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:
18838 \begin_inset VSpace -2mm
18844 \begin_layout Standard
18846 \begin_inset Tabular
18847 <lyxtabular version="3" rows="7" columns="3">
18848 <features tabularvalignment="middle">
18849 <column alignment="center" valignment="top">
18850 <column alignment="center" valignment="top">
18851 <column alignment="center" valignment="top">
18853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18856 \begin_layout Plain Layout
18862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18865 \begin_layout Plain Layout
18871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18874 \begin_layout Plain Layout
18882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18885 \begin_layout Plain Layout
18891 \begin_inset space \textvisiblespace{}
18901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18904 \begin_layout Plain Layout
18905 \begin_inset Formula $\mathbb{ABC}$
18913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18916 \begin_layout Plain Layout
18929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18932 \begin_layout Plain Layout
18938 \begin_inset space \textvisiblespace{}
18948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18951 \begin_layout Plain Layout
18952 \begin_inset Formula $\mathbf{AbC}$
18960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18963 \begin_layout Plain Layout
18976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18979 \begin_layout Plain Layout
18985 \begin_inset space \textvisiblespace{}
18995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18998 \begin_layout Plain Layout
18999 \begin_inset Formula $\boldsymbol{AbC}$
19007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19010 \begin_layout Plain Layout
19013 arg "font-boldsymbol"
19023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19026 \begin_layout Plain Layout
19032 \begin_inset space \textvisiblespace{}
19042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19045 \begin_layout Plain Layout
19046 \begin_inset Formula $\mathcal{ABC}$
19054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19057 \begin_layout Plain Layout
19070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19073 \begin_layout Plain Layout
19079 \begin_inset space \textvisiblespace{}
19089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19092 \begin_layout Plain Layout
19093 \begin_inset Formula $\mathfrak{AbC}$
19101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19104 \begin_layout Plain Layout
19112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19115 \begin_layout Plain Layout
19121 \begin_inset space \textvisiblespace{}
19131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19134 \begin_layout Plain Layout
19135 \begin_inset Formula $\mathscr{AbC}$
19143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19146 \begin_layout Plain Layout
19160 \begin_layout Standard
19162 \begin_inset Tabular
19163 <lyxtabular version="3" rows="5" columns="3">
19164 <features tabularvalignment="middle">
19165 <column alignment="center" valignment="top">
19166 <column alignment="center" valignment="top">
19167 <column alignment="center" valignment="top">
19169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19172 \begin_layout Plain Layout
19178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19181 \begin_layout Plain Layout
19187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19190 \begin_layout Plain Layout
19198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19201 \begin_layout Plain Layout
19207 \begin_inset space \textvisiblespace{}
19217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19220 \begin_layout Plain Layout
19221 \begin_inset Formula $\mathit{AbC}$
19229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19232 \begin_layout Plain Layout
19240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19243 \begin_layout Plain Layout
19249 \begin_inset space \textvisiblespace{}
19259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19262 \begin_layout Plain Layout
19263 \begin_inset Formula $\mathrm{AbC}$
19271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19274 \begin_layout Plain Layout
19287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19290 \begin_layout Plain Layout
19296 \begin_inset space \textvisiblespace{}
19306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19309 \begin_layout Plain Layout
19310 \begin_inset Formula $\mathsf{AbC}$
19318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19321 \begin_layout Plain Layout
19334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19337 \begin_layout Plain Layout
19343 \begin_inset space \textvisiblespace{}
19353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19356 \begin_layout Plain Layout
19357 \begin_inset Formula $\mathtt{AbC}$
19365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19368 \begin_layout Plain Layout
19371 arg "font-typewriter"
19387 \begin_layout Standard
19388 \begin_inset Note Greyedout
19391 \begin_layout Plain Layout
19408 can only be used for big letters.
19416 \begin_layout Standard
19417 Predefined is the style
19426 \begin_layout Standard
19427 The style commands work also for letters in mathematical constructs:
19428 \begin_inset Formula
19430 \mathfrak{A=\frac{b}{C}}
19438 \begin_layout Standard
19439 Characters in mathematical text don't appear in a math font style but in
19440 the text font style
19447 That their style can't be set correctly via the text style dialog is a
19448 bug in \SpecialChar LyX
19453 \begin_layout Plain Layout
19454 \begin_inset CommandInset href
19456 name "LyX-bug #4629"
19457 target "http://www.lyx.org/trac/ticket/4629"
19469 \begin_layout Standard
19470 Instead of the style commands the dialog
19472 Edit\SpecialChar menuseparator
19473 Math\SpecialChar menuseparator
19476 or the toolbar button
19479 arg "math-insert \\font"
19485 \begin_layout Subsection
19487 \begin_inset CommandInset label
19489 name "subsec:Bold-Formulas"
19494 \begin_inset Index idx
19497 \begin_layout Plain Layout
19506 \begin_layout Standard
19507 To make a complete formula bold, the command
19513 from the previous subsection cannot be used, because it doesn't work for
19514 small Greek letters.
19515 Furthermore it prints Latin letters always upright, like in the following
19519 \begin_layout Standard
19520 \begin_inset Formula
19522 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
19530 \begin_layout Standard
19531 To display the formula correctly, the command
19538 \begin_inset Formula
19540 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
19545 It is also possible to set the formula in a
19547 boldmath environment
19550 This environment is created by inserting the command
19557 \begin_inset Index idx
19560 \begin_layout Plain Layout
19568 in \SpecialChar TeX
19570 To end the environment, the command
19577 \begin_inset Index idx
19580 \begin_layout Plain Layout
19588 is inserted in \SpecialChar TeX
19593 \begin_layout Plain Layout
19603 \begin_inset Formula
19605 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19614 \begin_layout Plain Layout
19626 \begin_layout Subsection
19628 \begin_inset Index idx
19631 \begin_layout Plain Layout
19640 \begin_layout Standard
19641 Formulas can be colored like normal text: Highlight a formula or a formula
19647 Here is a formula in magenta:
19648 \begin_inset Formula
19650 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19658 \begin_layout Standard
19659 You can also define your own colors as described in
19660 \begin_inset CommandInset ref
19662 reference "subsec:Colored-Boxes"
19667 They can be used with the \SpecialChar TeX
19675 \begin_inset Index idx
19678 \begin_layout Plain Layout
19689 \begin_layout Standard
19694 textcolor{color}{characters or formula}
19697 \begin_layout Standard
19698 The following example was colored completely dark green and partly red:
19701 \begin_layout Standard
19705 \begin_layout Plain Layout
19709 textcolor{darkgreen}{
19715 \begin_inset Formula
19717 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19726 \begin_layout Plain Layout
19736 \begin_layout Standard
19737 Due to a bug in \SpecialChar LyX
19738 only complete formulas can be colored with self-defined
19743 \begin_layout Plain Layout
19744 \begin_inset CommandInset href
19746 name "LyX-bug #5269"
19747 target "http://www.lyx.org/trac/ticket/5269"
19759 \begin_layout Subsection
19761 \begin_inset CommandInset label
19763 name "subsec:Font-Sizes"
19768 \begin_inset Index idx
19771 \begin_layout Plain Layout
19780 \begin_layout Standard
19781 For characters in formulas there are, analog to characters in text, the
19782 following size commands:
19785 \begin_layout Standard
19829 \begin_inset Newline newline
19851 \begin_layout Standard
19852 The size produced by the commands depends on the document font size, which
19853 corresponds to the command
19860 The other commands produce smaller or larger sizes than
19867 The font size can however not exceed a certain value.
19868 Is for example the document font size 12
19869 \begin_inset space \thinspace{}
19878 switches to the same size as
19888 \begin_layout Standard
19889 A size command is inserted in \SpecialChar TeX
19890 mode before the formula and sets the size
19891 for all following formula and text characters.
19892 To switch back to the initial size, the command
19898 is inserted behind the formula in \SpecialChar TeX
19902 \begin_layout Standard
19903 Within a formula the size can be changed using the following size commands
19904 or the toolbar button
19907 arg "math-insert \\style"
19911 \begin_inset Separator parbreak
19917 \begin_layout Standard
19920 \begin_inset Tabular
19921 <lyxtabular version="3" rows="5" columns="2">
19922 <features tabularvalignment="middle">
19923 <column alignment="center" valignment="top">
19924 <column alignment="center" valignment="top">
19926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19929 \begin_layout Plain Layout
19935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19938 \begin_layout Plain Layout
19940 \begin_inset Note Note
19943 \begin_layout Plain Layout
19950 is only used as spacer.
19962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19965 \begin_layout Plain Layout
19969 \begin_inset Index idx
19972 \begin_layout Plain Layout
19985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19988 \begin_layout Plain Layout
19989 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20002 \begin_layout Plain Layout
20010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20013 \begin_layout Plain Layout
20014 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
20024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20027 \begin_layout Plain Layout
20035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20038 \begin_layout Plain Layout
20039 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
20049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20052 \begin_layout Plain Layout
20060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20063 \begin_layout Plain Layout
20064 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
20080 \begin_layout Standard
20081 After entering these commands, a blue box appears in which the formula parts
20085 \begin_layout Standard
20086 There is a further method to change the font size, that though only works
20087 for symbols or letters in mathematical text.
20088 To use it, one of the above text size commands is inserted in mathematical
20090 All following characters until the end of the mathematical text or until
20091 another size command will have the selected size.
20093 \begin_inset VSpace -2mm
20099 \begin_layout Standard
20103 \begin_layout Plain Layout
20113 \begin_inset Formula
20115 A=\frac{B}{c}\cdot\maltese
20121 \begin_inset Formula
20123 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
20132 \begin_layout Plain Layout
20144 \begin_layout Standard
20145 \begin_inset VSpace medskip
20148 Before both formulas the command
20155 The command for the second formula is:
20156 \begin_inset Newline newline
20164 \begin_inset space \textvisiblespace{}
20170 \begin_inset space \textvisiblespace{}
20176 \begin_inset space \textvisiblespace{}
20182 \begin_inset space \textvisiblespace{}
20186 \begin_inset Formula $\to$
20190 \begin_inset Formula $\to$
20194 \begin_inset Newline newline
20198 \begin_inset space \hspace*{}
20209 \begin_inset space \textvisiblespace{}
20215 \begin_inset space \textvisiblespace{}
20221 \begin_inset space \textvisiblespace{}
20227 \begin_layout Standard
20228 If a symbol cannot be displayed in different sizes, it will always be displayed
20229 in the default size.
20232 \begin_layout Section
20234 \begin_inset Index idx
20237 \begin_layout Plain Layout
20246 \begin_layout Standard
20247 Greek letters can also be inserted via the toolbar button
20250 arg "math-insert \\alpha"
20254 All international typesetting norms purport that Greek letters in math
20255 have to be typeset italic/slanted.
20256 In some languages, like French or Russian, they are nevertheless sometimes
20260 \begin_layout Subsection
20262 \begin_inset Index idx
20265 \begin_layout Plain Layout
20266 Greek letters ! small
20274 \begin_layout Standard
20275 \begin_inset space \hfill{}
20279 \begin_inset Tabular
20280 <lyxtabular version="3" rows="11" columns="2">
20281 <features tabularvalignment="middle">
20282 <column alignment="center" valignment="top" width="0pt">
20283 <column alignment="center" valignment="top" width="0pt">
20285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20288 \begin_layout Plain Layout
20294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20297 \begin_layout Plain Layout
20305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20308 \begin_layout Plain Layout
20316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20319 \begin_layout Plain Layout
20320 \begin_inset Formula $\alpha$
20330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20333 \begin_layout Plain Layout
20341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20344 \begin_layout Plain Layout
20345 \begin_inset Formula $\beta$
20355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20358 \begin_layout Plain Layout
20366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20369 \begin_layout Plain Layout
20370 \begin_inset Formula $\gamma$
20380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20383 \begin_layout Plain Layout
20391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20394 \begin_layout Plain Layout
20395 \begin_inset Formula $\delta$
20405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20408 \begin_layout Plain Layout
20416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20419 \begin_layout Plain Layout
20420 \begin_inset Formula $\epsilon$
20430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20433 \begin_layout Plain Layout
20441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20444 \begin_layout Plain Layout
20445 \begin_inset Formula $\varepsilon$
20455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20458 \begin_layout Plain Layout
20466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20469 \begin_layout Plain Layout
20470 \begin_inset Formula $\zeta$
20480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20483 \begin_layout Plain Layout
20491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20494 \begin_layout Plain Layout
20495 \begin_inset Formula $\eta$
20505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20508 \begin_layout Plain Layout
20516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20519 \begin_layout Plain Layout
20520 \begin_inset Formula $\theta$
20530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20533 \begin_layout Plain Layout
20541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20544 \begin_layout Plain Layout
20545 \begin_inset Formula $\vartheta$
20559 \begin_inset space \hfill{}
20563 \begin_inset Tabular
20564 <lyxtabular version="3" rows="12" columns="2">
20565 <features tabularvalignment="middle">
20566 <column alignment="center" valignment="top" width="0pt">
20567 <column alignment="center" valignment="top" width="0pt">
20569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20572 \begin_layout Plain Layout
20578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20581 \begin_layout Plain Layout
20589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20592 \begin_layout Plain Layout
20600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20603 \begin_layout Plain Layout
20604 \begin_inset Formula $\iota$
20614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20617 \begin_layout Plain Layout
20625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20628 \begin_layout Plain Layout
20629 \begin_inset Formula $\kappa$
20639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20642 \begin_layout Plain Layout
20650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20653 \begin_layout Plain Layout
20654 \begin_inset Formula $\varkappa$
20664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20667 \begin_layout Plain Layout
20675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20678 \begin_layout Plain Layout
20679 \begin_inset Formula $\lambda$
20689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20692 \begin_layout Plain Layout
20700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20703 \begin_layout Plain Layout
20704 \begin_inset Formula $\mu$
20714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20717 \begin_layout Plain Layout
20725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20728 \begin_layout Plain Layout
20729 \begin_inset Formula $\nu$
20739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20742 \begin_layout Plain Layout
20750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20753 \begin_layout Plain Layout
20754 \begin_inset Formula $\xi$
20764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20767 \begin_layout Plain Layout
20773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20776 \begin_layout Plain Layout
20777 \begin_inset Formula $o$
20787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20790 \begin_layout Plain Layout
20798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20801 \begin_layout Plain Layout
20802 \begin_inset Formula $\pi$
20812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20815 \begin_layout Plain Layout
20823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20826 \begin_layout Plain Layout
20827 \begin_inset Formula $\varpi$
20837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20840 \begin_layout Plain Layout
20848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20851 \begin_layout Plain Layout
20852 \begin_inset Formula $\rho$
20866 \begin_inset space \hfill{}
20870 \begin_inset Tabular
20871 <lyxtabular version="3" rows="11" columns="2">
20872 <features tabularvalignment="middle">
20873 <column alignment="center" valignment="top" width="0pt">
20874 <column alignment="center" valignment="top" width="0pt">
20876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20879 \begin_layout Plain Layout
20885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20888 \begin_layout Plain Layout
20896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20899 \begin_layout Plain Layout
20907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20910 \begin_layout Plain Layout
20911 \begin_inset Formula $\varrho$
20921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20924 \begin_layout Plain Layout
20932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20935 \begin_layout Plain Layout
20936 \begin_inset Formula $\sigma$
20946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20949 \begin_layout Plain Layout
20957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20960 \begin_layout Plain Layout
20961 \begin_inset Formula $\varsigma$
20971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20974 \begin_layout Plain Layout
20982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20985 \begin_layout Plain Layout
20986 \begin_inset Formula $\tau$
20996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20999 \begin_layout Plain Layout
21007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21010 \begin_layout Plain Layout
21011 \begin_inset Formula $\upsilon$
21021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21024 \begin_layout Plain Layout
21032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21035 \begin_layout Plain Layout
21036 \begin_inset Formula $\phi$
21046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21049 \begin_layout Plain Layout
21057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21060 \begin_layout Plain Layout
21061 \begin_inset Formula $\varphi$
21071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21074 \begin_layout Plain Layout
21082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21085 \begin_layout Plain Layout
21086 \begin_inset Formula $\chi$
21096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21099 \begin_layout Plain Layout
21107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21110 \begin_layout Plain Layout
21111 \begin_inset Formula $\psi$
21121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21124 \begin_layout Plain Layout
21132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21135 \begin_layout Plain Layout
21136 \begin_inset Formula $\omega$
21150 \begin_inset space \hfill{}
21156 \begin_layout Standard
21157 \begin_inset VSpace medskip
21163 \begin_layout Standard
21164 How to create special upright Greek letters is explained in
21165 \begin_inset CommandInset ref
21167 reference "subsec:Upright-small-Greek"
21174 \begin_layout Subsection
21176 \begin_inset Index idx
21179 \begin_layout Plain Layout
21180 Greek letters ! big
21188 \begin_layout Standard
21189 \begin_inset space \hfill{}
21193 \begin_inset Tabular
21194 <lyxtabular version="3" rows="7" columns="2">
21195 <features tabularvalignment="middle">
21196 <column alignment="center" valignment="top" width="0pt">
21197 <column alignment="center" valignment="top" width="0pt">
21199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21202 \begin_layout Plain Layout
21208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21211 \begin_layout Plain Layout
21219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21222 \begin_layout Plain Layout
21230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21233 \begin_layout Plain Layout
21234 \begin_inset Formula $\Gamma$
21244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21247 \begin_layout Plain Layout
21255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21258 \begin_layout Plain Layout
21259 \begin_inset Formula $\Delta$
21269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21272 \begin_layout Plain Layout
21280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21283 \begin_layout Plain Layout
21284 \begin_inset Formula $\Theta$
21294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21297 \begin_layout Plain Layout
21305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21308 \begin_layout Plain Layout
21309 \begin_inset Formula $\Lambda$
21319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21322 \begin_layout Plain Layout
21330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21333 \begin_layout Plain Layout
21334 \begin_inset Formula $\Xi$
21344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21347 \begin_layout Plain Layout
21355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21358 \begin_layout Plain Layout
21359 \begin_inset Formula $\Pi$
21373 \begin_inset space \hfill{}
21377 \begin_inset Tabular
21378 <lyxtabular version="3" rows="6" columns="2">
21379 <features tabularvalignment="middle">
21380 <column alignment="center" valignment="top" width="0pt">
21381 <column alignment="center" valignment="top" width="0pt">
21383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21386 \begin_layout Plain Layout
21392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21395 \begin_layout Plain Layout
21403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21406 \begin_layout Plain Layout
21414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21417 \begin_layout Plain Layout
21418 \begin_inset Formula $\Sigma$
21428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21431 \begin_layout Plain Layout
21439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21442 \begin_layout Plain Layout
21443 \begin_inset Formula $\Upsilon$
21453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21456 \begin_layout Plain Layout
21464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21467 \begin_layout Plain Layout
21468 \begin_inset Formula $\Phi$
21478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21481 \begin_layout Plain Layout
21489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21492 \begin_layout Plain Layout
21493 \begin_inset Formula $\Psi$
21503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21506 \begin_layout Plain Layout
21514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21517 \begin_layout Plain Layout
