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:
21 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
22 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
24 % increase link area for cross-references and autoname them,
25 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
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27 \@ifpackageloaded{babel}{
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31 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
32 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
36 % don't load packages twice
37 % see first footnote in sec. 9.3
38 \@ifundefined{textcolor}{\usepackage{color}}{}
40 % the pages of the TOC are numbered roman
41 % and a PDF-bookmark for the TOC is added
43 \let\myTOC\tableofcontents
44 \renewcommand{\tableofcontents}{%
46 \pdfbookmark[1]{\contentsname}{}
49 \pagenumbering{arabic}}
51 % add 0.5 mm vertical space for table rows
52 \@ifundefined{extrarowheight} {\usepackage{array}}{}
53 \setlength{\extrarowheight}{0.5mm}
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
98 \newboolean{undertilde}
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
122 \IfFileExists{cancel.sty}
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
135 \use_default_options false
136 \maintain_unincluded_children false
138 \language_package default
141 \font_roman "lmodern" "default"
142 \font_sans "lmss" "default"
143 \font_typewriter "lmtt" "default"
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 false
211 \output_changes false
214 \html_be_strict false
221 's detailed Math manual
225 by the \SpecialChar LyX
230 \begin_layout Plain Layout
232 If you have comments or error corrections, please send them to the \SpecialChar LyX
237 \begin_inset CommandInset href
239 name "lyx-docs@lists.lyx.org"
240 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
251 \begin_inset Note Note
254 \begin_layout Plain Layout
261 \begin_inset Newline newline
265 \begin_inset Newline newline
273 \begin_layout Standard
274 \begin_inset CommandInset toc
275 LatexCommand tableofcontents
282 \begin_layout Standard
283 \begin_inset Note Note
286 \begin_layout Plain Layout
287 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
290 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
297 If they are not installed the document can be exported anyway but the sections
298 where the packages are required will not appear in the output.
303 ; if it is not installed, this file cannot be exported.
306 \begin_layout Plain Layout
307 The latest PDF-version of this document can be found here:
308 \begin_inset Newline newline
313 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
321 \begin_layout Standard
322 \begin_inset Newpage newpage
328 \begin_layout Section
332 \begin_layout Standard
333 This document explains \SpecialChar LyX
334 's math features and is furthermore a collection
335 of \SpecialChar LaTeX
336 -commands used for mathematical characters and constructs.
337 The explanations are designed for the usage of commands.
338 It is therefore required that you have read the section
349 \begin_layout Standard
350 Most of the characters and many constructs explained in this manual are
351 also accessible via the menu
355 \SpecialChar menuseparator
371 But everybody who has to write lots of formulas will notice that it is
372 much faster to use commands instead of the math toolbar.
373 Therefore this manual is focused on commands but also mentions the correspondin
374 g toolbar buttons when available.
377 \begin_layout Standard
378 If not specially mentioned the commands are only available within formulas.
379 To be able to use all commands explained in this document, the option
383 must be checked in the document settings (menu
385 Document\SpecialChar menuseparator
386 Settings\SpecialChar menuseparator
397 \begin_layout Plain Layout
400 Use AMS math package automatically
406 \begin_layout Plain Layout
415 -math when math constructs are found that are supported by \SpecialChar LyX
424 \begin_layout Standard
425 This document doesn't list all
429 \begin_layout Plain Layout
442 \begin_layout Plain Layout
447 \begin_layout Plain Layout
456 -math commands is in the file
459 \begin_inset CommandInset href
462 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
468 , which is part of every \SpecialChar LaTeX
469 standard installation.
474 for lucidity reasons.
477 \begin_layout Section
481 \begin_layout Standard
482 To create an inline formula
483 \begin_inset Index idx
486 \begin_layout Plain Layout
492 that is embedded into a text line, use one of the shortcuts
498 or the toolbar button
505 \begin_inset Newline newline
508 To create a display style formula
509 \begin_inset Index idx
512 \begin_layout Plain Layout
513 Formula ! display style
518 which will appear bigger, has a different format, and will be in a separate
519 paragraph, use one of these shortcuts:
528 \begin_layout Standard
529 To change a display style formula to an inline formula, set the cursor into
530 the formula and use one of the shortcuts
538 Edit\SpecialChar menuseparator
539 Math\SpecialChar menuseparator
543 The same way is used to change an inline formula to a display style formula.
546 \begin_layout Standard
547 To display parts of an inline formula in the size of a display style formula,
555 \begin_inset Index idx
558 \begin_layout Plain Layout
567 Then a new blue box appears in which the desired formula part is inserted.
570 \begin_layout Standard
571 Only inline formulas are allowed inside tables.
574 \begin_layout Standard
579 can be turned on in the menu
581 View\SpecialChar menuseparator
585 When you click there on
586 \begin_inset Quotes eld
590 \begin_inset Quotes erd
593 the toolbar will be shown permanently at the bottom; this state is visualized
598 menu with a checkmark.
599 When you click in this state again on
600 \begin_inset Quotes eld
604 \begin_inset Quotes erd
615 is only shown when the cursor is within a formula; this state is visualized
616 by the renaming of the menu entry from
617 \begin_inset Quotes eld
621 \begin_inset Quotes erd
625 \begin_inset Quotes eld
633 \begin_inset Quotes erd
639 \begin_layout Standard
642 \begin_inset Index idx
645 \begin_layout Plain Layout
652 is invoked by pressing the toolbar button
660 Insert\SpecialChar menuseparator
672 \begin_layout Standard
673 To change the \SpecialChar LaTeX
675 \begin_inset Index idx
678 \begin_layout Plain Layout
687 Document\SpecialChar menuseparator
688 Settings\SpecialChar menuseparator
698 \begin_layout Standard
699 To edit matrices, case differentiations and multiline formulas subsequently,
702 Edit\SpecialChar menuseparator
707 Edit\SpecialChar menuseparator
709 \begin_inset space \thinspace{}
713 \begin_inset space \thinspace{}
723 When lines and columns are swapped via the menu, the column or line where
724 the cursor is in is exchanged with the column to the right or the line
726 Is the cursor in the last column or row, the exchange is done with the
727 column to the left or the line above.
730 \begin_layout Standard
731 To write text in formulas
735 \begin_layout Plain Layout
736 For multiline formulas the command
743 \begin_inset CommandInset ref
745 reference "subsec:Text-in-multiline"
759 \begin_inset Index idx
762 \begin_layout Plain Layout
769 \begin_inset Index idx
772 \begin_layout Plain Layout
779 This mode is invoked with the shortcut
785 or by the insertion of the command
792 \begin_inset Index idx
795 \begin_layout Plain Layout
804 The text appears black in \SpecialChar LyX
805 and can therefore be distinguished from the
806 other formula parts which appear blue.
807 In the output mathematical text is set upright, in contrary to other formula
811 \begin_layout Subsection*
815 \begin_layout Standard
816 Most of the \SpecialChar LaTeX
817 -commands for math constructs have the following scheme:
820 \begin_layout Standard
836 \begin_layout Standard
837 A command always starts with a backslash
838 \begin_inset Quotes gld
848 \begin_inset Quotes grd
852 To omit optional arguments, also omit the associated brackets.
853 The braces around the required arguments are named in this document as
856 \begin_inset Index idx
859 \begin_layout Plain Layout
867 If you add in a formula a left brace to a command name, \SpecialChar LyX
869 creates a \SpecialChar TeX
871 In all other cases \SpecialChar TeX
872 braces are created in formulas with the command
880 braces appear red in \SpecialChar LyX
881 , in contrary to normal braces which appear blue.
883 mode no command is needed to get \SpecialChar TeX
886 braces don't appear in the output.
889 \begin_layout Standard
890 When commands without arguments, like commands for symbols are entered in
892 mode, a space character must
896 be behind the command to end it.
897 This space doesn't appear in the output.
898 When the space should appear in the output, the space must be followed
899 by a protected space in normal text.
902 \begin_layout Standard
903 A protected space is inserted with
906 arg "command-alternatives space-insert protected ; math-space"
912 \begin_layout Subsection*
913 \begin_inset Newpage newpage
919 \begin_layout Itemize
921 \begin_inset space \textvisiblespace{}
924 denotes a space character to be input.
927 \begin_layout Itemize
929 \begin_inset Formula $\to$
932 denotes the usage of the corresponding arrow key on the keyboard.
937 key can often be used instead of
938 \begin_inset Formula $\to$
942 \begin_inset Formula $\downarrow$
950 \begin_inset Formula $\leftarrow$
954 \begin_inset Formula $\uparrow$
960 \begin_layout Subsection*
964 \begin_layout Standard
966 \begin_inset Float table
972 \begin_layout Plain Layout
974 \begin_inset Caption Standard
976 \begin_layout Plain Layout
977 \begin_inset CommandInset label
979 name "tab:Available-units"
991 \begin_layout Plain Layout
994 <lyxtabular version="3" rows="13" columns="2">
995 <features booktabs="true" tabularvalignment="middle">
996 <column alignment="center" valignment="top">
997 <column alignment="center" valignment="top" width="0pt">
999 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1002 \begin_layout Plain Layout
1008 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1011 \begin_layout Plain Layout
1019 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1022 \begin_layout Plain Layout
1028 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1031 \begin_layout Plain Layout
1039 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1042 \begin_layout Plain Layout
1048 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1051 \begin_layout Plain Layout
1059 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1062 \begin_layout Plain Layout
1068 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1071 \begin_layout Plain Layout
1073 \begin_inset space \thinspace{}
1077 \begin_inset space \thinspace{}
1087 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1090 \begin_layout Plain Layout
1096 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1099 \begin_layout Plain Layout
1101 \begin_inset space \thinspace{}
1105 \begin_inset space \thinspace{}
1115 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1118 \begin_layout Plain Layout
1124 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1127 \begin_layout Plain Layout
1129 \begin_inset space \thinspace{}
1133 \begin_inset space \thinspace{}
1143 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1146 \begin_layout Plain Layout
1152 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1155 \begin_layout Plain Layout
1157 \begin_inset space \thinspace{}
1161 \begin_inset space \thinspace{}
1171 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1174 \begin_layout Plain Layout
1180 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1183 \begin_layout Plain Layout
1185 \begin_inset space \thinspace{}
1189 \begin_inset space \thinspace{}
1199 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1202 \begin_layout Plain Layout
1208 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1211 \begin_layout Plain Layout
1213 \begin_inset space \thinspace{}
1217 \begin_inset Formula $\approx$
1221 \begin_inset space \thinspace{}
1231 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1234 \begin_layout Plain Layout
1240 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1243 \begin_layout Plain Layout
1245 \begin_inset space \thinspace{}
1249 \begin_inset space \thinspace{}
1259 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1262 \begin_layout Plain Layout
1268 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1271 \begin_layout Plain Layout
1275 \begin_inset Quotes eld
1281 \begin_inset Quotes erd
1291 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1294 \begin_layout Plain Layout
1300 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1303 \begin_layout Plain Layout
1305 \begin_inset Quotes eld
1313 \begin_inset Quotes erd
1323 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1326 \begin_layout Plain Layout
1332 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1335 \begin_layout Plain Layout
1337 \begin_inset space \thinspace{}
1341 \begin_inset Formula $\nicefrac{1}{18}$
1345 \begin_inset space \thinspace{}
1366 \begin_layout Standard
1367 \begin_inset Newpage newpage
1373 \begin_layout Section
1377 \begin_layout Subsection
1379 \begin_inset Index idx
1382 \begin_layout Plain Layout
1389 \begin_inset Index idx
1392 \begin_layout Plain Layout
1399 \begin_inset Index idx
1402 \begin_layout Plain Layout
1407 \begin_layout Plain Layout
1418 \begin_layout Plain Layout
1431 \begin_inset Index idx
1434 \begin_layout Plain Layout
1439 \begin_layout Plain Layout
1450 \begin_layout Plain Layout
1465 \begin_layout Standard
1466 Indices are created with an underscore
1467 \begin_inset Quotes eld
1471 \begin_inset Quotes erd
1474 or via the math toolbar button
1477 arg "math-subscript"
1480 , exponents with a caret
1481 \begin_inset Quotes eld
1485 \begin_inset Quotes erd
1488 or via the math toolbar button
1491 arg "math-superscript"
1495 \begin_inset Separator parbreak
1501 \begin_layout Standard
1503 \begin_inset Tabular
1504 <lyxtabular version="3" rows="4" columns="2">
1505 <features booktabs="true" tabularvalignment="middle">
1506 <column alignment="center" valignment="top" width="0pt">
1507 <column alignment="center" valignment="top" width="0pt">
1509 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1512 \begin_layout Plain Layout
1518 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1521 \begin_layout Plain Layout
1529 <cell alignment="center" valignment="top" usebox="none">
1532 \begin_layout Plain Layout
1538 <cell alignment="center" valignment="top" usebox="none">
1541 \begin_layout Plain Layout
1542 \begin_inset Formula $B_{V}$
1551 <row topspace="1.5mm">
1552 <cell alignment="center" valignment="top" usebox="none">
1555 \begin_layout Plain Layout
1561 <cell alignment="center" valignment="top" usebox="none">
1564 \begin_layout Plain Layout
1565 \begin_inset Formula $B^{V}$
1574 <row topspace="1.5mm">
1575 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1578 \begin_layout Plain Layout
1580 \begin_inset space \textvisiblespace{}
1588 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1591 \begin_layout Plain Layout
1592 \begin_inset Formula $B^{A}$
1608 \begin_layout Standard
1609 As the caret is in some languages an accent, vowels will be accentuated
1610 in this case and not set as exponents
1614 \begin_layout Plain Layout
1615 Depending on the used keyboard settings this can also happen for characters
1622 To get exponents in this case, press
1626 after the caret as in the last example.
1629 \begin_layout Subsection
1631 \begin_inset CommandInset label
1633 name "subsec:Fractions"
1638 \begin_inset Index idx
1641 \begin_layout Plain Layout
1650 \begin_layout Standard
1651 Fractions are generated with the command
1658 \begin_inset Index idx
1661 \begin_layout Plain Layout
1669 or via the math toolbar button
1672 arg "math-insert \\frac"
1676 The font size is adjusted automatically, depending on whether the fraction
1677 is in an inline or display style formula.
1678 With the math toolbar button
1681 arg "math-insert \\frac-square"
1684 you can select different fraction types.
1687 \begin_layout Standard
1695 \begin_inset Index idx
1698 \begin_layout Plain Layout
1706 a fraction can be created that always has the size of a display style formula.
1714 \begin_inset Index idx
1717 \begin_layout Plain Layout
1725 the fraction appears always with the size of an inline formula.
1729 \begin_layout Standard
1730 A line with the fraction
1731 \begin_inset Formula $\frac{1}{2}$
1734 that was created with the command
1743 \begin_layout Standard
1744 A line with the fraction
1745 \begin_inset Formula $\dfrac{1}{2}$
1748 that was created with the command
1755 \begin_inset Separator parbreak
1761 \begin_layout Standard
1763 \begin_inset Tabular
1764 <lyxtabular version="3" rows="4" columns="2">
1765 <features booktabs="true" tabularvalignment="middle">
1766 <column alignment="center" valignment="top" width="0pt">
1767 <column alignment="center" valignment="top" width="0pt">
1769 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1772 \begin_layout Plain Layout
1778 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1781 \begin_layout Plain Layout
1788 <row topspace="1.5mm">
1789 <cell alignment="center" valignment="top" usebox="none">
1792 \begin_layout Plain Layout
1796 \begin_inset space \textvisiblespace{}
1800 \begin_inset Formula $\downarrow$
1808 <cell alignment="center" valignment="top" usebox="none">
1811 \begin_layout Plain Layout
1812 \begin_inset Formula $\frac{A}{B}$
1821 <row topspace="2mm">
1822 <cell alignment="center" valignment="top" usebox="none">
1825 \begin_layout Plain Layout
1829 \begin_inset space \textvisiblespace{}
1833 \begin_inset Formula $\downarrow$
1841 <cell alignment="center" valignment="top" usebox="none">
1844 \begin_layout Plain Layout
1845 \begin_inset Formula $\dfrac{A}{B}$
1854 <row topspace="2mm" bottomspace="1mm">
1855 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1858 \begin_layout Plain Layout
1862 \begin_inset space \textvisiblespace{}
1868 \begin_inset space \textvisiblespace{}
1872 \begin_inset Formula $\downarrow$
1876 \begin_inset Formula $\downarrow\downarrow$
1884 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1887 \begin_layout Plain Layout
1888 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1904 \begin_layout Standard
1905 \begin_inset VSpace bigskip
1909 \begin_inset Newpage newpage
1912 For nested fractions the command
1919 \begin_inset Index idx
1922 \begin_layout Plain Layout
1932 \begin_inset VSpace -3mm
1938 \begin_layout Standard
1939 \begin_inset Formula
1941 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1942 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1950 \begin_layout Standard
1951 The command for the example above is:
1954 \begin_layout Standard
1960 \begin_inset space \textvisiblespace{}
1964 \begin_inset Formula $\downarrow$
1970 \begin_inset space \textvisiblespace{}
1976 \begin_inset space \textvisiblespace{}
1980 \begin_inset Formula $\downarrow$
1984 \begin_inset Formula $\downarrow$
1990 \begin_layout Standard
1991 \begin_inset VSpace medskip
1997 \begin_layout Standard
2004 sets the fraction always in the size of a displayed formula, also when
2005 it is part of another fraction.
2008 \begin_layout Standard
2009 It is possible to specify the alignment of the numerator.
2016 is used to left align it, the command
2029 centers the numerator.
2030 These fractions demonstrate the different alignments:
2033 \begin_layout Standard
2036 \begin_inset Formula
2038 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2046 \begin_layout Standard
2047 \begin_inset Note Greyedout
2050 \begin_layout Plain Layout
2067 are no real \SpecialChar LaTeX
2068 commands but represent the command
2072 cfrac[alignment]{numerator}{denominator}
2075 Therefore you cannot use them in \SpecialChar TeX
2084 \begin_layout Standard
2085 \begin_inset VSpace medskip
2088 It is often advantageous to combine
2101 \begin_inset Formula
2103 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2111 \begin_layout Standard
2112 For inline fractions with a sloped fraction stroke you can use the command
2120 \begin_inset Index idx
2123 \begin_layout Plain Layout
2132 \begin_inset Formula $\nicefrac{5}{31}$
2142 \begin_inset Index idx
2145 \begin_layout Plain Layout
2154 \begin_inset Formula $\unitfrac{5}{31}$
2157 There is furthermore the command
2163 that offers to write a fraction in combination with a number:
2164 \begin_inset Formula $\unitfrac[2]{1}{3}$
2170 \begin_layout Standard
2171 \begin_inset Note Greyedout
2174 \begin_layout Plain Layout
2185 is not a real \SpecialChar LaTeX
2186 command but the command
2187 \begin_inset Newline newline
2194 unitfrac[number]{numerator}{denominator}
2197 Therefore you cannot use it in \SpecialChar TeX
2206 \begin_layout Standard
2207 How to define own fractions where the fraction stroke can be changed, is
2209 \begin_inset CommandInset ref
2211 reference "subsec:Self-defined-Fractions"
2218 \begin_layout Standard
2219 Multiline fractions are explained in
2220 \begin_inset CommandInset ref
2222 reference "subsec:Multiline-Fractions"
2229 \begin_layout Subsection
2231 \begin_inset Index idx
2234 \begin_layout Plain Layout
2243 \begin_layout Standard
2244 Square roots are created with
2251 \begin_inset Index idx
2254 \begin_layout Plain Layout
2262 or the math toolbar button
2265 arg "math-insert \\sqrt"
2268 , all other roots with the command
2275 \begin_inset Index idx
2278 \begin_layout Plain Layout
2286 or with the math toolbar button
2289 arg "math-insert \\root"
2293 \begin_inset Separator parbreak
2299 \begin_layout Standard
2301 \begin_inset Tabular
2302 <lyxtabular version="3" rows="3" columns="2">
2303 <features booktabs="true" tabularvalignment="middle">
2304 <column alignment="center" valignment="top" width="0pt">
2305 <column alignment="center" valignment="top" width="0pt">
2307 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2310 \begin_layout Plain Layout
2316 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2319 \begin_layout Plain Layout
2326 <row topspace="1mm">
2327 <cell alignment="center" valignment="top" usebox="none">
2330 \begin_layout Plain Layout
2334 \begin_inset space \textvisiblespace{}
2342 <cell alignment="center" valignment="top" usebox="none">
2345 \begin_layout Plain Layout
2346 \begin_inset Formula $\sqrt{A-B}$
2355 <row topspace="1mm">
2356 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2359 \begin_layout Plain Layout
2363 \begin_inset space \textvisiblespace{}
2367 \begin_inset Formula $\downarrow$
2375 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2378 \begin_layout Plain Layout
2379 \begin_inset Formula $\sqrt[3]{A-B}$
2395 \begin_layout Standard
2396 A square root can also be created with
2402 when the root index field is left empty.
2405 \begin_layout Standard
2406 With certain indices the distance to the root is too small, like in this
2408 \begin_inset Formula $\sqrt[\beta]{B}$
2412 \begin_inset Newline newline
2416 \begin_inset Formula $\beta$
2420 To avoid this, the commands
2427 \begin_inset Index idx
2430 \begin_layout Plain Layout
2445 \begin_inset Index idx
2448 \begin_layout Plain Layout
2456 are used with the following scheme:
2459 \begin_layout Standard
2473 \begin_layout Standard
2474 Distance is the number of Big Points (unit bp;
2475 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2478 ), that the index should be moved to the left or top, resp..
2479 The commands are written to the index.
2480 This way the command
2481 \begin_inset Newline newline
2491 \begin_inset Formula $\to$
2497 \begin_inset Formula $\to$
2503 \begin_inset space \textvisiblespace{}
2507 \begin_inset Formula $\to$
2511 \begin_inset Newline newline
2516 produces a correct typeset formula:
2517 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2523 \begin_layout Subsection
2524 Binomial Coefficients
2525 \begin_inset Index idx
2528 \begin_layout Plain Layout
2529 Binomial coefficients
2537 \begin_layout Standard
2538 Binomial coefficients are inserted with the command
2545 \begin_inset Index idx
2548 \begin_layout Plain Layout
2556 or with the submenu of the math toolbar button
2559 arg "math-insert \\frac-square"
2575 there are the commands
2582 \begin_inset Index idx
2585 \begin_layout Plain Layout
2600 \begin_inset Index idx
2603 \begin_layout Plain Layout
2612 For other brackets around binomial coeficients there are the commands
2619 \begin_inset Index idx
2622 \begin_layout Plain Layout
2637 \begin_inset Index idx
2640 \begin_layout Plain Layout
2649 \begin_inset Separator parbreak
2655 \begin_layout Standard
2657 \begin_inset Tabular
2658 <lyxtabular version="3" rows="6" columns="2">
2659 <features booktabs="true" tabularvalignment="middle">
2660 <column alignment="center" valignment="top" width="0pt">
2661 <column alignment="center" valignment="top" width="0pt">
2663 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2666 \begin_layout Plain Layout
2672 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2675 \begin_layout Plain Layout
2682 <row topspace="1mm">
2683 <cell alignment="center" valignment="top" usebox="none">
2686 \begin_layout Plain Layout
2690 \begin_inset space \textvisiblespace{}
2694 \begin_inset Formula $\downarrow$
2702 <cell alignment="center" valignment="top" usebox="none">
2705 \begin_layout Plain Layout
2706 \begin_inset Formula $\binom{A}{B}$
2715 <row topspace="2mm">
2716 <cell alignment="center" valignment="top" usebox="none">
2719 \begin_layout Plain Layout
2723 \begin_inset space \textvisiblespace{}
2727 \begin_inset Formula $\downarrow$
2735 <cell alignment="center" valignment="top" usebox="none">
2738 \begin_layout Plain Layout
2739 \begin_inset Formula $\dbinom{A}{B}$
2748 <row topspace="2mm" bottomspace="0.5mm">
2749 <cell alignment="center" valignment="top" usebox="none">
2752 \begin_layout Plain Layout
2756 \begin_inset space \textvisiblespace{}
2760 \begin_inset Formula $\downarrow$
2768 <cell alignment="center" valignment="top" usebox="none">
2771 \begin_layout Plain Layout
2772 \begin_inset Formula $\tbinom{A}{B}$
2781 <row topspace="1mm">
2782 <cell alignment="center" valignment="top" topline="true" usebox="none">
2785 \begin_layout Plain Layout
2789 \begin_inset space \textvisiblespace{}
2793 \begin_inset Formula $\downarrow$
2801 <cell alignment="center" valignment="top" topline="true" usebox="none">
2804 \begin_layout Plain Layout
2805 \begin_inset Formula ${A \brack B}$
2814 <row topspace="2mm" bottomspace="0.5mm">
2815 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2818 \begin_layout Plain Layout
2822 \begin_inset space \textvisiblespace{}
2826 \begin_inset Formula $\downarrow$
2834 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2837 \begin_layout Plain Layout
2838 \begin_inset Formula ${A \brace B}$
2854 \begin_layout Subsection
2855 Case Differentiations
2856 \begin_inset Index idx
2859 \begin_layout Plain Layout
2860 Case differentiations
2868 \begin_layout Standard
2870 \begin_inset Tabular
2871 <lyxtabular version="3" rows="3" columns="2">
2872 <features booktabs="true" tabularvalignment="middle">
2873 <column alignment="center" valignment="top" width="0pt">
2874 <column alignment="center" valignment="top" width="0pt">
2876 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2879 \begin_layout Plain Layout
2885 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2888 \begin_layout Plain Layout
2896 <cell alignment="center" valignment="top" usebox="none">
2899 \begin_layout Plain Layout
2903 \begin_inset space \textvisiblespace{}
2907 \begin_inset Formula $\to$
2911 \begin_inset Index idx
2914 \begin_layout Plain Layout
2927 <cell alignment="center" valignment="top" usebox="none">
2930 \begin_layout Plain Layout
2931 \begin_inset Formula $\begin{cases}
2941 <row topspace="1.5mm">
2942 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2945 \begin_layout Plain Layout
2949 \begin_inset space \textvisiblespace{}
2955 arg "newline-insert newline"
2963 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2966 \begin_layout Plain Layout
2967 \begin_inset Formula $\begin{cases}
2968 A & \textrm{for }x>0\\
2969 B & \textrm{for }x=0
2986 \begin_layout Standard
2993 or pressing the math toolbar button
2996 arg "math-insert \\cases"
2999 you can create new lines with the shortcut
3002 arg "newline-insert newline"
3005 or the table toolbar button
3008 arg "inset-modify tabular append-row"
3014 \begin_layout Standard
3021 is also available via the menu
3023 Insert\SpecialChar menuseparator
3024 Math\SpecialChar menuseparator
3030 \begin_layout Subsection
3032 \begin_inset Index idx
3035 \begin_layout Plain Layout
3044 \begin_layout Standard
3052 \begin_inset Index idx
3055 \begin_layout Plain Layout
3063 every character can be displayed canceled.
3064 The characters are quasi accentuated by a slash.
3065 \begin_inset Separator parbreak
3071 \begin_layout Standard
3073 \begin_inset Tabular
3074 <lyxtabular version="3" rows="4" columns="2">
3075 <features booktabs="true" tabularvalignment="middle">
3076 <column alignment="center" valignment="top" width="0pt">
3077 <column alignment="center" valignment="top" width="0pt">
3079 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3082 \begin_layout Plain Layout
3088 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3091 \begin_layout Plain Layout
3099 <cell alignment="center" valignment="top" usebox="none">
3102 \begin_layout Plain Layout
3110 <cell alignment="center" valignment="top" usebox="none">
3113 \begin_layout Plain Layout
3114 \begin_inset Formula $\not=$
3124 <cell alignment="center" valignment="top" usebox="none">
3127 \begin_layout Plain Layout
3137 <cell alignment="center" valignment="top" usebox="none">
3140 \begin_layout Plain Layout
3141 \begin_inset Formula $\not\le$
3151 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3154 \begin_layout Plain Layout
3164 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3167 \begin_layout Plain Layout
3168 \begin_inset Formula $\not\parallel$
3184 \begin_layout Standard
3185 The last example shows that not all negations look good.
3186 Therefore there are special commands for some negations (see
3187 \begin_inset CommandInset ref
3189 reference "subsec:Mathematical-Symbols"
3194 \begin_inset CommandInset ref
3196 reference "sec:Relations"
3203 \begin_layout Subsection
3205 \begin_inset CommandInset label
3207 name "subsec:Placeholders"
3212 \begin_inset Index idx
3215 \begin_layout Plain Layout
3222 \begin_inset Index idx
3225 \begin_layout Plain Layout
3226 Chemical characters ! Isotopes
3232 \begin_inset Index idx
3235 \begin_layout Plain Layout
3240 \begin_layout Plain Layout
3251 \begin_layout Plain Layout
3266 \begin_layout Standard
3268 \begin_inset space \thinspace{}
3272 \begin_inset space \space{}
3279 \begin_layout Plain Layout
3280 Typesetting isotopes and chemical symbols is described in
3281 \begin_inset CommandInset ref
3283 reference "subsec:Chemical-Symbols-and"
3292 the following problem occurs:
3293 \begin_inset Separator parbreak
3299 \begin_layout Standard
3301 \begin_inset Tabular
3302 <lyxtabular version="3" rows="2" columns="2">
3303 <features booktabs="true" tabularvalignment="middle">
3304 <column alignment="center" valignment="top" width="0pt">
3305 <column alignment="center" valignment="top" width="0pt">
3307 <cell alignment="center" valignment="top" usebox="none">
3310 \begin_layout Plain Layout
3311 Indices created with sub- and superscripts:
3316 <cell alignment="center" valignment="top" usebox="none">
3319 \begin_layout Plain Layout
3320 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3329 <row topspace="1.5mm">
3330 <cell alignment="center" valignment="top" usebox="none">
3333 \begin_layout Plain Layout
3339 <cell alignment="center" valignment="top" usebox="none">
3342 \begin_layout Plain Layout
3343 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3359 \begin_layout Standard
3360 The shorter index is by default placed below or above the first character
3361 of the longer index.
3362 To avoid this there is the command
3369 \begin_inset Index idx
3372 \begin_layout Plain Layout
3380 or the math toolbar button
3381 \begin_inset space \thinspace{}
3388 \begin_layout Plain Layout
3389 can be found in the submenu of the toolbar button
3392 arg "math-insert \\space"
3401 \begin_inset Graphics
3402 filename ../images/math/phantom.svgz
3408 that creates one or more phantom characters.
3415 a small blue box appears that is superposed with two red arrows.
3416 The arrows indicate that the complete width and height of the box content
3417 will be created as placeholder.
3418 Phantom characters are accordingly placeholders with the size of the characters.
3419 \begin_inset Separator parbreak
3425 \begin_layout Standard
3427 \begin_inset Tabular
3428 <lyxtabular version="3" rows="4" columns="2">
3429 <features booktabs="true" tabularvalignment="middle">
3430 <column alignment="center" valignment="top" width="0pt">
3431 <column alignment="center" valignment="top" width="0pt">
3433 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3436 \begin_layout Plain Layout
3442 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3445 \begin_layout Plain Layout
3452 <row topspace="1.5mm">
3453 <cell alignment="center" valignment="top" usebox="none">
3456 \begin_layout Plain Layout
3458 \begin_inset space \textvisiblespace{}
3464 \begin_inset space \textvisiblespace{}
3468 \begin_inset Formula $\to$
3472 \begin_inset space \textvisiblespace{}
3480 <cell alignment="center" valignment="top" usebox="none">
3483 \begin_layout Plain Layout
3484 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3493 <row topspace="1.5mm" bottomspace="0.5mm">
3494 <cell alignment="center" valignment="top" usebox="none">
3497 \begin_layout Plain Layout
3499 \begin_inset space \textvisiblespace{}
3505 \begin_inset space \textvisiblespace{}
3509 \begin_inset Formula $\to$
3513 \begin_inset space \textvisiblespace{}
3521 <cell alignment="center" valignment="top" usebox="none">
3524 \begin_layout Plain Layout
3525 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3534 <row topspace="1.5mm" bottomspace="0.5mm">
3535 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3538 \begin_layout Plain Layout
3542 \begin_inset space \textvisiblespace{}
3548 \begin_inset space \textvisiblespace{}
3552 \begin_inset Formula $\to$
3556 \begin_inset space \textvisiblespace{}
3564 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3567 \begin_layout Plain Layout
3568 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3584 \begin_layout Standard
3585 Furthermore there are the commands
3592 \begin_inset Index idx
3595 \begin_layout Plain Layout
3604 \begin_inset space ~
3608 \begin_inset Graphics
3609 filename ../images/math/vphantom.svgz
3622 \begin_inset Index idx
3625 \begin_layout Plain Layout
3634 \begin_inset space ~
3638 \begin_inset Graphics
3639 filename ../images/math/hphantom.svgz
3652 creates only space for the maximal height of the characters in the box
3653 but not for its width.
3660 creates only space for the width of the box content.
3661 Therefore the boxes of both commands have only one red arrow.
3664 \begin_layout Standard
3665 For example the command
3670 \begin_inset space \textvisiblespace{}
3677 creates space for the height of the integral sign,
3681 \begin_layout Plain Layout
3688 creates an integral sign, see
3689 \begin_inset CommandInset ref
3691 reference "subsec:Big-Operators"
3700 because this is the larger character.
3701 An example application is in
3702 \begin_inset CommandInset ref
3704 reference "subsec:Multiline-Brackets"
3711 \begin_layout Standard
3712 Placeholders can also be used for text when they are inserted via the menu
3715 Insert\SpecialChar menuseparator
3716 Formatting\SpecialChar menuseparator
3722 \begin_layout Standard
3724 \begin_inset Newline newline
3728 \begin_inset Phantom Phantom
3731 \begin_layout Plain Layout
3740 \begin_layout Subsection
3742 \begin_inset Index idx
3745 \begin_layout Plain Layout
3752 \begin_inset Index idx
3755 \begin_layout Plain Layout
3756 Formula ! underlined
3764 \begin_layout Standard
3766 \begin_inset Tabular
3767 <lyxtabular version="3" rows="4" columns="2">
3768 <features booktabs="true" tabularvalignment="middle">
3769 <column alignment="center" valignment="top" width="0pt">
3770 <column alignment="center" valignment="top" width="0pt">
3772 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3775 \begin_layout Plain Layout
3781 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3784 \begin_layout Plain Layout
3791 <row topspace="2mm">
3792 <cell alignment="center" valignment="top" usebox="none">
3795 \begin_layout Plain Layout
3799 \begin_inset space \textvisiblespace{}
3803 \begin_inset Index idx
3806 \begin_layout Plain Layout
3819 <cell alignment="center" valignment="top" usebox="none">
3822 \begin_layout Plain Layout
3823 \begin_inset Formula $\overline{A+B}$
3832 <row bottomspace="1mm">
3833 <cell alignment="center" valignment="top" usebox="none">
3836 \begin_layout Plain Layout
3840 \begin_inset space \textvisiblespace{}
3844 \begin_inset Index idx
3847 \begin_layout Plain Layout
3860 <cell alignment="center" valignment="top" usebox="none">
3863 \begin_layout Plain Layout
3864 \begin_inset Formula $\underline{A+B}$
3873 <row topspace="2mm" bottomspace="1mm">
3874 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3877 \begin_layout Plain Layout
3881 \begin_inset space \textvisiblespace{}
3887 \begin_inset space \textvisiblespace{}
3895 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3898 \begin_layout Plain Layout
3899 \begin_inset Formula $\overline{\underline{A+B}}$
3915 \begin_layout Standard
3916 In the last example it doesn't matter if first
3931 \begin_layout Standard
3932 To double underline use
3941 \begin_layout Standard
3942 It is possible to place up to 6 lines above or below characters.
3945 \begin_layout Standard
3946 \begin_inset VSpace bigskip
3949 Custom lines can be created using the command
3956 \begin_inset Index idx
3959 \begin_layout Plain Layout
3967 which has the following scheme:
3970 \begin_layout Standard
3975 rule[vertical offset]{length}{thickness}
3978 \begin_layout Standard
3979 The optional vertical offset shifts the line upwards (or downwards, when
3980 the value is negative).
3982 \begin_inset CommandInset ref
3984 reference "tab:Available-units"
3988 can be used for the values.
3989 Here are two example lines created with the commands
3990 \begin_inset Newline newline
3997 rule[-2ex]{3cm}{2pt}
4008 \begin_layout Standard
4010 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4016 \begin_layout Standard
4023 can also be used for text when a line is inserted via the menu
4025 Insert\SpecialChar menuseparator
4026 Formatting\SpecialChar menuseparator
4028 \begin_inset space ~
4036 \begin_layout Standard
4038 \begin_inset CommandInset line
4049 \begin_layout Subsection
4051 \begin_inset CommandInset label
4053 name "subsec:Ellipses"
4058 \begin_inset Index idx
4061 \begin_layout Plain Layout
4070 \begin_layout Standard
4071 There are different types of ellipses available.
4075 \begin_layout Plain Layout
4076 In the math toolbar in the submenu of the button
4079 arg "math-insert \\ldots"
4087 For listings dots at the baseline are used (
4094 \begin_inset Index idx
4097 \begin_layout Plain Layout
4105 ), while for operations dots are needed that are on the same height as the
4113 \begin_inset Index idx
4116 \begin_layout Plain Layout
4125 When using the command
4132 \begin_inset Index idx
4135 \begin_layout Plain Layout
4143 , \SpecialChar LaTeX
4144 decides on the basis of the next character what type is used.
