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
17 % solves the following problem:
18 % If the dection number consits of too many numerals the section heading
19 % will be printed in the TOC without a space between it and the section number.
20 % As solution more space between the number and the heading is inserted:
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22 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
24 % increase link area for cross-references and autoname them,
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36 % don't load packages twice
37 % see first footnote in sec. 9.3
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40 % the pages of the TOC are numbered roman
41 % and a PDF-bookmark for the TOC is added
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44 \renewcommand{\tableofcontents}{%
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49 \pagenumbering{arabic}}
51 % add 0.5 mm vertical space for table rows
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55 % insert additional vertical space of 1.5 mm between footnotes,
57 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
59 % makes caption labels bold
60 \setkomafont{captionlabel}{\bfseries}
62 % enables calculation of values
65 % for multiple columns used in sec. 24.7
71 % for the Fourier transformation symbol
74 % define a color, used in sec.9.3
75 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
77 % declare operators (see sec. 10.4 and sec. 15.2)
78 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
79 \DeclareMathOperator{\sgn}{sgn}
81 % example definitions for sec. 20.1
82 \newcommand{\gr}{\Longrightarrow}
83 \newcommand{\us}[1]{\underline{#1}}
84 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
85 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
86 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
88 % example macro from sec. 19.4
89 %\def\tagform@#1{\maketag@@@{|#1|}}
92 % ------------------------------------
93 % used to check for needed LaTeX packages
96 % check for package undertilde
97 % used for the command \utilde
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99 \IfFileExists{undertilde.sty}
100 {\usepackage{undertilde}
101 \setboolean{undertilde}{true}}
102 {\setboolean{undertilde}{false}}
104 % check for package eurosym
105 % used for the Euro symbol
107 \IfFileExists{eurosym.sty}
108 {\usepackage[gennarrow]{eurosym}
109 \setboolean{eurosym}{true}}
110 {\setboolean{eurosym}{false}}
112 % check for package braket
113 % used for physical vectors
115 \IfFileExists{braket.sty}
117 \setboolean{braket}{true}}
118 {\setboolean{braket}{false}}
120 % check for package cancel
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124 \setboolean{cancel}{true}}
125 {\setboolean{cancel}{false}}
127 % check for package upgreek
129 \IfFileExists{upgreek.sty}
130 {\usepackage{upgreek}
131 \setboolean{upgreek}{true}}
132 {\setboolean{upgreek}{false}}
134 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
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144 \font_math "auto" "auto"
145 \font_default_family default
146 \use_non_tex_fonts false
149 \font_sf_scale 100 100
150 \font_tt_scale 100 100
152 \default_output_format pdf2
154 \bibtex_command default
155 \index_command default
159 \pdf_title "LyX's Math Manual"
160 \pdf_author "LyX Team, Uwe Stöhr"
161 \pdf_subject "LyX-documentation about math"
162 \pdf_keywords "LyX, Mathed"
164 \pdf_bookmarksnumbered true
165 \pdf_bookmarksopen true
166 \pdf_bookmarksopenlevel 1
167 \pdf_breaklinks false
171 \pdf_pdfusetitle false
172 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
175 \use_package amsmath 2
176 \use_package amssymb 2
177 \use_package cancel 0
179 \use_package mathdots 1
180 \use_package mathtools 2
181 \use_package mhchem 1
182 \use_package stackrel 0
183 \use_package stmaryrd 0
184 \use_package undertilde 0
186 \cite_engine_type default
190 \paperorientation portrait
194 \notefontcolor #0000ff
201 \paragraph_separation skip
203 \quotes_language english
206 \paperpagestyle plain
210 \tracking_changes true
211 \output_changes false
214 \html_be_strict false
215 \author 2047637253 "Guillaume Munch"
222 's detailed Math manual
226 by the \SpecialChar LyX
231 \begin_layout Plain Layout
233 If you have comments or error corrections, please send them to the \SpecialChar LyX
238 \begin_inset CommandInset href
240 name "lyx-docs@lists.lyx.org"
241 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
252 \begin_inset Note Note
255 \begin_layout Plain Layout
262 \begin_inset Newline newline
266 \begin_inset Newline newline
274 \begin_layout Standard
275 \begin_inset CommandInset toc
276 LatexCommand tableofcontents
283 \begin_layout Standard
284 \begin_inset Note Note
287 \begin_layout Plain Layout
288 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
291 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
298 If they are not installed the document can be exported anyway but the sections
299 where the packages are required will not appear in the output.
304 ; if it is not installed, this file cannot be exported.
307 \begin_layout Plain Layout
308 The latest PDF-version of this document can be found here:
309 \begin_inset Newline newline
314 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
322 \begin_layout Standard
323 \begin_inset Newpage newpage
329 \begin_layout Section
333 \begin_layout Standard
334 This document explains \SpecialChar LyX
335 's math features and is furthermore a collection
336 of \SpecialChar LaTeX
337 -commands used for mathematical characters and constructs.
338 The explanations are designed for the usage of commands.
339 It is therefore required that you have read the section
350 \begin_layout Standard
351 Most of the characters and many constructs explained in this manual are
352 also accessible via the menu
356 \SpecialChar menuseparator
372 But everybody who has to write lots of formulas will notice that it is
373 much faster to use commands instead of the math toolbar.
374 Therefore this manual is focused on commands but also mentions the correspondin
375 g toolbar buttons when available.
378 \begin_layout Standard
379 If not specially mentioned the commands are only available within formulas.
380 To be able to use all commands explained in this document, the option
384 must be checked in the document settings (menu
386 Document\SpecialChar menuseparator
387 Settings\SpecialChar menuseparator
398 \begin_layout Plain Layout
401 Use AMS math package automatically
407 \begin_layout Plain Layout
416 -math when math constructs are found that are supported by \SpecialChar LyX
425 \begin_layout Standard
426 This document doesn't list all
430 \begin_layout Plain Layout
443 \begin_layout Plain Layout
448 \begin_layout Plain Layout
457 -math commands is in the file
460 \begin_inset CommandInset href
463 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
469 , which is part of every \SpecialChar LaTeX
470 standard installation.
475 for lucidity reasons.
478 \begin_layout Section
482 \begin_layout Standard
483 To create an inline formula
484 \begin_inset Index idx
487 \begin_layout Plain Layout
493 that is embedded into a text line, use one of the shortcuts
499 or the toolbar button
506 \begin_inset Newline newline
509 To create a display style formula
510 \begin_inset Index idx
513 \begin_layout Plain Layout
514 Formula ! display style
519 which will appear bigger, has a different format, and will be in a separate
520 paragraph, use one of these shortcuts:
529 \begin_layout Standard
530 To change a display style formula to an inline formula, set the cursor into
531 the formula and use one of the shortcuts
539 Edit\SpecialChar menuseparator
540 Math\SpecialChar menuseparator
544 The same way is used to change an inline formula to a display style formula.
547 \begin_layout Standard
548 To display parts of an inline formula in the size of a display style formula,
556 \begin_inset Index idx
559 \begin_layout Plain Layout
568 Then a new blue box appears in which the desired formula part is inserted.
571 \begin_layout Standard
572 Only inline formulas are allowed inside tables.
575 \begin_layout Standard
580 can be turned on in the menu
582 View\SpecialChar menuseparator
586 When you click there on
587 \begin_inset Quotes eld
591 \begin_inset Quotes erd
594 the toolbar will be shown permanently at the bottom; this state is visualized
599 menu with a checkmark.
600 When you click in this state again on
601 \begin_inset Quotes eld
605 \begin_inset Quotes erd
616 is only shown when the cursor is within a formula; this state is visualized
617 by the renaming of the menu entry from
618 \begin_inset Quotes eld
622 \begin_inset Quotes erd
626 \begin_inset Quotes eld
634 \begin_inset Quotes erd
640 \begin_layout Standard
643 \begin_inset Index idx
646 \begin_layout Plain Layout
653 is invoked by pressing the toolbar button
661 Insert\SpecialChar menuseparator
673 \begin_layout Standard
674 To change the \SpecialChar LaTeX
676 \begin_inset Index idx
679 \begin_layout Plain Layout
688 Document\SpecialChar menuseparator
689 Settings\SpecialChar menuseparator
699 \begin_layout Standard
700 To edit matrices, case differentiations and multiline formulas subsequently,
703 Edit\SpecialChar menuseparator
708 Edit\SpecialChar menuseparator
710 \begin_inset space \thinspace{}
714 \begin_inset space \thinspace{}
724 When lines and columns are swapped via the menu, the column or line where
725 the cursor is in is exchanged with the column to the right or the line
727 Is the cursor in the last column or row, the exchange is done with the
728 column to the left or the line above.
731 \begin_layout Standard
732 To write text in formulas
736 \begin_layout Plain Layout
737 For multiline formulas the command
744 \begin_inset CommandInset ref
746 reference "subsec:Text-in-multiline"
760 \begin_inset Index idx
763 \begin_layout Plain Layout
770 \begin_inset Index idx
773 \begin_layout Plain Layout
780 This mode is invoked with the shortcut
786 or by the insertion of the command
793 \begin_inset Index idx
796 \begin_layout Plain Layout
805 The text appears black in \SpecialChar LyX
806 and can therefore be distinguished from the
807 other formula parts which appear blue.
808 In the output mathematical text is set upright, in contrary to other formula
812 \begin_layout Subsection*
816 \begin_layout Standard
817 Most of the \SpecialChar LaTeX
818 -commands for math constructs have the following scheme:
821 \begin_layout Standard
837 \begin_layout Standard
838 A command always starts with a backslash
839 \begin_inset Quotes gld
849 \begin_inset Quotes grd
853 To omit optional arguments, also omit the associated brackets.
854 The braces around the required arguments are named in this document as
857 \begin_inset Index idx
860 \begin_layout Plain Layout
868 If you add in a formula a left brace to a command name, \SpecialChar LyX
870 creates a \SpecialChar TeX
872 In all other cases \SpecialChar TeX
873 braces are created in formulas with the command
881 braces appear red in \SpecialChar LyX
882 , in contrary to normal braces which appear blue.
884 mode no command is needed to get \SpecialChar TeX
887 braces don't appear in the output.
890 \begin_layout Standard
891 When commands without arguments, like commands for symbols are entered in
893 mode, a space character must
897 be behind the command to end it.
898 This space doesn't appear in the output.
899 When the space should appear in the output, the space must be followed
900 by a protected space in normal text.
903 \begin_layout Standard
904 A protected space is inserted with
907 arg "command-alternatives space-insert protected ; math-space"
913 \begin_layout Subsection*
914 \begin_inset Newpage newpage
920 \begin_layout Itemize
922 \begin_inset space \textvisiblespace{}
925 denotes a space character to be input.
928 \begin_layout Itemize
930 \begin_inset Formula $\to$
933 denotes the usage of the corresponding arrow key on the keyboard.
938 key can often be used instead of
939 \begin_inset Formula $\to$
943 \begin_inset Formula $\downarrow$
951 \begin_inset Formula $\leftarrow$
955 \begin_inset Formula $\uparrow$
961 \begin_layout Subsection*
965 \begin_layout Standard
967 \begin_inset Float table
973 \begin_layout Plain Layout
975 \begin_inset Caption Standard
977 \begin_layout Plain Layout
978 \begin_inset CommandInset label
980 name "tab:Available-units"
992 \begin_layout Plain Layout
995 <lyxtabular version="3" rows="13" columns="2">
996 <features booktabs="true" tabularvalignment="middle">
997 <column alignment="center" valignment="top">
998 <column alignment="center" valignment="top" width="0pt">
1000 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1003 \begin_layout Plain Layout
1009 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1012 \begin_layout Plain Layout
1020 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1023 \begin_layout Plain Layout
1029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1032 \begin_layout Plain Layout
1040 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1043 \begin_layout Plain Layout
1049 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1052 \begin_layout Plain Layout
1060 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1063 \begin_layout Plain Layout
1069 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1072 \begin_layout Plain Layout
1074 \begin_inset space \thinspace{}
1078 \begin_inset space \thinspace{}
1088 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1091 \begin_layout Plain Layout
1097 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1100 \begin_layout Plain Layout
1102 \begin_inset space \thinspace{}
1106 \begin_inset space \thinspace{}
1116 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1119 \begin_layout Plain Layout
1125 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1128 \begin_layout Plain Layout
1130 \begin_inset space \thinspace{}
1134 \begin_inset space \thinspace{}
1144 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1147 \begin_layout Plain Layout
1153 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1156 \begin_layout Plain Layout
1158 \begin_inset space \thinspace{}
1162 \begin_inset space \thinspace{}
1172 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1175 \begin_layout Plain Layout
1181 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1184 \begin_layout Plain Layout
1186 \begin_inset space \thinspace{}
1190 \begin_inset space \thinspace{}
1200 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1203 \begin_layout Plain Layout
1209 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1212 \begin_layout Plain Layout
1214 \begin_inset space \thinspace{}
1218 \begin_inset Formula $\approx$
1222 \begin_inset space \thinspace{}
1232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1235 \begin_layout Plain Layout
1241 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1244 \begin_layout Plain Layout
1246 \begin_inset space \thinspace{}
1250 \begin_inset space \thinspace{}
1260 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1263 \begin_layout Plain Layout
1269 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1272 \begin_layout Plain Layout
1276 \begin_inset Quotes eld
1282 \begin_inset Quotes erd
1292 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1295 \begin_layout Plain Layout
1301 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1304 \begin_layout Plain Layout
1306 \begin_inset Quotes eld
1314 \begin_inset Quotes erd
1324 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1327 \begin_layout Plain Layout
1333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1336 \begin_layout Plain Layout
1338 \begin_inset space \thinspace{}
1342 \begin_inset Formula $\nicefrac{1}{18}$
1346 \begin_inset space \thinspace{}
1367 \begin_layout Standard
1368 \begin_inset Newpage newpage
1374 \begin_layout Section
1378 \begin_layout Subsection
1380 \begin_inset Index idx
1383 \begin_layout Plain Layout
1390 \begin_inset Index idx
1393 \begin_layout Plain Layout
1400 \begin_inset Index idx
1403 \begin_layout Plain Layout
1408 \begin_layout Plain Layout
1419 \begin_layout Plain Layout
1432 \begin_inset Index idx
1435 \begin_layout Plain Layout
1440 \begin_layout Plain Layout
1451 \begin_layout Plain Layout
1466 \begin_layout Standard
1467 Indices are created with an underscore
1468 \begin_inset Quotes eld
1472 \begin_inset Quotes erd
1475 or via the math toolbar button
1478 arg "math-subscript"
1481 , exponents with a caret
1482 \begin_inset Quotes eld
1486 \begin_inset Quotes erd
1489 or via the math toolbar button
1492 arg "math-superscript"
1496 \begin_inset Separator parbreak
1502 \begin_layout Standard
1504 \begin_inset Tabular
1505 <lyxtabular version="3" rows="4" columns="2">
1506 <features booktabs="true" tabularvalignment="middle">
1507 <column alignment="center" valignment="top" width="0pt">
1508 <column alignment="center" valignment="top" width="0pt">
1510 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1513 \begin_layout Plain Layout
1519 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1522 \begin_layout Plain Layout
1530 <cell alignment="center" valignment="top" usebox="none">
1533 \begin_layout Plain Layout
1539 <cell alignment="center" valignment="top" usebox="none">
1542 \begin_layout Plain Layout
1543 \begin_inset Formula $B_{V}$
1552 <row topspace="1.5mm">
1553 <cell alignment="center" valignment="top" usebox="none">
1556 \begin_layout Plain Layout
1562 <cell alignment="center" valignment="top" usebox="none">
1565 \begin_layout Plain Layout
1566 \begin_inset Formula $B^{V}$
1575 <row topspace="1.5mm">
1576 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1579 \begin_layout Plain Layout
1581 \begin_inset space \textvisiblespace{}
1589 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1592 \begin_layout Plain Layout
1593 \begin_inset Formula $B^{A}$
1609 \begin_layout Standard
1610 As the caret is in some languages an accent, vowels will be accentuated
1611 in this case and not set as exponents
1615 \begin_layout Plain Layout
1616 Depending on the used keyboard settings this can also happen for characters
1623 To get exponents in this case, press
1627 after the caret as in the last example.
1630 \begin_layout Subsection
1632 \begin_inset CommandInset label
1634 name "subsec:Fractions"
1639 \begin_inset Index idx
1642 \begin_layout Plain Layout
1651 \begin_layout Standard
1652 Fractions are generated with the command
1659 \begin_inset Index idx
1662 \begin_layout Plain Layout
1670 or via the math toolbar button
1673 arg "math-insert \\frac"
1677 The font size is adjusted automatically, depending on whether the fraction
1678 is in an inline or display style formula.
1679 With the math toolbar button
1682 arg "math-insert \\frac-square"
1685 you can select different fraction types.
1688 \begin_layout Standard
1696 \begin_inset Index idx
1699 \begin_layout Plain Layout
1707 a fraction can be created that always has the size of a display style formula.
1715 \begin_inset Index idx
1718 \begin_layout Plain Layout
1726 the fraction appears always with the size of an inline formula.
1730 \begin_layout Standard
1731 A line with the fraction
1732 \begin_inset Formula $\frac{1}{2}$
1735 that was created with the command
1744 \begin_layout Standard
1745 A line with the fraction
1746 \begin_inset Formula $\dfrac{1}{2}$
1749 that was created with the command
1756 \begin_inset Separator parbreak
1762 \begin_layout Standard
1764 \begin_inset Tabular
1765 <lyxtabular version="3" rows="4" columns="2">
1766 <features booktabs="true" tabularvalignment="middle">
1767 <column alignment="center" valignment="top" width="0pt">
1768 <column alignment="center" valignment="top" width="0pt">
1770 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1773 \begin_layout Plain Layout
1779 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1782 \begin_layout Plain Layout
1789 <row topspace="1.5mm">
1790 <cell alignment="center" valignment="top" usebox="none">
1793 \begin_layout Plain Layout
1797 \begin_inset space \textvisiblespace{}
1801 \begin_inset Formula $\downarrow$
1809 <cell alignment="center" valignment="top" usebox="none">
1812 \begin_layout Plain Layout
1813 \begin_inset Formula $\frac{A}{B}$
1822 <row topspace="2mm">
1823 <cell alignment="center" valignment="top" usebox="none">
1826 \begin_layout Plain Layout
1830 \begin_inset space \textvisiblespace{}
1834 \begin_inset Formula $\downarrow$
1842 <cell alignment="center" valignment="top" usebox="none">
1845 \begin_layout Plain Layout
1846 \begin_inset Formula $\dfrac{A}{B}$
1855 <row topspace="2mm" bottomspace="1mm">
1856 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1859 \begin_layout Plain Layout
1863 \begin_inset space \textvisiblespace{}
1869 \begin_inset space \textvisiblespace{}
1873 \begin_inset Formula $\downarrow$
1877 \begin_inset Formula $\downarrow\downarrow$
1885 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1888 \begin_layout Plain Layout
1889 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1905 \begin_layout Standard
1906 \begin_inset VSpace bigskip
1910 \begin_inset Newpage newpage
1913 For nested fractions the command
1920 \begin_inset Index idx
1923 \begin_layout Plain Layout
1933 \begin_inset VSpace -3mm
1939 \begin_layout Standard
1940 \begin_inset Formula
1942 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1943 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1951 \begin_layout Standard
1952 The command for the example above is:
1955 \begin_layout Standard
1961 \begin_inset space \textvisiblespace{}
1965 \begin_inset Formula $\downarrow$
1971 \begin_inset space \textvisiblespace{}
1977 \begin_inset space \textvisiblespace{}
1981 \begin_inset Formula $\downarrow$
1985 \begin_inset Formula $\downarrow$
1991 \begin_layout Standard
1992 \begin_inset VSpace medskip
1998 \begin_layout Standard
2005 sets the fraction always in the size of a displayed formula, also when
2006 it is part of another fraction.
2009 \begin_layout Standard
2010 It is possible to specify the alignment of the numerator.
2017 is used to left align it, the command
2030 centers the numerator.
2031 These fractions demonstrate the different alignments:
2034 \begin_layout Standard
2037 \begin_inset Formula
2039 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2047 \begin_layout Standard
2048 \begin_inset Note Greyedout
2051 \begin_layout Plain Layout
2068 are no real \SpecialChar LaTeX
2069 commands but represent the command
2073 cfrac[alignment]{numerator}{denominator}
2076 Therefore you cannot use them in \SpecialChar TeX
2085 \begin_layout Standard
2086 \begin_inset VSpace medskip
2089 It is often advantageous to combine
2102 \begin_inset Formula
2104 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2112 \begin_layout Standard
2113 For inline fractions with a sloped fraction stroke you can use the command
2121 \begin_inset Index idx
2124 \begin_layout Plain Layout
2133 \begin_inset Formula $\nicefrac{5}{31}$
2143 \begin_inset Index idx
2146 \begin_layout Plain Layout
2155 \begin_inset Formula $\unitfrac{5}{31}$
2158 There is furthermore the command
2164 that offers to write a fraction in combination with a number:
2165 \begin_inset Formula $\unitfrac[2]{1}{3}$
2171 \begin_layout Standard
2172 \begin_inset Note Greyedout
2175 \begin_layout Plain Layout
2186 is not a real \SpecialChar LaTeX
2187 command but the command
2188 \begin_inset Newline newline
2195 unitfrac[number]{numerator}{denominator}
2198 Therefore you cannot use it in \SpecialChar TeX
2207 \begin_layout Standard
2208 How to define own fractions where the fraction stroke can be changed, is
2210 \begin_inset CommandInset ref
2212 reference "subsec:Self-defined-Fractions"
2219 \begin_layout Standard
2220 Multiline fractions are explained in
2221 \begin_inset CommandInset ref
2223 reference "subsec:Multiline-Fractions"
2230 \begin_layout Subsection
2232 \begin_inset Index idx
2235 \begin_layout Plain Layout
2244 \begin_layout Standard
2245 Square roots are created with
2252 \begin_inset Index idx
2255 \begin_layout Plain Layout
2263 or the math toolbar button
2266 arg "math-insert \\sqrt"
2269 , all other roots with the command
2276 \begin_inset Index idx
2279 \begin_layout Plain Layout
2287 or with the math toolbar button
2290 arg "math-insert \\root"
2294 \begin_inset Separator parbreak
2300 \begin_layout Standard
2302 \begin_inset Tabular
2303 <lyxtabular version="3" rows="3" columns="2">
2304 <features booktabs="true" tabularvalignment="middle">
2305 <column alignment="center" valignment="top" width="0pt">
2306 <column alignment="center" valignment="top" width="0pt">
2308 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2311 \begin_layout Plain Layout
2317 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2320 \begin_layout Plain Layout
2327 <row topspace="1mm">
2328 <cell alignment="center" valignment="top" usebox="none">
2331 \begin_layout Plain Layout
2335 \begin_inset space \textvisiblespace{}
2343 <cell alignment="center" valignment="top" usebox="none">
2346 \begin_layout Plain Layout
2347 \begin_inset Formula $\sqrt{A-B}$
2356 <row topspace="1mm">
2357 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2360 \begin_layout Plain Layout
2364 \begin_inset space \textvisiblespace{}
2368 \begin_inset Formula $\downarrow$
2376 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2379 \begin_layout Plain Layout
2380 \begin_inset Formula $\sqrt[3]{A-B}$
2396 \begin_layout Standard
2397 A square root can also be created with
2403 when the root index field is left empty.
2406 \begin_layout Standard
2407 With certain indices the distance to the root is too small, like in this
2409 \begin_inset Formula $\sqrt[\beta]{B}$
2413 \begin_inset Newline newline
2417 \begin_inset Formula $\beta$
2421 To avoid this, the commands
2428 \begin_inset Index idx
2431 \begin_layout Plain Layout
2446 \begin_inset Index idx
2449 \begin_layout Plain Layout
2457 are used with the following scheme:
2460 \begin_layout Standard
2474 \begin_layout Standard
2475 Distance is the number of Big Points (unit bp;
2476 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2479 ), that the index should be moved to the left or top, resp..
2480 The commands are written to the index.
2481 This way the command
2482 \begin_inset Newline newline
2492 \begin_inset Formula $\to$
2498 \begin_inset Formula $\to$
2504 \begin_inset space \textvisiblespace{}
2508 \begin_inset Formula $\to$
2512 \begin_inset Newline newline
2517 produces a correct typeset formula:
2518 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2524 \begin_layout Subsection
2525 Binomial Coefficients
2526 \begin_inset Index idx
2529 \begin_layout Plain Layout
2530 Binomial coefficients
2538 \begin_layout Standard
2539 Binomial coefficients are inserted with the command
2546 \begin_inset Index idx
2549 \begin_layout Plain Layout
2557 or with the submenu of the math toolbar button
2560 arg "math-insert \\frac-square"
2576 there are the commands
2583 \begin_inset Index idx
2586 \begin_layout Plain Layout
2601 \begin_inset Index idx
2604 \begin_layout Plain Layout
2613 For other brackets around binomial coeficients there are the commands
2620 \begin_inset Index idx
2623 \begin_layout Plain Layout
2638 \begin_inset Index idx
2641 \begin_layout Plain Layout
2650 \begin_inset Separator parbreak
2656 \begin_layout Standard
2658 \begin_inset Tabular
2659 <lyxtabular version="3" rows="6" columns="2">
2660 <features booktabs="true" tabularvalignment="middle">
2661 <column alignment="center" valignment="top" width="0pt">
2662 <column alignment="center" valignment="top" width="0pt">
2664 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2667 \begin_layout Plain Layout
2673 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2676 \begin_layout Plain Layout
2683 <row topspace="1mm">
2684 <cell alignment="center" valignment="top" usebox="none">
2687 \begin_layout Plain Layout
2691 \begin_inset space \textvisiblespace{}
2695 \begin_inset Formula $\downarrow$
2703 <cell alignment="center" valignment="top" usebox="none">
2706 \begin_layout Plain Layout
2707 \begin_inset Formula $\binom{A}{B}$
2716 <row topspace="2mm">
2717 <cell alignment="center" valignment="top" usebox="none">
2720 \begin_layout Plain Layout
2724 \begin_inset space \textvisiblespace{}
2728 \begin_inset Formula $\downarrow$
2736 <cell alignment="center" valignment="top" usebox="none">
2739 \begin_layout Plain Layout
2740 \begin_inset Formula $\dbinom{A}{B}$
2749 <row topspace="2mm" bottomspace="0.5mm">
2750 <cell alignment="center" valignment="top" usebox="none">
2753 \begin_layout Plain Layout
2757 \begin_inset space \textvisiblespace{}
2761 \begin_inset Formula $\downarrow$
2769 <cell alignment="center" valignment="top" usebox="none">
2772 \begin_layout Plain Layout
2773 \begin_inset Formula $\tbinom{A}{B}$
2782 <row topspace="1mm">
2783 <cell alignment="center" valignment="top" topline="true" usebox="none">
2786 \begin_layout Plain Layout
2790 \begin_inset space \textvisiblespace{}
2794 \begin_inset Formula $\downarrow$
2802 <cell alignment="center" valignment="top" topline="true" usebox="none">
2805 \begin_layout Plain Layout
2806 \begin_inset Formula ${A \brack B}$
2815 <row topspace="2mm" bottomspace="0.5mm">
2816 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2819 \begin_layout Plain Layout
2823 \begin_inset space \textvisiblespace{}
2827 \begin_inset Formula $\downarrow$
2835 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2838 \begin_layout Plain Layout
2839 \begin_inset Formula ${A \brace B}$
2855 \begin_layout Subsection
2856 Case Differentiations
2857 \begin_inset Index idx
2860 \begin_layout Plain Layout
2861 Case differentiations
2869 \begin_layout Standard
2871 \begin_inset Tabular
2872 <lyxtabular version="3" rows="3" columns="2">
2873 <features booktabs="true" tabularvalignment="middle">
2874 <column alignment="center" valignment="top" width="0pt">
2875 <column alignment="center" valignment="top" width="0pt">
2877 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2880 \begin_layout Plain Layout
2886 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2889 \begin_layout Plain Layout
2897 <cell alignment="center" valignment="top" usebox="none">
2900 \begin_layout Plain Layout
2904 \begin_inset space \textvisiblespace{}
2908 \begin_inset Formula $\to$
2912 \begin_inset Index idx
2915 \begin_layout Plain Layout
2928 <cell alignment="center" valignment="top" usebox="none">
2931 \begin_layout Plain Layout
2932 \begin_inset Formula $\begin{cases}
2942 <row topspace="1.5mm">
2943 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2946 \begin_layout Plain Layout
2950 \begin_inset space \textvisiblespace{}
2956 arg "newline-insert newline"
2964 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2967 \begin_layout Plain Layout
2968 \begin_inset Formula $\begin{cases}
2969 A & \textrm{for }x>0\\
2970 B & \textrm{for }x=0
2987 \begin_layout Standard
2994 or pressing the math toolbar button
2997 arg "math-insert \\cases"
3000 you can create new lines with the shortcut
3003 arg "newline-insert newline"
3006 or the table toolbar button
3009 arg "inset-modify tabular append-row"
3015 \begin_layout Standard
3022 is also available via the menu
3024 Insert\SpecialChar menuseparator
3025 Math\SpecialChar menuseparator
3031 \begin_layout Subsection
3033 \begin_inset Index idx
3036 \begin_layout Plain Layout
3045 \begin_layout Standard
3053 \begin_inset Index idx
3056 \begin_layout Plain Layout
3064 every character can be displayed canceled.
3065 The characters are quasi accentuated by a slash.
3066 \begin_inset Separator parbreak
3072 \begin_layout Standard
3074 \begin_inset Tabular
3075 <lyxtabular version="3" rows="4" columns="2">
3076 <features booktabs="true" tabularvalignment="middle">
3077 <column alignment="center" valignment="top" width="0pt">
3078 <column alignment="center" valignment="top" width="0pt">
3080 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3083 \begin_layout Plain Layout
3089 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3092 \begin_layout Plain Layout
3100 <cell alignment="center" valignment="top" usebox="none">
3103 \begin_layout Plain Layout
3111 <cell alignment="center" valignment="top" usebox="none">
3114 \begin_layout Plain Layout
3115 \begin_inset Formula $\not=$
3125 <cell alignment="center" valignment="top" usebox="none">
3128 \begin_layout Plain Layout
3138 <cell alignment="center" valignment="top" usebox="none">
3141 \begin_layout Plain Layout
3142 \begin_inset Formula $\not\le$
3152 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3155 \begin_layout Plain Layout
3165 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3168 \begin_layout Plain Layout
3169 \begin_inset Formula $\not\parallel$
3185 \begin_layout Standard
3186 The last example shows that not all negations look good.
3187 Therefore there are special commands for some negations (see
3188 \begin_inset CommandInset ref
3190 reference "subsec:Mathematical-Symbols"
3195 \begin_inset CommandInset ref
3197 reference "sec:Relations"
3204 \begin_layout Subsection
3206 \begin_inset CommandInset label
3208 name "subsec:Placeholders"
3213 \begin_inset Index idx
3216 \begin_layout Plain Layout
3223 \begin_inset Index idx
3226 \begin_layout Plain Layout
3227 Chemical characters ! Isotopes
3233 \begin_inset Index idx
3236 \begin_layout Plain Layout
3241 \begin_layout Plain Layout
3252 \begin_layout Plain Layout
3267 \begin_layout Standard
3269 \begin_inset space \thinspace{}
3273 \begin_inset space \space{}
3280 \begin_layout Plain Layout
3281 Typesetting isotopes and chemical symbols is described in
3282 \begin_inset CommandInset ref
3284 reference "subsec:Chemical-Symbols-and"
3293 the following problem occurs:
3294 \begin_inset Separator parbreak
3300 \begin_layout Standard
3302 \begin_inset Tabular
3303 <lyxtabular version="3" rows="2" columns="2">
3304 <features booktabs="true" tabularvalignment="middle">
3305 <column alignment="center" valignment="top" width="0pt">
3306 <column alignment="center" valignment="top" width="0pt">
3308 <cell alignment="center" valignment="top" usebox="none">
3311 \begin_layout Plain Layout
3312 Indices created with sub- and superscripts:
3317 <cell alignment="center" valignment="top" usebox="none">
3320 \begin_layout Plain Layout
3321 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3330 <row topspace="1.5mm">
3331 <cell alignment="center" valignment="top" usebox="none">
3334 \begin_layout Plain Layout
3340 <cell alignment="center" valignment="top" usebox="none">
3343 \begin_layout Plain Layout
3344 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3360 \begin_layout Standard
3361 The shorter index is by default placed below or above the first character
3362 of the longer index.
3363 To avoid this there is the command
3370 \begin_inset Index idx
3373 \begin_layout Plain Layout
3381 or the math toolbar button
3382 \begin_inset space \thinspace{}
3389 \begin_layout Plain Layout
3390 can be found in the submenu of the toolbar button
3393 arg "math-insert \\space"
3407 that creates one or more phantom characters.
3414 a small blue box appears that is superposed with two red arrows.
3415 The arrows indicate that the complete width and height of the box content
3416 will be created as placeholder.
3417 Phantom characters are accordingly placeholders with the size of the characters.
3418 \begin_inset Separator parbreak
3424 \begin_layout Standard
3426 \begin_inset Tabular
3427 <lyxtabular version="3" rows="4" columns="2">
3428 <features booktabs="true" tabularvalignment="middle">
3429 <column alignment="center" valignment="top" width="0pt">
3430 <column alignment="center" valignment="top" width="0pt">
3432 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3435 \begin_layout Plain Layout
3441 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3444 \begin_layout Plain Layout
3451 <row topspace="1.5mm">
3452 <cell alignment="center" valignment="top" usebox="none">
3455 \begin_layout Plain Layout
3457 \begin_inset space \textvisiblespace{}
3463 \begin_inset space \textvisiblespace{}
3467 \begin_inset Formula $\to$
3471 \begin_inset space \textvisiblespace{}
3479 <cell alignment="center" valignment="top" usebox="none">
3482 \begin_layout Plain Layout
3483 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3492 <row topspace="1.5mm" bottomspace="0.5mm">
3493 <cell alignment="center" valignment="top" usebox="none">
3496 \begin_layout Plain Layout
3498 \begin_inset space \textvisiblespace{}
3504 \begin_inset space \textvisiblespace{}
3508 \begin_inset Formula $\to$
3512 \begin_inset space \textvisiblespace{}
3520 <cell alignment="center" valignment="top" usebox="none">
3523 \begin_layout Plain Layout
3524 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3533 <row topspace="1.5mm" bottomspace="0.5mm">
3534 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3537 \begin_layout Plain Layout
3541 \begin_inset space \textvisiblespace{}
3547 \begin_inset space \textvisiblespace{}
3551 \begin_inset Formula $\to$
3555 \begin_inset space \textvisiblespace{}
3563 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3566 \begin_layout Plain Layout
3567 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3583 \begin_layout Standard
3584 Furthermore there are the commands
3591 \begin_inset Index idx
3594 \begin_layout Plain Layout
3615 \begin_inset Index idx
3618 \begin_layout Plain Layout
3639 creates only space for the maximal height of the characters in the box
3640 but not for its width.
3647 creates only space for the width of the box content.
3648 Therefore the boxes of both commands have only one red arrow.
3651 \begin_layout Standard
3652 For example the command
3657 \begin_inset space \textvisiblespace{}
3664 creates space for the height of the integral sign,
3668 \begin_layout Plain Layout
3675 creates an integral sign, see
3676 \begin_inset CommandInset ref
3678 reference "subsec:Big-Operators"
3687 because this is the larger character.
3688 An example application is in
3689 \begin_inset CommandInset ref
3691 reference "subsec:Multiline-Brackets"
3698 \begin_layout Standard
3699 Placeholders can also be used for text when they are inserted via the menu
3702 Insert\SpecialChar menuseparator
3703 Formatting\SpecialChar menuseparator
3709 \begin_layout Standard
3711 \begin_inset Newline newline
3715 \begin_inset Phantom Phantom
3718 \begin_layout Plain Layout
3727 \begin_layout Subsection
3729 \begin_inset Index idx
3732 \begin_layout Plain Layout
3739 \begin_inset Index idx
3742 \begin_layout Plain Layout
3743 Formula ! underlined
3751 \begin_layout Standard
3753 \begin_inset Tabular
3754 <lyxtabular version="3" rows="4" columns="2">
3755 <features booktabs="true" tabularvalignment="middle">
3756 <column alignment="center" valignment="top" width="0pt">
3757 <column alignment="center" valignment="top" width="0pt">
3759 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3762 \begin_layout Plain Layout
3768 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3771 \begin_layout Plain Layout
3778 <row topspace="2mm">
3779 <cell alignment="center" valignment="top" usebox="none">
3782 \begin_layout Plain Layout
3786 \begin_inset space \textvisiblespace{}
3790 \begin_inset Index idx
3793 \begin_layout Plain Layout
3806 <cell alignment="center" valignment="top" usebox="none">
3809 \begin_layout Plain Layout
3810 \begin_inset Formula $\overline{A+B}$
3819 <row bottomspace="1mm">
3820 <cell alignment="center" valignment="top" usebox="none">
3823 \begin_layout Plain Layout
3827 \begin_inset space \textvisiblespace{}
3831 \begin_inset Index idx
3834 \begin_layout Plain Layout
3847 <cell alignment="center" valignment="top" usebox="none">
3850 \begin_layout Plain Layout
3851 \begin_inset Formula $\underline{A+B}$
3860 <row topspace="2mm" bottomspace="1mm">
3861 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3864 \begin_layout Plain Layout
3868 \begin_inset space \textvisiblespace{}
3874 \begin_inset space \textvisiblespace{}
3882 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3885 \begin_layout Plain Layout
3886 \begin_inset Formula $\overline{\underline{A+B}}$
3902 \begin_layout Standard
3903 In the last example it doesn't matter if first
3918 \begin_layout Standard
3919 To double underline use
3928 \begin_layout Standard
3929 It is possible to place up to 6 lines above or below characters.
3932 \begin_layout Standard
3933 \begin_inset VSpace bigskip
3936 Custom lines can be created using the command
3943 \begin_inset Index idx
3946 \begin_layout Plain Layout
3954 which has the following scheme:
3957 \begin_layout Standard
3962 rule[vertical offset]{length}{thickness}
3965 \begin_layout Standard
3966 The optional vertical offset shifts the line upwards (or downwards, when
3967 the value is negative).
3969 \begin_inset CommandInset ref
3971 reference "tab:Available-units"
3975 can be used for the values.
3976 Here are two example lines created with the commands
3977 \begin_inset Newline newline
3984 rule[-2ex]{3cm}{2pt}
3995 \begin_layout Standard
3997 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4003 \begin_layout Standard
4010 can also be used for text when a line is inserted via the menu
4012 Insert\SpecialChar menuseparator
4013 Formatting\SpecialChar menuseparator
4015 \begin_inset space ~
4023 \begin_layout Standard
4025 \begin_inset CommandInset line
4036 \begin_layout Subsection
4038 \begin_inset CommandInset label
4040 name "subsec:Ellipses"
4045 \begin_inset Index idx
4048 \begin_layout Plain Layout
4057 \begin_layout Standard
4058 There are different types of ellipses available.
4062 \begin_layout Plain Layout
4063 In the math toolbar in the submenu of the button
4066 arg "math-insert \\ldots"
4074 For listings dots at the baseline are used (
4081 \begin_inset Index idx
4084 \begin_layout Plain Layout
4092 ), while for operations dots are needed that are on the same height as the
4100 \begin_inset Index idx
4103 \begin_layout Plain Layout
4112 When using the command
4119 \begin_inset Index idx
4122 \begin_layout Plain Layout
4130 , \SpecialChar LaTeX
4131 decides on the basis of the next character what type is used.