21518 \begin_inset Formula $\Omega$
21532 \begin_inset space \hfill{}
21538 \begin_layout Standard
21539 \begin_inset VSpace medskip
21542 That the big Greek letters appear upright is caused by a design bug when
21545 To get correct italic big letters, begin every command with
21550 For example the command
21557 \begin_inset Formula $\varGamma$
21561 Another way is to load the package
21569 \begin_layout Plain Layout
21574 is part of the \SpecialChar LaTeX
21580 \begin_inset Index idx
21583 \begin_layout Plain Layout
21588 \begin_layout Plain Layout
21608 \begin_inset Index idx
21611 \begin_layout Plain Layout
21617 with the \SpecialChar LaTeX
21621 \begin_layout Standard
21626 usepackage{fixmath}
21629 \begin_layout Standard
21630 Then all big Greek letters in a document will automatically be typeset italic.
21633 \begin_layout Subsection
21635 \begin_inset Index idx
21638 \begin_layout Plain Layout
21639 Greek letters ! bold
21647 \begin_layout Standard
21648 Greek letters cannot be set with different font styles like Latin letters.
21649 They can only be made bold with the command
21656 \begin_inset Index idx
21659 \begin_layout Plain Layout
21668 \begin_inset Separator parbreak
21674 \begin_layout Standard
21676 \begin_inset Tabular
21677 <lyxtabular version="3" rows="3" columns="2">
21678 <features tabularvalignment="middle">
21679 <column alignment="center" valignment="top">
21680 <column alignment="center" valignment="top">
21682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21685 \begin_layout Plain Layout
21691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21694 \begin_layout Plain Layout
21702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21705 \begin_layout Plain Layout
21717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21720 \begin_layout Plain Layout
21721 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21734 \begin_layout Plain Layout
21746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21749 \begin_layout Plain Layout
21750 \begin_inset Formula $\theta\boldsymbol{\theta}$
21766 \begin_layout Section
21771 \begin_layout Plain Layout
21784 \begin_layout Plain Layout
21785 A list with all symbols of most of the \SpecialChar LaTeX
21786 -packages can be found in
21787 \begin_inset CommandInset citation
21802 \begin_layout Plain Layout
21810 \begin_inset Note Note
21813 \begin_layout Plain Layout
21816 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21819 \begin_layout Plain Layout
21822 texorpdfstring is in section
21823 \begin_inset CommandInset ref
21825 reference "subsec:Formulas-in-Section"
21835 \begin_inset Index idx
21838 \begin_layout Plain Layout
21847 \begin_layout Standard
21848 Many of the symbols listed in this section can also be inserted via the
21852 arg "math-insert \\nabla"
21858 arg "math-insert \\digamma"
21864 \begin_layout Subsection
21865 Mathematical Symbols
21866 \begin_inset CommandInset label
21868 name "subsec:Mathematical-Symbols"
21873 \begin_inset Index idx
21876 \begin_layout Plain Layout
21877 Symbols ! mathematical
21885 \begin_layout Standard
21886 \begin_inset space \hfill{}
21890 \begin_inset Tabular
21891 <lyxtabular version="3" rows="10" columns="2">
21892 <features tabularvalignment="middle">
21893 <column alignment="center" valignment="top" width="0pt">
21894 <column alignment="center" valignment="top" width="0pt">
21896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21899 \begin_layout Plain Layout
21905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21908 \begin_layout Plain Layout
21916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21919 \begin_layout Plain Layout
21927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21930 \begin_layout Plain Layout
21931 \begin_inset Formula $\neg$
21941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21944 \begin_layout Plain Layout
21952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21955 \begin_layout Plain Layout
21956 \begin_inset Formula $\Im$
21966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21969 \begin_layout Plain Layout
21977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21980 \begin_layout Plain Layout
21981 \begin_inset Formula $\Re$
21991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21994 \begin_layout Plain Layout
22002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22005 \begin_layout Plain Layout
22006 \begin_inset Formula $\aleph$
22016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22019 \begin_layout Plain Layout
22027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22030 \begin_layout Plain Layout
22031 \begin_inset Formula $\partial$
22041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22044 \begin_layout Plain Layout
22052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22055 \begin_layout Plain Layout
22056 \begin_inset Formula $\infty$
22066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22069 \begin_layout Plain Layout
22077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22080 \begin_layout Plain Layout
22081 \begin_inset Formula $\wp$
22091 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22094 \begin_layout Plain Layout
22102 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22105 \begin_layout Plain Layout
22106 \begin_inset Formula $\imath$
22116 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22119 \begin_layout Plain Layout
22127 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22130 \begin_layout Plain Layout
22131 \begin_inset Formula $\jmath$
22145 \begin_inset space \hfill{}
22149 \begin_inset Tabular
22150 <lyxtabular version="3" rows="10" columns="2">
22151 <features tabularvalignment="middle">
22152 <column alignment="center" valignment="top" width="0pt">
22153 <column alignment="center" valignment="top" width="0pt">
22155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22158 \begin_layout Plain Layout
22164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22167 \begin_layout Plain Layout
22169 \begin_inset Note Note
22172 \begin_layout Plain Layout
22179 is only used as spacer.
22191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22194 \begin_layout Plain Layout
22202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22205 \begin_layout Plain Layout
22206 \begin_inset Formula $\forall$
22216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22219 \begin_layout Plain Layout
22227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22230 \begin_layout Plain Layout
22231 \begin_inset Formula $\exists$
22241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22244 \begin_layout Plain Layout
22252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22255 \begin_layout Plain Layout
22256 \begin_inset Formula $\nexists$
22266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22269 \begin_layout Plain Layout
22277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22280 \begin_layout Plain Layout
22281 \begin_inset Formula $\emptyset$
22291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22294 \begin_layout Plain Layout
22302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22305 \begin_layout Plain Layout
22306 \begin_inset Formula $\varnothing$
22316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22319 \begin_layout Plain Layout
22327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22330 \begin_layout Plain Layout
22331 \begin_inset Formula $\dag$
22341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22344 \begin_layout Plain Layout
22352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22355 \begin_layout Plain Layout
22356 \begin_inset Formula $\ddag$
22366 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22369 \begin_layout Plain Layout
22377 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22380 \begin_layout Plain Layout
22384 \begin_layout Plain Layout
22394 \begin_inset Formula $\complement$
22401 \begin_layout Plain Layout
22415 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22418 \begin_layout Plain Layout
22426 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22429 \begin_layout Plain Layout
22430 \begin_inset Formula $\Bbbk$
22444 \begin_inset space \hfill{}
22448 \begin_inset Tabular
22449 <lyxtabular version="3" rows="10" columns="2">
22450 <features tabularvalignment="middle">
22451 <column alignment="center" valignment="top" width="0pt">
22452 <column alignment="center" valignment="top" width="0pt">
22454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22457 \begin_layout Plain Layout
22463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22466 \begin_layout Plain Layout
22474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22477 \begin_layout Plain Layout
22485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22488 \begin_layout Plain Layout
22489 \begin_inset Formula $\prime$
22499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22502 \begin_layout Plain Layout
22510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22513 \begin_layout Plain Layout
22514 \begin_inset Formula $\backprime$
22524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22527 \begin_layout Plain Layout
22535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22538 \begin_layout Plain Layout
22539 \begin_inset Formula $\mho$
22549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22552 \begin_layout Plain Layout
22560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22563 \begin_layout Plain Layout
22564 \begin_inset Formula $\triangle$
22574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22577 \begin_layout Plain Layout
22585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22588 \begin_layout Plain Layout
22589 \begin_inset Formula $\angle$
22599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22602 \begin_layout Plain Layout
22610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22613 \begin_layout Plain Layout
22614 \begin_inset Formula $\measuredangle$
22624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22627 \begin_layout Plain Layout
22635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22638 \begin_layout Plain Layout
22639 \begin_inset Formula $\sphericalangle$
22649 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22652 \begin_layout Plain Layout
22660 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22663 \begin_layout Plain Layout
22664 \begin_inset Formula $\top$
22674 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22677 \begin_layout Plain Layout
22685 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22688 \begin_layout Plain Layout
22689 \begin_inset Formula $\bot$
22703 \begin_inset space \hfill{}
22709 \begin_layout Subsection
22710 Miscellaneous Symbols
22711 \begin_inset CommandInset label
22713 name "subsec:Miscellaneous-Symbols"
22718 \begin_inset Index idx
22721 \begin_layout Plain Layout
22722 Symbols ! miscellaneous
22730 \begin_layout Standard
22733 \begin_inset Tabular
22734 <lyxtabular version="3" rows="10" columns="2">
22735 <features tabularvalignment="middle">
22736 <column alignment="center" valignment="top" width="0pt">
22737 <column alignment="center" valignment="top" width="0pt">
22739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22742 \begin_layout Plain Layout
22748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22751 \begin_layout Plain Layout
22759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22762 \begin_layout Plain Layout
22770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22773 \begin_layout Plain Layout
22774 \begin_inset Formula $\flat$
22784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22787 \begin_layout Plain Layout
22795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22798 \begin_layout Plain Layout
22799 \begin_inset Formula $\natural$
22809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22812 \begin_layout Plain Layout
22820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22823 \begin_layout Plain Layout
22824 \begin_inset Formula $\sharp$
22834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22837 \begin_layout Plain Layout
22845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22848 \begin_layout Plain Layout
22849 \begin_inset Formula $\surd$
22859 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22862 \begin_layout Plain Layout
22870 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22873 \begin_layout Plain Layout
22874 \begin_inset Formula $\checkmark$
22884 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22887 \begin_layout Plain Layout
22895 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22898 \begin_layout Plain Layout
22899 \begin_inset Formula $\yen$
22909 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22912 \begin_layout Plain Layout
22920 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22923 \begin_layout Plain Layout
22924 \begin_inset Formula $\pounds$
22934 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22937 \begin_layout Plain Layout
22943 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22946 \begin_layout Plain Layout
22947 \begin_inset Formula $\$$
22957 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22960 \begin_layout Plain Layout
22966 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22969 \begin_layout Plain Layout
22970 \begin_inset Formula $§$
22984 \begin_inset Tabular
22985 <lyxtabular version="3" rows="10" columns="2">
22986 <features tabularvalignment="middle">
22987 <column alignment="center" valignment="top">
22988 <column alignment="center" valignment="top">
22990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22993 \begin_layout Plain Layout
22999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23002 \begin_layout Plain Layout
23010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23013 \begin_layout Plain Layout
23021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23024 \begin_layout Plain Layout
23025 \begin_inset Formula $\hbar$
23035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23038 \begin_layout Plain Layout
23046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23049 \begin_layout Plain Layout
23050 \begin_inset Formula $\hslash$
23060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23063 \begin_layout Plain Layout
23071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23074 \begin_layout Plain Layout
23075 \begin_inset Formula $\clubsuit$
23085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23088 \begin_layout Plain Layout
23096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23099 \begin_layout Plain Layout
23100 \begin_inset Formula $\spadesuit$
23110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23113 \begin_layout Plain Layout
23121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23124 \begin_layout Plain Layout
23125 \begin_inset Formula $\bigstar$
23135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23138 \begin_layout Plain Layout
23146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23149 \begin_layout Plain Layout
23150 \begin_inset Formula $\blacklozenge$
23160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23163 \begin_layout Plain Layout
23171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23174 \begin_layout Plain Layout
23175 \begin_inset Formula $\blacktriangle$
23185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23188 \begin_layout Plain Layout
23196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23199 \begin_layout Plain Layout
23200 \begin_inset Formula $\blacktriangledown$
23210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23213 \begin_layout Plain Layout
23221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23224 \begin_layout Plain Layout
23225 \begin_inset Formula $\bullet$
23239 \begin_inset Tabular
23240 <lyxtabular version="3" rows="10" columns="2">
23241 <features tabularvalignment="middle">
23242 <column alignment="center" valignment="top" width="0pt">
23243 <column alignment="center" valignment="top" width="0pt">
23245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23248 \begin_layout Plain Layout
23254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23257 \begin_layout Plain Layout
23265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23268 \begin_layout Plain Layout
23276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23279 \begin_layout Plain Layout
23280 \begin_inset Formula $\diamondsuit$
23290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23293 \begin_layout Plain Layout
23301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23304 \begin_layout Plain Layout
23305 \begin_inset Formula $\Diamond$
23315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23318 \begin_layout Plain Layout
23326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23329 \begin_layout Plain Layout
23330 \begin_inset Formula $\heartsuit$
23340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23343 \begin_layout Plain Layout
23351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23354 \begin_layout Plain Layout
23355 \begin_inset Formula $\P$
23365 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23368 \begin_layout Plain Layout
23376 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23379 \begin_layout Plain Layout
23380 \begin_inset Formula $\copyright$
23390 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23393 \begin_layout Plain Layout
23401 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23404 \begin_layout Plain Layout
23405 \begin_inset Formula $\circledR$
23415 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23418 \begin_layout Plain Layout
23426 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23429 \begin_layout Plain Layout
23430 \begin_inset Formula $\maltese$
23440 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23443 \begin_layout Plain Layout
23451 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23454 \begin_layout Plain Layout
23455 \begin_inset Formula $\diagup$
23465 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23468 \begin_layout Plain Layout
23476 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23479 \begin_layout Plain Layout
23480 \begin_inset Formula $\diagdown$
23496 \begin_layout Standard
23497 \begin_inset VSpace medskip
23503 \begin_layout Standard
23504 Some symbols can be displayed in different sizes, see
23505 \begin_inset CommandInset ref
23507 reference "subsec:Font-Sizes"
23514 \begin_layout Subsection
23516 \begin_inset Index idx
23519 \begin_layout Plain Layout
23520 Symbols ! Euro-symbol
23526 \begin_inset Index idx
23529 \begin_layout Plain Layout
23536 \begin_layout Plain Layout
23553 \begin_layout Standard
23554 To use the Euro symbol in formulas, the \SpecialChar LaTeX
23560 \begin_inset Index idx
23563 \begin_layout Plain Layout
23569 must be installed and loaded with the \SpecialChar LaTeX
23573 \begin_layout Standard
23578 usepackage[gennarrow]{eurosym}
23581 \begin_layout Standard
23582 The Euro symbol can now be inserted with the command
23589 \begin_inset Index idx
23592 \begin_layout Plain Layout
23603 \begin_layout Standard
23604 The Euro symbol can directly be inserted with the € key in mathematical
23605 text, without having
23620 can also be inserted in \SpecialChar TeX
23622 The official currency symbol can then be inserted with the command
23629 \begin_inset Index idx
23632 \begin_layout Plain Layout
23640 , that is only available in \SpecialChar TeX
23644 \begin_layout Standard
23648 \begin_layout Plain Layout
23658 \begin_inset Note Note
23661 \begin_layout Plain Layout
23662 The following table will only be displayed when the \SpecialChar LaTeX
23675 \begin_layout Standard
23676 An overview about the different Euro symbols:
23677 \begin_inset Separator parbreak
23683 \begin_layout Standard
23685 \begin_inset Tabular
23686 <lyxtabular version="3" rows="4" columns="3">
23687 <features tabularvalignment="middle">
23688 <column alignment="center" valignment="top" width="0pt">
23689 <column alignment="center" valignment="top" width="0pt">
23690 <column alignment="center" valignment="top" width="0pt">
23692 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23695 \begin_layout Plain Layout
23701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23704 \begin_layout Plain Layout
23710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23713 \begin_layout Plain Layout
23721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23724 \begin_layout Plain Layout
23730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23733 \begin_layout Plain Layout
23741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23744 \begin_layout Plain Layout
23745 \begin_inset Formula $\euro$
23755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23758 \begin_layout Plain Layout
23764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23767 \begin_layout Plain Layout
23773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23776 \begin_layout Plain Layout
23777 \begin_inset Formula $\mbox{€}$
23787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23790 \begin_layout Plain Layout
23797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23800 \begin_layout Plain Layout
23808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23811 \begin_layout Plain Layout
23815 \begin_layout Plain Layout
23837 \begin_layout Standard
23841 \begin_layout Plain Layout
23851 \begin_inset Note Note
23854 \begin_layout Plain Layout
23855 The following will be displayed when the \SpecialChar LaTeX
23868 \begin_layout Standard
23869 You need to install the \SpecialChar LaTeX
23874 to see the rest of this subsection in the output.
23877 \begin_layout Standard
23881 \begin_layout Plain Layout
23893 \begin_layout Section
23895 \begin_inset CommandInset label
23897 name "sec:Relations"
23902 \begin_inset Index idx
23905 \begin_layout Plain Layout
23912 \begin_inset Index idx
23915 \begin_layout Plain Layout
23920 \begin_layout Plain Layout
23931 \begin_layout Plain Layout
23946 \begin_layout Standard
23947 All following relations can also be inserted via the toolbar button
23950 arg "math-insert \\leq"
23956 \begin_layout Standard
23957 \begin_inset space \hfill{}
23961 \begin_inset Tabular
23962 <lyxtabular version="3" rows="17" columns="2">
23963 <features tabularvalignment="middle">
23964 <column alignment="center" valignment="top" width="0pt">
23965 <column alignment="center" valignment="top" width="0pt">
23967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23970 \begin_layout Plain Layout
23976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23979 \begin_layout Plain Layout
23987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23990 \begin_layout Plain Layout
23996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23999 \begin_layout Plain Layout
24000 \begin_inset Formula $<$
24010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24013 \begin_layout Plain Layout
24021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24024 \begin_layout Plain Layout
24025 \begin_inset Formula $\le$
24035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24038 \begin_layout Plain Layout
24046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24049 \begin_layout Plain Layout
24050 \begin_inset Formula $\ll$
24060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24063 \begin_layout Plain Layout
24071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24074 \begin_layout Plain Layout
24075 \begin_inset Formula $\prec$
24085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24088 \begin_layout Plain Layout
24096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24099 \begin_layout Plain Layout
24100 \begin_inset Formula $\preceq$
24110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24113 \begin_layout Plain Layout
24121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24124 \begin_layout Plain Layout
24125 \begin_inset Formula $\subset$
24135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24138 \begin_layout Plain Layout
24146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24149 \begin_layout Plain Layout
24150 \begin_inset Formula $\subseteq$
24160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24163 \begin_layout Plain Layout
24171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24174 \begin_layout Plain Layout
24175 \begin_inset Formula $\sqsubseteq$
24185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24188 \begin_layout Plain Layout
24196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24199 \begin_layout Plain Layout
24200 \begin_inset Formula $\in$
24210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24213 \begin_layout Plain Layout
24221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24224 \begin_layout Plain Layout
24225 \begin_inset Formula $\vdash$
24235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24238 \begin_layout Plain Layout
24246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24249 \begin_layout Plain Layout
24250 \begin_inset Formula $\smile$
24260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24263 \begin_layout Plain Layout
24271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24274 \begin_layout Plain Layout
24275 \begin_inset Formula $\lhd$
24285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24288 \begin_layout Plain Layout
24296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24299 \begin_layout Plain Layout
24300 \begin_inset Formula $\unlhd$
24310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24313 \begin_layout Plain Layout
24321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24324 \begin_layout Plain Layout
24325 \begin_inset Formula $\gtrless$
24335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24338 \begin_layout Plain Layout
24346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24349 \begin_layout Plain Layout
24350 \begin_inset Formula $\mid$
24360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24363 \begin_layout Plain Layout
24371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24374 \begin_layout Plain Layout
24375 \begin_inset Formula $\nmid$
24389 \begin_inset space \hfill{}
24393 \begin_inset Tabular
24394 <lyxtabular version="3" rows="17" columns="2">
24395 <features tabularvalignment="middle">
24396 <column alignment="center" valignment="top" width="0pt">
24397 <column alignment="center" valignment="top" width="0pt">
24399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24402 \begin_layout Plain Layout
24408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24411 \begin_layout Plain Layout
24419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24422 \begin_layout Plain Layout
24428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24431 \begin_layout Plain Layout
24432 \begin_inset Formula $=$
24442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24445 \begin_layout Plain Layout
24453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24456 \begin_layout Plain Layout
24457 \begin_inset Formula $\not=$
24467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24470 \begin_layout Plain Layout
24478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24481 \begin_layout Plain Layout
24482 \begin_inset Formula $\equiv$
24492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24495 \begin_layout Plain Layout
24503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24506 \begin_layout Plain Layout
24507 \begin_inset Formula $\sim$
24517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24520 \begin_layout Plain Layout
24528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24531 \begin_layout Plain Layout
24532 \begin_inset Formula $\simeq$
24542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24545 \begin_layout Plain Layout
24553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24556 \begin_layout Plain Layout
24557 \begin_inset Formula $\approx$
24567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24570 \begin_layout Plain Layout
24578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24581 \begin_layout Plain Layout
24582 \begin_inset Formula $\cong$
24592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24595 \begin_layout Plain Layout
24603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24606 \begin_layout Plain Layout
24607 \begin_inset Formula $\bowtie$
24617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24620 \begin_layout Plain Layout
24628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24631 \begin_layout Plain Layout
24632 \begin_inset Formula $\notin$
24642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24645 \begin_layout Plain Layout
24653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24656 \begin_layout Plain Layout
24657 \begin_inset Formula $\perp$
24667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24670 \begin_layout Plain Layout
24678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24681 \begin_layout Plain Layout
24682 \begin_inset Formula $\propto$
24692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24695 \begin_layout Plain Layout
24703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24706 \begin_layout Plain Layout
24707 \begin_inset Formula $\asymp$
24717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24720 \begin_layout Plain Layout
24728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24731 \begin_layout Plain Layout
24732 \begin_inset Formula $\doteq$
24742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24745 \begin_layout Plain Layout
24753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24756 \begin_layout Plain Layout
24757 \begin_inset Formula $\circeq$
24767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24770 \begin_layout Plain Layout
24778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24781 \begin_layout Plain Layout
24782 \begin_inset Formula $\models$
24792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24795 \begin_layout Plain Layout
24803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24806 \begin_layout Plain Layout
24807 \begin_inset Formula $\widehat{=}$
24821 \begin_inset space \hfill{}
24825 \begin_inset Tabular
24826 <lyxtabular version="3" rows="17" columns="2">
24827 <features tabularvalignment="middle">
24828 <column alignment="center" valignment="top" width="0pt">
24829 <column alignment="center" valignment="top" width="0pt">
24831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24834 \begin_layout Plain Layout
24840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24843 \begin_layout Plain Layout
24851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24854 \begin_layout Plain Layout
24860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24863 \begin_layout Plain Layout
24864 \begin_inset Formula $>$
24874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24877 \begin_layout Plain Layout
24885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24888 \begin_layout Plain Layout
24889 \begin_inset Formula $\ge$
24899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24902 \begin_layout Plain Layout
24910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24913 \begin_layout Plain Layout
24914 \begin_inset Formula $\gg$
24924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24927 \begin_layout Plain Layout
24935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24938 \begin_layout Plain Layout
24939 \begin_inset Formula $\succ$
24949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24952 \begin_layout Plain Layout
24960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24963 \begin_layout Plain Layout
24964 \begin_inset Formula $\succeq$
24974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24977 \begin_layout Plain Layout
24985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24988 \begin_layout Plain Layout
24989 \begin_inset Formula $\supset$
24999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25002 \begin_layout Plain Layout
25010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25013 \begin_layout Plain Layout
25014 \begin_inset Formula $\supseteq$
25024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25027 \begin_layout Plain Layout
25035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25038 \begin_layout Plain Layout
25039 \begin_inset Formula $\sqsupseteq$
25049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25052 \begin_layout Plain Layout
25060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25063 \begin_layout Plain Layout
25064 \begin_inset Formula $\ni$
25074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25077 \begin_layout Plain Layout
25085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25088 \begin_layout Plain Layout
25089 \begin_inset Formula $\dashv$
25099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25102 \begin_layout Plain Layout
25110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25113 \begin_layout Plain Layout
25114 \begin_inset Formula $\frown$
25124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25127 \begin_layout Plain Layout
25135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25138 \begin_layout Plain Layout
25139 \begin_inset Formula $\rhd$
25149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25152 \begin_layout Plain Layout
25160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25163 \begin_layout Plain Layout
25164 \begin_inset Formula $\unrhd$
25174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25177 \begin_layout Plain Layout
25185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25188 \begin_layout Plain Layout
25189 \begin_inset Formula $\lessgtr$
25199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25202 \begin_layout Plain Layout
25210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25213 \begin_layout Plain Layout
25214 \begin_inset Formula $\parallel$
25224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25227 \begin_layout Plain Layout
25235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25238 \begin_layout Plain Layout
25239 \begin_inset Formula $\nparallel$
25253 \begin_inset space \hfill{}
25259 \begin_layout Standard
25260 \begin_inset VSpace medskip
25275 are bigger than the equal looking operators
25290 \begin_layout Standard
25292 supports also many special relations.