4145 \begin_inset Separator parbreak
4151 \begin_layout Standard
4153 \begin_inset Tabular
4154 <lyxtabular version="3" rows="9" columns="2">
4155 <features booktabs="true" tabularvalignment="middle">
4156 <column alignment="center" valignment="top" width="0pt">
4157 <column alignment="center" valignment="top" width="0pt">
4159 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4162 \begin_layout Plain Layout
4168 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4171 \begin_layout Plain Layout
4179 <cell alignment="center" valignment="top" usebox="none">
4182 \begin_layout Plain Layout
4184 \begin_inset space \textvisiblespace{}
4190 \begin_inset space \textvisiblespace{}
4198 <cell alignment="center" valignment="top" usebox="none">
4201 \begin_layout Plain Layout
4202 \begin_inset Formula $A_{1},\dots,A_{n}$
4212 <cell alignment="center" valignment="top" usebox="none">
4215 \begin_layout Plain Layout
4217 \begin_inset space \textvisiblespace{}
4223 \begin_inset space \textvisiblespace{}
4231 <cell alignment="center" valignment="top" usebox="none">
4234 \begin_layout Plain Layout
4235 \begin_inset Formula $A_{1}+\dots+A_{n}$
4245 <cell alignment="center" valignment="top" usebox="none">
4248 \begin_layout Plain Layout
4250 \begin_inset space \textvisiblespace{}
4256 \begin_inset space \textvisiblespace{}
4264 <cell alignment="center" valignment="top" usebox="none">
4267 \begin_layout Plain Layout
4268 \begin_inset Formula $A_{1},\ldots,A_{n}$
4278 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4281 \begin_layout Plain Layout
4283 \begin_inset space \textvisiblespace{}
4289 \begin_inset space \textvisiblespace{}
4297 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4300 \begin_layout Plain Layout
4301 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4311 <cell alignment="center" valignment="top" usebox="none">
4314 \begin_layout Plain Layout
4322 <cell alignment="center" valignment="top" usebox="none">
4325 \begin_layout Plain Layout
4326 \begin_inset Formula $\vdots$
4336 <cell alignment="center" valignment="top" usebox="none">
4339 \begin_layout Plain Layout
4347 <cell alignment="center" valignment="top" usebox="none">
4350 \begin_layout Plain Layout
4351 \begin_inset Formula $\ddots$
4361 <cell alignment="center" valignment="top" usebox="none">
4364 \begin_layout Plain Layout
4372 <cell alignment="center" valignment="top" usebox="none">
4375 \begin_layout Plain Layout
4376 \begin_inset Formula $\iddots$
4386 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4389 \begin_layout Plain Layout
4391 \begin_inset space \thinspace{}
4394 matrix with the different dots
4399 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4402 \begin_layout Plain Layout
4403 \begin_inset Formula $\begin{array}{ccc}
4404 A_{11} & \cdots & A_{1m}\\
4405 \vdots & \ddots & \vdots\\
4406 A_{n1} & \cdots & A_{nm}
4423 \begin_layout Standard
4424 The ellipses available in menu
4426 Insert\SpecialChar menuseparator
4428 \begin_inset space ~
4442 \begin_layout Standard
4443 \begin_inset VSpace medskip
4452 , one of the options
4454 Use mathdots package (automatically)
4456 must be set in the document settings under
4459 \begin_inset space ~
4465 \begin_inset Newline newline
4470 Use mathdots package
4472 will improve the appearance of all dots in the documents if their font
4473 style or size is not the default.
4476 \begin_layout Standard
4477 \begin_inset VSpace medskip
4480 Specially for matrices there are ellipses that span over several columns.
4481 They are created with the command
4488 \begin_inset Index idx
4491 \begin_layout Plain Layout
4499 , that has the following scheme:
4502 \begin_layout Standard
4507 hdotsfor[distance]{number of columns}
4510 \begin_layout Standard
4511 The number of columns specifies how many columns should be spanned.
4512 Distance is a factor for the distance between the dots.
4515 \begin_layout Standard
4516 In the following matrix the command
4522 was inserted in the first box of the second line, to get an ellipsis with
4523 a dot distance twice as long as with the command
4530 \begin_inset Formula
4532 \left(\begin{array}{cccc}
4541 Note that the matrix fields that should be spanned must be empty, otherwise
4542 you get \SpecialChar LaTeX
4546 \begin_layout Standard
4547 \begin_inset VSpace bigskip
4550 Furthermore you can fill with the command
4557 \begin_inset Index idx
4560 \begin_layout Plain Layout
4568 the rest of a line with dots.
4569 The effect of these commands is the same as with
4576 \begin_inset CommandInset ref
4578 reference "subsec:Variable-Space"
4585 \begin_layout Standard
4586 For example the command
4591 \begin_inset space \textvisiblespace{}
4599 \begin_layout Standard
4600 \begin_inset Formula $A\dotfill B$
4606 \begin_layout Standard
4613 there is for a line the command
4620 \begin_inset Index idx
4623 \begin_layout Plain Layout
4634 \begin_layout Standard
4635 \begin_inset Formula $A\hrulefill B$
4641 \begin_layout Standard
4642 To use the commands for text, they have to be inserted in \SpecialChar TeX
4646 \begin_layout Section
4648 \begin_inset CommandInset label
4655 \begin_inset Index idx
4658 \begin_layout Plain Layout
4667 \begin_layout Standard
4668 Matrices can be inserted via the math toolbar button
4671 arg "dialog-show mathmatrix"
4676 Insert\SpecialChar menuseparator
4677 Math\SpecialChar menuseparator
4681 In the matrix dialog you can specify the number of columns and rows, the
4682 alignment and the decoration.
4683 The vertical alignment is only of importance for matrices in inline formulas:
4686 \begin_layout Standard
4687 The first matrix is top
4688 \begin_inset Formula $\begin{array}[t]{cccc}
4696 \begin_inset Formula $\begin{array}{cccc}
4703 and the third bottom
4704 \begin_inset Formula $\begin{array}[b]{cccc}
4714 \begin_layout Standard
4715 The horizontal alignment specifies how the column entries should be aligned.
4716 It is set by entering a letter for every column.
4721 denotes left aligned,
4730 To create for example a 4
4735 \begin_inset space ~
4738 matrix where the first column is left aligned, the second and third are
4739 centered and the last one is right aligned, one enters for the horizontal
4745 Normally in a matrix all columns are centered, therefore the default for
4753 \begin_layout Standard
4754 Horizontal alignment:
4757 \begin_layout Standard
4763 \begin_inset Formula $\begin{array}{lll}
4775 \begin_inset Formula $\begin{array}{ccc}
4787 \begin_inset Formula $\begin{array}{rrr}
4797 \begin_layout Standard
4798 To add or delete rows and columns subsequently, the math toolbar buttons
4802 arg "inset-modify tabular append-row"
4808 arg "inset-modify tabular delete-row"
4812 \begin_inset space \thinspace{}
4817 Edit\SpecialChar menuseparator
4821 New rows can also be created with
4824 arg "newline-insert newline"
4830 \begin_layout Standard
4831 \begin_inset VSpace bigskip
4838 adds parentheses in the selected style around the matrix.
4839 Alternatively, parentheses can can either be created with the commands
4847 \begin_inset Index idx
4850 \begin_layout Plain Layout
4865 \begin_inset Index idx
4868 \begin_layout Plain Layout
4879 \begin_inset space ~
4885 \begin_inset CommandInset ref
4887 reference "subsec:Automatic-Bracket-Size"
4891 , or by using the following commands:
4892 \begin_inset VSpace medskip
4898 \begin_layout Standard
4899 \begin_inset space \hfill{}
4903 \begin_inset Tabular
4904 <lyxtabular version="3" rows="4" columns="2">
4905 <features booktabs="true" tabularvalignment="middle">
4906 <column alignment="center" valignment="top" width="0pt">
4907 <column alignment="center" valignment="top">
4909 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4912 \begin_layout Plain Layout
4918 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4921 \begin_layout Plain Layout
4928 <row topspace="1.5mm">
4929 <cell alignment="center" valignment="top" usebox="none">
4932 \begin_layout Plain Layout
4936 \begin_inset space \textvisiblespace{}
4944 \begin_inset space \thinspace{}
4952 <cell alignment="center" valignment="top" usebox="none">
4955 \begin_layout Plain Layout
4956 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4957 0 & \textrm{-}\mathrm{i}\\
4959 \end{array}\end{bmatrix}$
4968 <row topspace="1.5mm" bottomspace="0.5mm">
4969 <cell alignment="center" valignment="top" usebox="none">
4972 \begin_layout Plain Layout
4976 \begin_inset space \textvisiblespace{}
4984 \begin_inset space \thinspace{}
4992 <cell alignment="center" valignment="top" usebox="none">
4995 \begin_layout Plain Layout
4996 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
4997 0 & \textrm{-}\mathrm{i}\\
4999 \end{array}\end{Bmatrix}$
5009 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5012 \begin_layout Plain Layout
5016 \begin_inset space \textvisiblespace{}
5024 \begin_inset space \thinspace{}
5032 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5035 \begin_layout Plain Layout
5036 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5037 0 & \textrm{-}\mathrm{i}\\
5039 \end{array}\end{pmatrix}$
5053 \begin_inset space \hfill{}
5057 \begin_inset Tabular
5058 <lyxtabular version="3" rows="4" columns="2">
5059 <features booktabs="true" tabularvalignment="middle">
5060 <column alignment="center" valignment="top" width="0pt">
5061 <column alignment="center" valignment="top">
5063 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5066 \begin_layout Plain Layout
5072 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5075 \begin_layout Plain Layout
5082 <row topspace="1.5mm">
5083 <cell alignment="center" valignment="top" usebox="none">
5086 \begin_layout Plain Layout
5090 \begin_inset space \textvisiblespace{}
5098 \begin_inset space \thinspace{}
5106 <cell alignment="center" valignment="top" usebox="none">
5109 \begin_layout Plain Layout
5110 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5111 0 & \textrm{-}\mathrm{i}\\
5113 \end{array}\end{vmatrix}$
5122 <row topspace="1.5mm" bottomspace="0.5mm">
5123 <cell alignment="center" valignment="top" usebox="none">
5126 \begin_layout Plain Layout
5130 \begin_inset space \textvisiblespace{}
5138 \begin_inset space \thinspace{}
5146 <cell alignment="center" valignment="top" usebox="none">
5149 \begin_layout Plain Layout
5150 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5151 0 & \textrm{-}\mathrm{i}\\
5153 \end{array}\end{Vmatrix}$
5163 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5166 \begin_layout Plain Layout
5170 \begin_inset space \textvisiblespace{}
5178 \begin_inset space \thinspace{}
5186 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5189 \begin_layout Plain Layout
5190 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5191 0 & \textrm{-}\mathrm{i}\\
5193 \end{array}\end{matrix}$
5207 \begin_inset space \hfill{}
5213 \begin_layout Standard
5214 \begin_inset VSpace medskip
5218 \begin_inset space \thinspace{}
5222 \begin_inset space \space{}
5231 is inserted, a blue box appears between two vertical lines where the matrix
5233 \begin_inset Newline newline
5236 Note that decorated matrices ignore the vertical alignment.
5239 \begin_layout Standard
5240 \begin_inset VSpace bigskip
5243 As all multiline formulas are matrices, the length
5250 \begin_inset Index idx
5253 \begin_layout Plain Layout
5261 that is described in
5262 \begin_inset CommandInset ref
5264 reference "subsec:Column-Separation"
5268 can also be used to change the column separation of matrices.
5271 \begin_layout Standard
5272 To change the row separation, the command
5279 \begin_inset Index idx
5282 \begin_layout Plain Layout
5291 It is used as follows:
5294 \begin_layout Standard
5301 arraystretch}{stretch factor}
5302 \begin_inset Index idx
5305 \begin_layout Plain Layout
5316 \begin_layout Standard
5323 assigns the stretch factor to the predefined command
5331 \begin_inset space \thinspace{}
5335 \begin_inset space \space{}
5338 the row separation, use the factor 2.
5339 This is then used for all following matrices.
5340 To go back to the original separation, assign the factor 1 to
5349 \begin_layout Standard
5350 To set matrices into a text line, the command
5357 \begin_inset Index idx
5360 \begin_layout Plain Layout
5369 When it is inserted a blue box with two dashed lines appears.
5370 In this box the matrix is inserted.
5373 \begin_layout Standard
5375 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5377 \end{smallmatrix}\right)$
5383 \begin_layout Section
5384 Brackets and Delimiters
5385 \begin_inset Index idx
5388 \begin_layout Plain Layout
5395 \begin_inset Index idx
5398 \begin_layout Plain Layout
5407 \begin_layout Subsection
5408 Vertical Brackets and Delimiters
5409 \begin_inset Index idx
5412 \begin_layout Plain Layout
5421 \begin_layout Standard
5422 \begin_inset space \hfill{}
5426 \begin_inset Tabular
5427 <lyxtabular version="3" rows="9" columns="2">
5428 <features booktabs="true" tabularvalignment="middle">
5429 <column alignment="center" valignment="top" width="0pt">
5430 <column alignment="center" valignment="top" width="0pt">
5432 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5435 \begin_layout Plain Layout
5441 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5444 \begin_layout Plain Layout
5452 <cell alignment="center" valignment="top" usebox="none">
5455 \begin_layout Plain Layout
5461 <cell alignment="center" valignment="top" usebox="none">
5464 \begin_layout Plain Layout
5465 \begin_inset Formula $($
5475 <cell alignment="center" valignment="top" usebox="none">
5478 \begin_layout Plain Layout
5484 <cell alignment="center" valignment="top" usebox="none">
5487 \begin_layout Plain Layout
5488 \begin_inset Formula $\{$
5498 <cell alignment="center" valignment="top" usebox="none">
5501 \begin_layout Plain Layout
5507 <cell alignment="center" valignment="top" usebox="none">
5510 \begin_layout Plain Layout
5511 \begin_inset Formula $[$
5521 <cell alignment="center" valignment="top" usebox="none">
5524 \begin_layout Plain Layout
5532 <cell alignment="center" valignment="top" usebox="none">
5535 \begin_layout Plain Layout
5536 \begin_inset Formula $\langle$
5546 <cell alignment="center" valignment="top" usebox="none">
5549 \begin_layout Plain Layout
5557 <cell alignment="center" valignment="top" usebox="none">
5560 \begin_layout Plain Layout
5561 \begin_inset Formula $\lceil$
5571 <cell alignment="center" valignment="top" usebox="none">
5574 \begin_layout Plain Layout
5582 <cell alignment="center" valignment="top" usebox="none">
5585 \begin_layout Plain Layout
5586 \begin_inset Formula $\lfloor$
5596 <cell alignment="center" valignment="top" usebox="none">
5599 \begin_layout Plain Layout
5605 <cell alignment="center" valignment="top" usebox="none">
5608 \begin_layout Plain Layout
5609 \begin_inset Formula $/$
5619 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5622 \begin_layout Plain Layout
5628 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5631 \begin_layout Plain Layout
5632 \begin_inset Formula $|$
5646 \begin_inset space \hfill{}
5650 \begin_inset Tabular
5651 <lyxtabular version="3" rows="9" columns="2">
5652 <features booktabs="true" tabularvalignment="middle">
5653 <column alignment="center" valignment="top" width="0pt">
5654 <column alignment="center" valignment="top" width="0pt">
5656 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5659 \begin_layout Plain Layout
5665 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5668 \begin_layout Plain Layout
5676 <cell alignment="center" valignment="top" usebox="none">
5679 \begin_layout Plain Layout
5685 <cell alignment="center" valignment="top" usebox="none">
5688 \begin_layout Plain Layout
5689 \begin_inset Formula $)$
5699 <cell alignment="center" valignment="top" usebox="none">
5702 \begin_layout Plain Layout
5708 <cell alignment="center" valignment="top" usebox="none">
5711 \begin_layout Plain Layout
5712 \begin_inset Formula $\}$
5722 <cell alignment="center" valignment="top" usebox="none">
5725 \begin_layout Plain Layout
5731 <cell alignment="center" valignment="top" usebox="none">
5734 \begin_layout Plain Layout
5735 \begin_inset Formula $]$
5745 <cell alignment="center" valignment="top" usebox="none">
5748 \begin_layout Plain Layout
5756 <cell alignment="center" valignment="top" usebox="none">
5759 \begin_layout Plain Layout
5760 \begin_inset Formula $\rangle$
5770 <cell alignment="center" valignment="top" usebox="none">
5773 \begin_layout Plain Layout
5781 <cell alignment="center" valignment="top" usebox="none">
5784 \begin_layout Plain Layout
5785 \begin_inset Formula $\rceil$
5795 <cell alignment="center" valignment="top" usebox="none">
5798 \begin_layout Plain Layout
5806 <cell alignment="center" valignment="top" usebox="none">
5809 \begin_layout Plain Layout
5810 \begin_inset Formula $\rfloor$
5820 <cell alignment="center" valignment="top" usebox="none">
5823 \begin_layout Plain Layout
5833 <cell alignment="center" valignment="top" usebox="none">
5836 \begin_layout Plain Layout
5837 \begin_inset Formula $\backslash$
5847 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5850 \begin_layout Plain Layout
5858 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5861 \begin_layout Plain Layout
5862 \begin_inset Formula $\|$
5876 \begin_inset space \hfill{}
5882 \begin_layout Standard
5885 \begin_inset Note Greyedout
5888 \begin_layout Plain Layout
5901 \begin_inset Index idx
5904 \begin_layout Plain Layout
5912 must be used for the backslash, because the command
5920 produces a line break there.
5928 \begin_layout Standard
5929 For all characters listed above the size can be adjusted with the commands
5930 described in the following two subsections.
5931 When using these commands, the characters < and > can directly be used
5932 instead of the commands
5947 \begin_layout Subsubsection
5949 \begin_inset CommandInset label
5951 name "subsec:Manual-Bracket-Size"
5956 \begin_inset Index idx
5959 \begin_layout Plain Layout
5960 Bracket size ! manual
5968 \begin_layout Standard
5969 The bracket size can be specified manually by the \SpecialChar LaTeX
5977 \begin_inset Index idx
5980 \begin_layout Plain Layout
6013 denotes the smallest and
6019 the largest bracket size.
6022 \begin_layout Standard
6023 These commands are used to emphasize levels of brackets:
6024 \begin_inset Separator parbreak
6030 \begin_layout Standard
6032 \begin_inset Tabular
6033 <lyxtabular version="3" rows="2" columns="2">
6034 <features booktabs="true" tabularvalignment="middle">
6035 <column alignment="center" valignment="top" width="0pt">
6036 <column alignment="center" valignment="top" width="0pt">
6038 <cell alignment="center" valignment="top" usebox="none">
6041 \begin_layout Plain Layout
6042 all brackets in the same size:
6047 <cell alignment="center" valignment="top" usebox="none">
6050 \begin_layout Plain Layout
6051 \begin_inset Formula $((A+B)(A-B))^{C}$
6060 <row topspace="2mm">
6061 <cell alignment="center" valignment="top" usebox="none">
6064 \begin_layout Plain Layout
6070 <cell alignment="center" valignment="top" usebox="none">
6073 \begin_layout Plain Layout
6074 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6090 \begin_layout Standard
6091 For the second formula the command
6098 \begin_inset space \textvisiblespace{}
6106 \begin_layout Standard
6107 Here is an overview about all bracket sizes:
6108 \begin_inset Separator parbreak
6114 \begin_layout Standard
6131 \begin_inset space \textvisiblespace{}
6139 \begin_inset space \textvisiblespace{}
6143 \begin_inset space \textvisiblespace{}
6153 \begin_layout Standard
6155 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6161 \begin_layout Standard
6168 -commands there is the variant
6175 \begin_inset Index idx
6178 \begin_layout Plain Layout
6186 that adds a bit more space between the bracket and its content, and the
6200 \begin_inset Index idx
6203 \begin_layout Plain Layout
6213 , that don't add additional space.
6218 at the end of the command
6224 is for a left bracket; for a right bracket this will be replaced by an
6230 A left or right bracket can each be an opening or closing bracket.
6233 \begin_layout Standard
6234 In the following table is a comparison of the variants:
6235 \begin_inset Separator parbreak
6241 \begin_layout Standard
6243 \begin_inset Tabular
6244 <lyxtabular version="3" rows="5" columns="2">
6245 <features booktabs="true" tabularvalignment="middle">
6246 <column alignment="center" valignment="top" width="0pt">
6247 <column alignment="center" valignment="middle">
6249 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6252 \begin_layout Plain Layout
6258 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6261 \begin_layout Plain Layout
6268 <row topspace="2mm">
6269 <cell alignment="center" valignment="top" usebox="none">
6272 \begin_layout Plain Layout
6282 \begin_inset space \textvisiblespace{}
6292 <cell alignment="center" valignment="top" usebox="none">
6295 \begin_layout Plain Layout
6296 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6305 <row topspace="2mm">
6306 <cell alignment="center" valignment="top" usebox="none">
6309 \begin_layout Plain Layout
6319 \begin_inset space \textvisiblespace{}
6329 <cell alignment="center" valignment="top" usebox="none">
6332 \begin_layout Plain Layout
6333 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6342 <row topspace="2mm" bottomspace="0.5mm">
6343 <cell alignment="center" valignment="top" usebox="none">
6346 \begin_layout Plain Layout
6356 \begin_inset space \textvisiblespace{}
6366 <cell alignment="center" valignment="top" usebox="none">
6369 \begin_layout Plain Layout
6370 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6379 <row topspace="1.5mm" bottomspace="0.5mm">
6380 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6383 \begin_layout Plain Layout
6395 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6398 \begin_layout Plain Layout
6399 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6415 \begin_layout Subsubsection
6416 Automatic Bracket Size
6417 \begin_inset CommandInset label
6419 name "subsec:Automatic-Bracket-Size"
6424 \begin_inset Index idx
6427 \begin_layout Plain Layout
6428 Bracket size ! automatic
6436 \begin_layout Standard
6437 Brackets with variable size can be inserted with the commands
6444 \begin_inset Index idx
6447 \begin_layout Plain Layout
6462 \begin_inset Index idx
6465 \begin_layout Plain Layout
6473 or via the math toolbar button
6476 arg "dialog-show mathdelimiter"
6492 the wanted bracket must be inserted.
6493 The bracket size will then automatically be calculated for the output.
6494 \begin_inset Separator parbreak
6500 \begin_layout Standard
6502 normal bracket: The command
6509 \begin_inset space \textvisiblespace{}
6513 \begin_inset Formula $\downarrow$
6517 \begin_inset space \textvisiblespace{}
6523 \begin_inset Formula
6533 \begin_layout Standard
6535 multiline bracket: The command
6544 \begin_inset space \textvisiblespace{}
6548 \begin_inset Formula $\downarrow$
6552 \begin_inset space \textvisiblespace{}
6560 \begin_inset Formula
6562 \ln\left(\frac{A}{C}\right)
6570 \begin_layout Standard
6586 \begin_inset space ~
6592 This has the advantage that you can see in \SpecialChar LyX
6593 immediately the real bracket
6594 size and that the matching right bracket will be created too.
6595 \begin_inset Newline newline
6598 The command for the last example would then be:
6609 \begin_inset space \textvisiblespace{}
6613 \begin_inset Formula $\downarrow$
6619 \begin_layout Standard
6620 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6621 For example the command
6628 \begin_inset space \textvisiblespace{}
6632 \begin_inset Formula $\downarrow$
6636 \begin_inset space \textvisiblespace{}
6646 \begin_inset Formula
6648 \left.\frac{A}{B}\right\}
6667 will be converted by \SpecialChar LyX
6668 to brackets in the right size when the document is
6669 reloaded and an omitted bracket will appear as dashed line.
6672 \begin_layout Standard
6673 \begin_inset VSpace bigskip
6676 Because all popular \SpecialChar LaTeX
6677 distributions use e\SpecialChar TeX
6678 , an extension to \SpecialChar LaTeX
6687 \begin_inset Index idx
6690 \begin_layout Plain Layout
6698 is additionally available for all brackets and limits.
6699 With this command the height of the following character is adapted to the
6700 one of the surrounding brackets, what is e.
6701 \begin_inset space \thinspace{}
6705 \begin_inset space \space{}
6708 needed for physical vectors:
6709 \begin_inset Formula
6711 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6716 For physical vectors there is a special \SpecialChar LaTeX
6717 -package, described in
6718 \begin_inset CommandInset ref
6720 reference "subsec:Physical-Vectors"
6727 \begin_layout Subsection
6729 \begin_inset Index idx
6732 \begin_layout Plain Layout
6733 Brackets ! horizontal
6741 \begin_layout Standard
6743 \begin_inset Tabular
6744 <lyxtabular version="3" rows="4" columns="2">
6745 <features booktabs="true" tabularvalignment="middle">
6746 <column alignment="center" valignment="top" width="0pt">
6747 <column alignment="center" valignment="top" width="0pt">
6749 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6752 \begin_layout Plain Layout
6758 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6761 \begin_layout Plain Layout
6769 <cell alignment="center" valignment="top" usebox="none">
6772 \begin_layout Plain Layout
6776 \begin_inset space \textvisiblespace{}
6780 \begin_inset space \textvisiblespace{}
6784 \begin_inset Index idx
6787 \begin_layout Plain Layout
6800 <cell alignment="center" valignment="top" usebox="none">
6803 \begin_layout Plain Layout
6804 \begin_inset Formula $\overbrace{A+B}^{3}$
6813 <row topspace="2mm">
6814 <cell alignment="center" valignment="top" usebox="none">
6817 \begin_layout Plain Layout
6821 \begin_inset space \textvisiblespace{}
6825 \begin_inset space \textvisiblespace{}
6829 \begin_inset Index idx
6832 \begin_layout Plain Layout
6845 <cell alignment="center" valignment="top" usebox="none">
6848 \begin_layout Plain Layout
6849 \begin_inset Formula $\underbrace{A+B}_{5}$
6859 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6862 \begin_layout Plain Layout
6866 \begin_inset space \textvisiblespace{}
6872 \begin_inset space \textvisiblespace{}
6876 \begin_inset space \textvisiblespace{}
6880 \begin_inset space \textvisiblespace{}
6884 \begin_inset space \textvisiblespace{}
6888 \begin_inset space \textvisiblespace{}
6892 \begin_inset space \textvisiblespace{}
6900 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6903 \begin_layout Plain Layout
6904 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6920 \begin_layout Standard
6921 In the last example it doesn't matter if
6933 is inserted at first.
6936 \begin_layout Standard
6937 \begin_inset VSpace medskip
6943 \begin_layout Standard
6944 If you set in the document settings under
6947 \begin_inset space ~
6957 \begin_inset Index idx
6960 \begin_layout Plain Layout
6961 Packages ! mathtools
6969 \begin_inset space ~
6974 , you have access to square backets:
6975 \begin_inset Separator parbreak
6981 \begin_layout Standard
6983 \begin_inset Tabular
6984 <lyxtabular version="3" rows="4" columns="2">
6985 <features booktabs="true" tabularvalignment="middle">
6986 <column alignment="center" valignment="top" width="0pt">
6987 <column alignment="center" valignment="top" width="0pt">
6989 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6992 \begin_layout Plain Layout
6998 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7001 \begin_layout Plain Layout
7009 <cell alignment="center" valignment="top" usebox="none">
7012 \begin_layout Plain Layout
7040 \begin_inset space \textvisiblespace{}
7044 \begin_inset Index idx
7047 \begin_layout Plain Layout
7060 <cell alignment="center" valignment="top" usebox="none">
7063 \begin_layout Plain Layout
7064 \begin_inset Formula $\overbracket{A+B}^{3}$
7073 <row topspace="2mm">
7074 <cell alignment="center" valignment="top" usebox="none">
7077 \begin_layout Plain Layout
7105 \begin_inset space \textvisiblespace{}
7109 \begin_inset Index idx
7112 \begin_layout Plain Layout
7137 <cell alignment="center" valignment="top" usebox="none">
7140 \begin_layout Plain Layout
7141 \begin_inset Formula $\underbracket{A+B}_{5}$
7151 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7154 \begin_layout Plain Layout
7160 \begin_inset space \textvisiblespace{}
7164 \begin_inset space \textvisiblespace{}
7168 \begin_inset space \textvisiblespace{}
7172 \begin_inset space \textvisiblespace{}
7176 \begin_inset space \textvisiblespace{}
7184 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7187 \begin_layout Plain Layout
7188 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7204 \begin_layout Standard
7217 you can change the thickness of the bracket's stroke by specifying the
7218 desired thickness in square brackets behind the command:
7219 \begin_inset Separator parbreak
7225 \begin_layout Standard
7227 \begin_inset Tabular
7228 <lyxtabular version="3" rows="3" columns="2">
7229 <features booktabs="true" tabularvalignment="middle">
7230 <column alignment="center" valignment="top" width="0pt">
7231 <column alignment="center" valignment="top" width="0pt">
7233 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7236 \begin_layout Plain Layout
7242 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7245 \begin_layout Plain Layout
7253 <cell alignment="center" valignment="top" usebox="none">
7256 \begin_layout Plain Layout
7286 \begin_inset space \textvisiblespace{}
7294 <cell alignment="center" valignment="top" usebox="none">
7297 \begin_layout Plain Layout
7298 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7307 <row topspace="2mm">
7308 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7311 \begin_layout Plain Layout
7341 \begin_inset space \textvisiblespace{}
7349 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7352 \begin_layout Plain Layout
7353 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7369 \begin_layout Standard
7370 \begin_inset VSpace bigskip
7373 When brackets should overlap each other, multiline formulas, as described
7375 \begin_inset CommandInset ref
7377 reference "sec:Multiline-Formulas"
7382 \begin_inset Formula
7384 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7385 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7390 In the first row the formula is inserted together with the first brace.
7391 It is hereby important that the space command
7395 \begin_layout Plain Layout
7396 Space commands are explained in
7397 \begin_inset CommandInset ref
7399 reference "subsec:Predefined-Space"
7414 is inserted before the first
7415 \begin_inset Formula $d$
7418 , because the brace that ends behind the
7419 \begin_inset Formula $q$
7422 prevents that the following
7423 \begin_inset Quotes eld
7427 \begin_inset Quotes erd
7430 is surrounded by space.
7434 \begin_layout Plain Layout
7435 because a bracket is not handled as a character, see
7436 \begin_inset CommandInset ref
7438 reference "subsec:Binary-Operators"
7447 In the second row the second brace is inserted.
7448 As it should begin before the
7449 \begin_inset Formula $b$
7464 \begin_layout Plain Layout
7472 \begin_inset CommandInset ref
7474 reference "subsec:Placeholders"
7483 This space is needed because the
7484 \begin_inset Quotes eld
7488 \begin_inset Quotes erd
7491 is also surrounded by space in the formula.
7492 The brace is placed under the command
7501 \begin_layout Standard
7502 It gets more complicated when brackets overlap each other above and under
7503 the formula, like in the following example:
7507 \begin_layout Plain Layout
7519 \begin_inset Formula
7521 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7522 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7531 \begin_layout Plain Layout
7542 The first formula row is the same as the second row of the previous example,
7543 with the difference that the brace is above.
7544 The second row contains the formula together with the second brace.
7545 To avoid that there is space between the upper brace in the first row and
7546 the formula, the row spacing needs to be reduced.
7547 This is not easily possible due to a bug in \SpecialChar LyX
7552 \begin_layout Plain Layout
7553 \begin_inset CommandInset href
7555 name "LyX-bug #1505"
7556 target "http://www.lyx.org/trac/ticket/1505"
7565 As a solution for the problem, the global formula row separation
7572 \begin_inset Index idx
7575 \begin_layout Plain Layout
7583 must be changed to -6
7584 \begin_inset space \thinspace{}
7587 pt before the formula with the command
7603 is set back after the formula to the standard value of 3
7604 \begin_inset space \thinspace{}
7607 pt using the same command.
7608 More about the row separation in formulas is explained in
7609 \begin_inset CommandInset ref
7611 reference "subsec:Line-Separation"
7618 \begin_layout Section
7620 \begin_inset Index idx
7623 \begin_layout Plain Layout
7632 \begin_layout Standard
7633 Arrows can be inserted via the math toolbar button
7636 arg "math-insert \\leftarrow"
7639 or the commands listed in the following subsections.
7642 \begin_layout Subsection
7644 \begin_inset Index idx
7647 \begin_layout Plain Layout
7656 \begin_layout Standard
7657 \begin_inset space \hfill{}
7661 \begin_inset Tabular
7662 <lyxtabular version="3" rows="8" columns="2">
7663 <features booktabs="true" tabularvalignment="middle">
7664 <column alignment="center" valignment="top" width="0pt">
7665 <column alignment="center" valignment="top" width="0pt">
7667 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7670 \begin_layout Plain Layout
7676 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7679 \begin_layout Plain Layout
7687 <cell alignment="center" valignment="top" usebox="none">
7690 \begin_layout Plain Layout
7698 <cell alignment="center" valignment="top" usebox="none">
7701 \begin_layout Plain Layout
7702 \begin_inset Formula $\gets$
7712 <cell alignment="center" valignment="top" usebox="none">
7715 \begin_layout Plain Layout
7723 <cell alignment="center" valignment="top" usebox="none">
7726 \begin_layout Plain Layout
7727 \begin_inset Formula $\Leftarrow$
7737 <cell alignment="center" valignment="top" usebox="none">
7740 \begin_layout Plain Layout
7748 <cell alignment="center" valignment="top" usebox="none">
7751 \begin_layout Plain Layout
7752 \begin_inset Formula $\longleftarrow$
7762 <cell alignment="center" valignment="top" usebox="none">
7765 \begin_layout Plain Layout
7773 <cell alignment="center" valignment="top" usebox="none">
7776 \begin_layout Plain Layout
7777 \begin_inset Formula $\Longleftarrow$
7787 <cell alignment="center" valignment="top" usebox="none">
7790 \begin_layout Plain Layout
7798 <cell alignment="center" valignment="top" usebox="none">
7801 \begin_layout Plain Layout
7802 \begin_inset Formula $\leftharpoonup$
7812 <cell alignment="center" valignment="top" usebox="none">
7815 \begin_layout Plain Layout
7823 <cell alignment="center" valignment="top" usebox="none">
7826 \begin_layout Plain Layout
7827 \begin_inset Formula $\leftharpoondown$
7837 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7840 \begin_layout Plain Layout
7848 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7851 \begin_layout Plain Layout
7852 \begin_inset Formula $\hookleftarrow$
7866 \begin_inset space \hfill{}
7870 \begin_inset Tabular
7871 <lyxtabular version="3" rows="8" columns="2">
7872 <features booktabs="true" tabularvalignment="middle">
7873 <column alignment="center" valignment="top" width="0pt">
7874 <column alignment="center" valignment="top" width="0pt">
7876 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7879 \begin_layout Plain Layout
7885 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7888 \begin_layout Plain Layout
7896 <cell alignment="center" valignment="top" usebox="none">
7899 \begin_layout Plain Layout
7907 <cell alignment="center" valignment="top" usebox="none">
7910 \begin_layout Plain Layout
7911 \begin_inset Formula $\to$
7921 <cell alignment="center" valignment="top" usebox="none">
7924 \begin_layout Plain Layout
7932 <cell alignment="center" valignment="top" usebox="none">
7935 \begin_layout Plain Layout
7936 \begin_inset Formula $\Rightarrow$
7946 <cell alignment="center" valignment="top" usebox="none">
7949 \begin_layout Plain Layout
7957 <cell alignment="center" valignment="top" usebox="none">
7960 \begin_layout Plain Layout
7961 \begin_inset Formula $\longrightarrow$
7971 <cell alignment="center" valignment="top" usebox="none">
7974 \begin_layout Plain Layout
7982 <cell alignment="center" valignment="top" usebox="none">
7985 \begin_layout Plain Layout
7986 \begin_inset Formula $\Longrightarrow$
7996 <cell alignment="center" valignment="top" usebox="none">
7999 \begin_layout Plain Layout
8007 <cell alignment="center" valignment="top" usebox="none">
8010 \begin_layout Plain Layout
8011 \begin_inset Formula $\rightharpoonup$
8021 <cell alignment="center" valignment="top" usebox="none">
8024 \begin_layout Plain Layout
8032 <cell alignment="center" valignment="top" usebox="none">
8035 \begin_layout Plain Layout
8036 \begin_inset Formula $\rightharpoondown$
8046 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8049 \begin_layout Plain Layout
8057 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8060 \begin_layout Plain Layout
8061 \begin_inset Formula $\hookrightarrow$
8075 \begin_inset space \hfill{}
8081 \begin_layout Standard
8082 \begin_inset space \hfill{}
8086 \begin_inset Tabular
8087 <lyxtabular version="3" rows="6" columns="2">
8088 <features booktabs="true" tabularvalignment="middle">
8089 <column alignment="center" valignment="top" width="0pt">
8090 <column alignment="center" valignment="top" width="0pt">
8092 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8095 \begin_layout Plain Layout
8101 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8104 \begin_layout Plain Layout
8112 <cell alignment="center" valignment="top" usebox="none">
8115 \begin_layout Plain Layout
8123 <cell alignment="center" valignment="top" usebox="none">
8126 \begin_layout Plain Layout
8127 \begin_inset Formula $\leftrightarrow$
8137 <cell alignment="center" valignment="top" usebox="none">
8140 \begin_layout Plain Layout
8148 <cell alignment="center" valignment="top" usebox="none">
8151 \begin_layout Plain Layout
8152 \begin_inset Formula $\Leftrightarrow$
8162 <cell alignment="center" valignment="top" usebox="none">
8165 \begin_layout Plain Layout
8173 <cell alignment="center" valignment="top" usebox="none">
8176 \begin_layout Plain Layout
8177 \begin_inset Formula $\longleftrightarrow$
8187 <cell alignment="center" valignment="top" usebox="none">
8190 \begin_layout Plain Layout
8198 <cell alignment="center" valignment="top" usebox="none">
8201 \begin_layout Plain Layout
8202 \begin_inset Formula $\Longleftrightarrow$
8212 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8215 \begin_layout Plain Layout
8223 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8226 \begin_layout Plain Layout
8227 \begin_inset Formula $\rightleftharpoons$
8241 \begin_inset space \hspace{}
8246 \begin_inset space \hfill{}
8250 \begin_inset Tabular
8251 <lyxtabular version="3" rows="5" columns="2">
8252 <features booktabs="true" tabularvalignment="middle">
8253 <column alignment="center" valignment="top" width="0pt">
8254 <column alignment="center" valignment="top" width="0pt">
8256 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8259 \begin_layout Plain Layout
8265 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8268 \begin_layout Plain Layout
8276 <cell alignment="center" valignment="top" usebox="none">
8279 \begin_layout Plain Layout
8287 <cell alignment="center" valignment="top" usebox="none">
8290 \begin_layout Plain Layout
8291 \begin_inset Formula $\mapsto$
8301 <cell alignment="center" valignment="top" usebox="none">
8304 \begin_layout Plain Layout
8312 <cell alignment="center" valignment="top" usebox="none">
8315 \begin_layout Plain Layout
8316 \begin_inset Formula $\longmapsto$
8326 <cell alignment="center" valignment="top" usebox="none">
8329 \begin_layout Plain Layout
8337 <cell alignment="center" valignment="top" usebox="none">
8340 \begin_layout Plain Layout
8341 \begin_inset Formula $\leadsto$
8351 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8354 \begin_layout Plain Layout
8362 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8365 \begin_layout Plain Layout
8366 \begin_inset Formula $\dasharrow$
8380 \begin_inset space \hfill{}
8386 \begin_layout Standard
8387 \begin_inset VSpace medskip
8390 Arrows used as accents like e.
8391 \begin_inset space \thinspace{}
8395 \begin_inset space \space{}
8398 vector arrows are listed in
8399 \begin_inset CommandInset ref
8401 reference "sec:Accents"
8408 \begin_layout Standard
8409 \begin_inset VSpace bigskip
8412 Furthermore there are the labeled arrows
8413 \begin_inset Index idx
8416 \begin_layout Plain Layout
8429 \begin_inset Index idx
8432 \begin_layout Plain Layout
8447 \begin_inset Index idx
8450 \begin_layout Plain Layout
8457 \begin_layout Plain Layout
8472 When inserting one of these commands in a formula, an arrow with two blue
8473 boxes appear where the label can be inserted.