4132 \begin_inset Separator parbreak
4138 \begin_layout Standard
4140 \begin_inset Tabular
4141 <lyxtabular version="3" rows="9" columns="2">
4142 <features booktabs="true" tabularvalignment="middle">
4143 <column alignment="center" valignment="top" width="0pt">
4144 <column alignment="center" valignment="top" width="0pt">
4146 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4149 \begin_layout Plain Layout
4155 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4158 \begin_layout Plain Layout
4166 <cell alignment="center" valignment="top" usebox="none">
4169 \begin_layout Plain Layout
4171 \begin_inset space \textvisiblespace{}
4177 \begin_inset space \textvisiblespace{}
4185 <cell alignment="center" valignment="top" usebox="none">
4188 \begin_layout Plain Layout
4189 \begin_inset Formula $A_{1},\dots,A_{n}$
4199 <cell alignment="center" valignment="top" usebox="none">
4202 \begin_layout Plain Layout
4204 \begin_inset space \textvisiblespace{}
4210 \begin_inset space \textvisiblespace{}
4218 <cell alignment="center" valignment="top" usebox="none">
4221 \begin_layout Plain Layout
4222 \begin_inset Formula $A_{1}+\dots+A_{n}$
4232 <cell alignment="center" valignment="top" usebox="none">
4235 \begin_layout Plain Layout
4237 \begin_inset space \textvisiblespace{}
4243 \begin_inset space \textvisiblespace{}
4251 <cell alignment="center" valignment="top" usebox="none">
4254 \begin_layout Plain Layout
4255 \begin_inset Formula $A_{1},\ldots,A_{n}$
4265 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4268 \begin_layout Plain Layout
4270 \begin_inset space \textvisiblespace{}
4276 \begin_inset space \textvisiblespace{}
4284 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4287 \begin_layout Plain Layout
4288 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4298 <cell alignment="center" valignment="top" usebox="none">
4301 \begin_layout Plain Layout
4309 <cell alignment="center" valignment="top" usebox="none">
4312 \begin_layout Plain Layout
4313 \begin_inset Formula $\vdots$
4323 <cell alignment="center" valignment="top" usebox="none">
4326 \begin_layout Plain Layout
4334 <cell alignment="center" valignment="top" usebox="none">
4337 \begin_layout Plain Layout
4338 \begin_inset Formula $\ddots$
4348 <cell alignment="center" valignment="top" usebox="none">
4351 \begin_layout Plain Layout
4359 <cell alignment="center" valignment="top" usebox="none">
4362 \begin_layout Plain Layout
4363 \begin_inset Formula $\iddots$
4373 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4376 \begin_layout Plain Layout
4378 \begin_inset space \thinspace{}
4381 matrix with the different dots
4386 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4389 \begin_layout Plain Layout
4390 \begin_inset Formula $\begin{array}{ccc}
4391 A_{11} & \cdots & A_{1m}\\
4392 \vdots & \ddots & \vdots\\
4393 A_{n1} & \cdots & A_{nm}
4410 \begin_layout Standard
4411 The ellipses available in menu
4413 Insert\SpecialChar menuseparator
4415 \begin_inset space ~
4429 \begin_layout Standard
4430 \begin_inset VSpace medskip
4439 , one of the options
4441 Use mathdots package (automatically)
4443 must be set in the document settings under
4446 \begin_inset space ~
4452 \begin_inset Newline newline
4457 Use mathdots package
4459 will improve the appearance of all dots in the documents if their font
4460 style or size is not the default.
4463 \begin_layout Standard
4464 \begin_inset VSpace medskip
4467 Specially for matrices there are ellipses that span over several columns.
4468 They are created with the command
4475 \begin_inset Index idx
4478 \begin_layout Plain Layout
4486 , that has the following scheme:
4489 \begin_layout Standard
4494 hdotsfor[distance]{number of columns}
4497 \begin_layout Standard
4498 The number of columns specifies how many columns should be spanned.
4499 Distance is a factor for the distance between the dots.
4502 \begin_layout Standard
4503 In the following matrix the command
4509 was inserted in the first box of the second line, to get an ellipsis with
4510 a dot distance twice as long as with the command
4517 \begin_inset Formula
4519 \left(\begin{array}{cccc}
4528 Note that the matrix fields that should be spanned must be empty, otherwise
4529 you get \SpecialChar LaTeX
4533 \begin_layout Standard
4534 \begin_inset VSpace bigskip
4537 Furthermore you can fill with the command
4544 \begin_inset Index idx
4547 \begin_layout Plain Layout
4555 the rest of a line with dots.
4556 The effect of these commands is the same as with
4563 \begin_inset CommandInset ref
4565 reference "subsec:Variable-Space"
4572 \begin_layout Standard
4573 For example the command
4578 \begin_inset space \textvisiblespace{}
4586 \begin_layout Standard
4587 \begin_inset Formula $A\dotfill B$
4593 \begin_layout Standard
4600 there is for a line the command
4607 \begin_inset Index idx
4610 \begin_layout Plain Layout
4621 \begin_layout Standard
4622 \begin_inset Formula $A\hrulefill B$
4628 \begin_layout Standard
4629 To use the commands for text, they have to be inserted in \SpecialChar TeX
4633 \begin_layout Section
4635 \begin_inset CommandInset label
4642 \begin_inset Index idx
4645 \begin_layout Plain Layout
4654 \begin_layout Standard
4655 Matrices can be inserted via the math toolbar button
4658 arg "dialog-show mathmatrix"
4663 Insert\SpecialChar menuseparator
4664 Math\SpecialChar menuseparator
4668 In the matrix dialog you can specify the number of columns and rows, the
4669 alignment and the decoration.
4670 The vertical alignment is only of importance for matrices in inline formulas:
4673 \begin_layout Standard
4674 The first matrix is top
4675 \begin_inset Formula $\begin{array}[t]{cccc}
4683 \begin_inset Formula $\begin{array}{cccc}
4690 and the third bottom
4691 \begin_inset Formula $\begin{array}[b]{cccc}
4701 \begin_layout Standard
4702 The horizontal alignment specifies how the column entries should be aligned.
4703 It is set by entering a letter for every column.
4708 denotes left aligned,
4717 To create for example a 4
4722 \begin_inset space ~
4725 matrix where the first column is left aligned, the second and third are
4726 centered and the last one is right aligned, one enters for the horizontal
4732 Normally in a matrix all columns are centered, therefore the default for
4740 \begin_layout Standard
4741 Horizontal alignment:
4744 \begin_layout Standard
4750 \begin_inset Formula $\begin{array}{lll}
4762 \begin_inset Formula $\begin{array}{ccc}
4774 \begin_inset Formula $\begin{array}{rrr}
4784 \begin_layout Standard
4785 To add or delete rows and columns subsequently, the math toolbar buttons
4789 arg "inset-modify tabular append-row"
4795 arg "inset-modify tabular delete-row"
4799 \begin_inset space \thinspace{}
4804 Edit\SpecialChar menuseparator
4808 New rows can also be created with
4811 arg "newline-insert newline"
4817 \begin_layout Standard
4818 \begin_inset VSpace bigskip
4825 adds parentheses in the selected style around the matrix.
4826 Alternatively, parentheses can can either be created with the commands
4834 \begin_inset Index idx
4837 \begin_layout Plain Layout
4852 \begin_inset Index idx
4855 \begin_layout Plain Layout
4866 \begin_inset space ~
4872 \begin_inset CommandInset ref
4874 reference "subsec:Automatic-Bracket-Size"
4878 , or by using the following commands:
4879 \begin_inset VSpace medskip
4885 \begin_layout Standard
4886 \begin_inset space \hfill{}
4890 \begin_inset Tabular
4891 <lyxtabular version="3" rows="4" columns="2">
4892 <features booktabs="true" tabularvalignment="middle">
4893 <column alignment="center" valignment="top" width="0pt">
4894 <column alignment="center" valignment="top">
4896 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4899 \begin_layout Plain Layout
4905 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4908 \begin_layout Plain Layout
4915 <row topspace="1.5mm">
4916 <cell alignment="center" valignment="top" usebox="none">
4919 \begin_layout Plain Layout
4923 \begin_inset space \textvisiblespace{}
4931 \begin_inset space \thinspace{}
4939 <cell alignment="center" valignment="top" usebox="none">
4942 \begin_layout Plain Layout
4943 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4944 0 & \textrm{-}\mathrm{i}\\
4946 \end{array}\end{bmatrix}$
4955 <row topspace="1.5mm" bottomspace="0.5mm">
4956 <cell alignment="center" valignment="top" usebox="none">
4959 \begin_layout Plain Layout
4963 \begin_inset space \textvisiblespace{}
4971 \begin_inset space \thinspace{}
4979 <cell alignment="center" valignment="top" usebox="none">
4982 \begin_layout Plain Layout
4983 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
4984 0 & \textrm{-}\mathrm{i}\\
4986 \end{array}\end{Bmatrix}$
4996 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4999 \begin_layout Plain Layout
5003 \begin_inset space \textvisiblespace{}
5011 \begin_inset space \thinspace{}
5019 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5022 \begin_layout Plain Layout
5023 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5024 0 & \textrm{-}\mathrm{i}\\
5026 \end{array}\end{pmatrix}$
5040 \begin_inset space \hfill{}
5044 \begin_inset Tabular
5045 <lyxtabular version="3" rows="4" columns="2">
5046 <features booktabs="true" tabularvalignment="middle">
5047 <column alignment="center" valignment="top" width="0pt">
5048 <column alignment="center" valignment="top">
5050 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5053 \begin_layout Plain Layout
5059 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5062 \begin_layout Plain Layout
5069 <row topspace="1.5mm">
5070 <cell alignment="center" valignment="top" usebox="none">
5073 \begin_layout Plain Layout
5077 \begin_inset space \textvisiblespace{}
5085 \begin_inset space \thinspace{}
5093 <cell alignment="center" valignment="top" usebox="none">
5096 \begin_layout Plain Layout
5097 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5098 0 & \textrm{-}\mathrm{i}\\
5100 \end{array}\end{vmatrix}$
5109 <row topspace="1.5mm" bottomspace="0.5mm">
5110 <cell alignment="center" valignment="top" usebox="none">
5113 \begin_layout Plain Layout
5117 \begin_inset space \textvisiblespace{}
5125 \begin_inset space \thinspace{}
5133 <cell alignment="center" valignment="top" usebox="none">
5136 \begin_layout Plain Layout
5137 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5138 0 & \textrm{-}\mathrm{i}\\
5140 \end{array}\end{Vmatrix}$
5150 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5153 \begin_layout Plain Layout
5157 \begin_inset space \textvisiblespace{}
5165 \begin_inset space \thinspace{}
5173 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5176 \begin_layout Plain Layout
5177 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5178 0 & \textrm{-}\mathrm{i}\\
5180 \end{array}\end{matrix}$
5194 \begin_inset space \hfill{}
5200 \begin_layout Standard
5201 \begin_inset VSpace medskip
5205 \begin_inset space \thinspace{}
5209 \begin_inset space \space{}
5218 is inserted, a blue box appears between two vertical lines where the matrix
5220 \begin_inset Newline newline
5223 Note that decorated matrices ignore the vertical alignment.
5226 \begin_layout Standard
5227 \begin_inset VSpace bigskip
5230 As all multiline formulas are matrices, the length
5237 \begin_inset Index idx
5240 \begin_layout Plain Layout
5248 that is described in
5249 \begin_inset CommandInset ref
5251 reference "subsec:Column-Separation"
5255 can also be used to change the column separation of matrices.
5258 \begin_layout Standard
5259 To change the row separation, the command
5266 \begin_inset Index idx
5269 \begin_layout Plain Layout
5278 It is used as follows:
5281 \begin_layout Standard
5288 arraystretch}{stretch factor}
5289 \begin_inset Index idx
5292 \begin_layout Plain Layout
5303 \begin_layout Standard
5310 assigns the stretch factor to the predefined command
5318 \begin_inset space \thinspace{}
5322 \begin_inset space \space{}
5325 the row separation, use the factor 2.
5326 This is then used for all following matrices.
5327 To go back to the original separation, assign the factor 1 to
5336 \begin_layout Standard
5337 To set matrices into a text line, the command
5344 \begin_inset Index idx
5347 \begin_layout Plain Layout
5356 When it is inserted a blue box with two dashed lines appears.
5357 In this box the matrix is inserted.
5360 \begin_layout Standard
5362 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5364 \end{smallmatrix}\right)$
5370 \begin_layout Section
5371 Brackets and Delimiters
5372 \begin_inset Index idx
5375 \begin_layout Plain Layout
5382 \begin_inset Index idx
5385 \begin_layout Plain Layout
5394 \begin_layout Subsection
5395 Vertical Brackets and Delimiters
5396 \begin_inset Index idx
5399 \begin_layout Plain Layout
5408 \begin_layout Standard
5409 \begin_inset space \hfill{}
5413 \begin_inset Tabular
5414 <lyxtabular version="3" rows="9" columns="2">
5415 <features booktabs="true" tabularvalignment="middle">
5416 <column alignment="center" valignment="top" width="0pt">
5417 <column alignment="center" valignment="top" width="0pt">
5419 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5422 \begin_layout Plain Layout
5428 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5431 \begin_layout Plain Layout
5439 <cell alignment="center" valignment="top" usebox="none">
5442 \begin_layout Plain Layout
5448 <cell alignment="center" valignment="top" usebox="none">
5451 \begin_layout Plain Layout
5452 \begin_inset Formula $($
5462 <cell alignment="center" valignment="top" usebox="none">
5465 \begin_layout Plain Layout
5471 <cell alignment="center" valignment="top" usebox="none">
5474 \begin_layout Plain Layout
5475 \begin_inset Formula $\{$
5485 <cell alignment="center" valignment="top" usebox="none">
5488 \begin_layout Plain Layout
5494 <cell alignment="center" valignment="top" usebox="none">
5497 \begin_layout Plain Layout
5498 \begin_inset Formula $[$
5508 <cell alignment="center" valignment="top" usebox="none">
5511 \begin_layout Plain Layout
5519 <cell alignment="center" valignment="top" usebox="none">
5522 \begin_layout Plain Layout
5523 \begin_inset Formula $\langle$
5533 <cell alignment="center" valignment="top" usebox="none">
5536 \begin_layout Plain Layout
5544 <cell alignment="center" valignment="top" usebox="none">
5547 \begin_layout Plain Layout
5548 \begin_inset Formula $\lceil$
5558 <cell alignment="center" valignment="top" usebox="none">
5561 \begin_layout Plain Layout
5569 <cell alignment="center" valignment="top" usebox="none">
5572 \begin_layout Plain Layout
5573 \begin_inset Formula $\lfloor$
5583 <cell alignment="center" valignment="top" usebox="none">
5586 \begin_layout Plain Layout
5592 <cell alignment="center" valignment="top" usebox="none">
5595 \begin_layout Plain Layout
5596 \begin_inset Formula $/$
5606 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5609 \begin_layout Plain Layout
5615 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5618 \begin_layout Plain Layout
5619 \begin_inset Formula $|$
5633 \begin_inset space \hfill{}
5637 \begin_inset Tabular
5638 <lyxtabular version="3" rows="9" columns="2">
5639 <features booktabs="true" tabularvalignment="middle">
5640 <column alignment="center" valignment="top" width="0pt">
5641 <column alignment="center" valignment="top" width="0pt">
5643 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5646 \begin_layout Plain Layout
5652 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5655 \begin_layout Plain Layout
5663 <cell alignment="center" valignment="top" usebox="none">
5666 \begin_layout Plain Layout
5672 <cell alignment="center" valignment="top" usebox="none">
5675 \begin_layout Plain Layout
5676 \begin_inset Formula $)$
5686 <cell alignment="center" valignment="top" usebox="none">
5689 \begin_layout Plain Layout
5695 <cell alignment="center" valignment="top" usebox="none">
5698 \begin_layout Plain Layout
5699 \begin_inset Formula $\}$
5709 <cell alignment="center" valignment="top" usebox="none">
5712 \begin_layout Plain Layout
5718 <cell alignment="center" valignment="top" usebox="none">
5721 \begin_layout Plain Layout
5722 \begin_inset Formula $]$
5732 <cell alignment="center" valignment="top" usebox="none">
5735 \begin_layout Plain Layout
5743 <cell alignment="center" valignment="top" usebox="none">
5746 \begin_layout Plain Layout
5747 \begin_inset Formula $\rangle$
5757 <cell alignment="center" valignment="top" usebox="none">
5760 \begin_layout Plain Layout
5768 <cell alignment="center" valignment="top" usebox="none">
5771 \begin_layout Plain Layout
5772 \begin_inset Formula $\rceil$
5782 <cell alignment="center" valignment="top" usebox="none">
5785 \begin_layout Plain Layout
5793 <cell alignment="center" valignment="top" usebox="none">
5796 \begin_layout Plain Layout
5797 \begin_inset Formula $\rfloor$
5807 <cell alignment="center" valignment="top" usebox="none">
5810 \begin_layout Plain Layout
5820 <cell alignment="center" valignment="top" usebox="none">
5823 \begin_layout Plain Layout
5824 \begin_inset Formula $\backslash$
5834 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5837 \begin_layout Plain Layout
5845 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5848 \begin_layout Plain Layout
5849 \begin_inset Formula $\|$
5863 \begin_inset space \hfill{}
5869 \begin_layout Standard
5872 \begin_inset Note Greyedout
5875 \begin_layout Plain Layout
5888 \begin_inset Index idx
5891 \begin_layout Plain Layout
5899 must be used for the backslash, because the command
5907 produces a line break there.
5915 \begin_layout Standard
5916 For all characters listed above the size can be adjusted with the commands
5917 described in the following two subsections.
5918 When using these commands, the characters < and > can directly be used
5919 instead of the commands
5934 \begin_layout Subsubsection
5936 \begin_inset CommandInset label
5938 name "subsec:Manual-Bracket-Size"
5943 \begin_inset Index idx
5946 \begin_layout Plain Layout
5947 Bracket size ! manual
5955 \begin_layout Standard
5956 The bracket size can be specified manually by the \SpecialChar LaTeX
5964 \begin_inset Index idx
5967 \begin_layout Plain Layout
6000 denotes the smallest and
6006 the largest bracket size.
6009 \begin_layout Standard
6010 These commands are used to emphasize levels of brackets:
6011 \begin_inset Separator parbreak
6017 \begin_layout Standard
6019 \begin_inset Tabular
6020 <lyxtabular version="3" rows="2" columns="2">
6021 <features booktabs="true" tabularvalignment="middle">
6022 <column alignment="center" valignment="top" width="0pt">
6023 <column alignment="center" valignment="top" width="0pt">
6025 <cell alignment="center" valignment="top" usebox="none">
6028 \begin_layout Plain Layout
6029 all brackets in the same size:
6034 <cell alignment="center" valignment="top" usebox="none">
6037 \begin_layout Plain Layout
6038 \begin_inset Formula $((A+B)(A-B))^{C}$
6047 <row topspace="2mm">
6048 <cell alignment="center" valignment="top" usebox="none">
6051 \begin_layout Plain Layout
6057 <cell alignment="center" valignment="top" usebox="none">
6060 \begin_layout Plain Layout
6061 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6077 \begin_layout Standard
6078 For the second formula the command
6085 \begin_inset space \textvisiblespace{}
6093 \begin_layout Standard
6094 Here is an overview about all bracket sizes:
6095 \begin_inset Separator parbreak
6101 \begin_layout Standard
6118 \begin_inset space \textvisiblespace{}
6126 \begin_inset space \textvisiblespace{}
6130 \begin_inset space \textvisiblespace{}
6140 \begin_layout Standard
6142 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6148 \begin_layout Standard
6155 -commands there is the variant
6162 \begin_inset Index idx
6165 \begin_layout Plain Layout
6173 that adds a bit more space between the bracket and its content, and the
6187 \begin_inset Index idx
6190 \begin_layout Plain Layout
6200 , that don't add additional space.
6205 at the end of the command
6211 is for a left bracket; for a right bracket this will be replaced by an
6217 A left or right bracket can each be an opening or closing bracket.
6220 \begin_layout Standard
6221 In the following table is a comparison of the variants:
6222 \begin_inset Separator parbreak
6228 \begin_layout Standard
6230 \begin_inset Tabular
6231 <lyxtabular version="3" rows="5" columns="2">
6232 <features booktabs="true" tabularvalignment="middle">
6233 <column alignment="center" valignment="top" width="0pt">
6234 <column alignment="center" valignment="middle">
6236 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6239 \begin_layout Plain Layout
6245 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6248 \begin_layout Plain Layout
6255 <row topspace="2mm">
6256 <cell alignment="center" valignment="top" usebox="none">
6259 \begin_layout Plain Layout
6269 \begin_inset space \textvisiblespace{}
6279 <cell alignment="center" valignment="top" usebox="none">
6282 \begin_layout Plain Layout
6283 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6292 <row topspace="2mm">
6293 <cell alignment="center" valignment="top" usebox="none">
6296 \begin_layout Plain Layout
6306 \begin_inset space \textvisiblespace{}
6316 <cell alignment="center" valignment="top" usebox="none">
6319 \begin_layout Plain Layout
6320 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6329 <row topspace="2mm" bottomspace="0.5mm">
6330 <cell alignment="center" valignment="top" usebox="none">
6333 \begin_layout Plain Layout
6343 \begin_inset space \textvisiblespace{}
6353 <cell alignment="center" valignment="top" usebox="none">
6356 \begin_layout Plain Layout
6357 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6366 <row topspace="1.5mm" bottomspace="0.5mm">
6367 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6370 \begin_layout Plain Layout
6382 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6385 \begin_layout Plain Layout
6386 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6402 \begin_layout Subsubsection
6403 Automatic Bracket Size
6404 \begin_inset CommandInset label
6406 name "subsec:Automatic-Bracket-Size"
6411 \begin_inset Index idx
6414 \begin_layout Plain Layout
6415 Bracket size ! automatic
6423 \begin_layout Standard
6424 Brackets with variable size can be inserted with the commands
6431 \begin_inset Index idx
6434 \begin_layout Plain Layout
6449 \begin_inset Index idx
6452 \begin_layout Plain Layout
6460 or via the math toolbar button
6463 arg "dialog-show mathdelimiter"
6479 the wanted bracket must be inserted.
6480 The bracket size will then automatically be calculated for the output.
6481 \begin_inset Separator parbreak
6487 \begin_layout Standard
6489 normal bracket: The command
6496 \begin_inset space \textvisiblespace{}
6500 \begin_inset Formula $\downarrow$
6504 \begin_inset space \textvisiblespace{}
6510 \begin_inset Formula
6520 \begin_layout Standard
6522 multiline bracket: The command
6531 \begin_inset space \textvisiblespace{}
6535 \begin_inset Formula $\downarrow$
6539 \begin_inset space \textvisiblespace{}
6547 \begin_inset Formula
6549 \ln\left(\frac{A}{C}\right)
6557 \begin_layout Standard
6573 \begin_inset space ~
6579 This has the advantage that you can see in \SpecialChar LyX
6580 immediately the real bracket
6581 size and that the matching right bracket will be created too.
6582 \begin_inset Newline newline
6585 The command for the last example would then be:
6596 \begin_inset space \textvisiblespace{}
6600 \begin_inset Formula $\downarrow$
6606 \begin_layout Standard
6607 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6608 For example the command
6615 \begin_inset space \textvisiblespace{}
6619 \begin_inset Formula $\downarrow$
6623 \begin_inset space \textvisiblespace{}
6633 \begin_inset Formula
6635 \left.\frac{A}{B}\right\}
6654 will be converted by \SpecialChar LyX
6655 to brackets in the right size when the document is
6656 reloaded and an omitted bracket will appear as dashed line.
6659 \begin_layout Standard
6660 \begin_inset VSpace bigskip
6663 Because all popular \SpecialChar LaTeX
6664 distributions use e\SpecialChar TeX
6665 , an extension to \SpecialChar LaTeX
6674 \begin_inset Index idx
6677 \begin_layout Plain Layout
6685 is additionally available for all brackets and limits.
6686 With this command the height of the following character is adapted to the
6687 one of the surrounding brackets, what is e.
6688 \begin_inset space \thinspace{}
6692 \begin_inset space \space{}
6695 needed for physical vectors:
6696 \begin_inset Formula
6698 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6703 For physical vectors there is a special \SpecialChar LaTeX
6704 -package, described in
6705 \begin_inset CommandInset ref
6707 reference "subsec:Physical-Vectors"
6714 \begin_layout Subsection
6716 \begin_inset Index idx
6719 \begin_layout Plain Layout
6720 Brackets ! horizontal
6728 \begin_layout Standard
6730 \begin_inset Tabular
6731 <lyxtabular version="3" rows="4" columns="2">
6732 <features booktabs="true" tabularvalignment="middle">
6733 <column alignment="center" valignment="top" width="0pt">
6734 <column alignment="center" valignment="top" width="0pt">
6736 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6739 \begin_layout Plain Layout
6745 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6748 \begin_layout Plain Layout
6756 <cell alignment="center" valignment="top" usebox="none">
6759 \begin_layout Plain Layout
6763 \begin_inset space \textvisiblespace{}
6767 \begin_inset space \textvisiblespace{}
6771 \begin_inset Index idx
6774 \begin_layout Plain Layout
6787 <cell alignment="center" valignment="top" usebox="none">
6790 \begin_layout Plain Layout
6791 \begin_inset Formula $\overbrace{A+B}^{3}$
6800 <row topspace="2mm">
6801 <cell alignment="center" valignment="top" usebox="none">
6804 \begin_layout Plain Layout
6808 \begin_inset space \textvisiblespace{}
6812 \begin_inset space \textvisiblespace{}
6816 \begin_inset Index idx
6819 \begin_layout Plain Layout
6832 <cell alignment="center" valignment="top" usebox="none">
6835 \begin_layout Plain Layout
6836 \begin_inset Formula $\underbrace{A+B}_{5}$
6846 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6849 \begin_layout Plain Layout
6853 \begin_inset space \textvisiblespace{}
6859 \begin_inset space \textvisiblespace{}
6863 \begin_inset space \textvisiblespace{}
6867 \begin_inset space \textvisiblespace{}
6871 \begin_inset space \textvisiblespace{}
6875 \begin_inset space \textvisiblespace{}
6879 \begin_inset space \textvisiblespace{}
6887 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6890 \begin_layout Plain Layout
6891 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6907 \begin_layout Standard
6908 In the last example it doesn't matter if
6920 is inserted at first.
6923 \begin_layout Standard
6924 \begin_inset VSpace medskip
6930 \begin_layout Standard
6931 If you set in the document settings under
6934 \begin_inset space ~
6944 \begin_inset Index idx
6947 \begin_layout Plain Layout
6948 Packages ! mathtools
6956 \begin_inset space ~
6961 , you have access to square backets:
6962 \begin_inset Separator parbreak
6968 \begin_layout Standard
6970 \begin_inset Tabular
6971 <lyxtabular version="3" rows="4" columns="2">
6972 <features booktabs="true" tabularvalignment="middle">
6973 <column alignment="center" valignment="top" width="0pt">
6974 <column alignment="center" valignment="top" width="0pt">
6976 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6979 \begin_layout Plain Layout
6985 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6988 \begin_layout Plain Layout
6996 <cell alignment="center" valignment="top" usebox="none">
6999 \begin_layout Plain Layout
7027 \begin_inset space \textvisiblespace{}
7031 \begin_inset Index idx
7034 \begin_layout Plain Layout
7047 <cell alignment="center" valignment="top" usebox="none">
7050 \begin_layout Plain Layout
7051 \begin_inset Formula $\overbracket{A+B}^{3}$
7060 <row topspace="2mm">
7061 <cell alignment="center" valignment="top" usebox="none">
7064 \begin_layout Plain Layout
7092 \begin_inset space \textvisiblespace{}
7096 \begin_inset Index idx
7099 \begin_layout Plain Layout
7124 <cell alignment="center" valignment="top" usebox="none">
7127 \begin_layout Plain Layout
7128 \begin_inset Formula $\underbracket{A+B}_{5}$
7138 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7141 \begin_layout Plain Layout
7147 \begin_inset space \textvisiblespace{}
7151 \begin_inset space \textvisiblespace{}
7155 \begin_inset space \textvisiblespace{}
7159 \begin_inset space \textvisiblespace{}
7163 \begin_inset space \textvisiblespace{}
7171 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7174 \begin_layout Plain Layout
7175 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7191 \begin_layout Standard
7204 you can change the thickness of the bracket's stroke by specifying the
7205 desired thickness in square brackets behind the command:
7206 \begin_inset Separator parbreak
7212 \begin_layout Standard
7214 \begin_inset Tabular
7215 <lyxtabular version="3" rows="3" columns="2">
7216 <features booktabs="true" tabularvalignment="middle">
7217 <column alignment="center" valignment="top" width="0pt">
7218 <column alignment="center" valignment="top" width="0pt">
7220 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7223 \begin_layout Plain Layout
7229 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7232 \begin_layout Plain Layout
7240 <cell alignment="center" valignment="top" usebox="none">
7243 \begin_layout Plain Layout
7273 \begin_inset space \textvisiblespace{}
7281 <cell alignment="center" valignment="top" usebox="none">
7284 \begin_layout Plain Layout
7285 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7294 <row topspace="2mm">
7295 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7298 \begin_layout Plain Layout
7328 \begin_inset space \textvisiblespace{}
7336 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7339 \begin_layout Plain Layout
7340 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7356 \begin_layout Standard
7357 \begin_inset VSpace bigskip
7360 When brackets should overlap each other, multiline formulas, as described
7362 \begin_inset CommandInset ref
7364 reference "sec:Multiline-Formulas"
7369 \begin_inset Formula
7371 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7372 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7377 In the first row the formula is inserted together with the first brace.
7378 It is hereby important that the space command
7382 \begin_layout Plain Layout
7383 Space commands are explained in
7384 \begin_inset CommandInset ref
7386 reference "subsec:Predefined-Space"
7401 is inserted before the first
7402 \begin_inset Formula $d$
7405 , because the brace that ends behind the
7406 \begin_inset Formula $q$
7409 prevents that the following
7410 \begin_inset Quotes eld
7414 \begin_inset Quotes erd
7417 is surrounded by space.
7421 \begin_layout Plain Layout
7422 because a bracket is not handled as a character, see
7423 \begin_inset CommandInset ref
7425 reference "subsec:Binary-Operators"
7434 In the second row the second brace is inserted.
7435 As it should begin before the
7436 \begin_inset Formula $b$
7451 \begin_layout Plain Layout
7459 \begin_inset CommandInset ref
7461 reference "subsec:Placeholders"
7470 This space is needed because the
7471 \begin_inset Quotes eld
7475 \begin_inset Quotes erd
7478 is also surrounded by space in the formula.
7479 The brace is placed under the command
7488 \begin_layout Standard
7489 It gets more complicated when brackets overlap each other above and under
7490 the formula, like in the following example:
7494 \begin_layout Plain Layout
7506 \begin_inset Formula
7508 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7509 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7518 \begin_layout Plain Layout
7529 The first formula row is the same as the second row of the previous example,
7530 with the difference that the brace is above.
7531 The second row contains the formula together with the second brace.
7532 To avoid that there is space between the upper brace in the first row and
7533 the formula, the row spacing needs to be reduced.
7534 This is not easily possible due to a bug in \SpecialChar LyX
7539 \begin_layout Plain Layout
7540 \begin_inset CommandInset href
7542 name "LyX-bug #1505"
7543 target "http://www.lyx.org/trac/ticket/1505"
7552 As a solution for the problem, the global formula row separation
7559 \begin_inset Index idx
7562 \begin_layout Plain Layout
7570 must be changed to -6
7571 \begin_inset space \thinspace{}
7574 pt before the formula with the command
7590 is set back after the formula to the standard value of 3
7591 \begin_inset space \thinspace{}
7594 pt using the same command.
7595 More about the row separation in formulas is explained in
7596 \begin_inset CommandInset ref
7598 reference "subsec:Line-Separation"
7605 \begin_layout Section
7607 \begin_inset Index idx
7610 \begin_layout Plain Layout
7619 \begin_layout Standard
7620 Arrows can be inserted via the math toolbar button
7623 arg "math-insert \\leftarrow"
7626 or the commands listed in the following subsections.
7629 \begin_layout Subsection
7631 \begin_inset Index idx
7634 \begin_layout Plain Layout
7643 \begin_layout Standard
7644 \begin_inset space \hfill{}
7648 \begin_inset Tabular
7649 <lyxtabular version="3" rows="8" columns="2">
7650 <features booktabs="true" tabularvalignment="middle">
7651 <column alignment="center" valignment="top" width="0pt">
7652 <column alignment="center" valignment="top" width="0pt">
7654 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7657 \begin_layout Plain Layout
7663 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7666 \begin_layout Plain Layout
7674 <cell alignment="center" valignment="top" usebox="none">
7677 \begin_layout Plain Layout
7685 <cell alignment="center" valignment="top" usebox="none">
7688 \begin_layout Plain Layout
7689 \begin_inset Formula $\gets$
7699 <cell alignment="center" valignment="top" usebox="none">
7702 \begin_layout Plain Layout
7710 <cell alignment="center" valignment="top" usebox="none">
7713 \begin_layout Plain Layout
7714 \begin_inset Formula $\Leftarrow$
7724 <cell alignment="center" valignment="top" usebox="none">
7727 \begin_layout Plain Layout
7735 <cell alignment="center" valignment="top" usebox="none">
7738 \begin_layout Plain Layout
7739 \begin_inset Formula $\longleftarrow$
7749 <cell alignment="center" valignment="top" usebox="none">
7752 \begin_layout Plain Layout
7760 <cell alignment="center" valignment="top" usebox="none">
7763 \begin_layout Plain Layout
7764 \begin_inset Formula $\Longleftarrow$
7774 <cell alignment="center" valignment="top" usebox="none">
7777 \begin_layout Plain Layout
7785 <cell alignment="center" valignment="top" usebox="none">
7788 \begin_layout Plain Layout
7789 \begin_inset Formula $\leftharpoonup$
7799 <cell alignment="center" valignment="top" usebox="none">
7802 \begin_layout Plain Layout
7810 <cell alignment="center" valignment="top" usebox="none">
7813 \begin_layout Plain Layout
7814 \begin_inset Formula $\leftharpoondown$
7824 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7827 \begin_layout Plain Layout
7835 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7838 \begin_layout Plain Layout
7839 \begin_inset Formula $\hookleftarrow$
7853 \begin_inset space \hfill{}
7857 \begin_inset Tabular
7858 <lyxtabular version="3" rows="8" columns="2">
7859 <features booktabs="true" tabularvalignment="middle">
7860 <column alignment="center" valignment="top" width="0pt">
7861 <column alignment="center" valignment="top" width="0pt">
7863 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7866 \begin_layout Plain Layout
7872 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7875 \begin_layout Plain Layout
7883 <cell alignment="center" valignment="top" usebox="none">
7886 \begin_layout Plain Layout
7894 <cell alignment="center" valignment="top" usebox="none">
7897 \begin_layout Plain Layout
7898 \begin_inset Formula $\to$
7908 <cell alignment="center" valignment="top" usebox="none">
7911 \begin_layout Plain Layout
7919 <cell alignment="center" valignment="top" usebox="none">
7922 \begin_layout Plain Layout
7923 \begin_inset Formula $\Rightarrow$
7933 <cell alignment="center" valignment="top" usebox="none">
7936 \begin_layout Plain Layout
7944 <cell alignment="center" valignment="top" usebox="none">
7947 \begin_layout Plain Layout
7948 \begin_inset Formula $\longrightarrow$
7958 <cell alignment="center" valignment="top" usebox="none">
7961 \begin_layout Plain Layout
7969 <cell alignment="center" valignment="top" usebox="none">
7972 \begin_layout Plain Layout
7973 \begin_inset Formula $\Longrightarrow$
7983 <cell alignment="center" valignment="top" usebox="none">
7986 \begin_layout Plain Layout
7994 <cell alignment="center" valignment="top" usebox="none">
7997 \begin_layout Plain Layout
7998 \begin_inset Formula $\rightharpoonup$
8008 <cell alignment="center" valignment="top" usebox="none">
8011 \begin_layout Plain Layout
8019 <cell alignment="center" valignment="top" usebox="none">
8022 \begin_layout Plain Layout
8023 \begin_inset Formula $\rightharpoondown$
8033 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8036 \begin_layout Plain Layout
8044 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8047 \begin_layout Plain Layout
8048 \begin_inset Formula $\hookrightarrow$
8062 \begin_inset space \hfill{}
8068 \begin_layout Standard
8069 \begin_inset space \hfill{}
8073 \begin_inset Tabular
8074 <lyxtabular version="3" rows="6" columns="2">
8075 <features booktabs="true" tabularvalignment="middle">
8076 <column alignment="center" valignment="top" width="0pt">
8077 <column alignment="center" valignment="top" width="0pt">
8079 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8082 \begin_layout Plain Layout
8088 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8091 \begin_layout Plain Layout
8099 <cell alignment="center" valignment="top" usebox="none">
8102 \begin_layout Plain Layout
8110 <cell alignment="center" valignment="top" usebox="none">
8113 \begin_layout Plain Layout
8114 \begin_inset Formula $\leftrightarrow$
8124 <cell alignment="center" valignment="top" usebox="none">
8127 \begin_layout Plain Layout
8135 <cell alignment="center" valignment="top" usebox="none">
8138 \begin_layout Plain Layout
8139 \begin_inset Formula $\Leftrightarrow$
8149 <cell alignment="center" valignment="top" usebox="none">
8152 \begin_layout Plain Layout
8160 <cell alignment="center" valignment="top" usebox="none">
8163 \begin_layout Plain Layout
8164 \begin_inset Formula $\longleftrightarrow$
8174 <cell alignment="center" valignment="top" usebox="none">
8177 \begin_layout Plain Layout
8185 <cell alignment="center" valignment="top" usebox="none">
8188 \begin_layout Plain Layout
8189 \begin_inset Formula $\Longleftrightarrow$
8199 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8202 \begin_layout Plain Layout
8210 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8213 \begin_layout Plain Layout
8214 \begin_inset Formula $\rightleftharpoons$
8228 \begin_inset space \hspace{}
8233 \begin_inset space \hfill{}
8237 \begin_inset Tabular
8238 <lyxtabular version="3" rows="5" columns="2">
8239 <features booktabs="true" tabularvalignment="middle">
8240 <column alignment="center" valignment="top" width="0pt">
8241 <column alignment="center" valignment="top" width="0pt">
8243 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8246 \begin_layout Plain Layout
8252 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8255 \begin_layout Plain Layout
8263 <cell alignment="center" valignment="top" usebox="none">
8266 \begin_layout Plain Layout
8274 <cell alignment="center" valignment="top" usebox="none">
8277 \begin_layout Plain Layout
8278 \begin_inset Formula $\mapsto$
8288 <cell alignment="center" valignment="top" usebox="none">
8291 \begin_layout Plain Layout
8299 <cell alignment="center" valignment="top" usebox="none">
8302 \begin_layout Plain Layout
8303 \begin_inset Formula $\longmapsto$
8313 <cell alignment="center" valignment="top" usebox="none">
8316 \begin_layout Plain Layout
8324 <cell alignment="center" valignment="top" usebox="none">
8327 \begin_layout Plain Layout
8328 \begin_inset Formula $\leadsto$
8338 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8341 \begin_layout Plain Layout
8349 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8352 \begin_layout Plain Layout
8353 \begin_inset Formula $\dasharrow$
8367 \begin_inset space \hfill{}
8373 \begin_layout Standard
8374 \begin_inset VSpace medskip
8377 Arrows used as accents like e.
8378 \begin_inset space \thinspace{}
8382 \begin_inset space \space{}
8385 vector arrows are listed in
8386 \begin_inset CommandInset ref
8388 reference "sec:Accents"
8395 \begin_layout Standard
8396 \begin_inset VSpace bigskip
8399 Furthermore there are the labeled arrows
8400 \begin_inset Index idx
8403 \begin_layout Plain Layout
8416 \begin_inset Index idx
8419 \begin_layout Plain Layout
8434 \begin_inset Index idx
8437 \begin_layout Plain Layout
8444 \begin_layout Plain Layout
8459 When inserting one of these commands in a formula, an arrow with two blue
8460 boxes appear where the label can be inserted.