25293 Use the toolbar button
25296 arg "math-insert \\leqq"
25299 to see a list of these relations.
25302 \begin_layout Standard
25303 Relations are, in contrary to symbols, always surrounded by space.
25306 \begin_layout Standard
25307 Relations with labels can be created with the command
25314 \begin_inset Index idx
25317 \begin_layout Plain Layout
25326 \begin_inset Separator parbreak
25332 \begin_layout Standard
25334 \begin_inset Tabular
25335 <lyxtabular version="3" rows="2" columns="2">
25336 <features tabularvalignment="middle">
25337 <column alignment="center" valignment="top">
25338 <column alignment="center" valignment="top">
25340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25343 \begin_layout Plain Layout
25349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25352 \begin_layout Plain Layout
25354 \begin_inset Note Note
25357 \begin_layout Plain Layout
25364 is only used as spacer.
25376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25379 \begin_layout Plain Layout
25383 \begin_inset space \textvisiblespace{}
25391 \begin_inset space \textvisiblespace{}
25395 \begin_inset Formula $\downarrow$
25401 \begin_inset space \textvisiblespace{}
25405 \begin_inset space \textvisiblespace{}
25413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25416 \begin_layout Plain Layout
25417 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
25433 \begin_layout Section
25437 \begin_layout Subsection
25438 Predefined Functions
25439 \begin_inset CommandInset label
25441 name "subsec:Predefined-Functions"
25446 \begin_inset Index idx
25449 \begin_layout Plain Layout
25450 Functions ! predefined
25458 \begin_layout Standard
25459 In general, variables are set
25463 in mathematical expressions, but not function names, because
25464 \begin_inset Formula $sin$
25467 could be misunderstood as
25468 \begin_inset Formula $s\cdot i\cdot n$
25472 Therefore there are predefined functionswhich are additionally a bit separated
25474 They are inserted as commands starting with a backslash before their name.
25475 \begin_inset Separator parbreak
25481 \begin_layout Standard
25483 \begin_inset Tabular
25484 <lyxtabular version="3" rows="2" columns="4">
25485 <features tabularvalignment="middle">
25486 <column alignment="center" valignment="top" width="0pt">
25487 <column alignment="center" valignment="top" width="0pt">
25488 <column alignment="center" valignment="top" width="0pt">
25489 <column alignment="center" valignment="top" width="0pt">
25491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25494 \begin_layout Plain Layout
25500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25503 \begin_layout Plain Layout
25509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25512 \begin_layout Plain Layout
25518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25521 \begin_layout Plain Layout
25529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25532 \begin_layout Plain Layout
25538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25541 \begin_layout Plain Layout
25542 \begin_inset Formula $Asin(x)+B$
25550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25553 \begin_layout Plain Layout
25561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25564 \begin_layout Plain Layout
25565 \begin_inset Formula $A\sin(x)+B$
25581 \begin_layout Standard
25582 The following functions are predefined:
25585 \begin_layout Standard
25586 \begin_inset VSpace -2mm
25592 \begin_layout Standard
25594 \begin_inset Tabular
25595 <lyxtabular version="3" rows="9" columns="4">
25596 <features tabularvalignment="middle">
25597 <column alignment="center" valignment="top" width="0pt">
25598 <column alignment="center" valignment="top" width="0pt">
25599 <column alignment="center" valignment="top" width="0pt">
25600 <column alignment="center" valignment="top" width="0pt">
25602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25605 \begin_layout Plain Layout
25611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25614 \begin_layout Plain Layout
25620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25623 \begin_layout Plain Layout
25629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25632 \begin_layout Plain Layout
25640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25643 \begin_layout Plain Layout
25651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25654 \begin_layout Plain Layout
25662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25665 \begin_layout Plain Layout
25673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25676 \begin_layout Plain Layout
25686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25689 \begin_layout Plain Layout
25697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25700 \begin_layout Plain Layout
25708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25711 \begin_layout Plain Layout
25719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25722 \begin_layout Plain Layout
25732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25735 \begin_layout Plain Layout
25743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25746 \begin_layout Plain Layout
25754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25757 \begin_layout Plain Layout
25765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25768 \begin_layout Plain Layout
25778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25781 \begin_layout Plain Layout
25789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25792 \begin_layout Plain Layout
25800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25803 \begin_layout Plain Layout
25811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25814 \begin_layout Plain Layout
25824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25827 \begin_layout Plain Layout
25835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25838 \begin_layout Plain Layout
25846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25849 \begin_layout Plain Layout
25857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25860 \begin_layout Plain Layout
25870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25873 \begin_layout Plain Layout
25881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25884 \begin_layout Plain Layout
25892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25895 \begin_layout Plain Layout
25903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25906 \begin_layout Plain Layout
25916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25919 \begin_layout Plain Layout
25927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25930 \begin_layout Plain Layout
25938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25941 \begin_layout Plain Layout
25949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25952 \begin_layout Plain Layout
25962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25965 \begin_layout Plain Layout
25973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25976 \begin_layout Plain Layout
25984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25987 \begin_layout Plain Layout
25995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25998 \begin_layout Plain Layout
26014 \begin_layout Standard
26015 They can also be inserted with the math toolbar button
26018 arg "math-insert \\functions"
26024 \begin_layout Subsection
26025 Self-defined Functions
26026 \begin_inset Index idx
26029 \begin_layout Plain Layout
26030 Functions ! self-defined
26038 \begin_layout Standard
26039 To use a function that is not predefined, like for example the sign function
26040 sgn(x), there are two possibilities:
26043 \begin_layout Itemize
26044 Define the function by inserting the following line to the \SpecialChar LaTeX
26049 \begin_layout Plain Layout
26054 DeclareMathOperator
26057 \begin_inset CommandInset ref
26059 reference "subsec:Self-defined-Operators"
26069 \begin_inset Newline newline
26073 \begin_inset VSpace -3mm
26077 \begin_inset Newline newline
26084 DeclareMathOperator{
26089 \begin_inset Index idx
26092 \begin_layout Plain Layout
26097 DeclareMathOperator
26103 \begin_inset Newline newline
26107 \begin_inset VSpace -2mm
26111 \begin_inset Newline newline
26114 Now the new defined function can be called with the command
26123 \begin_layout Itemize
26124 Write the formula as usual, mark the formula name, in our example the letters
26129 , and change it to mathematical text.
26130 Finally, a space is inserted between prefactor and function.
26133 \begin_layout Standard
26134 The result is the same with both methods as with a predefined function
26138 \begin_layout Plain Layout
26139 In \SpecialChar LyX
26140 self-defined functions are displayed red, predefined ones black.
26146 \begin_inset Separator parbreak
26152 \begin_layout Standard
26154 \begin_inset Tabular
26155 <lyxtabular version="3" rows="3" columns="2">
26156 <features tabularvalignment="middle">
26157 <column alignment="center" valignment="top" width="0pt">
26158 <column alignment="center" valignment="top" width="0pt">
26160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26163 \begin_layout Plain Layout
26169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26172 \begin_layout Plain Layout
26180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26183 \begin_layout Plain Layout
26191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26194 \begin_layout Plain Layout
26195 \begin_inset Formula $A\sgn(x)+B$
26205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26208 \begin_layout Plain Layout
26212 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
26220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26223 \begin_layout Plain Layout
26224 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
26240 \begin_layout Standard
26241 The first method is more suitable when the self-defined function should
26242 be used several times.
26245 \begin_layout Subsection
26247 \begin_inset Index idx
26250 \begin_layout Plain Layout
26259 \begin_layout Standard
26260 For limits, in addition to the commands
26267 \begin_inset Index idx
26270 \begin_layout Plain Layout
26290 the following functions are defined:
26291 \begin_inset Separator parbreak
26297 \begin_layout Standard
26299 \begin_inset Tabular
26300 <lyxtabular version="3" rows="5" columns="2">
26301 <features tabularvalignment="middle">
26302 <column alignment="center" valignment="top">
26303 <column alignment="center" valignment="top">
26305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26308 \begin_layout Plain Layout
26314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26317 \begin_layout Plain Layout
26319 \begin_inset Note Note
26322 \begin_layout Plain Layout
26329 is only used as spacer.
26341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26344 \begin_layout Plain Layout
26352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26355 \begin_layout Plain Layout
26356 \begin_inset Formula $\varliminf$
26366 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26369 \begin_layout Plain Layout
26377 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26380 \begin_layout Plain Layout
26381 \begin_inset Formula $\varlimsup$
26391 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26394 \begin_layout Plain Layout
26402 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26405 \begin_layout Plain Layout
26406 \begin_inset Formula $\varprojlim$
26416 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26419 \begin_layout Plain Layout
26427 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26430 \begin_layout Plain Layout
26431 \begin_inset Formula $\varinjlim$
26435 \begin_inset Formula $\raisebox{-2.5mm}{}$
26451 \begin_layout Standard
26452 \begin_inset VSpace medskip
26455 The limit is created by inserting a subscript.
26456 It is set right beside the function in an inline formula:
26459 \begin_layout Standard
26461 \begin_inset Tabular
26462 <lyxtabular version="3" rows="2" columns="2">
26463 <features tabularvalignment="middle">
26464 <column alignment="center" valignment="top" width="0pt">
26465 <column alignment="center" valignment="top" width="0pt">
26467 <cell alignment="center" valignment="top" usebox="none">
26470 \begin_layout Plain Layout
26476 <cell alignment="center" valignment="top" usebox="none">
26479 \begin_layout Plain Layout
26480 \begin_inset space \hspace{}
26485 \begin_inset Note Note
26488 \begin_layout Plain Layout
26495 are used here as spacer.
26507 <cell alignment="center" valignment="top" usebox="none">
26510 \begin_layout Plain Layout
26516 \begin_inset space \textvisiblespace{}
26520 \begin_inset space \textvisiblespace{}
26528 <cell alignment="center" valignment="top" usebox="none">
26531 \begin_layout Plain Layout
26532 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
26548 \begin_layout Standard
26549 In a displayed formula the limit is set below the formula, as usual:
26550 \begin_inset Formula
26560 \begin_layout Standard
26561 \begin_inset VSpace medskip
26567 \begin_layout Standard
26568 How to adjust the typesetting of the limits see
26569 \begin_inset CommandInset ref
26571 reference "subsec:Operator-Limits"
26578 \begin_layout Subsection
26580 \begin_inset Index idx
26583 \begin_layout Plain Layout
26584 Functions ! modulo-
26592 \begin_layout Standard
26593 The modulo-function is special, because it exists in four variants.
26594 The variants in a displayed formula are:
26595 \begin_inset Formula
26597 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26598 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
26599 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
26600 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
26601 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
26609 \begin_layout Standard
26610 In an inline formula less space is set before the function names for all
26612 By default the modulo-functions take only the first following character
26614 To use more than one character, one has to put them into \SpecialChar TeX
26616 \begin_inset Formula
26618 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26619 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
26620 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26628 \begin_layout Section
26630 \begin_inset Index idx
26633 \begin_layout Plain Layout
26642 \begin_layout Standard
26643 The characters ^ and _ would normally create a superscript and subscript,
26645 To get these characters you have to insert them with a leading
26648 \begin_inset Separator parbreak
26654 \begin_layout Standard
26657 \begin_inset Tabular
26658 <lyxtabular version="3" rows="3" columns="2">
26659 <features tabularvalignment="middle">
26660 <column alignment="block" valignment="top">
26661 <column alignment="block" valignment="top">
26663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26666 \begin_layout Plain Layout
26672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26675 \begin_layout Plain Layout
26683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26686 \begin_layout Plain Layout
26690 \begin_inset space \textvisiblespace{}
26698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26701 \begin_layout Plain Layout
26702 \begin_inset Formula $\mathcircumflex$
26712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26715 \begin_layout Plain Layout
26723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26726 \begin_layout Plain Layout
26727 \begin_inset Formula $\_$
26743 \begin_layout Subsection
26744 Special Characters in Mathematical Text
26747 \begin_layout Standard
26748 The following commands can only be used in mathematical text or in \SpecialChar TeX
26752 \begin_layout Standard
26753 \begin_inset space \hfill{}
26757 \begin_inset Tabular
26758 <lyxtabular version="3" rows="8" columns="2">
26759 <features tabularvalignment="middle">
26760 <column alignment="block" valignment="top">
26761 <column alignment="block" valignment="top">
26763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26766 \begin_layout Plain Layout
26772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26775 \begin_layout Plain Layout
26783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26786 \begin_layout Plain Layout
26794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26797 \begin_layout Plain Layout
26798 \begin_inset Formula $\textrm{œ}$
26808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26811 \begin_layout Plain Layout
26819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26822 \begin_layout Plain Layout
26823 \begin_inset Formula $\textrm{Œ}$
26833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26836 \begin_layout Plain Layout
26844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26847 \begin_layout Plain Layout
26848 \begin_inset Formula $\textrm{æ}$
26858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26861 \begin_layout Plain Layout
26869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26872 \begin_layout Plain Layout
26873 \begin_inset Formula $\textrm{Æ}$
26883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26886 \begin_layout Plain Layout
26894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26897 \begin_layout Plain Layout
26898 \begin_inset Formula $\textrm{\aa}$
26908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26911 \begin_layout Plain Layout
26915 \begin_inset Index idx
26918 \begin_layout Plain Layout
26925 \begin_layout Plain Layout
26946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26949 \begin_layout Plain Layout
26950 \begin_inset Formula $\textrm{Å}$
26960 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26963 \begin_layout Plain Layout
26971 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26974 \begin_layout Plain Layout
26975 \begin_inset Formula $\textrm{ı}$
26989 \begin_inset space \hfill{}
26993 \begin_inset Tabular
26994 <lyxtabular version="3" rows="8" columns="2">
26995 <features tabularvalignment="middle">
26996 <column alignment="block" valignment="top">
26997 <column alignment="center" valignment="top">
26999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27002 \begin_layout Plain Layout
27004 \begin_inset Note Note
27007 \begin_layout Plain Layout
27009 \begin_inset space \thinspace{}
27012 mm is used for separation, because otherwise the output will be ¡ and ¿
27023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27026 \begin_layout Plain Layout
27034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27037 \begin_layout Plain Layout
27045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27048 \begin_layout Plain Layout
27049 \begin_inset Formula $\textrm{ø}$
27059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27062 \begin_layout Plain Layout
27070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27073 \begin_layout Plain Layout
27074 \begin_inset Formula $\textrm{Ø}$
27084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27087 \begin_layout Plain Layout
27095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27098 \begin_layout Plain Layout
27099 \begin_inset Formula $\textrm{ł}$
27109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27112 \begin_layout Plain Layout
27120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27123 \begin_layout Plain Layout
27124 \begin_inset Formula $\textrm{Ł}$
27134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27137 \begin_layout Plain Layout
27139 \begin_inset space \hspace{}
27144 \begin_inset space \textvisiblespace{}
27152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27155 \begin_layout Plain Layout
27156 \begin_inset Formula $\textrm{!`}$
27166 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27169 \begin_layout Plain Layout
27171 \begin_inset space \hspace{}
27176 \begin_inset space \textvisiblespace{}
27184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27187 \begin_layout Plain Layout
27188 \begin_inset Formula $\textrm{?`}$
27198 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27201 \begin_layout Plain Layout
27209 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27212 \begin_layout Plain Layout
27213 \begin_inset Formula $\textrm{ȷ}$
27227 \begin_inset space \hfill{}
27233 \begin_layout Standard
27235 \begin_inset Formula $\textrm{\textrm{Å}}$
27239 \begin_inset Formula $\textrm{\textrm{Ø}}$
27242 can also be inserted via the math toolbar button
27245 arg "math-insert \\digamma"
27251 \begin_layout Standard
27252 An exception are the commands
27255 \begin_inset space \hspace{}
27264 \begin_inset space \hspace{}
27270 , because they can be inserted in \SpecialChar LyX
27274 \begin_layout Subsection
27276 \begin_inset CommandInset label
27278 name "subsec:Accents-in-Text"
27283 \begin_inset Index idx
27286 \begin_layout Plain Layout
27295 \begin_layout Standard
27296 With the following commands all letters can be accented.
27297 The commands must be inserted in \SpecialChar TeX
27301 \begin_layout Standard
27302 \begin_inset space \hfill{}
27306 \begin_inset Tabular
27307 <lyxtabular version="3" rows="8" columns="2">
27308 <features tabularvalignment="middle">
27309 <column alignment="block" valignment="top">
27310 <column alignment="block" valignment="top">
27312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27315 \begin_layout Plain Layout
27321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27324 \begin_layout Plain Layout
27332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27335 \begin_layout Plain Layout
27339 \begin_inset Quotes grd
27347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27350 \begin_layout Plain Layout
27354 \begin_layout Plain Layout
27370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27373 \begin_layout Plain Layout
27381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27384 \begin_layout Plain Layout
27388 \begin_layout Plain Layout
27404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27407 \begin_layout Plain Layout
27411 \begin_inset space \textvisiblespace{}
27419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27422 \begin_layout Plain Layout
27426 \begin_layout Plain Layout
27442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27445 \begin_layout Plain Layout
27453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27456 \begin_layout Plain Layout
27460 \begin_layout Plain Layout
27476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27479 \begin_layout Plain Layout
27483 \begin_inset space \textvisiblespace{}
27491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27494 \begin_layout Plain Layout
27498 \begin_layout Plain Layout
27514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27517 \begin_layout Plain Layout
27521 \begin_inset space \textvisiblespace{}
27529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27532 \begin_layout Plain Layout
27536 \begin_layout Plain Layout
27552 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27555 \begin_layout Plain Layout
27559 \begin_inset space \textvisiblespace{}
27567 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27570 \begin_layout Plain Layout
27574 \begin_layout Plain Layout
27594 \begin_inset space \hfill{}
27598 \begin_inset Tabular
27599 <lyxtabular version="3" rows="8" columns="2">
27600 <features tabularvalignment="middle">
27601 <column alignment="block" valignment="top">
27602 <column alignment="center" valignment="top">
27604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27607 \begin_layout Plain Layout
27613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27616 \begin_layout Plain Layout
27624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27627 \begin_layout Plain Layout
27631 \begin_inset space \textvisiblespace{}
27639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27642 \begin_layout Plain Layout
27646 \begin_layout Plain Layout
27662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27665 \begin_layout Plain Layout
27673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27676 \begin_layout Plain Layout
27680 \begin_layout Plain Layout
27696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27699 \begin_layout Plain Layout
27703 \begin_inset Index idx
27706 \begin_layout Plain Layout
27717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27720 \begin_layout Plain Layout
27724 \begin_layout Plain Layout
27740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27743 \begin_layout Plain Layout
27751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27754 \begin_layout Plain Layout
27758 \begin_layout Plain Layout
27774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27777 \begin_layout Plain Layout
27781 \begin_inset space \textvisiblespace{}
27789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27792 \begin_layout Plain Layout
27796 \begin_layout Plain Layout
27812 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27815 \begin_layout Plain Layout
27819 \begin_inset space \textvisiblespace{}
27827 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27830 \begin_layout Plain Layout
27834 \begin_layout Plain Layout
27850 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27853 \begin_layout Plain Layout
27857 \begin_inset space \textvisiblespace{}
27865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27868 \begin_layout Plain Layout
27872 \begin_layout Plain Layout
27892 \begin_inset space \hfill{}
27898 \begin_layout Standard
27899 \begin_inset VSpace medskip
27908 also two different characters can be accented.