8474 The length of the arrow adapts to the label width.
8477 \begin_layout Standard
8479 \begin_inset Tabular
8480 <lyxtabular version="3" rows="3" columns="2">
8481 <features booktabs="true" tabularvalignment="middle">
8482 <column alignment="center" valignment="top" width="0pt">
8483 <column alignment="center" valignment="top" width="0pt">
8485 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8488 \begin_layout Plain Layout
8494 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8497 \begin_layout Plain Layout
8505 <cell alignment="center" valignment="top" usebox="none">
8508 \begin_layout Plain Layout
8512 \begin_inset space \textvisiblespace{}
8516 \begin_inset Formula $\downarrow$
8520 \begin_inset Formula $\to$
8528 <cell alignment="center" valignment="top" usebox="none">
8531 \begin_layout Plain Layout
8532 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8541 <row topspace="2mm">
8542 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8545 \begin_layout Plain Layout
8549 \begin_inset space \textvisiblespace{}
8553 \begin_inset Formula $\downarrow$
8557 \begin_inset Formula $\to$
8565 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8568 \begin_layout Plain Layout
8569 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8585 \begin_layout Standard
8586 \begin_inset VSpace medskip
8592 \begin_layout Standard
8593 If you set in the document settings under
8596 \begin_inset space ~
8606 \begin_inset Index idx
8609 \begin_layout Plain Layout
8610 Packages ! mathtools
8618 \begin_inset space ~
8623 , you have access to the following labeled arrows:
8626 \begin_layout Standard
8627 \begin_inset Newpage newpage
8631 \begin_inset Separator parbreak
8637 \begin_layout Standard
8639 \begin_inset space \hspace*{\fill}
8643 \begin_inset Tabular
8644 <lyxtabular version="3" rows="7" columns="2">
8645 <features booktabs="true" tabularvalignment="middle">
8646 <column alignment="center" valignment="top" width="0pt">
8647 <column alignment="center" valignment="top" width="0pt">
8649 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8652 \begin_layout Plain Layout
8658 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8661 \begin_layout Plain Layout
8669 <cell alignment="center" valignment="top" usebox="none">
8672 \begin_layout Plain Layout
8692 <cell alignment="center" valignment="top" usebox="none">
8695 \begin_layout Plain Layout
8696 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8705 <row topspace="2mm">
8706 <cell alignment="center" valignment="top" usebox="none">
8709 \begin_layout Plain Layout
8729 <cell alignment="center" valignment="top" usebox="none">
8732 \begin_layout Plain Layout
8733 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8742 <row topspace="2mm">
8743 <cell alignment="center" valignment="top" usebox="none">
8746 \begin_layout Plain Layout
8766 <cell alignment="center" valignment="top" usebox="none">
8769 \begin_layout Plain Layout
8770 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8779 <row topspace="2mm">
8780 <cell alignment="center" valignment="top" usebox="none">
8783 \begin_layout Plain Layout
8803 <cell alignment="center" valignment="top" usebox="none">
8806 \begin_layout Plain Layout
8807 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8816 <row topspace="2mm">
8817 <cell alignment="center" valignment="top" usebox="none">
8820 \begin_layout Plain Layout
8840 <cell alignment="center" valignment="top" usebox="none">
8843 \begin_layout Plain Layout
8844 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8853 <row topspace="2mm">
8854 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8857 \begin_layout Plain Layout
8877 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8880 \begin_layout Plain Layout
8881 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8895 \begin_inset space \hspace*{\fill}
8899 \begin_inset Tabular
8900 <lyxtabular version="3" rows="7" columns="2">
8901 <features booktabs="true" tabularvalignment="middle">
8902 <column alignment="center" valignment="top" width="0pt">
8903 <column alignment="center" valignment="top" width="0pt">
8905 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8908 \begin_layout Plain Layout
8914 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8917 \begin_layout Plain Layout
8925 <cell alignment="center" valignment="top" usebox="none">
8928 \begin_layout Plain Layout
8948 <cell alignment="center" valignment="top" usebox="none">
8951 \begin_layout Plain Layout
8952 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8961 <row topspace="2mm">
8962 <cell alignment="center" valignment="top" usebox="none">
8965 \begin_layout Plain Layout
8985 <cell alignment="center" valignment="top" usebox="none">
8988 \begin_layout Plain Layout
8989 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8998 <row topspace="2mm">
8999 <cell alignment="center" valignment="top" usebox="none">
9002 \begin_layout Plain Layout
9022 <cell alignment="center" valignment="top" usebox="none">
9025 \begin_layout Plain Layout
9026 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
9035 <row topspace="2mm">
9036 <cell alignment="center" valignment="top" usebox="none">
9039 \begin_layout Plain Layout
9059 <cell alignment="center" valignment="top" usebox="none">
9062 \begin_layout Plain Layout
9063 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9072 <row topspace="2mm">
9073 <cell alignment="center" valignment="top" usebox="none">
9076 \begin_layout Plain Layout
9096 <cell alignment="center" valignment="top" usebox="none">
9099 \begin_layout Plain Layout
9100 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9109 <row topspace="2mm">
9110 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9113 \begin_layout Plain Layout
9133 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9136 \begin_layout Plain Layout
9137 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9151 \begin_inset space \hspace*{\fill}
9157 \begin_layout Standard
9158 The command scheme is for all these arrows:
9159 \begin_inset Separator parbreak
9165 \begin_layout Standard
9167 \begin_inset Tabular
9168 <lyxtabular version="3" rows="2" columns="2">
9169 <features booktabs="true" tabularvalignment="middle">
9170 <column alignment="center" valignment="top" width="0pt">
9171 <column alignment="center" valignment="top" width="0pt">
9173 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9176 \begin_layout Plain Layout
9182 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9185 \begin_layout Plain Layout
9192 <row bottomspace="0.5mm">
9193 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9196 \begin_layout Plain Layout
9199 xleftrightarrow[x=a]
9202 \begin_inset Formula $\to$
9210 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9213 \begin_layout Plain Layout
9214 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9230 \begin_layout Subsection
9231 Vertical and diagonal Arrows
9232 \begin_inset Index idx
9235 \begin_layout Plain Layout
9242 \begin_inset Index idx
9245 \begin_layout Plain Layout
9254 \begin_layout Standard
9255 \begin_inset space \hfill{}
9259 \begin_inset Tabular
9260 <lyxtabular version="3" rows="7" columns="2">
9261 <features booktabs="true" tabularvalignment="middle">
9262 <column alignment="center" valignment="top" width="0pt">
9263 <column alignment="center" valignment="top" width="0pt">
9265 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9268 \begin_layout Plain Layout
9274 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9277 \begin_layout Plain Layout
9285 <cell alignment="center" valignment="top" usebox="none">
9288 \begin_layout Plain Layout
9296 <cell alignment="center" valignment="top" usebox="none">
9299 \begin_layout Plain Layout
9300 \begin_inset Formula $\uparrow$
9310 <cell alignment="center" valignment="top" usebox="none">
9313 \begin_layout Plain Layout
9321 <cell alignment="center" valignment="top" usebox="none">
9324 \begin_layout Plain Layout
9325 \begin_inset Formula $\Uparrow$
9335 <cell alignment="center" valignment="top" usebox="none">
9338 \begin_layout Plain Layout
9346 <cell alignment="center" valignment="top" usebox="none">
9349 \begin_layout Plain Layout
9350 \begin_inset Formula $\updownarrow$
9360 <cell alignment="center" valignment="top" usebox="none">
9363 \begin_layout Plain Layout
9371 <cell alignment="center" valignment="top" usebox="none">
9374 \begin_layout Plain Layout
9375 \begin_inset Formula $\Updownarrow$
9385 <cell alignment="center" valignment="top" usebox="none">
9388 \begin_layout Plain Layout
9396 <cell alignment="center" valignment="top" usebox="none">
9399 \begin_layout Plain Layout
9400 \begin_inset Formula $\Downarrow$
9410 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9413 \begin_layout Plain Layout
9421 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9424 \begin_layout Plain Layout
9425 \begin_inset Formula $\downarrow$
9439 \begin_inset space \hfill{}
9443 \begin_inset Tabular
9444 <lyxtabular version="3" rows="5" columns="2">
9445 <features booktabs="true" tabularvalignment="middle">
9446 <column alignment="center" valignment="top" width="0pt">
9447 <column alignment="center" valignment="top" width="0pt">
9449 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9452 \begin_layout Plain Layout
9458 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9461 \begin_layout Plain Layout
9469 <cell alignment="center" valignment="top" usebox="none">
9472 \begin_layout Plain Layout
9480 <cell alignment="center" valignment="top" usebox="none">
9483 \begin_layout Plain Layout
9484 \begin_inset Formula $\nearrow$
9494 <cell alignment="center" valignment="top" usebox="none">
9497 \begin_layout Plain Layout
9505 <cell alignment="center" valignment="top" usebox="none">
9508 \begin_layout Plain Layout
9509 \begin_inset Formula $\searrow$
9519 <cell alignment="center" valignment="top" usebox="none">
9522 \begin_layout Plain Layout
9530 <cell alignment="center" valignment="top" usebox="none">
9533 \begin_layout Plain Layout
9534 \begin_inset Formula $\swarrow$
9544 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9547 \begin_layout Plain Layout
9555 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9558 \begin_layout Plain Layout
9559 \begin_inset Formula $\nwarrow$
9573 \begin_inset space \hfill{}
9579 \begin_layout Standard
9580 \begin_inset VSpace medskip
9583 Vertical arrows can be used also as delimiters together with the commands
9585 \begin_inset CommandInset ref
9587 reference "subsec:Manual-Bracket-Size"
9592 \begin_inset CommandInset ref
9594 reference "subsec:Automatic-Bracket-Size"
9601 \begin_layout Section
9603 \begin_inset CommandInset label
9610 \begin_inset Index idx
9613 \begin_layout Plain Layout
9622 \begin_layout Standard
9623 Accents can be inserted via the math toolbar button
9626 arg "math-insert \\hat"
9629 or the commands listed in the following subsections.
9632 \begin_layout Subsection
9633 Accents for one Character
9637 \begin_layout Plain Layout
9650 \begin_layout Plain Layout
9652 \begin_inset CommandInset ref
9654 reference "subsec:Accents-in-Text"
9667 \begin_layout Plain Layout
9675 \begin_inset Note Note
9678 \begin_layout Plain Layout
9685 is used to avoid that the footnote appears in the PDF-bookmark.
9688 \begin_layout Plain Layout
9696 \begin_inset CommandInset ref
9698 reference "subsec:Formulas-in-Section"
9708 \begin_inset CommandInset label
9710 name "subsec:Accents-for-one"
9715 \begin_inset Index idx
9718 \begin_layout Plain Layout
9719 Accents ! for one character
9727 \begin_layout Standard
9728 \begin_inset space \hfill{}
9732 \begin_inset Tabular
9733 <lyxtabular version="3" rows="8" columns="2">
9734 <features booktabs="true" tabularvalignment="middle">
9735 <column alignment="center" valignment="top" width="0pt">
9736 <column alignment="center" valignment="top" width="0pt">
9738 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9741 \begin_layout Plain Layout
9747 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9750 \begin_layout Plain Layout
9757 <row topspace="1.5mm">
9758 <cell alignment="center" valignment="top" usebox="none">
9761 \begin_layout Plain Layout
9765 \begin_inset space \textvisiblespace{}
9773 <cell alignment="center" valignment="top" usebox="none">
9776 \begin_layout Plain Layout
9777 \begin_inset Formula $\dot{A}$
9786 <row topspace="1.5mm">
9787 <cell alignment="center" valignment="top" usebox="none">
9790 \begin_layout Plain Layout
9794 \begin_inset space \textvisiblespace{}
9802 <cell alignment="center" valignment="top" usebox="none">
9805 \begin_layout Plain Layout
9806 \begin_inset Formula $\ddot{A}$
9815 <row topspace="1.5mm">
9816 <cell alignment="center" valignment="top" usebox="none">
9819 \begin_layout Plain Layout
9823 \begin_inset space \textvisiblespace{}
9831 <cell alignment="center" valignment="top" usebox="none">
9834 \begin_layout Plain Layout
9835 \begin_inset Formula $\dddot{A}$
9844 <row topspace="1.5mm">
9845 <cell alignment="center" valignment="top" usebox="none">
9848 \begin_layout Plain Layout
9852 \begin_inset space \textvisiblespace{}
9860 <cell alignment="center" valignment="top" usebox="none">
9863 \begin_layout Plain Layout
9864 \begin_inset Formula $\ddddot{A}$
9873 <row topspace="1.5mm">
9874 <cell alignment="center" valignment="top" usebox="none">
9877 \begin_layout Plain Layout
9881 \begin_inset space \textvisiblespace{}
9885 \begin_inset Index idx
9888 \begin_layout Plain Layout
9899 <cell alignment="center" valignment="top" usebox="none">
9902 \begin_layout Plain Layout
9903 \begin_inset Formula $\vec{A}$
9912 <row topspace="1.5mm">
9913 <cell alignment="center" valignment="top" usebox="none">
9916 \begin_layout Plain Layout
9920 \begin_inset space \textvisiblespace{}
9928 <cell alignment="center" valignment="top" usebox="none">
9931 \begin_layout Plain Layout
9932 \begin_inset Formula $\bar{A}$
9941 <row topspace="1.5mm">
9942 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9945 \begin_layout Plain Layout
9949 \begin_inset space \textvisiblespace{}
9957 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9960 \begin_layout Plain Layout
9961 \begin_inset Formula $\mathring{A}$
9975 \begin_inset space \hfill{}
9979 \begin_inset Tabular
9980 <lyxtabular version="3" rows="7" columns="2">
9981 <features booktabs="true" tabularvalignment="middle">
9982 <column alignment="center" valignment="top" width="0pt">
9983 <column alignment="center" valignment="top" width="0pt">
9985 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9988 \begin_layout Plain Layout
9994 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9997 \begin_layout Plain Layout
10004 <row topspace="1.5mm">
10005 <cell alignment="center" valignment="top" usebox="none">
10008 \begin_layout Plain Layout
10012 \begin_inset space \textvisiblespace{}
10020 <cell alignment="center" valignment="top" usebox="none">
10023 \begin_layout Plain Layout
10024 \begin_inset Formula $\tilde{A}$
10033 <row topspace="1.5mm">
10034 <cell alignment="center" valignment="top" usebox="none">
10037 \begin_layout Plain Layout
10041 \begin_inset space \textvisiblespace{}
10049 <cell alignment="center" valignment="top" usebox="none">
10052 \begin_layout Plain Layout
10053 \begin_inset Formula $\hat{A}$
10062 <row topspace="1.5mm">
10063 <cell alignment="center" valignment="top" usebox="none">
10066 \begin_layout Plain Layout
10070 \begin_inset space \textvisiblespace{}
10078 <cell alignment="center" valignment="top" usebox="none">
10081 \begin_layout Plain Layout
10082 \begin_inset Formula $\check{A}$
10091 <row topspace="1.5mm">
10092 <cell alignment="center" valignment="top" usebox="none">
10095 \begin_layout Plain Layout
10099 \begin_inset space \textvisiblespace{}
10107 <cell alignment="center" valignment="top" usebox="none">
10110 \begin_layout Plain Layout
10111 \begin_inset Formula $\acute{A}$
10120 <row topspace="1.5mm">
10121 <cell alignment="center" valignment="top" usebox="none">
10124 \begin_layout Plain Layout
10128 \begin_inset space \textvisiblespace{}
10136 <cell alignment="center" valignment="top" usebox="none">
10139 \begin_layout Plain Layout
10140 \begin_inset Formula $\grave{A}$
10149 <row topspace="1.5mm">
10150 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10153 \begin_layout Plain Layout
10157 \begin_inset space \textvisiblespace{}
10165 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10168 \begin_layout Plain Layout
10169 \begin_inset Formula $\breve{A}$
10183 \begin_inset space \hfill{}
10189 \begin_layout Standard
10190 \begin_inset VSpace bigskip
10196 \begin_layout Standard
10197 You can directly insert accents like é to formulas.
10199 will transform them to the corresponding accent command.
10201 \begin_inset Index idx
10204 \begin_layout Plain Layout
10210 it is better to insert a quotation mark before the vowel.
10211 These two characters are then treated by \SpecialChar LaTeX
10216 character when the formula part with the umlaut is marked as German.
10224 \begin_inset Quotes eld
10228 \begin_inset Quotes erd
10231 umlauts are created as demonstrated in the following example:
10234 \begin_layout Standard
10235 \begin_inset VSpace -2mm
10241 \begin_layout Standard
10243 \begin_inset Tabular
10244 <lyxtabular version="3" rows="3" columns="2">
10245 <features booktabs="true" tabularvalignment="middle">
10246 <column alignment="center" valignment="top" width="0pt">
10247 <column alignment="center" valignment="top">
10249 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10252 \begin_layout Plain Layout
10258 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10261 \begin_layout Plain Layout
10269 <cell alignment="center" valignment="top" usebox="none">
10272 \begin_layout Plain Layout
10273 \begin_inset Quotes grd
10281 <cell alignment="center" valignment="top" usebox="none">
10284 \begin_layout Plain Layout
10285 \begin_inset space \hspace{}
10292 \begin_inset Formula $"i$
10301 <row topspace="1.5mm">
10302 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10305 \begin_layout Plain Layout
10309 \begin_inset space \textvisiblespace{}
10317 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10320 \begin_layout Plain Layout
10321 \begin_inset Formula $\ddot{i}$
10337 \begin_layout Standard
10338 Another advantage to
10344 is that umlauts can directly be converted to mathematical text because
10345 the accent commands above are
10351 in mathematical text
10354 To convert an accented character to mathematical text, only the character
10355 under the accent may be converted.
10356 This applies also for all other conversions, e.
10357 \begin_inset space \thinspace{}
10361 \begin_inset space \space{}
10367 \begin_layout Standard
10368 In mathematical text, umlauts and other accented characters can directly
10372 \begin_layout Standard
10373 \begin_inset VSpace bigskip
10379 \begin_layout Standard
10381 also supports a tilde under the character if the \SpecialChar LaTeX
10387 \begin_inset Index idx
10390 \begin_layout Plain Layout
10391 Packages ! undertilde
10396 is installed on your system:
10399 \begin_layout Standard
10403 \begin_layout Plain Layout
10413 \begin_inset Note Note
10416 \begin_layout Plain Layout
10417 The following table will only be displayed when the \SpecialChar LaTeX
10428 \begin_inset Separator parbreak
10434 \begin_layout Standard
10437 \begin_inset Tabular
10438 <lyxtabular version="3" rows="2" columns="2">
10439 <features booktabs="true" tabularvalignment="middle">
10440 <column alignment="center" valignment="top" width="0pt">
10441 <column alignment="center" valignment="top" width="0pt">
10443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10446 \begin_layout Plain Layout
10452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10455 \begin_layout Plain Layout
10463 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10466 \begin_layout Plain Layout
10470 \begin_inset space \textvisiblespace{}
10478 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10481 \begin_layout Plain Layout
10482 \begin_inset Formula $\utilde{A}$
10498 \begin_layout Standard
10502 \begin_layout Plain Layout
10512 \begin_inset Note Note
10515 \begin_layout Plain Layout
10516 The following will be displayed when the \SpecialChar LaTeX
10529 \begin_layout Standard
10530 You need to install the \SpecialChar LaTeX
10535 to see the rest of this subsection in the output.
10538 \begin_layout Standard
10542 \begin_layout Plain Layout
10554 \begin_layout Standard
10555 \begin_inset Newpage newpage
10561 \begin_layout Subsection
10562 Accents for several Characters
10563 \begin_inset Index idx
10566 \begin_layout Plain Layout
10567 Accents ! for several characters
10575 \begin_layout Standard
10576 \begin_inset space \hfill{}
10580 \begin_inset Tabular
10581 <lyxtabular version="3" rows="5" columns="2">
10582 <features booktabs="true" tabularvalignment="middle">
10583 <column alignment="center" valignment="top" width="0pt">
10584 <column alignment="center" valignment="top" width="0pt">
10586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10589 \begin_layout Plain Layout
10595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10598 \begin_layout Plain Layout
10605 <row topspace="1.5mm">
10606 <cell alignment="center" valignment="top" usebox="none">
10609 \begin_layout Plain Layout
10613 \begin_inset space \textvisiblespace{}
10621 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10624 \begin_layout Plain Layout
10625 \begin_inset Formula $\overleftarrow{A=B}$
10634 <row topspace="1.5mm">
10635 <cell alignment="center" valignment="top" usebox="none">
10638 \begin_layout Plain Layout
10642 \begin_inset space \textvisiblespace{}
10650 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10653 \begin_layout Plain Layout
10654 \begin_inset Formula $\underleftarrow{A=B}$
10663 <row topspace="1.5mm">
10664 <cell alignment="center" valignment="top" usebox="none">
10667 \begin_layout Plain Layout
10671 \begin_inset space \textvisiblespace{}
10679 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10682 \begin_layout Plain Layout
10683 \begin_inset Formula $\overleftrightarrow{A=B}$
10692 <row topspace="1.5mm" bottomspace="1mm">
10693 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10696 \begin_layout Plain Layout
10699 underleftrightarrow
10700 \begin_inset space \textvisiblespace{}
10708 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10711 \begin_layout Plain Layout
10712 \begin_inset Formula $\underleftrightarrow{A=B}$
10726 \begin_inset space \hfill{}
10730 \begin_inset Tabular
10731 <lyxtabular version="3" rows="5" columns="2">
10732 <features booktabs="true" tabularvalignment="middle">
10733 <column alignment="center" valignment="top" width="0pt">
10734 <column alignment="center" valignment="top" width="0pt">
10736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10739 \begin_layout Plain Layout
10745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10748 \begin_layout Plain Layout
10755 <row topspace="1.5mm">
10756 <cell alignment="center" valignment="top" usebox="none">
10759 \begin_layout Plain Layout
10763 \begin_inset space \textvisiblespace{}
10771 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10774 \begin_layout Plain Layout
10775 \begin_inset Formula $\overrightarrow{A=B}$
10784 <row topspace="1.5mm">
10785 <cell alignment="center" valignment="top" usebox="none">
10788 \begin_layout Plain Layout
10792 \begin_inset space \textvisiblespace{}
10800 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10803 \begin_layout Plain Layout
10804 \begin_inset Formula $\underrightarrow{A=B}$
10813 <row topspace="1.5mm">
10814 <cell alignment="center" valignment="top" usebox="none">
10817 \begin_layout Plain Layout
10821 \begin_inset space \textvisiblespace{}
10829 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10832 \begin_layout Plain Layout
10833 \begin_inset Formula $\widetilde{A=B}$
10842 <row topspace="1.5mm" bottomspace="1mm">
10843 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10846 \begin_layout Plain Layout
10850 \begin_inset space \textvisiblespace{}
10858 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10861 \begin_layout Plain Layout
10862 \begin_inset Formula $\widehat{A=B}$
10876 \begin_inset space \hfill{}
10882 \begin_layout Standard
10883 \begin_inset VSpace medskip
10886 With these commands as many characters as you like can be accented.
10899 will only be set in the output with a length of three characters, as shown
10900 in the following example:
10901 \begin_inset Formula
10903 \widetilde{A+B=C-D}
10911 \begin_layout Standard
10919 \begin_inset Index idx
10922 \begin_layout Plain Layout
10937 \begin_inset Index idx
10940 \begin_layout Plain Layout
10948 described in the previous subsection it is also possible to accent several
10955 \begin_inset space \textvisiblespace{}
10959 \begin_inset Formula $\downarrow$
10965 \begin_inset Formula
10967 \underset{***}{A=B}
10975 \begin_layout Section
10977 \begin_inset CommandInset label
10979 name "subsec:Space"
10984 \begin_inset Index idx
10987 \begin_layout Plain Layout
10996 \begin_layout Subsection
10998 \begin_inset CommandInset label
11000 name "subsec:Predefined-Space"
11005 \begin_inset Index idx
11008 \begin_layout Plain Layout
11009 Space ! horizontal ! predefined
11017 \begin_layout Standard
11018 Sometimes it is necessary to insert horizontal space into a formula.
11019 This is done by inserting a protected space (shortcut
11022 arg "command-alternatives space-insert protected ; math-space"
11027 \begin_inset Quotes eld
11033 \begin_inset space \textvisiblespace{}
11039 \begin_inset Quotes erd
11042 appears and by pressing
11046 several times one can select one of eight different space sizes.
11047 The spaces can also be inserted using the math toolbar button
11050 arg "math-insert \\space"
11053 or special commands.
11054 Independent from the inserted command, one can select the size again by
11060 \begin_inset Separator parbreak
11066 \begin_layout Standard
11069 \begin_inset Tabular
11070 <lyxtabular version="3" rows="6" columns="3">
11071 <features booktabs="true" tabularvalignment="middle">
11072 <column alignment="center" valignment="top">
11073 <column alignment="center" valignment="top" width="15col%">
11074 <column alignment="center" valignment="top">
11076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11079 \begin_layout Plain Layout
11085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11088 \begin_layout Plain Layout
11098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11101 \begin_layout Plain Layout
11109 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11112 \begin_layout Plain Layout
11120 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11123 \begin_layout Plain Layout
11129 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11132 \begin_layout Plain Layout
11133 \begin_inset Formula $A\,B$
11143 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11146 \begin_layout Plain Layout
11154 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11157 \begin_layout Plain Layout
11163 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11166 \begin_layout Plain Layout
11167 \begin_inset Formula $A\:B$
11177 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11180 \begin_layout Plain Layout
11188 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11191 \begin_layout Plain Layout
11197 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11200 \begin_layout Plain Layout
11201 \begin_inset Formula $A\;B$
11211 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11214 \begin_layout Plain Layout
11222 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11225 \begin_layout Plain Layout
11231 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11234 \begin_layout Plain Layout
11235 \begin_inset Formula $A\quad B$
11245 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11248 \begin_layout Plain Layout
11256 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11259 \begin_layout Plain Layout
11265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11268 \begin_layout Plain Layout
11269 \begin_inset Formula $A\qquad B$
11283 \begin_inset space \hfill{}
11287 \begin_inset Tabular
11288 <lyxtabular version="3" rows="6" columns="3">
11289 <features booktabs="true" tabularvalignment="middle">
11290 <column alignment="center" valignment="top">
11291 <column alignment="center" valignment="top" width="15col%">
11292 <column alignment="center" valignment="top">
11294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11297 \begin_layout Plain Layout
11303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11306 \begin_layout Plain Layout
11316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11319 \begin_layout Plain Layout
11327 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11330 \begin_layout Plain Layout
11338 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11341 \begin_layout Plain Layout
11347 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11350 \begin_layout Plain Layout
11351 \begin_inset Formula $A\hfill B$
11361 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11364 \begin_layout Plain Layout
11372 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11375 \begin_layout Plain Layout
11381 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11384 \begin_layout Plain Layout
11385 \begin_inset Formula $A\hspace*{1em}B$
11395 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11398 \begin_layout Plain Layout
11406 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11409 \begin_layout Plain Layout
11415 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11418 \begin_layout Plain Layout
11419 \begin_inset Formula $A\hspace{1em}B$
11429 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11432 \begin_layout Plain Layout
11436 \begin_inset space \textvisiblespace{}
11444 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11447 \begin_layout Plain Layout
11453 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11456 \begin_layout Plain Layout
11457 \begin_inset Formula $A\ B$
11467 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11470 \begin_layout Plain Layout
11478 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11481 \begin_layout Plain Layout
11487 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11490 \begin_layout Plain Layout
11491 \begin_inset Formula $A\!B$
11507 \begin_layout Standard
11509 \begin_inset space ~
11513 \begin_inset space \thinspace{}
11517 \begin_inset space \thinspace{}
11520 7 are variable spaces which are explained in
11521 \begin_inset CommandInset ref
11523 reference "subsec:Variable-Space"
11529 \begin_inset space ~
11532 9 seems to produce no space.
11533 It is displayed red in \SpecialChar LyX
11534 contrary to the other sizes, because it is a negative
11536 There are two more negative spaces:
11537 \begin_inset Separator parbreak
11543 \begin_layout Standard
11545 \begin_inset Tabular
11546 <lyxtabular version="3" rows="3" columns="3">
11547 <features booktabs="true" tabularvalignment="middle">
11548 <column alignment="center" valignment="middle" width="6.8cm">
11549 <column alignment="center" valignment="top" width="0pt">
11550 <column alignment="center" valignment="top" width="0pt">
11552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11555 \begin_layout Plain Layout
11561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11564 \begin_layout Plain Layout
11572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11575 \begin_layout Plain Layout
11585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11588 \begin_layout Plain Layout
11593 keystrokes after inserting the protected space
11598 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11601 \begin_layout Plain Layout
11607 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11610 \begin_layout Plain Layout
11618 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11621 \begin_layout Plain Layout
11627 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11630 \begin_layout Plain Layout
11631 \begin_inset Formula $A\negmedspace B$
11639 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11642 \begin_layout Plain Layout
11643 \begin_inset Formula $A\negthickspace B$
11659 \begin_layout Standard
11660 Negative spaces can lead to characters overlapping each other.
11661 Thus they can be used to enforce ligatures, which are e.
11662 \begin_inset space \thinspace{}
11666 \begin_inset space \space{}
11669 useful for summation operators:
11670 \begin_inset Separator parbreak
11676 \begin_layout Standard
11678 \begin_inset Tabular
11679 <lyxtabular version="3" rows="3" columns="2">
11680 <features booktabs="true" tabularvalignment="middle">
11681 <column alignment="center" valignment="top" width="0pt">
11682 <column alignment="center" valignment="top">
11684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11687 \begin_layout Plain Layout
11693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11696 \begin_layout Plain Layout
11704 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11707 \begin_layout Plain Layout
11713 \begin_inset space \textvisiblespace{}
11721 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11724 \begin_layout Plain Layout
11725 \begin_inset Formula $\sum\sum f_{kl}$
11735 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11738 \begin_layout Plain Layout
11746 \begin_inset space \textvisiblespace{}
11754 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11757 \begin_layout Plain Layout
11758 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11774 \begin_layout Standard
11776 \begin_inset VSpace medskip
11782 \begin_layout Standard
11784 Relations like for example equal signs, are always surrounded by space.
11785 To suppress this, the equal sign is placed into a \SpecialChar TeX
11787 The following example demonstrates this:
11788 \begin_inset Separator parbreak
11794 \begin_layout Standard
11796 \begin_inset Tabular
11797 <lyxtabular version="3" rows="2" columns="2">
11798 <features tabularvalignment="middle">
11799 <column alignment="center" valignment="top" width="0pt">
11800 <column alignment="center" valignment="top" width="0pt">
11802 <cell alignment="center" valignment="top" usebox="none">
11805 \begin_layout Plain Layout
11811 <cell alignment="center" valignment="top" usebox="none">
11814 \begin_layout Plain Layout
11815 \begin_inset Formula $A=B$
11825 <cell alignment="center" valignment="top" usebox="none">
11828 \begin_layout Plain Layout
11829 equation without space
11834 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11837 \begin_layout Plain Layout
11838 \begin_inset Formula $A{=}B$
11854 \begin_layout Standard
11856 The command for the last formula is:
11861 \begin_inset Formula $\to$
11867 \begin_layout Standard
11868 \begin_inset VSpace bigskip
11874 \begin_layout Standard
11875 Spaces are needed for physical units, because the space between the value
11876 and the unit is the smallest one and not a normal space.
11877 For units in text, the smallest space is inserted via the menu
11879 Insert\SpecialChar menuseparator
11880 Formatting\SpecialChar menuseparator
11882 \begin_inset space ~
11890 arg "space-insert thin"
11896 \begin_layout Standard
11897 An example to visualize the difference:
11900 \begin_layout Standard
11901 \begin_inset Tabular
11902 <lyxtabular version="3" rows="2" columns="2">
11903 <features tabularvalignment="middle">
11904 <column alignment="left" valignment="top">
11905 <column alignment="left" valignment="top">
11907 <cell alignment="center" valignment="top" usebox="none">
11910 \begin_layout Plain Layout
11912 \begin_inset Formula $\cdot$
11920 <cell alignment="center" valignment="top" usebox="none">
11923 \begin_layout Plain Layout
11924 space between value and unit
11931 <cell alignment="center" valignment="top" usebox="none">
11934 \begin_layout Plain Layout
11936 \begin_inset space \thinspace{}
11940 \begin_inset Formula $\cdot$
11948 <cell alignment="center" valignment="top" usebox="none">
11951 \begin_layout Plain Layout
11952 smallest space between value and unit
11965 \begin_layout Subsection
11970 \begin_layout Plain Layout
11983 \begin_layout Plain Layout
11984 for vertical space in formulas see
11985 \begin_inset CommandInset ref
11987 reference "subsec:Line-Separation"
12000 \begin_layout Plain Layout
12008 \begin_inset Note Note
12011 \begin_layout Plain Layout
12014 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12017 \begin_layout Plain Layout
12020 texorpdfstring is in section
12021 \begin_inset CommandInset ref
12023 reference "subsec:Formulas-in-Section"
12033 \begin_inset CommandInset label
12035 name "subsec:Variable-Space"
12040 \begin_inset Index idx
12043 \begin_layout Plain Layout
12044 Space ! horizontal ! variable
12052 \begin_layout Standard
12053 Space with a defined length can be inserted with the command
12060 \begin_inset Index idx
12063 \begin_layout Plain Layout
12073 \begin_inset Quotes eld
12079 \begin_inset space \textvisiblespace{}
12085 \begin_inset Quotes erd
12089 The length can be specified by left-clicking on the
12090 \begin_inset Quotes eld
12096 \begin_inset space \textvisiblespace{}
12102 \begin_inset Quotes erd
12106 The length may also be negative.
12107 When a space would be the first character in a line it would be omitted.
12108 To force its output use the command
12120 or left-click on the
12121 \begin_inset Quotes eld
12127 \begin_inset space \textvisiblespace{}
12133 \begin_inset Quotes erd
12136 and check the option
12141 \begin_inset Newline newline
12144 To insert as much space as is available, the command
12151 \begin_inset Index idx
12154 \begin_layout Plain Layout
12165 \begin_layout Standard
12167 \begin_inset Tabular
12168 <lyxtabular version="3" rows="4" columns="2">
12169 <features booktabs="true" tabularvalignment="middle">
12170 <column alignment="center" valignment="top" width="0pt">
12171 <column alignment="center" valignment="top">
12173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12176 \begin_layout Plain Layout
12184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12187 \begin_layout Plain Layout
12195 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12198 \begin_layout Plain Layout
12202 \begin_inset space \textvisiblespace{}
12208 \begin_inset space \thinspace{}
12216 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12219 \begin_layout Plain Layout
12220 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12230 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12233 \begin_layout Plain Layout
12237 \begin_inset space \textvisiblespace{}
12243 \begin_inset space \thinspace{}
12251 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12254 \begin_layout Plain Layout
12255 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12268 \begin_layout Plain Layout
12272 \begin_inset space \textvisiblespace{}
12280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12283 \begin_layout Plain Layout
12284 \begin_inset Formula $A=A\hfill B=B$
12300 \begin_layout Standard
12301 In the last example the available space is given by the longest column entry
12303 In an inline formula the space depends on the length of the line in which
12311 Thus, when the line uses the full width, no space will be created.
12318 only has an effect on displayed formulas when the formula style
12323 (Formula styles are explained in
12324 \begin_inset CommandInset ref
12326 reference "sec:Formula-Styles"
12333 \begin_layout Standard
12340 , there are the commands
12352 that fill the space with a pattern, see
12353 \begin_inset CommandInset ref
12355 reference "subsec:Ellipses"
12362 \begin_layout Standard
12363 For text, variable space can be inserted via the menu
12365 Insert\SpecialChar menuseparator
12366 Formatting\SpecialChar menuseparator
12368 \begin_inset space ~
12376 \begin_layout Standard
12377 This is a line with
12378 \begin_inset space \hspace{}
12383 \begin_inset space \thinspace{}
12389 \begin_layout Standard
12390 This is a line with
12391 \begin_inset space \hfill{}
12397 \begin_layout Subsection
12398 Space besides inline Formulas
12399 \begin_inset Index idx
12402 \begin_layout Plain Layout
12403 Space ! besides inline formulas
12411 \begin_layout Standard
12412 The space that surrounds inline formulas can be adjusted with the length
12420 \begin_inset Index idx
12423 \begin_layout Plain Layout
12432 The value of a length is set with the command
12439 \begin_inset Index idx
12442 \begin_layout Plain Layout
12450 which has the following scheme:
12453 \begin_layout Standard
12458 setlength{length name}{value}
12461 \begin_layout Standard
12469 \begin_inset space \thinspace{}
12475 \begin_layout Standard
12485 \begin_layout Standard
12486 is inserted in \SpecialChar TeX
12489 \begin_inset space \thinspace{}
12492 mm space will now be set around all inline formulas:
12496 \begin_layout Plain Layout
12510 \begin_layout Standard
12511 This is a line with an inline formula
12512 \begin_inset Formula $A=B$
12516 \begin_inset space \thinspace{}
12519 mm surrounding space.