8461 The length of the arrow adapts to the label width.
8464 \begin_layout Standard
8466 \begin_inset Tabular
8467 <lyxtabular version="3" rows="3" columns="2">
8468 <features booktabs="true" tabularvalignment="middle">
8469 <column alignment="center" valignment="top" width="0pt">
8470 <column alignment="center" valignment="top" width="0pt">
8472 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8475 \begin_layout Plain Layout
8481 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8484 \begin_layout Plain Layout
8492 <cell alignment="center" valignment="top" usebox="none">
8495 \begin_layout Plain Layout
8499 \begin_inset space \textvisiblespace{}
8503 \begin_inset Formula $\downarrow$
8507 \begin_inset Formula $\to$
8515 <cell alignment="center" valignment="top" usebox="none">
8518 \begin_layout Plain Layout
8519 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8528 <row topspace="2mm">
8529 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8532 \begin_layout Plain Layout
8536 \begin_inset space \textvisiblespace{}
8540 \begin_inset Formula $\downarrow$
8544 \begin_inset Formula $\to$
8552 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8555 \begin_layout Plain Layout
8556 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8572 \begin_layout Standard
8573 \begin_inset VSpace medskip
8579 \begin_layout Standard
8580 If you set in the document settings under
8583 \begin_inset space ~
8593 \begin_inset Index idx
8596 \begin_layout Plain Layout
8597 Packages ! mathtools
8605 \begin_inset space ~
8610 , you have access to the following labeled arrows:
8613 \begin_layout Standard
8614 \begin_inset Newpage newpage
8618 \begin_inset Separator parbreak
8624 \begin_layout Standard
8626 \begin_inset space \hspace*{\fill}
8630 \begin_inset Tabular
8631 <lyxtabular version="3" rows="7" columns="2">
8632 <features booktabs="true" tabularvalignment="middle">
8633 <column alignment="center" valignment="top" width="0pt">
8634 <column alignment="center" valignment="top" width="0pt">
8636 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8639 \begin_layout Plain Layout
8645 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8648 \begin_layout Plain Layout
8656 <cell alignment="center" valignment="top" usebox="none">
8659 \begin_layout Plain Layout
8679 <cell alignment="center" valignment="top" usebox="none">
8682 \begin_layout Plain Layout
8683 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8692 <row topspace="2mm">
8693 <cell alignment="center" valignment="top" usebox="none">
8696 \begin_layout Plain Layout
8716 <cell alignment="center" valignment="top" usebox="none">
8719 \begin_layout Plain Layout
8720 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8729 <row topspace="2mm">
8730 <cell alignment="center" valignment="top" usebox="none">
8733 \begin_layout Plain Layout
8753 <cell alignment="center" valignment="top" usebox="none">
8756 \begin_layout Plain Layout
8757 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8766 <row topspace="2mm">
8767 <cell alignment="center" valignment="top" usebox="none">
8770 \begin_layout Plain Layout
8790 <cell alignment="center" valignment="top" usebox="none">
8793 \begin_layout Plain Layout
8794 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8803 <row topspace="2mm">
8804 <cell alignment="center" valignment="top" usebox="none">
8807 \begin_layout Plain Layout
8827 <cell alignment="center" valignment="top" usebox="none">
8830 \begin_layout Plain Layout
8831 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8840 <row topspace="2mm">
8841 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8844 \begin_layout Plain Layout
8864 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8867 \begin_layout Plain Layout
8868 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8882 \begin_inset space \hspace*{\fill}
8886 \begin_inset Tabular
8887 <lyxtabular version="3" rows="7" columns="2">
8888 <features booktabs="true" tabularvalignment="middle">
8889 <column alignment="center" valignment="top" width="0pt">
8890 <column alignment="center" valignment="top" width="0pt">
8892 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8895 \begin_layout Plain Layout
8901 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8904 \begin_layout Plain Layout
8912 <cell alignment="center" valignment="top" usebox="none">
8915 \begin_layout Plain Layout
8935 <cell alignment="center" valignment="top" usebox="none">
8938 \begin_layout Plain Layout
8939 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8948 <row topspace="2mm">
8949 <cell alignment="center" valignment="top" usebox="none">
8952 \begin_layout Plain Layout
8972 <cell alignment="center" valignment="top" usebox="none">
8975 \begin_layout Plain Layout
8976 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8985 <row topspace="2mm">
8986 <cell alignment="center" valignment="top" usebox="none">
8989 \begin_layout Plain Layout
9009 <cell alignment="center" valignment="top" usebox="none">
9012 \begin_layout Plain Layout
9013 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
9022 <row topspace="2mm">
9023 <cell alignment="center" valignment="top" usebox="none">
9026 \begin_layout Plain Layout
9046 <cell alignment="center" valignment="top" usebox="none">
9049 \begin_layout Plain Layout
9050 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9059 <row topspace="2mm">
9060 <cell alignment="center" valignment="top" usebox="none">
9063 \begin_layout Plain Layout
9083 <cell alignment="center" valignment="top" usebox="none">
9086 \begin_layout Plain Layout
9087 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9096 <row topspace="2mm">
9097 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9100 \begin_layout Plain Layout
9120 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9123 \begin_layout Plain Layout
9124 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9138 \begin_inset space \hspace*{\fill}
9144 \begin_layout Standard
9145 The command scheme is for all these arrows:
9146 \begin_inset Separator parbreak
9152 \begin_layout Standard
9154 \begin_inset Tabular
9155 <lyxtabular version="3" rows="2" columns="2">
9156 <features booktabs="true" tabularvalignment="middle">
9157 <column alignment="center" valignment="top" width="0pt">
9158 <column alignment="center" valignment="top" width="0pt">
9160 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9163 \begin_layout Plain Layout
9169 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9172 \begin_layout Plain Layout
9179 <row bottomspace="0.5mm">
9180 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9183 \begin_layout Plain Layout
9186 xleftrightarrow[x=a]
9189 \begin_inset Formula $\to$
9197 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9200 \begin_layout Plain Layout
9201 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9217 \begin_layout Subsection
9218 Vertical and diagonal Arrows
9219 \begin_inset Index idx
9222 \begin_layout Plain Layout
9229 \begin_inset Index idx
9232 \begin_layout Plain Layout
9241 \begin_layout Standard
9242 \begin_inset space \hfill{}
9246 \begin_inset Tabular
9247 <lyxtabular version="3" rows="7" columns="2">
9248 <features booktabs="true" tabularvalignment="middle">
9249 <column alignment="center" valignment="top" width="0pt">
9250 <column alignment="center" valignment="top" width="0pt">
9252 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9255 \begin_layout Plain Layout
9261 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9264 \begin_layout Plain Layout
9272 <cell alignment="center" valignment="top" usebox="none">
9275 \begin_layout Plain Layout
9283 <cell alignment="center" valignment="top" usebox="none">
9286 \begin_layout Plain Layout
9287 \begin_inset Formula $\uparrow$
9297 <cell alignment="center" valignment="top" usebox="none">
9300 \begin_layout Plain Layout
9308 <cell alignment="center" valignment="top" usebox="none">
9311 \begin_layout Plain Layout
9312 \begin_inset Formula $\Uparrow$
9322 <cell alignment="center" valignment="top" usebox="none">
9325 \begin_layout Plain Layout
9333 <cell alignment="center" valignment="top" usebox="none">
9336 \begin_layout Plain Layout
9337 \begin_inset Formula $\updownarrow$
9347 <cell alignment="center" valignment="top" usebox="none">
9350 \begin_layout Plain Layout
9358 <cell alignment="center" valignment="top" usebox="none">
9361 \begin_layout Plain Layout
9362 \begin_inset Formula $\Updownarrow$
9372 <cell alignment="center" valignment="top" usebox="none">
9375 \begin_layout Plain Layout
9383 <cell alignment="center" valignment="top" usebox="none">
9386 \begin_layout Plain Layout
9387 \begin_inset Formula $\Downarrow$
9397 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9400 \begin_layout Plain Layout
9408 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9411 \begin_layout Plain Layout
9412 \begin_inset Formula $\downarrow$
9426 \begin_inset space \hfill{}
9430 \begin_inset Tabular
9431 <lyxtabular version="3" rows="5" columns="2">
9432 <features booktabs="true" tabularvalignment="middle">
9433 <column alignment="center" valignment="top" width="0pt">
9434 <column alignment="center" valignment="top" width="0pt">
9436 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9439 \begin_layout Plain Layout
9445 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9448 \begin_layout Plain Layout
9456 <cell alignment="center" valignment="top" usebox="none">
9459 \begin_layout Plain Layout
9467 <cell alignment="center" valignment="top" usebox="none">
9470 \begin_layout Plain Layout
9471 \begin_inset Formula $\nearrow$
9481 <cell alignment="center" valignment="top" usebox="none">
9484 \begin_layout Plain Layout
9492 <cell alignment="center" valignment="top" usebox="none">
9495 \begin_layout Plain Layout
9496 \begin_inset Formula $\searrow$
9506 <cell alignment="center" valignment="top" usebox="none">
9509 \begin_layout Plain Layout
9517 <cell alignment="center" valignment="top" usebox="none">
9520 \begin_layout Plain Layout
9521 \begin_inset Formula $\swarrow$
9531 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9534 \begin_layout Plain Layout
9542 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9545 \begin_layout Plain Layout
9546 \begin_inset Formula $\nwarrow$
9560 \begin_inset space \hfill{}
9566 \begin_layout Standard
9567 \begin_inset VSpace medskip
9570 Vertical arrows can be used also as delimiters together with the commands
9572 \begin_inset CommandInset ref
9574 reference "subsec:Manual-Bracket-Size"
9579 \begin_inset CommandInset ref
9581 reference "subsec:Automatic-Bracket-Size"
9588 \begin_layout Section
9590 \begin_inset CommandInset label
9597 \begin_inset Index idx
9600 \begin_layout Plain Layout
9609 \begin_layout Standard
9610 Accents can be inserted via the math toolbar button
9613 arg "math-insert \\hat"
9616 or the commands listed in the following subsections.
9619 \begin_layout Subsection
9620 Accents for one Character
9624 \begin_layout Plain Layout
9637 \begin_layout Plain Layout
9639 \begin_inset CommandInset ref
9641 reference "subsec:Accents-in-Text"
9654 \begin_layout Plain Layout
9662 \begin_inset Note Note
9665 \begin_layout Plain Layout
9672 is used to avoid that the footnote appears in the PDF-bookmark.
9675 \begin_layout Plain Layout
9683 \begin_inset CommandInset ref
9685 reference "subsec:Formulas-in-Section"
9695 \begin_inset CommandInset label
9697 name "subsec:Accents-for-one"
9702 \begin_inset Index idx
9705 \begin_layout Plain Layout
9706 Accents ! for one character
9714 \begin_layout Standard
9715 \begin_inset space \hfill{}
9719 \begin_inset Tabular
9720 <lyxtabular version="3" rows="8" columns="2">
9721 <features booktabs="true" tabularvalignment="middle">
9722 <column alignment="center" valignment="top" width="0pt">
9723 <column alignment="center" valignment="top" width="0pt">
9725 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9728 \begin_layout Plain Layout
9734 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9737 \begin_layout Plain Layout
9744 <row topspace="1.5mm">
9745 <cell alignment="center" valignment="top" usebox="none">
9748 \begin_layout Plain Layout
9752 \begin_inset space \textvisiblespace{}
9760 <cell alignment="center" valignment="top" usebox="none">
9763 \begin_layout Plain Layout
9764 \begin_inset Formula $\dot{A}$
9773 <row topspace="1.5mm">
9774 <cell alignment="center" valignment="top" usebox="none">
9777 \begin_layout Plain Layout
9781 \begin_inset space \textvisiblespace{}
9789 <cell alignment="center" valignment="top" usebox="none">
9792 \begin_layout Plain Layout
9793 \begin_inset Formula $\ddot{A}$
9802 <row topspace="1.5mm">
9803 <cell alignment="center" valignment="top" usebox="none">
9806 \begin_layout Plain Layout
9810 \begin_inset space \textvisiblespace{}
9818 <cell alignment="center" valignment="top" usebox="none">
9821 \begin_layout Plain Layout
9822 \begin_inset Formula $\dddot{A}$
9831 <row topspace="1.5mm">
9832 <cell alignment="center" valignment="top" usebox="none">
9835 \begin_layout Plain Layout
9839 \begin_inset space \textvisiblespace{}
9847 <cell alignment="center" valignment="top" usebox="none">
9850 \begin_layout Plain Layout
9851 \begin_inset Formula $\ddddot{A}$
9860 <row topspace="1.5mm">
9861 <cell alignment="center" valignment="top" usebox="none">
9864 \begin_layout Plain Layout
9868 \begin_inset space \textvisiblespace{}
9872 \begin_inset Index idx
9875 \begin_layout Plain Layout
9886 <cell alignment="center" valignment="top" usebox="none">
9889 \begin_layout Plain Layout
9890 \begin_inset Formula $\vec{A}$
9899 <row topspace="1.5mm">
9900 <cell alignment="center" valignment="top" usebox="none">
9903 \begin_layout Plain Layout
9907 \begin_inset space \textvisiblespace{}
9915 <cell alignment="center" valignment="top" usebox="none">
9918 \begin_layout Plain Layout
9919 \begin_inset Formula $\bar{A}$
9928 <row topspace="1.5mm">
9929 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9932 \begin_layout Plain Layout
9936 \begin_inset space \textvisiblespace{}
9944 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9947 \begin_layout Plain Layout
9948 \begin_inset Formula $\mathring{A}$
9962 \begin_inset space \hfill{}
9966 \begin_inset Tabular
9967 <lyxtabular version="3" rows="7" columns="2">
9968 <features booktabs="true" tabularvalignment="middle">
9969 <column alignment="center" valignment="top" width="0pt">
9970 <column alignment="center" valignment="top" width="0pt">
9972 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9975 \begin_layout Plain Layout
9981 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9984 \begin_layout Plain Layout
9991 <row topspace="1.5mm">
9992 <cell alignment="center" valignment="top" usebox="none">
9995 \begin_layout Plain Layout
9999 \begin_inset space \textvisiblespace{}
10007 <cell alignment="center" valignment="top" usebox="none">
10010 \begin_layout Plain Layout
10011 \begin_inset Formula $\tilde{A}$
10020 <row topspace="1.5mm">
10021 <cell alignment="center" valignment="top" usebox="none">
10024 \begin_layout Plain Layout
10028 \begin_inset space \textvisiblespace{}
10036 <cell alignment="center" valignment="top" usebox="none">
10039 \begin_layout Plain Layout
10040 \begin_inset Formula $\hat{A}$
10049 <row topspace="1.5mm">
10050 <cell alignment="center" valignment="top" usebox="none">
10053 \begin_layout Plain Layout
10057 \begin_inset space \textvisiblespace{}
10065 <cell alignment="center" valignment="top" usebox="none">
10068 \begin_layout Plain Layout
10069 \begin_inset Formula $\check{A}$
10078 <row topspace="1.5mm">
10079 <cell alignment="center" valignment="top" usebox="none">
10082 \begin_layout Plain Layout
10086 \begin_inset space \textvisiblespace{}
10094 <cell alignment="center" valignment="top" usebox="none">
10097 \begin_layout Plain Layout
10098 \begin_inset Formula $\acute{A}$
10107 <row topspace="1.5mm">
10108 <cell alignment="center" valignment="top" usebox="none">
10111 \begin_layout Plain Layout
10115 \begin_inset space \textvisiblespace{}
10123 <cell alignment="center" valignment="top" usebox="none">
10126 \begin_layout Plain Layout
10127 \begin_inset Formula $\grave{A}$
10136 <row topspace="1.5mm">
10137 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10140 \begin_layout Plain Layout
10144 \begin_inset space \textvisiblespace{}
10152 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10155 \begin_layout Plain Layout
10156 \begin_inset Formula $\breve{A}$
10170 \begin_inset space \hfill{}
10176 \begin_layout Standard
10177 \begin_inset VSpace bigskip
10183 \begin_layout Standard
10184 You can directly insert accents like é to formulas.
10186 will transform them to the corresponding accent command.
10188 \begin_inset Index idx
10191 \begin_layout Plain Layout
10197 it is better to insert a quotation mark before the vowel.
10198 These two characters are then treated by \SpecialChar LaTeX
10203 character when the formula part with the umlaut is marked as German.
10211 \begin_inset Quotes eld
10215 \begin_inset Quotes erd
10218 umlauts are created as demonstrated in the following example:
10221 \begin_layout Standard
10222 \begin_inset VSpace -2mm
10228 \begin_layout Standard
10230 \begin_inset Tabular
10231 <lyxtabular version="3" rows="3" columns="2">
10232 <features booktabs="true" tabularvalignment="middle">
10233 <column alignment="center" valignment="top" width="0pt">
10234 <column alignment="center" valignment="top">
10236 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10239 \begin_layout Plain Layout
10245 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10248 \begin_layout Plain Layout
10256 <cell alignment="center" valignment="top" usebox="none">
10259 \begin_layout Plain Layout
10260 \begin_inset Quotes grd
10268 <cell alignment="center" valignment="top" usebox="none">
10271 \begin_layout Plain Layout
10272 \begin_inset space \hspace{}
10279 \begin_inset Formula $"i$
10288 <row topspace="1.5mm">
10289 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10292 \begin_layout Plain Layout
10296 \begin_inset space \textvisiblespace{}
10304 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10307 \begin_layout Plain Layout
10308 \begin_inset Formula $\ddot{i}$
10324 \begin_layout Standard
10325 Another advantage to
10331 is that umlauts can directly be converted to mathematical text because
10332 the accent commands above are
10338 in mathematical text
10341 To convert an accented character to mathematical text, only the character
10342 under the accent may be converted.
10343 This applies also for all other conversions, e.
10344 \begin_inset space \thinspace{}
10348 \begin_inset space \space{}
10354 \begin_layout Standard
10355 In mathematical text, umlauts and other accented characters can directly
10359 \begin_layout Standard
10360 \begin_inset VSpace bigskip
10366 \begin_layout Standard
10368 also supports a tilde under the character if the \SpecialChar LaTeX
10374 \begin_inset Index idx
10377 \begin_layout Plain Layout
10378 Packages ! undertilde
10383 is installed on your system:
10386 \begin_layout Standard
10390 \begin_layout Plain Layout
10400 \begin_inset Note Note
10403 \begin_layout Plain Layout
10404 The following table will only be displayed when the \SpecialChar LaTeX
10415 \begin_inset Separator parbreak
10421 \begin_layout Standard
10424 \begin_inset Tabular
10425 <lyxtabular version="3" rows="2" columns="2">
10426 <features booktabs="true" tabularvalignment="middle">
10427 <column alignment="center" valignment="top" width="0pt">
10428 <column alignment="center" valignment="top" width="0pt">
10430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10433 \begin_layout Plain Layout
10439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10442 \begin_layout Plain Layout
10450 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10453 \begin_layout Plain Layout
10457 \begin_inset space \textvisiblespace{}
10465 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10468 \begin_layout Plain Layout
10469 \begin_inset Formula $\utilde{A}$
10485 \begin_layout Standard
10489 \begin_layout Plain Layout
10499 \begin_inset Note Note
10502 \begin_layout Plain Layout
10503 The following will be displayed when the \SpecialChar LaTeX
10516 \begin_layout Standard
10517 You need to install the \SpecialChar LaTeX
10522 to see the rest of this subsection in the output.
10525 \begin_layout Standard
10529 \begin_layout Plain Layout
10541 \begin_layout Standard
10542 \begin_inset Newpage newpage
10548 \begin_layout Subsection
10549 Accents for several Characters
10550 \begin_inset Index idx
10553 \begin_layout Plain Layout
10554 Accents ! for several characters
10562 \begin_layout Standard
10563 \begin_inset space \hfill{}
10567 \begin_inset Tabular
10568 <lyxtabular version="3" rows="5" columns="2">
10569 <features booktabs="true" tabularvalignment="middle">
10570 <column alignment="center" valignment="top" width="0pt">
10571 <column alignment="center" valignment="top" width="0pt">
10573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10576 \begin_layout Plain Layout
10582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10585 \begin_layout Plain Layout
10592 <row topspace="1.5mm">
10593 <cell alignment="center" valignment="top" usebox="none">
10596 \begin_layout Plain Layout
10600 \begin_inset space \textvisiblespace{}
10608 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10611 \begin_layout Plain Layout
10612 \begin_inset Formula $\overleftarrow{A=B}$
10621 <row topspace="1.5mm">
10622 <cell alignment="center" valignment="top" usebox="none">
10625 \begin_layout Plain Layout
10629 \begin_inset space \textvisiblespace{}
10637 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10640 \begin_layout Plain Layout
10641 \begin_inset Formula $\underleftarrow{A=B}$
10650 <row topspace="1.5mm">
10651 <cell alignment="center" valignment="top" usebox="none">
10654 \begin_layout Plain Layout
10658 \begin_inset space \textvisiblespace{}
10666 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10669 \begin_layout Plain Layout
10670 \begin_inset Formula $\overleftrightarrow{A=B}$
10679 <row topspace="1.5mm" bottomspace="1mm">
10680 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10683 \begin_layout Plain Layout
10686 underleftrightarrow
10687 \begin_inset space \textvisiblespace{}
10695 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10698 \begin_layout Plain Layout
10699 \begin_inset Formula $\underleftrightarrow{A=B}$
10713 \begin_inset space \hfill{}
10717 \begin_inset Tabular
10718 <lyxtabular version="3" rows="5" columns="2">
10719 <features booktabs="true" tabularvalignment="middle">
10720 <column alignment="center" valignment="top" width="0pt">
10721 <column alignment="center" valignment="top" width="0pt">
10723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10726 \begin_layout Plain Layout
10732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10735 \begin_layout Plain Layout
10742 <row topspace="1.5mm">
10743 <cell alignment="center" valignment="top" usebox="none">
10746 \begin_layout Plain Layout
10750 \begin_inset space \textvisiblespace{}
10758 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10761 \begin_layout Plain Layout
10762 \begin_inset Formula $\overrightarrow{A=B}$
10771 <row topspace="1.5mm">
10772 <cell alignment="center" valignment="top" usebox="none">
10775 \begin_layout Plain Layout
10779 \begin_inset space \textvisiblespace{}
10787 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10790 \begin_layout Plain Layout
10791 \begin_inset Formula $\underrightarrow{A=B}$
10800 <row topspace="1.5mm">
10801 <cell alignment="center" valignment="top" usebox="none">
10804 \begin_layout Plain Layout
10808 \begin_inset space \textvisiblespace{}
10816 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10819 \begin_layout Plain Layout
10820 \begin_inset Formula $\widetilde{A=B}$
10829 <row topspace="1.5mm" bottomspace="1mm">
10830 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10833 \begin_layout Plain Layout
10837 \begin_inset space \textvisiblespace{}
10845 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10848 \begin_layout Plain Layout
10849 \begin_inset Formula $\widehat{A=B}$
10863 \begin_inset space \hfill{}
10869 \begin_layout Standard
10870 \begin_inset VSpace medskip
10873 With these commands as many characters as you like can be accented.
10886 will only be set in the output with a length of three characters, as shown
10887 in the following example:
10888 \begin_inset Formula
10890 \widetilde{A+B=C-D}
10898 \begin_layout Standard
10906 \begin_inset Index idx
10909 \begin_layout Plain Layout
10924 \begin_inset Index idx
10927 \begin_layout Plain Layout
10935 described in the previous subsection it is also possible to accent several
10942 \begin_inset space \textvisiblespace{}
10946 \begin_inset Formula $\downarrow$
10952 \begin_inset Formula
10954 \underset{***}{A=B}
10962 \begin_layout Section
10964 \begin_inset CommandInset label
10966 name "subsec:Space"
10971 \begin_inset Index idx
10974 \begin_layout Plain Layout
10983 \begin_layout Subsection
10985 \begin_inset CommandInset label
10987 name "subsec:Predefined-Space"
10992 \begin_inset Index idx
10995 \begin_layout Plain Layout
10996 Space ! horizontal ! predefined
11004 \begin_layout Standard
11005 Sometimes it is necessary to insert horizontal space into a formula.
11006 This is done by inserting a protected space (shortcut
11009 arg "command-alternatives space-insert protected ; math-space"
11014 \begin_inset Quotes eld
11020 \begin_inset space \textvisiblespace{}
11026 \begin_inset Quotes erd
11029 appears and by pressing
11033 several times one can select one of eight different space sizes.
11034 The spaces can also be inserted using the math toolbar button
11037 arg "math-insert \\space"
11040 or special commands.
11041 Independent from the inserted command, one can select the size again by
11047 \begin_inset Separator parbreak
11053 \begin_layout Standard
11056 \begin_inset Tabular
11057 <lyxtabular version="3" rows="6" columns="3">
11058 <features booktabs="true" tabularvalignment="middle">
11059 <column alignment="center" valignment="top">
11060 <column alignment="center" valignment="top" width="15col%">
11061 <column alignment="center" valignment="top">
11063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11066 \begin_layout Plain Layout
11072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11075 \begin_layout Plain Layout
11085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11088 \begin_layout Plain Layout
11096 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11099 \begin_layout Plain Layout
11107 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11110 \begin_layout Plain Layout
11116 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11119 \begin_layout Plain Layout
11120 \begin_inset Formula $A\,B$
11130 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11133 \begin_layout Plain Layout
11141 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11144 \begin_layout Plain Layout
11150 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11153 \begin_layout Plain Layout
11154 \begin_inset Formula $A\:B$
11164 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11167 \begin_layout Plain Layout
11175 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11178 \begin_layout Plain Layout
11184 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11187 \begin_layout Plain Layout
11188 \begin_inset Formula $A\;B$
11198 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11201 \begin_layout Plain Layout
11209 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11212 \begin_layout Plain Layout
11218 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11221 \begin_layout Plain Layout
11222 \begin_inset Formula $A\quad B$
11232 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11235 \begin_layout Plain Layout
11243 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11246 \begin_layout Plain Layout
11252 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11255 \begin_layout Plain Layout
11256 \begin_inset Formula $A\qquad B$
11270 \begin_inset space \hfill{}
11274 \begin_inset Tabular
11275 <lyxtabular version="3" rows="6" columns="3">
11276 <features booktabs="true" tabularvalignment="middle">
11277 <column alignment="center" valignment="top">
11278 <column alignment="center" valignment="top" width="15col%">
11279 <column alignment="center" valignment="top">
11281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11284 \begin_layout Plain Layout
11290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11293 \begin_layout Plain Layout
11303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11306 \begin_layout Plain Layout
11314 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11317 \begin_layout Plain Layout
11325 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11328 \begin_layout Plain Layout
11334 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11337 \begin_layout Plain Layout
11338 \begin_inset Formula $A\hfill B$
11348 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11351 \begin_layout Plain Layout
11359 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11362 \begin_layout Plain Layout
11368 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11371 \begin_layout Plain Layout
11372 \begin_inset Formula $A\hspace*{1em}B$
11382 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11385 \begin_layout Plain Layout
11393 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11396 \begin_layout Plain Layout
11402 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11405 \begin_layout Plain Layout
11406 \begin_inset Formula $A\hspace{1em}B$
11416 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11419 \begin_layout Plain Layout
11423 \begin_inset space \textvisiblespace{}
11431 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11434 \begin_layout Plain Layout
11440 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11443 \begin_layout Plain Layout
11444 \begin_inset Formula $A\ B$
11454 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11457 \begin_layout Plain Layout
11465 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11468 \begin_layout Plain Layout
11474 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11477 \begin_layout Plain Layout
11478 \begin_inset Formula $A\!B$
11494 \begin_layout Standard
11496 \begin_inset space ~
11500 \begin_inset space \thinspace{}
11504 \begin_inset space \thinspace{}
11507 7 are variable spaces which are explained in
11508 \begin_inset CommandInset ref
11510 reference "subsec:Variable-Space"
11516 \begin_inset space ~
11519 9 seems to produce no space.
11520 It is displayed red in \SpecialChar LyX
11521 contrary to the other sizes, because it is a negative
11523 There are two more negative spaces:
11524 \begin_inset Separator parbreak
11530 \begin_layout Standard
11532 \begin_inset Tabular
11533 <lyxtabular version="3" rows="3" columns="3">
11534 <features booktabs="true" tabularvalignment="middle">
11535 <column alignment="center" valignment="middle" width="6.8cm">
11536 <column alignment="center" valignment="top" width="0pt">
11537 <column alignment="center" valignment="top" width="0pt">
11539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11542 \begin_layout Plain Layout
11548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11551 \begin_layout Plain Layout
11559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11562 \begin_layout Plain Layout
11572 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11575 \begin_layout Plain Layout
11580 keystrokes after inserting the protected space
11585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11588 \begin_layout Plain Layout
11594 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11597 \begin_layout Plain Layout
11605 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11608 \begin_layout Plain Layout
11614 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11617 \begin_layout Plain Layout
11618 \begin_inset Formula $A\negmedspace B$
11626 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11629 \begin_layout Plain Layout
11630 \begin_inset Formula $A\negthickspace B$
11646 \begin_layout Standard
11647 Negative spaces can lead to characters overlapping each other.
11648 Thus they can be used to enforce ligatures, which are e.
11649 \begin_inset space \thinspace{}
11653 \begin_inset space \space{}
11656 useful for summation operators:
11657 \begin_inset Separator parbreak
11663 \begin_layout Standard
11665 \begin_inset Tabular
11666 <lyxtabular version="3" rows="3" columns="2">
11667 <features booktabs="true" tabularvalignment="middle">
11668 <column alignment="center" valignment="top" width="0pt">
11669 <column alignment="center" valignment="top">
11671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11674 \begin_layout Plain Layout
11680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11683 \begin_layout Plain Layout
11691 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11694 \begin_layout Plain Layout
11700 \begin_inset space \textvisiblespace{}
11708 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11711 \begin_layout Plain Layout
11712 \begin_inset Formula $\sum\sum f_{kl}$
11722 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11725 \begin_layout Plain Layout
11733 \begin_inset space \textvisiblespace{}
11741 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11744 \begin_layout Plain Layout
11745 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11761 \begin_layout Standard
11763 \begin_inset VSpace medskip
11769 \begin_layout Standard
11771 Relations like for example equal signs, are always surrounded by space.
11772 To suppress this, the equal sign is placed into a \SpecialChar TeX
11774 The following example demonstrates this:
11775 \begin_inset Separator parbreak
11781 \begin_layout Standard
11783 \begin_inset Tabular
11784 <lyxtabular version="3" rows="2" columns="2">
11785 <features tabularvalignment="middle">
11786 <column alignment="center" valignment="top" width="0pt">
11787 <column alignment="center" valignment="top" width="0pt">
11789 <cell alignment="center" valignment="top" usebox="none">
11792 \begin_layout Plain Layout
11798 <cell alignment="center" valignment="top" usebox="none">
11801 \begin_layout Plain Layout
11802 \begin_inset Formula $A=B$
11812 <cell alignment="center" valignment="top" usebox="none">
11815 \begin_layout Plain Layout
11816 equation without space
11821 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11824 \begin_layout Plain Layout
11825 \begin_inset Formula $A{=}B$
11841 \begin_layout Standard
11843 The command for the last formula is:
11848 \begin_inset Formula $\to$
11854 \begin_layout Standard
11855 \begin_inset VSpace bigskip
11861 \begin_layout Standard
11862 Spaces are needed for physical units, because the space between the value
11863 and the unit is the smallest one and not a normal space.
11864 For units in text, the smallest space is inserted via the menu
11866 Insert\SpecialChar menuseparator
11867 Formatting\SpecialChar menuseparator
11869 \begin_inset space ~
11877 arg "space-insert thin"
11883 \begin_layout Standard
11884 An example to visualize the difference:
11887 \begin_layout Standard
11888 \begin_inset Tabular
11889 <lyxtabular version="3" rows="2" columns="2">
11890 <features tabularvalignment="middle">
11891 <column alignment="left" valignment="top">
11892 <column alignment="left" valignment="top">
11894 <cell alignment="center" valignment="top" usebox="none">
11897 \begin_layout Plain Layout
11899 \begin_inset Formula $\cdot$
11907 <cell alignment="center" valignment="top" usebox="none">
11910 \begin_layout Plain Layout
11911 space between value and unit
11918 <cell alignment="center" valignment="top" usebox="none">
11921 \begin_layout Plain Layout
11923 \begin_inset space \thinspace{}
11927 \begin_inset Formula $\cdot$
11935 <cell alignment="center" valignment="top" usebox="none">
11938 \begin_layout Plain Layout
11939 smallest space between value and unit
11952 \begin_layout Subsection
11957 \begin_layout Plain Layout
11970 \begin_layout Plain Layout
11971 for vertical space in formulas see
11972 \begin_inset CommandInset ref
11974 reference "subsec:Line-Separation"
11987 \begin_layout Plain Layout
11995 \begin_inset Note Note
11998 \begin_layout Plain Layout
12001 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12004 \begin_layout Plain Layout
12007 texorpdfstring is in section
12008 \begin_inset CommandInset ref
12010 reference "subsec:Formulas-in-Section"
12020 \begin_inset CommandInset label
12022 name "subsec:Variable-Space"
12027 \begin_inset Index idx
12030 \begin_layout Plain Layout
12031 Space ! horizontal ! variable
12039 \begin_layout Standard
12040 Space with a defined length can be inserted with the command
12047 \begin_inset Index idx
12050 \begin_layout Plain Layout
12060 \begin_inset Quotes eld
12066 \begin_inset space \textvisiblespace{}
12072 \begin_inset Quotes erd
12076 The length can be specified by left-clicking on the
12077 \begin_inset Quotes eld
12083 \begin_inset space \textvisiblespace{}
12089 \begin_inset Quotes erd
12093 The length may also be negative.
12094 When a space would be the first character in a line it would be omitted.
12095 To force its output use the command
12107 or left-click on the
12108 \begin_inset Quotes eld
12114 \begin_inset space \textvisiblespace{}
12120 \begin_inset Quotes erd
12123 and check the option
12128 \begin_inset Newline newline
12131 To insert as much space as is available, the command
12138 \begin_inset Index idx
12141 \begin_layout Plain Layout
12152 \begin_layout Standard
12154 \begin_inset Tabular
12155 <lyxtabular version="3" rows="4" columns="2">
12156 <features booktabs="true" tabularvalignment="middle">
12157 <column alignment="center" valignment="top" width="0pt">
12158 <column alignment="center" valignment="top">
12160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12163 \begin_layout Plain Layout
12171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12174 \begin_layout Plain Layout
12182 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12185 \begin_layout Plain Layout
12189 \begin_inset space \textvisiblespace{}
12195 \begin_inset space \thinspace{}
12203 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12206 \begin_layout Plain Layout
12207 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12217 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12220 \begin_layout Plain Layout
12224 \begin_inset space \textvisiblespace{}
12230 \begin_inset space \thinspace{}
12238 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12241 \begin_layout Plain Layout
12242 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12255 \begin_layout Plain Layout
12259 \begin_inset space \textvisiblespace{}
12267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12270 \begin_layout Plain Layout
12271 \begin_inset Formula $A=A\hfill B=B$
12287 \begin_layout Standard
12288 In the last example the available space is given by the longest column entry
12290 In an inline formula the space depends on the length of the line in which
12298 Thus, when the line uses the full width, no space will be created.
12305 only has an effect on displayed formulas when the formula style
12310 (Formula styles are explained in
12311 \begin_inset CommandInset ref
12313 reference "sec:Formula-Styles"
12320 \begin_layout Standard
12327 , there are the commands
12339 that fill the space with a pattern, see
12340 \begin_inset CommandInset ref
12342 reference "subsec:Ellipses"
12349 \begin_layout Standard
12350 For text, variable space can be inserted via the menu
12352 Insert\SpecialChar menuseparator
12353 Formatting\SpecialChar menuseparator
12355 \begin_inset space ~
12363 \begin_layout Standard
12364 This is a line with
12365 \begin_inset space \hspace{}
12370 \begin_inset space \thinspace{}
12376 \begin_layout Standard
12377 This is a line with
12378 \begin_inset space \hfill{}
12384 \begin_layout Subsection
12385 Space besides inline Formulas
12386 \begin_inset Index idx
12389 \begin_layout Plain Layout
12390 Space ! besides inline formulas
12398 \begin_layout Standard
12399 The space that surrounds inline formulas can be adjusted with the length
12407 \begin_inset Index idx
12410 \begin_layout Plain Layout
12419 The value of a length is set with the command
12426 \begin_inset Index idx
12429 \begin_layout Plain Layout
12437 which has the following scheme:
12440 \begin_layout Standard
12445 setlength{length name}{value}
12448 \begin_layout Standard
12456 \begin_inset space \thinspace{}
12462 \begin_layout Standard
12472 \begin_layout Standard
12473 is inserted in \SpecialChar TeX
12476 \begin_inset space \thinspace{}
12479 mm space will now be set around all inline formulas:
12483 \begin_layout Plain Layout
12497 \begin_layout Standard
12498 This is a line with an inline formula
12499 \begin_inset Formula $A=B$
12503 \begin_inset space \thinspace{}
12506 mm surrounding space.
12510 \begin_layout Plain Layout
12524 \begin_layout Standard
12525 To return to the predefined value,
12531 is set to the value 0
12532 \begin_inset space \thinspace{}
12538 \begin_layout Standard
12539 \begin_inset Newpage newpage
12545 \begin_layout Section
12547 \begin_inset Index idx
12550 \begin_layout Plain Layout
12557 \begin_inset Index idx
12560 \begin_layout Plain Layout
12565 \begin_layout Plain Layout
12576 \begin_layout Plain Layout
12591 \begin_layout Standard
12592 Boxes for text are described in chapter
12599 \begin_inset space ~
12607 \begin_layout Subsection
12609 \begin_inset CommandInset label
12611 name "subsec:Boxes-with-Frame"
12616 \begin_inset Index idx
12619 \begin_layout Plain Layout
12628 \begin_layout Standard
12629 It is possible to frame a formula or part of one with the commands
12636 \begin_inset Index idx
12639 \begin_layout Plain Layout
12654 \begin_inset Index idx
12657 \begin_layout Plain Layout
12668 \begin_layout Standard
12669 When one of these commands is inserted in a formula, a blue box appears
12670 within a frame to enter formula parts.
12677 an additional formula has to be created by
12681 within this box, because the box content will otherwise be treated as mathemati
12689 is used, a new formula is automatically created inside the frame.
12692 \begin_layout Standard
12699 is not suitable to frame displayed formulas because the formula will always
12700 be set in the size of the text.
12707 is in contrary not suitable to frame inline formulas, because the formula
12708 will always be set in the size of a displayed formula.
12711 \begin_layout Standard
12725 \begin_inset Index idx
12728 \begin_layout Plain Layout
12736 where additionally the frame width and the alignment can be specified.
12743 is used in the following scheme:
12746 \begin_layout Standard
12751 framebox[frame width][position]{box content}
12754 \begin_layout Standard
12755 The position can either be
12772 right aligns the formula in the box.
12773 When no position is given, the formula will be centered.
12774 \begin_inset Newline newline
12777 If no width is given, also no position can be given.
12778 In this case the frame width is adjusted to the box content like for
12787 \begin_layout Standard
12794 is inserted, a box appears containing three blue boxes.
12795 The first two boxes are surrounded by brackets and denote the two optional
12797 The third box is for formula parts like for
12804 \begin_inset Separator parbreak
12810 \begin_layout Standard
12812 \begin_inset Tabular
12813 <lyxtabular version="3" rows="5" columns="2">
12814 <features booktabs="true" tabularvalignment="middle">
12815 <column alignment="center" valignment="top" width="0pt">
12816 <column alignment="center" valignment="top">
12818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12821 \begin_layout Plain Layout
12827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12830 \begin_layout Plain Layout
12837 <row topspace="1.5mm">
12838 <cell alignment="center" valignment="top" usebox="none">
12841 \begin_layout Plain Layout
12845 \begin_inset space \textvisiblespace{}
12855 \begin_inset space \textvisiblespace{}
12863 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12866 \begin_layout Plain Layout
12867 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12876 <row topspace="1.5mm">
12877 <cell alignment="center" valignment="top" usebox="none">
12880 \begin_layout Plain Layout
12884 \begin_inset space \textvisiblespace{}
12890 \begin_inset space \textvisiblespace{}
12898 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12901 \begin_layout Plain Layout
12902 \begin_inset Formula $\boxed{\int A=B}$
12911 <row topspace="1.5mm">
12912 <cell alignment="center" valignment="top" usebox="none">
12915 \begin_layout Plain Layout
12919 \begin_inset space \textvisiblespace{}
12927 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12930 \begin_layout Plain Layout
12931 \begin_inset Formula $A+\fbox{B}$
12940 <row topspace="1.5mm" bottomspace="1mm">
12941 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12944 \begin_layout Plain Layout
12948 \begin_inset space \textvisiblespace{}
12952 \begin_inset Formula $\to$
12956 \begin_inset Formula $\to$
12966 \begin_inset space \textvisiblespace{}
12970 \begin_inset Formula $\downarrow$
12978 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12981 \begin_layout Plain Layout
12982 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12998 \begin_layout Standard
12999 The frame thickness can also be adjusted.
13000 To do this the following commands have to be inserted in \SpecialChar TeX
13005 \begin_layout Standard
13015 \begin_inset Quotes eld
13019 \begin_inset Quotes erd
13033 \begin_inset Quotes eld
13037 \begin_inset Quotes erd
13043 \begin_layout Standard
13044 \begin_inset Quotes eld
13048 \begin_inset Quotes erd
13051 specifies the minimal distance between the frame and the first character
13053 An example for this is the following framed formula:
13057 \begin_layout Plain Layout
13069 \begin_inset Formula
13076 Before this formula the commands
13079 \begin_layout Standard
13101 \begin_layout Standard
13102 were inserted in \SpecialChar TeX
13104 The given values are used for all following boxes.
13107 \begin_layout Standard
13108 To return to the standard frame size, the command
13111 \begin_layout Standard
13136 \begin_layout Plain Layout
13150 \begin_layout Standard
13151 is inserted in \SpecialChar TeX
13152 mode before the next formula.
13155 \begin_layout Subsection
13156 Boxes without Frame
13157 \begin_inset CommandInset label
13159 name "subsec:Boxes-without-Frame"
13164 \begin_inset Index idx
13167 \begin_layout Plain Layout
13168 Boxes ! without frame
13176 \begin_layout Standard
13177 For boxes without a frame there are the following box commands:
13184 \begin_inset Index idx
13187 \begin_layout Plain Layout
13202 \begin_inset Index idx
13205 \begin_layout Plain Layout
13220 \begin_inset Index idx
13223 \begin_layout Plain Layout
13234 \begin_layout Standard
13241 a box can be super- or subscripted.
13242 But in contrary to normal super- and subscripting, the characters in the
13243 box keep their font size.