27914 \begin_inset space \textvisiblespace{}
27923 \begin_layout Plain Layout
27935 \begin_layout Standard
27948 can in combination with vowels directly be inserted with the keyboard without
27949 using \SpecialChar TeX
27951 The same applies for the tilde
27955 \begin_layout Plain Layout
27956 This only applies for keyboards where the tilde is defined as accent.
27965 in combination with
27980 \begin_layout Standard
28023 and accents that are inserted directly with the keyboard are also available
28024 in mathematical text.
28025 For the other accents there are special math commands to be used in formulas,
28027 \begin_inset CommandInset ref
28029 reference "subsec:Accents-for-one"
28036 \begin_layout Standard
28037 \begin_inset VSpace bigskip
28040 Furthermore, with the command
28047 \begin_inset Index idx
28050 \begin_layout Plain Layout
28058 all numbers and letters can be set into a circle, quasi accented with a
28059 circle, similar to the copyright symbol.
28062 \begin_layout Standard
28064 \begin_inset Tabular
28065 <lyxtabular version="3" rows="3" columns="2">
28066 <features tabularvalignment="middle">
28067 <column alignment="center" valignment="top">
28068 <column alignment="center" valignment="top">
28070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28073 \begin_layout Plain Layout
28079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
28082 \begin_layout Plain Layout
28084 \begin_inset Note Note
28087 \begin_layout Plain Layout
28094 is only used as spacer.
28106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
28109 \begin_layout Plain Layout
28117 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
28120 \begin_layout Plain Layout
28124 \begin_layout Plain Layout
28140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28143 \begin_layout Plain Layout
28154 raisebox{-1.5pt}{W}}
28159 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
28162 \begin_layout Plain Layout
28163 \begin_inset Formula $\raisebox{4.5mm}{}$
28170 \begin_layout Plain Layout
28188 \begin_inset Formula $\raisebox{-2mm}{}$
28204 \begin_layout Standard
28205 One has to take care that the character fits in the circle.
28216 \begin_layout Plain Layout
28218 \begin_inset CommandInset ref
28220 reference "subsec:Font-Sizes"
28229 specifies thereby the size of the circle.
28240 \begin_layout Plain Layout
28242 \begin_inset CommandInset ref
28244 reference "subsec:Boxes-without-Frame"
28253 the character can be centered.
28256 \begin_layout Subsection
28258 \begin_inset Index idx
28261 \begin_layout Plain Layout
28270 \begin_layout Standard
28271 Old-style figures (also known as old-style numerals) are created with the
28279 \begin_inset Index idx
28282 \begin_layout Plain Layout
28291 The command can be used in formulas and in \SpecialChar TeX
28293 The command scheme is:
28296 \begin_layout Standard
28301 oldstylenums{number}
28304 \begin_layout Standard
28309 oldstylenums{0123456789
28312 \begin_inset Formula $\oldstylenums{0123456789}$
28318 \begin_layout Section
28320 \begin_inset CommandInset label
28322 name "sec:Formula-Styles"
28327 \begin_inset Index idx
28330 \begin_layout Plain Layout
28339 \begin_layout Itemize
28340 There are two different alignment styles:
28341 \begin_inset Separator parbreak
28348 \begin_layout Description
28349 Centered is the predefined standard
28352 \begin_layout Description
28353 Indented for this the option
28357 must be inserted in the menu
28359 Document\SpecialChar menuseparator
28365 \begin_inset space ~
28371 \begin_layout Standard
28376 is used, the indentation can be adjusted with the length
28383 \begin_inset Index idx
28386 \begin_layout Plain Layout
28395 Should the distance be 15
28396 \begin_inset space \thinspace{}
28399 mm, the following command line is inserted in the \SpecialChar LaTeX
28403 \begin_layout Standard
28413 \begin_layout Standard
28414 When no length is specified, the predefined value of 30
28415 \begin_inset space \thinspace{}
28422 \begin_layout Itemize
28423 And two different numbering styles:
28424 \begin_inset Separator parbreak
28431 \begin_layout Description
28432 Right is the predefined standard
28435 \begin_layout Description
28436 Left for this the option
28440 must be inserted in the menu
28442 Document\SpecialChar menuseparator
28448 \begin_inset space ~
28455 \begin_layout Standard
28464 can also be used together.
28465 In this case both options are inserted, separated by a comma.
28468 \begin_layout Standard
28469 The chosen styles are used for all displayed formulas of the document.
28470 When both, centered and indented formulas should be created in a document,
28476 The indented formulas are then set in a flalign environment, see
28477 \begin_inset CommandInset ref
28479 reference "subsec:Flalign-Environment"
28486 \begin_layout Section
28488 \begin_inset CommandInset label
28490 name "sec:Multiline-Formulas"
28495 \begin_inset Index idx
28498 \begin_layout Plain Layout
28499 Formula ! multiline
28507 \begin_layout Subsection
28511 \begin_layout Standard
28512 In \SpecialChar LyX
28513 multiline formulas are created by pressing
28516 arg "newline-insert newline"
28520 This creates either an
28522 eqnarray environment
28524 that is described in
28525 \begin_inset CommandInset ref
28527 reference "subsec:Eqnarray-Environment"
28531 or, when the option
28533 Use AMS math package
28535 in the document settings is selected, an
28539 that is described in
28540 \begin_inset CommandInset ref
28542 reference "subsec:Standard-align-Environment"
28547 The align environment is recommended because it provides in any case a
28548 typographically correct output.
28551 \begin_layout Standard
28552 There are other multiline formula environments that can be created via the
28555 Insert\SpecialChar menuseparator
28559 These environments are described in the following sections.
28562 \begin_layout Standard
28563 In all multiline formula environments a new line is created by pressing
28567 arg "newline-insert newline"
28571 To add or delete lines, the math toolbar buttons
28574 arg "inset-modify tabular append-row"
28580 arg "inset-modify tabular delete-row"
28583 , respectively, or the menu
28585 Edit\SpecialChar menuseparator
28591 \begin_layout Subsubsection
28593 \begin_inset CommandInset label
28595 name "subsec:Line-Separation"
28600 \begin_inset Index idx
28603 \begin_layout Plain Layout
28604 Formula ! multiline ! Line separation
28612 \begin_layout Standard
28613 There is sometimes not enough space in multiline formulas between the lines:
28614 \begin_inset Formula
28616 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}\\
28617 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
28625 \begin_layout Standard
28626 In \SpecialChar LaTeX
28627 additional line space is specified as optional argument of the new line
28629 This is not yet possible in \SpecialChar LyX
28634 \begin_layout Plain Layout
28636 \begin_inset CommandInset href
28638 name "LyX-bug #1505"
28639 target "http://www.lyx.org/trac/ticket/1505"
28648 , therefore the whole formula must be inserted in \SpecialChar TeX
28650 To add in our example space, the command
28658 is inserted at the end of the first line.
28663 \begin_layout Plain Layout
28670 \begin_layout Plain Layout
28672 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28675 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28682 \begin_layout Plain Layout
28686 left(B^{2}+x_{0}^{2}
28694 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28699 \begin_layout Plain Layout
28711 \begin_layout Standard
28712 \begin_inset VSpace bigskip
28715 To set the line separation for all lines in a formula, the length
28722 \begin_inset Index idx
28725 \begin_layout Plain Layout
28735 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
28746 \begin_inset space \thinspace{}
28751 \begin_inset space \thinspace{}
28754 mm additional line separation as in the previous example, the command
28757 \begin_layout Standard
28767 \begin_layout Standard
28768 is inserted in \SpecialChar TeX
28769 mode before the formula.
28770 This requires that the \SpecialChar LaTeX
28779 \begin_layout Plain Layout
28784 is part of every \SpecialChar LaTeX
28785 standard installation.
28791 \begin_inset Index idx
28794 \begin_layout Plain Layout
28800 was loaded in \SpecialChar LaTeX
28801 -preamble with the line
28804 \begin_layout Standard
28812 \begin_layout Standard
28817 \begin_layout Plain Layout
28829 \begin_inset Formula
28831 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}\\
28832 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
28840 \begin_layout Standard
28844 \begin_layout Plain Layout
28855 To get back to the predefined distance,
28861 is set to the value 3
28862 \begin_inset space \thinspace{}
28868 \begin_layout Subsubsection
28870 \begin_inset CommandInset label
28872 name "subsec:Column-Separation"
28877 \begin_inset Index idx
28880 \begin_layout Plain Layout
28881 Formula ! multiline ! Column separation
28889 \begin_layout Standard
28890 Multiline formulas form a matrix.
28891 A formula in the eqnarray environment is for example a matrix with three
28893 By changing the column separation in this environment, the space beside
28894 the relation sign can be changed.
28897 \begin_layout Standard
28898 The column separation is specified with the length
28905 \begin_inset Index idx
28908 \begin_layout Plain Layout
28917 \begin_inset Newline newline
28920 column separation = 2
28921 \begin_inset space \thinspace{}
28931 \begin_inset Newline newline
28937 \begin_layout Standard
28947 \begin_layout Standard
28948 inserted in \SpecialChar TeX
28949 mode, sets for all following formulas a column separation of
28951 \begin_inset space \thinspace{}
28955 To get back to the predefined distance,
28962 \begin_inset space \thinspace{}
28968 \begin_layout Standard
28970 \begin_inset space \thinspace{}
28973 cm column separation:
28977 \begin_layout Plain Layout
28989 \begin_inset Formula
28997 A formula with the predefined column separation for matrices of 10
28998 \begin_inset space \thinspace{}
29005 \begin_layout Plain Layout
29017 \begin_inset Formula
29028 \begin_layout Subsubsection
29030 \begin_inset Index idx
29033 \begin_layout Plain Layout
29042 \begin_layout Standard
29043 Long formulas can be typeset using these methods:
29046 \begin_layout Itemize
29047 When one side of the equation is much shorter than the line width, this
29048 one is chosen for the left side and the right side is typeset over two
29050 \begin_inset Formula
29052 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 \\
29053 & & -\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}
29058 The minus sign at the beginning of the second line does normally not appear
29059 as an operator because it is the first character of the line.
29060 Thus it would not be surrounded by space and could not be distinguished
29061 from the fraction bar.
29063 \begin_inset space \thinspace{}
29066 pt space was inserted behind the minus sign with the command
29076 \begin_layout Plain Layout
29084 \begin_inset CommandInset ref
29086 reference "subsec:Variable-Space"
29096 \begin_inset Index idx
29099 \begin_layout Plain Layout
29110 \begin_layout Itemize
29111 When both sides of the equation are too long, the command
29118 \begin_inset Index idx
29121 \begin_layout Plain Layout
29130 It is inserted in the first column of the first line and causes all further
29131 insertions to overwrite the following columns:
29132 \begin_inset Formula
29134 \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 \\
29135 & & -\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 \\
29136 & & =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}
29141 After the insertion of
29147 , the cursor is in a purple box that is a bit shifted to the left from the
29149 In this the formula is inserted.
29150 \begin_inset Newline newline
29153 The content of the further lines is inserted to the second or another formula
29155 The greater the column number where it was inserted, the larger the indentation.
29156 \begin_inset VSpace medskip
29160 \begin_inset Newline newline
29164 \begin_inset Note Greyedout
29167 \begin_layout Plain Layout
29168 Note the following when using
29177 \begin_layout Itemize
29178 The formula doesn't use the full page width.
29180 \begin_inset space \thinspace{}
29184 \begin_inset space \space{}
29188 \begin_inset Formula $-B^{2}$
29191 is added to the first line in the above example, it would have been outside
29193 To better use the width, negative space can be inserted at the beginning
29197 \begin_layout Itemize
29198 Due to a bug in \SpecialChar LyX
29199 the cursor cannot be set with the mouse into the first
29204 \begin_layout Plain Layout
29205 \begin_inset CommandInset href
29207 name "LyX-bug #1429"
29208 target "http://www.lyx.org/trac/ticket/1429"
29217 One can only set the cursor at the beginning of the line and move it with
29226 \begin_layout Itemize
29227 Other methods to set long formulas are offered by the environments described
29229 \begin_inset CommandInset ref
29231 reference "subsec:Multline-Environment"
29236 \begin_inset CommandInset ref
29238 reference "subsec:Multiline-Formula-Parts"
29245 \begin_layout Subsubsection
29246 Multiline Fractions
29247 \begin_inset CommandInset label
29249 name "subsec:Multiline-Fractions"
29254 \begin_inset Index idx
29257 \begin_layout Plain Layout
29258 Fractions ! multiline
29266 \begin_layout Standard
29267 There are cases where the denominator and/or the numerator of a fraction
29268 is so long that the fraction does not fit into one line.
29269 It is then necessary to add a line break within the fraction.
29270 This can be done using the command
29277 \begin_inset Index idx
29280 \begin_layout Plain Layout
29289 To activate it, set in the document settings under
29292 \begin_inset space ~
29302 \begin_inset Index idx
29305 \begin_layout Plain Layout
29306 Packages ! mathtools
29314 \begin_inset space ~
29329 \begin_layout Standard
29334 splitfrac{first line}{second line}
29337 \begin_layout Standard
29338 and is used as denominator and/or numerator:
29341 \begin_layout Standard
29342 \begin_inset Formula
29344 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}
29349 The command for the first numerator above is:
29352 \begin_layout Standard
29357 splitfrac{xy+xy+xy+xy+xy
29358 \begin_inset space \textvisiblespace{}
29366 \begin_layout Subsubsection
29368 \begin_inset CommandInset label
29370 name "subsec:Multiline-Brackets"
29375 \begin_inset Index idx
29378 \begin_layout Plain Layout
29379 Brackets ! for multiline expressions
29387 \begin_layout Standard
29388 For brackets spanning multiple lines the following problem occurs:
29389 \begin_inset Formula
29391 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29392 & & \left.\cdots+B-D\right]
29400 \begin_layout Standard
29401 The closing bracket is smaller than the opening bracket because brackets
29402 with variable size may not span multiple lines.
29405 \begin_layout Standard
29406 To set the bracket size for the second line correctly, the first line is
29414 \begin_inset Index idx
29417 \begin_layout Plain Layout
29425 and the second line with
29433 \begin_layout Plain Layout
29447 \begin_inset CommandInset ref
29449 reference "subsec:Automatic-Bracket-Size"
29461 \begin_inset Index idx
29464 \begin_layout Plain Layout
29487 \begin_inset space \textvisiblespace{}
29497 \begin_inset space \textvisiblespace{}
29507 \begin_inset space \textvisiblespace{}
29513 \begin_inset Formula $\downarrow$
29519 \begin_inset Index idx
29522 \begin_layout Plain Layout
29530 is inserted, because the multiplication operator with its limits is the
29531 largest symbol in the first line and this should be the size for the bracket
29532 in the second line.
29535 \begin_layout Standard
29536 The result is this:
29537 \begin_inset Formula
29539 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29540 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29548 \begin_layout Subsection
29552 \begin_layout Standard
29553 Align environments can be used for every kind of multiline formulas.
29554 They are especially useful to set several formulas side by side.
29557 \begin_layout Standard
29558 Align environments consist of columns.
29559 The odd columns are right aligned, the even ones left aligned.
29560 Every line in an Align environment can be numbered.
29563 \begin_layout Standard
29564 Align environments are created via the menu
29566 Insert\SpecialChar menuseparator
29572 Edit\SpecialChar menuseparator
29573 Math\SpecialChar menuseparator
29574 Change Formula Type
29576 already existing formulas can be converted to Align environments.
29579 \begin_layout Standard
29580 To add or delete columns, the math toolbar buttons
29583 arg "inset-modify tabular append-column"
29589 arg "inset-modify tabular delete-column"
29592 , respectively, or the menu
29594 Edit\SpecialChar menuseparator
29600 \begin_layout Subsubsection
29601 Standard align Environment
29602 \begin_inset CommandInset label
29604 name "subsec:Standard-align-Environment"
29609 \begin_inset Index idx
29612 \begin_layout Plain Layout
29613 Formula ! multiline ! align environment
29621 \begin_layout Standard
29622 This Align environment is created by pressing
29625 arg "newline-insert newline"
29628 in a formula or by the menu
29630 Insert\SpecialChar menuseparator
29631 Math\SpecialChar menuseparator
29632 AMS align Environment
29637 \begin_layout Standard
29638 An example for two formulas set side by side, that are created with a four
29639 column align environment:
29640 \begin_inset Formula
29642 A & =\sin(B) & C & =D\\
29643 C & \ne A & B & \ne D
29648 As it can be seen, the formulas in this environment are placed so as if
29657 \begin_layout Plain Layout
29665 \begin_inset CommandInset ref
29667 reference "subsec:Variable-Space"
29678 before the first and after every even column.
29679 When the formula style
29685 \begin_layout Plain Layout
29687 \begin_inset CommandInset ref
29689 reference "sec:Formula-Styles"
29700 is used, the formula is set without the
29706 before the first column.
29709 \begin_layout Subsubsection
29710 Alignat Environment
29711 \begin_inset Index idx
29714 \begin_layout Plain Layout
29715 Formula ! multiline ! alignat environment
29723 \begin_layout Standard
29724 The alignat environment has no predefined column separation.
29725 It can be inserted manually with the spaces that are described
29726 \begin_inset CommandInset ref
29728 reference "subsec:Space"
29735 \begin_layout Standard
29736 The above example in the alignat environment where 1
29737 \begin_inset space \thinspace{}
29740 cm space was inserted at the beginning of the second formula:
29741 \begin_inset Formula
29742 \begin{alignat*}{2}
29743 A & =\sin(B) & \hspace{1cm}C & =D\\
29744 C & \ne A & B & \ne D
29749 Because the column separation can be set separately for every column, this
29750 environment is especially suitable to set three and more formulas side
29754 \begin_layout Subsubsection
29755 Flalign Environment
29756 \begin_inset CommandInset label
29758 name "subsec:Flalign-Environment"
29763 \begin_inset Index idx
29766 \begin_layout Plain Layout
29767 Formula ! multiline ! flalign environment
29775 \begin_layout Standard
29776 In this environment the first two columns are always set as much as possible
29777 to the left and the last two ones to the right.
29779 \begin_inset Formula
29781 A & =1 & B & =2 & C & =3\\
29782 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29790 \begin_layout Standard
29791 By creating a flalign environment with an odd number of columns where an
29792 empty \SpecialChar TeX
29793 brace is inserted to the last column, several formulas in a document
29794 can be set to the left, although the formula style
29799 As example the indented formula
29800 \begin_inset CommandInset ref
29802 reference "eq:VolInt"
29807 \begin_inset Formula
29809 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29814 The first two columns contain the formula.
29815 To indent it as with the formula style
29820 \begin_inset space \thinspace{}
29823 pt space was inserted at the beginning of the first column.