12523 \begin_layout Plain Layout
12537 \begin_layout Standard
12538 To return to the predefined value,
12544 is set to the value 0
12545 \begin_inset space \thinspace{}
12551 \begin_layout Standard
12552 \begin_inset Newpage newpage
12558 \begin_layout Section
12560 \begin_inset Index idx
12563 \begin_layout Plain Layout
12570 \begin_inset Index idx
12573 \begin_layout Plain Layout
12578 \begin_layout Plain Layout
12589 \begin_layout Plain Layout
12604 \begin_layout Standard
12605 Boxes for text are described in chapter
12612 \begin_inset space ~
12620 \begin_layout Subsection
12622 \begin_inset CommandInset label
12624 name "subsec:Boxes-with-Frame"
12629 \begin_inset Index idx
12632 \begin_layout Plain Layout
12641 \begin_layout Standard
12642 It is possible to frame a formula or part of one with the commands
12649 \begin_inset Index idx
12652 \begin_layout Plain Layout
12667 \begin_inset Index idx
12670 \begin_layout Plain Layout
12681 \begin_layout Standard
12682 When one of these commands is inserted in a formula, a blue box appears
12683 within a frame to enter formula parts.
12690 an additional formula has to be created by
12694 within this box, because the box content will otherwise be treated as mathemati
12702 is used, a new formula is automatically created inside the frame.
12705 \begin_layout Standard
12712 is not suitable to frame displayed formulas because the formula will always
12713 be set in the size of the text.
12720 is in contrary not suitable to frame inline formulas, because the formula
12721 will always be set in the size of a displayed formula.
12724 \begin_layout Standard
12738 \begin_inset Index idx
12741 \begin_layout Plain Layout
12749 where additionally the frame width and the alignment can be specified.
12756 is used in the following scheme:
12759 \begin_layout Standard
12764 framebox[frame width][position]{box content}
12767 \begin_layout Standard
12768 The position can either be
12785 right aligns the formula in the box.
12786 When no position is given, the formula will be centered.
12787 \begin_inset Newline newline
12790 If no width is given, also no position can be given.
12791 In this case the frame width is adjusted to the box content like for
12800 \begin_layout Standard
12807 is inserted, a box appears containing three blue boxes.
12808 The first two boxes are surrounded by brackets and denote the two optional
12810 The third box is for formula parts like for
12817 \begin_inset Separator parbreak
12823 \begin_layout Standard
12825 \begin_inset Tabular
12826 <lyxtabular version="3" rows="5" columns="2">
12827 <features booktabs="true" tabularvalignment="middle">
12828 <column alignment="center" valignment="top" width="0pt">
12829 <column alignment="center" valignment="top">
12831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12834 \begin_layout Plain Layout
12840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12843 \begin_layout Plain Layout
12850 <row topspace="1.5mm">
12851 <cell alignment="center" valignment="top" usebox="none">
12854 \begin_layout Plain Layout
12858 \begin_inset space \textvisiblespace{}
12868 \begin_inset space \textvisiblespace{}
12876 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12879 \begin_layout Plain Layout
12880 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12889 <row topspace="1.5mm">
12890 <cell alignment="center" valignment="top" usebox="none">
12893 \begin_layout Plain Layout
12897 \begin_inset space \textvisiblespace{}
12903 \begin_inset space \textvisiblespace{}
12911 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12914 \begin_layout Plain Layout
12915 \begin_inset Formula $\boxed{\int A=B}$
12924 <row topspace="1.5mm">
12925 <cell alignment="center" valignment="top" usebox="none">
12928 \begin_layout Plain Layout
12932 \begin_inset space \textvisiblespace{}
12940 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12943 \begin_layout Plain Layout
12944 \begin_inset Formula $A+\fbox{B}$
12953 <row topspace="1.5mm" bottomspace="1mm">
12954 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12957 \begin_layout Plain Layout
12961 \begin_inset space \textvisiblespace{}
12965 \begin_inset Formula $\to$
12969 \begin_inset Formula $\to$
12979 \begin_inset space \textvisiblespace{}
12983 \begin_inset Formula $\downarrow$
12991 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12994 \begin_layout Plain Layout
12995 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13011 \begin_layout Standard
13012 The frame thickness can also be adjusted.
13013 To do this the following commands have to be inserted in \SpecialChar TeX
13018 \begin_layout Standard
13028 \begin_inset Quotes eld
13032 \begin_inset Quotes erd
13046 \begin_inset Quotes eld
13050 \begin_inset Quotes erd
13056 \begin_layout Standard
13057 \begin_inset Quotes eld
13061 \begin_inset Quotes erd
13064 specifies the minimal distance between the frame and the first character
13066 An example for this is the following framed formula:
13070 \begin_layout Plain Layout
13082 \begin_inset Formula
13089 Before this formula the commands
13092 \begin_layout Standard
13114 \begin_layout Standard
13115 were inserted in \SpecialChar TeX
13117 The given values are used for all following boxes.
13120 \begin_layout Standard
13121 To return to the standard frame size, the command
13124 \begin_layout Standard
13149 \begin_layout Plain Layout
13163 \begin_layout Standard
13164 is inserted in \SpecialChar TeX
13165 mode before the next formula.
13168 \begin_layout Subsection
13169 Boxes without Frame
13170 \begin_inset CommandInset label
13172 name "subsec:Boxes-without-Frame"
13177 \begin_inset Index idx
13180 \begin_layout Plain Layout
13181 Boxes ! without frame
13189 \begin_layout Standard
13190 For boxes without a frame there are the following box commands:
13197 \begin_inset Index idx
13200 \begin_layout Plain Layout
13215 \begin_inset Index idx
13218 \begin_layout Plain Layout
13233 \begin_inset Index idx
13236 \begin_layout Plain Layout
13247 \begin_layout Standard
13254 a box can be super- or subscripted.
13255 But in contrary to normal super- and subscripting, the characters in the
13256 box keep their font size.
13263 is used in the following scheme:
13266 \begin_layout Standard
13271 raisebox{height}{box content}
13274 \begin_layout Standard
13275 When the box should contain a formula, an extra formula is needed like for
13286 \begin_inset Note Greyedout
13289 \begin_layout Plain Layout
13300 this extra formula is created by pressing
13304 twice instead of once because \SpecialChar LyX
13305 doesn't yet support
13319 \begin_inset Separator parbreak
13325 \begin_layout Standard
13327 \begin_inset Tabular
13328 <lyxtabular version="3" rows="4" columns="2">
13329 <features booktabs="true" tabularvalignment="middle">
13330 <column alignment="center" valignment="top" width="0pt">
13331 <column alignment="center" valignment="top">
13333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13336 \begin_layout Plain Layout
13342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13345 \begin_layout Plain Layout
13353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13356 \begin_layout Plain Layout
13360 \begin_inset Formula $\to$
13366 \begin_inset Formula $\to$
13374 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13377 \begin_layout Plain Layout
13378 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13388 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13391 \begin_layout Plain Layout
13395 \begin_inset Formula $\to$
13401 \begin_inset Formula $\to$
13409 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13412 \begin_layout Plain Layout
13413 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13426 \begin_layout Plain Layout
13430 \begin_inset Formula $\to$
13446 \begin_inset space \textvisiblespace{}
13454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13457 \begin_layout Plain Layout
13458 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13474 \begin_layout Standard
13499 , with the difference that there is no frame.
13502 \begin_layout Subsection
13504 \begin_inset CommandInset label
13506 name "subsec:Colored-Boxes"
13511 \begin_inset Index idx
13514 \begin_layout Plain Layout
13523 \begin_layout Standard
13524 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13533 \begin_layout Plain Layout
13534 The \SpecialChar LaTeX
13539 is part of every \SpecialChar LaTeX
13540 standard installation.
13546 \begin_inset Index idx
13549 \begin_layout Plain Layout
13555 has to be loaded in the \SpecialChar LaTeX
13556 -preamble with the line
13560 \begin_layout Plain Layout
13561 When text is colored somewhere in the document with a predefined color,
13563 loads the \SpecialChar LaTeX
13569 Thus it is possible that the package is loaded twice, but this does not
13576 \begin_inset Note Note
13579 \begin_layout Plain Layout
13580 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13589 \begin_layout Standard
13597 \begin_layout Standard
13598 \begin_inset VSpace medskip
13601 To color boxes, the command
13608 \begin_inset Index idx
13611 \begin_layout Plain Layout
13619 is used in the following scheme:
13622 \begin_layout Standard
13627 colorbox{color}{box content}
13630 \begin_layout Standard
13631 The box content can also be a box and a
13637 can also be part of another box (see the 2nd and 3rd example).
13638 When the box should contain a formula, an extra formula has to be created,
13639 the same way as for
13649 \begin_layout Plain Layout
13650 This also applies for the command
13664 \begin_layout Standard
13665 One of the following predefined colors can be chosen:
13668 \begin_layout Standard
13702 \begin_inset Separator parbreak
13708 \begin_layout Standard
13710 \begin_inset Tabular
13711 <lyxtabular version="3" rows="4" columns="2">
13712 <features booktabs="true" tabularvalignment="middle">
13713 <column alignment="center" valignment="top" width="0pt">
13714 <column alignment="center" valignment="top">
13716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13719 \begin_layout Plain Layout
13725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13728 \begin_layout Plain Layout
13736 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13739 \begin_layout Plain Layout
13743 \begin_inset Formula $\to$
13753 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13756 \begin_layout Plain Layout
13757 \begin_inset Formula $\colorbox{yellow}{A=B}$
13766 <row topspace="1.5mm">
13767 <cell alignment="center" valignment="top" usebox="none">
13770 \begin_layout Plain Layout
13774 \begin_inset Formula $\to$
13782 \begin_inset space \textvisiblespace{}
13790 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13793 \begin_layout Plain Layout
13794 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13803 <row topspace="1.5mm" bottomspace="1mm">
13804 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13807 \begin_layout Plain Layout
13811 \begin_inset space \textvisiblespace{}
13817 \begin_inset Formula $\to$
13833 \begin_inset space \textvisiblespace{}
13841 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13844 \begin_layout Plain Layout
13845 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13861 \begin_layout Standard
13868 only colors the box but not the characters in the box.
13869 To color all characters, the whole formula is highlighted and the desired
13870 color is chosen in the
13873 \begin_inset space ~
13879 The dialog can be called with the toolbar button
13882 arg "dialog-show character"
13887 Edit\SpecialChar menuseparator
13889 \begin_inset space ~
13892 Style\SpecialChar menuseparator
13896 The formula number then has the same color as the formula.
13897 When the formula number should get another color than the formula characters,
13898 the color must be changed within the formula.
13901 \begin_layout Standard
13905 \begin_layout Standard
13908 \begin_inset Formula
13910 \int A=B\label{eq:red}
13918 \begin_inset Formula
13920 \textcolor{red}{\int A=B}\label{eq:redgreen}
13928 \begin_layout Standard
13930 \begin_inset CommandInset ref
13936 is completely colored red.
13937 \begin_inset Newline newline
13941 \begin_inset CommandInset ref
13943 reference "eq:redgreen"
13947 was first completely colored green to set the color for the formula number.
13948 Subsequently the formula characters were colored red.
13951 \begin_layout Standard
13952 \begin_inset VSpace bigskip
13955 To color the frame different than the rest of the box, the command
13962 \begin_inset Index idx
13965 \begin_layout Plain Layout
13973 is used in the following scheme:
13976 \begin_layout Standard
13981 fcolorbox{frame color}{color}{box content}
13984 \begin_layout Standard
13991 is an extension of the command
13998 The frame width is set, like for
14021 \begin_layout Plain Layout
14033 \begin_inset Formula
14035 \fcolorbox{cyan}{magenta}{A=B}
14044 \begin_layout Plain Layout
14058 \begin_layout Standard
14059 This formula was created with the command
14060 \begin_inset Newline newline
14068 \begin_inset Formula $\to$
14074 \begin_inset Formula $\to$
14084 \begin_layout Standard
14085 \begin_inset VSpace bigskip
14088 To use other colors than the predefined ones, they have to be defined first.
14091 \begin_layout Standard
14092 One can for example define the color
14093 \begin_inset Quotes eld
14101 \begin_inset Quotes erd
14104 with the \SpecialChar LaTeX
14108 \begin_layout Standard
14113 definecolor{darkgreen}{cmyk}{0.5,
14128 \begin_inset Index idx
14131 \begin_layout Plain Layout
14142 \begin_layout Standard
14147 is the color space that denotes the colors
14164 The four comma separated numbers are the portion factor for the corresponding
14165 colors of the color space.
14166 The factors can be in the range of 0
14167 \begin_inset space \thinspace{}
14171 \begin_inset space \thinspace{}
14179 also the color space
14183 can be used for definitions.
14200 , so that there are in this case three portion factors for the corresponding
14202 Furthermore there is the color space
14206 with one portion factor for the gray value.
14209 \begin_layout Standard
14210 As example a framed box with the new defined color
14214 where the characters have been colored
14219 \begin_inset Formula
14221 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14229 \begin_layout Standard
14230 Self-defined colors can also be used for text with the help of the command
14238 \begin_inset Index idx
14241 \begin_layout Plain Layout
14250 \begin_layout Standard
14254 \begin_layout Plain Layout
14258 textcolor{darkgreen}{
14264 \begin_inset Quotes eld
14268 \begin_inset Quotes erd
14275 \begin_layout Plain Layout
14285 \begin_layout Standard
14293 \begin_inset Index idx
14296 \begin_layout Plain Layout
14304 is used in the scheme
14308 textcolor{color}{characters to color}
14313 \begin_layout Subsection
14315 \begin_inset CommandInset label
14317 name "subsec:Paragraph-Boxes"
14322 \begin_inset Index idx
14325 \begin_layout Plain Layout
14326 Boxes ! as paragraph
14334 \begin_layout Standard
14335 A box that can contain several lines and paragraphs, a so-called paragraph
14336 box (parbox), can be created with the menu
14338 Insert\SpecialChar menuseparator
14341 or the toolbar button
14350 \begin_layout Standard
14351 The following example shows a framed parbox in a line:
14354 \begin_layout Standard
14355 \begin_inset VSpace medskip
14359 \begin_inset Box Boxed
14369 height_special "totalheight"
14374 backgroundcolor "none"
14377 \begin_layout Plain Layout
14378 This is a paragraph box.
14380 \begin_inset space \thinspace{}
14383 cm long and can also contain formulas:
14384 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14395 \begin_layout Standard
14396 \begin_inset VSpace medskip
14402 \begin_layout Standard
14403 Such a box is created by right-clicking on the gray box inset.
14404 A dialog pops up showing the box properties.
14418 \begin_inset space \thinspace{}
14423 Vertical Box Alignment
14428 \begin_layout Standard
14429 \begin_inset VSpace medskip
14432 In \SpecialChar LaTeX
14433 a parbox is created with the command
14440 \begin_inset Index idx
14443 \begin_layout Plain Layout
14451 which has the following scheme:
14454 \begin_layout Standard
14459 parbox[position]{width}{box content}
14462 \begin_layout Standard
14477 \begin_inset Quotes eld
14481 \begin_inset Quotes erd
14484 means that the box is aligned within the surrounding text with its last
14491 \begin_inset Quotes eld
14495 \begin_inset Quotes erd
14498 this is done with the first line.
14499 When no position is given, the box will be vertically centered, see section
14507 \begin_inset space ~
14512 manual for examples.
14515 \begin_layout Standard
14516 \begin_inset VSpace bigskip
14519 To frame formulas completely, including the formula number, the formula
14520 must be set into a parbox.
14521 To do this, the command
14535 is inserted in \SpecialChar TeX
14536 mode before the formula.
14544 \begin_inset Index idx
14547 \begin_layout Plain Layout
14555 is hereby the line width set for the document.
14556 Because the frame is outside the parbox, 2
14557 \begin_inset space \thinspace{}
14560 times the frame separation and the frame thickness must be subtracted from
14562 As this is not automatically done by \SpecialChar LyX
14567 \begin_layout Plain Layout
14568 \begin_inset CommandInset href
14570 name "LyX-bug #4483"
14571 target "http://www.lyx.org/trac/ticket/4483"
14581 mode has to be used.
14582 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14591 \begin_layout Plain Layout
14596 is part of every \SpecialChar LaTeX
14597 standard installation.
14603 \begin_inset Index idx
14606 \begin_layout Plain Layout
14612 must be loaded in the \SpecialChar LaTeX
14613 -preamble with the line
14616 \begin_layout Standard
14624 \begin_layout Standard
14625 Behind the formula both boxes are closed by entering
14629 in \SpecialChar TeX
14631 Here is an example:
14635 \begin_layout Plain Layout
14649 \begin_layout Standard
14653 \begin_layout Plain Layout
14671 \begin_inset Formula
14673 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14682 \begin_layout Plain Layout
14693 \begin_layout Plain Layout
14707 \begin_layout Standard
14708 \begin_inset VSpace medskip
14711 As a parbox is used as the argument of
14717 , there is in this case no difference between
14732 \begin_layout Standard
14733 \begin_inset VSpace bigskip
14736 Paragraph boxes are very useful to comment formulas directly.
14743 is used in combination with the command
14757 \begin_inset CommandInset ref
14759 reference "subsec:User-defined-Numbering"
14766 \begin_layout Standard
14767 An example of a formula commented with
14776 \begin_layout Standard
14780 \begin_layout Plain Layout
14793 This is a description.
14794 It is distinctly separated from the formula and multiline.
14798 \begin_layout Plain Layout
14810 \begin_layout Standard
14811 Such a formula must be inserted completely in \SpecialChar TeX
14812 mode because \SpecialChar LyX
14814 support the command
14821 The formula is created with the following command sequence:
14824 \begin_layout Standard
14837 is inserted in \SpecialChar TeX
14842 \begin_layout Plain Layout
14843 When the formula style
14855 can also be replaced by
14862 (formula styles see
14863 \begin_inset CommandInset ref
14865 reference "sec:Formula-Styles"
14874 Then the description follows as normal text and finally
14880 is inserted in \SpecialChar TeX
14894 hereby create a displayed formula.
14897 \begin_layout Standard
14904 can be seen in this example that was
14905 \begin_inset Quotes eld
14909 \begin_inset Quotes erd
14912 using the mathematical textmode:
14913 \begin_inset Formula
14915 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14923 \begin_layout Section
14925 \begin_inset Index idx
14928 \begin_layout Plain Layout
14937 \begin_layout Subsection
14939 \begin_inset CommandInset label
14941 name "subsec:Big-Operators"
14946 \begin_inset Index idx
14949 \begin_layout Plain Layout
14956 \begin_inset Index idx
14959 \begin_layout Plain Layout
14966 \begin_inset Index idx
14969 \begin_layout Plain Layout
14978 \begin_layout Standard
14979 To be able to use all integral operators listed here, the option
14981 Use esint package automatically
14983 must be set in the document settings under
14986 \begin_inset space ~
14994 \begin_layout Standard
14995 \begin_inset space \hfill{}
14999 \begin_inset Tabular
15000 <lyxtabular version="3" rows="11" columns="2">
15001 <features booktabs="true" tabularvalignment="middle">
15002 <column alignment="center" valignment="top" width="0pt">
15003 <column alignment="center" valignment="top" width="0pt">
15005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15008 \begin_layout Plain Layout
15014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15017 \begin_layout Plain Layout
15025 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15028 \begin_layout Plain Layout
15032 \begin_inset Index idx
15035 \begin_layout Plain Layout
15048 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15051 \begin_layout Plain Layout
15052 \begin_inset Formula $\int$
15062 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15065 \begin_layout Plain Layout
15073 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15076 \begin_layout Plain Layout
15077 \begin_inset Formula $\oint$
15087 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15090 \begin_layout Plain Layout
15098 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15101 \begin_layout Plain Layout
15102 \begin_inset Formula $\ointctrclockwise$
15112 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15115 \begin_layout Plain Layout
15123 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15126 \begin_layout Plain Layout
15127 \begin_inset Formula $\ointclockwise$
15137 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15140 \begin_layout Plain Layout
15148 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15151 \begin_layout Plain Layout
15152 \begin_inset Formula $\sqint$
15162 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15165 \begin_layout Plain Layout
15173 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15176 \begin_layout Plain Layout
15178 \begin_inset Formula $\fint$
15188 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15191 \begin_layout Plain Layout
15199 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15202 \begin_layout Plain Layout
15204 \begin_inset Formula $\landupint$
15214 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15217 \begin_layout Plain Layout
15225 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15228 \begin_layout Plain Layout
15230 \begin_inset Formula $\landdownint$
15240 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15243 \begin_layout Plain Layout
15251 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15254 \begin_layout Plain Layout
15255 \begin_inset Formula $\bigcap$
15265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15268 \begin_layout Plain Layout
15276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15279 \begin_layout Plain Layout
15280 \begin_inset Formula $\bigcup$
15294 \begin_inset space \hfill{}
15298 \begin_inset Tabular
15299 <lyxtabular version="3" rows="11" columns="2">
15300 <features booktabs="true" tabularvalignment="middle">
15301 <column alignment="center" valignment="top" width="0pt">
15302 <column alignment="center" valignment="top" width="0pt">
15304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15307 \begin_layout Plain Layout
15313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15316 \begin_layout Plain Layout
15324 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15327 \begin_layout Plain Layout
15331 \begin_inset Index idx
15334 \begin_layout Plain Layout
15347 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15350 \begin_layout Plain Layout
15351 \begin_inset Formula $\sum$
15361 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15364 \begin_layout Plain Layout
15368 \begin_inset Index idx
15371 \begin_layout Plain Layout
15378 \begin_layout Plain Layout
15397 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15400 \begin_layout Plain Layout
15401 \begin_inset Formula $\prod$
15411 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15414 \begin_layout Plain Layout
15422 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15425 \begin_layout Plain Layout
15426 \begin_inset Formula $\coprod$
15436 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15439 \begin_layout Plain Layout
15447 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15450 \begin_layout Plain Layout
15451 \begin_inset Formula $\bigodot$
15461 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15464 \begin_layout Plain Layout
15472 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15475 \begin_layout Plain Layout
15476 \begin_inset Formula $\bigotimes$
15486 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15489 \begin_layout Plain Layout
15497 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15500 \begin_layout Plain Layout
15501 \begin_inset Formula $\bigoplus$
15511 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15514 \begin_layout Plain Layout
15522 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15525 \begin_layout Plain Layout
15526 \begin_inset Formula $\bigwedge$
15536 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15539 \begin_layout Plain Layout
15547 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15550 \begin_layout Plain Layout
15551 \begin_inset Formula $\bigvee$
15561 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15564 \begin_layout Plain Layout
15572 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15575 \begin_layout Plain Layout
15576 \begin_inset Formula $\bigsqcup$
15586 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15589 \begin_layout Plain Layout
15597 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15600 \begin_layout Plain Layout
15601 \begin_inset Formula $\biguplus$
15615 \begin_inset space \hfill{}
15621 \begin_layout Standard
15622 All big operators can also be inserted via the math toolbar button
15625 arg "math-insert \\intop"
15631 \begin_layout Standard
15632 The operators are called big because they are bigger than the sometimes
15633 equal looking binary operators.
15634 All big operators can have limits as described in the next subsection.
15637 \begin_layout Standard
15638 For all integral operators there is a second version available, ending in
15656 These operators are different from
15663 \begin_inset space \space{}
15666 in the style the operator limits are displayed, see
15667 \begin_inset CommandInset ref
15669 reference "subsec:Operator-Limits"
15677 \begin_layout Subsubsection*
15678 Advice for Integrals
15681 \begin_layout Standard
15686 in an integral is an operator, that therefore has to be set upright.
15687 This is done by highlighting the
15691 and using the keyboard shortcut
15701 \begin_layout Plain Layout
15707 \begin_inset CommandInset ref
15709 reference "subsec:Font-Styles"
15719 Finally the smallest space is inserted before the
15723 , as this is usual for operators.
15727 \begin_layout Standard
15729 \begin_inset Formula $\int A(x)dx$
15733 \begin_inset Newline newline
15737 \begin_inset Phantom HPhantom
15740 \begin_layout Plain Layout
15747 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15753 \begin_layout Standard
15754 For multiple integrals there are the following commands:
15755 \begin_inset VSpace medskip
15761 \begin_layout Standard
15762 \begin_inset space \hfill{}
15766 \begin_inset Tabular
15767 <lyxtabular version="3" rows="4" columns="2">
15768 <features booktabs="true" tabularvalignment="middle">
15769 <column alignment="center" valignment="top" width="0pt">
15770 <column alignment="center" valignment="top" width="0pt">
15772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15775 \begin_layout Plain Layout
15781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15784 \begin_layout Plain Layout
15791 <row bottomspace="1mm">
15792 <cell alignment="center" valignment="top" usebox="none">
15795 \begin_layout Plain Layout
15803 <cell alignment="center" valignment="top" usebox="none">
15806 \begin_layout Plain Layout
15807 \begin_inset Formula $\iint$
15816 <row bottomspace="1mm">
15817 <cell alignment="center" valignment="top" usebox="none">
15820 \begin_layout Plain Layout
15828 <cell alignment="center" valignment="top" usebox="none">
15831 \begin_layout Plain Layout
15832 \begin_inset Formula $\oiint$
15841 <row bottomspace="1mm">
15842 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15845 \begin_layout Plain Layout
15853 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15856 \begin_layout Plain Layout
15857 \begin_inset Formula $\sqiint$
15871 \begin_inset space \hfill{}
15875 \begin_inset Tabular
15876 <lyxtabular version="3" rows="4" columns="2">
15877 <features booktabs="true" tabularvalignment="middle">
15878 <column alignment="center" valignment="top" width="0pt">
15879 <column alignment="center" valignment="top" width="0pt">
15881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15884 \begin_layout Plain Layout
15890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15893 \begin_layout Plain Layout
15900 <row bottomspace="1mm">
15901 <cell alignment="center" valignment="top" usebox="none">
15904 \begin_layout Plain Layout
15912 <cell alignment="center" valignment="top" usebox="none">
15915 \begin_layout Plain Layout
15916 \begin_inset Formula $\iiint$
15925 <row bottomspace="1mm">
15926 <cell alignment="center" valignment="top" usebox="none">
15929 \begin_layout Plain Layout
15937 <cell alignment="center" valignment="top" usebox="none">
15940 \begin_layout Plain Layout
15941 \begin_inset Formula $\iiiint$
15950 <row bottomspace="1mm">
15951 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15954 \begin_layout Plain Layout
15962 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15965 \begin_layout Plain Layout
15966 \begin_inset Formula $\dotsint$
15980 \begin_inset space \hfill{}
15986 \begin_layout Subsection
15988 \begin_inset CommandInset label
15990 name "subsec:Operator-Limits"
15995 \begin_inset Index idx
15998 \begin_layout Plain Layout
16007 \begin_layout Standard
16008 Limits are created by super- and subscripts:
16009 \begin_inset Separator parbreak
16015 \begin_layout Standard
16017 \begin_inset Tabular
16018 <lyxtabular version="3" rows="2" columns="2">
16019 <features booktabs="true" tabularvalignment="middle">
16020 <column alignment="center" valignment="top" width="0pt">
16021 <column alignment="center" valignment="top" width="0pt">
16023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16026 \begin_layout Plain Layout
16032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16035 \begin_layout Plain Layout
16043 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16046 \begin_layout Plain Layout
16052 \begin_inset space \textvisiblespace{}
16056 \begin_inset Formula $\to$
16060 \begin_inset Formula $\to$
16068 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16071 \begin_layout Plain Layout
16072 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
16088 \begin_layout Standard
16089 Limits of inline formulas are set right beside the operator.
16090 Limits in displayed formulas are set above or below the operator, except
16091 for integral limits.
16094 \begin_layout Standard
16095 To force that the limits are set beside the operator, the cursor is set
16096 directly behind the operator and the limits type is changed with the menu
16099 Edit\SpecialChar menuseparator
16100 Math\SpecialChar menuseparator
16119 \begin_layout Standard
16120 The default limits type is this:
16121 \begin_inset Formula
16123 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16128 This is how it looks when the limits type was changed to
16135 \begin_inset Formula
16137 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16142 For integrals, except those ending with
16158 etc., the limits are by default set beside the operator.
16159 But for multiple integrals the limits are often set below the operator.
16160 In the following example the limits type was therefore set to
16164 and so set below the integrals:
16165 \begin_inset Formula
16167 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16175 \begin_layout Standard
16176 \begin_inset VSpace medskip
16179 To specify conditions for limits, the commands
16186 \begin_inset Index idx
16189 \begin_layout Plain Layout
16204 \begin_inset Index idx
16207 \begin_layout Plain Layout
16216 To create for example this expression
16217 \begin_inset Formula
16219 \sum_{\begin{subarray}{c}
16223 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16231 \begin_layout Standard
16232 the following has to be done:
16233 \begin_inset Newline newline
16245 \begin_inset space \textvisiblespace{}
16251 One is now in a blue box under the summation operator and insert there
16257 \begin_inset space \textvisiblespace{}
16263 The blue box is now within a purple box and now several lines can be written
16265 A new line is created by inserting a line break (
16268 arg "newline-insert newline"
16273 \begin_inset Newline newline
16278 0<k<1000 Ctrl+Return
16279 \begin_inset Newline newline
16284 is typed in, a new box appears below for the new line.
16287 \begin_layout Standard
16288 The alignment of the lines can be changed to left aligned with the
16298 Edit\SpecialChar menuseparator
16302 To get right alignment,
16307 \begin_inset space \textvisiblespace{}
16312 is inserted at the beginning of the line.
16315 \begin_layout Standard
16328 with the difference that the lines are always centered.
16331 \begin_layout Standard
16332 \begin_inset VSpace bigskip
16336 \begin_inset CommandInset ref
16338 reference "eq:substack"
16342 there can be too much space beside an operator, because the characters
16343 following the operator are set beside the limits.
16344 To avoid this the command
16351 \begin_inset Index idx
16354 \begin_layout Plain Layout
16363 To activate it, set in the document settings under
16366 \begin_inset space ~
16376 \begin_inset Index idx
16379 \begin_layout Plain Layout
16380 Packages ! mathtools
16388 \begin_inset space ~
16400 sets the space besides the operator to 0
16401 \begin_inset space \thinspace{}
16405 \begin_inset Newline newline
16409 \begin_inset CommandInset ref
16411 reference "eq:substack"
16415 , one uses the command
16418 \begin_layout Standard
16426 \begin_layout Standard
16427 and inserts the operator with its limits into the braces.
16428 Behind the brace one continues the formula:
16429 \begin_inset Formula
16431 \smashoperator{\sum_{\begin{subarray}{c}
16435 \end{subarray}}^{n}}k^{-2}
16443 \begin_layout Standard
16444 It is possible to set the space of only one side of the operator to 0
16445 \begin_inset space \thinspace{}
16449 To do this write either
16468 stands for the left and
16472 for the right side of the operator.
16473 Here is an example of the possible
16482 \begin_layout Standard
16483 \begin_inset Formula
16485 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}
16493 \begin_layout Standard
16494 \begin_inset VSpace bigskip
16500 \begin_layout Standard
16501 When several consecutive operators have limits the typesetting of the limits
16502 looks often imperfect in the output, see this example:
16503 \begin_inset Formula
16505 \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}
16510 To improve the typesetting set in the document settings under
16513 \begin_inset space ~
16523 \begin_inset Index idx
16526 \begin_layout Plain Layout
16527 Packages ! mathtools
16535 \begin_inset space ~
16541 Then insert into your formula the command
16548 \begin_inset Index idx
16551 \begin_layout Plain Layout
16559 directly before the first operator.
16560 The example will then look like this:
16561 \begin_inset Formula
16563 \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}
16571 \begin_layout Standard
16572 \begin_inset VSpace bigskip
16575 How to use one limit for several operators is described in
16576 \begin_inset CommandInset ref
16578 reference "subsec:Self-defined-Operators"
16585 \begin_layout Subsection
16586 Decoration for Operators
16587 \begin_inset Index idx
16590 \begin_layout Plain Layout
16591 Operators ! Decoration
16599 \begin_layout Standard
16607 \begin_inset Index idx
16610 \begin_layout Plain Layout
16625 \begin_inset Index idx
16628 \begin_layout Plain Layout
16636 characters can be placed above or below an operator, respectively.
16644 \begin_inset Index idx
16647 \begin_layout Plain Layout
16655 characters can be set before and behind a big operator.
16658 \begin_layout Standard
16660 \begin_inset space ~
16672 \begin_layout Itemize
16679 is used to set characters at the corners of the operator
16682 \begin_layout Itemize
16689 is used to set characters before and/or behind the operator (this variant
16690 represents \SpecialChar LaTeX
16700 \begin_layout Itemize
16707 is used to set characters at the left corners and/or behind the operator
16710 \begin_layout Itemize
16717 is used to set characters at the right corners and/or before the operator
16720 \begin_layout Standard
16721 For example the command
16726 \begin_inset space \textvisiblespace{}
16732 \begin_inset space \textvisiblespace{}
16736 \begin_inset Formula $\to$
16740 \begin_inset Formula $\to$
16744 \begin_inset space \textvisiblespace{}
16754 \begin_inset Formula
16756 \sideset{}{'}\sum_{k=1}^{n}
16764 \begin_layout Standard
16765 \begin_inset Note Greyedout
16768 \begin_layout Plain Layout
16775 can only be used to decorate big operators, binary operators are not allowed.
16783 \begin_layout Standard
16796 can also be used to decorate symbols and characters.
16797 For example, the command
16802 \begin_inset space \textvisiblespace{}
16808 \begin_inset space \textvisiblespace{}
16814 \begin_inset Formula $\uparrow$
16822 \begin_inset Formula
16824 \overset{a}{\maltese}
16832 \begin_layout Subsection
16834 \begin_inset CommandInset label
16836 name "subsec:Binary-Operators"
16841 \begin_inset Index idx
16844 \begin_layout Plain Layout
16853 \begin_layout Standard
16854 Binary operators are surrounded by space when there is a character before
16856 \begin_inset VSpace medskip
16862 \begin_layout Standard
16863 \begin_inset Tabular
16864 <lyxtabular version="3" rows="13" columns="2">
16865 <features booktabs="true" tabularvalignment="middle">
16866 <column alignment="center" valignment="top" width="0pt">
16867 <column alignment="center" valignment="top" width="0pt">
16869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16872 \begin_layout Plain Layout
16874 \begin_inset Note Note
16877 \begin_layout Plain Layout
16884 is only used as spacer.