13250 is used in the following scheme:
13253 \begin_layout Standard
13258 raisebox{height}{box content}
13261 \begin_layout Standard
13262 When the box should contain a formula, an extra formula is needed like for
13273 \begin_inset Note Greyedout
13276 \begin_layout Plain Layout
13287 this extra formula is created by pressing
13291 twice instead of once because \SpecialChar LyX
13292 doesn't yet support
13306 \begin_inset Separator parbreak
13312 \begin_layout Standard
13314 \begin_inset Tabular
13315 <lyxtabular version="3" rows="4" columns="2">
13316 <features booktabs="true" tabularvalignment="middle">
13317 <column alignment="center" valignment="top" width="0pt">
13318 <column alignment="center" valignment="top">
13320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13323 \begin_layout Plain Layout
13329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13332 \begin_layout Plain Layout
13340 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13343 \begin_layout Plain Layout
13347 \begin_inset Formula $\to$
13353 \begin_inset Formula $\to$
13361 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13364 \begin_layout Plain Layout
13365 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13375 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13378 \begin_layout Plain Layout
13382 \begin_inset Formula $\to$
13388 \begin_inset Formula $\to$
13396 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13399 \begin_layout Plain Layout
13400 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13413 \begin_layout Plain Layout
13417 \begin_inset Formula $\to$
13433 \begin_inset space \textvisiblespace{}
13441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13444 \begin_layout Plain Layout
13445 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13461 \begin_layout Standard
13486 , with the difference that there is no frame.
13489 \begin_layout Subsection
13491 \begin_inset CommandInset label
13493 name "subsec:Colored-Boxes"
13498 \begin_inset Index idx
13501 \begin_layout Plain Layout
13510 \begin_layout Standard
13511 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13520 \begin_layout Plain Layout
13521 The \SpecialChar LaTeX
13526 is part of every \SpecialChar LaTeX
13527 standard installation.
13533 \begin_inset Index idx
13536 \begin_layout Plain Layout
13542 has to be loaded in the \SpecialChar LaTeX
13543 -preamble with the line
13547 \begin_layout Plain Layout
13548 When text is colored somewhere in the document with a predefined color,
13550 loads the \SpecialChar LaTeX
13556 Thus it is possible that the package is loaded twice, but this does not
13563 \begin_inset Note Note
13566 \begin_layout Plain Layout
13567 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13576 \begin_layout Standard
13584 \begin_layout Standard
13585 \begin_inset VSpace medskip
13588 To color boxes, the command
13595 \begin_inset Index idx
13598 \begin_layout Plain Layout
13606 is used in the following scheme:
13609 \begin_layout Standard
13614 colorbox{color}{box content}
13617 \begin_layout Standard
13618 The box content can also be a box and a
13624 can also be part of another box (see the 2nd and 3rd example).
13625 When the box should contain a formula, an extra formula has to be created,
13626 the same way as for
13636 \begin_layout Plain Layout
13637 This also applies for the command
13651 \begin_layout Standard
13652 One of the following predefined colors can be chosen:
13655 \begin_layout Standard
13689 \begin_inset Separator parbreak
13695 \begin_layout Standard
13697 \begin_inset Tabular
13698 <lyxtabular version="3" rows="4" columns="2">
13699 <features booktabs="true" tabularvalignment="middle">
13700 <column alignment="center" valignment="top" width="0pt">
13701 <column alignment="center" valignment="top">
13703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13706 \begin_layout Plain Layout
13712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13715 \begin_layout Plain Layout
13723 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13726 \begin_layout Plain Layout
13730 \begin_inset Formula $\to$
13740 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13743 \begin_layout Plain Layout
13744 \begin_inset Formula $\colorbox{yellow}{A=B}$
13753 <row topspace="1.5mm">
13754 <cell alignment="center" valignment="top" usebox="none">
13757 \begin_layout Plain Layout
13761 \begin_inset Formula $\to$
13769 \begin_inset space \textvisiblespace{}
13777 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13780 \begin_layout Plain Layout
13781 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13790 <row topspace="1.5mm" bottomspace="1mm">
13791 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13794 \begin_layout Plain Layout
13798 \begin_inset space \textvisiblespace{}
13804 \begin_inset Formula $\to$
13820 \begin_inset space \textvisiblespace{}
13828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13831 \begin_layout Plain Layout
13832 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13848 \begin_layout Standard
13855 only colors the box but not the characters in the box.
13856 To color all characters, the whole formula is highlighted and the desired
13857 color is chosen in the
13860 \begin_inset space ~
13866 The dialog can be called with the toolbar button
13869 arg "dialog-show character"
13874 Edit\SpecialChar menuseparator
13876 \begin_inset space ~
13879 Style\SpecialChar menuseparator
13883 The formula number then has the same color as the formula.
13884 When the formula number should get another color than the formula characters,
13885 the color must be changed within the formula.
13888 \begin_layout Standard
13892 \begin_layout Standard
13895 \begin_inset Formula
13897 \int A=B\label{eq:red}
13905 \begin_inset Formula
13907 \textcolor{red}{\int A=B}\label{eq:redgreen}
13915 \begin_layout Standard
13917 \begin_inset CommandInset ref
13923 is completely colored red.
13924 \begin_inset Newline newline
13928 \begin_inset CommandInset ref
13930 reference "eq:redgreen"
13934 was first completely colored green to set the color for the formula number.
13935 Subsequently the formula characters were colored red.
13938 \begin_layout Standard
13939 \begin_inset VSpace bigskip
13942 To color the frame different than the rest of the box, the command
13949 \begin_inset Index idx
13952 \begin_layout Plain Layout
13960 is used in the following scheme:
13963 \begin_layout Standard
13968 fcolorbox{frame color}{color}{box content}
13971 \begin_layout Standard
13978 is an extension of the command
13985 The frame width is set, like for
14008 \begin_layout Plain Layout
14020 \begin_inset Formula
14022 \fcolorbox{cyan}{magenta}{A=B}
14031 \begin_layout Plain Layout
14045 \begin_layout Standard
14046 This formula was created with the command
14047 \begin_inset Newline newline
14055 \begin_inset Formula $\to$
14061 \begin_inset Formula $\to$
14071 \begin_layout Standard
14072 \begin_inset VSpace bigskip
14075 To use other colors than the predefined ones, they have to be defined first.
14078 \begin_layout Standard
14079 One can for example define the color
14080 \begin_inset Quotes eld
14088 \begin_inset Quotes erd
14091 with the \SpecialChar LaTeX
14095 \begin_layout Standard
14100 definecolor{darkgreen}{cmyk}{0.5,
14115 \begin_inset Index idx
14118 \begin_layout Plain Layout
14129 \begin_layout Standard
14134 is the color space that denotes the colors
14151 The four comma separated numbers are the portion factor for the corresponding
14152 colors of the color space.
14153 The factors can be in the range of 0
14154 \begin_inset space \thinspace{}
14158 \begin_inset space \thinspace{}
14166 also the color space
14170 can be used for definitions.
14187 , so that there are in this case three portion factors for the corresponding
14189 Furthermore there is the color space
14193 with one portion factor for the gray value.
14196 \begin_layout Standard
14197 As example a framed box with the new defined color
14201 where the characters have been colored
14206 \begin_inset Formula
14208 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14216 \begin_layout Standard
14217 Self-defined colors can also be used for text with the help of the command
14225 \begin_inset Index idx
14228 \begin_layout Plain Layout
14237 \begin_layout Standard
14241 \begin_layout Plain Layout
14245 textcolor{darkgreen}{
14251 \begin_inset Quotes eld
14255 \begin_inset Quotes erd
14262 \begin_layout Plain Layout
14272 \begin_layout Standard
14280 \begin_inset Index idx
14283 \begin_layout Plain Layout
14291 is used in the scheme
14295 textcolor{color}{characters to color}
14300 \begin_layout Subsection
14302 \begin_inset CommandInset label
14304 name "subsec:Paragraph-Boxes"
14309 \begin_inset Index idx
14312 \begin_layout Plain Layout
14313 Boxes ! as paragraph
14321 \begin_layout Standard
14322 A box that can contain several lines and paragraphs, a so-called paragraph
14323 box (parbox), can be created with the menu
14325 Insert\SpecialChar menuseparator
14328 or the toolbar button
14337 \begin_layout Standard
14338 The following example shows a framed parbox in a line:
14341 \begin_layout Standard
14342 \begin_inset VSpace medskip
14346 \begin_inset Box Boxed
14356 height_special "totalheight"
14361 backgroundcolor "none"
14364 \begin_layout Plain Layout
14365 This is a paragraph box.
14367 \begin_inset space \thinspace{}
14370 cm long and can also contain formulas:
14371 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14382 \begin_layout Standard
14383 \begin_inset VSpace medskip
14389 \begin_layout Standard
14390 Such a box is created by right-clicking on the gray box inset.
14391 A dialog pops up showing the box properties.
14405 \begin_inset space \thinspace{}
14410 Vertical Box Alignment
14415 \begin_layout Standard
14416 \begin_inset VSpace medskip
14419 In \SpecialChar LaTeX
14420 a parbox is created with the command
14427 \begin_inset Index idx
14430 \begin_layout Plain Layout
14438 which has the following scheme:
14441 \begin_layout Standard
14446 parbox[position]{width}{box content}
14449 \begin_layout Standard
14464 \begin_inset Quotes eld
14468 \begin_inset Quotes erd
14471 means that the box is aligned within the surrounding text with its last
14478 \begin_inset Quotes eld
14482 \begin_inset Quotes erd
14485 this is done with the first line.
14486 When no position is given, the box will be vertically centered, see section
14494 \begin_inset space ~
14499 manual for examples.
14502 \begin_layout Standard
14503 \begin_inset VSpace bigskip
14506 To frame formulas completely, including the formula number, the formula
14507 must be set into a parbox.
14508 To do this, the command
14522 is inserted in \SpecialChar TeX
14523 mode before the formula.
14531 \begin_inset Index idx
14534 \begin_layout Plain Layout
14542 is hereby the line width set for the document.
14543 Because the frame is outside the parbox, 2
14544 \begin_inset space \thinspace{}
14547 times the frame separation and the frame thickness must be subtracted from
14549 As this is not automatically done by \SpecialChar LyX
14554 \begin_layout Plain Layout
14555 \begin_inset CommandInset href
14557 name "LyX-bug #4483"
14558 target "http://www.lyx.org/trac/ticket/4483"
14568 mode has to be used.
14569 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14578 \begin_layout Plain Layout
14583 is part of every \SpecialChar LaTeX
14584 standard installation.
14590 \begin_inset Index idx
14593 \begin_layout Plain Layout
14599 must be loaded in the \SpecialChar LaTeX
14600 -preamble with the line
14603 \begin_layout Standard
14611 \begin_layout Standard
14612 Behind the formula both boxes are closed by entering
14616 in \SpecialChar TeX
14618 Here is an example:
14622 \begin_layout Plain Layout
14636 \begin_layout Standard
14640 \begin_layout Plain Layout
14658 \begin_inset Formula
14660 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14669 \begin_layout Plain Layout
14680 \begin_layout Plain Layout
14694 \begin_layout Standard
14695 \begin_inset VSpace medskip
14698 As a parbox is used as the argument of
14704 , there is in this case no difference between
14719 \begin_layout Standard
14720 \begin_inset VSpace bigskip
14723 Paragraph boxes are very useful to comment formulas directly.
14730 is used in combination with the command
14744 \begin_inset CommandInset ref
14746 reference "subsec:User-defined-Numbering"
14753 \begin_layout Standard
14754 An example of a formula commented with
14763 \begin_layout Standard
14767 \begin_layout Plain Layout
14780 This is a description.
14781 It is distinctly separated from the formula and multiline.
14785 \begin_layout Plain Layout
14797 \begin_layout Standard
14798 Such a formula must be inserted completely in \SpecialChar TeX
14799 mode because \SpecialChar LyX
14801 support the command
14808 The formula is created with the following command sequence:
14811 \begin_layout Standard
14824 is inserted in \SpecialChar TeX
14829 \begin_layout Plain Layout
14830 When the formula style
14842 can also be replaced by
14849 (formula styles see
14850 \begin_inset CommandInset ref
14852 reference "sec:Formula-Styles"
14861 Then the description follows as normal text and finally
14867 is inserted in \SpecialChar TeX
14881 hereby create a displayed formula.
14884 \begin_layout Standard
14891 can be seen in this example that was
14892 \begin_inset Quotes eld
14896 \begin_inset Quotes erd
14899 using the mathematical textmode:
14900 \begin_inset Formula
14902 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14910 \begin_layout Section
14912 \begin_inset Index idx
14915 \begin_layout Plain Layout
14924 \begin_layout Subsection
14926 \begin_inset CommandInset label
14928 name "subsec:Big-Operators"
14933 \begin_inset Index idx
14936 \begin_layout Plain Layout
14943 \begin_inset Index idx
14946 \begin_layout Plain Layout
14953 \begin_inset Index idx
14956 \begin_layout Plain Layout
14965 \begin_layout Standard
14966 To be able to use all integral operators listed here, the option
14968 Use esint package automatically
14970 must be set in the document settings under
14973 \begin_inset space ~
14981 \begin_layout Standard
14982 \begin_inset space \hfill{}
14986 \begin_inset Tabular
14987 <lyxtabular version="3" rows="11" columns="2">
14988 <features booktabs="true" tabularvalignment="middle">
14989 <column alignment="center" valignment="top" width="0pt">
14990 <column alignment="center" valignment="top" width="0pt">
14992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14995 \begin_layout Plain Layout
15001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15004 \begin_layout Plain Layout
15012 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15015 \begin_layout Plain Layout
15019 \begin_inset Index idx
15022 \begin_layout Plain Layout
15035 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15038 \begin_layout Plain Layout
15039 \begin_inset Formula $\int$
15049 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15052 \begin_layout Plain Layout
15060 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15063 \begin_layout Plain Layout
15064 \begin_inset Formula $\oint$
15074 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15077 \begin_layout Plain Layout
15085 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15088 \begin_layout Plain Layout
15089 \begin_inset Formula $\ointctrclockwise$
15099 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15102 \begin_layout Plain Layout
15110 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15113 \begin_layout Plain Layout
15114 \begin_inset Formula $\ointclockwise$
15124 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15127 \begin_layout Plain Layout
15135 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15138 \begin_layout Plain Layout
15139 \begin_inset Formula $\sqint$
15149 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15152 \begin_layout Plain Layout
15160 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15163 \begin_layout Plain Layout
15165 \begin_inset Formula $\fint$
15175 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15178 \begin_layout Plain Layout
15186 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15189 \begin_layout Plain Layout
15191 \begin_inset Formula $\landupint$
15201 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15204 \begin_layout Plain Layout
15212 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15215 \begin_layout Plain Layout
15217 \begin_inset Formula $\landdownint$
15227 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15230 \begin_layout Plain Layout
15238 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15241 \begin_layout Plain Layout
15242 \begin_inset Formula $\bigcap$
15252 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15255 \begin_layout Plain Layout
15263 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15266 \begin_layout Plain Layout
15267 \begin_inset Formula $\bigcup$
15281 \begin_inset space \hfill{}
15285 \begin_inset Tabular
15286 <lyxtabular version="3" rows="11" columns="2">
15287 <features booktabs="true" tabularvalignment="middle">
15288 <column alignment="center" valignment="top" width="0pt">
15289 <column alignment="center" valignment="top" width="0pt">
15291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15294 \begin_layout Plain Layout
15300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15303 \begin_layout Plain Layout
15311 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15314 \begin_layout Plain Layout
15318 \begin_inset Index idx
15321 \begin_layout Plain Layout
15334 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15337 \begin_layout Plain Layout
15338 \begin_inset Formula $\sum$
15348 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15351 \begin_layout Plain Layout
15355 \begin_inset Index idx
15358 \begin_layout Plain Layout
15365 \begin_layout Plain Layout
15384 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15387 \begin_layout Plain Layout
15388 \begin_inset Formula $\prod$
15398 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15401 \begin_layout Plain Layout
15409 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15412 \begin_layout Plain Layout
15413 \begin_inset Formula $\coprod$
15423 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15426 \begin_layout Plain Layout
15434 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15437 \begin_layout Plain Layout
15438 \begin_inset Formula $\bigodot$
15448 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15451 \begin_layout Plain Layout
15459 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15462 \begin_layout Plain Layout
15463 \begin_inset Formula $\bigotimes$
15473 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15476 \begin_layout Plain Layout
15484 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15487 \begin_layout Plain Layout
15488 \begin_inset Formula $\bigoplus$
15498 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15501 \begin_layout Plain Layout
15509 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15512 \begin_layout Plain Layout
15513 \begin_inset Formula $\bigwedge$
15523 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15526 \begin_layout Plain Layout
15534 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15537 \begin_layout Plain Layout
15538 \begin_inset Formula $\bigvee$
15548 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15551 \begin_layout Plain Layout
15559 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15562 \begin_layout Plain Layout
15563 \begin_inset Formula $\bigsqcup$
15573 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15576 \begin_layout Plain Layout
15584 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15587 \begin_layout Plain Layout
15588 \begin_inset Formula $\biguplus$
15602 \begin_inset space \hfill{}
15608 \begin_layout Standard
15609 All big operators can also be inserted via the math toolbar button
15612 arg "math-insert \\intop"
15618 \begin_layout Standard
15619 The operators are called big because they are bigger than the sometimes
15620 equal looking binary operators.
15621 All big operators can have limits as described in the next subsection.
15624 \begin_layout Standard
15625 For all integral operators there is a second version available, ending in
15643 These operators are different from
15650 \begin_inset space \space{}
15653 in the style the operator limits are displayed, see
15654 \begin_inset CommandInset ref
15656 reference "subsec:Operator-Limits"
15664 \begin_layout Subsubsection*
15665 Advice for Integrals
15668 \begin_layout Standard
15673 in an integral is an operator, that therefore has to be set upright.
15674 This is done by highlighting the
15678 and using the keyboard shortcut
15688 \begin_layout Plain Layout
15694 \begin_inset CommandInset ref
15696 reference "subsec:Font-Styles"
15706 Finally the smallest space is inserted before the
15710 , as this is usual for operators.
15714 \begin_layout Standard
15716 \begin_inset Formula $\int A(x)dx$
15720 \begin_inset Newline newline
15724 \begin_inset Phantom HPhantom
15727 \begin_layout Plain Layout
15734 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15740 \begin_layout Standard
15741 For multiple integrals there are the following commands:
15742 \begin_inset VSpace medskip
15748 \begin_layout Standard
15749 \begin_inset space \hfill{}
15753 \begin_inset Tabular
15754 <lyxtabular version="3" rows="4" columns="2">
15755 <features booktabs="true" tabularvalignment="middle">
15756 <column alignment="center" valignment="top" width="0pt">
15757 <column alignment="center" valignment="top" width="0pt">
15759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15762 \begin_layout Plain Layout
15768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15771 \begin_layout Plain Layout
15778 <row bottomspace="1mm">
15779 <cell alignment="center" valignment="top" usebox="none">
15782 \begin_layout Plain Layout
15790 <cell alignment="center" valignment="top" usebox="none">
15793 \begin_layout Plain Layout
15794 \begin_inset Formula $\iint$
15803 <row bottomspace="1mm">
15804 <cell alignment="center" valignment="top" usebox="none">
15807 \begin_layout Plain Layout
15815 <cell alignment="center" valignment="top" usebox="none">
15818 \begin_layout Plain Layout
15819 \begin_inset Formula $\oiint$
15828 <row bottomspace="1mm">
15829 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15832 \begin_layout Plain Layout
15840 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15843 \begin_layout Plain Layout
15844 \begin_inset Formula $\sqiint$
15858 \begin_inset space \hfill{}
15862 \begin_inset Tabular
15863 <lyxtabular version="3" rows="4" columns="2">
15864 <features booktabs="true" tabularvalignment="middle">
15865 <column alignment="center" valignment="top" width="0pt">
15866 <column alignment="center" valignment="top" width="0pt">
15868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15871 \begin_layout Plain Layout
15877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15880 \begin_layout Plain Layout
15887 <row bottomspace="1mm">
15888 <cell alignment="center" valignment="top" usebox="none">
15891 \begin_layout Plain Layout
15899 <cell alignment="center" valignment="top" usebox="none">
15902 \begin_layout Plain Layout
15903 \begin_inset Formula $\iiint$
15912 <row bottomspace="1mm">
15913 <cell alignment="center" valignment="top" usebox="none">
15916 \begin_layout Plain Layout
15924 <cell alignment="center" valignment="top" usebox="none">
15927 \begin_layout Plain Layout
15928 \begin_inset Formula $\iiiint$
15937 <row bottomspace="1mm">
15938 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15941 \begin_layout Plain Layout
15949 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15952 \begin_layout Plain Layout
15953 \begin_inset Formula $\dotsint$
15967 \begin_inset space \hfill{}
15973 \begin_layout Subsection
15975 \begin_inset CommandInset label
15977 name "subsec:Operator-Limits"
15982 \begin_inset Index idx
15985 \begin_layout Plain Layout
15994 \begin_layout Standard
15995 Limits are created by super- and subscripts:
15996 \begin_inset Separator parbreak
16002 \begin_layout Standard
16004 \begin_inset Tabular
16005 <lyxtabular version="3" rows="2" columns="2">
16006 <features booktabs="true" tabularvalignment="middle">
16007 <column alignment="center" valignment="top" width="0pt">
16008 <column alignment="center" valignment="top" width="0pt">
16010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16013 \begin_layout Plain Layout
16019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16022 \begin_layout Plain Layout
16030 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16033 \begin_layout Plain Layout
16039 \begin_inset space \textvisiblespace{}
16043 \begin_inset Formula $\to$
16047 \begin_inset Formula $\to$
16055 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16058 \begin_layout Plain Layout
16059 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
16075 \begin_layout Standard
16076 Limits of inline formulas are set right beside the operator.
16077 Limits in displayed formulas are set above or below the operator, except
16078 for integral limits.
16081 \begin_layout Standard
16082 To force that the limits are set beside the operator, the cursor is set
16083 directly behind the operator and the limits type is changed with the menu
16086 Edit\SpecialChar menuseparator
16087 Math\SpecialChar menuseparator
16106 \begin_layout Standard
16107 The default limits type is this:
16108 \begin_inset Formula
16110 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16115 This is how it looks when the limits type was changed to
16122 \begin_inset Formula
16124 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16129 For integrals, except those ending with
16145 etc., the limits are by default set beside the operator.
16146 But for multiple integrals the limits are often set below the operator.
16147 In the following example the limits type was therefore set to
16151 and so set below the integrals:
16152 \begin_inset Formula
16154 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16162 \begin_layout Standard
16163 \begin_inset VSpace medskip
16166 To specify conditions for limits, the commands
16173 \begin_inset Index idx
16176 \begin_layout Plain Layout
16191 \begin_inset Index idx
16194 \begin_layout Plain Layout
16203 To create for example this expression
16204 \begin_inset Formula
16206 \sum_{\begin{subarray}{c}
16210 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16218 \begin_layout Standard
16219 the following has to be done:
16220 \begin_inset Newline newline
16232 \begin_inset space \textvisiblespace{}
16238 One is now in a blue box under the summation operator and insert there
16244 \begin_inset space \textvisiblespace{}
16250 The blue box is now within a purple box and now several lines can be written
16252 A new line is created by inserting a line break (
16255 arg "newline-insert newline"
16260 \begin_inset Newline newline
16265 0<k<1000 Ctrl+Return
16266 \begin_inset Newline newline
16271 is typed in, a new box appears below for the new line.
16274 \begin_layout Standard
16275 The alignment of the lines can be changed to left aligned with the
16285 Edit\SpecialChar menuseparator
16289 To get right alignment,
16294 \begin_inset space \textvisiblespace{}
16299 is inserted at the beginning of the line.
16302 \begin_layout Standard
16315 with the difference that the lines are always centered.
16318 \begin_layout Standard
16319 \begin_inset VSpace bigskip
16323 \begin_inset CommandInset ref
16325 reference "eq:substack"
16329 there can be too much space beside an operator, because the characters
16330 following the operator are set beside the limits.
16331 To avoid this the command
16338 \begin_inset Index idx
16341 \begin_layout Plain Layout
16350 To activate it, set in the document settings under
16353 \begin_inset space ~
16363 \begin_inset Index idx
16366 \begin_layout Plain Layout
16367 Packages ! mathtools
16375 \begin_inset space ~
16387 sets the space besides the operator to 0
16388 \begin_inset space \thinspace{}
16392 \begin_inset Newline newline
16396 \begin_inset CommandInset ref
16398 reference "eq:substack"
16402 , one uses the command
16405 \begin_layout Standard
16413 \begin_layout Standard
16414 and inserts the operator with its limits into the braces.
16415 Behind the brace one continues the formula:
16416 \begin_inset Formula
16418 \smashoperator{\sum_{\begin{subarray}{c}
16422 \end{subarray}}^{n}}k^{-2}
16430 \begin_layout Standard
16431 It is possible to set the space of only one side of the operator to 0
16432 \begin_inset space \thinspace{}
16436 To do this write either
16455 stands for the left and
16459 for the right side of the operator.
16460 Here is an example of the possible
16469 \begin_layout Standard
16470 \begin_inset Formula
16472 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}
16480 \begin_layout Standard
16481 \begin_inset VSpace bigskip
16487 \begin_layout Standard
16488 When several consecutive operators have limits the typesetting of the limits
16489 looks often imperfect in the output, see this example:
16490 \begin_inset Formula
16492 \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}
16497 To improve the typesetting set in the document settings under
16500 \begin_inset space ~
16510 \begin_inset Index idx
16513 \begin_layout Plain Layout
16514 Packages ! mathtools
16522 \begin_inset space ~
16528 Then insert into your formula the command
16535 \begin_inset Index idx
16538 \begin_layout Plain Layout
16546 directly before the first operator.
16547 The example will then look like this:
16548 \begin_inset Formula
16550 \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}
16558 \begin_layout Standard
16559 \begin_inset VSpace bigskip
16562 How to use one limit for several operators is described in
16563 \begin_inset CommandInset ref
16565 reference "subsec:Self-defined-Operators"
16572 \begin_layout Subsection
16573 Decoration for Operators
16574 \begin_inset Index idx
16577 \begin_layout Plain Layout
16578 Operators ! Decoration
16586 \begin_layout Standard
16594 \begin_inset Index idx
16597 \begin_layout Plain Layout
16612 \begin_inset Index idx
16615 \begin_layout Plain Layout
16623 characters can be placed above or below an operator, respectively.
16631 \begin_inset Index idx
16634 \begin_layout Plain Layout
16642 characters can be set before and behind a big operator.
16645 \begin_layout Standard
16647 \begin_inset space ~
16659 \begin_layout Itemize
16666 is used to set characters at the corners of the operator
16669 \begin_layout Itemize
16676 is used to set characters before and/or behind the operator (this variant
16677 represents \SpecialChar LaTeX
16687 \begin_layout Itemize
16694 is used to set characters at the left corners and/or behind the operator
16697 \begin_layout Itemize
16704 is used to set characters at the right corners and/or before the operator
16707 \begin_layout Standard
16708 For example the command
16713 \begin_inset space \textvisiblespace{}
16719 \begin_inset space \textvisiblespace{}
16723 \begin_inset Formula $\to$
16727 \begin_inset Formula $\to$
16731 \begin_inset space \textvisiblespace{}
16741 \begin_inset Formula
16743 \sideset{}{'}\sum_{k=1}^{n}
16751 \begin_layout Standard
16752 \begin_inset Note Greyedout
16755 \begin_layout Plain Layout
16762 can only be used to decorate big operators, binary operators are not allowed.
16770 \begin_layout Standard
16783 can also be used to decorate symbols and characters.
16784 For example, the command
16789 \begin_inset space \textvisiblespace{}
16795 \begin_inset space \textvisiblespace{}
16801 \begin_inset Formula $\uparrow$
16809 \begin_inset Formula
16811 \overset{a}{\maltese}
16819 \begin_layout Subsection
16821 \begin_inset CommandInset label
16823 name "subsec:Binary-Operators"
16828 \begin_inset Index idx
16831 \begin_layout Plain Layout
16840 \begin_layout Standard
16841 Binary operators are surrounded by space when there is a character before
16843 \begin_inset VSpace medskip
16849 \begin_layout Standard
16850 \begin_inset Tabular
16851 <lyxtabular version="3" rows="13" columns="2">
16852 <features booktabs="true" tabularvalignment="middle">
16853 <column alignment="center" valignment="top" width="0pt">
16854 <column alignment="center" valignment="top" width="0pt">
16856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16859 \begin_layout Plain Layout
16861 \begin_inset Note Note
16864 \begin_layout Plain Layout
16871 is only used as spacer.
16881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16884 \begin_layout Plain Layout
16892 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16895 \begin_layout Plain Layout
16901 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16904 \begin_layout Plain Layout
16905 \begin_inset Formula $+$
16915 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16918 \begin_layout Plain Layout
16924 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16927 \begin_layout Plain Layout
16928 \begin_inset Formula $-$
16938 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16941 \begin_layout Plain Layout
16949 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16952 \begin_layout Plain Layout
16953 \begin_inset Formula $\pm$
16963 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16966 \begin_layout Plain Layout
16974 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16977 \begin_layout Plain Layout
16978 \begin_inset Formula $\mp$
16988 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16991 \begin_layout Plain Layout
16999 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17002 \begin_layout Plain Layout
17003 \begin_inset Formula $\cdot$
17013 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17016 \begin_layout Plain Layout
17024 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17027 \begin_layout Plain Layout
17028 \begin_inset Formula $\times$
17038 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17041 \begin_layout Plain Layout
17049 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17052 \begin_layout Plain Layout
17053 \begin_inset Formula $\div$
17063 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17066 \begin_layout Plain Layout
17070 \begin_layout Plain Layout
17083 \begin_layout Plain Layout
17095 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17098 \begin_layout Plain Layout
17099 \begin_inset Formula $*$
17109 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17112 \begin_layout Plain Layout
17120 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17123 \begin_layout Plain Layout
17124 \begin_inset Formula $\star$
17134 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17137 \begin_layout Plain Layout
17145 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17148 \begin_layout Plain Layout
17149 \begin_inset Formula $\circ$
17159 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17162 \begin_layout Plain Layout
17170 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17173 \begin_layout Plain Layout
17174 \begin_inset Formula $\diamond$
17184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17187 \begin_layout Plain Layout
17195 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17198 \begin_layout Plain Layout
17199 \begin_inset Formula $\bullet$
17213 \begin_inset space \hfill{}
17217 \begin_inset Tabular
17218 <lyxtabular version="3" rows="13" columns="2">
17219 <features booktabs="true" tabularvalignment="middle">
17220 <column alignment="center" valignment="top" width="0pt">
17221 <column alignment="center" valignment="top" width="0pt">
17223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17226 \begin_layout Plain Layout
17232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17235 \begin_layout Plain Layout
17243 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17246 \begin_layout Plain Layout
17254 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17257 \begin_layout Plain Layout
17258 \begin_inset Formula $\nabla$
17268 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17271 \begin_layout Plain Layout
17279 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17282 \begin_layout Plain Layout
17283 \begin_inset Formula $\bigtriangledown$
17293 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17296 \begin_layout Plain Layout
17304 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17307 \begin_layout Plain Layout
17308 \begin_inset Formula $\bigtriangleup$
17318 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17321 \begin_layout Plain Layout
17329 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17332 \begin_layout Plain Layout
17333 \begin_inset Formula $\Box$
17343 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17346 \begin_layout Plain Layout
17354 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17357 \begin_layout Plain Layout
17358 \begin_inset Formula $\cap$
17368 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17371 \begin_layout Plain Layout
17379 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17382 \begin_layout Plain Layout
17383 \begin_inset Formula $\cup$
17393 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17396 \begin_layout Plain Layout
17404 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17407 \begin_layout Plain Layout
17408 \begin_inset Formula $\dagger$
17418 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17421 \begin_layout Plain Layout
17429 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17432 \begin_layout Plain Layout
17433 \begin_inset Formula $\ddagger$
17443 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17446 \begin_layout Plain Layout
17454 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17457 \begin_layout Plain Layout
17458 \begin_inset Formula $\wr$
17468 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17471 \begin_layout Plain Layout
17479 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17482 \begin_layout Plain Layout
17483 \begin_inset Formula $\bigcirc$
17493 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17496 \begin_layout Plain Layout
17504 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17507 \begin_layout Plain Layout
17508 \begin_inset Formula $\wedge$
17518 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17521 \begin_layout Plain Layout
17529 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17532 \begin_layout Plain Layout
17533 \begin_inset Formula $\vee$
17547 \begin_inset space \hfill{}
17551 \begin_inset Tabular
17552 <lyxtabular version="3" rows="13" columns="2">
17553 <features booktabs="true" tabularvalignment="middle">
17554 <column alignment="center" valignment="top" width="0pt">
17555 <column alignment="center" valignment="top" width="0pt">
17557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17560 \begin_layout Plain Layout
17566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17569 \begin_layout Plain Layout
17577 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17580 \begin_layout Plain Layout
17588 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17591 \begin_layout Plain Layout
17592 \begin_inset Formula $\oplus$
17602 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17605 \begin_layout Plain Layout
17613 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17616 \begin_layout Plain Layout
17617 \begin_inset Formula $\ominus$
17627 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17630 \begin_layout Plain Layout
17638 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17641 \begin_layout Plain Layout
17642 \begin_inset Formula $\otimes$
17652 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17655 \begin_layout Plain Layout
17663 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17666 \begin_layout Plain Layout
17667 \begin_inset Formula $\oslash$
17677 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17680 \begin_layout Plain Layout
17688 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17691 \begin_layout Plain Layout
17692 \begin_inset Formula $\odot$
17702 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17705 \begin_layout Plain Layout
17713 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17716 \begin_layout Plain Layout
17717 \begin_inset Formula $\amalg$
17727 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17730 \begin_layout Plain Layout
17738 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17741 \begin_layout Plain Layout
17742 \begin_inset Formula $\uplus$
17752 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17755 \begin_layout Plain Layout
17763 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17766 \begin_layout Plain Layout
17767 \begin_inset Formula $\setminus$
17777 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17780 \begin_layout Plain Layout
17788 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17791 \begin_layout Plain Layout
17792 \begin_inset Formula $\sqcap$
17802 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17805 \begin_layout Plain Layout
17813 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17816 \begin_layout Plain Layout
17817 \begin_inset Formula $\sqcup$
17827 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17830 \begin_layout Plain Layout
17838 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17841 \begin_layout Plain Layout
17842 \begin_inset Formula $\triangleleft$
17852 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17855 \begin_layout Plain Layout
17863 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17866 \begin_layout Plain Layout
17867 \begin_inset Formula $\triangleright$
17883 \begin_layout Standard
17884 All binary operators can also be inserted via the math toolbar button
17887 arg "math-insert \\pm"
17893 \begin_layout Standard
17894 To typeset the Laplace operator also
17911 \begin_inset Formula $\nabla^{2}$
17914 ) can be used instead of
17923 \begin_layout Standard
17930 Insert\SpecialChar menuseparator
17942 \begin_layout Subsection
17943 Self-defined Operators
17944 \begin_inset CommandInset label
17946 name "subsec:Self-defined-Operators"
17951 \begin_inset Index idx
17954 \begin_layout Plain Layout
17955 Operators ! self-defined
17963 \begin_layout Standard
17964 With the help of the command
17968 DeclareMathOperator
17971 \begin_inset Index idx
17974 \begin_layout Plain Layout
17979 DeclareMathOperator
17984 custom operators can be defined in the \SpecialChar LaTeX
17986 Its command scheme is:
17989 \begin_layout Standard
17994 DeclareMathOperator{new command}{display}
17997 \begin_layout Standard
17998 Display can be characters or symbols that define how the operator looks
18000 To define a big operator a * is set behind the command.
18001 All self-defined big operators can have limits as described in
18002 \begin_inset CommandInset ref
18004 reference "subsec:Operator-Limits"
18011 \begin_layout Standard
18012 For example the \SpecialChar LaTeX
18016 \begin_layout Standard
18021 DeclareMathOperator*{
18028 \begin_layout Standard
18029 defines the command
18035 , that inserts a big operator consisting of the lozenge symbol from
18036 \begin_inset CommandInset ref
18038 reference "subsec:Miscellaneous-Symbols"
18043 \begin_inset Formula
18045 \Lozenge_{n=1}^{\infty}
18050 The command for this formula is:
18061 \begin_inset Formula $\to$
18067 \begin_layout Standard
18068 \begin_inset VSpace bigskip
18071 When self-defined operators are not used several times in the document,
18072 they can also be defined with the commands
18079 \begin_inset Index idx
18082 \begin_layout Plain Layout
18097 \begin_inset Index idx
18100 \begin_layout Plain Layout
18108 , which have the following scheme:
18111 \begin_layout Standard
18125 \begin_layout Standard
18132 defines big operators,
18141 \begin_layout Standard
18149 \begin_inset space \thinspace{}
18153 \begin_inset space \space{}
18156 be used to use one limit for several operators:
18159 \begin_layout Standard
18160 \begin_inset Formula
18162 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18170 \begin_layout Standard
18171 The command for the formula above is:
18172 \begin_inset Newline newline
18188 \begin_inset space \textvisiblespace{}
18194 \begin_inset Formula $\to$
18200 \begin_inset space \textvisiblespace{}
18208 \begin_layout Section
18210 \begin_inset Index idx
18213 \begin_layout Plain Layout
18222 \begin_layout Subsection
18224 \begin_inset CommandInset label
18226 name "subsec:Font-Styles"
18231 \begin_inset Index idx
18234 \begin_layout Plain Layout
18243 \begin_layout Standard
18244 Latin letters in formulas can be set in one of the following font styles:
18247 \begin_layout Standard
18249 \begin_inset space \hfill{}
18253 \begin_inset Tabular
18254 <lyxtabular version="3" rows="6" columns="2">
18255 <features booktabs="true" tabularvalignment="middle">
18256 <column alignment="center" valignment="top" width="0pt">
18257 <column alignment="center" valignment="top">
18259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18262 \begin_layout Plain Layout
18268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18271 \begin_layout Plain Layout
18279 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18282 \begin_layout Plain Layout
18288 \begin_inset space \textvisiblespace{}
18298 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18301 \begin_layout Plain Layout
18302 \begin_inset Formula $\mathbb{ABC}$
18312 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18315 \begin_layout Plain Layout
18321 \begin_inset space \textvisiblespace{}
18331 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18334 \begin_layout Plain Layout
18335 \begin_inset Formula $\mathbf{AbC}$
18345 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18348 \begin_layout Plain Layout
18354 \begin_inset space \textvisiblespace{}
18364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18367 \begin_layout Plain Layout
18368 \begin_inset Formula $\boldsymbol{AbC}$
18378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18381 \begin_layout Plain Layout
18387 \begin_inset space \textvisiblespace{}
18397 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18400 \begin_layout Plain Layout
18401 \begin_inset Formula $\mathcal{ABC}$
18411 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18414 \begin_layout Plain Layout
18420 \begin_inset space \textvisiblespace{}
18430 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18433 \begin_layout Plain Layout
18434 \begin_inset Formula $\mathfrak{AbC}$
18448 \begin_inset space \hfill{}
18452 \begin_inset Tabular
18453 <lyxtabular version="3" rows="6" columns="2">
18454 <features booktabs="true" tabularvalignment="middle">
18455 <column alignment="center" valignment="top" width="0pt">
18456 <column alignment="center" valignment="top">
18458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18461 \begin_layout Plain Layout
18467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18470 \begin_layout Plain Layout
18478 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18481 \begin_layout Plain Layout
18487 \begin_inset space \textvisiblespace{}
18497 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18500 \begin_layout Plain Layout
18501 \begin_inset Formula $\mathit{AbC}$
18511 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18514 \begin_layout Plain Layout
18520 \begin_inset space \textvisiblespace{}
18530 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18533 \begin_layout Plain Layout
18534 \begin_inset Formula $\mathrm{AbC}$
18544 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18547 \begin_layout Plain Layout
18553 \begin_inset space \textvisiblespace{}
18563 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18566 \begin_layout Plain Layout
18567 \begin_inset Formula $\mathsf{AbC}$
18577 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18580 \begin_layout Plain Layout
18586 \begin_inset space \textvisiblespace{}
18596 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18599 \begin_layout Plain Layout
18600 \begin_inset Formula $\mathtt{AbC}$
18610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18613 \begin_layout Plain Layout
18619 \begin_inset space \textvisiblespace{}
18629 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18632 \begin_layout Plain Layout
18633 \begin_inset Formula $\mathscr{ABC}$
18647 \begin_inset space \hfill{}
18653 \begin_layout Standard
18654 \begin_inset Note Greyedout
18657 \begin_layout Plain Layout
18680 can only be used for big letters.
18688 \begin_layout Standard
18689 Predefined is the style
18698 \begin_layout Standard
18699 The style commands work also for letters in mathematical constructs:
18700 \begin_inset Formula
18702 \mathfrak{A=\frac{b}{C}}
18710 \begin_layout Standard
18711 Characters in mathematical text don't appear in a math font style but in
18712 the text font style
18719 That their style can't be set correctly via the text style dialog is a
18720 bug in \SpecialChar LyX
18725 \begin_layout Plain Layout
18726 \begin_inset CommandInset href
18728 name "LyX-bug #4629"
18729 target "http://www.lyx.org/trac/ticket/4629"
18741 \begin_layout Standard
18742 Instead of the style commands the dialog
18744 Edit\SpecialChar menuseparator
18745 Math\SpecialChar menuseparator
18748 or the toolbar button
18751 arg "math-insert \\font"
18757 \begin_layout Subsection
18759 \begin_inset CommandInset label
18761 name "subsec:Bold-Formulas"
18766 \begin_inset Index idx
18769 \begin_layout Plain Layout
18778 \begin_layout Standard
18779 To make a complete formula bold, the command
18785 from the previous subsection cannot be used, because it doesn't work for
18786 small Greek letters.
