33824 \begin_layout Subsection
33826 \begin_inset Index idx
33829 \begin_layout Plain Layout
33830 User-defined commands! Math macros
33836 \begin_inset Index idx
33839 \begin_layout Plain Layout
33848 \begin_layout Standard
33849 User-defined commands are especially convenient for complex expressions.
33850 When you are for example dealing with a document that has quadratic equations,
33851 the same solution type occurs several times.
33852 The general form of a quadratic equation is
33853 \begin_inset Formula
33855 0=\lambda^{2}+p\lambda+q
33860 The general form of the solution is
33861 \begin_inset Formula
33863 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33871 \begin_layout Standard
33872 To define a command for the solution formula where only the three parameters
33874 \begin_inset Formula $\lambda$
33878 \begin_inset Formula $p$
33882 \begin_inset Formula $q$
33885 need to be specified and the index of
33886 \begin_inset Formula $\lambda$
33889 can be given optionally, the \SpecialChar LaTeX
33891 \begin_inset Newline newline
33907 \begin_inset Newline newline
33911 \begin_inset Phantom HPhantom
33914 \begin_layout Plain Layout
33928 frac{#3^{2}}{4}-#4}}
33931 \begin_layout Standard
33932 To create with this the solution formula, the command
33933 \begin_inset Newline newline
33943 \begin_inset Formula $\to$
33949 \begin_inset Formula $\to$
33956 is inserted to a formula
33961 \begin_layout Standard
33962 The definition of the new command is unintuitive because one has to know
33963 the schemes of all used \SpecialChar LaTeX
33965 \begin_inset space \thinspace{}
33969 \begin_inset space \space{}
33972 that a fraction is inserted in \SpecialChar LaTeX
33977 frac{numerator}{denominator}
33980 Furthermore one can easily forget a brace in the definition and cannot
33981 see in \SpecialChar LyX
33982 what the new command is doing.
33983 To avoid these problems \SpecialChar LyX
33984 offers the possibility to use math macros instead
33994 \begin_layout Standard
33995 A math macro is created by using the menu
33997 Insert\SpecialChar menuseparator
33998 Math\SpecialChar menuseparator
34001 or the toolbar button
34004 arg "math-macro newmacroname_newcommand"
34008 The math macro toolbar appears together with the following box where the
34010 \begin_inset Newline newline
34014 \begin_inset space \hspace*{\fill}
34018 \begin_inset Graphics
34019 filename clipart/macrobox.png
34025 \begin_inset space \hspace*{\fill}
34029 \begin_inset Newline newline
34033 \begin_inset FormulaMacro
34034 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
34039 newmacroname is the default name of the macro that should be changed to
34040 something sensible.
34041 The wanted formula is inserted in the first blue box.
34042 An argument placeholder is inserted with the command
34049 \begin_inset space \thinspace{}
34053 \begin_inset space \space{}
34062 or by using the macro toolbar button
34065 arg "math-macro-add-param"
34069 Argument placeholders are displayed red.
34071 \begin_inset space ~
34074 arguments are possible.
34075 Optional arguments are created with the toolbar button
34078 arg "math-macro-add-optional-param"
34082 The first non-optional argument can be transformed to an optional one with
34086 arg "math-macro-make-optional"
34090 In the second blue box the appearance of the macro in \SpecialChar LyX
34092 Normally you want to see it as it is defined, so the box is kept empty.
34093 But when you have created a macro that needs lot of space on the screen,
34094 you can insert in the box for example
34095 \begin_inset Newline newline
34125 \begin_inset Newline newline
34130 For the macro only the arguments with the macro name in front of them will
34131 then be displayed in \SpecialChar LyX
34132 , leading to a better overview.
34133 The formula appears in the output as defined in the first box.
34134 \begin_inset Newline newline
34137 The appearance of macros in formulas can furthermore be changed for single
34138 macros by setting the cursor in the macro and using the menu
34140 View\SpecialChar menuseparator
34142 \begin_inset space ~
34146 \begin_inset space ~
34154 \begin_layout Standard
34155 To use a macro, the macro name is inserted as command to a formula, in our
34163 Our macro looks in \SpecialChar LyX
34165 \begin_inset Newline newline
34169 \begin_inset space \hspace*{\fill}
34173 \begin_inset Graphics
34174 filename clipart/macrouse.png
34180 \begin_inset space \hspace*{\fill}
34184 \begin_inset Newline newline
34187 Here is our macro example with the arguments
34188 \begin_inset Formula $x$
34192 \begin_inset Formula $\ln(x)$
34196 \begin_inset Formula $B$
34202 \begin_layout Standard
34203 \begin_inset Formula
34213 \begin_layout Standard
34217 Tools\SpecialChar menuseparator
34218 Preferences\SpecialChar menuseparator
34219 Editing\SpecialChar menuseparator
34222 different styles to edit macros.
34223 To find the style that suits you the most, choose a style and set the cursor
34224 in a macro formula to see the difference.
34227 \begin_layout Standard
34228 A math macro is transformed internally to a
34234 command when exporting the document.
34241 command is not placed in the \SpecialChar LaTeX
34242 -preamble, therefore macros can only be used
34243 in formulas that are in the document below the macro definition box.
34246 \begin_layout Standard
34247 Math macros can also be directly created from a
34254 When writing for example the command
34257 \begin_inset Newline newline
34266 xleftarrow[#2]{#1}}
34267 \begin_inset Newline newline
34272 in \SpecialChar LyX
34273 as normal text, highlighting it completely and using then the shortcut
34278 , the command will be transformed to a math macro.
34279 Using this method you need to be careful that the
34285 command is typed correctly, otherwise you get a faulty macro leading to
34290 \begin_layout Standard
34291 Math macros currently have the problem that further formulas in macro definition
34292 s are handled wrongly.
34293 Therefore the example
34300 \begin_inset CommandInset ref
34302 reference "subsec:The-Command-newcommand"
34306 cannot be created as macro.