29826 \begin_layout Subsection
29827 Eqnarray Environment
29828 \begin_inset CommandInset label
29830 name "subsec:Eqnarray-Environment"
29835 \begin_inset Index idx
29838 \begin_layout Plain Layout
29839 Formula ! multiline ! eqnarray environment
29847 \begin_layout Standard
29848 When this environment has been created, three blue boxes appear.
29849 The content of the first box is right aligned, the content of the last
29851 The content of the middle box appears centered and a bit smaller, because
29852 it is designed to insert there only relation characters.
29853 \begin_inset Formula
29855 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29865 \begin_layout Subsection
29867 \begin_inset Index idx
29870 \begin_layout Plain Layout
29871 Formula ! multiline ! gather environment
29879 \begin_layout Standard
29880 This environment consists of only one centered column.
29881 Every line can be numbered.
29882 \begin_inset Formula
29893 \begin_layout Subsection
29894 Multline Environment
29895 \begin_inset CommandInset label
29897 name "subsec:Multline-Environment"
29902 \begin_inset Index idx
29905 \begin_layout Plain Layout
29906 Formula ! multiline ! multline environment
29914 \begin_layout Standard
29915 The multline environment consists, like the gather environment, of only
29917 But the first line is left aligned, the last one right aligned.
29918 All other lines are centered.
29919 Therefore this environment is suitable for long formulas.
29921 \begin_inset CommandInset ref
29923 reference "eq:lefteqn"
29927 in the multline environment:
29928 \begin_inset Formula
29930 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}\\
29931 -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}\\
29932 =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}}
29940 \begin_layout Standard
29941 In the output only the last (first) line of a multline environment appears
29942 numbered when the document numbering is right (left).
29946 \begin_layout Plain Layout
29947 numbering styles see
29948 \begin_inset CommandInset ref
29950 reference "sec:Formula-Styles"
29962 \begin_layout Standard
29970 \begin_inset Index idx
29973 \begin_layout Plain Layout
29988 \begin_inset Index idx
29991 \begin_layout Plain Layout
29999 a centered line can be right or left aligned, respectively.
30000 The commands are used as follows:
30003 \begin_layout Standard
30008 shoveright{line content}
30014 shoveleft{line content}
30017 \begin_layout Standard
30018 \begin_inset VSpace medskip
30028 \begin_inset Index idx
30031 \begin_layout Plain Layout
30039 specifies the distance of the first line from the left page margin.
30040 Predefined is the length 0
30041 \begin_inset space \thinspace{}
30047 \begin_layout Standard
30048 As example the above formula where the command
30051 \begin_layout Standard
30061 \begin_layout Standard
30062 was inserted in \SpecialChar TeX
30067 \begin_layout Plain Layout
30079 \begin_inset Formula
30081 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}\\
30082 \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}}\\
30083 =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}}
30092 \begin_layout Plain Layout
30103 The second line was left aligned using
30112 \begin_layout Subsection
30113 Multiline Formula Parts
30114 \begin_inset CommandInset label
30116 name "subsec:Multiline-Formula-Parts"
30121 \begin_inset Index idx
30124 \begin_layout Plain Layout
30125 Formula ! multiline ! formula parts
30133 \begin_layout Standard
30134 To display only parts of a formula with multiple lines, one of the following
30135 environments is used:
30152 They can be inserted via the menu
30154 Insert\SpecialChar menuseparator
30157 or by using the commands described in this section.
30160 \begin_layout Standard
30161 The first three have the same properties as the corresponding multiline
30162 formula environments, but it is possible to set further formula parts beside
30165 \begin_inset Formula
30167 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
30168 \Delta E\Delta t & \ge\frac{\hbar}{2}
30170 \right\} \textrm{Uncertainty relations}
30178 \begin_layout Standard
30179 To get this formula, a displayed formula is created where the command
30186 \begin_inset Index idx
30189 \begin_layout Plain Layout
30198 A purple box appears around the blue formula box where now columns and
30199 lines can be added.
30200 Outside the multiline environment other formula parts can be set, like
30204 \begin_layout Standard
30205 The aligned environment is also suitable for long formulas whose lines are
30206 horizontally aligned.
30207 Using aligned in a displayed formula has the advantage that the formula
30208 number is vertically centered behind the lines.
30210 \begin_inset CommandInset ref
30212 reference "eq:shortlong"
30216 in the aligned environment:
30217 \begin_inset Formula
30219 \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}|}\\
30220 & -\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}|}
30229 \begin_layout Standard
30230 To use the environments
30249 \begin_inset Index idx
30252 \begin_layout Plain Layout
30267 \begin_inset Index idx
30270 \begin_layout Plain Layout
30285 \begin_inset Index idx
30288 \begin_layout Plain Layout
30296 are inserted, respectively.
30297 The split environment has the same properties as the aligned environment
30298 but it can only have two columns.
30301 \begin_layout Subsection
30302 Text in multiline Formulas
30303 \begin_inset CommandInset label
30305 name "subsec:Text-in-multiline"
30310 \begin_inset Index idx
30313 \begin_layout Plain Layout
30320 \begin_inset Index idx
30323 \begin_layout Plain Layout
30324 Formula ! multiline ! text
30332 \begin_layout Standard
30333 In the Align environments, and the multline and gather environment, text
30334 can be inserted that will appear in a separate line and doesn't affect
30335 the column alignment.
30336 To do this, the command
30343 \begin_inset Index idx
30346 \begin_layout Plain Layout
30354 is used in the following scheme:
30357 \begin_layout Standard
30365 \begin_layout Standard
30366 The text should not be longer than a line because it cannot be hyphenated.
30367 As \SpecialChar LyX
30368 doesn't yet support
30374 directly, the text is written as mathematical text.
30381 must hereby be at the beginning of a line and appears in the output above
30383 An example where the text was inserted at the beginning of the second line:
30384 \begin_inset Formula
30386 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
30387 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
30395 \begin_layout Standard
30402 always creates some vertical space between the text and the formula lines.
30403 To avoid this space, set in the document settings under
30406 \begin_inset space ~
30416 \begin_inset Index idx
30419 \begin_layout Plain Layout
30420 Packages ! mathtools
30428 \begin_inset space ~
30434 Then you can use the command
30441 \begin_inset Index idx
30444 \begin_layout Plain Layout
30461 \begin_layout Standard
30462 \begin_inset Formula
30464 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
30465 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
30473 \begin_layout Section
30475 \begin_inset Index idx
30478 \begin_layout Plain Layout
30485 \begin_inset Index idx
30488 \begin_layout Plain Layout
30489 Formula ! numbering|see
30493 \begin_layout Plain Layout
30504 \begin_layout Plain Layout
30519 \begin_layout Subsection
30523 \begin_layout Standard
30524 Numbered formulas can be created with the menu
30526 Insert\SpecialChar menuseparator
30527 Math\SpecialChar menuseparator
30529 \begin_inset space ~
30537 \begin_inset space ~
30543 Existing formulas can be numbered with the menu
30545 Edit\SpecialChar menuseparator
30546 Math\SpecialChar menuseparator
30548 \begin_inset space ~
30556 arg "math-number-toggle"
30560 The formula number is displayed in \SpecialChar LyX
30561 behind the formula as a number sign
30563 The number sign is replaced in the output by the formula number.
30566 \begin_layout Standard
30567 When numbering is turned on in multiline formulas, all lines will be numbered.
30568 But the numbering can be controlled with the menu
30570 Edit\SpecialChar menuseparator
30571 Math\SpecialChar menuseparator
30573 \begin_inset space ~
30577 \begin_inset space ~
30581 \begin_inset space ~
30589 arg "math-number-line-toggle"
30595 \begin_layout Standard
30596 Except for inline formulas, all formulas can be numbered with two different
30598 \begin_inset CommandInset ref
30600 reference "sec:Formula-Styles"
30607 \begin_layout Subsection
30609 \begin_inset Index idx
30612 \begin_layout Plain Layout
30613 Cross-references ! to formulas
30621 \begin_layout Standard
30622 All labeled formulas can be cross-referenced.
30623 A label is added by the menu
30625 Insert\SpecialChar menuseparator
30628 or the toolbar button
30635 The cursor must hereby be inside a displayed formula.
30636 Alternatively you can right-click on the formula and choose
30641 A dialog pops up displaying the prefix
30646 The label is inserted there behind the prefix.
30647 The predefined prefix means
30648 \begin_inset Quotes eld
30652 \begin_inset Quotes erd
30655 and makes it easier to find labels in large documents because it marks
30656 it as formula label to divide it from e.
30657 \begin_inset space \thinspace{}
30661 \begin_inset space \space{}
30665 To change a label, the menu
30667 Insert\SpecialChar menuseparator
30670 is used again or you right-click on a formula and then on
30677 \begin_layout Standard
30678 The name of the label is displayed in \SpecialChar LyX
30679 within two parentheses behind formula.
30680 A formula with a label is always numbered.
30683 \begin_layout Standard
30684 Cross-references are inserted via the menu
30686 Insert\SpecialChar menuseparator
30689 or with the toolbar button
30692 arg "dialog-show-new-inset ref"
30696 A formula cross-reference appears in the output as formula number.
30697 When in the cross-reference dialog window the format
30701 is chosen, the cross-reference appears in the output as formula number
30703 \begin_inset Newline newline
30706 By right-clicking on a cross-reference in \SpecialChar LyX
30707 , one jumps to the formula that
30711 \begin_layout Standard
30712 Here are as examples cross-references to formulas of the following subsections:
30713 \begin_inset Note Note
30716 \begin_layout Plain Layout
30717 Note the different cross-reference types.
30725 \begin_layout Standard
30727 \begin_inset CommandInset ref
30734 \begin_inset CommandInset ref
30742 \begin_inset CommandInset ref
30748 ) big Latin letters are used for the numbering in contrary to (
30749 \begin_inset CommandInset ref
30758 \begin_layout Standard
30759 \begin_inset VSpace medskip
30762 When the argument of
30770 \begin_layout Plain Layout
30778 \begin_inset CommandInset ref
30780 reference "subsec:User-defined-Numbering"
30791 contains a box like in
30792 \begin_inset CommandInset ref
30794 reference "subsec:Paragraph-Boxes"
30798 , the formula cannot be referenced.
30801 \begin_layout Subsection
30803 \begin_inset Index idx
30806 \begin_layout Plain Layout
30807 Formula numbering ! subnumbering
30815 \begin_layout Standard
30816 With the help of the commands
30820 begin{subequations}
30828 formulas can be subnumbered.
30829 Both commands are inserted in \SpecialChar TeX
30833 \begin_layout Standard
30835 \begin_inset Formula
30846 \begin_layout Plain Layout
30850 addtocounter{equation}{-1}
30859 \begin_layout Plain Layout
30863 begin{subequations}
30869 \begin_inset VSpace -5mm
30873 \begin_inset Formula
30881 \begin_inset Formula
30891 \begin_layout Standard
30895 \begin_layout Plain Layout
30907 \begin_layout Standard
30908 To create the example, the following is done:
30911 \begin_layout Enumerate
30912 first formula is inserted
30915 \begin_layout Enumerate
30920 addtocounter{equation}{-1}
30922 begin{subequations}
30923 \begin_inset Index idx
30926 \begin_layout Plain Layout
30935 \begin_inset Newline newline
30940 is inserted after the first formula
30943 \begin_layout Enumerate
30944 second formula is inserted
30947 \begin_layout Enumerate
30948 third formula is inserted
30951 \begin_layout Enumerate
30958 is inserted after the third formula
30961 \begin_layout Standard
30962 Every formula between the commands
30974 is subnumbered as a, b,
30975 \begin_inset Newline linebreak
30978 c, \SpecialChar ldots
30979 For multiline formulas every line will be subnumbered.
30980 All subnumbered formulas are treated as
30985 But as every numbered formula increases the counter
30989 by one, the command
30995 is needed to decrease it.
30996 Otherwise the formulas
30997 \begin_inset CommandInset ref
31004 \begin_inset CommandInset ref
31011 \begin_inset CommandInset ref
31017 would be numbered as
31018 \begin_inset CommandInset ref
31025 \begin_inset CommandInset ref
31032 \begin_inset CommandInset ref
31041 \begin_layout Standard
31042 By inserting the commands in \SpecialChar TeX
31043 mode, a space is created between the first
31046 \begin_inset space \thinspace{}
31049 mm vertical space is inserted after the command
31053 begin{subequations}
31056 When the formula style
31062 \begin_layout Plain Layout
31064 \begin_inset CommandInset ref
31066 reference "sec:Formula-Styles"
31078 \begin_inset space \thinspace{}
31081 mm space is inserted instead.
31084 \begin_layout Standard
31085 Here is an example for a multiline formula where the numbering was turned
31086 off for the second line:
31090 \begin_layout Plain Layout
31094 begin{subequations}
31100 \begin_inset Formula
31102 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
31103 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
31104 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
31113 \begin_layout Plain Layout
31125 \begin_layout Subsection
31126 User-defined Numbering
31127 \begin_inset CommandInset label
31129 name "subsec:User-defined-Numbering"
31134 \begin_inset Index idx
31137 \begin_layout Plain Layout
31138 Formula numbering ! user-defined
31146 \begin_layout Standard
31147 \begin_inset Index idx
31150 \begin_layout Plain Layout
31151 Formula numbering ! self-defined delimiters
31156 With the standard numbering parentheses are set around the formula number.
31157 To replace the parentheses for example by vertical bars, the following
31158 line is added to the \SpecialChar LaTeX
31162 \begin_layout Standard
31174 \begin_inset Note Note
31177 \begin_layout Plain Layout
31178 This macro is already declared in the \SpecialChar LaTeX
31179 -preamble for testing.
31180 To activate it, remove the percent sign at the beginning.
31188 \begin_layout Standard
31189 To use other characters, the vertical bars besides the
31193 are replaced by one ore more characters.
31194 To get only the formula number the vertical bars are omitted.
31197 \begin_layout Standard
31198 \begin_inset VSpace bigskip
31201 When there should be an expression of your choice instead of the consecutive
31202 formula number in parentheses behind the formula, the command
31209 \begin_inset Index idx
31212 \begin_layout Plain Layout
31221 \begin_inset Formula
31223 A+B=C\tag{something}\label{eq:tag}
31228 In this example the command
31233 \begin_inset space \textvisiblespace{}
31238 was inserted in the formula.
31241 \begin_layout Standard
31247 \begin_inset space \textvisiblespace{}
31252 is inserted instead, the star prevents the parentheses around the expression:
31253 \begin_inset Formula
31255 A+B=C\tag*{something}
31263 \begin_layout Standard
31264 \begin_inset VSpace bigskip
31267 To restart the formula numbering with new document parts or sections, the
31268 following command is used:
31271 \begin_layout Standard
31276 @addtoreset{equation}{part}
31279 \begin_inset Index idx
31282 \begin_layout Plain Layout
31287 \begin_layout Plain Layout
31298 \begin_layout Plain Layout
31311 \begin_layout Plain Layout
31322 \begin_layout Plain Layout
31335 \begin_inset Newline newline
31339 \begin_inset Newline newline
31346 @addtoreset{equation}{section}
31349 \begin_layout Standard
31350 To be able to use these commands in \SpecialChar TeX
31352 \begin_inset Quotes eld
31356 \begin_inset Quotes erd
31359 character has to be made
31360 \begin_inset Quotes eld
31364 \begin_inset Quotes erd
31367 for \SpecialChar LaTeX
31382 So the command sequence in \SpecialChar TeX
31386 \begin_layout Standard
31392 \begin_inset Newline newline
31397 @addtoreset{equation}{section}
31398 \begin_inset Newline newline
31406 \begin_layout Standard
31407 In the \SpecialChar LaTeX
31420 can be omitted as they are automatically internally inserted by \SpecialChar LyX
31424 \begin_layout Standard
31439 \begin_layout Plain Layout
31444 is part of the \SpecialChar LaTeX
31450 \begin_inset Index idx
31453 \begin_layout Plain Layout
31454 Packages ! carlisle
31459 that is part of every \SpecialChar LaTeX
31460 standard installation.
31466 \begin_inset Index idx
31469 \begin_layout Plain Layout
31470 Packages ! remreset
31475 has to be loaded in the \SpecialChar LaTeX
31476 -preamble with the line
31479 \begin_layout Standard
31484 usepackage{remreset}
31487 \begin_layout Standard
31495 \begin_inset Index idx
31498 \begin_layout Plain Layout
31503 \begin_layout Plain Layout
31514 \begin_layout Plain Layout
31527 \begin_layout Plain Layout
31538 \begin_layout Plain Layout
31550 can be used with the same scheme as
31559 \begin_layout Standard
31560 \begin_inset VSpace bigskip
31563 Sometimes formulas should be numbered in the following form:
31566 \begin_layout Standard
31569 (section number.formula number)
31572 \begin_layout Standard
31573 The formula number should start with every section with
31574 \begin_inset Quotes eld
31578 \begin_inset Quotes erd
31584 \begin_layout Standard
31585 For this case there is the command
31592 \begin_inset Index idx
31595 \begin_layout Plain Layout
31603 , which is used with the following scheme:
31606 \begin_layout Standard
31611 numberwithin{counter}{sectioning}
31614 \begin_layout Standard
31615 Counter denotes what kind of numbering is affected, sectioning denotes what
31616 number is before the dot.
31619 \begin_layout Standard
31620 Thus in our case the following \SpecialChar LaTeX
31621 preamble or \SpecialChar TeX
31625 \begin_layout Standard
31630 numberwithin{equation}{section}
31633 \begin_layout Standard
31634 This is the result:
31638 \begin_layout Plain Layout
31642 numberwithin{equation}{section}
31648 \begin_inset Formula
31658 \begin_layout Standard
31660 \begin_inset space \thinspace{}
31664 \begin_inset space \space{}
31667 tables so that the number of the part is the sectioning,
31668 \begin_inset Newline newline
31675 numberwithin{table}{part}
31680 \begin_layout Standard
31681 To go back to the standard numbering or to prevent this kind of numbering
31682 when it is defined by the document class, the following command is inserted
31683 as \SpecialChar TeX
31684 code or to the \SpecialChar LaTeX
31688 \begin_layout Standard
31698 \begin_inset Index idx
31701 \begin_layout Plain Layout
31715 \begin_layout Plain Layout
31731 \begin_inset Newline newline
31739 \begin_inset Newline newline
31751 \begin_layout Standard
31758 uses internally the command
31764 , described above, that also needs to be reverted.
31768 \begin_layout Plain Layout
31775 \begin_layout Plain Layout
31779 @removefromreset{equation}{section}
31782 \begin_layout Plain Layout
31794 \begin_layout Subsection
31795 Numbering with Roman Numbers and Letters
31796 \begin_inset Index idx
31799 \begin_layout Plain Layout
31800 Formula numbering ! with letters
31806 \begin_inset Index idx
31809 \begin_layout Plain Layout
31810 Formula numbering ! with Roman numbers
31818 \begin_layout Standard
31819 Formulas can also be numbered with Roman numbers and Latin letters.
31820 To number for example with small Roman numbers, the command
31823 \begin_layout Standard
31835 \begin_layout Standard
31836 is inserted before the formula in \SpecialChar TeX
31845 \begin_inset Index idx
31848 \begin_layout Plain Layout
31856 redefines the predefined command
31872 \begin_layout Plain Layout
31879 has the same scheme like the command
31885 that is described in
31886 \begin_inset CommandInset ref
31888 reference "subsec:The-Command-newcommand"
31901 is the formula counter.
31908 is used as prefix for a counter, the value of the counter is output as
31910 When a formula is numbered, \SpecialChar LaTeX
31911 sets internally the command
31917 behind the formula.
31923 \begin_inset Index idx
31926 \begin_layout Plain Layout
31936 outputs the counter as small Roman number.
31939 \begin_layout Standard
31940 All formulas behind the command
31950 are now numbered Roman.
31951 To switch to numbering with big Roman numbers, the command is inserted
31965 \begin_inset Index idx
31968 \begin_layout Plain Layout
31980 \begin_inset Quotes eld
31984 \begin_inset Quotes erd
31987 with small Latin letters there is the command
31994 \begin_inset Index idx
31997 \begin_layout Plain Layout
32005 , for big ones there is the command
32012 \begin_inset Index idx
32015 \begin_layout Plain Layout
32028 \begin_layout Standard
32029 \begin_inset Note Greyedout
32032 \begin_layout Plain Layout
32039 \begin_inset space ~
32042 formulas can be numbered with Latin letters in one document.