18787 Furthermore it prints Latin letters always upright, like in the following
18791 \begin_layout Standard
18792 \begin_inset Formula
18794 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18802 \begin_layout Standard
18803 To display the formula correctly, the command
18810 \begin_inset Formula
18812 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18817 It is also possible to set the formula in a
18819 boldmath environment
18822 This environment is created by inserting the command
18829 \begin_inset Index idx
18832 \begin_layout Plain Layout
18840 in \SpecialChar TeX
18842 To end the environment, the command
18849 \begin_inset Index idx
18852 \begin_layout Plain Layout
18860 is inserted in \SpecialChar TeX
18865 \begin_layout Plain Layout
18875 \begin_inset Formula
18877 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18886 \begin_layout Plain Layout
18898 \begin_layout Subsection
18900 \begin_inset Index idx
18903 \begin_layout Plain Layout
18912 \begin_layout Standard
18913 Formulas can be colored like normal text: Highlight a formula or a formula
18919 Here is a formula in magenta:
18920 \begin_inset Formula
18922 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18930 \begin_layout Standard
18931 You can also define your own colors as described in
18932 \begin_inset CommandInset ref
18934 reference "subsec:Colored-Boxes"
18939 They can be used with the \SpecialChar TeX
18947 \begin_inset Index idx
18950 \begin_layout Plain Layout
18961 \begin_layout Standard
18966 textcolor{color}{characters or formula}
18969 \begin_layout Standard
18970 The following example was colored completely dark green and partly red:
18973 \begin_layout Standard
18977 \begin_layout Plain Layout
18981 textcolor{darkgreen}{
18987 \begin_inset Formula
18989 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
18998 \begin_layout Plain Layout
19008 \begin_layout Standard
19009 Due to a bug in \SpecialChar LyX
19010 only complete formulas can be colored with self-defined
19015 \begin_layout Plain Layout
19016 \begin_inset CommandInset href
19018 name "LyX-bug #5269"
19019 target "http://www.lyx.org/trac/ticket/5269"
19031 \begin_layout Subsection
19033 \begin_inset CommandInset label
19035 name "subsec:Font-Sizes"
19040 \begin_inset Index idx
19043 \begin_layout Plain Layout
19052 \begin_layout Standard
19053 For characters in formulas there are, analog to characters in text, the
19054 following size commands:
19057 \begin_layout Standard
19101 \begin_inset Newline newline
19123 \begin_layout Standard
19124 The size produced by the commands depends on the document font size, which
19125 corresponds to the command
19132 The other commands produce smaller or larger sizes than
19139 The font size can however not exceed a certain value.
19140 Is for example the document font size 12
19141 \begin_inset space \thinspace{}
19150 switches to the same size as
19160 \begin_layout Standard
19161 A size command is inserted in \SpecialChar TeX
19162 mode before the formula and sets the size
19163 for all following formula and text characters.
19164 To switch back to the initial size, the command
19170 is inserted behind the formula in \SpecialChar TeX
19174 \begin_layout Standard
19175 Within a formula the size can be changed using the following size commands
19176 or the toolbar button
19179 arg "math-insert \\style"
19183 \begin_inset Separator parbreak
19189 \begin_layout Standard
19192 \begin_inset Tabular
19193 <lyxtabular version="3" rows="5" columns="2">
19194 <features booktabs="true" tabularvalignment="middle">
19195 <column alignment="center" valignment="top" width="0pt">
19196 <column alignment="center" valignment="top">
19198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19201 \begin_layout Plain Layout
19207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19210 \begin_layout Plain Layout
19218 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19221 \begin_layout Plain Layout
19225 \begin_inset Index idx
19228 \begin_layout Plain Layout
19241 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19244 \begin_layout Plain Layout
19245 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19254 <row topspace="1mm">
19255 <cell alignment="center" valignment="top" usebox="none">
19258 \begin_layout Plain Layout
19266 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19269 \begin_layout Plain Layout
19270 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19280 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19283 \begin_layout Plain Layout
19291 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19294 \begin_layout Plain Layout
19295 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19305 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19308 \begin_layout Plain Layout
19316 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19319 \begin_layout Plain Layout
19320 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19336 \begin_layout Standard
19337 After entering these commands, a blue box appears in which the formula parts
19341 \begin_layout Standard
19342 There is a further method to change the font size, that though only works
19343 for symbols or letters in mathematical text.
19344 To use it, one of the above text size commands is inserted in mathematical
19346 All following characters until the end of the mathematical text or until
19347 another size command will have the selected size.
19349 \begin_inset VSpace -2mm
19355 \begin_layout Standard
19359 \begin_layout Plain Layout
19369 \begin_inset Formula
19371 A=\frac{B}{c}\cdot\maltese
19377 \begin_inset Formula
19379 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19388 \begin_layout Plain Layout
19400 \begin_layout Standard
19401 \begin_inset VSpace medskip
19404 Before both formulas the command
19411 The command for the second formula is:
19412 \begin_inset Newline newline
19420 \begin_inset space \textvisiblespace{}
19426 \begin_inset space \textvisiblespace{}
19432 \begin_inset space \textvisiblespace{}
19438 \begin_inset space \textvisiblespace{}
19442 \begin_inset Formula $\to$
19446 \begin_inset Formula $\to$
19450 \begin_inset Newline newline
19454 \begin_inset space \hspace*{}
19465 \begin_inset space \textvisiblespace{}
19471 \begin_inset space \textvisiblespace{}
19477 \begin_inset space \textvisiblespace{}
19483 \begin_layout Standard
19484 If a symbol cannot be displayed in different sizes, it will always be displayed
19485 in the default size.
19488 \begin_layout Section
19490 \begin_inset Index idx
19493 \begin_layout Plain Layout
19502 \begin_layout Standard
19503 Greek letters can also be inserted via the toolbar button
19506 arg "math-insert \\alpha"
19510 All international typesetting norms purport that Greek letters in math
19511 have to be typeset italic/slanted.
19512 In some languages, like French or Russian, they are nevertheless sometimes
19516 \begin_layout Subsection
19518 \begin_inset Index idx
19521 \begin_layout Plain Layout
19522 Greek letters ! small
19530 \begin_layout Standard
19531 \begin_inset space \hfill{}
19535 \begin_inset Tabular
19536 <lyxtabular version="3" rows="11" columns="2">
19537 <features booktabs="true" tabularvalignment="middle">
19538 <column alignment="center" valignment="top" width="0pt">
19539 <column alignment="center" valignment="top" width="0pt">
19541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19544 \begin_layout Plain Layout
19550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19553 \begin_layout Plain Layout
19561 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19564 \begin_layout Plain Layout
19572 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19575 \begin_layout Plain Layout
19576 \begin_inset Formula $\alpha$
19586 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19589 \begin_layout Plain Layout
19597 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19600 \begin_layout Plain Layout
19601 \begin_inset Formula $\beta$
19611 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19614 \begin_layout Plain Layout
19622 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19625 \begin_layout Plain Layout
19626 \begin_inset Formula $\gamma$
19636 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19639 \begin_layout Plain Layout
19647 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19650 \begin_layout Plain Layout
19651 \begin_inset Formula $\delta$
19661 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19664 \begin_layout Plain Layout
19672 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19675 \begin_layout Plain Layout
19676 \begin_inset Formula $\epsilon$
19686 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19689 \begin_layout Plain Layout
19697 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19700 \begin_layout Plain Layout
19701 \begin_inset Formula $\varepsilon$
19711 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19714 \begin_layout Plain Layout
19722 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19725 \begin_layout Plain Layout
19726 \begin_inset Formula $\zeta$
19736 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19739 \begin_layout Plain Layout
19747 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19750 \begin_layout Plain Layout
19751 \begin_inset Formula $\eta$
19761 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19764 \begin_layout Plain Layout
19772 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19775 \begin_layout Plain Layout
19776 \begin_inset Formula $\theta$
19786 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19789 \begin_layout Plain Layout
19797 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19800 \begin_layout Plain Layout
19801 \begin_inset Formula $\vartheta$
19815 \begin_inset space \hfill{}
19819 \begin_inset Tabular
19820 <lyxtabular version="3" rows="12" columns="2">
19821 <features booktabs="true" tabularvalignment="middle">
19822 <column alignment="center" valignment="top" width="0pt">
19823 <column alignment="center" valignment="top" width="0pt">
19825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19828 \begin_layout Plain Layout
19834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19837 \begin_layout Plain Layout
19845 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19848 \begin_layout Plain Layout
19856 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19859 \begin_layout Plain Layout
19860 \begin_inset Formula $\iota$
19870 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19873 \begin_layout Plain Layout
19881 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19884 \begin_layout Plain Layout
19885 \begin_inset Formula $\kappa$
19895 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19898 \begin_layout Plain Layout
19906 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19909 \begin_layout Plain Layout
19910 \begin_inset Formula $\varkappa$
19920 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19923 \begin_layout Plain Layout
19931 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19934 \begin_layout Plain Layout
19935 \begin_inset Formula $\lambda$
19945 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19948 \begin_layout Plain Layout
19956 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19959 \begin_layout Plain Layout
19960 \begin_inset Formula $\mu$
19970 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19973 \begin_layout Plain Layout
19981 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19984 \begin_layout Plain Layout
19985 \begin_inset Formula $\nu$
19995 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19998 \begin_layout Plain Layout
20006 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20009 \begin_layout Plain Layout
20010 \begin_inset Formula $\xi$
20020 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20023 \begin_layout Plain Layout
20029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20032 \begin_layout Plain Layout
20033 \begin_inset Formula $o$
20043 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20046 \begin_layout Plain Layout
20054 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20057 \begin_layout Plain Layout
20058 \begin_inset Formula $\pi$
20068 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20071 \begin_layout Plain Layout
20079 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20082 \begin_layout Plain Layout
20083 \begin_inset Formula $\varpi$
20093 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20096 \begin_layout Plain Layout
20104 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20107 \begin_layout Plain Layout
20108 \begin_inset Formula $\rho$
20122 \begin_inset space \hfill{}
20126 \begin_inset Tabular
20127 <lyxtabular version="3" rows="11" columns="2">
20128 <features booktabs="true" tabularvalignment="middle">
20129 <column alignment="center" valignment="top" width="0pt">
20130 <column alignment="center" valignment="top" width="0pt">
20132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20135 \begin_layout Plain Layout
20141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20144 \begin_layout Plain Layout
20152 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20155 \begin_layout Plain Layout
20163 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20166 \begin_layout Plain Layout
20167 \begin_inset Formula $\varrho$
20177 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20180 \begin_layout Plain Layout
20188 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20191 \begin_layout Plain Layout
20192 \begin_inset Formula $\sigma$
20202 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20205 \begin_layout Plain Layout
20213 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20216 \begin_layout Plain Layout
20217 \begin_inset Formula $\varsigma$
20227 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20230 \begin_layout Plain Layout
20238 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20241 \begin_layout Plain Layout
20242 \begin_inset Formula $\tau$
20252 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20255 \begin_layout Plain Layout
20263 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20266 \begin_layout Plain Layout
20267 \begin_inset Formula $\upsilon$
20277 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20280 \begin_layout Plain Layout
20288 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20291 \begin_layout Plain Layout
20292 \begin_inset Formula $\phi$
20302 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20305 \begin_layout Plain Layout
20313 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20316 \begin_layout Plain Layout
20317 \begin_inset Formula $\varphi$
20327 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20330 \begin_layout Plain Layout
20338 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20341 \begin_layout Plain Layout
20342 \begin_inset Formula $\chi$
20352 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20355 \begin_layout Plain Layout
20363 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20366 \begin_layout Plain Layout
20367 \begin_inset Formula $\psi$
20377 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20380 \begin_layout Plain Layout
20388 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20391 \begin_layout Plain Layout
20392 \begin_inset Formula $\omega$
20406 \begin_inset space \hfill{}
20412 \begin_layout Standard
20413 \begin_inset VSpace medskip
20419 \begin_layout Standard
20420 How to create special upright Greek letters is explained in
20421 \begin_inset CommandInset ref
20423 reference "subsec:Upright-small-Greek"
20430 \begin_layout Subsection
20432 \begin_inset Index idx
20435 \begin_layout Plain Layout
20436 Greek letters ! big
20444 \begin_layout Standard
20445 \begin_inset space \hfill{}
20449 \begin_inset Tabular
20450 <lyxtabular version="3" rows="7" columns="2">
20451 <features booktabs="true" tabularvalignment="middle">
20452 <column alignment="center" valignment="top" width="0pt">
20453 <column alignment="center" valignment="top" width="0pt">
20455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20458 \begin_layout Plain Layout
20464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20467 \begin_layout Plain Layout
20475 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20478 \begin_layout Plain Layout
20486 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20489 \begin_layout Plain Layout
20490 \begin_inset Formula $\Gamma$
20500 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20503 \begin_layout Plain Layout
20511 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20514 \begin_layout Plain Layout
20515 \begin_inset Formula $\Delta$
20525 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20528 \begin_layout Plain Layout
20536 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20539 \begin_layout Plain Layout
20540 \begin_inset Formula $\Theta$
20550 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20553 \begin_layout Plain Layout
20561 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20564 \begin_layout Plain Layout
20565 \begin_inset Formula $\Lambda$
20575 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20578 \begin_layout Plain Layout
20586 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20589 \begin_layout Plain Layout
20590 \begin_inset Formula $\Xi$
20600 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20603 \begin_layout Plain Layout
20611 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20614 \begin_layout Plain Layout
20615 \begin_inset Formula $\Pi$
20629 \begin_inset space \hfill{}
20633 \begin_inset Tabular
20634 <lyxtabular version="3" rows="6" columns="2">
20635 <features booktabs="true" tabularvalignment="middle">
20636 <column alignment="center" valignment="top" width="0pt">
20637 <column alignment="center" valignment="top" width="0pt">
20639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20642 \begin_layout Plain Layout
20648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20651 \begin_layout Plain Layout
20659 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20662 \begin_layout Plain Layout
20670 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20673 \begin_layout Plain Layout
20674 \begin_inset Formula $\Sigma$
20684 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20687 \begin_layout Plain Layout
20695 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20698 \begin_layout Plain Layout
20699 \begin_inset Formula $\Upsilon$
20709 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20712 \begin_layout Plain Layout
20720 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20723 \begin_layout Plain Layout
20724 \begin_inset Formula $\Phi$
20734 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20737 \begin_layout Plain Layout
20745 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20748 \begin_layout Plain Layout
20749 \begin_inset Formula $\Psi$
20759 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20762 \begin_layout Plain Layout
20770 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20773 \begin_layout Plain Layout
20774 \begin_inset Formula $\Omega$
20788 \begin_inset space \hfill{}
20794 \begin_layout Standard
20795 \begin_inset VSpace medskip
20798 That the big Greek letters appear upright is caused by a design bug when
20801 To get correct italic big letters, begin every command with
20806 For example the command
20813 \begin_inset Formula $\varGamma$
20817 Another way is to load the package
20825 \begin_layout Plain Layout
20830 is part of the \SpecialChar LaTeX
20836 \begin_inset Index idx
20839 \begin_layout Plain Layout
20844 \begin_layout Plain Layout
20864 \begin_inset Index idx
20867 \begin_layout Plain Layout
20873 with the \SpecialChar LaTeX
20877 \begin_layout Standard
20882 usepackage{fixmath}
20885 \begin_layout Standard
20886 Then all big Greek letters in a document will automatically be typeset italic.
20889 \begin_layout Subsection
20891 \begin_inset Index idx
20894 \begin_layout Plain Layout
20895 Greek letters ! bold
20903 \begin_layout Standard
20904 Greek letters cannot be set with different font styles like Latin letters.
20905 They can only be made bold with the command
20912 \begin_inset Index idx
20915 \begin_layout Plain Layout
20924 \begin_inset Separator parbreak
20930 \begin_layout Standard
20932 \begin_inset Tabular
20933 <lyxtabular version="3" rows="3" columns="2">
20934 <features booktabs="true" tabularvalignment="middle">
20935 <column alignment="center" valignment="top" width="0pt">
20936 <column alignment="center" valignment="top">
20938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20941 \begin_layout Plain Layout
20947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20950 \begin_layout Plain Layout
20958 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20961 \begin_layout Plain Layout
20973 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20976 \begin_layout Plain Layout
20977 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20987 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20990 \begin_layout Plain Layout
21002 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21005 \begin_layout Plain Layout
21006 \begin_inset Formula $\theta\boldsymbol{\theta}$
21022 \begin_layout Section
21027 \begin_layout Plain Layout
21040 \begin_layout Plain Layout
21041 A list with all symbols of most of the \SpecialChar LaTeX
21042 -packages can be found in
21043 \begin_inset CommandInset citation
21058 \begin_layout Plain Layout
21066 \begin_inset Note Note
21069 \begin_layout Plain Layout
21072 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21075 \begin_layout Plain Layout
21078 texorpdfstring is in section
21079 \begin_inset CommandInset ref
21081 reference "subsec:Formulas-in-Section"
21091 \begin_inset Index idx
21094 \begin_layout Plain Layout
21103 \begin_layout Standard
21104 Many of the symbols listed in this section can also be inserted via the
21108 arg "math-insert \\nabla"
21114 arg "math-insert \\digamma"
21120 \begin_layout Subsection
21121 Mathematical Symbols
21122 \begin_inset CommandInset label
21124 name "subsec:Mathematical-Symbols"
21129 \begin_inset Index idx
21132 \begin_layout Plain Layout
21133 Symbols ! mathematical
21141 \begin_layout Standard
21142 \begin_inset Tabular
21143 <lyxtabular version="3" rows="10" columns="2">
21144 <features booktabs="true" tabularvalignment="middle">
21145 <column alignment="center" valignment="top" width="0pt">
21146 <column alignment="center" valignment="top" width="0pt">
21148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21151 \begin_layout Plain Layout
21157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21160 \begin_layout Plain Layout
21168 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21171 \begin_layout Plain Layout
21179 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21182 \begin_layout Plain Layout
21183 \begin_inset Formula $\neg$
21193 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21196 \begin_layout Plain Layout
21204 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21207 \begin_layout Plain Layout
21208 \begin_inset Formula $\Im$
21218 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21221 \begin_layout Plain Layout
21229 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21232 \begin_layout Plain Layout
21233 \begin_inset Formula $\Re$
21243 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21246 \begin_layout Plain Layout
21254 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21257 \begin_layout Plain Layout
21258 \begin_inset Formula $\aleph$
21268 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21271 \begin_layout Plain Layout
21279 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21282 \begin_layout Plain Layout
21283 \begin_inset Formula $\partial$
21293 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21296 \begin_layout Plain Layout
21304 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21307 \begin_layout Plain Layout
21308 \begin_inset Formula $\infty$
21318 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21321 \begin_layout Plain Layout
21329 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21332 \begin_layout Plain Layout
21333 \begin_inset Formula $\wp$
21343 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21346 \begin_layout Plain Layout
21354 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21357 \begin_layout Plain Layout
21358 \begin_inset Formula $\imath$
21368 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21371 \begin_layout Plain Layout
21379 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21382 \begin_layout Plain Layout
21383 \begin_inset Formula $\jmath$
21397 \begin_inset space \hfill{}
21401 \begin_inset Tabular
21402 <lyxtabular version="3" rows="10" columns="2">
21403 <features booktabs="true" tabularvalignment="middle">
21404 <column alignment="center" valignment="top" width="0pt">
21405 <column alignment="center" valignment="top" width="0pt">
21407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21410 \begin_layout Plain Layout
21416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21419 \begin_layout Plain Layout
21421 \begin_inset Note Note
21424 \begin_layout Plain Layout
21431 is only used as spacer.
21443 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21446 \begin_layout Plain Layout
21454 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21457 \begin_layout Plain Layout
21458 \begin_inset Formula $\forall$
21468 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21471 \begin_layout Plain Layout
21479 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21482 \begin_layout Plain Layout
21483 \begin_inset Formula $\exists$
21493 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21496 \begin_layout Plain Layout
21504 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21507 \begin_layout Plain Layout
21508 \begin_inset Formula $\nexists$
21518 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21521 \begin_layout Plain Layout
21529 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21532 \begin_layout Plain Layout
21533 \begin_inset Formula $\emptyset$
21543 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21546 \begin_layout Plain Layout
21554 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21557 \begin_layout Plain Layout
21558 \begin_inset Formula $\varnothing$
21568 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21571 \begin_layout Plain Layout
21579 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21582 \begin_layout Plain Layout
21583 \begin_inset Formula $\dag$
21593 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21596 \begin_layout Plain Layout
21604 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21607 \begin_layout Plain Layout
21608 \begin_inset Formula $\ddag$
21618 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21621 \begin_layout Plain Layout
21629 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21632 \begin_layout Plain Layout
21636 \begin_layout Plain Layout
21646 \begin_inset Formula $\complement$
21653 \begin_layout Plain Layout
21667 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21670 \begin_layout Plain Layout
21678 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21681 \begin_layout Plain Layout
21682 \begin_inset Formula $\Bbbk$
21696 \begin_inset space \hfill{}
21700 \begin_inset Tabular
21701 <lyxtabular version="3" rows="10" columns="2">
21702 <features booktabs="true" tabularvalignment="middle">
21703 <column alignment="center" valignment="top" width="0pt">
21704 <column alignment="center" valignment="top" width="0pt">
21706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21709 \begin_layout Plain Layout
21715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21718 \begin_layout Plain Layout
21726 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21729 \begin_layout Plain Layout
21737 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21740 \begin_layout Plain Layout
21741 \begin_inset Formula $\prime$
21751 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21754 \begin_layout Plain Layout
21762 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21765 \begin_layout Plain Layout
21766 \begin_inset Formula $\backprime$
21776 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21779 \begin_layout Plain Layout
21787 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21790 \begin_layout Plain Layout
21791 \begin_inset Formula $\mho$
21801 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21804 \begin_layout Plain Layout
21812 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21815 \begin_layout Plain Layout
21816 \begin_inset Formula $\triangle$
21826 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21829 \begin_layout Plain Layout
21837 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21840 \begin_layout Plain Layout
21841 \begin_inset Formula $\angle$
21851 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21854 \begin_layout Plain Layout
21862 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21865 \begin_layout Plain Layout
21866 \begin_inset Formula $\measuredangle$
21876 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21879 \begin_layout Plain Layout
21887 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21890 \begin_layout Plain Layout
21891 \begin_inset Formula $\sphericalangle$
21901 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21904 \begin_layout Plain Layout
21912 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21915 \begin_layout Plain Layout
21916 \begin_inset Formula $\top$
21926 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21929 \begin_layout Plain Layout
21937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21940 \begin_layout Plain Layout
21941 \begin_inset Formula $\bot$
21957 \begin_layout Standard
21958 \begin_inset Newpage newpage
21964 \begin_layout Subsection
21965 Miscellaneous Symbols
21966 \begin_inset CommandInset label
21968 name "subsec:Miscellaneous-Symbols"
21973 \begin_inset Index idx
21976 \begin_layout Plain Layout
21977 Symbols ! miscellaneous
21985 \begin_layout Standard
21988 \begin_inset Tabular
21989 <lyxtabular version="3" rows="10" columns="2">
21990 <features booktabs="true" tabularvalignment="middle">
21991 <column alignment="center" valignment="top" width="0pt">
21992 <column alignment="center" valignment="top" width="0pt">
21994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21997 \begin_layout Plain Layout
22003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22006 \begin_layout Plain Layout
22014 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22017 \begin_layout Plain Layout
22025 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22028 \begin_layout Plain Layout
22029 \begin_inset Formula $\flat$
22039 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22042 \begin_layout Plain Layout
22050 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22053 \begin_layout Plain Layout
22054 \begin_inset Formula $\natural$
22064 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22067 \begin_layout Plain Layout
22075 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22078 \begin_layout Plain Layout
22079 \begin_inset Formula $\sharp$
22089 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22092 \begin_layout Plain Layout
22100 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22103 \begin_layout Plain Layout
22104 \begin_inset Formula $\surd$
22114 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22117 \begin_layout Plain Layout
22125 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22128 \begin_layout Plain Layout
22129 \begin_inset Formula $\checkmark$
22139 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22142 \begin_layout Plain Layout
22150 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22153 \begin_layout Plain Layout
22154 \begin_inset Formula $\yen$
22164 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22167 \begin_layout Plain Layout
22175 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22178 \begin_layout Plain Layout
22179 \begin_inset Formula $\pounds$
22189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22192 \begin_layout Plain Layout
22198 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22201 \begin_layout Plain Layout
22202 \begin_inset Formula $\$$
22212 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22215 \begin_layout Plain Layout
22221 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22224 \begin_layout Plain Layout
22225 \begin_inset Formula $§$
22239 \begin_inset space \hfill{}
22243 \begin_inset Tabular
22244 <lyxtabular version="3" rows="10" columns="2">
22245 <features booktabs="true" tabularvalignment="middle">
22246 <column alignment="center" valignment="top" width="0pt">
22247 <column alignment="center" valignment="top">
22249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22252 \begin_layout Plain Layout
22258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22261 \begin_layout Plain Layout
22269 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22272 \begin_layout Plain Layout
22280 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22283 \begin_layout Plain Layout
22284 \begin_inset Formula $\hbar$
22294 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22297 \begin_layout Plain Layout
22305 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22308 \begin_layout Plain Layout
22309 \begin_inset Formula $\hslash$
22319 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22322 \begin_layout Plain Layout
22330 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22333 \begin_layout Plain Layout
22334 \begin_inset Formula $\clubsuit$
22344 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22347 \begin_layout Plain Layout
22355 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22358 \begin_layout Plain Layout
22359 \begin_inset Formula $\spadesuit$
22369 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22372 \begin_layout Plain Layout
22380 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22383 \begin_layout Plain Layout
22384 \begin_inset Formula $\bigstar$
22394 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22397 \begin_layout Plain Layout
22405 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22408 \begin_layout Plain Layout
22409 \begin_inset Formula $\blacklozenge$
22419 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22422 \begin_layout Plain Layout
22430 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22433 \begin_layout Plain Layout
22434 \begin_inset Formula $\blacktriangle$
22444 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22447 \begin_layout Plain Layout
22455 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22458 \begin_layout Plain Layout
22459 \begin_inset Formula $\blacktriangledown$
22469 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22472 \begin_layout Plain Layout
22480 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22483 \begin_layout Plain Layout
22484 \begin_inset Formula $\bullet$
22498 \begin_inset space \hfill{}
22502 \begin_inset Tabular
22503 <lyxtabular version="3" rows="10" columns="2">
22504 <features booktabs="true" tabularvalignment="middle">
22505 <column alignment="center" valignment="top" width="0pt">
22506 <column alignment="center" valignment="top" width="0pt">
22508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22511 \begin_layout Plain Layout
22517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22520 \begin_layout Plain Layout
22528 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22531 \begin_layout Plain Layout
22539 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22542 \begin_layout Plain Layout
22543 \begin_inset Formula $\diamondsuit$
22553 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22556 \begin_layout Plain Layout
22564 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22567 \begin_layout Plain Layout
22568 \begin_inset Formula $\Diamond$
22578 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22581 \begin_layout Plain Layout
22589 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22592 \begin_layout Plain Layout
22593 \begin_inset Formula $\heartsuit$
22603 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22606 \begin_layout Plain Layout
22614 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22617 \begin_layout Plain Layout
22618 \begin_inset Formula $\P$
22628 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22631 \begin_layout Plain Layout
22639 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22642 \begin_layout Plain Layout
22643 \begin_inset Formula $\copyright$
22653 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22656 \begin_layout Plain Layout
22664 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22667 \begin_layout Plain Layout
22668 \begin_inset Formula $\circledR$
22678 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22681 \begin_layout Plain Layout
22689 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22692 \begin_layout Plain Layout
22693 \begin_inset Formula $\maltese$
22703 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22706 \begin_layout Plain Layout
22714 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22717 \begin_layout Plain Layout
22718 \begin_inset Formula $\diagup$
22728 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22731 \begin_layout Plain Layout
22739 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22742 \begin_layout Plain Layout
22743 \begin_inset Formula $\diagdown$
22759 \begin_layout Standard
22760 \begin_inset VSpace medskip
22766 \begin_layout Standard
22767 Some symbols can be displayed in different sizes, see
22768 \begin_inset CommandInset ref
22770 reference "subsec:Font-Sizes"
22777 \begin_layout Subsection
22779 \begin_inset Index idx
22782 \begin_layout Plain Layout
22783 Symbols ! Euro-symbol
22789 \begin_inset Index idx
22792 \begin_layout Plain Layout
22799 \begin_layout Plain Layout
22816 \begin_layout Standard
22817 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22823 \begin_inset Index idx
22826 \begin_layout Plain Layout
22832 must be installed and loaded with the \SpecialChar LaTeX
22836 \begin_layout Standard
22841 usepackage[gennarrow]{eurosym}
22844 \begin_layout Standard
22845 The Euro symbol can now be inserted with the command
22852 \begin_inset Index idx
22855 \begin_layout Plain Layout
22866 \begin_layout Standard
22867 The Euro symbol can directly be inserted with the € key in mathematical
22868 text, without having
22883 can also be inserted in \SpecialChar TeX
22885 The official currency symbol can then be inserted with the command
22892 \begin_inset Index idx
22895 \begin_layout Plain Layout
22903 , that is only available in \SpecialChar TeX
22907 \begin_layout Standard
22911 \begin_layout Plain Layout
22921 \begin_inset Note Note
22924 \begin_layout Plain Layout
22925 The following table will only be displayed when the \SpecialChar LaTeX
22938 \begin_layout Standard
22939 An overview about the different Euro symbols:
22940 \begin_inset Separator parbreak
22946 \begin_layout Standard
22948 \begin_inset Tabular
22949 <lyxtabular version="3" rows="4" columns="3">
22950 <features booktabs="true" tabularvalignment="middle">
22951 <column alignment="center" valignment="top" width="0pt">
22952 <column alignment="center" valignment="top" width="0pt">
22953 <column alignment="center" valignment="top" width="0pt">
22955 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22958 \begin_layout Plain Layout
22962 \begin_layout Plain Layout
22966 cmidrule[0.08em]{2-3}
22976 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22979 \begin_layout Plain Layout
22985 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22988 \begin_layout Plain Layout
22996 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22999 \begin_layout Plain Layout
23005 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23008 \begin_layout Plain Layout
23016 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23019 \begin_layout Plain Layout
23020 \begin_inset Formula $\euro$
23030 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23033 \begin_layout Plain Layout
23039 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23042 \begin_layout Plain Layout
23048 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23051 \begin_layout Plain Layout
23052 \begin_inset Formula $\mbox{€}$
23062 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23065 \begin_layout Plain Layout
23072 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23075 \begin_layout Plain Layout
23083 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23086 \begin_layout Plain Layout
23090 \begin_layout Plain Layout
23110 \begin_inset Note Note
23113 \begin_layout Plain Layout
23120 is used here only for table borders.
23130 manual for details.
23138 \begin_layout Standard
23142 \begin_layout Plain Layout
23152 \begin_inset Note Note
23155 \begin_layout Plain Layout
23156 The following will be displayed when the \SpecialChar LaTeX
23169 \begin_layout Standard
23170 You need to install the \SpecialChar LaTeX
23175 to see the rest of this subsection in the output.
23178 \begin_layout Standard
23182 \begin_layout Plain Layout
23194 \begin_layout Standard
23195 \begin_inset Newpage newpage
23201 \begin_layout Section
23203 \begin_inset CommandInset label
23205 name "sec:Relations"
23210 \begin_inset Index idx
23213 \begin_layout Plain Layout
23220 \begin_inset Index idx
23223 \begin_layout Plain Layout
23228 \begin_layout Plain Layout
23239 \begin_layout Plain Layout
23254 \begin_layout Standard
23255 All following relations can also be inserted via the toolbar button
23258 arg "math-insert \\leq"
23264 \begin_layout Standard
23265 \begin_inset Tabular
23266 <lyxtabular version="3" rows="17" columns="2">
23267 <features booktabs="true" tabularvalignment="middle">
23268 <column alignment="center" valignment="top" width="0pt">
23269 <column alignment="center" valignment="top" width="0pt">
23271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23274 \begin_layout Plain Layout
23280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23283 \begin_layout Plain Layout
23291 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23294 \begin_layout Plain Layout
23300 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23303 \begin_layout Plain Layout
23304 \begin_inset Formula $<$
23314 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23317 \begin_layout Plain Layout
23325 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23328 \begin_layout Plain Layout
23329 \begin_inset Formula $\le$
23339 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23342 \begin_layout Plain Layout
23350 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23353 \begin_layout Plain Layout
23354 \begin_inset Formula $\ll$
23364 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23367 \begin_layout Plain Layout
23375 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23378 \begin_layout Plain Layout
23379 \begin_inset Formula $\prec$
23389 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23392 \begin_layout Plain Layout
23400 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23403 \begin_layout Plain Layout
23404 \begin_inset Formula $\preceq$
23414 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23417 \begin_layout Plain Layout
23425 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23428 \begin_layout Plain Layout
23429 \begin_inset Formula $\subset$
23439 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23442 \begin_layout Plain Layout
23450 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23453 \begin_layout Plain Layout
23454 \begin_inset Formula $\subseteq$
23464 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23467 \begin_layout Plain Layout
23475 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23478 \begin_layout Plain Layout
23479 \begin_inset Formula $\sqsubseteq$
23489 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23492 \begin_layout Plain Layout
23500 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23503 \begin_layout Plain Layout
23504 \begin_inset Formula $\in$
23514 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23517 \begin_layout Plain Layout
23525 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23528 \begin_layout Plain Layout
23529 \begin_inset Formula $\vdash$
23539 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23542 \begin_layout Plain Layout
23550 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23553 \begin_layout Plain Layout
23554 \begin_inset Formula $\smile$
23564 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23567 \begin_layout Plain Layout
23575 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23578 \begin_layout Plain Layout
23579 \begin_inset Formula $\lhd$
23589 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23592 \begin_layout Plain Layout
23600 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23603 \begin_layout Plain Layout
23604 \begin_inset Formula $\unlhd$
23614 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23617 \begin_layout Plain Layout
23625 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23628 \begin_layout Plain Layout
23629 \begin_inset Formula $\gtrless$
23639 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23642 \begin_layout Plain Layout
23650 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23653 \begin_layout Plain Layout
23654 \begin_inset Formula $\mid$
23664 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23667 \begin_layout Plain Layout
23675 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23678 \begin_layout Plain Layout
23679 \begin_inset Formula $\nmid$
23693 \begin_inset space \hfill{}
23697 \begin_inset Tabular
23698 <lyxtabular version="3" rows="17" columns="2">
23699 <features booktabs="true" tabularvalignment="middle">
23700 <column alignment="center" valignment="top" width="0pt">
23701 <column alignment="center" valignment="top" width="0pt">
23703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23706 \begin_layout Plain Layout
23712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23715 \begin_layout Plain Layout
23723 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23726 \begin_layout Plain Layout
23732 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23735 \begin_layout Plain Layout
23736 \begin_inset Formula $=$
23746 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23749 \begin_layout Plain Layout
23757 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23760 \begin_layout Plain Layout
23761 \begin_inset Formula $\not=$
23771 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23774 \begin_layout Plain Layout
23782 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23785 \begin_layout Plain Layout
23786 \begin_inset Formula $\equiv$
23796 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23799 \begin_layout Plain Layout
23807 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23810 \begin_layout Plain Layout
23811 \begin_inset Formula $\sim$
23821 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23824 \begin_layout Plain Layout
23832 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23835 \begin_layout Plain Layout
23836 \begin_inset Formula $\simeq$
23846 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23849 \begin_layout Plain Layout
23857 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23860 \begin_layout Plain Layout
23861 \begin_inset Formula $\approx$
23871 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23874 \begin_layout Plain Layout
23882 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23885 \begin_layout Plain Layout
23886 \begin_inset Formula $\cong$
23896 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23899 \begin_layout Plain Layout
23907 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23910 \begin_layout Plain Layout
23911 \begin_inset Formula $\bowtie$
23921 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23924 \begin_layout Plain Layout
23932 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23935 \begin_layout Plain Layout
23936 \begin_inset Formula $\notin$
23946 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23949 \begin_layout Plain Layout
23957 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23960 \begin_layout Plain Layout
23961 \begin_inset Formula $\perp$
23971 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23974 \begin_layout Plain Layout
23982 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23985 \begin_layout Plain Layout
23986 \begin_inset Formula $\propto$
23996 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23999 \begin_layout Plain Layout
24007 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24010 \begin_layout Plain Layout
24011 \begin_inset Formula $\asymp$
24021 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24024 \begin_layout Plain Layout
24032 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24035 \begin_layout Plain Layout
24036 \begin_inset Formula $\doteq$
24046 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24049 \begin_layout Plain Layout
24057 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24060 \begin_layout Plain Layout
24061 \begin_inset Formula $\circeq$
24071 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24074 \begin_layout Plain Layout
24082 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24085 \begin_layout Plain Layout
24086 \begin_inset Formula $\models$
24096 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24099 \begin_layout Plain Layout
24107 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24110 \begin_layout Plain Layout
24111 \begin_inset Formula $\widehat{=}$
24125 \begin_inset space \hfill{}
24129 \begin_inset Tabular
24130 <lyxtabular version="3" rows="17" columns="2">
24131 <features booktabs="true" tabularvalignment="middle">
24132 <column alignment="center" valignment="top" width="0pt">
24133 <column alignment="center" valignment="top" width="0pt">
24135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24138 \begin_layout Plain Layout
24144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24147 \begin_layout Plain Layout
24155 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24158 \begin_layout Plain Layout
24164 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24167 \begin_layout Plain Layout
24168 \begin_inset Formula $>$
24178 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24181 \begin_layout Plain Layout
24189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24192 \begin_layout Plain Layout
24193 \begin_inset Formula $\ge$
24203 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24206 \begin_layout Plain Layout
24214 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24217 \begin_layout Plain Layout
24218 \begin_inset Formula $\gg$
24228 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24231 \begin_layout Plain Layout
24239 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24242 \begin_layout Plain Layout
24243 \begin_inset Formula $\succ$
24253 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24256 \begin_layout Plain Layout
24264 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24267 \begin_layout Plain Layout
24268 \begin_inset Formula $\succeq$
24278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24281 \begin_layout Plain Layout
24289 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24292 \begin_layout Plain Layout
24293 \begin_inset Formula $\supset$
24303 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24306 \begin_layout Plain Layout
24314 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24317 \begin_layout Plain Layout
24318 \begin_inset Formula $\supseteq$
24328 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24331 \begin_layout Plain Layout
24339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24342 \begin_layout Plain Layout
24343 \begin_inset Formula $\sqsupseteq$
24353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24356 \begin_layout Plain Layout
24364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24367 \begin_layout Plain Layout
24368 \begin_inset Formula $\ni$
24378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24381 \begin_layout Plain Layout
24389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24392 \begin_layout Plain Layout
24393 \begin_inset Formula $\dashv$
24403 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24406 \begin_layout Plain Layout
24414 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24417 \begin_layout Plain Layout
24418 \begin_inset Formula $\frown$
24428 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24431 \begin_layout Plain Layout
24439 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24442 \begin_layout Plain Layout
24443 \begin_inset Formula $\rhd$
24453 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24456 \begin_layout Plain Layout
24464 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24467 \begin_layout Plain Layout
24468 \begin_inset Formula $\unrhd$
24478 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24481 \begin_layout Plain Layout
24489 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24492 \begin_layout Plain Layout
24493 \begin_inset Formula $\lessgtr$
24503 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24506 \begin_layout Plain Layout
24514 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24517 \begin_layout Plain Layout
24518 \begin_inset Formula $\parallel$
24528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24531 \begin_layout Plain Layout
24539 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24542 \begin_layout Plain Layout
24543 \begin_inset Formula $\nparallel$
24559 \begin_layout Standard
24560 \begin_inset VSpace medskip
24575 are bigger than the equal looking operators
24590 \begin_layout Standard
24592 supports also many special relations.
24593 Use the toolbar button
24596 arg "math-insert \\leqq"
24599 to see a list of these relations.