34309 \begin_layout Standard
34310 When the cursor is in a macro definition box, you will see the macro toolbar
34311 in \SpecialChar LyX
34315 \begin_layout Standard
34316 \begin_inset VSpace defskip
34322 \begin_layout Standard
34323 \begin_inset Graphics
34324 filename clipart/MacroToolbar.png
34329 \begin_inset Index idx
34332 \begin_layout Plain Layout
34341 \begin_layout Standard
34342 \begin_inset VSpace defskip
34348 \begin_layout Standard
34349 The macro toolbar contains from left to right the following buttons:
34352 \begin_layout Standard
34353 \begin_inset VSpace defskip
34359 \begin_layout Standard
34360 \begin_inset Tabular
34361 <lyxtabular version="3" rows="9" columns="2">
34362 <features islongtable="true" longtabularalignment="center">
34363 <column alignment="left" valignment="top">
34364 <column alignment="left" valignment="top" width="85col%">
34365 <row interlinespace="2.5mm">
34366 <cell alignment="center" valignment="top" usebox="none">
34369 \begin_layout Plain Layout
34372 arg "math-macro-remove-param"
34380 <cell alignment="center" valignment="top" usebox="none">
34383 \begin_layout Plain Layout
34386 Edit\SpecialChar menuseparator
34387 Math\SpecialChar menuseparator
34389 \begin_inset space ~
34392 Definition\SpecialChar menuseparator
34393 Remove Last Argument
34399 <row interlinespace="2.5mm">
34400 <cell alignment="center" valignment="top" usebox="none">
34403 \begin_layout Plain Layout
34406 arg "math-macro-add-param"
34414 <cell alignment="center" valignment="top" usebox="none">
34417 \begin_layout Plain Layout
34420 Edit\SpecialChar menuseparator
34421 Math\SpecialChar menuseparator
34423 \begin_inset space ~
34426 Definition\SpecialChar menuseparator
34433 <row interlinespace="2.5mm">
34434 <cell alignment="center" valignment="top" usebox="none">
34437 \begin_layout Plain Layout
34440 arg "math-macro-make-optional"
34448 <cell alignment="center" valignment="top" usebox="none">
34451 \begin_layout Plain Layout
34454 Edit\SpecialChar menuseparator
34455 Math\SpecialChar menuseparator
34457 \begin_inset space ~
34460 Definition\SpecialChar menuseparator
34461 Transform First Non-Optional to
34462 \begin_inset Newline newline
34466 \begin_inset Phantom HPhantom
34469 \begin_layout Plain Layout
34472 Edit\SpecialChar menuseparator
34473 Math\SpecialChar menuseparator
34475 \begin_inset space ~
34478 Definition\SpecialChar menuseparator
34490 <row interlinespace="2.5mm">
34491 <cell alignment="center" valignment="top" usebox="none">
34494 \begin_layout Plain Layout
34497 arg "math-macro-make-nonoptional"
34505 <cell alignment="center" valignment="top" usebox="none">
34508 \begin_layout Plain Layout
34511 Edit\SpecialChar menuseparator
34512 Math\SpecialChar menuseparator
34514 \begin_inset space ~
34517 Definition\SpecialChar menuseparator
34518 Transform Last Optional to
34519 \begin_inset Newline newline
34523 \begin_inset Phantom HPhantom
34526 \begin_layout Plain Layout
34529 Edit\SpecialChar menuseparator
34530 Math\SpecialChar menuseparator
34532 \begin_inset space ~
34535 Definition\SpecialChar menuseparator
34541 Non-Optional Argument
34547 <row interlinespace="2.5mm">
34548 <cell alignment="center" valignment="top" usebox="none">
34551 \begin_layout Plain Layout
34554 arg "math-macro-remove-optional-param"
34562 <cell alignment="center" valignment="top" usebox="none">
34565 \begin_layout Plain Layout
34568 Edit\SpecialChar menuseparator
34569 Math\SpecialChar menuseparator
34571 \begin_inset space ~
34574 Definition\SpecialChar menuseparator
34575 Remove Optional Argument
34581 <row interlinespace="2.5mm">
34582 <cell alignment="center" valignment="top" usebox="none">
34585 \begin_layout Plain Layout
34588 arg "math-macro-add-optional-param"
34596 <cell alignment="center" valignment="top" usebox="none">
34599 \begin_layout Plain Layout
34602 Edit\SpecialChar menuseparator
34603 Math\SpecialChar menuseparator
34605 \begin_inset space ~
34608 Definition\SpecialChar menuseparator
34609 Insert Optional Argument
34615 <row interlinespace="2.5mm">
34616 <cell alignment="center" valignment="top" usebox="none">
34619 \begin_layout Plain Layout
34622 arg "math-macro-remove-greedy-param"
34630 <cell alignment="center" valignment="top" usebox="none">
34633 \begin_layout Plain Layout
34636 Edit\SpecialChar menuseparator
34637 Math\SpecialChar menuseparator
34639 \begin_inset space ~
34642 Definition\SpecialChar menuseparator
34643 Remove Last Argument
34644 \begin_inset Newline newline
34648 \begin_inset Phantom HPhantom
34651 \begin_layout Plain Layout
34654 Edit\SpecialChar menuseparator
34655 Math\SpecialChar menuseparator
34657 \begin_inset space ~
34660 Definition\SpecialChar menuseparator
34666 Spitting Out To The Right
34672 <row interlinespace="2.5mm">
34673 <cell alignment="center" valignment="top" usebox="none">
34676 \begin_layout Plain Layout
34679 arg "math-macro-append-greedy-param"
34687 <cell alignment="center" valignment="top" usebox="none">
34690 \begin_layout Plain Layout
34693 Edit\SpecialChar menuseparator
34694 Math\SpecialChar menuseparator
34696 \begin_inset space ~
34699 Definition\SpecialChar menuseparator
34701 \begin_inset Newline newline
34705 \begin_inset Phantom HPhantom
34708 \begin_layout Plain Layout
34711 Edit\SpecialChar menuseparator
34712 Math\SpecialChar menuseparator
34714 \begin_inset space ~
34717 Definition\SpecialChar menuseparator
34723 Eating From The Right
34729 <row interlinespace="2.5mm">
34730 <cell alignment="center" valignment="top" usebox="none">
34733 \begin_layout Plain Layout
34736 arg "math-macro-add-greedy-optional-param"
34744 <cell alignment="center" valignment="top" usebox="none">
34747 \begin_layout Plain Layout
34750 Edit\SpecialChar menuseparator
34751 Math\SpecialChar menuseparator
34753 \begin_inset space ~
34756 Definition\SpecialChar menuseparator
34757 Append Optional Argument
34758 \begin_inset Newline newline
34762 \begin_inset Phantom HPhantom
34765 \begin_layout Plain Layout
34768 Edit\SpecialChar menuseparator
34769 Math\SpecialChar menuseparator
34771 \begin_inset space ~
34774 Definition\SpecialChar menuseparator
34780 Eating From The Right
34793 \begin_layout Section
34794 Computer Algebra Systems
34797 \begin_layout Standard
34799 offers the exchange between mathematical expressions written in \SpecialChar LyX
34801 editor and external applications or user defined scripts.