32050 \begin_layout Standard
32051 \begin_inset Newpage newpage
32057 \begin_layout Standard
32061 \begin_layout Plain Layout
32077 \begin_layout Standard
32078 \begin_inset Formula
32080 A=\textrm{small roman}
32089 \begin_layout Plain Layout
32103 \begin_inset Formula
32105 B=\textrm{big Roman}\label{eq:Rom}
32114 \begin_layout Plain Layout
32128 \begin_inset Formula
32130 C=\textrm{small Latin}
32139 \begin_layout Plain Layout
32153 \begin_inset Formula
32155 D=\textrm{big Latin}\label{eq:Lat}
32163 \begin_layout Standard
32164 To switch back to the default numbering, insert the command:
32167 \begin_layout Standard
32177 \begin_inset Index idx
32180 \begin_layout Plain Layout
32191 \begin_layout Standard
32195 \begin_layout Plain Layout
32209 \begin_inset Formula
32219 \begin_layout Standard
32220 \begin_inset VSpace medskip
32223 As you see, formulas are numbered serially independent from the numbering
32225 When then numbering should start with
32226 \begin_inset Quotes eld
32230 \begin_inset Quotes erd
32233 when the style is changed, new equation counters have to be defined.
32234 A description about this can be found in the file
32235 \begin_inset CommandInset href
32237 name "Formula-numbering.lyx"
32238 target "run:Formula-numbering.lyx"
32245 \begin_layout Section
32246 Chemical Symbols and Equations
32247 \begin_inset CommandInset label
32249 name "subsec:Chemical-Symbols-and"
32254 \begin_inset Index idx
32257 \begin_layout Plain Layout
32258 Chemical characters ! Symbols
32264 \begin_inset Index idx
32267 \begin_layout Plain Layout
32274 \begin_inset Index idx
32277 \begin_layout Plain Layout
32286 \begin_layout Standard
32287 An example text from chemistry:
32290 \begin_layout Quote
32292 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32295 -ion reacts with two
32296 \begin_inset Formula $\mathrm{Na^{+}}$
32299 -ions to sodium sulfate
32300 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32304 The chemical equation for this is:
32305 \begin_inset Formula
32307 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
32315 \begin_layout Standard
32316 This chemical equation can directly be created as formula.
32317 To avoid that the symbols appear italic, everything is highlighted and
32318 changed by the shortcut
32324 to the upright font style.
32328 \begin_layout Plain Layout
32334 \begin_inset CommandInset ref
32336 reference "subsec:Font-Styles"
32348 \begin_layout Standard
32349 A more convenient way to typeset chemical formulas is to use the command
32357 \begin_inset Index idx
32360 \begin_layout Plain Layout
32368 that is available when the \SpecialChar LaTeX
32374 \begin_inset Index idx
32377 \begin_layout Plain Layout
32390 to a formula a new blue box appears where chemical formulas can be inserted
32391 in an intuitive way.
32392 \begin_inset Separator parbreak
32398 \begin_layout Standard
32400 \begin_inset Tabular
32401 <lyxtabular version="3" rows="9" columns="2">
32402 <features tabularvalignment="middle">
32403 <column alignment="center" valignment="top">
32404 <column alignment="center" valignment="top">
32406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32409 \begin_layout Plain Layout
32415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32418 \begin_layout Plain Layout
32420 \begin_inset Note Note
32423 \begin_layout Plain Layout
32430 is only used as spacer.
32442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32445 \begin_layout Plain Layout
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 $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
32471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32474 \begin_layout Plain Layout
32478 \begin_inset space \textvisiblespace{}
32486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32489 \begin_layout Plain Layout
32490 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
32500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32503 \begin_layout Plain Layout
32507 \begin_inset space \textvisiblespace{}
32515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32518 \begin_layout Plain Layout
32519 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
32529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32532 \begin_layout Plain Layout
32536 \begin_inset space \textvisiblespace{}
32544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32547 \begin_layout Plain Layout
32548 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32561 \begin_layout Plain Layout
32565 \begin_inset space \textvisiblespace{}
32571 \begin_inset space \textvisiblespace{}
32577 \begin_inset space \textvisiblespace{}
32585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32588 \begin_layout Plain Layout
32589 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32602 \begin_layout Plain Layout
32606 \begin_inset space \textvisiblespace{}
32610 \begin_inset Formula $\downarrow$
32614 \begin_inset Formula $\to$
32622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32625 \begin_layout Plain Layout
32626 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32639 \begin_layout Plain Layout
32643 \begin_inset space \textvisiblespace{}
32647 \begin_inset space \textvisiblespace{}
32651 \begin_inset space \textvisiblespace{}
32655 \begin_inset space \textvisiblespace{}
32659 \begin_inset space \textvisiblespace{}
32667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32670 \begin_layout Plain Layout
32671 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32684 \begin_layout Plain Layout
32688 \begin_inset space \textvisiblespace{}
32692 \begin_inset space \textvisiblespace{}
32696 \begin_inset space \textvisiblespace{}
32700 \begin_inset space \textvisiblespace{}
32708 \begin_inset space \textvisiblespace{}
32716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32719 \begin_layout Plain Layout
32720 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32736 \begin_layout Standard
32737 \begin_inset Note Greyedout
32740 \begin_layout Plain Layout
32746 Inserting a formula to a
32752 box will lead to \SpecialChar LaTeX
32753 errors due to a \SpecialChar LyX
32760 \begin_layout Plain Layout
32761 \begin_inset CommandInset href
32763 name "LyX-bug #8566"
32764 target "http://www.lyx.org/trac/ticket/8566"
32775 In this case \SpecialChar TeX
32776 code has to be used like for
32790 \begin_layout Plain Layout
32811 \begin_layout Standard
32812 \begin_inset Note Greyedout
32815 \begin_layout Plain Layout
32821 It is not possible in \SpecialChar LyX
32822 to use the character ^ to get an up-arrow as described
32828 One instead uses a negative thin space followed by the command
32835 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32846 \begin_layout Standard
32853 the command for equation
32854 \begin_inset space ~
32858 \begin_inset CommandInset ref
32860 reference "eq:chem-reaction"
32865 \begin_inset Newline newline
32873 \begin_inset space \textvisiblespace{}
32877 \begin_inset space \textvisiblespace{}
32881 \begin_inset space \textvisiblespace{}
32885 \begin_inset space \textvisiblespace{}
32889 \begin_inset space \textvisiblespace{}
32893 \begin_inset space \textvisiblespace{}
32899 \begin_layout Standard
32900 To create multiline chemical equations first a multiline formula is created
32902 \begin_inset CommandInset ref
32904 reference "sec:Multiline-Formulas"
32909 Afterwards the command
32915 is used in every small blue box of the formula.
32917 \begin_inset CommandInset ref
32919 reference "eq:TEOS-reaction-1"
32924 \begin_inset CommandInset ref
32926 reference "eq:TEOS-reaction-2"
32930 are an example of a multi-stage chemical reaction where every equation
32931 has its own number.
32932 \begin_inset Formula
32934 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32935 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32943 \begin_layout Standard
32954 package provides the command
32961 \begin_inset Index idx
32964 \begin_layout Plain Layout
32972 that has to be used for special cases.
32973 For more information about
32979 and more examples have a look at the documentation of
32984 \begin_inset CommandInset citation
32993 \begin_layout Section
32997 \begin_layout Standard
32999 supports two types of commutative diagrams:
33007 that are explained in the following.
33010 \begin_layout Subsection
33012 \begin_inset Index idx
33015 \begin_layout Plain Layout
33024 \begin_layout Standard
33025 Diagrams of this type visualize relations by vertical and horizontal lines
33027 \begin_inset Formula
33029 \begin{CD}A@>>>B@>>>C\\
33040 \begin_layout Standard
33041 To get them, the command
33046 \begin_inset Index idx
33049 \begin_layout Plain Layout
33059 is inserted to a formula.
33060 A blue box appears with two dashed lines where further commands can be
33065 arg "newline-insert newline"
33068 a new line is created.
33069 Horizontal relations are inserted in odd, vertical in even formula lines.
33072 \begin_layout Standard
33073 To create the relations there are the following commands:
33076 \begin_layout Itemize
33081 creates a left arrow,
33092 \begin_layout Itemize
33097 creates an up arrow,
33105 a vertical equal sign
33108 \begin_layout Itemize
33114 is a placeholder for non-existent relations
33117 \begin_layout Standard
33118 All arrows can be labeled as follows:
33121 \begin_layout Itemize
33122 If text inserted between the first and second < or >, resp., it is placed
33124 When it is inserted between the second and third one, it appears under
33128 \begin_layout Itemize
33129 When text for vertical arrows is inserted between the first and second A
33130 or V, resp., it is placed left beside the arrow.
33131 When it is inserted between the second and third one, it appears right
33133 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
33137 \begin_layout Standard
33138 As example a diagram with all possible relations:
33141 \begin_layout Standard
33142 \begin_inset Formula
33144 \begin{CD}A@>j>>B@>>k>C@=F\\
33155 \begin_layout Standard
33156 The command for this is:
33157 \begin_inset Newline newline
33165 \begin_inset space \textvisiblespace{}
33168 A@>j>>B@>>k>C@=F Ctrl+Return
33169 \begin_inset Newline newline
33173 \begin_inset Phantom HPhantom
33176 \begin_layout Plain Layout
33182 \begin_inset space \textvisiblespace{}
33195 \begin_inset Formula $\to$
33201 \begin_inset Newline newline
33205 \begin_inset Phantom HPhantom
33208 \begin_layout Plain Layout
33214 \begin_inset space \textvisiblespace{}
33225 \begin_layout Subsection
33227 \begin_inset Index idx
33230 \begin_layout Plain Layout
33231 Diagrams ! xymatrix
33239 \begin_layout Standard
33240 To be able to use xymatrices, the \SpecialChar LaTeX
33246 A xymatrix is created by inserting the command
33253 Then you are able to add new matrix columns and rows like for normal matrices,
33255 \begin_inset CommandInset ref
33257 reference "sec:Matrices"
33264 \begin_layout Standard
33265 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
33267 All possibilities to create commutative diagrams and decorations are explained
33272 that you find in the menu
33274 Help\SpecialChar menuseparator
33276 \begin_inset space ~
33284 \begin_layout Subsection
33290 \begin_inset Index idx
33293 \begin_layout Plain Layout
33302 \begin_layout Standard
33307 -diagrams, the \SpecialChar LaTeX
33317 -diagram is created by inserting the command
33324 Then you are able to add new matrix columns and rows like for normal matrices,
33326 \begin_inset CommandInset ref
33328 reference "sec:Matrices"
33335 \begin_layout Standard
33336 Examples how to create
33340 diagrams in \SpecialChar LyX
33343 Feynman-diagram manual
33345 that you find in the menu
33347 Help\SpecialChar menuseparator
33349 \begin_inset space ~
33357 \begin_layout Section
33358 User-defined Commands
33359 \begin_inset Index idx
33362 \begin_layout Plain Layout
33363 User-defined commands
33371 \begin_layout Standard
33372 \begin_inset Note Greyedout
33375 \begin_layout Plain Layout
33380 The names of user-defined commands and macros may only consist of Latin
33389 \begin_layout Subsection
33393 \begin_inset CommandInset label
33395 name "subsec:The-Command-newcommand"
33400 \begin_inset Index idx
33403 \begin_layout Plain Layout
33404 User-defined commands !
33412 \begin_inset Index idx
33415 \begin_layout Plain Layout
33426 \begin_layout Standard
33427 Many \SpecialChar LaTeX
33428 -commands are too long to be used frequently.
33429 But it is possible to define with the command
33435 new shorter commands.
33438 \begin_layout Standard
33439 The command scheme of
33448 \begin_layout Standard
33453 newcommand{new command name}[number of arguments][optional
33458 \begin_inset Newline newline
33462 \begin_inset Phantom HPhantom
33465 \begin_layout Plain Layout
33475 {command definition}
33478 \begin_layout Standard
33479 \begin_inset Note Greyedout
33482 \begin_layout Plain Layout
33487 Assure that the name of the new command is not already used in your document
33488 or by \SpecialChar LaTeX
33489 -packages that you use.
33490 When you for example define the command
33502 , you get an error message because
33508 is already defined as command for
33509 \begin_inset Quotes eld
33513 \begin_inset Formula $\le$
33517 \begin_inset Quotes erd
33528 \begin_layout Standard
33529 The number of arguments is an integer in the range 0
33530 \begin_inset space \thinspace{}
33534 \begin_inset space \thinspace{}
33537 9 and specifies how many arguments the new command should have.
33538 With the optional value a value for an optional argument can be predefined.
33539 When this is done, the
33547 rgument of the new command is automatically an optional one.
33550 \begin_layout Standard
33551 Here are some examples:
33554 \begin_layout Itemize
33555 To define the command
33567 , the \SpecialChar LaTeX
33569 \begin_inset VSpace medskip
33573 \begin_inset Newline newline
33587 \begin_layout Itemize
33588 To define the command
33600 , the argument (that should be underlined) must be taken into account.
33601 For this the preamble line is:
33602 \begin_inset VSpace medskip
33606 \begin_inset Newline newline
33620 \begin_inset VSpace medskip
33624 \begin_inset Newline newline
33631 acts as argument placeholder, the
33635 behind it denotes that it is the placeholder for the first argument.
33638 \begin_layout Itemize
33646 \begin_inset space \thinspace{}
33650 \begin_inset space \space{}
33660 \begin_inset VSpace medskip
33664 \begin_inset Newline newline
33675 framebox#1#2{$#3$}}
33678 \begin_inset VSpace medskip
33682 \begin_inset Newline newline
33685 The two Dollar signs creates the extra formula needed for
33692 \begin_inset CommandInset ref
33694 reference "subsec:Boxes-with-Frame"
33701 \begin_layout Itemize
33702 To create a new command for
33708 where the color for the box need not be specified, the argument for the
33709 color is defined optional:
33710 \begin_inset VSpace medskip
33714 \begin_inset Newline newline
33725 fcolorbox{#2}{#1}{$#3$}}
33728 \begin_inset VSpace medskip
33732 \begin_inset Newline newline
33735 When the color is not specified when using
33741 , the predefined color
33748 \begin_layout Standard
33749 A test of the new defined commands:
33750 \begin_inset Separator parbreak
33756 \begin_layout Standard
33758 \begin_inset Tabular
33759 <lyxtabular version="3" rows="6" columns="2">
33760 <features tabularvalignment="middle">
33761 <column alignment="center" valignment="top">
33762 <column alignment="center" valignment="top">
33764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33767 \begin_layout Plain Layout
33773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33776 \begin_layout Plain Layout
33778 \begin_inset Note Note
33781 \begin_layout Plain Layout
33788 is only used as spacer.
33800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33803 \begin_layout Plain Layout
33807 \begin_inset space \textvisiblespace{}
33815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33818 \begin_layout Plain Layout
33819 \begin_inset Formula $A\gr B$
33829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33832 \begin_layout Plain Layout
33840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33843 \begin_layout Plain Layout
33844 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33857 \begin_layout Plain Layout
33861 \begin_inset Formula $\to$
33867 \begin_inset Formula $\to$
33875 \begin_inset space \textvisiblespace{}
33883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33886 \begin_layout Plain Layout
33887 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33900 \begin_layout Plain Layout
33904 \begin_inset Formula $\to$
33912 \begin_inset space \textvisiblespace{}
33920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33923 \begin_layout Plain Layout
33924 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33937 \begin_layout Plain Layout
33943 \begin_inset Formula $\to$
33951 \begin_inset space \textvisiblespace{}
33959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33962 \begin_layout Plain Layout
33963 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33979 \begin_layout Subsection
33981 \begin_inset Index idx
33984 \begin_layout Plain Layout
33985 User-defined commands! Math macros
33991 \begin_inset Index idx
33994 \begin_layout Plain Layout
34003 \begin_layout Standard
34004 User-defined commands are especially convenient for complex expressions.
34005 When you are for example dealing with a document that has quadratic equations,
34006 the same solution type occurs several times.
34007 The general form of a quadratic equation is
34008 \begin_inset Formula
34010 0=\lambda^{2}+p\lambda+q
34015 The general form of the solution is
34016 \begin_inset Formula
34018 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
34026 \begin_layout Standard
34027 To define a command for the solution formula where only the three parameters
34029 \begin_inset Formula $\lambda$
34033 \begin_inset Formula $p$
34037 \begin_inset Formula $q$
34040 need to be specified and the index of
34041 \begin_inset Formula $\lambda$
34044 can be given optionally, the \SpecialChar LaTeX
34046 \begin_inset Newline newline
34062 \begin_inset Newline newline
34066 \begin_inset Phantom HPhantom
34069 \begin_layout Plain Layout
34083 frac{#3^{2}}{4}-#4}}
34086 \begin_layout Standard
34087 To create with this the solution formula, the command
34088 \begin_inset Newline newline
34098 \begin_inset Formula $\to$
34104 \begin_inset Formula $\to$
34111 is inserted to a formula
34116 \begin_layout Standard
34117 The definition of the new command is unintuitive because one has to know
34118 the schemes of all used \SpecialChar LaTeX
34120 \begin_inset space \thinspace{}
34124 \begin_inset space \space{}
34127 that a fraction is inserted in \SpecialChar LaTeX
34132 frac{numerator}{denominator}
34135 Furthermore one can easily forget a brace in the definition and cannot
34136 see in \SpecialChar LyX
34137 what the new command is doing.
34138 To avoid these problems \SpecialChar LyX
34139 offers the possibility to use math macros instead
34149 \begin_layout Standard
34150 A math macro is created by using the menu
34152 Insert\SpecialChar menuseparator
34153 Math\SpecialChar menuseparator
34156 or the toolbar button
34159 arg "math-macro newmacroname_newcommand"
34163 The math macro toolbar appears together with the following box where the
34165 \begin_inset Newline newline
34169 \begin_inset space \hspace*{\fill}
34173 \begin_inset Graphics
34174 filename clipart/macrobox.png
34179 \begin_inset space \hspace*{\fill}
34183 \begin_inset Newline newline
34187 \begin_inset FormulaMacro
34188 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
34193 newmacroname is the default name of the macro that should be changed to
34194 something sensible.
34195 The wanted formula is inserted in the first blue box.
34196 An argument placeholder is inserted with the command
34203 \begin_inset space \thinspace{}
34207 \begin_inset space \space{}
34216 or by using the macro toolbar button
34219 arg "math-macro-add-param"
34223 Argument placeholders are displayed red.
34225 \begin_inset space ~
34228 arguments are possible.
34229 Optional arguments are created with the toolbar button
34232 arg "math-macro-add-optional-param"
34236 The first non-optional argument can be transformed to an optional one with
34240 arg "math-macro-make-optional"
34244 In the second blue box the appearance of the macro in \SpecialChar LyX
34246 Normally you want to see it as it is defined, so the box is kept empty.
34247 But when you have created a macro that needs lot of space on the screen,
34248 you can insert in the box for example
34249 \begin_inset Newline newline
34279 \begin_inset Newline newline
34284 For the macro only the arguments with the macro name in front of them will
34285 then be displayed in \SpecialChar LyX
34286 , leading to a better overview.
34287 The formula appears in the output as defined in the first box.
34288 \begin_inset Newline newline
34291 The appearance of macros in formulas can furthermore be changed for single
34292 macros by setting the cursor in the macro and using the menu
34294 View\SpecialChar menuseparator
34296 \begin_inset space ~
34300 \begin_inset space ~
34308 \begin_layout Standard
34309 To use a macro, the macro name is inserted as command to a formula, in our
34317 Our macro looks in \SpecialChar LyX
34319 \begin_inset Newline newline
34323 \begin_inset space \hspace*{\fill}
34327 \begin_inset Graphics
34328 filename clipart/macrouse.png
34333 \begin_inset space \hspace*{\fill}
34337 \begin_inset Newline newline
34340 Here is our macro example with the arguments
34341 \begin_inset Formula $x$
34345 \begin_inset Formula $\ln(x)$
34349 \begin_inset Formula $B$
34355 \begin_layout Standard
34356 \begin_inset Formula
34366 \begin_layout Standard
34370 Tools\SpecialChar menuseparator
34371 Preferences\SpecialChar menuseparator
34372 Editing\SpecialChar menuseparator
34375 different styles to edit macros.
34376 To find the style that suits you the most, choose a style and set the cursor
34377 in a macro formula to see the difference.
34380 \begin_layout Standard
34381 A math macro is transformed internally to a
34387 command when exporting the document.
34394 command is not placed in the \SpecialChar LaTeX
34395 -preamble, therefore macros can only be used
34396 in formulas that are in the document below the macro definition box.