16894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16897 \begin_layout Plain Layout
16905 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16908 \begin_layout Plain Layout
16914 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16917 \begin_layout Plain Layout
16918 \begin_inset Formula $+$
16928 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16931 \begin_layout Plain Layout
16937 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16940 \begin_layout Plain Layout
16941 \begin_inset Formula $-$
16951 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16954 \begin_layout Plain Layout
16962 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16965 \begin_layout Plain Layout
16966 \begin_inset Formula $\pm$
16976 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16979 \begin_layout Plain Layout
16987 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16990 \begin_layout Plain Layout
16991 \begin_inset Formula $\mp$
17001 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17004 \begin_layout Plain Layout
17012 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17015 \begin_layout Plain Layout
17016 \begin_inset Formula $\cdot$
17026 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17029 \begin_layout Plain Layout
17037 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17040 \begin_layout Plain Layout
17041 \begin_inset Formula $\times$
17051 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17054 \begin_layout Plain Layout
17062 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17065 \begin_layout Plain Layout
17066 \begin_inset Formula $\div$
17076 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17079 \begin_layout Plain Layout
17083 \begin_layout Plain Layout
17096 \begin_layout Plain Layout
17108 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17111 \begin_layout Plain Layout
17112 \begin_inset Formula $*$
17122 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17125 \begin_layout Plain Layout
17133 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17136 \begin_layout Plain Layout
17137 \begin_inset Formula $\star$
17147 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17150 \begin_layout Plain Layout
17158 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17161 \begin_layout Plain Layout
17162 \begin_inset Formula $\circ$
17172 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17175 \begin_layout Plain Layout
17183 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17186 \begin_layout Plain Layout
17187 \begin_inset Formula $\diamond$
17197 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17200 \begin_layout Plain Layout
17208 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17211 \begin_layout Plain Layout
17212 \begin_inset Formula $\bullet$
17226 \begin_inset space \hfill{}
17230 \begin_inset Tabular
17231 <lyxtabular version="3" rows="13" columns="2">
17232 <features booktabs="true" tabularvalignment="middle">
17233 <column alignment="center" valignment="top" width="0pt">
17234 <column alignment="center" valignment="top" width="0pt">
17236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17239 \begin_layout Plain Layout
17245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17248 \begin_layout Plain Layout
17256 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17259 \begin_layout Plain Layout
17267 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17270 \begin_layout Plain Layout
17271 \begin_inset Formula $\nabla$
17281 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17284 \begin_layout Plain Layout
17292 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17295 \begin_layout Plain Layout
17296 \begin_inset Formula $\bigtriangledown$
17306 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17309 \begin_layout Plain Layout
17317 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17320 \begin_layout Plain Layout
17321 \begin_inset Formula $\bigtriangleup$
17331 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17334 \begin_layout Plain Layout
17342 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17345 \begin_layout Plain Layout
17346 \begin_inset Formula $\Box$
17356 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17359 \begin_layout Plain Layout
17367 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17370 \begin_layout Plain Layout
17371 \begin_inset Formula $\cap$
17381 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17384 \begin_layout Plain Layout
17392 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17395 \begin_layout Plain Layout
17396 \begin_inset Formula $\cup$
17406 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17409 \begin_layout Plain Layout
17417 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17420 \begin_layout Plain Layout
17421 \begin_inset Formula $\dagger$
17431 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17434 \begin_layout Plain Layout
17442 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17445 \begin_layout Plain Layout
17446 \begin_inset Formula $\ddagger$
17456 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17459 \begin_layout Plain Layout
17467 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17470 \begin_layout Plain Layout
17471 \begin_inset Formula $\wr$
17481 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17484 \begin_layout Plain Layout
17492 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17495 \begin_layout Plain Layout
17496 \begin_inset Formula $\bigcirc$
17506 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17509 \begin_layout Plain Layout
17517 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17520 \begin_layout Plain Layout
17521 \begin_inset Formula $\wedge$
17531 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17534 \begin_layout Plain Layout
17542 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17545 \begin_layout Plain Layout
17546 \begin_inset Formula $\vee$
17560 \begin_inset space \hfill{}
17564 \begin_inset Tabular
17565 <lyxtabular version="3" rows="13" columns="2">
17566 <features booktabs="true" tabularvalignment="middle">
17567 <column alignment="center" valignment="top" width="0pt">
17568 <column alignment="center" valignment="top" width="0pt">
17570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17573 \begin_layout Plain Layout
17579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17582 \begin_layout Plain Layout
17590 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17593 \begin_layout Plain Layout
17601 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17604 \begin_layout Plain Layout
17605 \begin_inset Formula $\oplus$
17615 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17618 \begin_layout Plain Layout
17626 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17629 \begin_layout Plain Layout
17630 \begin_inset Formula $\ominus$
17640 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17643 \begin_layout Plain Layout
17651 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17654 \begin_layout Plain Layout
17655 \begin_inset Formula $\otimes$
17665 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17668 \begin_layout Plain Layout
17676 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17679 \begin_layout Plain Layout
17680 \begin_inset Formula $\oslash$
17690 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17693 \begin_layout Plain Layout
17701 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17704 \begin_layout Plain Layout
17705 \begin_inset Formula $\odot$
17715 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17718 \begin_layout Plain Layout
17726 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17729 \begin_layout Plain Layout
17730 \begin_inset Formula $\amalg$
17740 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17743 \begin_layout Plain Layout
17751 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17754 \begin_layout Plain Layout
17755 \begin_inset Formula $\uplus$
17765 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17768 \begin_layout Plain Layout
17776 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17779 \begin_layout Plain Layout
17780 \begin_inset Formula $\setminus$
17790 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17793 \begin_layout Plain Layout
17801 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17804 \begin_layout Plain Layout
17805 \begin_inset Formula $\sqcap$
17815 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17818 \begin_layout Plain Layout
17826 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17829 \begin_layout Plain Layout
17830 \begin_inset Formula $\sqcup$
17840 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17843 \begin_layout Plain Layout
17851 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17854 \begin_layout Plain Layout
17855 \begin_inset Formula $\triangleleft$
17865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17868 \begin_layout Plain Layout
17876 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17879 \begin_layout Plain Layout
17880 \begin_inset Formula $\triangleright$
17896 \begin_layout Standard
17897 All binary operators can also be inserted via the math toolbar button
17900 arg "math-insert \\pm"
17906 \begin_layout Standard
17907 To typeset the Laplace operator also
17924 \begin_inset Formula $\nabla^{2}$
17927 ) can be used instead of
17936 \begin_layout Standard
17943 Insert\SpecialChar menuseparator
17955 \begin_layout Subsection
17956 Self-defined Operators
17957 \begin_inset CommandInset label
17959 name "subsec:Self-defined-Operators"
17964 \begin_inset Index idx
17967 \begin_layout Plain Layout
17968 Operators ! self-defined
17976 \begin_layout Standard
17977 With the help of the command
17981 DeclareMathOperator
17984 \begin_inset Index idx
17987 \begin_layout Plain Layout
17992 DeclareMathOperator
17997 custom operators can be defined in the \SpecialChar LaTeX
17999 Its command scheme is:
18002 \begin_layout Standard
18007 DeclareMathOperator{new command}{display}
18010 \begin_layout Standard
18011 Display can be characters or symbols that define how the operator looks
18013 To define a big operator a * is set behind the command.
18014 All self-defined big operators can have limits as described in
18015 \begin_inset CommandInset ref
18017 reference "subsec:Operator-Limits"
18024 \begin_layout Standard
18025 For example the \SpecialChar LaTeX
18029 \begin_layout Standard
18034 DeclareMathOperator*{
18041 \begin_layout Standard
18042 defines the command
18048 , that inserts a big operator consisting of the lozenge symbol from
18049 \begin_inset CommandInset ref
18051 reference "subsec:Miscellaneous-Symbols"
18056 \begin_inset Formula
18058 \Lozenge_{n=1}^{\infty}
18063 The command for this formula is:
18074 \begin_inset Formula $\to$
18080 \begin_layout Standard
18081 \begin_inset VSpace bigskip
18084 When self-defined operators are not used several times in the document,
18085 they can also be defined with the commands
18092 \begin_inset Index idx
18095 \begin_layout Plain Layout
18110 \begin_inset Index idx
18113 \begin_layout Plain Layout
18121 , which have the following scheme:
18124 \begin_layout Standard
18138 \begin_layout Standard
18145 defines big operators,
18154 \begin_layout Standard
18162 \begin_inset space \thinspace{}
18166 \begin_inset space \space{}
18169 be used to use one limit for several operators:
18172 \begin_layout Standard
18173 \begin_inset Formula
18175 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18183 \begin_layout Standard
18184 The command for the formula above is:
18185 \begin_inset Newline newline
18201 \begin_inset space \textvisiblespace{}
18207 \begin_inset Formula $\to$
18213 \begin_inset space \textvisiblespace{}
18221 \begin_layout Section
18223 \begin_inset Index idx
18226 \begin_layout Plain Layout
18235 \begin_layout Subsection
18237 \begin_inset CommandInset label
18239 name "subsec:Font-Styles"
18244 \begin_inset Index idx
18247 \begin_layout Plain Layout
18256 \begin_layout Standard
18257 Latin letters in formulas can be set in one of the following font styles:
18260 \begin_layout Standard
18262 \begin_inset space \hfill{}
18266 \begin_inset Tabular
18267 <lyxtabular version="3" rows="6" columns="2">
18268 <features booktabs="true" tabularvalignment="middle">
18269 <column alignment="center" valignment="top" width="0pt">
18270 <column alignment="center" valignment="top">
18272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18275 \begin_layout Plain Layout
18281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18284 \begin_layout Plain Layout
18292 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18295 \begin_layout Plain Layout
18301 \begin_inset space \textvisiblespace{}
18311 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18314 \begin_layout Plain Layout
18315 \begin_inset Formula $\mathbb{ABC}$
18325 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18328 \begin_layout Plain Layout
18334 \begin_inset space \textvisiblespace{}
18344 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18347 \begin_layout Plain Layout
18348 \begin_inset Formula $\mathbf{AbC}$
18358 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18361 \begin_layout Plain Layout
18367 \begin_inset space \textvisiblespace{}
18377 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18380 \begin_layout Plain Layout
18381 \begin_inset Formula $\boldsymbol{AbC}$
18391 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18394 \begin_layout Plain Layout
18400 \begin_inset space \textvisiblespace{}
18410 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18413 \begin_layout Plain Layout
18414 \begin_inset Formula $\mathcal{ABC}$
18424 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18427 \begin_layout Plain Layout
18433 \begin_inset space \textvisiblespace{}
18443 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18446 \begin_layout Plain Layout
18447 \begin_inset Formula $\mathfrak{AbC}$
18461 \begin_inset space \hfill{}
18465 \begin_inset Tabular
18466 <lyxtabular version="3" rows="6" columns="2">
18467 <features booktabs="true" tabularvalignment="middle">
18468 <column alignment="center" valignment="top" width="0pt">
18469 <column alignment="center" valignment="top">
18471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18474 \begin_layout Plain Layout
18480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18483 \begin_layout Plain Layout
18491 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18494 \begin_layout Plain Layout
18500 \begin_inset space \textvisiblespace{}
18510 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18513 \begin_layout Plain Layout
18514 \begin_inset Formula $\mathit{AbC}$
18524 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18527 \begin_layout Plain Layout
18533 \begin_inset space \textvisiblespace{}
18543 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18546 \begin_layout Plain Layout
18547 \begin_inset Formula $\mathrm{AbC}$
18557 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18560 \begin_layout Plain Layout
18566 \begin_inset space \textvisiblespace{}
18576 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18579 \begin_layout Plain Layout
18580 \begin_inset Formula $\mathsf{AbC}$
18590 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18593 \begin_layout Plain Layout
18599 \begin_inset space \textvisiblespace{}
18609 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18612 \begin_layout Plain Layout
18613 \begin_inset Formula $\mathtt{AbC}$
18623 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18626 \begin_layout Plain Layout
18632 \begin_inset space \textvisiblespace{}
18642 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18645 \begin_layout Plain Layout
18646 \begin_inset Formula $\mathscr{ABC}$
18660 \begin_inset space \hfill{}
18666 \begin_layout Standard
18667 \begin_inset Note Greyedout
18670 \begin_layout Plain Layout
18693 can only be used for big letters.
18701 \begin_layout Standard
18702 Predefined is the style
18711 \begin_layout Standard
18712 The style commands work also for letters in mathematical constructs:
18713 \begin_inset Formula
18715 \mathfrak{A=\frac{b}{C}}
18723 \begin_layout Standard
18724 Characters in mathematical text don't appear in a math font style but in
18725 the text font style
18732 That their style can't be set correctly via the text style dialog is a
18733 bug in \SpecialChar LyX
18738 \begin_layout Plain Layout
18739 \begin_inset CommandInset href
18741 name "LyX-bug #4629"
18742 target "http://www.lyx.org/trac/ticket/4629"
18754 \begin_layout Standard
18755 Instead of the style commands the dialog
18757 Edit\SpecialChar menuseparator
18758 Math\SpecialChar menuseparator
18761 or the toolbar button
18764 arg "math-insert \\font"
18770 \begin_layout Subsection
18772 \begin_inset CommandInset label
18774 name "subsec:Bold-Formulas"
18779 \begin_inset Index idx
18782 \begin_layout Plain Layout
18791 \begin_layout Standard
18792 To make a complete formula bold, the command
18798 from the previous subsection cannot be used, because it doesn't work for
18799 small Greek letters.
18800 Furthermore it prints Latin letters always upright, like in the following
18804 \begin_layout Standard
18805 \begin_inset Formula
18807 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18815 \begin_layout Standard
18816 To display the formula correctly, the command
18823 \begin_inset Formula
18825 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18830 It is also possible to set the formula in a
18832 boldmath environment
18835 This environment is created by inserting the command
18842 \begin_inset Index idx
18845 \begin_layout Plain Layout
18853 in \SpecialChar TeX
18855 To end the environment, the command
18862 \begin_inset Index idx
18865 \begin_layout Plain Layout
18873 is inserted in \SpecialChar TeX
18878 \begin_layout Plain Layout
18888 \begin_inset Formula
18890 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18899 \begin_layout Plain Layout
18911 \begin_layout Subsection
18913 \begin_inset Index idx
18916 \begin_layout Plain Layout
18925 \begin_layout Standard
18926 Formulas can be colored like normal text: Highlight a formula or a formula
18932 Here is a formula in magenta:
18933 \begin_inset Formula
18935 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18943 \begin_layout Standard
18944 You can also define your own colors as described in
18945 \begin_inset CommandInset ref
18947 reference "subsec:Colored-Boxes"
18952 They can be used with the \SpecialChar TeX
18960 \begin_inset Index idx
18963 \begin_layout Plain Layout
18974 \begin_layout Standard
18979 textcolor{color}{characters or formula}
18982 \begin_layout Standard
18983 The following example was colored completely dark green and partly red:
18986 \begin_layout Standard
18990 \begin_layout Plain Layout
18994 textcolor{darkgreen}{
19000 \begin_inset Formula
19002 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19011 \begin_layout Plain Layout
19021 \begin_layout Standard
19022 Due to a bug in \SpecialChar LyX
19023 only complete formulas can be colored with self-defined
19028 \begin_layout Plain Layout
19029 \begin_inset CommandInset href
19031 name "LyX-bug #5269"
19032 target "http://www.lyx.org/trac/ticket/5269"
19044 \begin_layout Subsection
19046 \begin_inset CommandInset label
19048 name "subsec:Font-Sizes"
19053 \begin_inset Index idx
19056 \begin_layout Plain Layout
19065 \begin_layout Standard
19066 For characters in formulas there are, analog to characters in text, the
19067 following size commands:
19070 \begin_layout Standard
19114 \begin_inset Newline newline
19136 \begin_layout Standard
19137 The size produced by the commands depends on the document font size, which
19138 corresponds to the command
19145 The other commands produce smaller or larger sizes than
19152 The font size can however not exceed a certain value.
19153 Is for example the document font size 12
19154 \begin_inset space \thinspace{}
19163 switches to the same size as
19173 \begin_layout Standard
19174 A size command is inserted in \SpecialChar TeX
19175 mode before the formula and sets the size
19176 for all following formula and text characters.
19177 To switch back to the initial size, the command
19183 is inserted behind the formula in \SpecialChar TeX
19187 \begin_layout Standard
19188 Within a formula the size can be changed using the following size commands
19189 or the toolbar button
19192 arg "math-insert \\style"
19196 \begin_inset Separator parbreak
19202 \begin_layout Standard
19205 \begin_inset Tabular
19206 <lyxtabular version="3" rows="5" columns="2">
19207 <features booktabs="true" tabularvalignment="middle">
19208 <column alignment="center" valignment="top" width="0pt">
19209 <column alignment="center" valignment="top">
19211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19214 \begin_layout Plain Layout
19220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19223 \begin_layout Plain Layout
19231 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19234 \begin_layout Plain Layout
19238 \begin_inset Index idx
19241 \begin_layout Plain Layout
19254 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19257 \begin_layout Plain Layout
19258 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19267 <row topspace="1mm">
19268 <cell alignment="center" valignment="top" usebox="none">
19271 \begin_layout Plain Layout
19279 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19282 \begin_layout Plain Layout
19283 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19293 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19296 \begin_layout Plain Layout
19304 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19307 \begin_layout Plain Layout
19308 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19318 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19321 \begin_layout Plain Layout
19329 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19332 \begin_layout Plain Layout
19333 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19349 \begin_layout Standard
19350 After entering these commands, a blue box appears in which the formula parts
19354 \begin_layout Standard
19355 There is a further method to change the font size, that though only works
19356 for symbols or letters in mathematical text.
19357 To use it, one of the above text size commands is inserted in mathematical
19359 All following characters until the end of the mathematical text or until
19360 another size command will have the selected size.
19362 \begin_inset VSpace -2mm
19368 \begin_layout Standard
19372 \begin_layout Plain Layout
19382 \begin_inset Formula
19384 A=\frac{B}{c}\cdot\maltese
19390 \begin_inset Formula
19392 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19401 \begin_layout Plain Layout
19413 \begin_layout Standard
19414 \begin_inset VSpace medskip
19417 Before both formulas the command
19424 The command for the second formula is:
19425 \begin_inset Newline newline
19433 \begin_inset space \textvisiblespace{}
19439 \begin_inset space \textvisiblespace{}
19445 \begin_inset space \textvisiblespace{}
19451 \begin_inset space \textvisiblespace{}
19455 \begin_inset Formula $\to$
19459 \begin_inset Formula $\to$
19463 \begin_inset Newline newline
19467 \begin_inset space \hspace*{}
19478 \begin_inset space \textvisiblespace{}
19484 \begin_inset space \textvisiblespace{}
19490 \begin_inset space \textvisiblespace{}
19496 \begin_layout Standard
19497 If a symbol cannot be displayed in different sizes, it will always be displayed
19498 in the default size.
19501 \begin_layout Section
19503 \begin_inset Index idx
19506 \begin_layout Plain Layout
19515 \begin_layout Standard
19516 Greek letters can also be inserted via the toolbar button
19519 arg "math-insert \\alpha"
19523 All international typesetting norms purport that Greek letters in math
19524 have to be typeset italic/slanted.
19525 In some languages, like French or Russian, they are nevertheless sometimes
19529 \begin_layout Subsection
19531 \begin_inset Index idx
19534 \begin_layout Plain Layout
19535 Greek letters ! small
19543 \begin_layout Standard
19544 \begin_inset space \hfill{}
19548 \begin_inset Tabular
19549 <lyxtabular version="3" rows="11" columns="2">
19550 <features booktabs="true" tabularvalignment="middle">
19551 <column alignment="center" valignment="top" width="0pt">
19552 <column alignment="center" valignment="top" width="0pt">
19554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19557 \begin_layout Plain Layout
19563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19566 \begin_layout Plain Layout
19574 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19577 \begin_layout Plain Layout
19585 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19588 \begin_layout Plain Layout
19589 \begin_inset Formula $\alpha$
19599 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19602 \begin_layout Plain Layout
19610 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19613 \begin_layout Plain Layout
19614 \begin_inset Formula $\beta$
19624 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19627 \begin_layout Plain Layout
19635 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19638 \begin_layout Plain Layout
19639 \begin_inset Formula $\gamma$
19649 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19652 \begin_layout Plain Layout
19660 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19663 \begin_layout Plain Layout
19664 \begin_inset Formula $\delta$
19674 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19677 \begin_layout Plain Layout
19685 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19688 \begin_layout Plain Layout
19689 \begin_inset Formula $\epsilon$
19699 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19702 \begin_layout Plain Layout
19710 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19713 \begin_layout Plain Layout
19714 \begin_inset Formula $\varepsilon$
19724 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19727 \begin_layout Plain Layout
19735 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19738 \begin_layout Plain Layout
19739 \begin_inset Formula $\zeta$
19749 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19752 \begin_layout Plain Layout
19760 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19763 \begin_layout Plain Layout
19764 \begin_inset Formula $\eta$
19774 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19777 \begin_layout Plain Layout
19785 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19788 \begin_layout Plain Layout
19789 \begin_inset Formula $\theta$
19799 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19802 \begin_layout Plain Layout
19810 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19813 \begin_layout Plain Layout
19814 \begin_inset Formula $\vartheta$
19828 \begin_inset space \hfill{}
19832 \begin_inset Tabular
19833 <lyxtabular version="3" rows="12" columns="2">
19834 <features booktabs="true" tabularvalignment="middle">
19835 <column alignment="center" valignment="top" width="0pt">
19836 <column alignment="center" valignment="top" width="0pt">
19838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19841 \begin_layout Plain Layout
19847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19850 \begin_layout Plain Layout
19858 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19861 \begin_layout Plain Layout
19869 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19872 \begin_layout Plain Layout
19873 \begin_inset Formula $\iota$
19883 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19886 \begin_layout Plain Layout
19894 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19897 \begin_layout Plain Layout
19898 \begin_inset Formula $\kappa$
19908 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19911 \begin_layout Plain Layout
19919 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19922 \begin_layout Plain Layout
19923 \begin_inset Formula $\varkappa$
19933 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19936 \begin_layout Plain Layout
19944 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19947 \begin_layout Plain Layout
19948 \begin_inset Formula $\lambda$
19958 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19961 \begin_layout Plain Layout
19969 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19972 \begin_layout Plain Layout
19973 \begin_inset Formula $\mu$
19983 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19986 \begin_layout Plain Layout
19994 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19997 \begin_layout Plain Layout
19998 \begin_inset Formula $\nu$
20008 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20011 \begin_layout Plain Layout
20019 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20022 \begin_layout Plain Layout
20023 \begin_inset Formula $\xi$
20033 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20036 \begin_layout Plain Layout
20042 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20045 \begin_layout Plain Layout
20046 \begin_inset Formula $o$
20056 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20059 \begin_layout Plain Layout
20067 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20070 \begin_layout Plain Layout
20071 \begin_inset Formula $\pi$
20081 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20084 \begin_layout Plain Layout
20092 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20095 \begin_layout Plain Layout
20096 \begin_inset Formula $\varpi$
20106 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20109 \begin_layout Plain Layout
20117 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20120 \begin_layout Plain Layout
20121 \begin_inset Formula $\rho$
20135 \begin_inset space \hfill{}
20139 \begin_inset Tabular
20140 <lyxtabular version="3" rows="11" columns="2">
20141 <features booktabs="true" tabularvalignment="middle">
20142 <column alignment="center" valignment="top" width="0pt">
20143 <column alignment="center" valignment="top" width="0pt">
20145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20148 \begin_layout Plain Layout
20154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20157 \begin_layout Plain Layout
20165 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20168 \begin_layout Plain Layout
20176 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20179 \begin_layout Plain Layout
20180 \begin_inset Formula $\varrho$
20190 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20193 \begin_layout Plain Layout
20201 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20204 \begin_layout Plain Layout
20205 \begin_inset Formula $\sigma$
20215 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20218 \begin_layout Plain Layout
20226 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20229 \begin_layout Plain Layout
20230 \begin_inset Formula $\varsigma$
20240 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20243 \begin_layout Plain Layout
20251 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20254 \begin_layout Plain Layout
20255 \begin_inset Formula $\tau$
20265 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20268 \begin_layout Plain Layout
20276 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20279 \begin_layout Plain Layout
20280 \begin_inset Formula $\upsilon$
20290 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20293 \begin_layout Plain Layout
20301 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20304 \begin_layout Plain Layout
20305 \begin_inset Formula $\phi$
20315 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20318 \begin_layout Plain Layout
20326 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20329 \begin_layout Plain Layout
20330 \begin_inset Formula $\varphi$
20340 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20343 \begin_layout Plain Layout
20351 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20354 \begin_layout Plain Layout
20355 \begin_inset Formula $\chi$
20365 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20368 \begin_layout Plain Layout
20376 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20379 \begin_layout Plain Layout
20380 \begin_inset Formula $\psi$
20390 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20393 \begin_layout Plain Layout
20401 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20404 \begin_layout Plain Layout
20405 \begin_inset Formula $\omega$
20419 \begin_inset space \hfill{}
20425 \begin_layout Standard
20426 \begin_inset VSpace medskip
20432 \begin_layout Standard
20433 How to create special upright Greek letters is explained in
20434 \begin_inset CommandInset ref
20436 reference "subsec:Upright-small-Greek"
20443 \begin_layout Subsection
20445 \begin_inset Index idx
20448 \begin_layout Plain Layout
20449 Greek letters ! big
20457 \begin_layout Standard
20458 \begin_inset space \hfill{}
20462 \begin_inset Tabular
20463 <lyxtabular version="3" rows="7" columns="2">
20464 <features booktabs="true" tabularvalignment="middle">
20465 <column alignment="center" valignment="top" width="0pt">
20466 <column alignment="center" valignment="top" width="0pt">
20468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20471 \begin_layout Plain Layout
20477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20480 \begin_layout Plain Layout
20488 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20491 \begin_layout Plain Layout
20499 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20502 \begin_layout Plain Layout
20503 \begin_inset Formula $\Gamma$
20513 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20516 \begin_layout Plain Layout
20524 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20527 \begin_layout Plain Layout
20528 \begin_inset Formula $\Delta$
20538 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20541 \begin_layout Plain Layout
20549 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20552 \begin_layout Plain Layout
20553 \begin_inset Formula $\Theta$
20563 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20566 \begin_layout Plain Layout
20574 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20577 \begin_layout Plain Layout
20578 \begin_inset Formula $\Lambda$
20588 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20591 \begin_layout Plain Layout
20599 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20602 \begin_layout Plain Layout
20603 \begin_inset Formula $\Xi$
20613 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20616 \begin_layout Plain Layout
20624 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20627 \begin_layout Plain Layout
20628 \begin_inset Formula $\Pi$
20642 \begin_inset space \hfill{}
20646 \begin_inset Tabular
20647 <lyxtabular version="3" rows="6" columns="2">
20648 <features booktabs="true" tabularvalignment="middle">
20649 <column alignment="center" valignment="top" width="0pt">
20650 <column alignment="center" valignment="top" width="0pt">
20652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20655 \begin_layout Plain Layout
20661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20664 \begin_layout Plain Layout
20672 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20675 \begin_layout Plain Layout
20683 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20686 \begin_layout Plain Layout
20687 \begin_inset Formula $\Sigma$
20697 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20700 \begin_layout Plain Layout
20708 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20711 \begin_layout Plain Layout
20712 \begin_inset Formula $\Upsilon$
20722 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20725 \begin_layout Plain Layout
20733 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20736 \begin_layout Plain Layout
20737 \begin_inset Formula $\Phi$
20747 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20750 \begin_layout Plain Layout
20758 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20761 \begin_layout Plain Layout
20762 \begin_inset Formula $\Psi$
20772 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20775 \begin_layout Plain Layout
20783 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20786 \begin_layout Plain Layout
20787 \begin_inset Formula $\Omega$
20801 \begin_inset space \hfill{}
20807 \begin_layout Standard
20808 \begin_inset VSpace medskip
20811 That the big Greek letters appear upright is caused by a design bug when
20814 To get correct italic big letters, begin every command with
20819 For example the command
20826 \begin_inset Formula $\varGamma$
20830 Another way is to load the package
20838 \begin_layout Plain Layout
20843 is part of the \SpecialChar LaTeX
20849 \begin_inset Index idx
20852 \begin_layout Plain Layout
20857 \begin_layout Plain Layout
20877 \begin_inset Index idx
20880 \begin_layout Plain Layout
20886 with the \SpecialChar LaTeX
20890 \begin_layout Standard
20895 usepackage{fixmath}
20898 \begin_layout Standard
20899 Then all big Greek letters in a document will automatically be typeset italic.
20902 \begin_layout Subsection
20904 \begin_inset Index idx
20907 \begin_layout Plain Layout
20908 Greek letters ! bold
20916 \begin_layout Standard
20917 Greek letters cannot be set with different font styles like Latin letters.
20918 They can only be made bold with the command
20925 \begin_inset Index idx
20928 \begin_layout Plain Layout
20937 \begin_inset Separator parbreak
20943 \begin_layout Standard
20945 \begin_inset Tabular
20946 <lyxtabular version="3" rows="3" columns="2">
20947 <features booktabs="true" tabularvalignment="middle">
20948 <column alignment="center" valignment="top" width="0pt">
20949 <column alignment="center" valignment="top">
20951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20954 \begin_layout Plain Layout
20960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20963 \begin_layout Plain Layout
20971 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20974 \begin_layout Plain Layout
20986 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20989 \begin_layout Plain Layout
20990 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21000 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21003 \begin_layout Plain Layout
21015 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21018 \begin_layout Plain Layout
21019 \begin_inset Formula $\theta\boldsymbol{\theta}$
21035 \begin_layout Section
21040 \begin_layout Plain Layout
21053 \begin_layout Plain Layout
21054 A list with all symbols of most of the \SpecialChar LaTeX
21055 -packages can be found in
21056 \begin_inset CommandInset citation
21071 \begin_layout Plain Layout
21079 \begin_inset Note Note
21082 \begin_layout Plain Layout
21085 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21088 \begin_layout Plain Layout
21091 texorpdfstring is in section
21092 \begin_inset CommandInset ref
21094 reference "subsec:Formulas-in-Section"
21104 \begin_inset Index idx
21107 \begin_layout Plain Layout
21116 \begin_layout Standard
21117 Many of the symbols listed in this section can also be inserted via the
21121 arg "math-insert \\nabla"
21127 arg "math-insert \\digamma"
21133 \begin_layout Subsection
21134 Mathematical Symbols
21135 \begin_inset CommandInset label
21137 name "subsec:Mathematical-Symbols"
21142 \begin_inset Index idx
21145 \begin_layout Plain Layout
21146 Symbols ! mathematical
21154 \begin_layout Standard
21155 \begin_inset Tabular
21156 <lyxtabular version="3" rows="10" columns="2">
21157 <features booktabs="true" tabularvalignment="middle">
21158 <column alignment="center" valignment="top" width="0pt">
21159 <column alignment="center" valignment="top" width="0pt">
21161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21164 \begin_layout Plain Layout
21170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21173 \begin_layout Plain Layout
21181 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21184 \begin_layout Plain Layout
21192 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21195 \begin_layout Plain Layout
21196 \begin_inset Formula $\neg$
21206 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21209 \begin_layout Plain Layout
21217 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21220 \begin_layout Plain Layout
21221 \begin_inset Formula $\Im$
21231 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21234 \begin_layout Plain Layout
21242 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21245 \begin_layout Plain Layout
21246 \begin_inset Formula $\Re$
21256 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21259 \begin_layout Plain Layout
21267 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21270 \begin_layout Plain Layout
21271 \begin_inset Formula $\aleph$
21281 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21284 \begin_layout Plain Layout
21292 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21295 \begin_layout Plain Layout
21296 \begin_inset Formula $\partial$
21306 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21309 \begin_layout Plain Layout
21317 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21320 \begin_layout Plain Layout
21321 \begin_inset Formula $\infty$
21331 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21334 \begin_layout Plain Layout
21342 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21345 \begin_layout Plain Layout
21346 \begin_inset Formula $\wp$
21356 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21359 \begin_layout Plain Layout
21367 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21370 \begin_layout Plain Layout
21371 \begin_inset Formula $\imath$
21381 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21384 \begin_layout Plain Layout
21392 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21395 \begin_layout Plain Layout
21396 \begin_inset Formula $\jmath$
21410 \begin_inset space \hfill{}
21414 \begin_inset Tabular
21415 <lyxtabular version="3" rows="10" columns="2">
21416 <features booktabs="true" tabularvalignment="middle">
21417 <column alignment="center" valignment="top" width="0pt">
21418 <column alignment="center" valignment="top" width="0pt">
21420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21423 \begin_layout Plain Layout
21429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21432 \begin_layout Plain Layout
21434 \begin_inset Note Note
21437 \begin_layout Plain Layout
21444 is only used as spacer.
21456 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21459 \begin_layout Plain Layout
21467 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21470 \begin_layout Plain Layout
21471 \begin_inset Formula $\forall$
21481 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21484 \begin_layout Plain Layout
21492 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21495 \begin_layout Plain Layout
21496 \begin_inset Formula $\exists$
21506 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21509 \begin_layout Plain Layout
21517 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21520 \begin_layout Plain Layout
21521 \begin_inset Formula $\nexists$
21531 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21534 \begin_layout Plain Layout
21542 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21545 \begin_layout Plain Layout
21546 \begin_inset Formula $\emptyset$
21556 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21559 \begin_layout Plain Layout
21567 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21570 \begin_layout Plain Layout
21571 \begin_inset Formula $\varnothing$
21581 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21584 \begin_layout Plain Layout
21592 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21595 \begin_layout Plain Layout
21596 \begin_inset Formula $\dag$
21606 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21609 \begin_layout Plain Layout
21617 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21620 \begin_layout Plain Layout
21621 \begin_inset Formula $\ddag$
21631 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21634 \begin_layout Plain Layout
21642 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21645 \begin_layout Plain Layout
21649 \begin_layout Plain Layout
21659 \begin_inset Formula $\complement$
21666 \begin_layout Plain Layout
21680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21683 \begin_layout Plain Layout
21691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21694 \begin_layout Plain Layout
21695 \begin_inset Formula $\Bbbk$
21709 \begin_inset space \hfill{}
21713 \begin_inset Tabular
21714 <lyxtabular version="3" rows="10" columns="2">
21715 <features booktabs="true" tabularvalignment="middle">
21716 <column alignment="center" valignment="top" width="0pt">
21717 <column alignment="center" valignment="top" width="0pt">
21719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21722 \begin_layout Plain Layout
21728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21731 \begin_layout Plain Layout
21739 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21742 \begin_layout Plain Layout
21750 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21753 \begin_layout Plain Layout
21754 \begin_inset Formula $\prime$
21764 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21767 \begin_layout Plain Layout
21775 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21778 \begin_layout Plain Layout
21779 \begin_inset Formula $\backprime$
21789 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21792 \begin_layout Plain Layout
21800 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21803 \begin_layout Plain Layout
21804 \begin_inset Formula $\mho$
21814 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21817 \begin_layout Plain Layout
21825 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21828 \begin_layout Plain Layout
21829 \begin_inset Formula $\triangle$
21839 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21842 \begin_layout Plain Layout
21850 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21853 \begin_layout Plain Layout
21854 \begin_inset Formula $\angle$
21864 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21867 \begin_layout Plain Layout
21875 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21878 \begin_layout Plain Layout
21879 \begin_inset Formula $\measuredangle$
21889 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21892 \begin_layout Plain Layout
21900 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21903 \begin_layout Plain Layout
21904 \begin_inset Formula $\sphericalangle$
21914 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21917 \begin_layout Plain Layout
21925 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21928 \begin_layout Plain Layout
21929 \begin_inset Formula $\top$
21939 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21942 \begin_layout Plain Layout
21950 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21953 \begin_layout Plain Layout
21954 \begin_inset Formula $\bot$
21970 \begin_layout Standard
21971 \begin_inset Newpage newpage
21977 \begin_layout Subsection
21978 Miscellaneous Symbols
21979 \begin_inset CommandInset label
21981 name "subsec:Miscellaneous-Symbols"
21986 \begin_inset Index idx
21989 \begin_layout Plain Layout
21990 Symbols ! miscellaneous
21998 \begin_layout Standard
22001 \begin_inset Tabular
22002 <lyxtabular version="3" rows="10" columns="2">
22003 <features booktabs="true" tabularvalignment="middle">
22004 <column alignment="center" valignment="top" width="0pt">
22005 <column alignment="center" valignment="top" width="0pt">
22007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22010 \begin_layout Plain Layout
22016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22019 \begin_layout Plain Layout
22027 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22030 \begin_layout Plain Layout
22038 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22041 \begin_layout Plain Layout
22042 \begin_inset Formula $\flat$
22052 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22055 \begin_layout Plain Layout
22063 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22066 \begin_layout Plain Layout
22067 \begin_inset Formula $\natural$
22077 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22080 \begin_layout Plain Layout
22088 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22091 \begin_layout Plain Layout
22092 \begin_inset Formula $\sharp$
22102 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22105 \begin_layout Plain Layout
22113 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22116 \begin_layout Plain Layout
22117 \begin_inset Formula $\surd$
22127 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22130 \begin_layout Plain Layout
22138 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22141 \begin_layout Plain Layout
22142 \begin_inset Formula $\checkmark$
22152 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22155 \begin_layout Plain Layout
22163 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22166 \begin_layout Plain Layout
22167 \begin_inset Formula $\yen$
22177 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22180 \begin_layout Plain Layout
22188 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22191 \begin_layout Plain Layout
22192 \begin_inset Formula $\pounds$
22202 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22205 \begin_layout Plain Layout
22211 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22214 \begin_layout Plain Layout
22215 \begin_inset Formula $\$$
22225 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22228 \begin_layout Plain Layout
22234 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22237 \begin_layout Plain Layout
22238 \begin_inset Formula $§$
22252 \begin_inset space \hfill{}
22256 \begin_inset Tabular
22257 <lyxtabular version="3" rows="10" columns="2">
22258 <features booktabs="true" tabularvalignment="middle">
22259 <column alignment="center" valignment="top" width="0pt">
22260 <column alignment="center" valignment="top">
22262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22265 \begin_layout Plain Layout
22271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22274 \begin_layout Plain Layout
22282 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22285 \begin_layout Plain Layout
22293 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22296 \begin_layout Plain Layout
22297 \begin_inset Formula $\hbar$
22307 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22310 \begin_layout Plain Layout
22318 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22321 \begin_layout Plain Layout
22322 \begin_inset Formula $\hslash$
22332 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22335 \begin_layout Plain Layout
22343 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22346 \begin_layout Plain Layout
22347 \begin_inset Formula $\clubsuit$
22357 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22360 \begin_layout Plain Layout
22368 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22371 \begin_layout Plain Layout
22372 \begin_inset Formula $\spadesuit$
22382 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22385 \begin_layout Plain Layout
22393 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22396 \begin_layout Plain Layout
22397 \begin_inset Formula $\bigstar$
22407 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22410 \begin_layout Plain Layout
22418 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22421 \begin_layout Plain Layout
22422 \begin_inset Formula $\blacklozenge$
22432 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22435 \begin_layout Plain Layout
22443 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22446 \begin_layout Plain Layout
22447 \begin_inset Formula $\blacktriangle$
22457 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22460 \begin_layout Plain Layout
22468 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22471 \begin_layout Plain Layout
22472 \begin_inset Formula $\blacktriangledown$
22482 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22485 \begin_layout Plain Layout
22493 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22496 \begin_layout Plain Layout
22497 \begin_inset Formula $\bullet$
22511 \begin_inset space \hfill{}
22515 \begin_inset Tabular
22516 <lyxtabular version="3" rows="10" columns="2">
22517 <features booktabs="true" tabularvalignment="middle">
22518 <column alignment="center" valignment="top" width="0pt">
22519 <column alignment="center" valignment="top" width="0pt">
22521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22524 \begin_layout Plain Layout
22530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22533 \begin_layout Plain Layout
22541 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22544 \begin_layout Plain Layout
22552 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22555 \begin_layout Plain Layout
22556 \begin_inset Formula $\diamondsuit$
22566 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22569 \begin_layout Plain Layout
22577 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22580 \begin_layout Plain Layout
22581 \begin_inset Formula $\Diamond$
22591 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22594 \begin_layout Plain Layout
22602 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22605 \begin_layout Plain Layout
22606 \begin_inset Formula $\heartsuit$
22616 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22619 \begin_layout Plain Layout
22627 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22630 \begin_layout Plain Layout
22631 \begin_inset Formula $\P$
22641 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22644 \begin_layout Plain Layout
22652 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22655 \begin_layout Plain Layout
22656 \begin_inset Formula $\copyright$
22666 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22669 \begin_layout Plain Layout
22677 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22680 \begin_layout Plain Layout
22681 \begin_inset Formula $\circledR$
22691 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22694 \begin_layout Plain Layout
22702 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22705 \begin_layout Plain Layout
22706 \begin_inset Formula $\maltese$
22716 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22719 \begin_layout Plain Layout
22727 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22730 \begin_layout Plain Layout
22731 \begin_inset Formula $\diagup$
22741 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22744 \begin_layout Plain Layout
22752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22755 \begin_layout Plain Layout
22756 \begin_inset Formula $\diagdown$
22772 \begin_layout Standard
22773 \begin_inset VSpace medskip
22779 \begin_layout Standard
22780 Some symbols can be displayed in different sizes, see
22781 \begin_inset CommandInset ref
22783 reference "subsec:Font-Sizes"
22790 \begin_layout Subsection
22792 \begin_inset Index idx
22795 \begin_layout Plain Layout
22796 Symbols ! Euro-symbol
22802 \begin_inset Index idx
22805 \begin_layout Plain Layout
22812 \begin_layout Plain Layout
22829 \begin_layout Standard
22830 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22836 \begin_inset Index idx
22839 \begin_layout Plain Layout
22845 must be installed and loaded with the \SpecialChar LaTeX
22849 \begin_layout Standard
22854 usepackage[gennarrow]{eurosym}
22857 \begin_layout Standard
22858 The Euro symbol can now be inserted with the command
22865 \begin_inset Index idx
22868 \begin_layout Plain Layout
22879 \begin_layout Standard
22880 The Euro symbol can directly be inserted with the € key in mathematical
22881 text, without having
22896 can also be inserted in \SpecialChar TeX
22898 The official currency symbol can then be inserted with the command
22905 \begin_inset Index idx
22908 \begin_layout Plain Layout
22916 , that is only available in \SpecialChar TeX
22920 \begin_layout Standard
22924 \begin_layout Plain Layout
22934 \begin_inset Note Note
22937 \begin_layout Plain Layout
22938 The following table will only be displayed when the \SpecialChar LaTeX
22951 \begin_layout Standard
22952 An overview about the different Euro symbols:
22953 \begin_inset Separator parbreak
22959 \begin_layout Standard
22961 \begin_inset Tabular
22962 <lyxtabular version="3" rows="4" columns="3">
22963 <features booktabs="true" tabularvalignment="middle">
22964 <column alignment="center" valignment="top" width="0pt">
22965 <column alignment="center" valignment="top" width="0pt">
22966 <column alignment="center" valignment="top" width="0pt">
22968 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22971 \begin_layout Plain Layout
22975 \begin_layout Plain Layout
22979 cmidrule[0.08em]{2-3}
22989 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22992 \begin_layout Plain Layout
22998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23001 \begin_layout Plain Layout
23009 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23012 \begin_layout Plain Layout
23018 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23021 \begin_layout Plain Layout
23029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23032 \begin_layout Plain Layout
23033 \begin_inset Formula $\euro$
23043 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23046 \begin_layout Plain Layout
23052 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23055 \begin_layout Plain Layout
23061 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23064 \begin_layout Plain Layout
23065 \begin_inset Formula $\mbox{€}$
23075 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23078 \begin_layout Plain Layout
23085 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23088 \begin_layout Plain Layout
23096 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23099 \begin_layout Plain Layout
23103 \begin_layout Plain Layout
23123 \begin_inset Note Note
23126 \begin_layout Plain Layout
23133 is used here only for table borders.