34802 Currently supported applications are
34819 Note that the set of supported mathematical constructs is limited only
34820 to very simple cases.
34823 \begin_layout Subsection
34827 \begin_layout Standard
34828 Write some expression in a formula, go to the
34830 Edit\SpecialChar menuseparator
34831 Math\SpecialChar menuseparator
34832 Use Computer Algebra System
34834 menu and choose the application you have installed on the computer.
34835 After that the result of computation should show on the right side of the
34836 expression together with the
34837 \begin_inset Quotes eld
34841 \begin_inset Quotes erd
34847 \begin_layout Standard
34848 Here are few simple examples (with results from
34852 ) to show what kind of computations can be performed:
34855 \begin_layout Itemize
34856 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34862 \begin_layout Itemize
34863 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34869 \begin_layout Itemize
34870 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34876 \begin_layout Itemize
34877 \begin_inset Formula $\det\left[\begin{array}{ccc}
34881 \end{array}\right]=-56$
34887 \begin_layout Itemize
34888 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34894 \begin_layout Subsection
34898 \begin_layout Standard
34899 Currently there is no keyboard shortcut for calling the algebra applications.
34900 One can easily bind a shortcut to the
34914 \begin_inset space \thinspace{}
34918 \begin_inset space \space{}
34925 key inside the math editor.
34930 one would use this shortcut definition command:
34933 \begin_layout Standard
34936 command-alternatives paragraph-break;math-extern maxima
34939 \begin_layout Section
34941 \begin_inset Index idx
34944 \begin_layout Plain Layout
34953 \begin_layout Subsection
34955 \begin_inset Index idx
34958 \begin_layout Plain Layout
34967 \begin_layout Standard
34968 Negative numbers often look ugly in formulas because the minus sign before
34969 the number is set with the same length as the minus operator sign.
34970 When writing the negative number in normal text, the minus sign appears
34974 \begin_layout Standard
34975 Thus, the problem disappears when converting the minus sign to mathematical
34979 \begin_layout Standard
34980 An example to visualize the problem:
34981 \begin_inset Separator parbreak
34987 \begin_layout Standard
34989 \begin_inset Tabular
34990 <lyxtabular version="3" rows="3" columns="2">
34991 <features tabularvalignment="middle">
34992 <column alignment="right" valignment="top">
34993 <column alignment="left" valignment="top">
34995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34998 \begin_layout Plain Layout
35004 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
35007 \begin_layout Plain Layout
35015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35018 \begin_layout Plain Layout
35024 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
35027 \begin_layout Plain Layout
35028 \begin_inset Formula $x=-2$
35038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35041 \begin_layout Plain Layout
35047 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
35050 \begin_layout Plain Layout
35051 \begin_inset Formula $x=\textrm{-}2$
35067 \begin_layout Subsection
35068 Comma as decimal Separator
35069 \begin_inset Index idx
35072 \begin_layout Plain Layout
35081 \begin_layout Standard
35082 In \SpecialChar LaTeX
35083 a comma inside a formula is used, according to the English convention,
35084 as number group separator.
35085 So there will be space added behind all commas in formulas.
35088 \begin_layout Standard
35089 To avoid this, the comma is highlighted and changed to mathematical text
35099 \begin_layout Standard
35100 To use all formula commas in the document as decimal separator, the file
35109 \begin_layout Plain Layout
35114 is part of the \SpecialChar LaTeX
35120 \begin_inset Index idx
35123 \begin_layout Plain Layout
35128 \begin_layout Plain Layout
35148 \begin_inset Index idx
35151 \begin_layout Plain Layout
35157 is loaded with the \SpecialChar LaTeX
35161 \begin_layout Standard
35169 \begin_layout Subsection
35171 \begin_inset CommandInset label
35173 name "subsec:Physical-Vectors"
35178 \begin_inset Index idx
35181 \begin_layout Plain Layout
35190 \begin_layout Standard
35191 Predefined vectors are offered by the \SpecialChar LaTeX
35197 \begin_inset Index idx
35200 \begin_layout Plain Layout
35206 that is loaded with the \SpecialChar LaTeX
35210 \begin_layout Standard
35218 \begin_layout Standard
35222 \begin_layout Plain Layout
35232 \begin_inset Note Note
35235 \begin_layout Plain Layout
35236 The following table will only be displayed when the \SpecialChar LaTeX
35249 \begin_layout Standard
35250 The following commands are defined:
35251 \begin_inset Separator parbreak
35257 \begin_layout Standard
35259 \begin_inset Tabular
35260 <lyxtabular version="3" rows="4" columns="2">
35261 <features tabularvalignment="middle">
35262 <column alignment="center" valignment="top">
35263 <column alignment="center" valignment="top">
35265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35268 \begin_layout Plain Layout
35274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35277 \begin_layout Plain Layout
35285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35288 \begin_layout Plain Layout
35298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35301 \begin_layout Plain Layout
35302 \begin_inset Formula $\Bra{\psi}$
35312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35315 \begin_layout Plain Layout
35325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35328 \begin_layout Plain Layout
35329 \begin_inset Formula $\Ket{\psi}$
35339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35342 \begin_layout Plain Layout
35354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35357 \begin_layout Plain Layout
35358 \begin_inset Formula $\Braket{\psi|\phi}$
35374 \begin_layout Standard
35381 assures that all vertical bars are set in the size of the surrounding brackets:
35382 \begin_inset Formula
35384 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
35393 \begin_layout Plain Layout
35403 \begin_inset Note Note
35406 \begin_layout Plain Layout
35407 The following will be displayed when the \SpecialChar LaTeX
35420 \begin_layout Standard
35421 You need to install the \SpecialChar LaTeX
35426 to see the rest of this subsection in the output.