34399 \begin_layout Standard
34400 Math macros can also be directly created from a
34407 When writing for example the command
34410 \begin_inset Newline newline
34419 xleftarrow[#2]{#1}}
34420 \begin_inset Newline newline
34425 in \SpecialChar LyX
34426 as normal text, highlighting it completely and using then the shortcut
34431 , the command will be transformed to a math macro.
34432 Using this method you need to be careful that the
34438 command is typed correctly, otherwise you get a faulty macro leading to
34443 \begin_layout Standard
34444 Math macros currently have the problem that further formulas in macro definition
34445 s are handled wrongly.
34446 Therefore the example
34453 \begin_inset CommandInset ref
34455 reference "subsec:The-Command-newcommand"
34459 cannot be created as macro.
34462 \begin_layout Standard
34463 When the cursor is in a macro definition box, you will see the macro toolbar
34464 in \SpecialChar LyX
34468 \begin_layout Standard
34469 \begin_inset VSpace defskip
34475 \begin_layout Standard
34476 \begin_inset Graphics
34477 filename clipart/MacroToolbar.png
34482 \begin_inset Index idx
34485 \begin_layout Plain Layout
34494 \begin_layout Standard
34495 \begin_inset VSpace defskip
34501 \begin_layout Standard
34502 The macro toolbar contains from left to right the following buttons:
34505 \begin_layout Standard
34506 \begin_inset VSpace defskip
34512 \begin_layout Standard
34513 \begin_inset Tabular
34514 <lyxtabular version="3" rows="9" columns="2">
34515 <features islongtable="true" longtabularalignment="center">
34516 <column alignment="left" valignment="top">
34517 <column alignment="left" valignment="top" width="85col%">
34518 <row interlinespace="2.5mm">
34519 <cell alignment="center" valignment="top" usebox="none">
34522 \begin_layout Plain Layout
34525 arg "math-macro-remove-param"
34533 <cell alignment="center" valignment="top" usebox="none">
34536 \begin_layout Plain Layout
34539 Edit\SpecialChar menuseparator
34540 Math\SpecialChar menuseparator
34542 \begin_inset space ~
34545 Definition\SpecialChar menuseparator
34546 Remove Last Argument
34552 <row interlinespace="2.5mm">
34553 <cell alignment="center" valignment="top" usebox="none">
34556 \begin_layout Plain Layout
34559 arg "math-macro-add-param"
34567 <cell alignment="center" valignment="top" usebox="none">
34570 \begin_layout Plain Layout
34573 Edit\SpecialChar menuseparator
34574 Math\SpecialChar menuseparator
34576 \begin_inset space ~
34579 Definition\SpecialChar menuseparator
34586 <row interlinespace="2.5mm">
34587 <cell alignment="center" valignment="top" usebox="none">
34590 \begin_layout Plain Layout
34593 arg "math-macro-make-optional"
34601 <cell alignment="center" valignment="top" usebox="none">
34604 \begin_layout Plain Layout
34607 Edit\SpecialChar menuseparator
34608 Math\SpecialChar menuseparator
34610 \begin_inset space ~
34613 Definition\SpecialChar menuseparator
34614 Transform First Non-Optional to
34615 \begin_inset Newline newline
34619 \begin_inset Phantom HPhantom
34622 \begin_layout Plain Layout
34625 Edit\SpecialChar menuseparator
34626 Math\SpecialChar menuseparator
34628 \begin_inset space ~
34631 Definition\SpecialChar menuseparator
34643 <row interlinespace="2.5mm">
34644 <cell alignment="center" valignment="top" usebox="none">
34647 \begin_layout Plain Layout
34650 arg "math-macro-make-nonoptional"
34658 <cell alignment="center" valignment="top" usebox="none">
34661 \begin_layout Plain Layout
34664 Edit\SpecialChar menuseparator
34665 Math\SpecialChar menuseparator
34667 \begin_inset space ~
34670 Definition\SpecialChar menuseparator
34671 Transform Last Optional to
34672 \begin_inset Newline newline
34676 \begin_inset Phantom HPhantom
34679 \begin_layout Plain Layout
34682 Edit\SpecialChar menuseparator
34683 Math\SpecialChar menuseparator
34685 \begin_inset space ~
34688 Definition\SpecialChar menuseparator
34694 Non-Optional Argument
34700 <row interlinespace="2.5mm">
34701 <cell alignment="center" valignment="top" usebox="none">
34704 \begin_layout Plain Layout
34707 arg "math-macro-remove-optional-param"
34715 <cell alignment="center" valignment="top" usebox="none">
34718 \begin_layout Plain Layout
34721 Edit\SpecialChar menuseparator
34722 Math\SpecialChar menuseparator
34724 \begin_inset space ~
34727 Definition\SpecialChar menuseparator
34728 Remove Optional Argument
34734 <row interlinespace="2.5mm">
34735 <cell alignment="center" valignment="top" usebox="none">
34738 \begin_layout Plain Layout
34741 arg "math-macro-add-optional-param"
34749 <cell alignment="center" valignment="top" usebox="none">
34752 \begin_layout Plain Layout
34755 Edit\SpecialChar menuseparator
34756 Math\SpecialChar menuseparator
34758 \begin_inset space ~
34761 Definition\SpecialChar menuseparator
34762 Insert Optional Argument
34768 <row interlinespace="2.5mm">
34769 <cell alignment="center" valignment="top" usebox="none">
34772 \begin_layout Plain Layout
34775 arg "math-macro-remove-greedy-param"
34783 <cell alignment="center" valignment="top" usebox="none">
34786 \begin_layout Plain Layout
34789 Edit\SpecialChar menuseparator
34790 Math\SpecialChar menuseparator
34792 \begin_inset space ~
34795 Definition\SpecialChar menuseparator
34796 Remove Last Argument
34797 \begin_inset Newline newline
34801 \begin_inset Phantom HPhantom
34804 \begin_layout Plain Layout
34807 Edit\SpecialChar menuseparator
34808 Math\SpecialChar menuseparator
34810 \begin_inset space ~
34813 Definition\SpecialChar menuseparator
34819 Spitting Out To The Right
34825 <row interlinespace="2.5mm">
34826 <cell alignment="center" valignment="top" usebox="none">
34829 \begin_layout Plain Layout
34832 arg "math-macro-append-greedy-param"
34840 <cell alignment="center" valignment="top" usebox="none">
34843 \begin_layout Plain Layout
34846 Edit\SpecialChar menuseparator
34847 Math\SpecialChar menuseparator
34849 \begin_inset space ~
34852 Definition\SpecialChar menuseparator
34854 \begin_inset Newline newline
34858 \begin_inset Phantom HPhantom
34861 \begin_layout Plain Layout
34864 Edit\SpecialChar menuseparator
34865 Math\SpecialChar menuseparator
34867 \begin_inset space ~
34870 Definition\SpecialChar menuseparator
34876 Eating From The Right
34882 <row interlinespace="2.5mm">
34883 <cell alignment="center" valignment="top" usebox="none">
34886 \begin_layout Plain Layout
34889 arg "math-macro-add-greedy-optional-param"
34897 <cell alignment="center" valignment="top" usebox="none">
34900 \begin_layout Plain Layout
34903 Edit\SpecialChar menuseparator
34904 Math\SpecialChar menuseparator
34906 \begin_inset space ~
34909 Definition\SpecialChar menuseparator
34910 Append Optional Argument
34911 \begin_inset Newline newline
34915 \begin_inset Phantom HPhantom
34918 \begin_layout Plain Layout
34921 Edit\SpecialChar menuseparator
34922 Math\SpecialChar menuseparator
34924 \begin_inset space ~
34927 Definition\SpecialChar menuseparator
34933 Eating From The Right
34946 \begin_layout Section
34947 Computer Algebra Systems
34950 \begin_layout Standard
34952 offers the exchange between mathematical expressions written in \SpecialChar LyX
34954 editor and external applications or user defined scripts.
34955 Currently supported applications are
34972 Note that the set of supported mathematical constructs is limited only
34973 to very simple cases.
34976 \begin_layout Subsection
34980 \begin_layout Standard
34981 Write some expression in a formula, go to the
34983 Edit\SpecialChar menuseparator
34984 Math\SpecialChar menuseparator
34985 Use Computer Algebra System
34987 menu and choose the application you have installed on the computer.
34988 After that the result of computation should show on the right side of the
34989 expression together with the
34990 \begin_inset Quotes eld
34994 \begin_inset Quotes erd
35000 \begin_layout Standard
35001 Here are few simple examples (with results from
35005 ) to show what kind of computations can be performed:
35008 \begin_layout Itemize
35009 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
35015 \begin_layout Itemize
35016 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
35022 \begin_layout Itemize
35023 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
35029 \begin_layout Itemize
35030 \begin_inset Formula $\det\left[\begin{array}{ccc}
35034 \end{array}\right]=-56$
35040 \begin_layout Itemize
35041 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
35047 \begin_layout Subsection
35051 \begin_layout Standard
35052 Currently there is no keyboard shortcut for calling the algebra applications.
35053 One can easily bind a shortcut to the
35067 \begin_inset space \thinspace{}
35071 \begin_inset space \space{}
35078 key inside the math editor.
35083 one would use this shortcut definition command:
35086 \begin_layout Standard
35089 command-alternatives paragraph-break;math-extern maxima
35092 \begin_layout Section
35094 \begin_inset Index idx
35097 \begin_layout Plain Layout
35106 \begin_layout Subsection
35108 \begin_inset Index idx
35111 \begin_layout Plain Layout
35120 \begin_layout Standard
35121 Negative numbers often look ugly in formulas because the minus sign before
35122 the number is set with the same length as the minus operator sign.
35123 When writing the negative number in normal text, the minus sign appears
35127 \begin_layout Standard
35128 Thus, the problem disappears when converting the minus sign to mathematical
35132 \begin_layout Standard
35133 An example to visualize the problem:
35134 \begin_inset Separator parbreak
35140 \begin_layout Standard
35142 \begin_inset Tabular
35143 <lyxtabular version="3" rows="3" columns="2">
35144 <features tabularvalignment="middle">
35145 <column alignment="right" valignment="top">
35146 <column alignment="left" valignment="top">
35148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35151 \begin_layout Plain Layout
35157 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
35160 \begin_layout Plain Layout
35168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35171 \begin_layout Plain Layout
35177 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
35180 \begin_layout Plain Layout
35181 \begin_inset Formula $x=-2$
35191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35194 \begin_layout Plain Layout
35200 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
35203 \begin_layout Plain Layout
35204 \begin_inset Formula $x=\textrm{-}2$
35220 \begin_layout Subsection
35221 Comma as decimal Separator
35222 \begin_inset Index idx
35225 \begin_layout Plain Layout
35234 \begin_layout Standard
35235 In \SpecialChar LaTeX
35236 a comma inside a formula is used, according to the English convention,
35237 as number group separator.
35238 So there will be space added behind all commas in formulas.
35241 \begin_layout Standard
35242 To avoid this, the comma is highlighted and changed to mathematical text
35252 \begin_layout Standard
35253 To use all formula commas in the document as decimal separator, the file
35262 \begin_layout Plain Layout
35267 is part of the \SpecialChar LaTeX
35273 \begin_inset Index idx
35276 \begin_layout Plain Layout
35281 \begin_layout Plain Layout
35301 \begin_inset Index idx
35304 \begin_layout Plain Layout
35310 is loaded with the \SpecialChar LaTeX
35314 \begin_layout Standard
35322 \begin_layout Subsection
35324 \begin_inset CommandInset label
35326 name "subsec:Physical-Vectors"
35331 \begin_inset Index idx
35334 \begin_layout Plain Layout
35343 \begin_layout Standard
35344 Predefined vectors are offered by the \SpecialChar LaTeX
35350 \begin_inset Index idx
35353 \begin_layout Plain Layout
35359 that is loaded with the \SpecialChar LaTeX
35363 \begin_layout Standard
35371 \begin_layout Standard
35375 \begin_layout Plain Layout
35385 \begin_inset Note Note
35388 \begin_layout Plain Layout
35389 The following table will only be displayed when the \SpecialChar LaTeX
35402 \begin_layout Standard
35403 The following commands are defined:
35404 \begin_inset Separator parbreak
35410 \begin_layout Standard
35412 \begin_inset Tabular
35413 <lyxtabular version="3" rows="4" columns="2">
35414 <features tabularvalignment="middle">
35415 <column alignment="center" valignment="top">
35416 <column alignment="center" valignment="top">
35418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35421 \begin_layout Plain Layout
35427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35430 \begin_layout Plain Layout
35438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35441 \begin_layout Plain Layout
35451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35454 \begin_layout Plain Layout
35455 \begin_inset Formula $\Bra{\psi}$
35465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35468 \begin_layout Plain Layout
35478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35481 \begin_layout Plain Layout
35482 \begin_inset Formula $\Ket{\psi}$
35492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35495 \begin_layout Plain Layout
35507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35510 \begin_layout Plain Layout
35511 \begin_inset Formula $\Braket{\psi|\phi}$
35527 \begin_layout Standard
35534 assures that all vertical bars are set in the size of the surrounding brackets:
35535 \begin_inset Formula
35537 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
35546 \begin_layout Plain Layout
35556 \begin_inset Note Note
35559 \begin_layout Plain Layout
35560 The following will be displayed when the \SpecialChar LaTeX
35573 \begin_layout Standard
35574 You need to install the \SpecialChar LaTeX
35579 to see the rest of this subsection in the output.
35582 \begin_layout Standard
35586 \begin_layout Plain Layout
35598 \begin_layout Standard
35605 can also be achieved using the command
35611 , that is described in
35612 \begin_inset CommandInset ref
35614 reference "subsec:Automatic-Bracket-Size"
35621 \begin_layout Subsection
35622 Self-defined Fractions
35623 \begin_inset CommandInset label
35625 name "subsec:Self-defined-Fractions"
35630 \begin_inset Index idx
35633 \begin_layout Plain Layout
35634 Fractions ! self-defined
35642 \begin_layout Standard
35643 To define custom commands for fractions, the command
35650 \begin_inset Index idx
35653 \begin_layout Plain Layout
35660 \begin_layout Plain Layout
35674 is used in the following scheme:
35677 \begin_layout Standard
35690 bracket}{fraction bar thickness}{style}
35691 \begin_inset Newline newline
35695 \begin_inset Phantom HPhantom
35698 \begin_layout Plain Layout
35708 {numerator}{denominator}
35711 \begin_layout Standard
35712 The style is a number in the range of 0
35713 \begin_inset space \thinspace{}
35717 \begin_inset space \thinspace{}
35721 \begin_inset Separator parbreak
35727 \begin_layout Standard
35729 \begin_inset Tabular
35730 <lyxtabular version="3" rows="5" columns="2">
35731 <features tabularvalignment="middle">
35732 <column alignment="center" valignment="top">
35733 <column alignment="center" valignment="top">
35735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35738 \begin_layout Plain Layout
35744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35747 \begin_layout Plain Layout
35755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35758 \begin_layout Plain Layout
35764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35767 \begin_layout Plain Layout
35768 display style formula
35775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35778 \begin_layout Plain Layout
35784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35787 \begin_layout Plain Layout
35795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35798 \begin_layout Plain Layout
35804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35807 \begin_layout Plain Layout
35815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35818 \begin_layout Plain Layout
35824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35827 \begin_layout Plain Layout
35841 \begin_layout Standard
35842 When no style is given, the size is adjusted to the surrounding environment
35843 like for the command
35852 \begin_layout Standard
35853 When no fraction bar thickness is given, the predefined value of 0.4
35854 \begin_inset space \thinspace{}
35860 \begin_layout Standard
35861 \begin_inset VSpace medskip
35864 For example, the commands
35877 \begin_inset CommandInset ref
35879 reference "subsec:Fractions"
35883 are defined with the commands
35886 \begin_layout Standard
35895 genfrac{}{}{}{0}{#1}{#2}}
35898 \begin_layout Standard
35902 \begin_layout Standard
35911 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35914 \begin_layout Standard
35915 \begin_inset VSpace medskip
35918 To define a fraction where the fraction bar thickness can be given as optional
35919 argument, the following line is inserted to the \SpecialChar LaTeX
35923 \begin_layout Standard
35932 genfrac{}{}{#1}{}{#2}{#3}}
35935 \begin_layout Standard
35937 \begin_inset Formula
35939 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35940 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35945 As one can see, the distance of the numerator and the denominator to the
35946 fraction bar is round about three times the bar thickness.
35949 \begin_layout Subsection
35951 \begin_inset Index idx
35954 \begin_layout Plain Layout
35963 \begin_layout Standard
35964 There are four ways to cancel formulas or parts of formulas:
35967 \begin_layout Standard
35971 \begin_layout Plain Layout
35981 \begin_inset Note Note
35984 \begin_layout Plain Layout
35985 The following table will only be displayed when the \SpecialChar LaTeX
35996 \begin_inset Separator parbreak
36002 \begin_layout Standard
36004 \begin_inset Tabular
36005 <lyxtabular version="3" rows="5" columns="2">
36006 <features tabularvalignment="middle">
36007 <column alignment="center" valignment="top">
36008 <column alignment="center" valignment="top">
36010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36013 \begin_layout Plain Layout
36019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36022 \begin_layout Plain Layout
36024 \begin_inset Note Note
36027 \begin_layout Plain Layout
36034 are used here as spacer.
36046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36049 \begin_layout Plain Layout
36053 \begin_inset space \textvisiblespace{}
36059 \begin_inset space \textvisiblespace{}
36067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36070 \begin_layout Plain Layout
36071 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
36081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36084 \begin_layout Plain Layout
36088 \begin_inset space \textvisiblespace{}
36094 \begin_inset space \textvisiblespace{}
36102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36105 \begin_layout Plain Layout
36106 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
36116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36119 \begin_layout Plain Layout
36123 \begin_inset space \textvisiblespace{}
36129 \begin_inset space \textvisiblespace{}
36137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36140 \begin_layout Plain Layout
36141 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
36151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36154 \begin_layout Plain Layout
36158 \begin_inset space \textvisiblespace{}
36164 \begin_inset space \textvisiblespace{}
36168 \begin_inset Formula $\to$
36176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36179 \begin_layout Plain Layout
36180 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
36196 \begin_layout Standard
36203 is especially suitable to visualize the reduction of fractions within formulas:
36204 \begin_inset Formula
36206 \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}}}
36214 \begin_layout Standard
36215 To change the size of
36222 \begin_inset Quotes eld
36226 \begin_inset Quotes erd
36229 value one can add the \SpecialChar LaTeX
36233 \begin_layout Standard
36238 PassOptionsToPackage{option}{cancel}
36241 \begin_layout Standard
36250 which leads to the same size as for the canceled value, or
36254 which makes is it a bit smaller than normal.
36257 \begin_layout Standard
36258 To color the cancellation bar one adds this command as \SpecialChar TeX
36262 \begin_layout Standard
36274 \begin_layout Standard
36279 can be replaced by a color of your choice.
36282 \begin_layout Standard
36286 \begin_layout Plain Layout
36302 \begin_layout Standard
36303 \begin_inset Formula
36305 \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}}}
36313 \begin_layout Standard
36317 \begin_layout Plain Layout
36331 \begin_inset Note Note
36334 \begin_layout Plain Layout
36343 \begin_layout Standard
36344 For further customizations, see the documentation of the package
36349 \begin_inset CommandInset citation
36356 \begin_inset Index idx
36359 \begin_layout Plain Layout
36368 \begin_layout Standard
36372 \begin_layout Plain Layout
36382 \begin_inset Note Note
36385 \begin_layout Plain Layout
36386 The following will be displayed when the \SpecialChar LaTeX
36399 \begin_layout Standard
36400 You need to install the \SpecialChar LaTeX
36405 to see the rest of this subsection in the output.
36408 \begin_layout Standard
36412 \begin_layout Plain Layout
36424 \begin_layout Subsection
36425 Formulas in Section Headings
36426 \begin_inset CommandInset label
36428 name "subsec:Formulas-in-Section"
36433 \begin_inset Index idx
36436 \begin_layout Plain Layout
36437 Formula ! in section headings
36445 \begin_layout Standard
36446 When formulas are used in section headings, the following has to be taken
36450 \begin_layout Standard
36451 \begin_inset Note Greyedout
36454 \begin_layout Plain Layout
36460 \begin_inset Index idx
36463 \begin_layout Plain Layout
36464 Packages ! hyperref
36469 support is enabled in the document settings dialog under
36472 \begin_inset space ~
36477 , PDF-bookmarks are created for every section heading in the table of contents.