24602 \begin_layout Standard
24603 Relations are, in contrary to symbols, always surrounded by space.
24606 \begin_layout Standard
24607 Relations with labels can be created with the command
24614 \begin_inset Index idx
24617 \begin_layout Plain Layout
24626 \begin_inset Separator parbreak
24632 \begin_layout Standard
24634 \begin_inset Tabular
24635 <lyxtabular version="3" rows="2" columns="2">
24636 <features booktabs="true" tabularvalignment="middle">
24637 <column alignment="center" valignment="top" width="0pt">
24638 <column alignment="center" valignment="top">
24640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24643 \begin_layout Plain Layout
24649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24652 \begin_layout Plain Layout
24659 <row topspace="1.5mm">
24660 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24663 \begin_layout Plain Layout
24667 \begin_inset space \textvisiblespace{}
24675 \begin_inset space \textvisiblespace{}
24679 \begin_inset Formula $\downarrow$
24685 \begin_inset space \textvisiblespace{}
24689 \begin_inset space \textvisiblespace{}
24697 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24700 \begin_layout Plain Layout
24701 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24717 \begin_layout Section
24721 \begin_layout Subsection
24722 Predefined Functions
24723 \begin_inset CommandInset label
24725 name "subsec:Predefined-Functions"
24730 \begin_inset Index idx
24733 \begin_layout Plain Layout
24734 Functions ! predefined
24742 \begin_layout Standard
24743 In general, variables are set
24747 in mathematical expressions, but not function names, because
24748 \begin_inset Formula $sin$
24751 could be misunderstood as
24752 \begin_inset Formula $s\cdot i\cdot n$
24756 Therefore there are predefined functionswhich are additionally a bit separated
24758 They are inserted as commands starting with a backslash before their name.
24759 \begin_inset Separator parbreak
24765 \begin_layout Standard
24767 \begin_inset Tabular
24768 <lyxtabular version="3" rows="2" columns="2">
24769 <features booktabs="true" tabularvalignment="middle">
24770 <column alignment="center" valignment="top" width="0pt">
24771 <column alignment="center" valignment="top" width="0pt">
24773 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24776 \begin_layout Plain Layout
24782 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24785 \begin_layout Plain Layout
24793 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24796 \begin_layout Plain Layout
24802 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24805 \begin_layout Plain Layout
24806 \begin_inset Formula $Asin(x)+B$
24820 \begin_inset space \quad{}
24824 \begin_inset Tabular
24825 <lyxtabular version="3" rows="2" columns="2">
24826 <features booktabs="true" tabularvalignment="middle">
24827 <column alignment="center" valignment="top" width="0pt">
24828 <column alignment="center" valignment="top" width="0pt">
24830 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24833 \begin_layout Plain Layout
24839 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24842 \begin_layout Plain Layout
24850 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24853 \begin_layout Plain Layout
24861 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24864 \begin_layout Plain Layout
24865 \begin_inset Formula $A\sin(x)+B$
24881 \begin_layout Standard
24882 The following functions are predefined:
24885 \begin_layout Standard
24886 \begin_inset VSpace -2mm
24892 \begin_layout Standard
24894 \begin_inset Tabular
24895 <lyxtabular version="3" rows="9" columns="4">
24896 <features booktabs="true" tabularvalignment="middle">
24897 <column alignment="center" valignment="top" width="0pt">
24898 <column alignment="center" valignment="top" width="0pt">
24899 <column alignment="center" valignment="top" width="0pt">
24900 <column alignment="center" valignment="top" width="0pt">
24902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24905 \begin_layout Plain Layout
24911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24914 \begin_layout Plain Layout
24920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24923 \begin_layout Plain Layout
24929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24932 \begin_layout Plain Layout
24940 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24943 \begin_layout Plain Layout
24951 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24954 \begin_layout Plain Layout
24962 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24965 \begin_layout Plain Layout
24973 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24976 \begin_layout Plain Layout
24986 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24989 \begin_layout Plain Layout
24997 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25000 \begin_layout Plain Layout
25008 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25011 \begin_layout Plain Layout
25019 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25022 \begin_layout Plain Layout
25032 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25035 \begin_layout Plain Layout
25043 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25046 \begin_layout Plain Layout
25054 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25057 \begin_layout Plain Layout
25065 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25068 \begin_layout Plain Layout
25078 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25081 \begin_layout Plain Layout
25089 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25092 \begin_layout Plain Layout
25100 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25103 \begin_layout Plain Layout
25111 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25114 \begin_layout Plain Layout
25124 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25127 \begin_layout Plain Layout
25135 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25138 \begin_layout Plain Layout
25146 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25149 \begin_layout Plain Layout
25157 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25160 \begin_layout Plain Layout
25170 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25173 \begin_layout Plain Layout
25181 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25184 \begin_layout Plain Layout
25192 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25195 \begin_layout Plain Layout
25203 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25206 \begin_layout Plain Layout
25216 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25219 \begin_layout Plain Layout
25227 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25230 \begin_layout Plain Layout
25238 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25241 \begin_layout Plain Layout
25249 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25252 \begin_layout Plain Layout
25262 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25265 \begin_layout Plain Layout
25273 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25276 \begin_layout Plain Layout
25284 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25287 \begin_layout Plain Layout
25295 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25298 \begin_layout Plain Layout
25314 \begin_layout Standard
25315 They can also be inserted with the math toolbar button
25318 arg "math-insert \\functions"
25324 \begin_layout Subsection
25325 Self-defined Functions
25326 \begin_inset Index idx
25329 \begin_layout Plain Layout
25330 Functions ! self-defined
25338 \begin_layout Standard
25339 To use a function that is not predefined, like for example the sign function
25340 sgn(x), there are two possibilities:
25343 \begin_layout Itemize
25344 Define the function by inserting the following line to the \SpecialChar LaTeX
25349 \begin_layout Plain Layout
25354 DeclareMathOperator
25357 \begin_inset CommandInset ref
25359 reference "subsec:Self-defined-Operators"
25369 \begin_inset Newline newline
25373 \begin_inset VSpace -3mm
25377 \begin_inset Newline newline
25384 DeclareMathOperator{
25389 \begin_inset Index idx
25392 \begin_layout Plain Layout
25397 DeclareMathOperator
25403 \begin_inset Newline newline
25407 \begin_inset VSpace -2mm
25411 \begin_inset Newline newline
25414 Now the new defined function can be called with the command
25423 \begin_layout Itemize
25424 Write the formula as usual, mark the formula name, in our example the letters
25429 , and change it to mathematical text.
25430 Finally, a space is inserted between prefactor and function.
25433 \begin_layout Standard
25434 The result is the same with both methods as with a predefined function
25438 \begin_layout Plain Layout
25439 In \SpecialChar LyX
25440 self-defined functions are displayed red, predefined ones black.
25446 \begin_inset Separator parbreak
25452 \begin_layout Standard
25454 \begin_inset Tabular
25455 <lyxtabular version="3" rows="3" columns="2">
25456 <features booktabs="true" tabularvalignment="middle">
25457 <column alignment="center" valignment="top" width="0pt">
25458 <column alignment="center" valignment="top" width="0pt">
25460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25463 \begin_layout Plain Layout
25469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25472 \begin_layout Plain Layout
25480 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25483 \begin_layout Plain Layout
25491 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25494 \begin_layout Plain Layout
25495 \begin_inset Formula $A\sgn(x)+B$
25505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25508 \begin_layout Plain Layout
25512 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25523 \begin_layout Plain Layout
25524 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25540 \begin_layout Standard
25541 The first method is more suitable when the self-defined function should
25542 be used several times.
25545 \begin_layout Subsection
25547 \begin_inset Index idx
25550 \begin_layout Plain Layout
25559 \begin_layout Standard
25560 For limits, in addition to the commands
25567 \begin_inset Index idx
25570 \begin_layout Plain Layout
25590 the following functions are defined:
25591 \begin_inset Separator parbreak
25597 \begin_layout Standard
25599 \begin_inset Tabular
25600 <lyxtabular version="3" rows="5" columns="2">
25601 <features booktabs="true" tabularvalignment="middle">
25602 <column alignment="center" valignment="top" width="0pt">
25603 <column alignment="center" valignment="top" width="0pt">
25605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25608 \begin_layout Plain Layout
25614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25617 \begin_layout Plain Layout
25625 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25628 \begin_layout Plain Layout
25636 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25639 \begin_layout Plain Layout
25640 \begin_inset Formula $\varliminf$
25649 <row topspace="1.5mm">
25650 <cell alignment="center" valignment="top" usebox="none">
25653 \begin_layout Plain Layout
25661 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25664 \begin_layout Plain Layout
25665 \begin_inset Formula $\varlimsup$
25674 <row topspace="1.5mm">
25675 <cell alignment="center" valignment="top" usebox="none">
25678 \begin_layout Plain Layout
25686 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25689 \begin_layout Plain Layout
25690 \begin_inset Formula $\varprojlim$
25699 <row topspace="1.5mm" bottomspace="1mm">
25700 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25703 \begin_layout Plain Layout
25711 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25714 \begin_layout Plain Layout
25715 \begin_inset Formula $\varinjlim$
25731 \begin_layout Standard
25732 \begin_inset VSpace medskip
25735 The limit is created by inserting a subscript.
25736 It is set right beside the function in an inline formula:
25739 \begin_layout Standard
25741 \begin_inset Tabular
25742 <lyxtabular version="3" rows="2" columns="2">
25743 <features booktabs="true" tabularvalignment="middle">
25744 <column alignment="center" valignment="top" width="0pt">
25745 <column alignment="center" valignment="top" width="0pt">
25747 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25750 \begin_layout Plain Layout
25756 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25759 \begin_layout Plain Layout
25767 <cell alignment="center" valignment="top" usebox="none">
25770 \begin_layout Plain Layout
25776 \begin_inset space \textvisiblespace{}
25780 \begin_inset space \textvisiblespace{}
25788 <cell alignment="center" valignment="top" usebox="none">
25791 \begin_layout Plain Layout
25792 \begin_inset Formula $\lim_{x\to A}x=B$
25808 \begin_layout Standard
25809 In a displayed formula the limit is set below the formula, as usual:
25810 \begin_inset Formula
25820 \begin_layout Standard
25821 \begin_inset VSpace medskip
25827 \begin_layout Standard
25828 How to adjust the typesetting of the limits see
25829 \begin_inset CommandInset ref
25831 reference "subsec:Operator-Limits"
25838 \begin_layout Subsection
25840 \begin_inset Index idx
25843 \begin_layout Plain Layout
25844 Functions ! modulo-
25852 \begin_layout Standard
25853 The modulo-function is special, because it exists in four variants.
25854 The variants in a displayed formula are:
25855 \begin_inset Formula
25857 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25858 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25859 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25860 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25861 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25869 \begin_layout Standard
25870 In an inline formula less space is set before the function names for all
25872 By default the modulo-functions take only the first following character
25874 To use more than one character, one has to put them into \SpecialChar TeX
25876 \begin_inset Formula
25878 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25879 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25880 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25888 \begin_layout Section
25890 \begin_inset Index idx
25893 \begin_layout Plain Layout
25902 \begin_layout Standard
25903 The characters ^ and _ would normally create a superscript and subscript,
25905 To get these characters you have to insert them with a leading
25908 \begin_inset Separator parbreak
25914 \begin_layout Standard
25917 \begin_inset Tabular
25918 <lyxtabular version="3" rows="3" columns="2">
25919 <features booktabs="true" tabularvalignment="middle">
25920 <column alignment="left" valignment="top" width="0pt">
25921 <column alignment="block" valignment="top">
25923 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25926 \begin_layout Plain Layout
25932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25935 \begin_layout Plain Layout
25943 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25946 \begin_layout Plain Layout
25950 \begin_inset space \textvisiblespace{}
25958 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25961 \begin_layout Plain Layout
25962 \begin_inset Formula $\mathcircumflex$
25972 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25975 \begin_layout Plain Layout
25983 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25986 \begin_layout Plain Layout
25987 \begin_inset Formula $\_$
26003 \begin_layout Subsection
26004 Special Characters in Mathematical Text
26007 \begin_layout Standard
26008 The following commands can only be used in mathematical text or in \SpecialChar TeX
26012 \begin_layout Standard
26013 \begin_inset space \hfill{}
26017 \begin_inset Tabular
26018 <lyxtabular version="3" rows="8" columns="2">
26019 <features booktabs="true" tabularvalignment="middle">
26020 <column alignment="left" valignment="top" width="0pt">
26021 <column alignment="block" valignment="top">
26023 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26026 \begin_layout Plain Layout
26032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26035 \begin_layout Plain Layout
26043 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26046 \begin_layout Plain Layout
26054 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26057 \begin_layout Plain Layout
26058 \begin_inset Formula $\textrm{œ}$
26068 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26071 \begin_layout Plain Layout
26079 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26082 \begin_layout Plain Layout
26083 \begin_inset Formula $\textrm{Œ}$
26093 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26096 \begin_layout Plain Layout
26104 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26107 \begin_layout Plain Layout
26108 \begin_inset Formula $\textrm{æ}$
26118 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26121 \begin_layout Plain Layout
26129 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26132 \begin_layout Plain Layout
26133 \begin_inset Formula $\textrm{Æ}$
26143 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26146 \begin_layout Plain Layout
26154 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26157 \begin_layout Plain Layout
26158 \begin_inset Formula $\textrm{\aa}$
26168 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26171 \begin_layout Plain Layout
26175 \begin_inset Index idx
26178 \begin_layout Plain Layout
26185 \begin_layout Plain Layout
26206 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26209 \begin_layout Plain Layout
26210 \begin_inset Formula $\textrm{Å}$
26220 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26223 \begin_layout Plain Layout
26231 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26234 \begin_layout Plain Layout
26235 \begin_inset Formula $\textrm{ı}$
26249 \begin_inset space \hfill{}
26253 \begin_inset Tabular
26254 <lyxtabular version="3" rows="8" columns="2">
26255 <features booktabs="true" tabularvalignment="middle">
26256 <column alignment="left" valignment="top" width="0pt">
26257 <column alignment="center" valignment="top">
26259 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26262 \begin_layout Plain Layout
26264 \begin_inset Note Note
26267 \begin_layout Plain Layout
26269 \begin_inset space \thinspace{}
26272 mm is used for separation, because otherwise the output will be ¡ and ¿
26283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26286 \begin_layout Plain Layout
26294 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26297 \begin_layout Plain Layout
26305 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26308 \begin_layout Plain Layout
26309 \begin_inset Formula $\textrm{ø}$
26319 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26322 \begin_layout Plain Layout
26330 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26333 \begin_layout Plain Layout
26334 \begin_inset Formula $\textrm{Ø}$
26344 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26347 \begin_layout Plain Layout
26355 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26358 \begin_layout Plain Layout
26359 \begin_inset Formula $\textrm{ł}$
26369 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26372 \begin_layout Plain Layout
26380 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26383 \begin_layout Plain Layout
26384 \begin_inset Formula $\textrm{Ł}$
26394 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26397 \begin_layout Plain Layout
26399 \begin_inset space \hspace{}
26404 \begin_inset space \textvisiblespace{}
26412 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26415 \begin_layout Plain Layout
26416 \begin_inset Formula $\textrm{!`}$
26426 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26429 \begin_layout Plain Layout
26431 \begin_inset space \hspace{}
26436 \begin_inset space \textvisiblespace{}
26444 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26447 \begin_layout Plain Layout
26448 \begin_inset Formula $\textrm{?`}$
26458 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26461 \begin_layout Plain Layout
26469 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26472 \begin_layout Plain Layout
26473 \begin_inset Formula $\textrm{ȷ}$
26487 \begin_inset space \hfill{}
26493 \begin_layout Standard
26495 \begin_inset Formula $\textrm{\textrm{Å}}$
26499 \begin_inset Formula $\textrm{\textrm{Ø}}$
26502 can also be inserted via the math toolbar button
26505 arg "math-insert \\digamma"
26511 \begin_layout Standard
26512 An exception are the commands
26515 \begin_inset space \hspace{}
26524 \begin_inset space \hspace{}
26530 , because they can be inserted in \SpecialChar LyX
26534 \begin_layout Subsection
26536 \begin_inset CommandInset label
26538 name "subsec:Accents-in-Text"
26543 \begin_inset Index idx
26546 \begin_layout Plain Layout
26555 \begin_layout Standard
26556 With the following commands all letters can be accented.
26557 The commands must be inserted in \SpecialChar TeX
26561 \begin_layout Standard
26562 \begin_inset space \hfill{}
26566 \begin_inset Tabular
26567 <lyxtabular version="3" rows="8" columns="2">
26568 <features booktabs="true" tabularvalignment="middle">
26569 <column alignment="left" valignment="top" width="0pt">
26570 <column alignment="block" valignment="top">
26572 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26575 \begin_layout Plain Layout
26581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26584 \begin_layout Plain Layout
26592 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26595 \begin_layout Plain Layout
26599 \begin_inset Quotes grd
26607 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26610 \begin_layout Plain Layout
26614 \begin_layout Plain Layout
26630 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26633 \begin_layout Plain Layout
26641 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26644 \begin_layout Plain Layout
26648 \begin_layout Plain Layout
26664 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26667 \begin_layout Plain Layout
26671 \begin_inset space \textvisiblespace{}
26679 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26682 \begin_layout Plain Layout
26686 \begin_layout Plain Layout
26702 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26705 \begin_layout Plain Layout
26713 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26716 \begin_layout Plain Layout
26720 \begin_layout Plain Layout
26736 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26739 \begin_layout Plain Layout
26743 \begin_inset space \textvisiblespace{}
26751 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26754 \begin_layout Plain Layout
26758 \begin_layout Plain Layout
26774 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26777 \begin_layout Plain Layout
26781 \begin_inset space \textvisiblespace{}
26789 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26792 \begin_layout Plain Layout
26796 \begin_layout Plain Layout
26812 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26815 \begin_layout Plain Layout
26819 \begin_inset space \textvisiblespace{}
26827 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26830 \begin_layout Plain Layout
26834 \begin_layout Plain Layout
26854 \begin_inset space \hfill{}
26858 \begin_inset Tabular
26859 <lyxtabular version="3" rows="8" columns="2">
26860 <features booktabs="true" tabularvalignment="middle">
26861 <column alignment="left" valignment="top" width="0pt">
26862 <column alignment="center" valignment="top">
26864 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26867 \begin_layout Plain Layout
26873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26876 \begin_layout Plain Layout
26884 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26887 \begin_layout Plain Layout
26891 \begin_inset space \textvisiblespace{}
26899 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26902 \begin_layout Plain Layout
26906 \begin_layout Plain Layout
26922 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26925 \begin_layout Plain Layout
26933 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26936 \begin_layout Plain Layout
26940 \begin_layout Plain Layout
26956 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26959 \begin_layout Plain Layout
26963 \begin_inset Index idx
26966 \begin_layout Plain Layout
26977 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26980 \begin_layout Plain Layout
26984 \begin_layout Plain Layout
27000 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27003 \begin_layout Plain Layout
27011 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27014 \begin_layout Plain Layout
27018 \begin_layout Plain Layout
27034 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27037 \begin_layout Plain Layout
27041 \begin_inset space \textvisiblespace{}
27049 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27052 \begin_layout Plain Layout
27056 \begin_layout Plain Layout
27072 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27075 \begin_layout Plain Layout
27079 \begin_inset space \textvisiblespace{}
27087 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27090 \begin_layout Plain Layout
27094 \begin_layout Plain Layout
27110 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27113 \begin_layout Plain Layout
27117 \begin_inset space \textvisiblespace{}
27125 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27128 \begin_layout Plain Layout
27132 \begin_layout Plain Layout
27152 \begin_inset space \hfill{}
27158 \begin_layout Standard
27159 \begin_inset VSpace medskip
27168 also two different characters can be accented.
27174 \begin_inset space \textvisiblespace{}
27183 \begin_layout Plain Layout
27195 \begin_layout Standard
27208 can in combination with vowels directly be inserted with the keyboard without
27209 using \SpecialChar TeX
27211 The same applies for the tilde
27215 \begin_layout Plain Layout
27216 This only applies for keyboards where the tilde is defined as accent.
27225 in combination with
27240 \begin_layout Standard
27283 and accents that are inserted directly with the keyboard are also available
27284 in mathematical text.
27285 For the other accents there are special math commands to be used in formulas,
27287 \begin_inset CommandInset ref
27289 reference "subsec:Accents-for-one"
27296 \begin_layout Standard
27297 \begin_inset VSpace bigskip
27300 Furthermore, with the command
27307 \begin_inset Index idx
27310 \begin_layout Plain Layout
27318 all numbers and letters can be set into a circle, quasi accented with a
27319 circle, similar to the copyright symbol.
27322 \begin_layout Standard
27324 \begin_inset Tabular
27325 <lyxtabular version="3" rows="3" columns="2">
27326 <features booktabs="true" tabularvalignment="middle">
27327 <column alignment="center" valignment="top" width="0pt">
27328 <column alignment="center" valignment="top">
27330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27333 \begin_layout Plain Layout
27339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27342 \begin_layout Plain Layout
27350 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27353 \begin_layout Plain Layout
27361 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27364 \begin_layout Plain Layout
27368 \begin_layout Plain Layout
27383 <row topspace="1mm">
27384 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27387 \begin_layout Plain Layout
27398 raisebox{-1.5pt}{W}}
27403 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27406 \begin_layout Plain Layout
27410 \begin_layout Plain Layout
27440 \begin_layout Standard
27441 One has to take care that the character fits in the circle.
27452 \begin_layout Plain Layout
27454 \begin_inset CommandInset ref
27456 reference "subsec:Font-Sizes"
27465 specifies thereby the size of the circle.
27476 \begin_layout Plain Layout
27478 \begin_inset CommandInset ref
27480 reference "subsec:Boxes-without-Frame"
27489 the character can be centered.
27492 \begin_layout Subsection
27494 \begin_inset Index idx
27497 \begin_layout Plain Layout
27506 \begin_layout Standard
27507 Old-style figures (also known as old-style numerals) are created with the
27515 \begin_inset Index idx
27518 \begin_layout Plain Layout
27527 The command can be used in formulas and in \SpecialChar TeX
27529 The command scheme is:
27532 \begin_layout Standard
27537 oldstylenums{number}
27540 \begin_layout Standard
27545 oldstylenums{0123456789
27548 \begin_inset Formula $\oldstylenums{0123456789}$
27554 \begin_layout Section
27556 \begin_inset CommandInset label
27558 name "sec:Formula-Styles"
27563 \begin_inset Index idx
27566 \begin_layout Plain Layout
27575 \begin_layout Itemize
27576 There are two different alignment styles:
27577 \begin_inset Separator parbreak
27584 \begin_layout Description
27585 Centered is the predefined standard
27588 \begin_layout Description
27589 Indented for this the option
27593 must be inserted in the menu
27595 Document\SpecialChar menuseparator
27601 \begin_inset space ~
27607 \begin_layout Standard
27612 is used, the indentation can be adjusted with the length
27619 \begin_inset Index idx
27622 \begin_layout Plain Layout
27631 Should the distance be 15
27632 \begin_inset space \thinspace{}
27635 mm, the following command line is inserted in the \SpecialChar LaTeX
27639 \begin_layout Standard
27649 \begin_layout Standard
27650 When no length is specified, the predefined value of 30
27651 \begin_inset space \thinspace{}
27658 \begin_layout Itemize
27659 And two different numbering styles:
27660 \begin_inset Separator parbreak
27667 \begin_layout Description
27668 Right is the predefined standard
27671 \begin_layout Description
27672 Left for this the option
27676 must be inserted in the menu
27678 Document\SpecialChar menuseparator
27684 \begin_inset space ~
27691 \begin_layout Standard
27700 can also be used together.
27701 In this case both options are inserted, separated by a comma.
27704 \begin_layout Standard
27705 The chosen styles are used for all displayed formulas of the document.
27706 When both, centered and indented formulas should be created in a document,
27712 The indented formulas are then set in a flalign environment, see
27713 \begin_inset CommandInset ref
27715 reference "subsec:Flalign-Environment"
27722 \begin_layout Section
27724 \begin_inset CommandInset label
27726 name "sec:Multiline-Formulas"
27731 \begin_inset Index idx
27734 \begin_layout Plain Layout
27735 Formula ! multiline
27743 \begin_layout Subsection
27747 \begin_layout Standard
27748 In \SpecialChar LyX
27749 multiline formulas are created by pressing
27752 arg "newline-insert newline"
27757 \change_deleted 2047637253 1449850740
27758 This creates either an
27760 eqnarray environment
27762 that is described in
27763 \begin_inset CommandInset ref
27765 reference "subsec:Eqnarray-Environment"
27769 or, when the option
27771 Use AMS math package
27773 in the document settings is selected, an
27777 that is described in
27778 \begin_inset CommandInset ref
27780 reference "subsec:Standard-align-Environment"
27786 \change_inserted 2047637253 1449851860
27787 This creates either an
27791 that is described in
27792 \begin_inset CommandInset ref
27794 reference "subsec:Standard-align-Environment"
27798 or, when automatically loading the package
27802 is disabled in the document settings, an
27804 eqnarray environment
27806 that is described in
27807 \begin_inset CommandInset ref
27809 reference "subsec:Eqnarray-Environment"
27816 The align environment is recommended because it provides in any case a typograph
27817 ically correct output.
27820 \begin_layout Standard
27821 There are other multiline formula environments that can be created via the
27824 Insert\SpecialChar menuseparator
27828 These environments are described in the following sections.
27831 \begin_layout Standard
27832 In all multiline formula environments a new line is created by pressing
27836 arg "newline-insert newline"
27840 To add or delete lines, the math toolbar buttons
27843 arg "inset-modify tabular append-row"
27849 arg "inset-modify tabular delete-row"
27852 , respectively, or the menu
27854 Edit\SpecialChar menuseparator
27860 \begin_layout Subsubsection
27862 \begin_inset CommandInset label
27864 name "subsec:Line-Separation"
27869 \begin_inset Index idx
27872 \begin_layout Plain Layout
27873 Formula ! multiline ! Line separation
27881 \begin_layout Standard
27882 There is sometimes not enough space in multiline formulas between the lines:
27883 \begin_inset Formula
27885 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}\\
27886 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
27894 \begin_layout Standard
27895 In \SpecialChar LaTeX
27896 additional line space is specified as optional argument of the new line
27898 This is not yet possible in \SpecialChar LyX
27903 \begin_layout Plain Layout
27905 \begin_inset CommandInset href
27907 name "LyX-bug #1505"
27908 target "http://www.lyx.org/trac/ticket/1505"
27917 , therefore the whole formula must be inserted in \SpecialChar TeX
27919 To add in our example space, the command
27927 is inserted at the end of the first line.
27932 \begin_layout Plain Layout
27939 \begin_layout Plain Layout
27941 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27944 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27951 \begin_layout Plain Layout
27955 left(B^{2}+x_{0}^{2}
27963 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27968 \begin_layout Plain Layout
27980 \begin_layout Standard
27981 \begin_inset VSpace bigskip
27984 To set the line separation for all lines in a formula, the length
27991 \begin_inset Index idx
27994 \begin_layout Plain Layout
28004 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
28015 \begin_inset space \thinspace{}
28020 \begin_inset space \thinspace{}
28023 mm additional line separation as in the previous example, the command
28026 \begin_layout Standard
28036 \begin_layout Standard
28037 is inserted in \SpecialChar TeX
28038 mode before the formula.
28039 This requires that the \SpecialChar LaTeX
28048 \begin_layout Plain Layout
28053 is part of every \SpecialChar LaTeX
28054 standard installation.
28060 \begin_inset Index idx
28063 \begin_layout Plain Layout
28069 was loaded in \SpecialChar LaTeX
28070 -preamble with the line
28073 \begin_layout Standard
28081 \begin_layout Standard
28086 \begin_layout Plain Layout
28098 \begin_inset Formula
28100 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}\\
28101 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
28109 \begin_layout Standard
28113 \begin_layout Plain Layout
28124 To get back to the predefined distance,
28130 is set to the value 3
28131 \begin_inset space \thinspace{}
28137 \begin_layout Subsubsection
28139 \begin_inset CommandInset label
28141 name "subsec:Column-Separation"
28146 \begin_inset Index idx
28149 \begin_layout Plain Layout
28150 Formula ! multiline ! Column separation
28158 \begin_layout Standard
28159 Multiline formulas form a matrix.
28160 A formula in the eqnarray environment is for example a matrix with three
28162 By changing the column separation in this environment, the space beside
28163 the relation sign can be changed.
28166 \begin_layout Standard
28167 The column separation is specified with the length
28174 \begin_inset Index idx
28177 \begin_layout Plain Layout
28186 \begin_inset Newline newline
28189 column separation = 2
28190 \begin_inset space \thinspace{}
28200 \begin_inset Newline newline
28206 \begin_layout Standard
28216 \begin_layout Standard
28217 inserted in \SpecialChar TeX
28218 mode, sets for all following formulas a column separation of
28220 \begin_inset space \thinspace{}
28224 To get back to the predefined distance,
28231 \begin_inset space \thinspace{}
28237 \begin_layout Standard
28239 \begin_inset space \thinspace{}
28242 cm column separation:
28246 \begin_layout Plain Layout
28258 \begin_inset Formula
28266 A formula with the predefined column separation for matrices of 10
28267 \begin_inset space \thinspace{}
28274 \begin_layout Plain Layout
28286 \begin_inset Formula
28297 \begin_layout Subsubsection
28299 \begin_inset Index idx
28302 \begin_layout Plain Layout
28311 \begin_layout Standard
28312 Long formulas can be typeset using these methods:
28315 \begin_layout Itemize
28316 When one side of the equation is much shorter than the line width, this
28317 one is chosen for the left side and the right side is typeset over two
28319 \begin_inset Formula
28321 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 \\
28322 & & -\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}
28327 The minus sign at the beginning of the second line does normally not appear
28328 as an operator because it is the first character of the line.
28329 Thus it would not be surrounded by space and could not be distinguished
28330 from the fraction bar.
28332 \begin_inset space \thinspace{}
28335 pt space was inserted behind the minus sign with the command
28345 \begin_layout Plain Layout
28353 \begin_inset CommandInset ref
28355 reference "subsec:Variable-Space"
28365 \begin_inset Index idx
28368 \begin_layout Plain Layout
28379 \begin_layout Itemize
28380 When both sides of the equation are too long, the command
28387 \begin_inset Index idx
28390 \begin_layout Plain Layout
28399 It is inserted in the first column of the first line and causes all further
28400 insertions to overwrite the following columns:
28401 \begin_inset Formula
28403 \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 \\
28404 & & -\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 \\
28405 & & =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}
28410 After the insertion of
28416 , the cursor is in a purple box that is a bit shifted to the left from the
28418 In this the formula is inserted.
28419 \begin_inset Newline newline
28422 The content of the further lines is inserted to the second or another formula
28424 The greater the column number where it was inserted, the larger the indentation.
28425 \begin_inset VSpace medskip
28429 \begin_inset Newline newline
28433 \begin_inset Note Greyedout
28436 \begin_layout Plain Layout
28437 Note the following when using
28446 \begin_layout Itemize
28447 The formula doesn't use the full page width.
28449 \begin_inset space \thinspace{}
28453 \begin_inset space \space{}
28457 \begin_inset Formula $-B^{2}$
28460 is added to the first line in the above example, it would have been outside
28462 To better use the width, negative space can be inserted at the beginning
28466 \begin_layout Itemize
28467 Due to a bug in \SpecialChar LyX
28468 the cursor cannot be set with the mouse into the first
28473 \begin_layout Plain Layout
28474 \begin_inset CommandInset href
28476 name "LyX-bug #1429"
28477 target "http://www.lyx.org/trac/ticket/1429"
28486 One can only set the cursor at the beginning of the line and move it with
28495 \begin_layout Itemize
28496 Other methods to set long formulas are offered by the environments described
28498 \begin_inset CommandInset ref
28500 reference "subsec:Multline-Environment"
28505 \begin_inset CommandInset ref
28507 reference "subsec:Multiline-Formula-Parts"
28514 \begin_layout Subsubsection
28515 Multiline Fractions
28516 \begin_inset CommandInset label
28518 name "subsec:Multiline-Fractions"
28523 \begin_inset Index idx
28526 \begin_layout Plain Layout
28527 Fractions ! multiline
28535 \begin_layout Standard
28536 There are cases where the denominator and/or the numerator of a fraction
28537 is so long that the fraction does not fit into one line.
28538 It is then necessary to add a line break within the fraction.
28539 This can be done using the command
28546 \begin_inset Index idx
28549 \begin_layout Plain Layout
28558 To activate it, set in the document settings under
28561 \begin_inset space ~
28571 \begin_inset Index idx
28574 \begin_layout Plain Layout
28575 Packages ! mathtools
28583 \begin_inset space ~
28598 \begin_layout Standard
28603 splitfrac{first line}{second line}
28606 \begin_layout Standard
28607 and is used as denominator and/or numerator:
28610 \begin_layout Standard
28611 \begin_inset Formula
28613 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}
28618 The command for the first numerator above is:
28621 \begin_layout Standard
28626 splitfrac{xy+xy+xy+xy+xy
28627 \begin_inset space \textvisiblespace{}
28635 \begin_layout Subsubsection
28637 \begin_inset CommandInset label
28639 name "subsec:Multiline-Brackets"
28644 \begin_inset Index idx
28647 \begin_layout Plain Layout
28648 Brackets ! for multiline expressions
28656 \begin_layout Standard
28657 For brackets spanning multiple lines the following problem occurs:
28658 \begin_inset Formula
28660 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28661 & & \left.\cdots+B-D\right]
28669 \begin_layout Standard
28670 The closing bracket is smaller than the opening bracket because brackets
28671 with variable size may not span multiple lines.
28674 \begin_layout Standard
28675 To set the bracket size for the second line correctly, the first line is
28683 \begin_inset Index idx
28686 \begin_layout Plain Layout
28694 and the second line with
28702 \begin_layout Plain Layout
28716 \begin_inset CommandInset ref
28718 reference "subsec:Automatic-Bracket-Size"
28730 \begin_inset Index idx
28733 \begin_layout Plain Layout
28756 \begin_inset space \textvisiblespace{}
28766 \begin_inset space \textvisiblespace{}
28776 \begin_inset space \textvisiblespace{}
28782 \begin_inset Formula $\downarrow$
28788 \begin_inset Index idx
28791 \begin_layout Plain Layout
28799 is inserted, because the multiplication operator with its limits is the
28800 largest symbol in the first line and this should be the size for the bracket
28801 in the second line.
28804 \begin_layout Standard
28805 The result is this:
28806 \begin_inset Formula
28808 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28809 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28817 \begin_layout Subsection
28821 \begin_layout Standard
28822 Align environments can be used for every kind of multiline formulas.
28823 They are especially useful to set several formulas side by side.
28826 \begin_layout Standard
28827 Align environments consist of columns.
28828 The odd columns are right aligned, the even ones left aligned.
28829 Every line in an Align environment can be numbered.
28832 \begin_layout Standard
28833 Align environments are created via the menu
28835 Insert\SpecialChar menuseparator
28841 Edit\SpecialChar menuseparator
28842 Math\SpecialChar menuseparator
28843 Change Formula Type
28845 already existing formulas can be converted to Align environments.
28848 \begin_layout Standard
28849 To add or delete columns, the math toolbar buttons
28852 arg "inset-modify tabular append-column"
28858 arg "inset-modify tabular delete-column"
28861 , respectively, or the menu
28863 Edit\SpecialChar menuseparator
28869 \begin_layout Subsubsection
28870 Standard align Environment
28871 \begin_inset CommandInset label
28873 name "subsec:Standard-align-Environment"
28878 \begin_inset Index idx
28881 \begin_layout Plain Layout
28882 Formula ! multiline ! align environment
28890 \begin_layout Standard
28891 This Align environment is created by pressing
28894 arg "newline-insert newline"
28897 in a formula or by the menu
28899 Insert\SpecialChar menuseparator
28900 Math\SpecialChar menuseparator
28901 AMS align Environment
28906 \begin_layout Standard
28907 An example for two formulas set side by side, that are created with a four
28908 column align environment:
28909 \begin_inset Formula
28911 A & =\sin(B) & C & =D\\
28912 C & \ne A & B & \ne D
28917 As it can be seen, the formulas in this environment are placed so as if
28926 \begin_layout Plain Layout
28934 \begin_inset CommandInset ref
28936 reference "subsec:Variable-Space"
28947 before the first and after every even column.
28948 When the formula style
28954 \begin_layout Plain Layout
28956 \begin_inset CommandInset ref
28958 reference "sec:Formula-Styles"
28969 is used, the formula is set without the
28975 before the first column.
28978 \begin_layout Subsubsection
28979 Alignat Environment
28980 \begin_inset Index idx
28983 \begin_layout Plain Layout
28984 Formula ! multiline ! alignat environment
28992 \begin_layout Standard
28993 The alignat environment has no predefined column separation.
28994 It can be inserted manually with the spaces that are described
28995 \begin_inset CommandInset ref
28997 reference "subsec:Space"
29004 \begin_layout Standard
29005 The above example in the alignat environment where 1
29006 \begin_inset space \thinspace{}
29009 cm space was inserted at the beginning of the second formula:
29010 \begin_inset Formula
29011 \begin{alignat*}{2}
29012 A & =\sin(B) & \hspace{1cm}C & =D\\
29013 C & \ne A & B & \ne D
29018 Because the column separation can be set separately for every column, this
29019 environment is especially suitable to set three and more formulas side
29023 \begin_layout Subsubsection
29024 Flalign Environment
29025 \begin_inset CommandInset label
29027 name "subsec:Flalign-Environment"
29032 \begin_inset Index idx
29035 \begin_layout Plain Layout
29036 Formula ! multiline ! flalign environment
29044 \begin_layout Standard
29045 In this environment the first two columns are always set as much as possible
29046 to the left and the last two ones to the right.
29048 \begin_inset Formula
29050 A & =1 & B & =2 & C & =3\\
29051 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29059 \begin_layout Standard
29060 By creating a flalign environment with an odd number of columns where an
29061 empty \SpecialChar TeX
29062 brace is inserted to the last column, several formulas in a document
29063 can be set to the left, although the formula style
29068 As example the indented formula
29069 \begin_inset CommandInset ref
29071 reference "eq:VolInt"
29076 \begin_inset Formula
29078 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29083 The first two columns contain the formula.
29084 To indent it as with the formula style
29089 \begin_inset space \thinspace{}
29092 pt space was inserted at the beginning of the first column.
29095 \begin_layout Subsection
29096 Eqnarray Environment
29097 \begin_inset CommandInset label
29099 name "subsec:Eqnarray-Environment"
29104 \begin_inset Index idx
29107 \begin_layout Plain Layout
29108 Formula ! multiline ! eqnarray environment
29116 \begin_layout Standard
29117 When this environment has been created, three blue boxes appear.
29118 The content of the first box is right aligned, the content of the last
29120 The content of the middle box appears centered and a bit smaller, because
29121 it is designed to insert there only relation characters.
29122 \begin_inset Formula
29124 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29134 \begin_layout Subsection
29136 \begin_inset Index idx
29139 \begin_layout Plain Layout
29140 Formula ! multiline ! gather environment
29148 \begin_layout Standard
29149 This environment consists of only one centered column.
29150 Every line can be numbered.
29151 \begin_inset Formula
29162 \begin_layout Subsection
29163 Multline Environment
29164 \begin_inset CommandInset label
29166 name "subsec:Multline-Environment"
29171 \begin_inset Index idx
29174 \begin_layout Plain Layout
29175 Formula ! multiline ! multline environment
29183 \begin_layout Standard
29184 The multline environment consists, like the gather environment, of only
29186 But the first line is left aligned, the last one right aligned.
29187 All other lines are centered.
29188 Therefore this environment is suitable for long formulas.
29190 \begin_inset CommandInset ref
29192 reference "eq:lefteqn"
29196 in the multline environment:
29197 \begin_inset Formula
29199 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}\\
29200 -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}\\
29201 =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}}
29209 \begin_layout Standard
29210 In the output only the last (first) line of a multline environment appears
29211 numbered when the document numbering is right (left).
29215 \begin_layout Plain Layout
29216 numbering styles see
29217 \begin_inset CommandInset ref
29219 reference "sec:Formula-Styles"
29231 \begin_layout Standard
29239 \begin_inset Index idx
29242 \begin_layout Plain Layout
29257 \begin_inset Index idx
29260 \begin_layout Plain Layout
29268 a centered line can be right or left aligned, respectively.
29269 The commands are used as follows:
29272 \begin_layout Standard
29277 shoveright{line content}
29283 shoveleft{line content}
29286 \begin_layout Standard
29287 \begin_inset VSpace medskip
29297 \begin_inset Index idx
29300 \begin_layout Plain Layout
29308 specifies the distance of the first line from the left page margin.
29309 Predefined is the length 0
29310 \begin_inset space \thinspace{}
29316 \begin_layout Standard
29317 As example the above formula where the command
29320 \begin_layout Standard
29330 \begin_layout Standard
29331 was inserted in \SpecialChar TeX
29336 \begin_layout Plain Layout
29348 \begin_inset Formula
29350 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}\\
29351 \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}}\\
29352 =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}}
29361 \begin_layout Plain Layout
29372 The second line was left aligned using
29381 \begin_layout Subsection
29382 Multiline Formula Parts
29383 \begin_inset CommandInset label
29385 name "subsec:Multiline-Formula-Parts"
29390 \begin_inset Index idx
29393 \begin_layout Plain Layout
29394 Formula ! multiline ! formula parts
29402 \begin_layout Standard
29403 To display only parts of a formula with multiple lines, one of the following
29404 environments is used:
29421 They can be inserted via the menu
29423 Insert\SpecialChar menuseparator
29426 or by using the commands described in this section.