35429 \begin_layout Standard
35433 \begin_layout Plain Layout
35445 \begin_layout Standard
35452 can also be achieved using the command
35458 , that is described in
35459 \begin_inset CommandInset ref
35461 reference "subsec:Automatic-Bracket-Size"
35468 \begin_layout Subsection
35469 Self-defined Fractions
35470 \begin_inset CommandInset label
35472 name "subsec:Self-defined-Fractions"
35477 \begin_inset Index idx
35480 \begin_layout Plain Layout
35481 Fractions ! self-defined
35489 \begin_layout Standard
35490 To define custom commands for fractions, the command
35497 \begin_inset Index idx
35500 \begin_layout Plain Layout
35507 \begin_layout Plain Layout
35521 is used in the following scheme:
35524 \begin_layout Standard
35537 bracket}{fraction bar thickness}{style}
35538 \begin_inset Newline newline
35542 \begin_inset Phantom HPhantom
35545 \begin_layout Plain Layout
35555 {numerator}{denominator}
35558 \begin_layout Standard
35559 The style is a number in the range of 0
35560 \begin_inset space \thinspace{}
35564 \begin_inset space \thinspace{}
35568 \begin_inset Separator parbreak
35574 \begin_layout Standard
35576 \begin_inset Tabular
35577 <lyxtabular version="3" rows="5" columns="2">
35578 <features tabularvalignment="middle">
35579 <column alignment="center" valignment="top">
35580 <column alignment="center" valignment="top">
35582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35585 \begin_layout Plain Layout
35591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35594 \begin_layout Plain Layout
35602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35605 \begin_layout Plain Layout
35611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35614 \begin_layout Plain Layout
35615 display style formula
35622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35625 \begin_layout Plain Layout
35631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35634 \begin_layout Plain Layout
35642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35645 \begin_layout Plain Layout
35651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35654 \begin_layout Plain Layout
35662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35665 \begin_layout Plain Layout
35671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35674 \begin_layout Plain Layout
35688 \begin_layout Standard
35689 When no style is given, the size is adjusted to the surrounding environment
35690 like for the command
35699 \begin_layout Standard
35700 When no fraction bar thickness is given, the predefined value of 0.4
35701 \begin_inset space \thinspace{}
35707 \begin_layout Standard
35708 \begin_inset VSpace medskip
35711 For example, the commands
35724 \begin_inset CommandInset ref
35726 reference "subsec:Fractions"
35730 are defined with the commands
35733 \begin_layout Standard
35742 genfrac{}{}{}{0}{#1}{#2}}
35745 \begin_layout Standard
35749 \begin_layout Standard
35758 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35761 \begin_layout Standard
35762 \begin_inset VSpace medskip
35765 To define a fraction where the fraction bar thickness can be given as optional
35766 argument, the following line is inserted to the \SpecialChar LaTeX
35770 \begin_layout Standard
35779 genfrac{}{}{#1}{}{#2}{#3}}
35782 \begin_layout Standard
35784 \begin_inset Formula
35786 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35787 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35792 As one can see, the distance of the numerator and the denominator to the
35793 fraction bar is round about three times the bar thickness.
35796 \begin_layout Subsection
35798 \begin_inset Index idx
35801 \begin_layout Plain Layout
35810 \begin_layout Standard
35811 There are four ways to cancel formulas or parts of formulas:
35814 \begin_layout Standard
35818 \begin_layout Plain Layout
35828 \begin_inset Note Note
35831 \begin_layout Plain Layout
35832 The following table will only be displayed when the \SpecialChar LaTeX
35843 \begin_inset Separator parbreak
35849 \begin_layout Standard
35851 \begin_inset Tabular
35852 <lyxtabular version="3" rows="5" columns="2">
35853 <features tabularvalignment="middle">
35854 <column alignment="center" valignment="top">
35855 <column alignment="center" valignment="top">
35857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35860 \begin_layout Plain Layout
35866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35869 \begin_layout Plain Layout
35871 \begin_inset Note Note
35874 \begin_layout Plain Layout
35881 are used here as spacer.
35893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35896 \begin_layout Plain Layout
35900 \begin_inset space \textvisiblespace{}
35906 \begin_inset space \textvisiblespace{}
35914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35917 \begin_layout Plain Layout
35918 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35931 \begin_layout Plain Layout
35935 \begin_inset space \textvisiblespace{}
35941 \begin_inset space \textvisiblespace{}
35949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35952 \begin_layout Plain Layout
35953 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35966 \begin_layout Plain Layout
35970 \begin_inset space \textvisiblespace{}
35976 \begin_inset space \textvisiblespace{}
35984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35987 \begin_layout Plain Layout
35988 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36001 \begin_layout Plain Layout
36005 \begin_inset space \textvisiblespace{}
36011 \begin_inset space \textvisiblespace{}
36015 \begin_inset Formula $\to$
36023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36026 \begin_layout Plain Layout
36027 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
36043 \begin_layout Standard
36050 is especially suitable to visualize the reduction of fractions within formulas:
36051 \begin_inset Formula
36053 \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}}}
36061 \begin_layout Standard
36062 To change the size of
36069 \begin_inset Quotes eld
36073 \begin_inset Quotes erd
36076 value one can add the \SpecialChar LaTeX
36080 \begin_layout Standard
36085 PassOptionsToPackage{option}{cancel}
36088 \begin_layout Standard
36097 which leads to the same size as for the canceled value, or
36101 which makes is it a bit smaller than normal.