36478 If a section heading contains formulas, they are incorrectly displayed
36479 in the bookmark text, because formulas in bookmarks infringe the PDF convention
36488 \begin_layout Standard
36489 Both problems can be solved by inserting at the end of the section heading
36490 a short title with the menu
36492 Insert\SpecialChar menuseparator
36494 \begin_inset space ~
36500 Short titles are used as alternative for multiline section headings to
36501 keep the table of contents clearly arranged.
36502 Only the short title appears in the table of contents and therefore also
36503 in the PDF-bookmark.
36506 \begin_layout Standard
36507 When formulas should be used in the table of contents but
36511 is used, one can use the following command in \SpecialChar TeX
36515 \begin_layout Standard
36520 texorpdfstring{part}{alternative}
36521 \begin_inset Index idx
36524 \begin_layout Plain Layout
36535 \begin_layout Standard
36536 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36537 This can be characters, formulas, footnotes, but also cross-references.
36538 The alternative is used instead of the part for the bookmark.
36541 \begin_layout Standard
36542 Here are two example headings:
36543 \begin_inset VSpace -3mm
36550 \begin_layout Plain Layout
36562 \begin_layout Subsubsection
36563 Heading without formula in table of contents
36564 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36568 \begin_inset Argument 1
36571 \begin_layout Plain Layout
36572 Heading without formula in table of contents
36580 \begin_layout Subsubsection
36581 Heading with formula in table of contents
36585 \begin_layout Plain Layout
36595 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36602 \begin_layout Plain Layout
36612 \begin_layout Standard
36616 \begin_layout Plain Layout
36625 In the first heading a short title was used, in the second one
36634 \begin_layout Standard
36635 To get the same formatting as for the other headings, the complete heading
36644 \begin_layout Plain Layout
36646 \begin_inset CommandInset ref
36648 reference "subsec:Bold-Formulas"
36660 \begin_layout Subsection
36661 Formulas in multi-column Text
36662 \begin_inset Index idx
36665 \begin_layout Plain Layout
36666 Formula ! in multi-column text
36674 \begin_layout Standard
36675 Formulas in multi-column text are often too wide to fit into a column and
36676 thus need to be set over the whole page width.
36677 This is done by using the \SpecialChar LaTeX
36686 \begin_layout Plain Layout
36691 is part of every \SpecialChar LaTeX
36692 standard installation.
36698 \begin_inset Index idx
36701 \begin_layout Plain Layout
36702 Packages ! multicol
36707 , that is loaded with the \SpecialChar LaTeX
36711 \begin_layout Standard
36716 usepackage{multicol}
36719 \begin_layout Standard
36720 \begin_inset Note Greyedout
36723 \begin_layout Plain Layout
36724 Note that in this case the setting
36727 \begin_inset space ~
36734 Document\SpecialChar menuseparator
36740 \begin_inset space ~
36760 \begin_layout Standard
36761 Before the multi-column text the command
36764 \begin_layout Standard
36769 begin{multicols}{column number}
36772 \begin_layout Standard
36773 is written in \SpecialChar TeX
36775 The column number is a number in the range of 2
36776 \begin_inset space \thinspace{}
36780 \begin_inset space \thinspace{}
36784 Before the formula the multi-column text is ended by inserting the command
36787 \begin_layout Standard
36795 \begin_layout Standard
36796 in \SpecialChar TeX
36800 \begin_layout Standard
36801 Due to the command some space is automatically added before the formula.
36803 \begin_inset space \thinspace{}
36806 mm vertical space is inserted before the formula.
36807 When the formula style
36813 \begin_layout Plain Layout
36815 \begin_inset CommandInset ref
36817 reference "sec:Formula-Styles"
36829 \begin_inset space \thinspace{}
36832 mm space is inserted instead.
36835 \begin_layout Standard
36836 As example a multi-column text with a displayed formula:
36839 \begin_layout Standard
36845 \begin_layout Plain Layout
36849 begin{multicols}{2}
36854 Das Spektrum wird fouriertransformiert.
36855 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36856 , Lösungsmittel) zu trennen.
36857 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36858 nun das Aussehen des Ausgangssignals.
36859 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36860 über alle Phasen integrieren muss.
36862 \begin_inset Formula $S$
36865 unser normiertes Ausgangssignal und
36866 \begin_inset Formula $P$
36869 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36873 \begin_layout Plain Layout
36883 \begin_inset VSpace -6mm
36887 \begin_inset Formula
36889 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36898 \begin_layout Plain Layout
36902 begin{multicols}{2}
36908 \begin_inset Formula $S_{0}$
36911 das Signal ohne Gradient ist und die Normierungsbedingung
36912 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36916 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36918 \begin_inset Formula $\nicefrac{\pi}{2}$
36922 \begin_inset space \thinspace{}
36925 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36926 das Signal zusätzlich abschwächt.
36927 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36929 \begin_inset Formula $T_{2}$
36935 \begin_layout Standard
36941 \begin_layout Plain Layout
36953 \begin_layout Subsection
36954 Formulas with Description of Variables
36955 \begin_inset Index idx
36958 \begin_layout Plain Layout
36959 Formula ! with description of variables
36967 \begin_layout Standard
36968 To describe variables within a formula, like in formula
36969 \begin_inset CommandInset ref
36971 reference "eq:within"
36980 \begin_inset Formula $n$
36984 \begin_inset space ~
36987 matrix is used with left aligned columns for the
36988 \begin_inset Formula $n$
36995 \begin_layout Plain Layout
36997 \begin_inset CommandInset ref
36999 reference "sec:Matrices"
37008 To set the description in a smaller size, before the matrix e.
37009 \begin_inset space \thinspace{}
37013 \begin_inset space \space{}
37026 \begin_layout Plain Layout
37028 \begin_inset CommandInset ref
37030 reference "subsec:Font-Sizes"
37042 \begin_layout Standard
37043 When the formula style
37049 \begin_layout Plain Layout
37051 \begin_inset CommandInset ref
37053 reference "sec:Formula-Styles"
37074 \begin_layout Plain Layout
37081 only works in formulas with the style
37086 \begin_inset CommandInset ref
37088 reference "subsec:Variable-Space"
37097 is inserted before and after the matrix to have the same separation of
37098 the matrix from the equation and the side margin.
37101 \begin_layout Standard
37102 When the formula style
37106 is used, the method described in
37107 \begin_inset CommandInset ref
37109 reference "subsec:Flalign-Environment"
37113 is used to indent formulas.
37115 \begin_inset CommandInset ref
37117 reference "eq:within"
37121 consists of five columns where in the first two columns contain the equation,
37122 the third the matrix and the last one an empty \SpecialChar TeX
37124 \begin_inset Formula
37126 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
37127 \rho & \textrm{density}\\
37128 V & \textrm{volume}\\
37129 g & \textrm{gravitational acceleration}
37130 \end{array} & & {}\label{eq:within}
37138 \begin_layout Subsection
37139 Upright small Greek Letters
37140 \begin_inset CommandInset label
37142 name "subsec:Upright-small-Greek"
37147 \begin_inset Index idx
37150 \begin_layout Plain Layout
37151 Greek letters ! upright
37159 \begin_layout Standard
37160 Most of the math fonts only provide italic small Greek letters.
37161 But for symbols of elementary particles like pions and neutrinos, upright
37162 Greek letters are needed.
37171 \begin_layout Plain Layout
37176 is part of the \SpecialChar LaTeX
37182 \begin_inset Index idx
37185 \begin_layout Plain Layout
37190 \begin_layout Plain Layout
37210 \begin_inset Index idx
37213 \begin_layout Plain Layout
37219 that is loaded with the \SpecialChar LaTeX
37223 \begin_layout Standard
37228 usepackage{upgreek}
37231 \begin_layout Standard
37237 \begin_layout Plain Layout
37247 \begin_inset Note Note
37250 \begin_layout Plain Layout
37251 The following table will only be displayed when the \SpecialChar LaTeX
37261 They are created when the command for a small Greek letter is started with
37267 For example the command
37274 \begin_inset Formula $\uptau$
37280 \begin_layout Standard
37281 With these commands reactions of elementary particles can be typeset:
37282 \begin_inset Formula
37284 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
37292 \begin_layout Standard
37293 The upright letters are more bold and wider than the italic ones.
37294 They should therefore not be used for units like
37295 \begin_inset Quotes eld
37299 \begin_inset Quotes erd
37305 \begin_layout Standard
37309 \begin_layout Plain Layout
37319 \begin_inset Note Note
37322 \begin_layout Plain Layout
37323 The following will be displayed when the \SpecialChar LaTeX
37336 \begin_layout Standard
37337 You need to install the \SpecialChar LaTeX
37342 to see the rest of this subsection in the output.
37345 \begin_layout Standard
37349 \begin_layout Plain Layout
37361 \begin_layout Subsection
37362 Text Characters in Formulas
37363 \begin_inset Index idx
37366 \begin_layout Plain Layout
37375 \begin_layout Standard
37376 In some cases you might want to insert text characters directly into formulas.
37377 When for example the centered dot · is often used in formulas like
37378 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
37381 , one would have to insert the command
37391 \begin_layout Plain Layout
37393 \begin_inset CommandInset ref
37395 reference "subsec:Binary-Operators"
37404 all the time, because this character is defined in all encodings as text
37406 But the encoding can be changed by this \SpecialChar LaTeX
37410 \begin_layout Standard
37415 Declare Inputtext{183}{
37425 f\SpecialChar ligaturebreak
37429 \begin_layout Standard
37430 The character encoding (menu
37432 Document\SpecialChar menuseparator
37433 Settings\SpecialChar menuseparator
37436 ) specifies what character appears when a keyboard key is pressed.
37437 When the key for the character '·' is pressed, internally the command
37444 But this command is not available in a formula so that you would get \SpecialChar LaTeX
37446 With the changed encoding the right command is chosen automatically, depending
37447 on if the character was inserted into a formula or not.
37450 \begin_layout Standard
37451 The encoding of several characters is saved in definition files.
37452 For example the encoding
37456 is defined in the file
37460 which is in the installation folder of \SpecialChar LaTeX
37462 Encodings should only be changed via the \SpecialChar LaTeX
37463 -preamble and not in the definition
37465 Otherwise documents could not be edited by other \SpecialChar LyX
37466 users working on other
37470 \begin_layout Standard
37471 \begin_inset VSpace medskip
37474 Besides the centered dot, in this document the degree sign ° is defined
37475 with the following \SpecialChar LaTeX
37476 -preamble line so that it can be directly inserted into
37480 \begin_layout Standard
37485 DeclareInputtext{176}{
37495 f\SpecialChar ligaturebreak
37499 \begin_layout Subsection
37501 -comments in formulas
37502 \begin_inset Index idx
37505 \begin_layout Plain Layout
37515 \begin_layout Standard
37516 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
37518 code of your file with the menu
37520 Insert\SpecialChar menuseparator
37521 Note\SpecialChar menuseparator
37525 This is not possible in a formula but you can insert \SpecialChar LaTeX
37530 \begin_layout Standard
37538 \begin_layout Standard
37539 This creates a box in which you can write your comment.
37540 Due to a bug in \SpecialChar LyX
37545 \begin_layout Plain Layout
37546 \begin_inset CommandInset href
37548 name "LyX-bug #9002"
37549 target "http://www.lyx.org/trac/ticket/9002"
37558 you cannot write normal text inside the comment, even when you use mathematical
37559 text, you will see its \SpecialChar LaTeX
37560 -commands in the \SpecialChar LaTeX
37562 \begin_inset Newline newline
37565 This a formula with a \SpecialChar LaTeX
37567 \begin_inset Formula
37569 A=B%\text{This is the comment}
37577 \begin_layout Standard
37578 \begin_inset Newpage newpage
37584 \begin_layout Section
37587 \begin_inset Index idx
37590 \begin_layout Plain Layout
37599 \begin_layout Standard
37600 This section is a summary of the most important typographic rules, listed
37605 \begin_layout Plain Layout
37606 This collection was partly taken from the German semi-official dictionary
37608 \begin_inset Quotes eld
37612 \begin_inset Quotes erd
37616 \begin_inset CommandInset citation
37622 that lists some of the ISO rules.
37623 More rules are listed in
37624 \begin_inset CommandInset citation
37638 \begin_layout Itemize
37647 \begin_layout Plain Layout
37648 done with font styles, see
37649 \begin_inset CommandInset ref
37651 reference "subsec:Font-Styles"
37660 , no matter if they appear in italic text: 30
37661 \begin_inset space \thinspace{}
37665 \begin_inset Newline newline
37668 Between the value and the unit is the smallest space, see
37669 \begin_inset CommandInset ref
37671 reference "subsec:Predefined-Space"
37676 \begin_inset Newline newline
37679 This convention is automatically fulfilled when the command
37686 When it is entered to a formula, two boxes appear.
37687 In the first one the value is inserted, in the second one the unit, and
37689 \begin_inset Formula $\unit[30]{km/h}$
37693 \begin_inset space \thinspace{}
37703 is not a real \SpecialChar LaTeX
37704 command but the command
37710 , therefore you cannot use it in \SpecialChar TeX
37714 \begin_layout Itemize
37715 Percent and perthousand signs are set like physical units:
37716 \begin_inset Newline newline
37720 \begin_inset space \thinspace{}
37726 \begin_layout Itemize
37727 The degree sign follows directly on the value: 15°, but not when it is used
37729 \begin_inset space \thinspace{}
37735 \begin_layout Itemize
37736 In numbers with more than four digits the smallest space is inserted before
37737 every third digit to group them:
37747 \begin_inset space \thinspace{}
37751 \begin_inset space \thinspace{}
37757 \begin_layout Itemize
37758 For dimensions like 120×90×40
37759 \begin_inset space \thinspace{}
37762 cm the multiplication sign
37763 \begin_inset Quotes eld
37767 \begin_inset Quotes erd
37771 It is available either via the command
37779 Insert\SpecialChar menuseparator
37780 Special Character\SpecialChar menuseparator
37786 \begin_layout Itemize
37787 Functions with names consisting of several letters are set upright to avoid
37789 \begin_inset CommandInset ref
37791 reference "subsec:Predefined-Functions"
37798 \begin_layout Itemize
37799 Indices consisting of several letters, are set upright:
37800 \begin_inset Formula $E_{\mathrm{kin}}$
37804 \begin_inset Newline newline
37807 Components of matrices are set italic:
37808 \begin_inset Formula $\hat{H}_{kl}$
37814 \begin_layout Itemize
37815 The differentiation/integration operator 'd', the Euler's number 'e' and
37816 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37820 \begin_layout Itemize
37821 The character that denotes a
37825 transformation is inserted either by the command
37830 \begin_inset space \textvisiblespace{}
37837 Insert\SpecialChar menuseparator
37838 Special Character\SpecialChar menuseparator
37839 Symbols\SpecialChar menuseparator
37841 \begin_inset space ~
37847 \begin_inset Formula $\mathscr{F}$
37853 \begin_layout Standard
37854 \begin_inset Newpage newpage
37860 \begin_layout Section
37862 \begin_inset Index idx
37865 \begin_layout Plain Layout
37874 \begin_layout Standard
37875 Some characters and symbols can be created with several commands.
37876 Here is a list of the synonym commands:
37879 \begin_layout Standard
37880 \begin_inset VSpace bigskip
37884 \begin_inset space \hfill{}
37888 \begin_inset Tabular
37889 <lyxtabular version="3" rows="12" columns="2">
37890 <features tabularvalignment="middle">
37891 <column alignment="center" valignment="top" width="0pt">
37892 <column alignment="center" valignment="top" width="0pt">
37894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37897 \begin_layout Plain Layout
37903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37906 \begin_layout Plain Layout
37908 \begin_inset Note Note
37911 \begin_layout Plain Layout
37918 is only used as spacer.
37930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37933 \begin_layout Plain Layout
37941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37944 \begin_layout Plain Layout
37948 \begin_layout Plain Layout
37961 \begin_layout Plain Layout
37975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37978 \begin_layout Plain Layout
37986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37989 \begin_layout Plain Layout
37999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38002 \begin_layout Plain Layout
38010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38013 \begin_layout Plain Layout
38023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38026 \begin_layout Plain Layout
38034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38037 \begin_layout Plain Layout
38045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38048 \begin_layout Plain Layout
38056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38059 \begin_layout Plain Layout
38067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38070 \begin_layout Plain Layout
38078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38081 \begin_layout Plain Layout
38091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38094 \begin_layout Plain Layout
38102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38105 \begin_layout Plain Layout
38115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38118 \begin_layout Plain Layout
38126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38129 \begin_layout Plain Layout
38139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38142 \begin_layout Plain Layout
38150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38153 \begin_layout Plain Layout
38163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38166 \begin_layout Plain Layout
38174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38177 \begin_layout Plain Layout
38185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
38188 \begin_layout Plain Layout
38196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
38199 \begin_layout Plain Layout
38211 \begin_inset space \hfill{}
38215 \begin_inset Tabular
38216 <lyxtabular version="3" rows="12" columns="2">
38217 <features tabularvalignment="middle">
38218 <column alignment="center" valignment="top" width="0pt">
38219 <column alignment="center" valignment="top" width="0pt">
38221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
38224 \begin_layout Plain Layout
38230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
38233 \begin_layout Plain Layout
38241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38244 \begin_layout Plain Layout
38252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38255 \begin_layout Plain Layout
38267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38270 \begin_layout Plain Layout
38278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38281 \begin_layout Plain Layout
38291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38294 \begin_layout Plain Layout
38302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38305 \begin_layout Plain Layout
38315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38318 \begin_layout Plain Layout
38326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38329 \begin_layout Plain Layout
38337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38340 \begin_layout Plain Layout
38348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38351 \begin_layout Plain Layout
38359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38362 \begin_layout Plain Layout
38370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38373 \begin_layout Plain Layout
38383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38386 \begin_layout Plain Layout
38394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38397 \begin_layout Plain Layout
38407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38410 \begin_layout Plain Layout
38418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38421 \begin_layout Plain Layout
38431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38434 \begin_layout Plain Layout
38442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38445 \begin_layout Plain Layout
38455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38458 \begin_layout Plain Layout
38466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38469 \begin_layout Plain Layout
38479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
38482 \begin_layout Plain Layout
38490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
38493 \begin_layout Plain Layout
38507 \begin_inset space \hfill{}
38513 \begin_layout Standard
38514 \begin_inset Newpage newpage
38520 \begin_layout Bibliography
38521 \begin_inset CommandInset bibitem
38522 LatexCommand bibitem
38534 The \SpecialChar LaTeX
38538 Addison Wesley, 2004
38541 \begin_layout Bibliography
38542 \begin_inset CommandInset bibitem
38543 LatexCommand bibitem
38549 \begin_inset CommandInset href
38552 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
38556 of \SpecialChar LaTeX
38560 \begin_layout Bibliography
38561 \begin_inset CommandInset bibitem
38562 LatexCommand bibitem
38568 \begin_inset CommandInset href
38571 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
38579 \begin_layout Plain Layout
38588 -\SpecialChar LaTeX
38592 \begin_layout Bibliography
38593 \begin_inset CommandInset bibitem
38594 LatexCommand bibitem
38600 \begin_inset CommandInset href
38603 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38607 of all symbols available with \SpecialChar LaTeX
38611 \begin_layout Bibliography
38612 \begin_inset CommandInset bibitem
38613 LatexCommand bibitem
38619 \begin_inset CommandInset href
38621 name "Documentation"
38622 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
38626 of the \SpecialChar LaTeX
38632 \begin_inset Index idx
38635 \begin_layout Plain Layout
38644 \begin_layout Bibliography
38645 \begin_inset CommandInset bibitem
38646 LatexCommand bibitem
38652 \begin_inset CommandInset href
38654 name "Documentation"
38655 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38659 of the \SpecialChar LaTeX
38665 \begin_inset Index idx
38668 \begin_layout Plain Layout
38669 Packages ! hyperref
38677 \begin_layout Bibliography
38678 \begin_inset CommandInset bibitem
38679 LatexCommand bibitem
38685 \begin_inset CommandInset href
38687 name "Documentation"
38688 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38692 of the \SpecialChar LaTeX
38698 \begin_inset Index idx
38701 \begin_layout Plain Layout
38710 \begin_layout Bibliography
38711 \begin_inset CommandInset bibitem
38712 LatexCommand bibitem
38723 Auflage, Duden 2001
38726 \begin_layout Bibliography
38727 \begin_inset CommandInset bibitem
38728 LatexCommand bibitem
38734 \begin_inset CommandInset href
38737 target "http://physics.nist.gov/Document/checklist.pdf"
38741 for reviewing manuscripts
38744 \begin_layout Standard
38745 \begin_inset CommandInset index_print
38746 LatexCommand printindex