29429 \begin_layout Standard
29430 The first three have the same properties as the corresponding multiline
29431 formula environments, but it is possible to set further formula parts beside
29434 \begin_inset Formula
29436 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29437 \Delta E\Delta t & \ge\frac{\hbar}{2}
29439 \right\} \textrm{Uncertainty relations}
29447 \begin_layout Standard
29448 To get this formula, a displayed formula is created where the command
29455 \begin_inset Index idx
29458 \begin_layout Plain Layout
29467 A purple box appears around the blue formula box where now columns and
29468 lines can be added.
29469 Outside the multiline environment other formula parts can be set, like
29473 \begin_layout Standard
29474 The aligned environment is also suitable for long formulas whose lines are
29475 horizontally aligned.
29476 Using aligned in a displayed formula has the advantage that the formula
29477 number is vertically centered behind the lines.
29479 \begin_inset CommandInset ref
29481 reference "eq:shortlong"
29485 in the aligned environment:
29486 \begin_inset Formula
29488 \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}|}\\
29489 & -\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}|}
29498 \begin_layout Standard
29499 To use the environments
29518 \begin_inset Index idx
29521 \begin_layout Plain Layout
29536 \begin_inset Index idx
29539 \begin_layout Plain Layout
29554 \begin_inset Index idx
29557 \begin_layout Plain Layout
29565 are inserted, respectively.
29566 The split environment has the same properties as the aligned environment
29567 but it can only have two columns.
29570 \begin_layout Subsection
29571 Text in multiline Formulas
29572 \begin_inset CommandInset label
29574 name "subsec:Text-in-multiline"
29579 \begin_inset Index idx
29582 \begin_layout Plain Layout
29589 \begin_inset Index idx
29592 \begin_layout Plain Layout
29593 Formula ! multiline ! text
29601 \begin_layout Standard
29602 In the Align environments, and the multline and gather environment, text
29603 can be inserted that will appear in a separate line and doesn't affect
29604 the column alignment.
29605 To do this, the command
29612 \begin_inset Index idx
29615 \begin_layout Plain Layout
29623 is used in the following scheme:
29626 \begin_layout Standard
29634 \begin_layout Standard
29635 The text should not be longer than a line because it cannot be hyphenated.
29636 As \SpecialChar LyX
29637 doesn't yet support
29643 directly, the text is written as mathematical text.
29650 must hereby be at the beginning of a line and appears in the output above
29652 An example where the text was inserted at the beginning of the second line:
29653 \begin_inset Formula
29655 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29656 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29664 \begin_layout Standard
29671 always creates some vertical space between the text and the formula lines.
29672 To avoid this space, set in the document settings under
29675 \begin_inset space ~
29685 \begin_inset Index idx
29688 \begin_layout Plain Layout
29689 Packages ! mathtools
29697 \begin_inset space ~
29703 Then you can use the command
29710 \begin_inset Index idx
29713 \begin_layout Plain Layout
29730 \begin_layout Standard
29731 \begin_inset Formula
29733 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29734 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29742 \begin_layout Section
29744 \begin_inset Index idx
29747 \begin_layout Plain Layout
29754 \begin_inset Index idx
29757 \begin_layout Plain Layout
29758 Formula ! numbering|see
29762 \begin_layout Plain Layout
29773 \begin_layout Plain Layout
29788 \begin_layout Subsection
29792 \begin_layout Standard
29793 Numbered formulas can be created with the menu
29795 Insert\SpecialChar menuseparator
29796 Math\SpecialChar menuseparator
29798 \begin_inset space ~
29806 \begin_inset space ~
29812 Existing formulas can be numbered with the menu
29814 Edit\SpecialChar menuseparator
29815 Math\SpecialChar menuseparator
29817 \begin_inset space ~
29825 arg "math-number-toggle"
29829 The formula number is displayed in \SpecialChar LyX
29830 behind the formula as a number sign
29832 The number sign is replaced in the output by the formula number.
29835 \begin_layout Standard
29836 When numbering is turned on in multiline formulas, all lines will be numbered.
29837 But the numbering can be controlled with the menu
29839 Edit\SpecialChar menuseparator
29840 Math\SpecialChar menuseparator
29842 \begin_inset space ~
29846 \begin_inset space ~
29850 \begin_inset space ~
29858 arg "math-number-line-toggle"
29864 \begin_layout Standard
29865 Except for inline formulas, all formulas can be numbered with two different
29867 \begin_inset CommandInset ref
29869 reference "sec:Formula-Styles"
29876 \begin_layout Subsection
29878 \begin_inset Index idx
29881 \begin_layout Plain Layout
29882 Cross-references ! to formulas
29890 \begin_layout Standard
29891 All labeled formulas can be cross-referenced.
29892 A label is added by the menu
29894 Insert\SpecialChar menuseparator
29897 or the toolbar button
29904 The cursor must hereby be inside a displayed formula.
29905 Alternatively you can right-click on the formula and choose
29910 A dialog pops up displaying the prefix
29915 The label is inserted there behind the prefix.
29916 The predefined prefix means
29917 \begin_inset Quotes eld
29921 \begin_inset Quotes erd
29924 and makes it easier to find labels in large documents because it marks
29925 it as formula label to divide it from e.
29926 \begin_inset space \thinspace{}
29930 \begin_inset space \space{}
29934 To change a label, the menu
29936 Insert\SpecialChar menuseparator
29939 is used again or you right-click on a formula and then on
29946 \begin_layout Standard
29947 The name of the label is displayed in \SpecialChar LyX
29948 within two parentheses behind formula.
29949 A formula with a label is always numbered.
29952 \begin_layout Standard
29953 Cross-references are inserted via the menu
29955 Insert\SpecialChar menuseparator
29958 or with the toolbar button
29961 arg "dialog-show-new-inset ref"
29965 A formula cross-reference appears in the output as formula number.
29966 When in the cross-reference dialog window the format
29970 is chosen, the cross-reference appears in the output as formula number
29972 \begin_inset Newline newline
29975 By right-clicking on a cross-reference in \SpecialChar LyX
29976 , one jumps to the formula that
29980 \begin_layout Standard
29981 Here are as examples cross-references to formulas of the following subsections:
29982 \begin_inset Note Note
29985 \begin_layout Plain Layout
29986 Note the different cross-reference types.
29994 \begin_layout Standard
29996 \begin_inset CommandInset ref
30003 \begin_inset CommandInset ref
30011 \begin_inset CommandInset ref
30017 ) big Latin letters are used for the numbering in contrary to (
30018 \begin_inset CommandInset ref
30027 \begin_layout Standard
30028 \begin_inset VSpace medskip
30031 When the argument of
30039 \begin_layout Plain Layout
30047 \begin_inset CommandInset ref
30049 reference "subsec:User-defined-Numbering"
30060 contains a box like in
30061 \begin_inset CommandInset ref
30063 reference "subsec:Paragraph-Boxes"
30067 , the formula cannot be referenced.
30070 \begin_layout Subsection
30072 \begin_inset Index idx
30075 \begin_layout Plain Layout
30076 Formula numbering ! subnumbering
30084 \begin_layout Standard
30085 With the help of the commands
30089 begin{subequations}
30097 formulas can be subnumbered.
30098 Both commands are inserted in \SpecialChar TeX
30102 \begin_layout Standard
30104 \begin_inset Formula
30115 \begin_layout Plain Layout
30119 addtocounter{equation}{-1}
30128 \begin_layout Plain Layout
30132 begin{subequations}
30138 \begin_inset VSpace -5mm
30142 \begin_inset Formula
30150 \begin_inset Formula
30160 \begin_layout Standard
30164 \begin_layout Plain Layout
30176 \begin_layout Standard
30177 To create the example, the following is done:
30180 \begin_layout Enumerate
30181 first formula is inserted
30184 \begin_layout Enumerate
30189 addtocounter{equation}{-1}
30191 begin{subequations}
30192 \begin_inset Index idx
30195 \begin_layout Plain Layout
30204 \begin_inset Newline newline
30209 is inserted after the first formula
30212 \begin_layout Enumerate
30213 second formula is inserted
30216 \begin_layout Enumerate
30217 third formula is inserted
30220 \begin_layout Enumerate
30227 is inserted after the third formula
30230 \begin_layout Standard
30231 Every formula between the commands
30243 is subnumbered as a, b,
30244 \begin_inset Newline linebreak
30247 c, \SpecialChar ldots
30248 For multiline formulas every line will be subnumbered.
30249 All subnumbered formulas are treated as
30254 But as every numbered formula increases the counter
30258 by one, the command
30264 is needed to decrease it.
30265 Otherwise the formulas
30266 \begin_inset CommandInset ref
30273 \begin_inset CommandInset ref
30280 \begin_inset CommandInset ref
30286 would be numbered as
30287 \begin_inset CommandInset ref
30294 \begin_inset CommandInset ref
30301 \begin_inset CommandInset ref
30310 \begin_layout Standard
30311 By inserting the commands in \SpecialChar TeX
30312 mode, a space is created between the first
30315 \begin_inset space \thinspace{}
30318 mm vertical space is inserted after the command
30322 begin{subequations}
30325 When the formula style
30331 \begin_layout Plain Layout
30333 \begin_inset CommandInset ref
30335 reference "sec:Formula-Styles"
30347 \begin_inset space \thinspace{}
30350 mm space is inserted instead.
30353 \begin_layout Standard
30354 Here is an example for a multiline formula where the numbering was turned
30355 off for the second line:
30359 \begin_layout Plain Layout
30363 begin{subequations}
30369 \begin_inset Formula
30371 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30372 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30373 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30382 \begin_layout Plain Layout
30394 \begin_layout Subsection
30395 User-defined Numbering
30396 \begin_inset CommandInset label
30398 name "subsec:User-defined-Numbering"
30403 \begin_inset Index idx
30406 \begin_layout Plain Layout
30407 Formula numbering ! user-defined
30415 \begin_layout Standard
30416 \begin_inset Index idx
30419 \begin_layout Plain Layout
30420 Formula numbering ! self-defined delimiters
30425 With the standard numbering parentheses are set around the formula number.
30426 To replace the parentheses for example by vertical bars, the following
30427 line is added to the \SpecialChar LaTeX
30431 \begin_layout Standard
30443 \begin_inset Note Note
30446 \begin_layout Plain Layout
30447 This macro is already declared in the \SpecialChar LaTeX
30448 -preamble for testing.
30449 To activate it, remove the percent sign at the beginning.
30457 \begin_layout Standard
30458 To use other characters, the vertical bars besides the
30462 are replaced by one ore more characters.
30463 To get only the formula number the vertical bars are omitted.
30466 \begin_layout Standard
30467 \begin_inset VSpace bigskip
30470 When there should be an expression of your choice instead of the consecutive
30471 formula number in parentheses behind the formula, the command
30478 \begin_inset Index idx
30481 \begin_layout Plain Layout
30490 \begin_inset Formula
30492 A+B=C\tag{something}\label{eq:tag}
30497 In this example the command
30502 \begin_inset space \textvisiblespace{}
30507 was inserted in the formula.
30510 \begin_layout Standard
30516 \begin_inset space \textvisiblespace{}
30521 is inserted instead, the star prevents the parentheses around the expression:
30522 \begin_inset Formula
30524 A+B=C\tag*{something}
30532 \begin_layout Standard
30533 \begin_inset VSpace bigskip
30536 To restart the formula numbering with new document parts or sections, the
30537 following command is used:
30540 \begin_layout Standard
30545 @addtoreset{equation}{part}
30548 \begin_inset Index idx
30551 \begin_layout Plain Layout
30556 \begin_layout Plain Layout
30567 \begin_layout Plain Layout
30580 \begin_layout Plain Layout
30591 \begin_layout Plain Layout
30604 \begin_inset Newline newline
30608 \begin_inset Newline newline
30615 @addtoreset{equation}{section}
30618 \begin_layout Standard
30619 To be able to use these commands in \SpecialChar TeX
30621 \begin_inset Quotes eld
30625 \begin_inset Quotes erd
30628 character has to be made
30629 \begin_inset Quotes eld
30633 \begin_inset Quotes erd
30636 for \SpecialChar LaTeX
30651 So the command sequence in \SpecialChar TeX
30655 \begin_layout Standard
30661 \begin_inset Newline newline
30666 @addtoreset{equation}{section}
30667 \begin_inset Newline newline
30675 \begin_layout Standard
30676 In the \SpecialChar LaTeX
30689 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30693 \begin_layout Standard
30708 \begin_layout Plain Layout
30713 is part of the \SpecialChar LaTeX
30719 \begin_inset Index idx
30722 \begin_layout Plain Layout
30723 Packages ! carlisle
30728 that is part of every \SpecialChar LaTeX
30729 standard installation.
30735 \begin_inset Index idx
30738 \begin_layout Plain Layout
30739 Packages ! remreset
30744 has to be loaded in the \SpecialChar LaTeX
30745 -preamble with the line
30748 \begin_layout Standard
30753 usepackage{remreset}
30756 \begin_layout Standard
30764 \begin_inset Index idx
30767 \begin_layout Plain Layout
30772 \begin_layout Plain Layout
30783 \begin_layout Plain Layout
30796 \begin_layout Plain Layout
30807 \begin_layout Plain Layout
30819 can be used with the same scheme as
30828 \begin_layout Standard
30829 \begin_inset VSpace bigskip
30832 Sometimes formulas should be numbered in the following form:
30835 \begin_layout Standard
30838 (section number.formula number)
30841 \begin_layout Standard
30842 The formula number should start with every section with
30843 \begin_inset Quotes eld
30847 \begin_inset Quotes erd
30853 \begin_layout Standard
30854 For this case there is the command
30861 \begin_inset Index idx
30864 \begin_layout Plain Layout
30872 , which is used with the following scheme:
30875 \begin_layout Standard
30880 numberwithin{counter}{sectioning}
30883 \begin_layout Standard
30884 Counter denotes what kind of numbering is affected, sectioning denotes what
30885 number is before the dot.
30888 \begin_layout Standard
30889 Thus in our case the following \SpecialChar LaTeX
30890 preamble or \SpecialChar TeX
30894 \begin_layout Standard
30899 numberwithin{equation}{section}
30902 \begin_layout Standard
30903 This is the result:
30907 \begin_layout Plain Layout
30911 numberwithin{equation}{section}
30917 \begin_inset Formula
30927 \begin_layout Standard
30929 \begin_inset space \thinspace{}
30933 \begin_inset space \space{}
30936 tables so that the number of the part is the sectioning,
30937 \begin_inset Newline newline
30944 numberwithin{table}{part}
30949 \begin_layout Standard
30950 To go back to the standard numbering or to prevent this kind of numbering
30951 when it is defined by the document class, the following command is inserted
30952 as \SpecialChar TeX
30953 code or to the \SpecialChar LaTeX
30957 \begin_layout Standard
30967 \begin_inset Index idx
30970 \begin_layout Plain Layout
30984 \begin_layout Plain Layout
31000 \begin_inset Newline newline
31008 \begin_inset Newline newline
31020 \begin_layout Standard
31027 uses internally the command
31033 , described above, that also needs to be reverted.
31037 \begin_layout Plain Layout
31044 \begin_layout Plain Layout
31048 @removefromreset{equation}{section}
31051 \begin_layout Plain Layout
31063 \begin_layout Subsection
31064 Numbering with Roman Numbers and Letters
31065 \begin_inset Index idx
31068 \begin_layout Plain Layout
31069 Formula numbering ! with letters
31075 \begin_inset Index idx
31078 \begin_layout Plain Layout
31079 Formula numbering ! with Roman numbers
31087 \begin_layout Standard
31088 Formulas can also be numbered with Roman numbers and Latin letters.
31089 To number for example with small Roman numbers, the command
31092 \begin_layout Standard
31104 \begin_layout Standard
31105 is inserted before the formula in \SpecialChar TeX
31114 \begin_inset Index idx
31117 \begin_layout Plain Layout
31125 redefines the predefined command
31141 \begin_layout Plain Layout
31148 has the same scheme like the command
31154 that is described in
31155 \begin_inset CommandInset ref
31157 reference "subsec:The-Command-newcommand"
31170 is the formula counter.
31177 is used as prefix for a counter, the value of the counter is output as
31179 When a formula is numbered, \SpecialChar LaTeX
31180 sets internally the command
31186 behind the formula.
31192 \begin_inset Index idx
31195 \begin_layout Plain Layout
31205 outputs the counter as small Roman number.
31208 \begin_layout Standard
31209 All formulas behind the command
31219 are now numbered Roman.
31220 To switch to numbering with big Roman numbers, the command is inserted
31234 \begin_inset Index idx
31237 \begin_layout Plain Layout
31249 \begin_inset Quotes eld
31253 \begin_inset Quotes erd
31256 with small Latin letters there is the command
31263 \begin_inset Index idx
31266 \begin_layout Plain Layout
31274 , for big ones there is the command
31281 \begin_inset Index idx
31284 \begin_layout Plain Layout
31297 \begin_layout Standard
31298 \begin_inset Note Greyedout
31301 \begin_layout Plain Layout
31308 \begin_inset space ~
31311 formulas can be numbered with Latin letters in one document.
31319 \begin_layout Standard
31323 \begin_layout Plain Layout
31339 \begin_layout Standard
31340 \begin_inset Formula
31342 A=\textrm{small roman}
31351 \begin_layout Plain Layout
31365 \begin_inset Formula
31367 B=\textrm{big Roman}\label{eq:Rom}
31376 \begin_layout Plain Layout
31390 \begin_inset Formula
31392 C=\textrm{small Latin}
31401 \begin_layout Plain Layout
31415 \begin_inset Formula
31417 D=\textrm{big Latin}\label{eq:Lat}
31425 \begin_layout Standard
31426 To switch back to the default numbering, insert the command:
31429 \begin_layout Standard
31439 \begin_inset Index idx
31442 \begin_layout Plain Layout
31453 \begin_layout Standard
31457 \begin_layout Plain Layout
31471 \begin_inset Formula
31481 \begin_layout Standard
31482 \begin_inset VSpace medskip
31485 As you see, formulas are numbered serially independent from the numbering
31487 When then numbering should start with
31488 \begin_inset Quotes eld
31492 \begin_inset Quotes erd
31495 when the style is changed, new equation counters have to be defined.
31496 A description about this can be found in the file
31497 \begin_inset CommandInset href
31499 name "Formula-numbering.lyx"
31500 target "run:Formula-numbering.lyx"
31507 \begin_layout Section
31508 Chemical Symbols and Equations
31509 \begin_inset CommandInset label
31511 name "subsec:Chemical-Symbols-and"
31516 \begin_inset Index idx
31519 \begin_layout Plain Layout
31520 Chemical characters ! Symbols
31526 \begin_inset Index idx
31529 \begin_layout Plain Layout
31536 \begin_inset Index idx
31539 \begin_layout Plain Layout
31548 \begin_layout Standard
31549 An example text from chemistry:
31552 \begin_layout Quote
31554 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31557 -ion reacts with two
31558 \begin_inset Formula $\mathrm{Na^{+}}$
31561 -ions to sodium sulfate
31562 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31566 The chemical equation for this is:
31567 \begin_inset Formula
31569 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31577 \begin_layout Standard
31578 This chemical equation can directly be created as formula.
31579 To avoid that the symbols appear italic, everything is highlighted and
31580 changed by the shortcut
31586 to the upright font style.
31590 \begin_layout Plain Layout
31596 \begin_inset CommandInset ref
31598 reference "subsec:Font-Styles"
31610 \begin_layout Standard
31611 A more convenient way to typeset chemical formulas is to use the command
31619 \begin_inset Index idx
31622 \begin_layout Plain Layout
31630 that is available when the \SpecialChar LaTeX
31636 \begin_inset Index idx
31639 \begin_layout Plain Layout
31652 to a formula a new blue box appears where chemical formulas can be inserted
31653 in an intuitive way.
31654 \begin_inset Separator parbreak
31660 \begin_layout Standard
31662 \begin_inset Tabular
31663 <lyxtabular version="3" rows="10" columns="2">
31664 <features booktabs="true" tabularvalignment="middle">
31665 <column alignment="center" valignment="top" width="0pt">
31666 <column alignment="center" valignment="top">
31668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31671 \begin_layout Plain Layout
31677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31680 \begin_layout Plain Layout
31688 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31691 \begin_layout Plain Layout
31695 \begin_inset space \textvisiblespace{}
31703 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31706 \begin_layout Plain Layout
31707 \begin_inset Formula $\ce{H2CO3}$
31716 <row topspace="1.5mm">
31717 <cell alignment="center" valignment="top" usebox="none">
31720 \begin_layout Plain Layout
31724 \begin_inset space \textvisiblespace{}
31732 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31735 \begin_layout Plain Layout
31736 \begin_inset Formula $\ce{SO4^{2-}}$
31745 <row topspace="1.5mm">
31746 <cell alignment="center" valignment="top" usebox="none">
31749 \begin_layout Plain Layout
31753 \begin_inset space \textvisiblespace{}
31761 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31764 \begin_layout Plain Layout
31765 \begin_inset Formula $\ce{(NH4)2S}$
31774 <row topspace="1.5mm">
31775 <cell alignment="center" valignment="top" usebox="none">
31778 \begin_layout Plain Layout
31782 \begin_inset space \textvisiblespace{}
31790 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31793 \begin_layout Plain Layout
31794 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31803 <row topspace="1.5mm">
31804 <cell alignment="center" valignment="top" usebox="none">
31807 \begin_layout Plain Layout
31811 \begin_inset space \textvisiblespace{}
31817 \begin_inset space \textvisiblespace{}
31823 \begin_inset space \textvisiblespace{}
31831 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31834 \begin_layout Plain Layout
31835 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31844 <row topspace="1.5mm">
31845 <cell alignment="center" valignment="top" usebox="none">
31848 \begin_layout Plain Layout
31852 \begin_inset space \textvisiblespace{}
31856 \begin_inset Formula $\downarrow$
31860 \begin_inset Formula $\to$
31868 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31871 \begin_layout Plain Layout
31872 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31882 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31885 \begin_layout Plain Layout
31889 \begin_inset space \textvisiblespace{}
31895 \begin_inset space \textvisiblespace{}
31901 \begin_inset space \textvisiblespace{}
31909 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31912 \begin_layout Plain Layout
31913 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31926 \begin_layout Plain Layout
31930 \begin_inset space \textvisiblespace{}
31934 \begin_inset space \textvisiblespace{}
31938 \begin_inset space \textvisiblespace{}
31942 \begin_inset space \textvisiblespace{}
31946 \begin_inset space \textvisiblespace{}
31954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31957 \begin_layout Plain Layout
31958 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31967 <row topspace="1.5mm">
31968 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31971 \begin_layout Plain Layout
31975 \begin_inset space \textvisiblespace{}
31979 \begin_inset space \textvisiblespace{}
31983 \begin_inset space \textvisiblespace{}
31987 \begin_inset space \textvisiblespace{}
31995 \begin_inset space \textvisiblespace{}
32003 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
32006 \begin_layout Plain Layout
32007 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
32023 \begin_layout Standard
32024 \begin_inset Note Greyedout
32027 \begin_layout Plain Layout
32033 It is not possible in \SpecialChar LyX
32034 to use the character ^ to get an up-arrow as described
32040 One instead uses a negative thin space followed by the command
32047 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32058 \begin_layout Standard
32065 the command for equation
32066 \begin_inset space ~
32070 \begin_inset CommandInset ref
32072 reference "eq:chem-reaction"
32077 \begin_inset Newline newline
32085 \begin_inset space \textvisiblespace{}
32089 \begin_inset space \textvisiblespace{}
32093 \begin_inset space \textvisiblespace{}
32097 \begin_inset space \textvisiblespace{}
32101 \begin_inset space \textvisiblespace{}
32105 \begin_inset space \textvisiblespace{}
32111 \begin_layout Standard
32112 To create multiline chemical equations first a multiline formula is created
32114 \begin_inset CommandInset ref
32116 reference "sec:Multiline-Formulas"
32121 Afterwards the command
32127 is used in every small blue box of the formula.
32129 \begin_inset CommandInset ref
32131 reference "eq:TEOS-reaction-1"
32136 \begin_inset CommandInset ref
32138 reference "eq:TEOS-reaction-2"
32142 are an example of a multi-stage chemical reaction where every equation
32143 has its own number.
32144 \begin_inset Formula
32146 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32147 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32155 \begin_layout Standard
32166 package provides the command
32173 \begin_inset Index idx
32176 \begin_layout Plain Layout
32184 that has to be used for special cases.
32185 For more information about
32191 and more examples have a look at the documentation of
32196 \begin_inset CommandInset citation
32205 \begin_layout Section
32209 \begin_layout Standard
32211 supports two types of commutative diagrams:
32219 that are explained in the following.
32222 \begin_layout Subsection
32224 \begin_inset Index idx
32227 \begin_layout Plain Layout
32236 \begin_layout Standard
32237 Diagrams of this type visualize relations by vertical and horizontal lines
32239 \begin_inset Formula
32241 \begin{CD}A@>>>B@>>>C\\
32252 \begin_layout Standard
32253 To get them, the command
32258 \begin_inset Index idx
32261 \begin_layout Plain Layout
32271 is inserted to a formula.
32272 A blue box appears with two dashed lines where further commands can be
32277 arg "newline-insert newline"
32280 a new line is created.
32281 Horizontal relations are inserted in odd, vertical in even formula lines.
32284 \begin_layout Standard
32285 To create the relations there are the following commands:
32288 \begin_layout Itemize
32293 creates a left arrow,
32304 \begin_layout Itemize
32309 creates an up arrow,
32317 a vertical equal sign
32320 \begin_layout Itemize
32326 is a placeholder for non-existent relations
32329 \begin_layout Standard
32330 All arrows can be labeled as follows:
32333 \begin_layout Itemize
32334 If text inserted between the first and second < or >, resp., it is placed
32336 When it is inserted between the second and third one, it appears under
32340 \begin_layout Itemize
32341 When text for vertical arrows is inserted between the first and second A
32342 or V, resp., it is placed left beside the arrow.
32343 When it is inserted between the second and third one, it appears right
32345 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32349 \begin_layout Standard
32350 As example a diagram with all possible relations:
32353 \begin_layout Standard
32354 \begin_inset Formula
32356 \begin{CD}A@>j>>B@>>k>C@=F\\
32367 \begin_layout Standard
32368 The command for this is:
32369 \begin_inset Newline newline
32377 \begin_inset space \textvisiblespace{}
32380 A@>j>>B@>>k>C@=F Ctrl+Return
32381 \begin_inset Newline newline
32385 \begin_inset Phantom HPhantom
32388 \begin_layout Plain Layout
32394 \begin_inset space \textvisiblespace{}
32407 \begin_inset Formula $\to$
32413 \begin_inset Newline newline
32417 \begin_inset Phantom HPhantom
32420 \begin_layout Plain Layout
32426 \begin_inset space \textvisiblespace{}
32437 \begin_layout Subsection
32439 \begin_inset Index idx
32442 \begin_layout Plain Layout
32443 Diagrams ! xymatrix
32451 \begin_layout Standard
32452 To be able to use xymatrices, the \SpecialChar LaTeX
32458 A xymatrix is created by inserting the command
32465 Then you are able to add new matrix columns and rows like for normal matrices,
32467 \begin_inset CommandInset ref
32469 reference "sec:Matrices"
32476 \begin_layout Standard
32477 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32479 All possibilities to create commutative diagrams and decorations are explained
32484 that you find in the menu
32486 Help\SpecialChar menuseparator
32488 \begin_inset space ~
32496 \begin_layout Subsection
32502 \begin_inset Index idx
32505 \begin_layout Plain Layout
32514 \begin_layout Standard
32519 -diagrams, the \SpecialChar LaTeX
32529 -diagram is created by inserting the command
32536 Then you are able to add new matrix columns and rows like for normal matrices,
32538 \begin_inset CommandInset ref
32540 reference "sec:Matrices"
32547 \begin_layout Standard
32548 Examples how to create
32552 diagrams in \SpecialChar LyX
32555 Feynman-diagram manual
32557 that you find in the menu
32559 Help\SpecialChar menuseparator
32561 \begin_inset space ~
32569 \begin_layout Standard
32570 \begin_inset Newpage newpage
32576 \begin_layout Section
32577 User-defined Commands
32578 \begin_inset Index idx
32581 \begin_layout Plain Layout
32582 User-defined commands
32590 \begin_layout Standard
32591 \begin_inset Note Greyedout
32594 \begin_layout Plain Layout
32599 The names of user-defined commands and macros may only consist of Latin
32608 \begin_layout Subsection
32612 \begin_inset CommandInset label
32614 name "subsec:The-Command-newcommand"
32619 \begin_inset Index idx
32622 \begin_layout Plain Layout
32623 User-defined commands !
32631 \begin_inset Index idx
32634 \begin_layout Plain Layout
32645 \begin_layout Standard
32646 Many \SpecialChar LaTeX
32647 -commands are too long to be used frequently.
32648 But it is possible to define with the command
32654 new shorter commands.
32657 \begin_layout Standard
32658 The command scheme of
32667 \begin_layout Standard
32672 newcommand{new command name}[number of arguments][optional
32677 \begin_inset Newline newline
32681 \begin_inset Phantom HPhantom
32684 \begin_layout Plain Layout
32694 {command definition}
32697 \begin_layout Standard
32698 \begin_inset Note Greyedout
32701 \begin_layout Plain Layout
32706 Assure that the name of the new command is not already used in your document
32707 or by \SpecialChar LaTeX
32708 -packages that you use.
32709 When you for example define the command
32721 , you get an error message because
32727 is already defined as command for
32728 \begin_inset Quotes eld
32732 \begin_inset Formula $\le$
32736 \begin_inset Quotes erd
32747 \begin_layout Standard
32748 The number of arguments is an integer in the range 0
32749 \begin_inset space \thinspace{}
32753 \begin_inset space \thinspace{}
32756 9 and specifies how many arguments the new command should have.
32757 With the optional value a value for an optional argument can be predefined.
32758 When this is done, the
32766 rgument of the new command is automatically an optional one.
32769 \begin_layout Standard
32770 Here are some examples:
32773 \begin_layout Itemize
32774 To define the command
32786 , the \SpecialChar LaTeX
32788 \begin_inset VSpace medskip
32792 \begin_inset Newline newline
32806 \begin_layout Itemize
32807 To define the command
32819 , the argument (that should be underlined) must be taken into account.
32820 For this the preamble line is:
32821 \begin_inset VSpace medskip
32825 \begin_inset Newline newline
32839 \begin_inset VSpace medskip
32843 \begin_inset Newline newline
32850 acts as argument placeholder, the
32854 behind it denotes that it is the placeholder for the first argument.
32857 \begin_layout Itemize
32865 \begin_inset space \thinspace{}
32869 \begin_inset space \space{}
32879 \begin_inset VSpace medskip
32883 \begin_inset Newline newline
32894 framebox#1#2{$#3$}}
32897 \begin_inset VSpace medskip
32901 \begin_inset Newline newline
32904 The two Dollar signs creates the extra formula needed for
32911 \begin_inset CommandInset ref
32913 reference "subsec:Boxes-with-Frame"
32920 \begin_layout Itemize
32921 To create a new command for
32927 where the color for the box need not be specified, the argument for the
32928 color is defined optional:
32929 \begin_inset VSpace medskip
32933 \begin_inset Newline newline
32944 fcolorbox{#2}{#1}{$#3$}}
32947 \begin_inset VSpace medskip
32951 \begin_inset Newline newline
32954 When the color is not specified when using
32960 , the predefined color
32967 \begin_layout Standard
32968 A test of the new defined commands:
32969 \begin_inset Separator parbreak
32975 \begin_layout Standard
32977 \begin_inset Tabular
32978 <lyxtabular version="3" rows="6" columns="2">
32979 <features booktabs="true" tabularvalignment="middle">
32980 <column alignment="center" valignment="top" width="0pt">
32981 <column alignment="center" valignment="top">
32983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32986 \begin_layout Plain Layout
32992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32995 \begin_layout Plain Layout
33003 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33006 \begin_layout Plain Layout
33010 \begin_inset space \textvisiblespace{}
33018 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33021 \begin_layout Plain Layout
33022 \begin_inset Formula $A\gr B$
33032 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33035 \begin_layout Plain Layout
33043 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33046 \begin_layout Plain Layout
33047 \begin_inset Formula $\us{ABcd}$
33056 <row topspace="1mm">
33057 <cell alignment="center" valignment="top" usebox="none">
33060 \begin_layout Plain Layout
33064 \begin_inset Formula $\to$
33070 \begin_inset Formula $\to$
33078 \begin_inset space \textvisiblespace{}
33086 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33089 \begin_layout Plain Layout
33090 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33099 <row topspace="1.5mm">
33100 <cell alignment="center" valignment="top" usebox="none">
33103 \begin_layout Plain Layout
33107 \begin_inset Formula $\to$
33115 \begin_inset space \textvisiblespace{}
33123 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33126 \begin_layout Plain Layout
33127 \begin_inset Formula $\cb{red}{\int A=B}$
33136 <row topspace="1.5mm" bottomspace="1mm">
33137 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33140 \begin_layout Plain Layout
33146 \begin_inset Formula $\to$
33154 \begin_inset space \textvisiblespace{}
33162 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33165 \begin_layout Plain Layout
33166 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33182 \begin_layout Subsection
33184 \begin_inset Index idx
33187 \begin_layout Plain Layout
33188 User-defined commands! Math macros
33194 \begin_inset Index idx
33197 \begin_layout Plain Layout
33206 \begin_layout Standard
33207 User-defined commands are especially convenient for complex expressions.
33208 When you are for example dealing with a document that has quadratic equations,
33209 the same solution type occurs several times.
33210 The general form of a quadratic equation is
33211 \begin_inset Formula
33213 0=\lambda^{2}+p\lambda+q
33218 The general form of the solution is
33219 \begin_inset Formula
33221 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33229 \begin_layout Standard
33230 To define a command for the solution formula where only the three parameters
33232 \begin_inset Formula $\lambda$
33236 \begin_inset Formula $p$
33240 \begin_inset Formula $q$
33243 need to be specified and the index of
33244 \begin_inset Formula $\lambda$
33247 can be given optionally, the \SpecialChar LaTeX
33249 \begin_inset Newline newline
33265 \begin_inset Newline newline
33269 \begin_inset Phantom HPhantom
33272 \begin_layout Plain Layout
33286 frac{#3^{2}}{4}-#4}}
33289 \begin_layout Standard
33290 To create with this the solution formula, the command
33291 \begin_inset Newline newline
33301 \begin_inset Formula $\to$
33307 \begin_inset Formula $\to$
33314 is inserted to a formula
33319 \begin_layout Standard
33320 The definition of the new command is unintuitive because one has to know
33321 the schemes of all used \SpecialChar LaTeX
33323 \begin_inset space \thinspace{}
33327 \begin_inset space \space{}
33330 that a fraction is inserted in \SpecialChar LaTeX
33335 frac{numerator}{denominator}
33338 Furthermore one can easily forget a brace in the definition and cannot
33339 see in \SpecialChar LyX
33340 what the new command is doing.
33341 To avoid these problems \SpecialChar LyX
33342 offers the possibility to use math macros instead
33352 \begin_layout Standard
33353 A math macro is created by using the menu
33355 Insert\SpecialChar menuseparator
33356 Math\SpecialChar menuseparator
33359 or the toolbar button
33362 arg "math-macro newmacroname_newcommand"
33366 The math macro toolbar appears together with the following box where the
33368 \begin_inset Newline newline
33372 \begin_inset space \hspace*{\fill}
33376 \begin_inset Graphics
33377 filename clipart/macrobox.png
33383 \begin_inset space \hspace*{\fill}
33387 \begin_inset Newline newline
33391 \begin_inset FormulaMacro
33392 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33397 newmacroname is the default name of the macro that should be changed to
33398 something sensible.
33399 The wanted formula is inserted in the first blue box.
33400 An argument placeholder is inserted with the command
33407 \begin_inset space \thinspace{}
33411 \begin_inset space \space{}
33420 or by using the macro toolbar button
33423 arg "math-macro-add-param"
33427 Argument placeholders are displayed red.
33429 \begin_inset space ~
33432 arguments are possible.
33433 Optional arguments are created with the toolbar button
33436 arg "math-macro-add-optional-param"
33440 The first non-optional argument can be transformed to an optional one with
33444 arg "math-macro-make-optional"
33448 In the second blue box the appearance of the macro in \SpecialChar LyX
33450 Normally you want to see it as it is defined, so the box is kept empty.
33451 But when you have created a macro that needs lot of space on the screen,
33452 you can insert in the box for example
33453 \begin_inset Newline newline
33483 \begin_inset Newline newline
33488 For the macro only the arguments with the macro name in front of them will
33489 then be displayed in \SpecialChar LyX
33490 , leading to a better overview.
33491 The formula appears in the output as defined in the first box.
33492 \begin_inset Newline newline
33495 The appearance of macros in formulas can furthermore be changed for single
33496 macros by setting the cursor in the macro and using the menu
33498 View\SpecialChar menuseparator
33500 \begin_inset space ~
33504 \begin_inset space ~
33512 \begin_layout Standard
33513 To use a macro, the macro name is inserted as command to a formula, in our
33521 Our macro looks in \SpecialChar LyX
33523 \begin_inset Newline newline
33527 \begin_inset space \hspace*{\fill}
33531 \begin_inset Graphics
33532 filename clipart/macrouse.png
33538 \begin_inset space \hspace*{\fill}
33542 \begin_inset Newline newline
33545 Here is our macro example with the arguments
33546 \begin_inset Formula $x$
33550 \begin_inset Formula $\ln(x)$
33554 \begin_inset Formula $B$
33560 \begin_layout Standard
33561 \begin_inset Formula
33571 \begin_layout Standard
33575 Tools\SpecialChar menuseparator
33576 Preferences\SpecialChar menuseparator
33577 Editing\SpecialChar menuseparator
33580 different styles to edit macros.
33581 To find the style that suits you the most, choose a style and set the cursor
33582 in a macro formula to see the difference.
33585 \begin_layout Standard
33586 A math macro is transformed internally to a
33592 command when exporting the document.
33599 command is not placed in the \SpecialChar LaTeX
33600 -preamble, therefore macros can only be used
33601 in formulas that are in the document below the macro definition box.
33604 \begin_layout Standard
33605 Math macros can also be directly created from a
33612 When writing for example the command
33615 \begin_inset Newline newline
33624 xleftarrow[#2]{#1}}
33625 \begin_inset Newline newline
33630 in \SpecialChar LyX
33631 as normal text, highlighting it completely and using then the shortcut
33636 , the command will be transformed to a math macro.
33637 Using this method you need to be careful that the
33643 command is typed correctly, otherwise you get a faulty macro leading to
33648 \begin_layout Standard
33649 Math macros currently have the problem that further formulas in macro definition
33650 s are handled wrongly.
33651 Therefore the example
33658 \begin_inset CommandInset ref
33660 reference "subsec:The-Command-newcommand"
33664 cannot be created as macro.