36104 \begin_layout Standard
36105 To color the cancellation bar one adds this command as \SpecialChar TeX
36109 \begin_layout Standard
36121 \begin_layout Standard
36126 can be replaced by a color of your choice.
36129 \begin_layout Standard
36133 \begin_layout Plain Layout
36149 \begin_layout Standard
36150 \begin_inset Formula
36152 \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}}}
36160 \begin_layout Standard
36164 \begin_layout Plain Layout
36178 \begin_inset Note Note
36181 \begin_layout Plain Layout
36190 \begin_layout Standard
36191 For further customizations, see the documentation of the package
36196 \begin_inset CommandInset citation
36203 \begin_inset Index idx
36206 \begin_layout Plain Layout
36215 \begin_layout Standard
36219 \begin_layout Plain Layout
36229 \begin_inset Note Note
36232 \begin_layout Plain Layout
36233 The following will be displayed when the \SpecialChar LaTeX
36246 \begin_layout Standard
36247 You need to install the \SpecialChar LaTeX
36252 to see the rest of this subsection in the output.
36255 \begin_layout Standard
36259 \begin_layout Plain Layout
36271 \begin_layout Subsection
36272 Formulas in Section Headings
36273 \begin_inset CommandInset label
36275 name "subsec:Formulas-in-Section"
36280 \begin_inset Index idx
36283 \begin_layout Plain Layout
36284 Formula ! in section headings
36292 \begin_layout Standard
36293 When formulas are used in section headings, the following has to be taken
36297 \begin_layout Standard
36298 \begin_inset Note Greyedout
36301 \begin_layout Plain Layout
36307 \begin_inset Index idx
36310 \begin_layout Plain Layout
36311 Packages ! hyperref
36316 support is enabled in the document settings dialog under
36319 \begin_inset space ~
36324 , PDF-bookmarks are created for every section heading in the table of contents.
36325 If a section heading contains formulas, they are incorrectly displayed
36326 in the bookmark text, because formulas in bookmarks infringe the PDF convention
36335 \begin_layout Standard
36336 Both problems can be solved by inserting at the end of the section heading
36337 a short title with the menu
36339 Insert\SpecialChar menuseparator
36341 \begin_inset space ~
36347 Short titles are used as alternative for multiline section headings to
36348 keep the table of contents clearly arranged.
36349 Only the short title appears in the table of contents and therefore also
36350 in the PDF-bookmark.
36353 \begin_layout Standard
36354 When formulas should be used in the table of contents but
36358 is used, one can use the following command in \SpecialChar TeX
36362 \begin_layout Standard
36367 texorpdfstring{part}{alternative}
36368 \begin_inset Index idx
36371 \begin_layout Plain Layout
36382 \begin_layout Standard
36383 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36384 This can be characters, formulas, footnotes, but also cross-references.
36385 The alternative is used instead of the part for the bookmark.
36388 \begin_layout Standard
36389 Here are two example headings:
36390 \begin_inset VSpace -3mm
36397 \begin_layout Plain Layout
36409 \begin_layout Subsubsection
36410 Heading without formula in table of contents
36411 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36415 \begin_inset Argument 1
36418 \begin_layout Plain Layout
36419 Heading without formula in table of contents
36427 \begin_layout Subsubsection
36428 Heading with formula in table of contents
36432 \begin_layout Plain Layout
36442 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36449 \begin_layout Plain Layout
36459 \begin_layout Standard
36463 \begin_layout Plain Layout
36472 In the first heading a short title was used, in the second one
36481 \begin_layout Standard
36482 To get the same formatting as for the other headings, the complete heading
36491 \begin_layout Plain Layout
36493 \begin_inset CommandInset ref
36495 reference "subsec:Bold-Formulas"
36507 \begin_layout Subsection
36508 Formulas in multi-column Text
36509 \begin_inset Index idx
36512 \begin_layout Plain Layout
36513 Formula ! in multi-column text
36521 \begin_layout Standard
36522 Formulas in multi-column text are often too wide to fit into a column and
36523 thus need to be set over the whole page width.
36524 This is done by using the \SpecialChar LaTeX
36533 \begin_layout Plain Layout
36538 is part of every \SpecialChar LaTeX
36539 standard installation.
36545 \begin_inset Index idx
36548 \begin_layout Plain Layout
36549 Packages ! multicol
36554 , that is loaded with the \SpecialChar LaTeX
36558 \begin_layout Standard
36563 usepackage{multicol}
36566 \begin_layout Standard
36567 \begin_inset Note Greyedout
36570 \begin_layout Plain Layout
36571 Note that in this case the setting
36574 \begin_inset space ~
36581 Document\SpecialChar menuseparator
36587 \begin_inset space ~
36607 \begin_layout Standard
36608 Before the multi-column text the command
36611 \begin_layout Standard
36616 begin{multicols}{column number}
36619 \begin_layout Standard
36620 is written in \SpecialChar TeX
36622 The column number is a number in the range of 2
36623 \begin_inset space \thinspace{}
36627 \begin_inset space \thinspace{}
36631 Before the formula the multi-column text is ended by inserting the command
36634 \begin_layout Standard
36642 \begin_layout Standard
36643 in \SpecialChar TeX
36647 \begin_layout Standard
36648 Due to the command some space is automatically added before the formula.
36650 \begin_inset space \thinspace{}
36653 mm vertical space is inserted before the formula.