23143 manual for details.
23151 \begin_layout Standard
23155 \begin_layout Plain Layout
23165 \begin_inset Note Note
23168 \begin_layout Plain Layout
23169 The following will be displayed when the \SpecialChar LaTeX
23182 \begin_layout Standard
23183 You need to install the \SpecialChar LaTeX
23188 to see the rest of this subsection in the output.
23191 \begin_layout Standard
23195 \begin_layout Plain Layout
23207 \begin_layout Standard
23208 \begin_inset Newpage newpage
23214 \begin_layout Section
23216 \begin_inset CommandInset label
23218 name "sec:Relations"
23223 \begin_inset Index idx
23226 \begin_layout Plain Layout
23233 \begin_inset Index idx
23236 \begin_layout Plain Layout
23241 \begin_layout Plain Layout
23252 \begin_layout Plain Layout
23267 \begin_layout Standard
23268 All following relations can also be inserted via the toolbar button
23271 arg "math-insert \\leq"
23277 \begin_layout Standard
23278 \begin_inset Tabular
23279 <lyxtabular version="3" rows="17" columns="2">
23280 <features booktabs="true" tabularvalignment="middle">
23281 <column alignment="center" valignment="top" width="0pt">
23282 <column alignment="center" valignment="top" width="0pt">
23284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23287 \begin_layout Plain Layout
23293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23296 \begin_layout Plain Layout
23304 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23307 \begin_layout Plain Layout
23313 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23316 \begin_layout Plain Layout
23317 \begin_inset Formula $<$
23327 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23330 \begin_layout Plain Layout
23338 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23341 \begin_layout Plain Layout
23342 \begin_inset Formula $\le$
23352 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23355 \begin_layout Plain Layout
23363 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23366 \begin_layout Plain Layout
23367 \begin_inset Formula $\ll$
23377 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23380 \begin_layout Plain Layout
23388 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23391 \begin_layout Plain Layout
23392 \begin_inset Formula $\prec$
23402 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23405 \begin_layout Plain Layout
23413 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23416 \begin_layout Plain Layout
23417 \begin_inset Formula $\preceq$
23427 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23430 \begin_layout Plain Layout
23438 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23441 \begin_layout Plain Layout
23442 \begin_inset Formula $\subset$
23452 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23455 \begin_layout Plain Layout
23463 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23466 \begin_layout Plain Layout
23467 \begin_inset Formula $\subseteq$
23477 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23480 \begin_layout Plain Layout
23488 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23491 \begin_layout Plain Layout
23492 \begin_inset Formula $\sqsubseteq$
23502 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23505 \begin_layout Plain Layout
23513 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23516 \begin_layout Plain Layout
23517 \begin_inset Formula $\in$
23527 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23530 \begin_layout Plain Layout
23538 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23541 \begin_layout Plain Layout
23542 \begin_inset Formula $\vdash$
23552 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23555 \begin_layout Plain Layout
23563 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23566 \begin_layout Plain Layout
23567 \begin_inset Formula $\smile$
23577 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23580 \begin_layout Plain Layout
23588 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23591 \begin_layout Plain Layout
23592 \begin_inset Formula $\lhd$
23602 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23605 \begin_layout Plain Layout
23613 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23616 \begin_layout Plain Layout
23617 \begin_inset Formula $\unlhd$
23627 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23630 \begin_layout Plain Layout
23638 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23641 \begin_layout Plain Layout
23642 \begin_inset Formula $\gtrless$
23652 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23655 \begin_layout Plain Layout
23663 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23666 \begin_layout Plain Layout
23667 \begin_inset Formula $\mid$
23677 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23680 \begin_layout Plain Layout
23688 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23691 \begin_layout Plain Layout
23692 \begin_inset Formula $\nmid$
23706 \begin_inset space \hfill{}
23710 \begin_inset Tabular
23711 <lyxtabular version="3" rows="17" columns="2">
23712 <features booktabs="true" tabularvalignment="middle">
23713 <column alignment="center" valignment="top" width="0pt">
23714 <column alignment="center" valignment="top" width="0pt">
23716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23719 \begin_layout Plain Layout
23725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23728 \begin_layout Plain Layout
23736 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23739 \begin_layout Plain Layout
23745 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23748 \begin_layout Plain Layout
23749 \begin_inset Formula $=$
23759 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23762 \begin_layout Plain Layout
23770 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23773 \begin_layout Plain Layout
23774 \begin_inset Formula $\not=$
23784 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23787 \begin_layout Plain Layout
23795 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23798 \begin_layout Plain Layout
23799 \begin_inset Formula $\equiv$
23809 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23812 \begin_layout Plain Layout
23820 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23823 \begin_layout Plain Layout
23824 \begin_inset Formula $\sim$
23834 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23837 \begin_layout Plain Layout
23845 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23848 \begin_layout Plain Layout
23849 \begin_inset Formula $\simeq$
23859 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23862 \begin_layout Plain Layout
23870 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23873 \begin_layout Plain Layout
23874 \begin_inset Formula $\approx$
23884 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23887 \begin_layout Plain Layout
23895 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23898 \begin_layout Plain Layout
23899 \begin_inset Formula $\cong$
23909 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23912 \begin_layout Plain Layout
23920 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23923 \begin_layout Plain Layout
23924 \begin_inset Formula $\bowtie$
23934 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23937 \begin_layout Plain Layout
23945 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23948 \begin_layout Plain Layout
23949 \begin_inset Formula $\notin$
23959 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23962 \begin_layout Plain Layout
23970 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23973 \begin_layout Plain Layout
23974 \begin_inset Formula $\perp$
23984 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23987 \begin_layout Plain Layout
23995 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23998 \begin_layout Plain Layout
23999 \begin_inset Formula $\propto$
24009 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24012 \begin_layout Plain Layout
24020 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24023 \begin_layout Plain Layout
24024 \begin_inset Formula $\asymp$
24034 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24037 \begin_layout Plain Layout
24045 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24048 \begin_layout Plain Layout
24049 \begin_inset Formula $\doteq$
24059 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24062 \begin_layout Plain Layout
24070 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24073 \begin_layout Plain Layout
24074 \begin_inset Formula $\circeq$
24084 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24087 \begin_layout Plain Layout
24095 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24098 \begin_layout Plain Layout
24099 \begin_inset Formula $\models$
24109 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24112 \begin_layout Plain Layout
24120 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24123 \begin_layout Plain Layout
24124 \begin_inset Formula $\widehat{=}$
24138 \begin_inset space \hfill{}
24142 \begin_inset Tabular
24143 <lyxtabular version="3" rows="17" columns="2">
24144 <features booktabs="true" tabularvalignment="middle">
24145 <column alignment="center" valignment="top" width="0pt">
24146 <column alignment="center" valignment="top" width="0pt">
24148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24151 \begin_layout Plain Layout
24157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24160 \begin_layout Plain Layout
24168 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24171 \begin_layout Plain Layout
24177 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24180 \begin_layout Plain Layout
24181 \begin_inset Formula $>$
24191 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24194 \begin_layout Plain Layout
24202 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24205 \begin_layout Plain Layout
24206 \begin_inset Formula $\ge$
24216 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24219 \begin_layout Plain Layout
24227 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24230 \begin_layout Plain Layout
24231 \begin_inset Formula $\gg$
24241 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24244 \begin_layout Plain Layout
24252 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24255 \begin_layout Plain Layout
24256 \begin_inset Formula $\succ$
24266 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24269 \begin_layout Plain Layout
24277 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24280 \begin_layout Plain Layout
24281 \begin_inset Formula $\succeq$
24291 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24294 \begin_layout Plain Layout
24302 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24305 \begin_layout Plain Layout
24306 \begin_inset Formula $\supset$
24316 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24319 \begin_layout Plain Layout
24327 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24330 \begin_layout Plain Layout
24331 \begin_inset Formula $\supseteq$
24341 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24344 \begin_layout Plain Layout
24352 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24355 \begin_layout Plain Layout
24356 \begin_inset Formula $\sqsupseteq$
24366 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24369 \begin_layout Plain Layout
24377 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24380 \begin_layout Plain Layout
24381 \begin_inset Formula $\ni$
24391 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24394 \begin_layout Plain Layout
24402 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24405 \begin_layout Plain Layout
24406 \begin_inset Formula $\dashv$
24416 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24419 \begin_layout Plain Layout
24427 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24430 \begin_layout Plain Layout
24431 \begin_inset Formula $\frown$
24441 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24444 \begin_layout Plain Layout
24452 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24455 \begin_layout Plain Layout
24456 \begin_inset Formula $\rhd$
24466 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24469 \begin_layout Plain Layout
24477 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24480 \begin_layout Plain Layout
24481 \begin_inset Formula $\unrhd$
24491 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24494 \begin_layout Plain Layout
24502 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24505 \begin_layout Plain Layout
24506 \begin_inset Formula $\lessgtr$
24516 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24519 \begin_layout Plain Layout
24527 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24530 \begin_layout Plain Layout
24531 \begin_inset Formula $\parallel$
24541 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24544 \begin_layout Plain Layout
24552 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24555 \begin_layout Plain Layout
24556 \begin_inset Formula $\nparallel$
24572 \begin_layout Standard
24573 \begin_inset VSpace medskip
24588 are bigger than the equal looking operators
24603 \begin_layout Standard
24605 supports also many special relations.
24606 Use the toolbar button
24609 arg "math-insert \\leqq"
24612 to see a list of these relations.
24615 \begin_layout Standard
24616 Relations are, in contrary to symbols, always surrounded by space.
24619 \begin_layout Standard
24620 Relations with labels can be created with the command
24627 \begin_inset Index idx
24630 \begin_layout Plain Layout
24639 \begin_inset Separator parbreak
24645 \begin_layout Standard
24647 \begin_inset Tabular
24648 <lyxtabular version="3" rows="2" columns="2">
24649 <features booktabs="true" tabularvalignment="middle">
24650 <column alignment="center" valignment="top" width="0pt">
24651 <column alignment="center" valignment="top">
24653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24656 \begin_layout Plain Layout
24662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24665 \begin_layout Plain Layout
24672 <row topspace="1.5mm">
24673 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24676 \begin_layout Plain Layout
24680 \begin_inset space \textvisiblespace{}
24688 \begin_inset space \textvisiblespace{}
24692 \begin_inset Formula $\downarrow$
24698 \begin_inset space \textvisiblespace{}
24702 \begin_inset space \textvisiblespace{}
24710 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24713 \begin_layout Plain Layout
24714 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24730 \begin_layout Section
24734 \begin_layout Subsection
24735 Predefined Functions
24736 \begin_inset CommandInset label
24738 name "subsec:Predefined-Functions"
24743 \begin_inset Index idx
24746 \begin_layout Plain Layout
24747 Functions ! predefined
24755 \begin_layout Standard
24756 In general, variables are set
24760 in mathematical expressions, but not function names, because
24761 \begin_inset Formula $sin$
24764 could be misunderstood as
24765 \begin_inset Formula $s\cdot i\cdot n$
24769 Therefore there are predefined functionswhich are additionally a bit separated
24771 They are inserted as commands starting with a backslash before their name.
24772 \begin_inset Separator parbreak
24778 \begin_layout Standard
24780 \begin_inset Tabular
24781 <lyxtabular version="3" rows="2" columns="2">
24782 <features booktabs="true" tabularvalignment="middle">
24783 <column alignment="center" valignment="top" width="0pt">
24784 <column alignment="center" valignment="top" width="0pt">
24786 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24789 \begin_layout Plain Layout
24795 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24798 \begin_layout Plain Layout
24806 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24809 \begin_layout Plain Layout
24815 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24818 \begin_layout Plain Layout
24819 \begin_inset Formula $Asin(x)+B$
24833 \begin_inset space \quad{}
24837 \begin_inset Tabular
24838 <lyxtabular version="3" rows="2" columns="2">
24839 <features booktabs="true" tabularvalignment="middle">
24840 <column alignment="center" valignment="top" width="0pt">
24841 <column alignment="center" valignment="top" width="0pt">
24843 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24846 \begin_layout Plain Layout
24852 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24855 \begin_layout Plain Layout
24863 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24866 \begin_layout Plain Layout
24874 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24877 \begin_layout Plain Layout
24878 \begin_inset Formula $A\sin(x)+B$
24894 \begin_layout Standard
24895 The following functions are predefined:
24898 \begin_layout Standard
24899 \begin_inset VSpace -2mm
24905 \begin_layout Standard
24907 \begin_inset Tabular
24908 <lyxtabular version="3" rows="9" columns="4">
24909 <features booktabs="true" tabularvalignment="middle">
24910 <column alignment="center" valignment="top" width="0pt">
24911 <column alignment="center" valignment="top" width="0pt">
24912 <column alignment="center" valignment="top" width="0pt">
24913 <column alignment="center" valignment="top" width="0pt">
24915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24918 \begin_layout Plain Layout
24924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24927 \begin_layout Plain Layout
24933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24936 \begin_layout Plain Layout
24942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24945 \begin_layout Plain Layout
24953 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24956 \begin_layout Plain Layout
24964 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24967 \begin_layout Plain Layout
24975 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24978 \begin_layout Plain Layout
24986 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24989 \begin_layout Plain Layout
24999 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25002 \begin_layout Plain Layout
25010 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25013 \begin_layout Plain Layout
25021 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25024 \begin_layout Plain Layout
25032 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25035 \begin_layout Plain Layout
25045 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25048 \begin_layout Plain Layout
25056 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25059 \begin_layout Plain Layout
25067 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25070 \begin_layout Plain Layout
25078 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25081 \begin_layout Plain Layout
25091 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25094 \begin_layout Plain Layout
25102 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25105 \begin_layout Plain Layout
25113 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25116 \begin_layout Plain Layout
25124 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25127 \begin_layout Plain Layout
25137 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25140 \begin_layout Plain Layout
25148 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25151 \begin_layout Plain Layout
25159 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25162 \begin_layout Plain Layout
25170 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25173 \begin_layout Plain Layout
25183 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25186 \begin_layout Plain Layout
25194 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25197 \begin_layout Plain Layout
25205 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25208 \begin_layout Plain Layout
25216 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25219 \begin_layout Plain Layout
25229 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25232 \begin_layout Plain Layout
25240 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25243 \begin_layout Plain Layout
25251 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25254 \begin_layout Plain Layout
25262 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25265 \begin_layout Plain Layout
25275 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25278 \begin_layout Plain Layout
25286 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25289 \begin_layout Plain Layout
25297 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25300 \begin_layout Plain Layout
25308 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25311 \begin_layout Plain Layout
25327 \begin_layout Standard
25328 They can also be inserted with the math toolbar button
25331 arg "math-insert \\functions"
25337 \begin_layout Subsection
25338 Self-defined Functions
25339 \begin_inset Index idx
25342 \begin_layout Plain Layout
25343 Functions ! self-defined
25351 \begin_layout Standard
25352 To use a function that is not predefined, like for example the sign function
25353 sgn(x), there are two possibilities:
25356 \begin_layout Itemize
25357 Define the function by inserting the following line to the \SpecialChar LaTeX
25362 \begin_layout Plain Layout
25367 DeclareMathOperator
25370 \begin_inset CommandInset ref
25372 reference "subsec:Self-defined-Operators"
25382 \begin_inset Newline newline
25386 \begin_inset VSpace -3mm
25390 \begin_inset Newline newline
25397 DeclareMathOperator{
25402 \begin_inset Index idx
25405 \begin_layout Plain Layout
25410 DeclareMathOperator
25416 \begin_inset Newline newline
25420 \begin_inset VSpace -2mm
25424 \begin_inset Newline newline
25427 Now the new defined function can be called with the command
25436 \begin_layout Itemize
25437 Write the formula as usual, mark the formula name, in our example the letters
25442 , and change it to mathematical text.
25443 Finally, a space is inserted between prefactor and function.
25446 \begin_layout Standard
25447 The result is the same with both methods as with a predefined function
25451 \begin_layout Plain Layout
25452 In \SpecialChar LyX
25453 self-defined functions are displayed red, predefined ones black.
25459 \begin_inset Separator parbreak
25465 \begin_layout Standard
25467 \begin_inset Tabular
25468 <lyxtabular version="3" rows="3" columns="2">
25469 <features booktabs="true" tabularvalignment="middle">
25470 <column alignment="center" valignment="top" width="0pt">
25471 <column alignment="center" valignment="top" width="0pt">
25473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25476 \begin_layout Plain Layout
25482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25485 \begin_layout Plain Layout
25493 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25496 \begin_layout Plain Layout
25504 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25507 \begin_layout Plain Layout
25508 \begin_inset Formula $A\sgn(x)+B$
25518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25521 \begin_layout Plain Layout
25525 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25536 \begin_layout Plain Layout
25537 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25553 \begin_layout Standard
25554 The first method is more suitable when the self-defined function should
25555 be used several times.
25558 \begin_layout Subsection
25560 \begin_inset Index idx
25563 \begin_layout Plain Layout
25572 \begin_layout Standard
25573 For limits, in addition to the commands
25580 \begin_inset Index idx
25583 \begin_layout Plain Layout
25603 the following functions are defined:
25604 \begin_inset Separator parbreak
25610 \begin_layout Standard
25612 \begin_inset Tabular
25613 <lyxtabular version="3" rows="5" columns="2">
25614 <features booktabs="true" tabularvalignment="middle">
25615 <column alignment="center" valignment="top" width="0pt">
25616 <column alignment="center" valignment="top" width="0pt">
25618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25621 \begin_layout Plain Layout
25627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25630 \begin_layout Plain Layout
25638 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25641 \begin_layout Plain Layout
25649 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25652 \begin_layout Plain Layout
25653 \begin_inset Formula $\varliminf$
25662 <row topspace="1.5mm">
25663 <cell alignment="center" valignment="top" usebox="none">
25666 \begin_layout Plain Layout
25674 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25677 \begin_layout Plain Layout
25678 \begin_inset Formula $\varlimsup$
25687 <row topspace="1.5mm">
25688 <cell alignment="center" valignment="top" usebox="none">
25691 \begin_layout Plain Layout
25699 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25702 \begin_layout Plain Layout
25703 \begin_inset Formula $\varprojlim$
25712 <row topspace="1.5mm" bottomspace="1mm">
25713 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25716 \begin_layout Plain Layout
25724 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25727 \begin_layout Plain Layout
25728 \begin_inset Formula $\varinjlim$
25744 \begin_layout Standard
25745 \begin_inset VSpace medskip
25748 The limit is created by inserting a subscript.
25749 It is set right beside the function in an inline formula:
25752 \begin_layout Standard
25754 \begin_inset Tabular
25755 <lyxtabular version="3" rows="2" columns="2">
25756 <features booktabs="true" tabularvalignment="middle">
25757 <column alignment="center" valignment="top" width="0pt">
25758 <column alignment="center" valignment="top" width="0pt">
25760 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25763 \begin_layout Plain Layout
25769 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25772 \begin_layout Plain Layout
25780 <cell alignment="center" valignment="top" usebox="none">
25783 \begin_layout Plain Layout
25789 \begin_inset space \textvisiblespace{}
25793 \begin_inset space \textvisiblespace{}
25801 <cell alignment="center" valignment="top" usebox="none">
25804 \begin_layout Plain Layout
25805 \begin_inset Formula $\lim_{x\to A}x=B$
25821 \begin_layout Standard
25822 In a displayed formula the limit is set below the formula, as usual:
25823 \begin_inset Formula
25833 \begin_layout Standard
25834 \begin_inset VSpace medskip
25840 \begin_layout Standard
25841 How to adjust the typesetting of the limits see
25842 \begin_inset CommandInset ref
25844 reference "subsec:Operator-Limits"
25851 \begin_layout Subsection
25853 \begin_inset Index idx
25856 \begin_layout Plain Layout
25857 Functions ! modulo-
25865 \begin_layout Standard
25866 The modulo-function is special, because it exists in four variants.
25867 The variants in a displayed formula are:
25868 \begin_inset Formula
25870 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25871 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25872 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25873 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25874 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25882 \begin_layout Standard
25883 In an inline formula less space is set before the function names for all
25885 By default the modulo-functions take only the first following character
25887 To use more than one character, one has to put them into \SpecialChar TeX
25889 \begin_inset Formula
25891 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25892 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25893 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25901 \begin_layout Section
25903 \begin_inset Index idx
25906 \begin_layout Plain Layout
25915 \begin_layout Standard
25916 The characters ^ and _ would normally create a superscript and subscript,
25918 To get these characters you have to insert them with a leading
25921 \begin_inset Separator parbreak
25927 \begin_layout Standard
25930 \begin_inset Tabular
25931 <lyxtabular version="3" rows="3" columns="2">
25932 <features booktabs="true" tabularvalignment="middle">
25933 <column alignment="left" valignment="top" width="0pt">
25934 <column alignment="block" valignment="top">
25936 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25939 \begin_layout Plain Layout
25945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25948 \begin_layout Plain Layout
25956 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25959 \begin_layout Plain Layout
25963 \begin_inset space \textvisiblespace{}
25971 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25974 \begin_layout Plain Layout
25975 \begin_inset Formula $\mathcircumflex$
25985 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25988 \begin_layout Plain Layout
25996 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25999 \begin_layout Plain Layout
26000 \begin_inset Formula $\_$
26016 \begin_layout Subsection
26017 Special Characters in Mathematical Text
26020 \begin_layout Standard
26021 The following commands can only be used in mathematical text or in \SpecialChar TeX
26025 \begin_layout Standard
26026 \begin_inset space \hfill{}
26030 \begin_inset Tabular
26031 <lyxtabular version="3" rows="8" columns="2">
26032 <features booktabs="true" tabularvalignment="middle">
26033 <column alignment="left" valignment="top" width="0pt">
26034 <column alignment="block" valignment="top">
26036 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26039 \begin_layout Plain Layout
26045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26048 \begin_layout Plain Layout
26056 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26059 \begin_layout Plain Layout
26067 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26070 \begin_layout Plain Layout
26071 \begin_inset Formula $\textrm{œ}$
26081 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26084 \begin_layout Plain Layout
26092 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26095 \begin_layout Plain Layout
26096 \begin_inset Formula $\textrm{Œ}$
26106 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26109 \begin_layout Plain Layout
26117 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26120 \begin_layout Plain Layout
26121 \begin_inset Formula $\textrm{æ}$
26131 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26134 \begin_layout Plain Layout
26142 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26145 \begin_layout Plain Layout
26146 \begin_inset Formula $\textrm{Æ}$
26156 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26159 \begin_layout Plain Layout
26167 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26170 \begin_layout Plain Layout
26171 \begin_inset Formula $\textrm{\aa}$
26181 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26184 \begin_layout Plain Layout
26188 \begin_inset Index idx
26191 \begin_layout Plain Layout
26198 \begin_layout Plain Layout
26219 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26222 \begin_layout Plain Layout
26223 \begin_inset Formula $\textrm{Å}$
26233 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26236 \begin_layout Plain Layout
26244 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26247 \begin_layout Plain Layout
26248 \begin_inset Formula $\textrm{ı}$
26262 \begin_inset space \hfill{}
26266 \begin_inset Tabular
26267 <lyxtabular version="3" rows="8" columns="2">
26268 <features booktabs="true" tabularvalignment="middle">
26269 <column alignment="left" valignment="top" width="0pt">
26270 <column alignment="center" valignment="top">
26272 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26275 \begin_layout Plain Layout
26277 \begin_inset Note Note
26280 \begin_layout Plain Layout
26282 \begin_inset space \thinspace{}
26285 mm is used for separation, because otherwise the output will be ¡ and ¿
26296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26299 \begin_layout Plain Layout
26307 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26310 \begin_layout Plain Layout
26318 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26321 \begin_layout Plain Layout
26322 \begin_inset Formula $\textrm{ø}$
26332 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26335 \begin_layout Plain Layout
26343 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26346 \begin_layout Plain Layout
26347 \begin_inset Formula $\textrm{Ø}$
26357 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26360 \begin_layout Plain Layout
26368 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26371 \begin_layout Plain Layout
26372 \begin_inset Formula $\textrm{ł}$
26382 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26385 \begin_layout Plain Layout
26393 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26396 \begin_layout Plain Layout
26397 \begin_inset Formula $\textrm{Ł}$
26407 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26410 \begin_layout Plain Layout
26412 \begin_inset space \hspace{}
26417 \begin_inset space \textvisiblespace{}
26425 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26428 \begin_layout Plain Layout
26429 \begin_inset Formula $\textrm{!`}$
26439 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26442 \begin_layout Plain Layout
26444 \begin_inset space \hspace{}
26449 \begin_inset space \textvisiblespace{}
26457 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26460 \begin_layout Plain Layout
26461 \begin_inset Formula $\textrm{?`}$
26471 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26474 \begin_layout Plain Layout
26482 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26485 \begin_layout Plain Layout
26486 \begin_inset Formula $\textrm{ȷ}$
26500 \begin_inset space \hfill{}
26506 \begin_layout Standard
26508 \begin_inset Formula $\textrm{\textrm{Å}}$
26512 \begin_inset Formula $\textrm{\textrm{Ø}}$
26515 can also be inserted via the math toolbar button
26518 arg "math-insert \\digamma"
26524 \begin_layout Standard
26525 An exception are the commands
26528 \begin_inset space \hspace{}
26537 \begin_inset space \hspace{}
26543 , because they can be inserted in \SpecialChar LyX
26547 \begin_layout Subsection
26549 \begin_inset CommandInset label
26551 name "subsec:Accents-in-Text"
26556 \begin_inset Index idx
26559 \begin_layout Plain Layout
26568 \begin_layout Standard
26569 With the following commands all letters can be accented.
26570 The commands must be inserted in \SpecialChar TeX
26574 \begin_layout Standard
26575 \begin_inset space \hfill{}
26579 \begin_inset Tabular
26580 <lyxtabular version="3" rows="8" columns="2">
26581 <features booktabs="true" tabularvalignment="middle">
26582 <column alignment="left" valignment="top" width="0pt">
26583 <column alignment="block" valignment="top">
26585 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26588 \begin_layout Plain Layout
26594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26597 \begin_layout Plain Layout
26605 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26608 \begin_layout Plain Layout
26612 \begin_inset Quotes grd
26620 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26623 \begin_layout Plain Layout
26627 \begin_layout Plain Layout
26643 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26646 \begin_layout Plain Layout
26654 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26657 \begin_layout Plain Layout
26661 \begin_layout Plain Layout
26677 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26680 \begin_layout Plain Layout
26684 \begin_inset space \textvisiblespace{}
26692 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26695 \begin_layout Plain Layout
26699 \begin_layout Plain Layout
26715 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26718 \begin_layout Plain Layout
26726 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26729 \begin_layout Plain Layout
26733 \begin_layout Plain Layout
26749 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26752 \begin_layout Plain Layout
26756 \begin_inset space \textvisiblespace{}
26764 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26767 \begin_layout Plain Layout
26771 \begin_layout Plain Layout
26787 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26790 \begin_layout Plain Layout
26794 \begin_inset space \textvisiblespace{}
26802 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26805 \begin_layout Plain Layout
26809 \begin_layout Plain Layout
26825 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26828 \begin_layout Plain Layout
26832 \begin_inset space \textvisiblespace{}
26840 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26843 \begin_layout Plain Layout
26847 \begin_layout Plain Layout
26867 \begin_inset space \hfill{}
26871 \begin_inset Tabular
26872 <lyxtabular version="3" rows="8" columns="2">
26873 <features booktabs="true" tabularvalignment="middle">
26874 <column alignment="left" valignment="top" width="0pt">
26875 <column alignment="center" valignment="top">
26877 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26880 \begin_layout Plain Layout
26886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26889 \begin_layout Plain Layout
26897 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26900 \begin_layout Plain Layout
26904 \begin_inset space \textvisiblespace{}
26912 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26915 \begin_layout Plain Layout
26919 \begin_layout Plain Layout
26935 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26938 \begin_layout Plain Layout
26946 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26949 \begin_layout Plain Layout
26953 \begin_layout Plain Layout
26969 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26972 \begin_layout Plain Layout
26976 \begin_inset Index idx
26979 \begin_layout Plain Layout
26990 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26993 \begin_layout Plain Layout
26997 \begin_layout Plain Layout
27013 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27016 \begin_layout Plain Layout
27024 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27027 \begin_layout Plain Layout
27031 \begin_layout Plain Layout
27047 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27050 \begin_layout Plain Layout
27054 \begin_inset space \textvisiblespace{}
27062 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27065 \begin_layout Plain Layout
27069 \begin_layout Plain Layout
27085 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27088 \begin_layout Plain Layout
27092 \begin_inset space \textvisiblespace{}
27100 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27103 \begin_layout Plain Layout
27107 \begin_layout Plain Layout
27123 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27126 \begin_layout Plain Layout
27130 \begin_inset space \textvisiblespace{}
27138 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27141 \begin_layout Plain Layout
27145 \begin_layout Plain Layout
27165 \begin_inset space \hfill{}
27171 \begin_layout Standard
27172 \begin_inset VSpace medskip
27181 also two different characters can be accented.
27187 \begin_inset space \textvisiblespace{}
27196 \begin_layout Plain Layout
27208 \begin_layout Standard
27221 can in combination with vowels directly be inserted with the keyboard without
27222 using \SpecialChar TeX
27224 The same applies for the tilde
27228 \begin_layout Plain Layout
27229 This only applies for keyboards where the tilde is defined as accent.
27238 in combination with
27253 \begin_layout Standard
27296 and accents that are inserted directly with the keyboard are also available
27297 in mathematical text.
27298 For the other accents there are special math commands to be used in formulas,
27300 \begin_inset CommandInset ref
27302 reference "subsec:Accents-for-one"
27309 \begin_layout Standard
27310 \begin_inset VSpace bigskip
27313 Furthermore, with the command
27320 \begin_inset Index idx
27323 \begin_layout Plain Layout
27331 all numbers and letters can be set into a circle, quasi accented with a
27332 circle, similar to the copyright symbol.
27335 \begin_layout Standard
27337 \begin_inset Tabular
27338 <lyxtabular version="3" rows="3" columns="2">
27339 <features booktabs="true" tabularvalignment="middle">
27340 <column alignment="center" valignment="top" width="0pt">
27341 <column alignment="center" valignment="top">
27343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27346 \begin_layout Plain Layout
27352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27355 \begin_layout Plain Layout
27363 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27366 \begin_layout Plain Layout
27374 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27377 \begin_layout Plain Layout
27381 \begin_layout Plain Layout
27396 <row topspace="1mm">
27397 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27400 \begin_layout Plain Layout
27411 raisebox{-1.5pt}{W}}
27416 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27419 \begin_layout Plain Layout
27423 \begin_layout Plain Layout
27453 \begin_layout Standard
27454 One has to take care that the character fits in the circle.
27465 \begin_layout Plain Layout
27467 \begin_inset CommandInset ref
27469 reference "subsec:Font-Sizes"
27478 specifies thereby the size of the circle.
27489 \begin_layout Plain Layout
27491 \begin_inset CommandInset ref
27493 reference "subsec:Boxes-without-Frame"
27502 the character can be centered.
27505 \begin_layout Subsection
27507 \begin_inset Index idx
27510 \begin_layout Plain Layout
27519 \begin_layout Standard
27520 Old-style figures (also known as old-style numerals) are created with the
27528 \begin_inset Index idx
27531 \begin_layout Plain Layout
27540 The command can be used in formulas and in \SpecialChar TeX
27542 The command scheme is:
27545 \begin_layout Standard
27550 oldstylenums{number}
27553 \begin_layout Standard
27558 oldstylenums{0123456789
27561 \begin_inset Formula $\oldstylenums{0123456789}$
27567 \begin_layout Section
27569 \begin_inset CommandInset label
27571 name "sec:Formula-Styles"
27576 \begin_inset Index idx
27579 \begin_layout Plain Layout
27588 \begin_layout Itemize
27589 There are two different alignment styles:
27590 \begin_inset Separator parbreak
27597 \begin_layout Description
27598 Centered is the predefined standard
27601 \begin_layout Description
27602 Indented for this the option
27606 must be inserted in the menu
27608 Document\SpecialChar menuseparator
27614 \begin_inset space ~
27620 \begin_layout Standard
27625 is used, the indentation can be adjusted with the length
27632 \begin_inset Index idx
27635 \begin_layout Plain Layout
27644 Should the distance be 15
27645 \begin_inset space \thinspace{}
27648 mm, the following command line is inserted in the \SpecialChar LaTeX
27652 \begin_layout Standard
27662 \begin_layout Standard
27663 When no length is specified, the predefined value of 30
27664 \begin_inset space \thinspace{}
27671 \begin_layout Itemize
27672 And two different numbering styles:
27673 \begin_inset Separator parbreak
27680 \begin_layout Description
27681 Right is the predefined standard
27684 \begin_layout Description
27685 Left for this the option
27689 must be inserted in the menu
27691 Document\SpecialChar menuseparator
27697 \begin_inset space ~
27704 \begin_layout Standard
27713 can also be used together.
27714 In this case both options are inserted, separated by a comma.
27717 \begin_layout Standard
27718 The chosen styles are used for all displayed formulas of the document.
27719 When both, centered and indented formulas should be created in a document,
27725 The indented formulas are then set in a flalign environment, see
27726 \begin_inset CommandInset ref
27728 reference "subsec:Flalign-Environment"
27735 \begin_layout Section
27737 \begin_inset CommandInset label
27739 name "sec:Multiline-Formulas"
27744 \begin_inset Index idx
27747 \begin_layout Plain Layout
27748 Formula ! multiline
27756 \begin_layout Subsection
27760 \begin_layout Standard
27761 In \SpecialChar LyX
27762 multiline formulas are created by pressing
27765 arg "newline-insert newline"
27769 This creates either an
27771 eqnarray environment
27773 that is described in
27774 \begin_inset CommandInset ref
27776 reference "subsec:Eqnarray-Environment"
27780 or, when the option
27782 Use AMS math package
27784 in the document settings is selected, an
27788 that is described in
27789 \begin_inset CommandInset ref
27791 reference "subsec:Standard-align-Environment"
27796 The align environment is recommended because it provides in any case a
27797 typographically correct output.
27800 \begin_layout Standard
27801 There are other multiline formula environments that can be created via the
27804 Insert\SpecialChar menuseparator
27808 These environments are described in the following sections.
27811 \begin_layout Standard
27812 In all multiline formula environments a new line is created by pressing
27816 arg "newline-insert newline"
27820 To add or delete lines, the math toolbar buttons
27823 arg "inset-modify tabular append-row"
27829 arg "inset-modify tabular delete-row"
27832 , respectively, or the menu
27834 Edit\SpecialChar menuseparator
27840 \begin_layout Subsubsection
27842 \begin_inset CommandInset label
27844 name "subsec:Line-Separation"
27849 \begin_inset Index idx
27852 \begin_layout Plain Layout
27853 Formula ! multiline ! Line separation
27861 \begin_layout Standard
27862 There is sometimes not enough space in multiline formulas between the lines:
27863 \begin_inset Formula
27865 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}\\
27866 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
27874 \begin_layout Standard
27875 In \SpecialChar LaTeX
27876 additional line space is specified as optional argument of the new line
27878 This is not yet possible in \SpecialChar LyX
27883 \begin_layout Plain Layout
27885 \begin_inset CommandInset href
27887 name "LyX-bug #1505"
27888 target "http://www.lyx.org/trac/ticket/1505"
27897 , therefore the whole formula must be inserted in \SpecialChar TeX
27899 To add in our example space, the command
27907 is inserted at the end of the first line.
27912 \begin_layout Plain Layout
27919 \begin_layout Plain Layout
27921 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27924 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27931 \begin_layout Plain Layout
27935 left(B^{2}+x_{0}^{2}
27943 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27948 \begin_layout Plain Layout
27960 \begin_layout Standard
27961 \begin_inset VSpace bigskip
27964 To set the line separation for all lines in a formula, the length
27971 \begin_inset Index idx
27974 \begin_layout Plain Layout
27984 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27995 \begin_inset space \thinspace{}
28000 \begin_inset space \thinspace{}
28003 mm additional line separation as in the previous example, the command
28006 \begin_layout Standard
28016 \begin_layout Standard
28017 is inserted in \SpecialChar TeX
28018 mode before the formula.
28019 This requires that the \SpecialChar LaTeX
28028 \begin_layout Plain Layout
28033 is part of every \SpecialChar LaTeX
28034 standard installation.
28040 \begin_inset Index idx
28043 \begin_layout Plain Layout
28049 was loaded in \SpecialChar LaTeX
28050 -preamble with the line
28053 \begin_layout Standard
28061 \begin_layout Standard
28066 \begin_layout Plain Layout
28078 \begin_inset Formula
28080 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}\\
28081 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
28089 \begin_layout Standard
28093 \begin_layout Plain Layout
28104 To get back to the predefined distance,
28110 is set to the value 3
28111 \begin_inset space \thinspace{}
28117 \begin_layout Subsubsection
28119 \begin_inset CommandInset label
28121 name "subsec:Column-Separation"
28126 \begin_inset Index idx
28129 \begin_layout Plain Layout
28130 Formula ! multiline ! Column separation
28138 \begin_layout Standard
28139 Multiline formulas form a matrix.
28140 A formula in the eqnarray environment is for example a matrix with three
28142 By changing the column separation in this environment, the space beside
28143 the relation sign can be changed.