33667 \begin_layout Standard
33668 When the cursor is in a macro definition box, you will see the macro toolbar
33669 in \SpecialChar LyX
33673 \begin_layout Standard
33674 \begin_inset VSpace defskip
33680 \begin_layout Standard
33681 \begin_inset Graphics
33682 filename clipart/MacroToolbar.png
33687 \begin_inset Index idx
33690 \begin_layout Plain Layout
33699 \begin_layout Standard
33700 \begin_inset VSpace defskip
33706 \begin_layout Standard
33707 The macro toolbar contains from left to right the following buttons:
33710 \begin_layout Standard
33711 \begin_inset VSpace defskip
33717 \begin_layout Standard
33718 \begin_inset Tabular
33719 <lyxtabular version="3" rows="9" columns="2">
33720 <features islongtable="true" longtabularalignment="center">
33721 <column alignment="left" valignment="top">
33722 <column alignment="left" valignment="top" width="85col%">
33723 <row interlinespace="2.5mm">
33724 <cell alignment="center" valignment="top" usebox="none">
33727 \begin_layout Plain Layout
33730 arg "math-macro-remove-param"
33738 <cell alignment="center" valignment="top" usebox="none">
33741 \begin_layout Plain Layout
33744 Edit\SpecialChar menuseparator
33745 Math\SpecialChar menuseparator
33747 \begin_inset space ~
33750 Definition\SpecialChar menuseparator
33751 Remove Last Argument
33757 <row interlinespace="2.5mm">
33758 <cell alignment="center" valignment="top" usebox="none">
33761 \begin_layout Plain Layout
33764 arg "math-macro-add-param"
33772 <cell alignment="center" valignment="top" usebox="none">
33775 \begin_layout Plain Layout
33778 Edit\SpecialChar menuseparator
33779 Math\SpecialChar menuseparator
33781 \begin_inset space ~
33784 Definition\SpecialChar menuseparator
33791 <row interlinespace="2.5mm">
33792 <cell alignment="center" valignment="top" usebox="none">
33795 \begin_layout Plain Layout
33798 arg "math-macro-make-optional"
33806 <cell alignment="center" valignment="top" usebox="none">
33809 \begin_layout Plain Layout
33812 Edit\SpecialChar menuseparator
33813 Math\SpecialChar menuseparator
33815 \begin_inset space ~
33818 Definition\SpecialChar menuseparator
33819 Transform First Non-Optional to
33820 \begin_inset Newline newline
33824 \begin_inset Phantom HPhantom
33827 \begin_layout Plain Layout
33830 Edit\SpecialChar menuseparator
33831 Math\SpecialChar menuseparator
33833 \begin_inset space ~
33836 Definition\SpecialChar menuseparator
33848 <row interlinespace="2.5mm">
33849 <cell alignment="center" valignment="top" usebox="none">
33852 \begin_layout Plain Layout
33855 arg "math-macro-make-nonoptional"
33863 <cell alignment="center" valignment="top" usebox="none">
33866 \begin_layout Plain Layout
33869 Edit\SpecialChar menuseparator
33870 Math\SpecialChar menuseparator
33872 \begin_inset space ~
33875 Definition\SpecialChar menuseparator
33876 Transform Last Optional to
33877 \begin_inset Newline newline
33881 \begin_inset Phantom HPhantom
33884 \begin_layout Plain Layout
33887 Edit\SpecialChar menuseparator
33888 Math\SpecialChar menuseparator
33890 \begin_inset space ~
33893 Definition\SpecialChar menuseparator
33899 Non-Optional Argument
33905 <row interlinespace="2.5mm">
33906 <cell alignment="center" valignment="top" usebox="none">
33909 \begin_layout Plain Layout
33912 arg "math-macro-remove-optional-param"
33920 <cell alignment="center" valignment="top" usebox="none">
33923 \begin_layout Plain Layout
33926 Edit\SpecialChar menuseparator
33927 Math\SpecialChar menuseparator
33929 \begin_inset space ~
33932 Definition\SpecialChar menuseparator
33933 Remove Optional Argument
33939 <row interlinespace="2.5mm">
33940 <cell alignment="center" valignment="top" usebox="none">
33943 \begin_layout Plain Layout
33946 arg "math-macro-add-optional-param"
33954 <cell alignment="center" valignment="top" usebox="none">
33957 \begin_layout Plain Layout
33960 Edit\SpecialChar menuseparator
33961 Math\SpecialChar menuseparator
33963 \begin_inset space ~
33966 Definition\SpecialChar menuseparator
33967 Insert Optional Argument
33973 <row interlinespace="2.5mm">
33974 <cell alignment="center" valignment="top" usebox="none">
33977 \begin_layout Plain Layout
33980 arg "math-macro-remove-greedy-param"
33988 <cell alignment="center" valignment="top" usebox="none">
33991 \begin_layout Plain Layout
33994 Edit\SpecialChar menuseparator
33995 Math\SpecialChar menuseparator
33997 \begin_inset space ~
34000 Definition\SpecialChar menuseparator
34001 Remove Last Argument
34002 \begin_inset Newline newline
34006 \begin_inset Phantom HPhantom
34009 \begin_layout Plain Layout
34012 Edit\SpecialChar menuseparator
34013 Math\SpecialChar menuseparator
34015 \begin_inset space ~
34018 Definition\SpecialChar menuseparator
34024 Spitting Out To The Right
34030 <row interlinespace="2.5mm">
34031 <cell alignment="center" valignment="top" usebox="none">
34034 \begin_layout Plain Layout
34037 arg "math-macro-append-greedy-param"
34045 <cell alignment="center" valignment="top" usebox="none">
34048 \begin_layout Plain Layout
34051 Edit\SpecialChar menuseparator
34052 Math\SpecialChar menuseparator
34054 \begin_inset space ~
34057 Definition\SpecialChar menuseparator
34059 \begin_inset Newline newline
34063 \begin_inset Phantom HPhantom
34066 \begin_layout Plain Layout
34069 Edit\SpecialChar menuseparator
34070 Math\SpecialChar menuseparator
34072 \begin_inset space ~
34075 Definition\SpecialChar menuseparator
34081 Eating From The Right
34087 <row interlinespace="2.5mm">
34088 <cell alignment="center" valignment="top" usebox="none">
34091 \begin_layout Plain Layout
34094 arg "math-macro-add-greedy-optional-param"
34102 <cell alignment="center" valignment="top" usebox="none">
34105 \begin_layout Plain Layout
34108 Edit\SpecialChar menuseparator
34109 Math\SpecialChar menuseparator
34111 \begin_inset space ~
34114 Definition\SpecialChar menuseparator
34115 Append Optional Argument
34116 \begin_inset Newline newline
34120 \begin_inset Phantom HPhantom
34123 \begin_layout Plain Layout
34126 Edit\SpecialChar menuseparator
34127 Math\SpecialChar menuseparator
34129 \begin_inset space ~
34132 Definition\SpecialChar menuseparator
34138 Eating From The Right
34151 \begin_layout Section
34152 Computer Algebra Systems
34155 \begin_layout Standard
34157 offers the exchange between mathematical expressions written in \SpecialChar LyX
34159 editor and external applications or user defined scripts.
34160 Currently supported applications are
34177 Note that the set of supported mathematical constructs is limited only
34178 to very simple cases.
34181 \begin_layout Subsection
34185 \begin_layout Standard
34186 Write some expression in a formula, go to the
34188 Edit\SpecialChar menuseparator
34189 Math\SpecialChar menuseparator
34190 Use Computer Algebra System
34192 menu and choose the application you have installed on the computer.
34193 After that the result of computation should show on the right side of the
34194 expression together with the
34195 \begin_inset Quotes eld
34199 \begin_inset Quotes erd
34205 \begin_layout Standard
34206 Here are few simple examples (with results from
34210 ) to show what kind of computations can be performed:
34213 \begin_layout Itemize
34214 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34220 \begin_layout Itemize
34221 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34227 \begin_layout Itemize
34228 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34234 \begin_layout Itemize
34235 \begin_inset Formula $\det\left[\begin{array}{ccc}
34239 \end{array}\right]=-56$
34245 \begin_layout Itemize
34246 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34252 \begin_layout Subsection
34256 \begin_layout Standard
34257 Currently there is no keyboard shortcut for calling the algebra applications.
34258 One can easily bind a shortcut to the
34272 \begin_inset space \thinspace{}
34276 \begin_inset space \space{}
34283 key inside the math editor.
34288 one would use this shortcut definition command:
34291 \begin_layout Standard
34294 command-alternatives paragraph-break;math-extern maxima
34297 \begin_layout Section
34299 \begin_inset Index idx
34302 \begin_layout Plain Layout
34311 \begin_layout Subsection
34313 \begin_inset Index idx
34316 \begin_layout Plain Layout
34325 \begin_layout Standard
34326 Negative numbers often look ugly in formulas because the minus sign before
34327 the number is set with the same length as the minus operator sign.
34328 When writing the negative number in normal text, the minus sign appears
34332 \begin_layout Standard
34333 Thus, the problem disappears when converting the minus sign to mathematical
34337 \begin_layout Standard
34338 An example to visualize the problem:
34339 \begin_inset Separator parbreak
34345 \begin_layout Standard
34347 \begin_inset Tabular
34348 <lyxtabular version="3" rows="3" columns="2">
34349 <features booktabs="true" tabularvalignment="middle">
34350 <column alignment="right" valignment="top" width="0pt">
34351 <column alignment="left" valignment="top">
34353 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34356 \begin_layout Plain Layout
34362 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34365 \begin_layout Plain Layout
34373 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34376 \begin_layout Plain Layout
34382 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34385 \begin_layout Plain Layout
34386 \begin_inset Formula $x=-2$
34396 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34399 \begin_layout Plain Layout
34405 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34408 \begin_layout Plain Layout
34409 \begin_inset Formula $x=\textrm{-}2$
34425 \begin_layout Subsection
34426 Comma as decimal Separator
34427 \begin_inset Index idx
34430 \begin_layout Plain Layout
34439 \begin_layout Standard
34440 In \SpecialChar LaTeX
34441 a comma inside a formula is used, according to the English convention,
34442 as number group separator.
34443 So there will be space added behind all commas in formulas.
34446 \begin_layout Standard
34447 To avoid this, the comma is highlighted and changed to mathematical text
34457 \begin_layout Standard
34458 To use all formula commas in the document as decimal separator, the file
34467 \begin_layout Plain Layout
34472 is part of the \SpecialChar LaTeX
34478 \begin_inset Index idx
34481 \begin_layout Plain Layout
34486 \begin_layout Plain Layout
34506 \begin_inset Index idx
34509 \begin_layout Plain Layout
34515 is loaded with the \SpecialChar LaTeX
34519 \begin_layout Standard
34527 \begin_layout Subsection
34529 \begin_inset CommandInset label
34531 name "subsec:Physical-Vectors"
34536 \begin_inset Index idx
34539 \begin_layout Plain Layout
34548 \begin_layout Standard
34549 Predefined vectors are offered by the \SpecialChar LaTeX
34555 \begin_inset Index idx
34558 \begin_layout Plain Layout
34564 that is loaded with the \SpecialChar LaTeX
34568 \begin_layout Standard
34576 \begin_layout Standard
34580 \begin_layout Plain Layout
34590 \begin_inset Note Note
34593 \begin_layout Plain Layout
34594 The following table will only be displayed when the \SpecialChar LaTeX
34607 \begin_layout Standard
34608 The following commands are defined:
34609 \begin_inset Separator parbreak
34615 \begin_layout Standard
34617 \begin_inset Tabular
34618 <lyxtabular version="3" rows="4" columns="2">
34619 <features booktabs="true" tabularvalignment="middle">
34620 <column alignment="center" valignment="top" width="0pt">
34621 <column alignment="center" valignment="top">
34623 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34626 \begin_layout Plain Layout
34632 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34635 \begin_layout Plain Layout
34643 <cell alignment="center" valignment="top" usebox="none">
34646 \begin_layout Plain Layout
34656 <cell alignment="center" valignment="top" usebox="none">
34659 \begin_layout Plain Layout
34660 \begin_inset Formula $\Bra{\psi}$
34670 <cell alignment="center" valignment="top" usebox="none">
34673 \begin_layout Plain Layout
34683 <cell alignment="center" valignment="top" usebox="none">
34686 \begin_layout Plain Layout
34687 \begin_inset Formula $\Ket{\psi}$
34697 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34700 \begin_layout Plain Layout
34712 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34715 \begin_layout Plain Layout
34716 \begin_inset Formula $\Braket{\psi|\phi}$
34732 \begin_layout Standard
34739 assures that all vertical bars are set in the size of the surrounding brackets:
34740 \begin_inset Formula
34742 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34751 \begin_layout Plain Layout
34761 \begin_inset Note Note
34764 \begin_layout Plain Layout
34765 The following will be displayed when the \SpecialChar LaTeX
34778 \begin_layout Standard
34779 You need to install the \SpecialChar LaTeX
34784 to see the rest of this subsection in the output.
34787 \begin_layout Standard
34791 \begin_layout Plain Layout
34803 \begin_layout Standard
34810 can also be achieved using the command
34816 , that is described in
34817 \begin_inset CommandInset ref
34819 reference "subsec:Automatic-Bracket-Size"
34826 \begin_layout Subsection
34827 Self-defined Fractions
34828 \begin_inset CommandInset label
34830 name "subsec:Self-defined-Fractions"
34835 \begin_inset Index idx
34838 \begin_layout Plain Layout
34839 Fractions ! self-defined
34847 \begin_layout Standard
34848 To define custom commands for fractions, the command
34855 \begin_inset Index idx
34858 \begin_layout Plain Layout
34865 \begin_layout Plain Layout
34879 is used in the following scheme:
34882 \begin_layout Standard
34895 bracket}{fraction bar thickness}{style}
34896 \begin_inset Newline newline
34900 \begin_inset Phantom HPhantom
34903 \begin_layout Plain Layout
34913 {numerator}{denominator}
34916 \begin_layout Standard
34917 The style is a number in the range of 0
34918 \begin_inset space \thinspace{}
34922 \begin_inset space \thinspace{}
34926 \begin_inset Separator parbreak
34932 \begin_layout Standard
34934 \begin_inset Tabular
34935 <lyxtabular version="3" rows="5" columns="2">
34936 <features booktabs="true" tabularvalignment="middle">
34937 <column alignment="center" valignment="top" width="0pt">
34938 <column alignment="center" valignment="top">
34940 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34943 \begin_layout Plain Layout
34949 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34952 \begin_layout Plain Layout
34960 <cell alignment="center" valignment="top" usebox="none">
34963 \begin_layout Plain Layout
34969 <cell alignment="center" valignment="top" usebox="none">
34972 \begin_layout Plain Layout
34973 display style formula
34980 <cell alignment="center" valignment="top" usebox="none">
34983 \begin_layout Plain Layout
34989 <cell alignment="center" valignment="top" usebox="none">
34992 \begin_layout Plain Layout
35000 <cell alignment="center" valignment="top" usebox="none">
35003 \begin_layout Plain Layout
35009 <cell alignment="center" valignment="top" usebox="none">
35012 \begin_layout Plain Layout
35020 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35023 \begin_layout Plain Layout
35029 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35032 \begin_layout Plain Layout
35046 \begin_layout Standard
35047 When no style is given, the size is adjusted to the surrounding environment
35048 like for the command
35057 \begin_layout Standard
35058 When no fraction bar thickness is given, the predefined value of 0.4
35059 \begin_inset space \thinspace{}
35065 \begin_layout Standard
35066 \begin_inset VSpace medskip
35069 For example, the commands
35082 \begin_inset CommandInset ref
35084 reference "subsec:Fractions"
35088 are defined with the commands
35091 \begin_layout Standard
35100 genfrac{}{}{}{0}{#1}{#2}}
35103 \begin_layout Standard
35107 \begin_layout Standard
35116 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35119 \begin_layout Standard
35120 \begin_inset VSpace medskip
35123 To define a fraction where the fraction bar thickness can be given as optional
35124 argument, the following line is inserted to the \SpecialChar LaTeX
35128 \begin_layout Standard
35137 genfrac{}{}{#1}{}{#2}{#3}}
35140 \begin_layout Standard
35142 \begin_inset Formula
35144 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35145 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35150 As one can see, the distance of the numerator and the denominator to the
35151 fraction bar is round about three times the bar thickness.
35154 \begin_layout Subsection
35156 \begin_inset Index idx
35159 \begin_layout Plain Layout
35168 \begin_layout Standard
35169 There are four ways to cancel formulas or parts of formulas:
35172 \begin_layout Standard
35176 \begin_layout Plain Layout
35186 \begin_inset Note Note
35189 \begin_layout Plain Layout
35190 The following table will only be displayed when the \SpecialChar LaTeX
35201 \begin_inset Separator parbreak
35207 \begin_layout Standard
35209 \begin_inset Tabular
35210 <lyxtabular version="3" rows="5" columns="2">
35211 <features booktabs="true" tabularvalignment="middle">
35212 <column alignment="center" valignment="top" width="0pt">
35213 <column alignment="center" valignment="top">
35215 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35218 \begin_layout Plain Layout
35224 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35227 \begin_layout Plain Layout
35235 <cell alignment="center" valignment="top" usebox="none">
35238 \begin_layout Plain Layout
35242 \begin_inset space \textvisiblespace{}
35248 \begin_inset space \textvisiblespace{}
35256 <cell alignment="center" valignment="top" usebox="none">
35259 \begin_layout Plain Layout
35260 \begin_inset Formula $\cancel{\int A=B}$
35269 <row topspace="1.5mm">
35270 <cell alignment="center" valignment="top" usebox="none">
35273 \begin_layout Plain Layout
35277 \begin_inset space \textvisiblespace{}
35283 \begin_inset space \textvisiblespace{}
35291 <cell alignment="center" valignment="top" usebox="none">
35294 \begin_layout Plain Layout
35295 \begin_inset Formula $\bcancel{\int A=B}$
35304 <row topspace="1.5mm">
35305 <cell alignment="center" valignment="top" usebox="none">
35308 \begin_layout Plain Layout
35312 \begin_inset space \textvisiblespace{}
35318 \begin_inset space \textvisiblespace{}
35326 <cell alignment="center" valignment="top" usebox="none">
35329 \begin_layout Plain Layout
35330 \begin_inset Formula $\xcancel{\int A=B}$
35340 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35343 \begin_layout Plain Layout
35347 \begin_inset space \textvisiblespace{}
35353 \begin_inset space \textvisiblespace{}
35357 \begin_inset Formula $\to$
35365 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35368 \begin_layout Plain Layout
35369 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35385 \begin_layout Standard
35392 is especially suitable to visualize the reduction of fractions within formulas:
35393 \begin_inset Formula
35395 \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}}}
35403 \begin_layout Standard
35404 To change the size of
35411 \begin_inset Quotes eld
35415 \begin_inset Quotes erd
35418 value one can add the \SpecialChar LaTeX
35422 \begin_layout Standard
35427 PassOptionsToPackage{option}{cancel}
35430 \begin_layout Standard
35439 which leads to the same size as for the canceled value, or
35443 which makes is it a bit smaller than normal.
35446 \begin_layout Standard
35447 To color the cancellation bar one adds this command as \SpecialChar TeX
35451 \begin_layout Standard
35463 \begin_layout Standard
35468 can be replaced by a color of your choice.
35471 \begin_layout Standard
35475 \begin_layout Plain Layout
35491 \begin_layout Standard
35492 \begin_inset Formula
35494 \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}}}
35502 \begin_layout Standard
35506 \begin_layout Plain Layout
35520 \begin_inset Note Note
35523 \begin_layout Plain Layout
35532 \begin_layout Standard
35533 For further customizations, see the documentation of the package
35538 \begin_inset CommandInset citation
35545 \begin_inset Index idx
35548 \begin_layout Plain Layout
35557 \begin_layout Standard
35561 \begin_layout Plain Layout
35571 \begin_inset Note Note
35574 \begin_layout Plain Layout
35575 The following will be displayed when the \SpecialChar LaTeX
35588 \begin_layout Standard
35589 You need to install the \SpecialChar LaTeX
35594 to see the rest of this subsection in the output.
35597 \begin_layout Standard
35601 \begin_layout Plain Layout
35613 \begin_layout Subsection
35614 Formulas in Section Headings
35615 \begin_inset CommandInset label
35617 name "subsec:Formulas-in-Section"
35622 \begin_inset Index idx
35625 \begin_layout Plain Layout
35626 Formula ! in section headings
35634 \begin_layout Standard
35635 When formulas are used in section headings, the following has to be taken
35639 \begin_layout Standard
35640 \begin_inset Note Greyedout
35643 \begin_layout Plain Layout
35649 \begin_inset Index idx
35652 \begin_layout Plain Layout
35653 Packages ! hyperref
35658 support is enabled in the document settings dialog under
35661 \begin_inset space ~
35666 , PDF-bookmarks are created for every section heading in the table of contents.
35667 If a section heading contains formulas, they are incorrectly displayed
35668 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35677 \begin_layout Standard
35678 Both problems can be solved by inserting at the end of the section heading
35679 a short title with the menu
35681 Insert\SpecialChar menuseparator
35683 \begin_inset space ~
35689 Short titles are used as alternative for multiline section headings to
35690 keep the table of contents clearly arranged.
35691 Only the short title appears in the table of contents and therefore also
35692 in the PDF-bookmark.
35695 \begin_layout Standard
35696 When formulas should be used in the table of contents but
35700 is used, one can use the following command in \SpecialChar TeX
35704 \begin_layout Standard
35709 texorpdfstring{part}{alternative}
35710 \begin_inset Index idx
35713 \begin_layout Plain Layout
35724 \begin_layout Standard
35725 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35726 This can be characters, formulas, footnotes, but also cross-references.
35727 The alternative is used instead of the part for the bookmark.
35730 \begin_layout Standard
35731 Here are two example headings:
35732 \begin_inset VSpace -3mm
35739 \begin_layout Plain Layout
35751 \begin_layout Subsubsection
35752 Heading without formula in table of contents
35753 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35757 \begin_inset Argument 1
35760 \begin_layout Plain Layout
35761 Heading without formula in table of contents
35769 \begin_layout Subsubsection
35770 Heading with formula in table of contents
35774 \begin_layout Plain Layout
35784 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35791 \begin_layout Plain Layout
35801 \begin_layout Standard
35805 \begin_layout Plain Layout
35814 In the first heading a short title was used, in the second one
35823 \begin_layout Standard
35824 To get the same formatting as for the other headings, the complete heading
35833 \begin_layout Plain Layout
35835 \begin_inset CommandInset ref
35837 reference "subsec:Bold-Formulas"
35849 \begin_layout Subsection
35850 Formulas in multi-column Text
35851 \begin_inset Index idx
35854 \begin_layout Plain Layout
35855 Formula ! in multi-column text
35863 \begin_layout Standard
35864 Formulas in multi-column text are often too wide to fit into a column and
35865 thus need to be set over the whole page width.
35866 This is done by using the \SpecialChar LaTeX
35875 \begin_layout Plain Layout
35880 is part of every \SpecialChar LaTeX
35881 standard installation.
35887 \begin_inset Index idx
35890 \begin_layout Plain Layout
35891 Packages ! multicol
35896 , that is loaded with the \SpecialChar LaTeX
35900 \begin_layout Standard
35905 usepackage{multicol}
35908 \begin_layout Standard
35909 \begin_inset Note Greyedout
35912 \begin_layout Plain Layout
35913 Note that in this case the setting
35916 \begin_inset space ~
35923 Document\SpecialChar menuseparator
35929 \begin_inset space ~
35949 \begin_layout Standard
35950 Before the multi-column text the command
35953 \begin_layout Standard
35958 begin{multicols}{column number}
35961 \begin_layout Standard
35962 is written in \SpecialChar TeX
35964 The column number is a number in the range of 2
35965 \begin_inset space \thinspace{}
35969 \begin_inset space \thinspace{}
35973 Before the formula the multi-column text is ended by inserting the command
35976 \begin_layout Standard
35984 \begin_layout Standard
35985 in \SpecialChar TeX
35989 \begin_layout Standard
35990 Due to the command some space is automatically added before the formula.
35992 \begin_inset space \thinspace{}
35995 mm vertical space is inserted before the formula.
35996 When the formula style
36002 \begin_layout Plain Layout
36004 \begin_inset CommandInset ref
36006 reference "sec:Formula-Styles"
36018 \begin_inset space \thinspace{}
36021 mm space is inserted instead.
36024 \begin_layout Standard
36025 As example a multi-column text with a displayed formula:
36028 \begin_layout Standard
36034 \begin_layout Plain Layout
36038 begin{multicols}{2}
36043 Das Spektrum wird fouriertransformiert.
36044 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36045 , Lösungsmittel) zu trennen.
36046 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36047 nun das Aussehen des Ausgangssignals.
36048 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36049 über alle Phasen integrieren muss.
36051 \begin_inset Formula $S$
36054 unser normiertes Ausgangssignal und
36055 \begin_inset Formula $P$
36058 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36062 \begin_layout Plain Layout
36072 \begin_inset VSpace -6mm
36076 \begin_inset Formula
36078 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36087 \begin_layout Plain Layout
36091 begin{multicols}{2}
36097 \begin_inset Formula $S_{0}$
36100 das Signal ohne Gradient ist und die Normierungsbedingung
36101 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36105 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36107 \begin_inset Formula $\nicefrac{\pi}{2}$
36111 \begin_inset space \thinspace{}
36114 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36115 das Signal zusätzlich abschwächt.
36116 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36118 \begin_inset Formula $T_{2}$
36124 \begin_layout Standard
36130 \begin_layout Plain Layout
36142 \begin_layout Subsection
36143 Formulas with Description of Variables
36144 \begin_inset Index idx
36147 \begin_layout Plain Layout
36148 Formula ! with description of variables
36156 \begin_layout Standard
36157 To describe variables within a formula, like in formula
36158 \begin_inset CommandInset ref
36160 reference "eq:within"
36169 \begin_inset Formula $n$
36173 \begin_inset space ~
36176 matrix is used with left aligned columns for the
36177 \begin_inset Formula $n$
36184 \begin_layout Plain Layout
36186 \begin_inset CommandInset ref
36188 reference "sec:Matrices"
36197 To set the description in a smaller size, before the matrix e.
36198 \begin_inset space \thinspace{}
36202 \begin_inset space \space{}
36215 \begin_layout Plain Layout
36217 \begin_inset CommandInset ref
36219 reference "subsec:Font-Sizes"
36231 \begin_layout Standard
36232 When the formula style
36238 \begin_layout Plain Layout
36240 \begin_inset CommandInset ref
36242 reference "sec:Formula-Styles"
36263 \begin_layout Plain Layout
36270 only works in formulas with the style
36275 \begin_inset CommandInset ref
36277 reference "subsec:Variable-Space"
36286 is inserted before and after the matrix to have the same separation of
36287 the matrix from the equation and the side margin.
36290 \begin_layout Standard
36291 When the formula style
36295 is used, the method described in
36296 \begin_inset CommandInset ref
36298 reference "subsec:Flalign-Environment"
36302 is used to indent formulas.
36304 \begin_inset CommandInset ref
36306 reference "eq:within"
36310 consists of five columns where in the first two columns contain the equation,
36311 the third the matrix and the last one an empty \SpecialChar TeX
36313 \begin_inset Formula
36315 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36316 \rho & \textrm{density}\\
36317 V & \textrm{volume}\\
36318 g & \textrm{gravitational acceleration}
36319 \end{array} & & {}\label{eq:within}
36327 \begin_layout Subsection
36328 Upright small Greek Letters
36329 \begin_inset CommandInset label
36331 name "subsec:Upright-small-Greek"
36336 \begin_inset Index idx
36339 \begin_layout Plain Layout
36340 Greek letters ! upright
36348 \begin_layout Standard
36349 Most of the math fonts only provide italic small Greek letters.
36350 But for symbols of elementary particles like pions and neutrinos, upright
36351 Greek letters are needed.
36360 \begin_layout Plain Layout
36365 is part of the \SpecialChar LaTeX
36371 \begin_inset Index idx
36374 \begin_layout Plain Layout
36379 \begin_layout Plain Layout
36399 \begin_inset Index idx
36402 \begin_layout Plain Layout
36408 that is loaded with the \SpecialChar LaTeX
36412 \begin_layout Standard
36417 usepackage{upgreek}
36420 \begin_layout Standard
36426 \begin_layout Plain Layout
36436 \begin_inset Note Note
36439 \begin_layout Plain Layout
36440 The following table will only be displayed when the \SpecialChar LaTeX
36450 They are created when the command for a small Greek letter is started with
36456 For example the command
36463 \begin_inset Formula $\uptau$
36469 \begin_layout Standard
36470 With these commands reactions of elementary particles can be typeset:
36471 \begin_inset Formula
36473 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36481 \begin_layout Standard
36482 The upright letters are more bold and wider than the italic ones.
36483 They should therefore not be used for units like
36484 \begin_inset Quotes eld
36488 \begin_inset Quotes erd
36494 \begin_layout Standard
36498 \begin_layout Plain Layout
36508 \begin_inset Note Note
36511 \begin_layout Plain Layout
36512 The following will be displayed when the \SpecialChar LaTeX
36525 \begin_layout Standard
36526 You need to install the \SpecialChar LaTeX
36531 to see the rest of this subsection in the output.
36534 \begin_layout Standard
36538 \begin_layout Plain Layout
36550 \begin_layout Subsection
36551 Text Characters in Formulas
36552 \begin_inset Index idx
36555 \begin_layout Plain Layout
36564 \begin_layout Standard
36565 In some cases you might want to insert text characters directly into formulas.
36566 When for example the centered dot · is often used in formulas like
36567 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36570 , one would have to insert the command
36580 \begin_layout Plain Layout
36582 \begin_inset CommandInset ref
36584 reference "subsec:Binary-Operators"
36593 all the time, because this character is defined in all encodings as text
36595 But the encoding can be changed by this \SpecialChar LaTeX
36599 \begin_layout Standard
36604 Declare Inputtext{183}{
36614 f\SpecialChar ligaturebreak
36618 \begin_layout Standard
36619 The character encoding (menu
36621 Document\SpecialChar menuseparator
36622 Settings\SpecialChar menuseparator
36625 ) specifies what character appears when a keyboard key is pressed.
36626 When the key for the character '·' is pressed, internally the command
36633 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36635 With the changed encoding the right command is chosen automatically, depending
36636 on if the character was inserted into a formula or not.
36639 \begin_layout Standard
36640 The encoding of several characters is saved in definition files.
36641 For example the encoding
36645 is defined in the file
36649 which is in the installation folder of \SpecialChar LaTeX
36651 Encodings should only be changed via the \SpecialChar LaTeX
36652 -preamble and not in the definition
36654 Otherwise documents could not be edited by other \SpecialChar LyX
36655 users working on other
36659 \begin_layout Standard
36660 \begin_inset VSpace medskip
36663 Besides the centered dot, in this document the degree sign ° is defined
36664 with the following \SpecialChar LaTeX
36665 -preamble line so that it can be directly inserted into
36669 \begin_layout Standard
36674 DeclareInputtext{176}{
36684 f\SpecialChar ligaturebreak
36688 \begin_layout Subsection
36690 -comments in formulas
36691 \begin_inset Index idx
36694 \begin_layout Plain Layout
36704 \begin_layout Standard
36705 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36707 code of your file with the menu
36709 Insert\SpecialChar menuseparator
36710 Note\SpecialChar menuseparator
36714 This is not possible in a formula but you can insert \SpecialChar LaTeX
36719 \begin_layout Standard
36727 \begin_layout Standard
36728 This creates a box in which you can write your comment.
36729 Due to a bug in \SpecialChar LyX
36734 \begin_layout Plain Layout
36735 \begin_inset CommandInset href
36737 name "LyX-bug #9002"
36738 target "http://www.lyx.org/trac/ticket/9002"
36747 you cannot write normal text inside the comment, even when you use mathematical
36748 text, you will see its \SpecialChar LaTeX
36749 -commands in the \SpecialChar LaTeX
36751 \begin_inset Newline newline
36754 This a formula with a \SpecialChar LaTeX
36756 \begin_inset Formula
36758 A=B%\text{This is the comment}
36766 \begin_layout Standard
36767 \begin_inset Newpage newpage
36773 \begin_layout Section
36776 \begin_inset Index idx
36779 \begin_layout Plain Layout
36788 \begin_layout Standard
36789 This section is a summary of the most important typographic rules, listed
36794 \begin_layout Plain Layout
36795 This collection was partly taken from the German semi-official dictionary
36797 \begin_inset Quotes eld
36801 \begin_inset Quotes erd
36805 \begin_inset CommandInset citation
36811 that lists some of the ISO rules.
36812 More rules are listed in
36813 \begin_inset CommandInset citation
36827 \begin_layout Itemize
36836 \begin_layout Plain Layout
36837 done with font styles, see
36838 \begin_inset CommandInset ref
36840 reference "subsec:Font-Styles"
36849 , no matter if they appear in italic text: 30
36850 \begin_inset space \thinspace{}
36854 \begin_inset Newline newline
36857 Between the value and the unit is the smallest space, see
36858 \begin_inset CommandInset ref
36860 reference "subsec:Predefined-Space"
36865 \begin_inset Newline newline
36868 This convention is automatically fulfilled when the command
36875 When it is entered to a formula, two boxes appear.
36876 In the first one the value is inserted, in the second one the unit, and
36878 \begin_inset Formula $\unit[30]{km/h}$
36882 \begin_inset space \thinspace{}
36892 is not a real \SpecialChar LaTeX
36893 command but the command
36899 , therefore you cannot use it in \SpecialChar TeX
36903 \begin_layout Itemize
36904 Percent and perthousand signs are set like physical units:
36905 \begin_inset Newline newline
36909 \begin_inset space \thinspace{}
36915 \begin_layout Itemize
36916 The degree sign follows directly on the value: 15°, but not when it is used
36918 \begin_inset space \thinspace{}
36924 \begin_layout Itemize
36925 In numbers with more than four digits the smallest space is inserted before
36926 every third digit to group them:
36936 \begin_inset space \thinspace{}
36940 \begin_inset space \thinspace{}
36946 \begin_layout Itemize
36947 For dimensions like 120×90×40
36948 \begin_inset space \thinspace{}
36951 cm the multiplication sign
36952 \begin_inset Quotes eld
36956 \begin_inset Quotes erd
36960 It is available either via the command
36968 Insert\SpecialChar menuseparator
36969 Special Character\SpecialChar menuseparator
36975 \begin_layout Itemize
36976 Functions with names consisting of several letters are set upright to avoid
36978 \begin_inset CommandInset ref
36980 reference "subsec:Predefined-Functions"
36987 \begin_layout Itemize
36988 Indices consisting of several letters, are set upright:
36989 \begin_inset Formula $E_{\mathrm{kin}}$
36993 \begin_inset Newline newline
36996 Components of matrices are set italic:
36997 \begin_inset Formula $\hat{H}_{kl}$
37003 \begin_layout Itemize
37004 The differentiation/integration operator 'd', the Euler's number 'e' and
37005 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37009 \begin_layout Itemize
37010 The character that denotes a
37014 transformation is inserted either by the command
37019 \begin_inset space \textvisiblespace{}
37026 Insert\SpecialChar menuseparator
37027 Special Character\SpecialChar menuseparator
37028 Symbols\SpecialChar menuseparator
37030 \begin_inset space ~
37036 \begin_inset Formula $\mathscr{F}$
37042 \begin_layout Standard
37043 \begin_inset Newpage newpage
37049 \begin_layout Section
37051 \begin_inset Index idx
37054 \begin_layout Plain Layout
37063 \begin_layout Standard
37064 Some characters and symbols can be created with several commands.
37065 Here is a list of the synonym commands:
37068 \begin_layout Standard
37069 \begin_inset VSpace bigskip
37073 \begin_inset space \hfill{}
37077 \begin_inset Tabular
37078 <lyxtabular version="3" rows="12" columns="2">
37079 <features booktabs="true" tabularvalignment="middle">
37080 <column alignment="center" valignment="top" width="0pt">
37081 <column alignment="center" valignment="top" width="0pt">
37083 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37086 \begin_layout Plain Layout
37092 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37095 \begin_layout Plain Layout
37103 <cell alignment="center" valignment="top" usebox="none">
37106 \begin_layout Plain Layout
37114 <cell alignment="center" valignment="top" usebox="none">
37117 \begin_layout Plain Layout
37125 <cell alignment="center" valignment="top" usebox="none">
37128 \begin_layout Plain Layout
37136 <cell alignment="center" valignment="top" usebox="none">
37139 \begin_layout Plain Layout
37149 <cell alignment="center" valignment="top" usebox="none">
37152 \begin_layout Plain Layout
37160 <cell alignment="center" valignment="top" usebox="none">
37163 \begin_layout Plain Layout
37173 <cell alignment="center" valignment="top" usebox="none">
37176 \begin_layout Plain Layout
37184 <cell alignment="center" valignment="top" usebox="none">
37187 \begin_layout Plain Layout
37195 <cell alignment="center" valignment="top" usebox="none">
37198 \begin_layout Plain Layout
37206 <cell alignment="center" valignment="top" usebox="none">
37209 \begin_layout Plain Layout
37217 <cell alignment="center" valignment="top" usebox="none">
37220 \begin_layout Plain Layout
37228 <cell alignment="center" valignment="top" usebox="none">
37231 \begin_layout Plain Layout
37241 <cell alignment="center" valignment="top" usebox="none">
37244 \begin_layout Plain Layout
37252 <cell alignment="center" valignment="top" usebox="none">
37255 \begin_layout Plain Layout
37265 <cell alignment="center" valignment="top" usebox="none">
37268 \begin_layout Plain Layout
37276 <cell alignment="center" valignment="top" usebox="none">
37279 \begin_layout Plain Layout
37289 <cell alignment="center" valignment="top" usebox="none">
37292 \begin_layout Plain Layout
37300 <cell alignment="center" valignment="top" usebox="none">
37303 \begin_layout Plain Layout
37313 <cell alignment="center" valignment="top" usebox="none">
37316 \begin_layout Plain Layout
37324 <cell alignment="center" valignment="top" usebox="none">
37327 \begin_layout Plain Layout
37335 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37338 \begin_layout Plain Layout
37346 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37349 \begin_layout Plain Layout
37361 \begin_inset space \hfill{}
37365 \begin_inset Tabular
37366 <lyxtabular version="3" rows="12" columns="2">
37367 <features booktabs="true" tabularvalignment="middle">
37368 <column alignment="center" valignment="top" width="0pt">
37369 <column alignment="center" valignment="top" width="0pt">
37371 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37374 \begin_layout Plain Layout
37380 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37383 \begin_layout Plain Layout
37391 <cell alignment="center" valignment="top" usebox="none">
37394 \begin_layout Plain Layout
37402 <cell alignment="center" valignment="top" usebox="none">
37405 \begin_layout Plain Layout
37417 <cell alignment="center" valignment="top" usebox="none">
37420 \begin_layout Plain Layout
37428 <cell alignment="center" valignment="top" usebox="none">
37431 \begin_layout Plain Layout
37441 <cell alignment="center" valignment="top" usebox="none">
37444 \begin_layout Plain Layout
37452 <cell alignment="center" valignment="top" usebox="none">
37455 \begin_layout Plain Layout
37465 <cell alignment="center" valignment="top" usebox="none">
37468 \begin_layout Plain Layout
37476 <cell alignment="center" valignment="top" usebox="none">
37479 \begin_layout Plain Layout
37487 <cell alignment="center" valignment="top" usebox="none">
37490 \begin_layout Plain Layout
37498 <cell alignment="center" valignment="top" usebox="none">
37501 \begin_layout Plain Layout
37509 <cell alignment="center" valignment="top" usebox="none">
37512 \begin_layout Plain Layout
37520 <cell alignment="center" valignment="top" usebox="none">
37523 \begin_layout Plain Layout
37533 <cell alignment="center" valignment="top" usebox="none">
37536 \begin_layout Plain Layout
37544 <cell alignment="center" valignment="top" usebox="none">
37547 \begin_layout Plain Layout
37557 <cell alignment="center" valignment="top" usebox="none">
37560 \begin_layout Plain Layout
37568 <cell alignment="center" valignment="top" usebox="none">
37571 \begin_layout Plain Layout
37581 <cell alignment="center" valignment="top" usebox="none">
37584 \begin_layout Plain Layout
37592 <cell alignment="center" valignment="top" usebox="none">
37595 \begin_layout Plain Layout
37605 <cell alignment="center" valignment="top" usebox="none">
37608 \begin_layout Plain Layout
37616 <cell alignment="center" valignment="top" usebox="none">
37619 \begin_layout Plain Layout
37629 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37632 \begin_layout Plain Layout
37640 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37643 \begin_layout Plain Layout
37657 \begin_inset space \hfill{}
37663 \begin_layout Standard
37664 \begin_inset Newpage newpage
37670 \begin_layout Bibliography
37671 \begin_inset CommandInset bibitem
37672 LatexCommand bibitem
37684 The \SpecialChar LaTeX
37688 Addison Wesley, 2004
37691 \begin_layout Bibliography
37692 \begin_inset CommandInset bibitem
37693 LatexCommand bibitem
37699 \begin_inset CommandInset href
37702 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37706 of \SpecialChar LaTeX
37710 \begin_layout Bibliography
37711 \begin_inset CommandInset bibitem
37712 LatexCommand bibitem
37718 \begin_inset CommandInset href
37721 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37729 \begin_layout Plain Layout
37738 -\SpecialChar LaTeX
37742 \begin_layout Bibliography
37743 \begin_inset CommandInset bibitem
37744 LatexCommand bibitem
37750 \begin_inset CommandInset href
37753 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37757 of all symbols available with \SpecialChar LaTeX
37761 \begin_layout Bibliography
37762 \begin_inset CommandInset bibitem
37763 LatexCommand bibitem
37769 \begin_inset CommandInset href
37771 name "Documentation"
37772 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37776 of the \SpecialChar LaTeX
37782 \begin_inset Index idx
37785 \begin_layout Plain Layout
37794 \begin_layout Bibliography
37795 \begin_inset CommandInset bibitem
37796 LatexCommand bibitem
37802 \begin_inset CommandInset href
37804 name "Documentation"
37805 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37809 of the \SpecialChar LaTeX
37815 \begin_inset Index idx
37818 \begin_layout Plain Layout
37819 Packages ! hyperref
37827 \begin_layout Bibliography
37828 \begin_inset CommandInset bibitem
37829 LatexCommand bibitem
37835 \begin_inset CommandInset href
37837 name "Documentation"
37838 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37842 of the \SpecialChar LaTeX
37848 \begin_inset Index idx
37851 \begin_layout Plain Layout
37860 \begin_layout Bibliography
37861 \begin_inset CommandInset bibitem
37862 LatexCommand bibitem
37873 Auflage, Duden 2001
37876 \begin_layout Bibliography
37877 \begin_inset CommandInset bibitem
37878 LatexCommand bibitem
37884 \begin_inset CommandInset href
37887 target "http://physics.nist.gov/Document/checklist.pdf"
37891 for reviewing manuscripts
37894 \begin_layout Standard
37895 \begin_inset CommandInset index_print
37896 LatexCommand printindex