36654 When the formula style
36660 \begin_layout Plain Layout
36662 \begin_inset CommandInset ref
36664 reference "sec:Formula-Styles"
36676 \begin_inset space \thinspace{}
36679 mm space is inserted instead.
36682 \begin_layout Standard
36683 As example a multi-column text with a displayed formula:
36686 \begin_layout Standard
36692 \begin_layout Plain Layout
36696 begin{multicols}{2}
36701 Das Spektrum wird fouriertransformiert.
36702 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36703 , Lösungsmittel) zu trennen.
36704 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36705 nun das Aussehen des Ausgangssignals.
36706 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36707 über alle Phasen integrieren muss.
36709 \begin_inset Formula $S$
36712 unser normiertes Ausgangssignal und
36713 \begin_inset Formula $P$
36716 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36720 \begin_layout Plain Layout
36730 \begin_inset VSpace -6mm
36734 \begin_inset Formula
36736 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36745 \begin_layout Plain Layout
36749 begin{multicols}{2}
36755 \begin_inset Formula $S_{0}$
36758 das Signal ohne Gradient ist und die Normierungsbedingung
36759 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36763 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36765 \begin_inset Formula $\nicefrac{\pi}{2}$
36769 \begin_inset space \thinspace{}
36772 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36773 das Signal zusätzlich abschwächt.
36774 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36776 \begin_inset Formula $T_{2}$
36782 \begin_layout Standard
36788 \begin_layout Plain Layout
36800 \begin_layout Subsection
36801 Formulas with Description of Variables
36802 \begin_inset Index idx
36805 \begin_layout Plain Layout
36806 Formula ! with description of variables
36814 \begin_layout Standard
36815 To describe variables within a formula, like in formula
36816 \begin_inset CommandInset ref
36818 reference "eq:within"
36827 \begin_inset Formula $n$
36831 \begin_inset space ~
36834 matrix is used with left aligned columns for the
36835 \begin_inset Formula $n$
36842 \begin_layout Plain Layout
36844 \begin_inset CommandInset ref
36846 reference "sec:Matrices"
36855 To set the description in a smaller size, before the matrix e.
36856 \begin_inset space \thinspace{}
36860 \begin_inset space \space{}
36873 \begin_layout Plain Layout
36875 \begin_inset CommandInset ref
36877 reference "subsec:Font-Sizes"
36889 \begin_layout Standard
36890 When the formula style
36896 \begin_layout Plain Layout
36898 \begin_inset CommandInset ref
36900 reference "sec:Formula-Styles"
36921 \begin_layout Plain Layout
36928 only works in formulas with the style
36933 \begin_inset CommandInset ref
36935 reference "subsec:Variable-Space"
36944 is inserted before and after the matrix to have the same separation of
36945 the matrix from the equation and the side margin.
36948 \begin_layout Standard
36949 When the formula style
36953 is used, the method described in
36954 \begin_inset CommandInset ref
36956 reference "subsec:Flalign-Environment"
36960 is used to indent formulas.
36962 \begin_inset CommandInset ref
36964 reference "eq:within"
36968 consists of five columns where in the first two columns contain the equation,
36969 the third the matrix and the last one an empty \SpecialChar TeX
36971 \begin_inset Formula
36973 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36974 \rho & \textrm{density}\\
36975 V & \textrm{volume}\\
36976 g & \textrm{gravitational acceleration}
36977 \end{array} & & {}\label{eq:within}
36985 \begin_layout Subsection
36986 Upright small Greek Letters
36987 \begin_inset CommandInset label
36989 name "subsec:Upright-small-Greek"
36994 \begin_inset Index idx
36997 \begin_layout Plain Layout
36998 Greek letters ! upright
37006 \begin_layout Standard
37007 Most of the math fonts only provide italic small Greek letters.
37008 But for symbols of elementary particles like pions and neutrinos, upright
37009 Greek letters are needed.
37018 \begin_layout Plain Layout
37023 is part of the \SpecialChar LaTeX
37029 \begin_inset Index idx
37032 \begin_layout Plain Layout
37037 \begin_layout Plain Layout
37057 \begin_inset Index idx
37060 \begin_layout Plain Layout
37066 that is loaded with the \SpecialChar LaTeX
37070 \begin_layout Standard
37075 usepackage{upgreek}
37078 \begin_layout Standard
37084 \begin_layout Plain Layout
37094 \begin_inset Note Note
37097 \begin_layout Plain Layout
37098 The following table will only be displayed when the \SpecialChar LaTeX
37108 They are created when the command for a small Greek letter is started with
37114 For example the command
37121 \begin_inset Formula $\uptau$
37127 \begin_layout Standard
37128 With these commands reactions of elementary particles can be typeset:
37129 \begin_inset Formula
37131 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
37139 \begin_layout Standard
37140 The upright letters are more bold and wider than the italic ones.
37141 They should therefore not be used for units like
37142 \begin_inset Quotes eld
37146 \begin_inset Quotes erd
37152 \begin_layout Standard
37156 \begin_layout Plain Layout
37166 \begin_inset Note Note
37169 \begin_layout Plain Layout
37170 The following will be displayed when the \SpecialChar LaTeX
37183 \begin_layout Standard
37184 You need to install the \SpecialChar LaTeX
37189 to see the rest of this subsection in the output.
37192 \begin_layout Standard
37196 \begin_layout Plain Layout
37208 \begin_layout Subsection
37209 Text Characters in Formulas
37210 \begin_inset Index idx
37213 \begin_layout Plain Layout
37222 \begin_layout Standard
37223 In some cases you might want to insert text characters directly into formulas.
37224 When for example the centered dot · is often used in formulas like
37225 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
37228 , one would have to insert the command
37238 \begin_layout Plain Layout
37240 \begin_inset CommandInset ref
37242 reference "subsec:Binary-Operators"
37251 all the time, because this character is defined in all encodings as text
37253 But the encoding can be changed by this \SpecialChar LaTeX
37257 \begin_layout Standard
37262 Declare Inputtext{183}{
37272 f\SpecialChar ligaturebreak
37276 \begin_layout Standard
37277 The character encoding (menu
37279 Document\SpecialChar menuseparator
37280 Settings\SpecialChar menuseparator
37283 ) specifies what character appears when a keyboard key is pressed.