28146 \begin_layout Standard
28147 The column separation is specified with the length
28154 \begin_inset Index idx
28157 \begin_layout Plain Layout
28166 \begin_inset Newline newline
28169 column separation = 2
28170 \begin_inset space \thinspace{}
28180 \begin_inset Newline newline
28186 \begin_layout Standard
28196 \begin_layout Standard
28197 inserted in \SpecialChar TeX
28198 mode, sets for all following formulas a column separation of
28200 \begin_inset space \thinspace{}
28204 To get back to the predefined distance,
28211 \begin_inset space \thinspace{}
28217 \begin_layout Standard
28219 \begin_inset space \thinspace{}
28222 cm column separation:
28226 \begin_layout Plain Layout
28238 \begin_inset Formula
28246 A formula with the predefined column separation for matrices of 10
28247 \begin_inset space \thinspace{}
28254 \begin_layout Plain Layout
28266 \begin_inset Formula
28277 \begin_layout Subsubsection
28279 \begin_inset Index idx
28282 \begin_layout Plain Layout
28291 \begin_layout Standard
28292 Long formulas can be typeset using these methods:
28295 \begin_layout Itemize
28296 When one side of the equation is much shorter than the line width, this
28297 one is chosen for the left side and the right side is typeset over two
28299 \begin_inset Formula
28301 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 \\
28302 & & -\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}
28307 The minus sign at the beginning of the second line does normally not appear
28308 as an operator because it is the first character of the line.
28309 Thus it would not be surrounded by space and could not be distinguished
28310 from the fraction bar.
28312 \begin_inset space \thinspace{}
28315 pt space was inserted behind the minus sign with the command
28325 \begin_layout Plain Layout
28333 \begin_inset CommandInset ref
28335 reference "subsec:Variable-Space"
28345 \begin_inset Index idx
28348 \begin_layout Plain Layout
28359 \begin_layout Itemize
28360 When both sides of the equation are too long, the command
28367 \begin_inset Index idx
28370 \begin_layout Plain Layout
28379 It is inserted in the first column of the first line and causes all further
28380 insertions to overwrite the following columns:
28381 \begin_inset Formula
28383 \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 \\
28384 & & -\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 \\
28385 & & =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}
28390 After the insertion of
28396 , the cursor is in a purple box that is a bit shifted to the left from the
28398 In this the formula is inserted.
28399 \begin_inset Newline newline
28402 The content of the further lines is inserted to the second or another formula
28404 The greater the column number where it was inserted, the larger the indentation.
28405 \begin_inset VSpace medskip
28409 \begin_inset Newline newline
28413 \begin_inset Note Greyedout
28416 \begin_layout Plain Layout
28417 Note the following when using
28426 \begin_layout Itemize
28427 The formula doesn't use the full page width.
28429 \begin_inset space \thinspace{}
28433 \begin_inset space \space{}
28437 \begin_inset Formula $-B^{2}$
28440 is added to the first line in the above example, it would have been outside
28442 To better use the width, negative space can be inserted at the beginning
28446 \begin_layout Itemize
28447 Due to a bug in \SpecialChar LyX
28448 the cursor cannot be set with the mouse into the first
28453 \begin_layout Plain Layout
28454 \begin_inset CommandInset href
28456 name "LyX-bug #1429"
28457 target "http://www.lyx.org/trac/ticket/1429"
28466 One can only set the cursor at the beginning of the line and move it with
28475 \begin_layout Itemize
28476 Other methods to set long formulas are offered by the environments described
28478 \begin_inset CommandInset ref
28480 reference "subsec:Multline-Environment"
28485 \begin_inset CommandInset ref
28487 reference "subsec:Multiline-Formula-Parts"
28494 \begin_layout Subsubsection
28495 Multiline Fractions
28496 \begin_inset CommandInset label
28498 name "subsec:Multiline-Fractions"
28503 \begin_inset Index idx
28506 \begin_layout Plain Layout
28507 Fractions ! multiline
28515 \begin_layout Standard
28516 There are cases where the denominator and/or the numerator of a fraction
28517 is so long that the fraction does not fit into one line.
28518 It is then necessary to add a line break within the fraction.
28519 This can be done using the command
28526 \begin_inset Index idx
28529 \begin_layout Plain Layout
28538 To activate it, set in the document settings under
28541 \begin_inset space ~
28551 \begin_inset Index idx
28554 \begin_layout Plain Layout
28555 Packages ! mathtools
28563 \begin_inset space ~
28578 \begin_layout Standard
28583 splitfrac{first line}{second line}
28586 \begin_layout Standard
28587 and is used as denominator and/or numerator:
28590 \begin_layout Standard
28591 \begin_inset Formula
28593 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}
28598 The command for the first numerator above is:
28601 \begin_layout Standard
28606 splitfrac{xy+xy+xy+xy+xy
28607 \begin_inset space \textvisiblespace{}
28615 \begin_layout Subsubsection
28617 \begin_inset CommandInset label
28619 name "subsec:Multiline-Brackets"
28624 \begin_inset Index idx
28627 \begin_layout Plain Layout
28628 Brackets ! for multiline expressions
28636 \begin_layout Standard
28637 For brackets spanning multiple lines the following problem occurs:
28638 \begin_inset Formula
28640 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28641 & & \left.\cdots+B-D\right]
28649 \begin_layout Standard
28650 The closing bracket is smaller than the opening bracket because brackets
28651 with variable size may not span multiple lines.
28654 \begin_layout Standard
28655 To set the bracket size for the second line correctly, the first line is
28663 \begin_inset Index idx
28666 \begin_layout Plain Layout
28674 and the second line with
28682 \begin_layout Plain Layout
28696 \begin_inset CommandInset ref
28698 reference "subsec:Automatic-Bracket-Size"
28710 \begin_inset Index idx
28713 \begin_layout Plain Layout
28736 \begin_inset space \textvisiblespace{}
28746 \begin_inset space \textvisiblespace{}
28756 \begin_inset space \textvisiblespace{}
28762 \begin_inset Formula $\downarrow$
28768 \begin_inset Index idx
28771 \begin_layout Plain Layout
28779 is inserted, because the multiplication operator with its limits is the
28780 largest symbol in the first line and this should be the size for the bracket
28781 in the second line.
28784 \begin_layout Standard
28785 The result is this:
28786 \begin_inset Formula
28788 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28789 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28797 \begin_layout Subsection
28801 \begin_layout Standard
28802 Align environments can be used for every kind of multiline formulas.
28803 They are especially useful to set several formulas side by side.
28806 \begin_layout Standard
28807 Align environments consist of columns.
28808 The odd columns are right aligned, the even ones left aligned.
28809 Every line in an Align environment can be numbered.
28812 \begin_layout Standard
28813 Align environments are created via the menu
28815 Insert\SpecialChar menuseparator
28821 Edit\SpecialChar menuseparator
28822 Math\SpecialChar menuseparator
28823 Change Formula Type
28825 already existing formulas can be converted to Align environments.
28828 \begin_layout Standard
28829 To add or delete columns, the math toolbar buttons
28832 arg "inset-modify tabular append-column"
28838 arg "inset-modify tabular delete-column"
28841 , respectively, or the menu
28843 Edit\SpecialChar menuseparator
28849 \begin_layout Subsubsection
28850 Standard align Environment
28851 \begin_inset CommandInset label
28853 name "subsec:Standard-align-Environment"
28858 \begin_inset Index idx
28861 \begin_layout Plain Layout
28862 Formula ! multiline ! align environment
28870 \begin_layout Standard
28871 This Align environment is created by pressing
28874 arg "newline-insert newline"
28877 in a formula or by the menu
28879 Insert\SpecialChar menuseparator
28880 Math\SpecialChar menuseparator
28881 AMS align Environment
28886 \begin_layout Standard
28887 An example for two formulas set side by side, that are created with a four
28888 column align environment:
28889 \begin_inset Formula
28891 A & =\sin(B) & C & =D\\
28892 C & \ne A & B & \ne D
28897 As it can be seen, the formulas in this environment are placed so as if
28906 \begin_layout Plain Layout
28914 \begin_inset CommandInset ref
28916 reference "subsec:Variable-Space"
28927 before the first and after every even column.
28928 When the formula style
28934 \begin_layout Plain Layout
28936 \begin_inset CommandInset ref
28938 reference "sec:Formula-Styles"
28949 is used, the formula is set without the
28955 before the first column.
28958 \begin_layout Subsubsection
28959 Alignat Environment
28960 \begin_inset Index idx
28963 \begin_layout Plain Layout
28964 Formula ! multiline ! alignat environment
28972 \begin_layout Standard
28973 The alignat environment has no predefined column separation.
28974 It can be inserted manually with the spaces that are described
28975 \begin_inset CommandInset ref
28977 reference "subsec:Space"
28984 \begin_layout Standard
28985 The above example in the alignat environment where 1
28986 \begin_inset space \thinspace{}
28989 cm space was inserted at the beginning of the second formula:
28990 \begin_inset Formula
28991 \begin{alignat*}{2}
28992 A & =\sin(B) & \hspace{1cm}C & =D\\
28993 C & \ne A & B & \ne D
28998 Because the column separation can be set separately for every column, this
28999 environment is especially suitable to set three and more formulas side
29003 \begin_layout Subsubsection
29004 Flalign Environment
29005 \begin_inset CommandInset label
29007 name "subsec:Flalign-Environment"
29012 \begin_inset Index idx
29015 \begin_layout Plain Layout
29016 Formula ! multiline ! flalign environment
29024 \begin_layout Standard
29025 In this environment the first two columns are always set as much as possible
29026 to the left and the last two ones to the right.
29028 \begin_inset Formula
29030 A & =1 & B & =2 & C & =3\\
29031 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29039 \begin_layout Standard
29040 By creating a flalign environment with an odd number of columns where an
29041 empty \SpecialChar TeX
29042 brace is inserted to the last column, several formulas in a document
29043 can be set to the left, although the formula style
29048 As example the indented formula
29049 \begin_inset CommandInset ref
29051 reference "eq:VolInt"
29056 \begin_inset Formula
29058 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29063 The first two columns contain the formula.
29064 To indent it as with the formula style
29069 \begin_inset space \thinspace{}
29072 pt space was inserted at the beginning of the first column.
29075 \begin_layout Subsection
29076 Eqnarray Environment
29077 \begin_inset CommandInset label
29079 name "subsec:Eqnarray-Environment"
29084 \begin_inset Index idx
29087 \begin_layout Plain Layout
29088 Formula ! multiline ! eqnarray environment
29096 \begin_layout Standard
29097 When this environment has been created, three blue boxes appear.
29098 The content of the first box is right aligned, the content of the last
29100 The content of the middle box appears centered and a bit smaller, because
29101 it is designed to insert there only relation characters.
29102 \begin_inset Formula
29104 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29114 \begin_layout Subsection
29116 \begin_inset Index idx
29119 \begin_layout Plain Layout
29120 Formula ! multiline ! gather environment
29128 \begin_layout Standard
29129 This environment consists of only one centered column.
29130 Every line can be numbered.
29131 \begin_inset Formula
29142 \begin_layout Subsection
29143 Multline Environment
29144 \begin_inset CommandInset label
29146 name "subsec:Multline-Environment"
29151 \begin_inset Index idx
29154 \begin_layout Plain Layout
29155 Formula ! multiline ! multline environment
29163 \begin_layout Standard
29164 The multline environment consists, like the gather environment, of only
29166 But the first line is left aligned, the last one right aligned.
29167 All other lines are centered.
29168 Therefore this environment is suitable for long formulas.
29170 \begin_inset CommandInset ref
29172 reference "eq:lefteqn"
29176 in the multline environment:
29177 \begin_inset Formula
29179 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}\\
29180 -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}\\
29181 =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}}
29189 \begin_layout Standard
29190 In the output only the last (first) line of a multline environment appears
29191 numbered when the document numbering is right (left).
29195 \begin_layout Plain Layout
29196 numbering styles see
29197 \begin_inset CommandInset ref
29199 reference "sec:Formula-Styles"
29211 \begin_layout Standard
29219 \begin_inset Index idx
29222 \begin_layout Plain Layout
29237 \begin_inset Index idx
29240 \begin_layout Plain Layout
29248 a centered line can be right or left aligned, respectively.
29249 The commands are used as follows:
29252 \begin_layout Standard
29257 shoveright{line content}
29263 shoveleft{line content}
29266 \begin_layout Standard
29267 \begin_inset VSpace medskip
29277 \begin_inset Index idx
29280 \begin_layout Plain Layout
29288 specifies the distance of the first line from the left page margin.
29289 Predefined is the length 0
29290 \begin_inset space \thinspace{}
29296 \begin_layout Standard
29297 As example the above formula where the command
29300 \begin_layout Standard
29310 \begin_layout Standard
29311 was inserted in \SpecialChar TeX
29316 \begin_layout Plain Layout
29328 \begin_inset Formula
29330 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}\\
29331 \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}}\\
29332 =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}}
29341 \begin_layout Plain Layout
29352 The second line was left aligned using
29361 \begin_layout Subsection
29362 Multiline Formula Parts
29363 \begin_inset CommandInset label
29365 name "subsec:Multiline-Formula-Parts"
29370 \begin_inset Index idx
29373 \begin_layout Plain Layout
29374 Formula ! multiline ! formula parts
29382 \begin_layout Standard
29383 To display only parts of a formula with multiple lines, one of the following
29384 environments is used:
29401 They can be inserted via the menu
29403 Insert\SpecialChar menuseparator
29406 or by using the commands described in this section.
29409 \begin_layout Standard
29410 The first three have the same properties as the corresponding multiline
29411 formula environments, but it is possible to set further formula parts beside
29414 \begin_inset Formula
29416 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29417 \Delta E\Delta t & \ge\frac{\hbar}{2}
29419 \right\} \textrm{Uncertainty relations}
29427 \begin_layout Standard
29428 To get this formula, a displayed formula is created where the command
29435 \begin_inset Index idx
29438 \begin_layout Plain Layout
29447 A purple box appears around the blue formula box where now columns and
29448 lines can be added.
29449 Outside the multiline environment other formula parts can be set, like
29453 \begin_layout Standard
29454 The aligned environment is also suitable for long formulas whose lines are
29455 horizontally aligned.
29456 Using aligned in a displayed formula has the advantage that the formula
29457 number is vertically centered behind the lines.
29459 \begin_inset CommandInset ref
29461 reference "eq:shortlong"
29465 in the aligned environment:
29466 \begin_inset Formula
29468 \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}|}\\
29469 & -\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}|}
29478 \begin_layout Standard
29479 To use the environments
29498 \begin_inset Index idx
29501 \begin_layout Plain Layout
29516 \begin_inset Index idx
29519 \begin_layout Plain Layout
29534 \begin_inset Index idx
29537 \begin_layout Plain Layout
29545 are inserted, respectively.
29546 The split environment has the same properties as the aligned environment
29547 but it can only have two columns.
29550 \begin_layout Subsection
29551 Text in multiline Formulas
29552 \begin_inset CommandInset label
29554 name "subsec:Text-in-multiline"
29559 \begin_inset Index idx
29562 \begin_layout Plain Layout
29569 \begin_inset Index idx
29572 \begin_layout Plain Layout
29573 Formula ! multiline ! text
29581 \begin_layout Standard
29582 In the Align environments, and the multline and gather environment, text
29583 can be inserted that will appear in a separate line and doesn't affect
29584 the column alignment.
29585 To do this, the command
29592 \begin_inset Index idx
29595 \begin_layout Plain Layout
29603 is used in the following scheme:
29606 \begin_layout Standard
29614 \begin_layout Standard
29615 The text should not be longer than a line because it cannot be hyphenated.
29616 As \SpecialChar LyX
29617 doesn't yet support
29623 directly, the text is written as mathematical text.
29630 must hereby be at the beginning of a line and appears in the output above
29632 An example where the text was inserted at the beginning of the second line:
29633 \begin_inset Formula
29635 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29636 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29644 \begin_layout Standard
29651 always creates some vertical space between the text and the formula lines.
29652 To avoid this space, set in the document settings under
29655 \begin_inset space ~
29665 \begin_inset Index idx
29668 \begin_layout Plain Layout
29669 Packages ! mathtools
29677 \begin_inset space ~
29683 Then you can use the command
29690 \begin_inset Index idx
29693 \begin_layout Plain Layout
29710 \begin_layout Standard
29711 \begin_inset Formula
29713 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29714 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29722 \begin_layout Section
29724 \begin_inset Index idx
29727 \begin_layout Plain Layout
29734 \begin_inset Index idx
29737 \begin_layout Plain Layout
29738 Formula ! numbering|see
29742 \begin_layout Plain Layout
29753 \begin_layout Plain Layout
29768 \begin_layout Subsection
29772 \begin_layout Standard
29773 Numbered formulas can be created with the menu
29775 Insert\SpecialChar menuseparator
29776 Math\SpecialChar menuseparator
29778 \begin_inset space ~
29786 \begin_inset space ~
29792 Existing formulas can be numbered with the menu
29794 Edit\SpecialChar menuseparator
29795 Math\SpecialChar menuseparator
29797 \begin_inset space ~
29805 arg "math-number-toggle"
29809 The formula number is displayed in \SpecialChar LyX
29810 behind the formula as a number sign
29812 The number sign is replaced in the output by the formula number.
29815 \begin_layout Standard
29816 When numbering is turned on in multiline formulas, all lines will be numbered.
29817 But the numbering can be controlled with the menu
29819 Edit\SpecialChar menuseparator
29820 Math\SpecialChar menuseparator
29822 \begin_inset space ~
29826 \begin_inset space ~
29830 \begin_inset space ~
29838 arg "math-number-line-toggle"
29844 \begin_layout Standard
29845 Except for inline formulas, all formulas can be numbered with two different
29847 \begin_inset CommandInset ref
29849 reference "sec:Formula-Styles"
29856 \begin_layout Subsection
29858 \begin_inset Index idx
29861 \begin_layout Plain Layout
29862 Cross-references ! to formulas
29870 \begin_layout Standard
29871 All labeled formulas can be cross-referenced.
29872 A label is added by the menu
29874 Insert\SpecialChar menuseparator
29877 or the toolbar button
29884 The cursor must hereby be inside a displayed formula.
29885 Alternatively you can right-click on the formula and choose
29890 A dialog pops up displaying the prefix
29895 The label is inserted there behind the prefix.
29896 The predefined prefix means
29897 \begin_inset Quotes eld
29901 \begin_inset Quotes erd
29904 and makes it easier to find labels in large documents because it marks
29905 it as formula label to divide it from e.
29906 \begin_inset space \thinspace{}
29910 \begin_inset space \space{}
29914 To change a label, the menu
29916 Insert\SpecialChar menuseparator
29919 is used again or you right-click on a formula and then on
29926 \begin_layout Standard
29927 The name of the label is displayed in \SpecialChar LyX
29928 within two parentheses behind formula.
29929 A formula with a label is always numbered.
29932 \begin_layout Standard
29933 Cross-references are inserted via the menu
29935 Insert\SpecialChar menuseparator
29938 or with the toolbar button
29941 arg "dialog-show-new-inset ref"
29945 A formula cross-reference appears in the output as formula number.
29946 When in the cross-reference dialog window the format
29950 is chosen, the cross-reference appears in the output as formula number
29952 \begin_inset Newline newline
29955 By right-clicking on a cross-reference in \SpecialChar LyX
29956 , one jumps to the formula that
29960 \begin_layout Standard
29961 Here are as examples cross-references to formulas of the following subsections:
29962 \begin_inset Note Note
29965 \begin_layout Plain Layout
29966 Note the different cross-reference types.
29974 \begin_layout Standard
29976 \begin_inset CommandInset ref
29983 \begin_inset CommandInset ref
29991 \begin_inset CommandInset ref
29997 ) big Latin letters are used for the numbering in contrary to (
29998 \begin_inset CommandInset ref
30007 \begin_layout Standard
30008 \begin_inset VSpace medskip
30011 When the argument of
30019 \begin_layout Plain Layout
30027 \begin_inset CommandInset ref
30029 reference "subsec:User-defined-Numbering"
30040 contains a box like in
30041 \begin_inset CommandInset ref
30043 reference "subsec:Paragraph-Boxes"
30047 , the formula cannot be referenced.
30050 \begin_layout Subsection
30052 \begin_inset Index idx
30055 \begin_layout Plain Layout
30056 Formula numbering ! subnumbering
30064 \begin_layout Standard
30065 With the help of the commands
30069 begin{subequations}
30077 formulas can be subnumbered.
30078 Both commands are inserted in \SpecialChar TeX
30082 \begin_layout Standard
30084 \begin_inset Formula
30095 \begin_layout Plain Layout
30099 addtocounter{equation}{-1}
30108 \begin_layout Plain Layout
30112 begin{subequations}
30118 \begin_inset VSpace -5mm
30122 \begin_inset Formula
30130 \begin_inset Formula
30140 \begin_layout Standard
30144 \begin_layout Plain Layout
30156 \begin_layout Standard
30157 To create the example, the following is done:
30160 \begin_layout Enumerate
30161 first formula is inserted
30164 \begin_layout Enumerate
30169 addtocounter{equation}{-1}
30171 begin{subequations}
30172 \begin_inset Index idx
30175 \begin_layout Plain Layout
30184 \begin_inset Newline newline
30189 is inserted after the first formula
30192 \begin_layout Enumerate
30193 second formula is inserted
30196 \begin_layout Enumerate
30197 third formula is inserted
30200 \begin_layout Enumerate
30207 is inserted after the third formula
30210 \begin_layout Standard
30211 Every formula between the commands
30223 is subnumbered as a, b,
30224 \begin_inset Newline linebreak
30227 c, \SpecialChar ldots
30228 For multiline formulas every line will be subnumbered.
30229 All subnumbered formulas are treated as
30234 But as every numbered formula increases the counter
30238 by one, the command
30244 is needed to decrease it.
30245 Otherwise the formulas
30246 \begin_inset CommandInset ref
30253 \begin_inset CommandInset ref
30260 \begin_inset CommandInset ref
30266 would be numbered as
30267 \begin_inset CommandInset ref
30274 \begin_inset CommandInset ref
30281 \begin_inset CommandInset ref
30290 \begin_layout Standard
30291 By inserting the commands in \SpecialChar TeX
30292 mode, a space is created between the first
30295 \begin_inset space \thinspace{}
30298 mm vertical space is inserted after the command
30302 begin{subequations}
30305 When the formula style
30311 \begin_layout Plain Layout
30313 \begin_inset CommandInset ref
30315 reference "sec:Formula-Styles"
30327 \begin_inset space \thinspace{}
30330 mm space is inserted instead.
30333 \begin_layout Standard
30334 Here is an example for a multiline formula where the numbering was turned
30335 off for the second line:
30339 \begin_layout Plain Layout
30343 begin{subequations}
30349 \begin_inset Formula
30351 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30352 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30353 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30362 \begin_layout Plain Layout
30374 \begin_layout Subsection
30375 User-defined Numbering
30376 \begin_inset CommandInset label
30378 name "subsec:User-defined-Numbering"
30383 \begin_inset Index idx
30386 \begin_layout Plain Layout
30387 Formula numbering ! user-defined
30395 \begin_layout Standard
30396 \begin_inset Index idx
30399 \begin_layout Plain Layout
30400 Formula numbering ! self-defined delimiters
30405 With the standard numbering parentheses are set around the formula number.
30406 To replace the parentheses for example by vertical bars, the following
30407 line is added to the \SpecialChar LaTeX
30411 \begin_layout Standard
30423 \begin_inset Note Note
30426 \begin_layout Plain Layout
30427 This macro is already declared in the \SpecialChar LaTeX
30428 -preamble for testing.
30429 To activate it, remove the percent sign at the beginning.
30437 \begin_layout Standard
30438 To use other characters, the vertical bars besides the
30442 are replaced by one ore more characters.
30443 To get only the formula number the vertical bars are omitted.
30446 \begin_layout Standard
30447 \begin_inset VSpace bigskip
30450 When there should be an expression of your choice instead of the consecutive
30451 formula number in parentheses behind the formula, the command
30458 \begin_inset Index idx
30461 \begin_layout Plain Layout
30470 \begin_inset Formula
30472 A+B=C\tag{something}\label{eq:tag}
30477 In this example the command
30482 \begin_inset space \textvisiblespace{}
30487 was inserted in the formula.
30490 \begin_layout Standard
30496 \begin_inset space \textvisiblespace{}
30501 is inserted instead, the star prevents the parentheses around the expression:
30502 \begin_inset Formula
30504 A+B=C\tag*{something}
30512 \begin_layout Standard
30513 \begin_inset VSpace bigskip
30516 To restart the formula numbering with new document parts or sections, the
30517 following command is used:
30520 \begin_layout Standard
30525 @addtoreset{equation}{part}
30528 \begin_inset Index idx
30531 \begin_layout Plain Layout
30536 \begin_layout Plain Layout
30547 \begin_layout Plain Layout
30560 \begin_layout Plain Layout
30571 \begin_layout Plain Layout
30584 \begin_inset Newline newline
30588 \begin_inset Newline newline
30595 @addtoreset{equation}{section}
30598 \begin_layout Standard
30599 To be able to use these commands in \SpecialChar TeX
30601 \begin_inset Quotes eld
30605 \begin_inset Quotes erd
30608 character has to be made
30609 \begin_inset Quotes eld
30613 \begin_inset Quotes erd
30616 for \SpecialChar LaTeX
30631 So the command sequence in \SpecialChar TeX
30635 \begin_layout Standard
30641 \begin_inset Newline newline
30646 @addtoreset{equation}{section}
30647 \begin_inset Newline newline
30655 \begin_layout Standard
30656 In the \SpecialChar LaTeX
30669 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30673 \begin_layout Standard
30688 \begin_layout Plain Layout
30693 is part of the \SpecialChar LaTeX
30699 \begin_inset Index idx
30702 \begin_layout Plain Layout
30703 Packages ! carlisle
30708 that is part of every \SpecialChar LaTeX
30709 standard installation.
30715 \begin_inset Index idx
30718 \begin_layout Plain Layout
30719 Packages ! remreset
30724 has to be loaded in the \SpecialChar LaTeX
30725 -preamble with the line
30728 \begin_layout Standard
30733 usepackage{remreset}
30736 \begin_layout Standard
30744 \begin_inset Index idx
30747 \begin_layout Plain Layout
30752 \begin_layout Plain Layout
30763 \begin_layout Plain Layout
30776 \begin_layout Plain Layout
30787 \begin_layout Plain Layout
30799 can be used with the same scheme as
30808 \begin_layout Standard
30809 \begin_inset VSpace bigskip
30812 Sometimes formulas should be numbered in the following form:
30815 \begin_layout Standard
30818 (section number.formula number)
30821 \begin_layout Standard
30822 The formula number should start with every section with
30823 \begin_inset Quotes eld
30827 \begin_inset Quotes erd
30833 \begin_layout Standard
30834 For this case there is the command
30841 \begin_inset Index idx
30844 \begin_layout Plain Layout
30852 , which is used with the following scheme:
30855 \begin_layout Standard
30860 numberwithin{counter}{sectioning}
30863 \begin_layout Standard
30864 Counter denotes what kind of numbering is affected, sectioning denotes what
30865 number is before the dot.
30868 \begin_layout Standard
30869 Thus in our case the following \SpecialChar LaTeX
30870 preamble or \SpecialChar TeX
30874 \begin_layout Standard
30879 numberwithin{equation}{section}
30882 \begin_layout Standard
30883 This is the result:
30887 \begin_layout Plain Layout
30891 numberwithin{equation}{section}
30897 \begin_inset Formula
30907 \begin_layout Standard
30909 \begin_inset space \thinspace{}
30913 \begin_inset space \space{}
30916 tables so that the number of the part is the sectioning,
30917 \begin_inset Newline newline
30924 numberwithin{table}{part}
30929 \begin_layout Standard
30930 To go back to the standard numbering or to prevent this kind of numbering
30931 when it is defined by the document class, the following command is inserted
30932 as \SpecialChar TeX
30933 code or to the \SpecialChar LaTeX
30937 \begin_layout Standard
30947 \begin_inset Index idx
30950 \begin_layout Plain Layout
30964 \begin_layout Plain Layout
30980 \begin_inset Newline newline
30988 \begin_inset Newline newline
31000 \begin_layout Standard
31007 uses internally the command
31013 , described above, that also needs to be reverted.
31017 \begin_layout Plain Layout
31024 \begin_layout Plain Layout
31028 @removefromreset{equation}{section}
31031 \begin_layout Plain Layout
31043 \begin_layout Subsection
31044 Numbering with Roman Numbers and Letters
31045 \begin_inset Index idx
31048 \begin_layout Plain Layout
31049 Formula numbering ! with letters
31055 \begin_inset Index idx
31058 \begin_layout Plain Layout
31059 Formula numbering ! with Roman numbers
31067 \begin_layout Standard
31068 Formulas can also be numbered with Roman numbers and Latin letters.
31069 To number for example with small Roman numbers, the command
31072 \begin_layout Standard
31084 \begin_layout Standard
31085 is inserted before the formula in \SpecialChar TeX
31094 \begin_inset Index idx
31097 \begin_layout Plain Layout
31105 redefines the predefined command
31121 \begin_layout Plain Layout
31128 has the same scheme like the command
31134 that is described in
31135 \begin_inset CommandInset ref
31137 reference "subsec:The-Command-newcommand"
31150 is the formula counter.
31157 is used as prefix for a counter, the value of the counter is output as
31159 When a formula is numbered, \SpecialChar LaTeX
31160 sets internally the command
31166 behind the formula.
31172 \begin_inset Index idx
31175 \begin_layout Plain Layout
31185 outputs the counter as small Roman number.
31188 \begin_layout Standard
31189 All formulas behind the command
31199 are now numbered Roman.
31200 To switch to numbering with big Roman numbers, the command is inserted
31214 \begin_inset Index idx
31217 \begin_layout Plain Layout
31229 \begin_inset Quotes eld
31233 \begin_inset Quotes erd
31236 with small Latin letters there is the command
31243 \begin_inset Index idx
31246 \begin_layout Plain Layout
31254 , for big ones there is the command
31261 \begin_inset Index idx
31264 \begin_layout Plain Layout
31277 \begin_layout Standard
31278 \begin_inset Note Greyedout
31281 \begin_layout Plain Layout
31288 \begin_inset space ~
31291 formulas can be numbered with Latin letters in one document.
31299 \begin_layout Standard
31303 \begin_layout Plain Layout
31319 \begin_layout Standard
31320 \begin_inset Formula
31322 A=\textrm{small roman}
31331 \begin_layout Plain Layout
31345 \begin_inset Formula
31347 B=\textrm{big Roman}\label{eq:Rom}
31356 \begin_layout Plain Layout
31370 \begin_inset Formula
31372 C=\textrm{small Latin}
31381 \begin_layout Plain Layout
31395 \begin_inset Formula
31397 D=\textrm{big Latin}\label{eq:Lat}
31405 \begin_layout Standard
31406 To switch back to the default numbering, insert the command:
31409 \begin_layout Standard
31419 \begin_inset Index idx
31422 \begin_layout Plain Layout
31433 \begin_layout Standard
31437 \begin_layout Plain Layout
31451 \begin_inset Formula
31461 \begin_layout Standard
31462 \begin_inset VSpace medskip
31465 As you see, formulas are numbered serially independent from the numbering
31467 When then numbering should start with
31468 \begin_inset Quotes eld
31472 \begin_inset Quotes erd
31475 when the style is changed, new equation counters have to be defined.
31476 A description about this can be found in the file
31477 \begin_inset CommandInset href
31479 name "Formula-numbering.lyx"
31480 target "run:Formula-numbering.lyx"
31487 \begin_layout Section
31488 Chemical Symbols and Equations
31489 \begin_inset CommandInset label
31491 name "subsec:Chemical-Symbols-and"
31496 \begin_inset Index idx
31499 \begin_layout Plain Layout
31500 Chemical characters ! Symbols
31506 \begin_inset Index idx
31509 \begin_layout Plain Layout
31516 \begin_inset Index idx
31519 \begin_layout Plain Layout
31528 \begin_layout Standard
31529 An example text from chemistry:
31532 \begin_layout Quote
31534 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31537 -ion reacts with two
31538 \begin_inset Formula $\mathrm{Na^{+}}$
31541 -ions to sodium sulfate
31542 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31546 The chemical equation for this is:
31547 \begin_inset Formula
31549 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31557 \begin_layout Standard
31558 This chemical equation can directly be created as formula.
31559 To avoid that the symbols appear italic, everything is highlighted and
31560 changed by the shortcut
31566 to the upright font style.
31570 \begin_layout Plain Layout
31576 \begin_inset CommandInset ref
31578 reference "subsec:Font-Styles"
31590 \begin_layout Standard
31591 A more convenient way to typeset chemical formulas is to use the command
31599 \begin_inset Index idx
31602 \begin_layout Plain Layout
31610 that is available when the \SpecialChar LaTeX
31616 \begin_inset Index idx
31619 \begin_layout Plain Layout
31632 to a formula a new blue box appears where chemical formulas can be inserted
31633 in an intuitive way.
31634 \begin_inset Separator parbreak
31640 \begin_layout Standard
31642 \begin_inset Tabular
31643 <lyxtabular version="3" rows="10" columns="2">
31644 <features booktabs="true" tabularvalignment="middle">
31645 <column alignment="center" valignment="top" width="0pt">
31646 <column alignment="center" valignment="top">
31648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31651 \begin_layout Plain Layout
31657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31660 \begin_layout Plain Layout
31668 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31671 \begin_layout Plain Layout
31675 \begin_inset space \textvisiblespace{}
31683 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31686 \begin_layout Plain Layout
31687 \begin_inset Formula $\ce{H2CO3}$
31696 <row topspace="1.5mm">
31697 <cell alignment="center" valignment="top" usebox="none">
31700 \begin_layout Plain Layout
31704 \begin_inset space \textvisiblespace{}
31712 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31715 \begin_layout Plain Layout
31716 \begin_inset Formula $\ce{SO4^{2-}}$
31725 <row topspace="1.5mm">
31726 <cell alignment="center" valignment="top" usebox="none">
31729 \begin_layout Plain Layout
31733 \begin_inset space \textvisiblespace{}
31741 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31744 \begin_layout Plain Layout
31745 \begin_inset Formula $\ce{(NH4)2S}$
31754 <row topspace="1.5mm">
31755 <cell alignment="center" valignment="top" usebox="none">
31758 \begin_layout Plain Layout
31762 \begin_inset space \textvisiblespace{}
31770 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31773 \begin_layout Plain Layout
31774 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31783 <row topspace="1.5mm">
31784 <cell alignment="center" valignment="top" usebox="none">
31787 \begin_layout Plain Layout
31791 \begin_inset space \textvisiblespace{}
31797 \begin_inset space \textvisiblespace{}
31803 \begin_inset space \textvisiblespace{}
31811 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31814 \begin_layout Plain Layout
31815 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31824 <row topspace="1.5mm">
31825 <cell alignment="center" valignment="top" usebox="none">
31828 \begin_layout Plain Layout
31832 \begin_inset space \textvisiblespace{}
31836 \begin_inset Formula $\downarrow$
31840 \begin_inset Formula $\to$
31848 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31851 \begin_layout Plain Layout
31852 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31862 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31865 \begin_layout Plain Layout
31869 \begin_inset space \textvisiblespace{}
31875 \begin_inset space \textvisiblespace{}
31881 \begin_inset space \textvisiblespace{}
31889 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31892 \begin_layout Plain Layout
31893 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31906 \begin_layout Plain Layout
31910 \begin_inset space \textvisiblespace{}
31914 \begin_inset space \textvisiblespace{}
31918 \begin_inset space \textvisiblespace{}
31922 \begin_inset space \textvisiblespace{}
31926 \begin_inset space \textvisiblespace{}
31934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31937 \begin_layout Plain Layout
31938 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31947 <row topspace="1.5mm">
31948 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31951 \begin_layout Plain Layout
31955 \begin_inset space \textvisiblespace{}
31959 \begin_inset space \textvisiblespace{}
31963 \begin_inset space \textvisiblespace{}
31967 \begin_inset space \textvisiblespace{}
31975 \begin_inset space \textvisiblespace{}
31983 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31986 \begin_layout Plain Layout
31987 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
32003 \begin_layout Standard
32004 \begin_inset Note Greyedout
32007 \begin_layout Plain Layout
32013 It is not possible in \SpecialChar LyX
32014 to use the character ^ to get an up-arrow as described
32020 One instead uses a negative thin space followed by the command
32027 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32038 \begin_layout Standard
32045 the command for equation
32046 \begin_inset space ~
32050 \begin_inset CommandInset ref
32052 reference "eq:chem-reaction"
32057 \begin_inset Newline newline
32065 \begin_inset space \textvisiblespace{}
32069 \begin_inset space \textvisiblespace{}
32073 \begin_inset space \textvisiblespace{}
32077 \begin_inset space \textvisiblespace{}
32081 \begin_inset space \textvisiblespace{}
32085 \begin_inset space \textvisiblespace{}
32091 \begin_layout Standard
32092 To create multiline chemical equations first a multiline formula is created
32094 \begin_inset CommandInset ref
32096 reference "sec:Multiline-Formulas"
32101 Afterwards the command
32107 is used in every small blue box of the formula.
32109 \begin_inset CommandInset ref
32111 reference "eq:TEOS-reaction-1"
32116 \begin_inset CommandInset ref
32118 reference "eq:TEOS-reaction-2"
32122 are an example of a multi-stage chemical reaction where every equation
32123 has its own number.
32124 \begin_inset Formula
32126 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32127 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32135 \begin_layout Standard
32146 package provides the command
32153 \begin_inset Index idx
32156 \begin_layout Plain Layout
32164 that has to be used for special cases.
32165 For more information about
32171 and more examples have a look at the documentation of
32176 \begin_inset CommandInset citation
32185 \begin_layout Section
32189 \begin_layout Standard
32191 supports two types of commutative diagrams:
32199 that are explained in the following.
32202 \begin_layout Subsection
32204 \begin_inset Index idx
32207 \begin_layout Plain Layout
32216 \begin_layout Standard
32217 Diagrams of this type visualize relations by vertical and horizontal lines
32219 \begin_inset Formula
32221 \begin{CD}A@>>>B@>>>C\\
32232 \begin_layout Standard
32233 To get them, the command
32238 \begin_inset Index idx
32241 \begin_layout Plain Layout
32251 is inserted to a formula.