37284 When the key for the character '·' is pressed, internally the command
37291 But this command is not available in a formula so that you would get \SpecialChar LaTeX
37293 With the changed encoding the right command is chosen automatically, depending
37294 on if the character was inserted into a formula or not.
37297 \begin_layout Standard
37298 The encoding of several characters is saved in definition files.
37299 For example the encoding
37303 is defined in the file
37307 which is in the installation folder of \SpecialChar LaTeX
37309 Encodings should only be changed via the \SpecialChar LaTeX
37310 -preamble and not in the definition
37312 Otherwise documents could not be edited by other \SpecialChar LyX
37313 users working on other
37317 \begin_layout Standard
37318 \begin_inset VSpace medskip
37321 Besides the centered dot, in this document the degree sign ° is defined
37322 with the following \SpecialChar LaTeX
37323 -preamble line so that it can be directly inserted into
37327 \begin_layout Standard
37332 DeclareInputtext{176}{
37342 f\SpecialChar ligaturebreak
37346 \begin_layout Subsection
37348 -comments in formulas
37349 \begin_inset Index idx
37352 \begin_layout Plain Layout
37362 \begin_layout Standard
37363 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
37365 code of your file with the menu
37367 Insert\SpecialChar menuseparator
37368 Note\SpecialChar menuseparator
37372 This is not possible in a formula but you can insert \SpecialChar LaTeX
37377 \begin_layout Standard
37385 \begin_layout Standard
37386 This creates a box in which you can write your comment.
37387 Due to a bug in \SpecialChar LyX
37392 \begin_layout Plain Layout
37393 \begin_inset CommandInset href
37395 name "LyX-bug #9002"
37396 target "http://www.lyx.org/trac/ticket/9002"
37405 you cannot write normal text inside the comment, even when you use mathematical
37406 text, you will see its \SpecialChar LaTeX
37407 -commands in the \SpecialChar LaTeX
37409 \begin_inset Newline newline
37412 This a formula with a \SpecialChar LaTeX
37414 \begin_inset Formula
37416 A=B%\text{This is the comment}
37424 \begin_layout Standard
37425 \begin_inset Newpage newpage
37431 \begin_layout Section
37434 \begin_inset Index idx
37437 \begin_layout Plain Layout
37446 \begin_layout Standard
37447 This section is a summary of the most important typographic rules, listed
37452 \begin_layout Plain Layout
37453 This collection was partly taken from the German semi-official dictionary
37455 \begin_inset Quotes eld
37459 \begin_inset Quotes erd
37463 \begin_inset CommandInset citation
37469 that lists some of the ISO rules.
37470 More rules are listed in
37471 \begin_inset CommandInset citation
37485 \begin_layout Itemize
37494 \begin_layout Plain Layout
37495 done with font styles, see
37496 \begin_inset CommandInset ref
37498 reference "subsec:Font-Styles"
37507 , no matter if they appear in italic text: 30
37508 \begin_inset space \thinspace{}
37512 \begin_inset Newline newline
37515 Between the value and the unit is the smallest space, see
37516 \begin_inset CommandInset ref
37518 reference "subsec:Predefined-Space"
37523 \begin_inset Newline newline
37526 This convention is automatically fulfilled when the command
37533 When it is entered to a formula, two boxes appear.
37534 In the first one the value is inserted, in the second one the unit, and
37536 \begin_inset Formula $\unit[30]{km/h}$
37540 \begin_inset space \thinspace{}
37550 is not a real \SpecialChar LaTeX
37551 command but the command
37557 , therefore you cannot use it in \SpecialChar TeX
37561 \begin_layout Itemize
37562 Percent and perthousand signs are set like physical units:
37563 \begin_inset Newline newline
37567 \begin_inset space \thinspace{}
37573 \begin_layout Itemize
37574 The degree sign follows directly on the value: 15°, but not when it is used
37576 \begin_inset space \thinspace{}
37582 \begin_layout Itemize
37583 In numbers with more than four digits the smallest space is inserted before
37584 every third digit to group them:
37594 \begin_inset space \thinspace{}
37598 \begin_inset space \thinspace{}
37604 \begin_layout Itemize
37605 For dimensions like 120×90×40
37606 \begin_inset space \thinspace{}
37609 cm the multiplication sign
37610 \begin_inset Quotes eld
37614 \begin_inset Quotes erd
37618 It is available either via the command
37626 Insert\SpecialChar menuseparator
37627 Special Character\SpecialChar menuseparator
37633 \begin_layout Itemize
37634 Functions with names consisting of several letters are set upright to avoid
37636 \begin_inset CommandInset ref
37638 reference "subsec:Predefined-Functions"
37645 \begin_layout Itemize
37646 Indices consisting of several letters, are set upright:
37647 \begin_inset Formula $E_{\mathrm{kin}}$
37651 \begin_inset Newline newline
37654 Components of matrices are set italic:
37655 \begin_inset Formula $\hat{H}_{kl}$
37661 \begin_layout Itemize
37662 The differentiation/integration operator 'd', the Euler's number 'e' and
37663 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37667 \begin_layout Itemize
37668 The character that denotes a
37672 transformation is inserted either by the command
37677 \begin_inset space \textvisiblespace{}
37684 Insert\SpecialChar menuseparator
37685 Special Character\SpecialChar menuseparator
37686 Symbols\SpecialChar menuseparator
37688 \begin_inset space ~
37694 \begin_inset Formula $\mathscr{F}$
37700 \begin_layout Standard
37701 \begin_inset Newpage newpage
37707 \begin_layout Section
37709 \begin_inset Index idx
37712 \begin_layout Plain Layout
37721 \begin_layout Standard
37722 Some characters and symbols can be created with several commands.
37723 Here is a list of the synonym commands:
37726 \begin_layout Standard
37727 \begin_inset VSpace bigskip
37731 \begin_inset space \hfill{}
37735 \begin_inset Tabular
37736 <lyxtabular version="3" rows="12" columns="2">
37737 <features tabularvalignment="middle">
37738 <column alignment="center" valignment="top" width="0pt">
37739 <column alignment="center" valignment="top" width="0pt">
37741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37744 \begin_layout Plain Layout
37750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37753 \begin_layout Plain Layout
37755 \begin_inset Note Note
37758 \begin_layout Plain Layout
37765 is only used as spacer.
37777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37780 \begin_layout Plain Layout
37788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37791 \begin_layout Plain Layout
37795 \begin_layout Plain Layout
37808 \begin_layout Plain Layout
37822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37825 \begin_layout Plain Layout
37833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37836 \begin_layout Plain Layout
37846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37849 \begin_layout Plain Layout
37857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37860 \begin_layout Plain Layout
37870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37873 \begin_layout Plain Layout
37881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37884 \begin_layout Plain Layout
37892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37895 \begin_layout Plain Layout
37903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37906 \begin_layout Plain Layout
37914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37917 \begin_layout Plain Layout
37925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37928 \begin_layout Plain Layout
37938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37941 \begin_layout Plain Layout
37949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37952 \begin_layout Plain Layout
37962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37965 \begin_layout Plain Layout
37973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37976 \begin_layout Plain Layout
37986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37989 \begin_layout Plain Layout
37997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38000 \begin_layout Plain Layout
38010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38013 \begin_layout Plain Layout
38021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38024 \begin_layout Plain Layout
38032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
38035 \begin_layout Plain Layout
38043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
38046 \begin_layout Plain Layout
38058 \begin_inset space \hfill{}
38062 \begin_inset Tabular
38063 <lyxtabular version="3" rows="12" columns="2">
38064 <features tabularvalignment="middle">
38065 <column alignment="center" valignment="top" width="0pt">
38066 <column alignment="center" valignment="top" width="0pt">
38068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
38071 \begin_layout Plain Layout
38077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
38080 \begin_layout Plain Layout
38088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38091 \begin_layout Plain Layout
38099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38102 \begin_layout Plain Layout
38114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38117 \begin_layout Plain Layout
38125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38128 \begin_layout Plain Layout
38138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38141 \begin_layout Plain Layout
38149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38152 \begin_layout Plain Layout
38162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38165 \begin_layout Plain Layout
38173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38176 \begin_layout Plain Layout
38184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38187 \begin_layout Plain Layout
38195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38198 \begin_layout Plain Layout
38206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38209 \begin_layout Plain Layout
38217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38220 \begin_layout Plain Layout
38230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38233 \begin_layout Plain Layout
38241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38244 \begin_layout Plain Layout
38254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38257 \begin_layout Plain Layout
38265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38268 \begin_layout Plain Layout
38278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38281 \begin_layout Plain Layout
38289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38292 \begin_layout Plain Layout
38302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38305 \begin_layout Plain Layout
38313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38316 \begin_layout Plain Layout
38326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
38329 \begin_layout Plain Layout
38337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
38340 \begin_layout Plain Layout
38354 \begin_inset space \hfill{}
38360 \begin_layout Standard
38361 \begin_inset Newpage newpage
38367 \begin_layout Bibliography
38368 \begin_inset CommandInset bibitem
38369 LatexCommand bibitem
38381 The \SpecialChar LaTeX
38385 Addison Wesley, 2004
38388 \begin_layout Bibliography
38389 \begin_inset CommandInset bibitem
38390 LatexCommand bibitem
38396 \begin_inset CommandInset href
38399 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
38403 of \SpecialChar LaTeX
38407 \begin_layout Bibliography
38408 \begin_inset CommandInset bibitem
38409 LatexCommand bibitem
38415 \begin_inset CommandInset href
38418 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
38426 \begin_layout Plain Layout
38435 -\SpecialChar LaTeX
38439 \begin_layout Bibliography
38440 \begin_inset CommandInset bibitem
38441 LatexCommand bibitem
38447 \begin_inset CommandInset href
38450 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38454 of all symbols available with \SpecialChar LaTeX
38458 \begin_layout Bibliography
38459 \begin_inset CommandInset bibitem
38460 LatexCommand bibitem
38466 \begin_inset CommandInset href
38468 name "Documentation"
38469 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
38473 of the \SpecialChar LaTeX
38479 \begin_inset Index idx
38482 \begin_layout Plain Layout
38491 \begin_layout Bibliography
38492 \begin_inset CommandInset bibitem
38493 LatexCommand bibitem
38499 \begin_inset CommandInset href
38501 name "Documentation"
38502 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38506 of the \SpecialChar LaTeX
38512 \begin_inset Index idx
38515 \begin_layout Plain Layout
38516 Packages ! hyperref
38524 \begin_layout Bibliography
38525 \begin_inset CommandInset bibitem
38526 LatexCommand bibitem
38532 \begin_inset CommandInset href
38534 name "Documentation"
38535 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38539 of the \SpecialChar LaTeX
38545 \begin_inset Index idx
38548 \begin_layout Plain Layout
38557 \begin_layout Bibliography
38558 \begin_inset CommandInset bibitem
38559 LatexCommand bibitem
38570 Auflage, Duden 2001
38573 \begin_layout Bibliography
38574 \begin_inset CommandInset bibitem
38575 LatexCommand bibitem
38581 \begin_inset CommandInset href
38584 target "http://physics.nist.gov/Document/checklist.pdf"
38588 for reviewing manuscripts
38591 \begin_layout Standard
38592 \begin_inset CommandInset index_print
38593 LatexCommand printindex