32252 A blue box appears with two dashed lines where further commands can be
32257 arg "newline-insert newline"
32260 a new line is created.
32261 Horizontal relations are inserted in odd, vertical in even formula lines.
32264 \begin_layout Standard
32265 To create the relations there are the following commands:
32268 \begin_layout Itemize
32273 creates a left arrow,
32284 \begin_layout Itemize
32289 creates an up arrow,
32297 a vertical equal sign
32300 \begin_layout Itemize
32306 is a placeholder for non-existent relations
32309 \begin_layout Standard
32310 All arrows can be labeled as follows:
32313 \begin_layout Itemize
32314 If text inserted between the first and second < or >, resp., it is placed
32316 When it is inserted between the second and third one, it appears under
32320 \begin_layout Itemize
32321 When text for vertical arrows is inserted between the first and second A
32322 or V, resp., it is placed left beside the arrow.
32323 When it is inserted between the second and third one, it appears right
32325 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32329 \begin_layout Standard
32330 As example a diagram with all possible relations:
32333 \begin_layout Standard
32334 \begin_inset Formula
32336 \begin{CD}A@>j>>B@>>k>C@=F\\
32347 \begin_layout Standard
32348 The command for this is:
32349 \begin_inset Newline newline
32357 \begin_inset space \textvisiblespace{}
32360 A@>j>>B@>>k>C@=F Ctrl+Return
32361 \begin_inset Newline newline
32365 \begin_inset Phantom HPhantom
32368 \begin_layout Plain Layout
32374 \begin_inset space \textvisiblespace{}
32387 \begin_inset Formula $\to$
32393 \begin_inset Newline newline
32397 \begin_inset Phantom HPhantom
32400 \begin_layout Plain Layout
32406 \begin_inset space \textvisiblespace{}
32417 \begin_layout Subsection
32419 \begin_inset Index idx
32422 \begin_layout Plain Layout
32423 Diagrams ! xymatrix
32431 \begin_layout Standard
32432 To be able to use xymatrices, the \SpecialChar LaTeX
32438 A xymatrix is created by inserting the command
32445 Then you are able to add new matrix columns and rows like for normal matrices,
32447 \begin_inset CommandInset ref
32449 reference "sec:Matrices"
32456 \begin_layout Standard
32457 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32459 All possibilities to create commutative diagrams and decorations are explained
32464 that you find in the menu
32466 Help\SpecialChar menuseparator
32468 \begin_inset space ~
32476 \begin_layout Subsection
32482 \begin_inset Index idx
32485 \begin_layout Plain Layout
32494 \begin_layout Standard
32499 -diagrams, the \SpecialChar LaTeX
32509 -diagram is created by inserting the command
32516 Then you are able to add new matrix columns and rows like for normal matrices,
32518 \begin_inset CommandInset ref
32520 reference "sec:Matrices"
32527 \begin_layout Standard
32528 Examples how to create
32532 diagrams in \SpecialChar LyX
32535 Feynman-diagram manual
32537 that you find in the menu
32539 Help\SpecialChar menuseparator
32541 \begin_inset space ~
32549 \begin_layout Standard
32550 \begin_inset Newpage newpage
32556 \begin_layout Section
32557 User-defined Commands
32558 \begin_inset Index idx
32561 \begin_layout Plain Layout
32562 User-defined commands
32570 \begin_layout Standard
32571 \begin_inset Note Greyedout
32574 \begin_layout Plain Layout
32579 The names of user-defined commands and macros may only consist of Latin
32588 \begin_layout Subsection
32592 \begin_inset CommandInset label
32594 name "subsec:The-Command-newcommand"
32599 \begin_inset Index idx
32602 \begin_layout Plain Layout
32603 User-defined commands !
32611 \begin_inset Index idx
32614 \begin_layout Plain Layout
32625 \begin_layout Standard
32626 Many \SpecialChar LaTeX
32627 -commands are too long to be used frequently.
32628 But it is possible to define with the command
32634 new shorter commands.
32637 \begin_layout Standard
32638 The command scheme of
32647 \begin_layout Standard
32652 newcommand{new command name}[number of arguments][optional
32657 \begin_inset Newline newline
32661 \begin_inset Phantom HPhantom
32664 \begin_layout Plain Layout
32674 {command definition}
32677 \begin_layout Standard
32678 \begin_inset Note Greyedout
32681 \begin_layout Plain Layout
32686 Assure that the name of the new command is not already used in your document
32687 or by \SpecialChar LaTeX
32688 -packages that you use.
32689 When you for example define the command
32701 , you get an error message because
32707 is already defined as command for
32708 \begin_inset Quotes eld
32712 \begin_inset Formula $\le$
32716 \begin_inset Quotes erd
32727 \begin_layout Standard
32728 The number of arguments is an integer in the range 0
32729 \begin_inset space \thinspace{}
32733 \begin_inset space \thinspace{}
32736 9 and specifies how many arguments the new command should have.
32737 With the optional value a value for an optional argument can be predefined.
32738 When this is done, the
32746 rgument of the new command is automatically an optional one.
32749 \begin_layout Standard
32750 Here are some examples:
32753 \begin_layout Itemize
32754 To define the command
32766 , the \SpecialChar LaTeX
32768 \begin_inset VSpace medskip
32772 \begin_inset Newline newline
32786 \begin_layout Itemize
32787 To define the command
32799 , the argument (that should be underlined) must be taken into account.
32800 For this the preamble line is:
32801 \begin_inset VSpace medskip
32805 \begin_inset Newline newline
32819 \begin_inset VSpace medskip
32823 \begin_inset Newline newline
32830 acts as argument placeholder, the
32834 behind it denotes that it is the placeholder for the first argument.
32837 \begin_layout Itemize
32845 \begin_inset space \thinspace{}
32849 \begin_inset space \space{}
32859 \begin_inset VSpace medskip
32863 \begin_inset Newline newline
32874 framebox#1#2{$#3$}}
32877 \begin_inset VSpace medskip
32881 \begin_inset Newline newline
32884 The two Dollar signs creates the extra formula needed for
32891 \begin_inset CommandInset ref
32893 reference "subsec:Boxes-with-Frame"
32900 \begin_layout Itemize
32901 To create a new command for
32907 where the color for the box need not be specified, the argument for the
32908 color is defined optional:
32909 \begin_inset VSpace medskip
32913 \begin_inset Newline newline
32924 fcolorbox{#2}{#1}{$#3$}}
32927 \begin_inset VSpace medskip
32931 \begin_inset Newline newline
32934 When the color is not specified when using
32940 , the predefined color
32947 \begin_layout Standard
32948 A test of the new defined commands:
32949 \begin_inset Separator parbreak
32955 \begin_layout Standard
32957 \begin_inset Tabular
32958 <lyxtabular version="3" rows="6" columns="2">
32959 <features booktabs="true" tabularvalignment="middle">
32960 <column alignment="center" valignment="top" width="0pt">
32961 <column alignment="center" valignment="top">
32963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32966 \begin_layout Plain Layout
32972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32975 \begin_layout Plain Layout
32983 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32986 \begin_layout Plain Layout
32990 \begin_inset space \textvisiblespace{}
32998 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33001 \begin_layout Plain Layout
33002 \begin_inset Formula $A\gr B$
33012 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33015 \begin_layout Plain Layout
33023 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33026 \begin_layout Plain Layout
33027 \begin_inset Formula $\us{ABcd}$
33036 <row topspace="1mm">
33037 <cell alignment="center" valignment="top" usebox="none">
33040 \begin_layout Plain Layout
33044 \begin_inset Formula $\to$
33050 \begin_inset Formula $\to$
33058 \begin_inset space \textvisiblespace{}
33066 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33069 \begin_layout Plain Layout
33070 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33079 <row topspace="1.5mm">
33080 <cell alignment="center" valignment="top" usebox="none">
33083 \begin_layout Plain Layout
33087 \begin_inset Formula $\to$
33095 \begin_inset space \textvisiblespace{}
33103 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33106 \begin_layout Plain Layout
33107 \begin_inset Formula $\cb{red}{\int A=B}$
33116 <row topspace="1.5mm" bottomspace="1mm">
33117 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33120 \begin_layout Plain Layout
33126 \begin_inset Formula $\to$
33134 \begin_inset space \textvisiblespace{}
33142 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33145 \begin_layout Plain Layout
33146 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33162 \begin_layout Subsection
33164 \begin_inset Index idx
33167 \begin_layout Plain Layout
33168 User-defined commands! Math macros
33174 \begin_inset Index idx
33177 \begin_layout Plain Layout
33186 \begin_layout Standard
33187 User-defined commands are especially convenient for complex expressions.
33188 When you are for example dealing with a document that has quadratic equations,
33189 the same solution type occurs several times.
33190 The general form of a quadratic equation is
33191 \begin_inset Formula
33193 0=\lambda^{2}+p\lambda+q
33198 The general form of the solution is
33199 \begin_inset Formula
33201 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33209 \begin_layout Standard
33210 To define a command for the solution formula where only the three parameters
33212 \begin_inset Formula $\lambda$
33216 \begin_inset Formula $p$
33220 \begin_inset Formula $q$
33223 need to be specified and the index of
33224 \begin_inset Formula $\lambda$
33227 can be given optionally, the \SpecialChar LaTeX
33229 \begin_inset Newline newline
33245 \begin_inset Newline newline
33249 \begin_inset Phantom HPhantom
33252 \begin_layout Plain Layout
33266 frac{#3^{2}}{4}-#4}}
33269 \begin_layout Standard
33270 To create with this the solution formula, the command
33271 \begin_inset Newline newline
33281 \begin_inset Formula $\to$
33287 \begin_inset Formula $\to$
33294 is inserted to a formula
33299 \begin_layout Standard
33300 The definition of the new command is unintuitive because one has to know
33301 the schemes of all used \SpecialChar LaTeX
33303 \begin_inset space \thinspace{}
33307 \begin_inset space \space{}
33310 that a fraction is inserted in \SpecialChar LaTeX
33315 frac{numerator}{denominator}
33318 Furthermore one can easily forget a brace in the definition and cannot
33319 see in \SpecialChar LyX
33320 what the new command is doing.
33321 To avoid these problems \SpecialChar LyX
33322 offers the possibility to use math macros instead
33332 \begin_layout Standard
33333 A math macro is created by using the menu
33335 Insert\SpecialChar menuseparator
33336 Math\SpecialChar menuseparator
33339 or the toolbar button
33342 arg "math-macro newmacroname_newcommand"
33346 The math macro toolbar appears together with the following box where the
33348 \begin_inset Newline newline
33352 \begin_inset space \hspace*{\fill}
33356 \begin_inset Graphics
33357 filename clipart/macrobox.png
33363 \begin_inset space \hspace*{\fill}
33367 \begin_inset Newline newline
33371 \begin_inset FormulaMacro
33372 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33377 newmacroname is the default name of the macro that should be changed to
33378 something sensible.
33379 The wanted formula is inserted in the first blue box.
33380 An argument placeholder is inserted with the command
33387 \begin_inset space \thinspace{}
33391 \begin_inset space \space{}
33400 or by using the macro toolbar button
33403 arg "math-macro-add-param"
33407 Argument placeholders are displayed red.
33409 \begin_inset space ~
33412 arguments are possible.
33413 Optional arguments are created with the toolbar button
33416 arg "math-macro-add-optional-param"
33420 The first non-optional argument can be transformed to an optional one with
33424 arg "math-macro-make-optional"
33428 In the second blue box the appearance of the macro in \SpecialChar LyX
33430 Normally you want to see it as it is defined, so the box is kept empty.
33431 But when you have created a macro that needs lot of space on the screen,
33432 you can insert in the box for example
33433 \begin_inset Newline newline
33463 \begin_inset Newline newline
33468 For the macro only the arguments with the macro name in front of them will
33469 then be displayed in \SpecialChar LyX
33470 , leading to a better overview.
33471 The formula appears in the output as defined in the first box.
33472 \begin_inset Newline newline
33475 The appearance of macros in formulas can furthermore be changed for single
33476 macros by setting the cursor in the macro and using the menu
33478 View\SpecialChar menuseparator
33480 \begin_inset space ~
33484 \begin_inset space ~
33492 \begin_layout Standard
33493 To use a macro, the macro name is inserted as command to a formula, in our
33501 Our macro looks in \SpecialChar LyX
33503 \begin_inset Newline newline
33507 \begin_inset space \hspace*{\fill}
33511 \begin_inset Graphics
33512 filename clipart/macrouse.png
33518 \begin_inset space \hspace*{\fill}
33522 \begin_inset Newline newline
33525 Here is our macro example with the arguments
33526 \begin_inset Formula $x$
33530 \begin_inset Formula $\ln(x)$
33534 \begin_inset Formula $B$
33540 \begin_layout Standard
33541 \begin_inset Formula
33551 \begin_layout Standard
33555 Tools\SpecialChar menuseparator
33556 Preferences\SpecialChar menuseparator
33557 Editing\SpecialChar menuseparator
33560 different styles to edit macros.
33561 To find the style that suits you the most, choose a style and set the cursor
33562 in a macro formula to see the difference.
33565 \begin_layout Standard
33566 A math macro is transformed internally to a
33572 command when exporting the document.
33579 command is not placed in the \SpecialChar LaTeX
33580 -preamble, therefore macros can only be used
33581 in formulas that are in the document below the macro definition box.
33584 \begin_layout Standard
33585 Math macros can also be directly created from a
33592 When writing for example the command
33595 \begin_inset Newline newline
33604 xleftarrow[#2]{#1}}
33605 \begin_inset Newline newline
33610 in \SpecialChar LyX
33611 as normal text, highlighting it completely and using then the shortcut
33616 , the command will be transformed to a math macro.
33617 Using this method you need to be careful that the
33623 command is typed correctly, otherwise you get a faulty macro leading to
33628 \begin_layout Standard
33629 Math macros currently have the problem that further formulas in macro definition
33630 s are handled wrongly.
33631 Therefore the example
33638 \begin_inset CommandInset ref
33640 reference "subsec:The-Command-newcommand"
33644 cannot be created as macro.
33647 \begin_layout Standard
33648 When the cursor is in a macro definition box, you will see the macro toolbar
33649 in \SpecialChar LyX
33653 \begin_layout Standard
33654 \begin_inset VSpace defskip
33660 \begin_layout Standard
33661 \begin_inset Graphics
33662 filename clipart/MacroToolbar.png
33667 \begin_inset Index idx
33670 \begin_layout Plain Layout
33679 \begin_layout Standard
33680 \begin_inset VSpace defskip
33686 \begin_layout Standard
33687 The macro toolbar contains from left to right the following buttons:
33690 \begin_layout Standard
33691 \begin_inset VSpace defskip
33697 \begin_layout Standard
33698 \begin_inset Tabular
33699 <lyxtabular version="3" rows="9" columns="2">
33700 <features islongtable="true" longtabularalignment="center">
33701 <column alignment="left" valignment="top">
33702 <column alignment="left" valignment="top" width="85col%">
33703 <row interlinespace="2.5mm">
33704 <cell alignment="center" valignment="top" usebox="none">
33707 \begin_layout Plain Layout
33710 arg "math-macro-remove-param"
33718 <cell alignment="center" valignment="top" usebox="none">
33721 \begin_layout Plain Layout
33724 Edit\SpecialChar menuseparator
33725 Math\SpecialChar menuseparator
33727 \begin_inset space ~
33730 Definition\SpecialChar menuseparator
33731 Remove Last Argument
33737 <row interlinespace="2.5mm">
33738 <cell alignment="center" valignment="top" usebox="none">
33741 \begin_layout Plain Layout
33744 arg "math-macro-add-param"
33752 <cell alignment="center" valignment="top" usebox="none">
33755 \begin_layout Plain Layout
33758 Edit\SpecialChar menuseparator
33759 Math\SpecialChar menuseparator
33761 \begin_inset space ~
33764 Definition\SpecialChar menuseparator
33771 <row interlinespace="2.5mm">
33772 <cell alignment="center" valignment="top" usebox="none">
33775 \begin_layout Plain Layout
33778 arg "math-macro-make-optional"
33786 <cell alignment="center" valignment="top" usebox="none">
33789 \begin_layout Plain Layout
33792 Edit\SpecialChar menuseparator
33793 Math\SpecialChar menuseparator
33795 \begin_inset space ~
33798 Definition\SpecialChar menuseparator
33799 Transform First Non-Optional to
33800 \begin_inset Newline newline
33804 \begin_inset Phantom HPhantom
33807 \begin_layout Plain Layout
33810 Edit\SpecialChar menuseparator
33811 Math\SpecialChar menuseparator
33813 \begin_inset space ~
33816 Definition\SpecialChar menuseparator
33828 <row interlinespace="2.5mm">
33829 <cell alignment="center" valignment="top" usebox="none">
33832 \begin_layout Plain Layout
33835 arg "math-macro-make-nonoptional"
33843 <cell alignment="center" valignment="top" usebox="none">
33846 \begin_layout Plain Layout
33849 Edit\SpecialChar menuseparator
33850 Math\SpecialChar menuseparator
33852 \begin_inset space ~
33855 Definition\SpecialChar menuseparator
33856 Transform Last Optional to
33857 \begin_inset Newline newline
33861 \begin_inset Phantom HPhantom
33864 \begin_layout Plain Layout
33867 Edit\SpecialChar menuseparator
33868 Math\SpecialChar menuseparator
33870 \begin_inset space ~
33873 Definition\SpecialChar menuseparator
33879 Non-Optional Argument
33885 <row interlinespace="2.5mm">
33886 <cell alignment="center" valignment="top" usebox="none">
33889 \begin_layout Plain Layout
33892 arg "math-macro-remove-optional-param"
33900 <cell alignment="center" valignment="top" usebox="none">
33903 \begin_layout Plain Layout
33906 Edit\SpecialChar menuseparator
33907 Math\SpecialChar menuseparator
33909 \begin_inset space ~
33912 Definition\SpecialChar menuseparator
33913 Remove Optional Argument
33919 <row interlinespace="2.5mm">
33920 <cell alignment="center" valignment="top" usebox="none">
33923 \begin_layout Plain Layout
33926 arg "math-macro-add-optional-param"
33934 <cell alignment="center" valignment="top" usebox="none">
33937 \begin_layout Plain Layout
33940 Edit\SpecialChar menuseparator
33941 Math\SpecialChar menuseparator
33943 \begin_inset space ~
33946 Definition\SpecialChar menuseparator
33947 Insert Optional Argument
33953 <row interlinespace="2.5mm">
33954 <cell alignment="center" valignment="top" usebox="none">
33957 \begin_layout Plain Layout
33960 arg "math-macro-remove-greedy-param"
33968 <cell alignment="center" valignment="top" usebox="none">
33971 \begin_layout Plain Layout
33974 Edit\SpecialChar menuseparator
33975 Math\SpecialChar menuseparator
33977 \begin_inset space ~
33980 Definition\SpecialChar menuseparator
33981 Remove Last Argument
33982 \begin_inset Newline newline
33986 \begin_inset Phantom HPhantom
33989 \begin_layout Plain Layout
33992 Edit\SpecialChar menuseparator
33993 Math\SpecialChar menuseparator
33995 \begin_inset space ~
33998 Definition\SpecialChar menuseparator
34004 Spitting Out To The Right
34010 <row interlinespace="2.5mm">
34011 <cell alignment="center" valignment="top" usebox="none">
34014 \begin_layout Plain Layout
34017 arg "math-macro-append-greedy-param"
34025 <cell alignment="center" valignment="top" usebox="none">
34028 \begin_layout Plain Layout
34031 Edit\SpecialChar menuseparator
34032 Math\SpecialChar menuseparator
34034 \begin_inset space ~
34037 Definition\SpecialChar menuseparator
34039 \begin_inset Newline newline
34043 \begin_inset Phantom HPhantom
34046 \begin_layout Plain Layout
34049 Edit\SpecialChar menuseparator
34050 Math\SpecialChar menuseparator
34052 \begin_inset space ~
34055 Definition\SpecialChar menuseparator
34061 Eating From The Right
34067 <row interlinespace="2.5mm">
34068 <cell alignment="center" valignment="top" usebox="none">
34071 \begin_layout Plain Layout
34074 arg "math-macro-add-greedy-optional-param"
34082 <cell alignment="center" valignment="top" usebox="none">
34085 \begin_layout Plain Layout
34088 Edit\SpecialChar menuseparator
34089 Math\SpecialChar menuseparator
34091 \begin_inset space ~
34094 Definition\SpecialChar menuseparator
34095 Append Optional Argument
34096 \begin_inset Newline newline
34100 \begin_inset Phantom HPhantom
34103 \begin_layout Plain Layout
34106 Edit\SpecialChar menuseparator
34107 Math\SpecialChar menuseparator
34109 \begin_inset space ~
34112 Definition\SpecialChar menuseparator
34118 Eating From The Right
34131 \begin_layout Section
34132 Computer Algebra Systems
34135 \begin_layout Standard
34137 offers the exchange between mathematical expressions written in \SpecialChar LyX
34139 editor and external applications or user defined scripts.
34140 Currently supported applications are
34157 Note that the set of supported mathematical constructs is limited only
34158 to very simple cases.
34161 \begin_layout Subsection
34165 \begin_layout Standard
34166 Write some expression in a formula, go to the
34168 Edit\SpecialChar menuseparator
34169 Math\SpecialChar menuseparator
34170 Use Computer Algebra System
34172 menu and choose the application you have installed on the computer.
34173 After that the result of computation should show on the right side of the
34174 expression together with the
34175 \begin_inset Quotes eld
34179 \begin_inset Quotes erd
34185 \begin_layout Standard
34186 Here are few simple examples (with results from
34190 ) to show what kind of computations can be performed:
34193 \begin_layout Itemize
34194 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34200 \begin_layout Itemize
34201 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34207 \begin_layout Itemize
34208 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34214 \begin_layout Itemize
34215 \begin_inset Formula $\det\left[\begin{array}{ccc}
34219 \end{array}\right]=-56$
34225 \begin_layout Itemize
34226 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34232 \begin_layout Subsection
34236 \begin_layout Standard
34237 Currently there is no keyboard shortcut for calling the algebra applications.
34238 One can easily bind a shortcut to the
34252 \begin_inset space \thinspace{}
34256 \begin_inset space \space{}
34263 key inside the math editor.
34268 one would use this shortcut definition command:
34271 \begin_layout Standard
34274 command-alternatives paragraph-break;math-extern maxima
34277 \begin_layout Section
34279 \begin_inset Index idx
34282 \begin_layout Plain Layout
34291 \begin_layout Subsection
34293 \begin_inset Index idx
34296 \begin_layout Plain Layout
34305 \begin_layout Standard
34306 Negative numbers often look ugly in formulas because the minus sign before
34307 the number is set with the same length as the minus operator sign.
34308 When writing the negative number in normal text, the minus sign appears
34312 \begin_layout Standard
34313 Thus, the problem disappears when converting the minus sign to mathematical
34317 \begin_layout Standard
34318 An example to visualize the problem:
34319 \begin_inset Separator parbreak
34325 \begin_layout Standard
34327 \begin_inset Tabular
34328 <lyxtabular version="3" rows="3" columns="2">
34329 <features booktabs="true" tabularvalignment="middle">
34330 <column alignment="right" valignment="top" width="0pt">
34331 <column alignment="left" valignment="top">
34333 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34336 \begin_layout Plain Layout
34342 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34345 \begin_layout Plain Layout
34353 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34356 \begin_layout Plain Layout
34362 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34365 \begin_layout Plain Layout
34366 \begin_inset Formula $x=-2$
34376 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34379 \begin_layout Plain Layout
34385 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34388 \begin_layout Plain Layout
34389 \begin_inset Formula $x=\textrm{-}2$
34405 \begin_layout Subsection
34406 Comma as decimal Separator
34407 \begin_inset Index idx
34410 \begin_layout Plain Layout
34419 \begin_layout Standard
34420 In \SpecialChar LaTeX
34421 a comma inside a formula is used, according to the English convention,
34422 as number group separator.
34423 So there will be space added behind all commas in formulas.
34426 \begin_layout Standard
34427 To avoid this, the comma is highlighted and changed to mathematical text
34437 \begin_layout Standard
34438 To use all formula commas in the document as decimal separator, the file
34447 \begin_layout Plain Layout
34452 is part of the \SpecialChar LaTeX
34458 \begin_inset Index idx
34461 \begin_layout Plain Layout
34466 \begin_layout Plain Layout
34486 \begin_inset Index idx
34489 \begin_layout Plain Layout
34495 is loaded with the \SpecialChar LaTeX
34499 \begin_layout Standard
34507 \begin_layout Subsection
34509 \begin_inset CommandInset label
34511 name "subsec:Physical-Vectors"
34516 \begin_inset Index idx
34519 \begin_layout Plain Layout
34528 \begin_layout Standard
34529 Predefined vectors are offered by the \SpecialChar LaTeX
34535 \begin_inset Index idx
34538 \begin_layout Plain Layout
34544 that is loaded with the \SpecialChar LaTeX
34548 \begin_layout Standard
34556 \begin_layout Standard
34560 \begin_layout Plain Layout
34570 \begin_inset Note Note
34573 \begin_layout Plain Layout
34574 The following table will only be displayed when the \SpecialChar LaTeX
34587 \begin_layout Standard
34588 The following commands are defined:
34589 \begin_inset Separator parbreak
34595 \begin_layout Standard
34597 \begin_inset Tabular
34598 <lyxtabular version="3" rows="4" columns="2">
34599 <features booktabs="true" tabularvalignment="middle">
34600 <column alignment="center" valignment="top" width="0pt">
34601 <column alignment="center" valignment="top">
34603 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34606 \begin_layout Plain Layout
34612 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34615 \begin_layout Plain Layout
34623 <cell alignment="center" valignment="top" usebox="none">
34626 \begin_layout Plain Layout
34636 <cell alignment="center" valignment="top" usebox="none">
34639 \begin_layout Plain Layout
34640 \begin_inset Formula $\Bra{\psi}$
34650 <cell alignment="center" valignment="top" usebox="none">
34653 \begin_layout Plain Layout
34663 <cell alignment="center" valignment="top" usebox="none">
34666 \begin_layout Plain Layout
34667 \begin_inset Formula $\Ket{\psi}$
34677 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34680 \begin_layout Plain Layout
34692 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34695 \begin_layout Plain Layout
34696 \begin_inset Formula $\Braket{\psi|\phi}$
34712 \begin_layout Standard
34719 assures that all vertical bars are set in the size of the surrounding brackets:
34720 \begin_inset Formula
34722 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34731 \begin_layout Plain Layout
34741 \begin_inset Note Note
34744 \begin_layout Plain Layout
34745 The following will be displayed when the \SpecialChar LaTeX
34758 \begin_layout Standard
34759 You need to install the \SpecialChar LaTeX
34764 to see the rest of this subsection in the output.
34767 \begin_layout Standard
34771 \begin_layout Plain Layout
34783 \begin_layout Standard
34790 can also be achieved using the command
34796 , that is described in
34797 \begin_inset CommandInset ref
34799 reference "subsec:Automatic-Bracket-Size"
34806 \begin_layout Subsection
34807 Self-defined Fractions
34808 \begin_inset CommandInset label
34810 name "subsec:Self-defined-Fractions"
34815 \begin_inset Index idx
34818 \begin_layout Plain Layout
34819 Fractions ! self-defined
34827 \begin_layout Standard
34828 To define custom commands for fractions, the command
34835 \begin_inset Index idx
34838 \begin_layout Plain Layout
34845 \begin_layout Plain Layout
34859 is used in the following scheme:
34862 \begin_layout Standard
34875 bracket}{fraction bar thickness}{style}
34876 \begin_inset Newline newline
34880 \begin_inset Phantom HPhantom
34883 \begin_layout Plain Layout
34893 {numerator}{denominator}
34896 \begin_layout Standard
34897 The style is a number in the range of 0
34898 \begin_inset space \thinspace{}
34902 \begin_inset space \thinspace{}
34906 \begin_inset Separator parbreak
34912 \begin_layout Standard
34914 \begin_inset Tabular
34915 <lyxtabular version="3" rows="5" columns="2">
34916 <features booktabs="true" tabularvalignment="middle">
34917 <column alignment="center" valignment="top" width="0pt">
34918 <column alignment="center" valignment="top">
34920 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34923 \begin_layout Plain Layout
34929 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34932 \begin_layout Plain Layout
34940 <cell alignment="center" valignment="top" usebox="none">
34943 \begin_layout Plain Layout
34949 <cell alignment="center" valignment="top" usebox="none">
34952 \begin_layout Plain Layout
34953 display style formula
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
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" bottomline="true" usebox="none">
35003 \begin_layout Plain Layout
35009 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35012 \begin_layout Plain Layout
35026 \begin_layout Standard
35027 When no style is given, the size is adjusted to the surrounding environment
35028 like for the command
35037 \begin_layout Standard
35038 When no fraction bar thickness is given, the predefined value of 0.4
35039 \begin_inset space \thinspace{}
35045 \begin_layout Standard
35046 \begin_inset VSpace medskip
35049 For example, the commands
35062 \begin_inset CommandInset ref
35064 reference "subsec:Fractions"
35068 are defined with the commands
35071 \begin_layout Standard
35080 genfrac{}{}{}{0}{#1}{#2}}
35083 \begin_layout Standard
35087 \begin_layout Standard
35096 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35099 \begin_layout Standard
35100 \begin_inset VSpace medskip
35103 To define a fraction where the fraction bar thickness can be given as optional
35104 argument, the following line is inserted to the \SpecialChar LaTeX
35108 \begin_layout Standard
35117 genfrac{}{}{#1}{}{#2}{#3}}
35120 \begin_layout Standard
35122 \begin_inset Formula
35124 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35125 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35130 As one can see, the distance of the numerator and the denominator to the
35131 fraction bar is round about three times the bar thickness.
35134 \begin_layout Subsection
35136 \begin_inset Index idx
35139 \begin_layout Plain Layout
35148 \begin_layout Standard
35149 There are four ways to cancel formulas or parts of formulas:
35152 \begin_layout Standard
35156 \begin_layout Plain Layout
35166 \begin_inset Note Note
35169 \begin_layout Plain Layout
35170 The following table will only be displayed when the \SpecialChar LaTeX
35181 \begin_inset Separator parbreak
35187 \begin_layout Standard
35189 \begin_inset Tabular
35190 <lyxtabular version="3" rows="5" columns="2">
35191 <features booktabs="true" tabularvalignment="middle">
35192 <column alignment="center" valignment="top" width="0pt">
35193 <column alignment="center" valignment="top">
35195 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35198 \begin_layout Plain Layout
35204 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35207 \begin_layout Plain Layout
35215 <cell alignment="center" valignment="top" usebox="none">
35218 \begin_layout Plain Layout
35222 \begin_inset space \textvisiblespace{}
35228 \begin_inset space \textvisiblespace{}
35236 <cell alignment="center" valignment="top" usebox="none">
35239 \begin_layout Plain Layout
35240 \begin_inset Formula $\cancel{\int A=B}$
35249 <row topspace="1.5mm">
35250 <cell alignment="center" valignment="top" usebox="none">
35253 \begin_layout Plain Layout
35257 \begin_inset space \textvisiblespace{}
35263 \begin_inset space \textvisiblespace{}
35271 <cell alignment="center" valignment="top" usebox="none">
35274 \begin_layout Plain Layout
35275 \begin_inset Formula $\bcancel{\int A=B}$
35284 <row topspace="1.5mm">
35285 <cell alignment="center" valignment="top" usebox="none">
35288 \begin_layout Plain Layout
35292 \begin_inset space \textvisiblespace{}
35298 \begin_inset space \textvisiblespace{}
35306 <cell alignment="center" valignment="top" usebox="none">
35309 \begin_layout Plain Layout
35310 \begin_inset Formula $\xcancel{\int A=B}$
35320 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35323 \begin_layout Plain Layout
35327 \begin_inset space \textvisiblespace{}
35333 \begin_inset space \textvisiblespace{}
35337 \begin_inset Formula $\to$
35345 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35348 \begin_layout Plain Layout
35349 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35365 \begin_layout Standard
35372 is especially suitable to visualize the reduction of fractions within formulas:
35373 \begin_inset Formula
35375 \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}}}
35383 \begin_layout Standard
35384 To change the size of
35391 \begin_inset Quotes eld
35395 \begin_inset Quotes erd
35398 value one can add the \SpecialChar LaTeX
35402 \begin_layout Standard
35407 PassOptionsToPackage{option}{cancel}
35410 \begin_layout Standard
35419 which leads to the same size as for the canceled value, or
35423 which makes is it a bit smaller than normal.
35426 \begin_layout Standard
35427 To color the cancellation bar one adds this command as \SpecialChar TeX
35431 \begin_layout Standard
35443 \begin_layout Standard
35448 can be replaced by a color of your choice.
35451 \begin_layout Standard
35455 \begin_layout Plain Layout
35471 \begin_layout Standard
35472 \begin_inset Formula
35474 \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}}}
35482 \begin_layout Standard
35486 \begin_layout Plain Layout
35500 \begin_inset Note Note
35503 \begin_layout Plain Layout
35512 \begin_layout Standard
35513 For further customizations, see the documentation of the package
35518 \begin_inset CommandInset citation
35525 \begin_inset Index idx
35528 \begin_layout Plain Layout
35537 \begin_layout Standard
35541 \begin_layout Plain Layout
35551 \begin_inset Note Note
35554 \begin_layout Plain Layout
35555 The following will be displayed when the \SpecialChar LaTeX
35568 \begin_layout Standard
35569 You need to install the \SpecialChar LaTeX
35574 to see the rest of this subsection in the output.
35577 \begin_layout Standard
35581 \begin_layout Plain Layout
35593 \begin_layout Subsection
35594 Formulas in Section Headings
35595 \begin_inset CommandInset label
35597 name "subsec:Formulas-in-Section"
35602 \begin_inset Index idx
35605 \begin_layout Plain Layout
35606 Formula ! in section headings
35614 \begin_layout Standard
35615 When formulas are used in section headings, the following has to be taken
35619 \begin_layout Standard
35620 \begin_inset Note Greyedout
35623 \begin_layout Plain Layout
35629 \begin_inset Index idx
35632 \begin_layout Plain Layout
35633 Packages ! hyperref
35638 support is enabled in the document settings dialog under
35641 \begin_inset space ~
35646 , PDF-bookmarks are created for every section heading in the table of contents.
35647 If a section heading contains formulas, they are incorrectly displayed
35648 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35657 \begin_layout Standard
35658 Both problems can be solved by inserting at the end of the section heading
35659 a short title with the menu
35661 Insert\SpecialChar menuseparator
35663 \begin_inset space ~
35669 Short titles are used as alternative for multiline section headings to
35670 keep the table of contents clearly arranged.
35671 Only the short title appears in the table of contents and therefore also
35672 in the PDF-bookmark.
35675 \begin_layout Standard
35676 When formulas should be used in the table of contents but
35680 is used, one can use the following command in \SpecialChar TeX
35684 \begin_layout Standard
35689 texorpdfstring{part}{alternative}
35690 \begin_inset Index idx
35693 \begin_layout Plain Layout
35704 \begin_layout Standard
35705 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35706 This can be characters, formulas, footnotes, but also cross-references.
35707 The alternative is used instead of the part for the bookmark.
35710 \begin_layout Standard
35711 Here are two example headings:
35712 \begin_inset VSpace -3mm
35719 \begin_layout Plain Layout
35731 \begin_layout Subsubsection
35732 Heading without formula in table of contents
35733 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35737 \begin_inset Argument 1
35740 \begin_layout Plain Layout
35741 Heading without formula in table of contents
35749 \begin_layout Subsubsection
35750 Heading with formula in table of contents
35754 \begin_layout Plain Layout
35764 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35771 \begin_layout Plain Layout
35781 \begin_layout Standard
35785 \begin_layout Plain Layout
35794 In the first heading a short title was used, in the second one
35803 \begin_layout Standard
35804 To get the same formatting as for the other headings, the complete heading
35813 \begin_layout Plain Layout
35815 \begin_inset CommandInset ref
35817 reference "subsec:Bold-Formulas"
35829 \begin_layout Subsection
35830 Formulas in multi-column Text
35831 \begin_inset Index idx
35834 \begin_layout Plain Layout
35835 Formula ! in multi-column text
35843 \begin_layout Standard
35844 Formulas in multi-column text are often too wide to fit into a column and
35845 thus need to be set over the whole page width.
35846 This is done by using the \SpecialChar LaTeX
35855 \begin_layout Plain Layout
35860 is part of every \SpecialChar LaTeX
35861 standard installation.
35867 \begin_inset Index idx
35870 \begin_layout Plain Layout
35871 Packages ! multicol
35876 , that is loaded with the \SpecialChar LaTeX
35880 \begin_layout Standard
35885 usepackage{multicol}
35888 \begin_layout Standard
35889 \begin_inset Note Greyedout
35892 \begin_layout Plain Layout
35893 Note that in this case the setting
35896 \begin_inset space ~
35903 Document\SpecialChar menuseparator
35909 \begin_inset space ~
35929 \begin_layout Standard
35930 Before the multi-column text the command
35933 \begin_layout Standard
35938 begin{multicols}{column number}
35941 \begin_layout Standard
35942 is written in \SpecialChar TeX
35944 The column number is a number in the range of 2
35945 \begin_inset space \thinspace{}
35949 \begin_inset space \thinspace{}
35953 Before the formula the multi-column text is ended by inserting the command
35956 \begin_layout Standard
35964 \begin_layout Standard
35965 in \SpecialChar TeX
35969 \begin_layout Standard
35970 Due to the command some space is automatically added before the formula.
35972 \begin_inset space \thinspace{}
35975 mm vertical space is inserted before the formula.
35976 When the formula style
35982 \begin_layout Plain Layout
35984 \begin_inset CommandInset ref
35986 reference "sec:Formula-Styles"
35998 \begin_inset space \thinspace{}
36001 mm space is inserted instead.
36004 \begin_layout Standard
36005 As example a multi-column text with a displayed formula:
36008 \begin_layout Standard
36014 \begin_layout Plain Layout
36018 begin{multicols}{2}
36023 Das Spektrum wird fouriertransformiert.
36024 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36025 , Lösungsmittel) zu trennen.
36026 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36027 nun das Aussehen des Ausgangssignals.
36028 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36029 über alle Phasen integrieren muss.
36031 \begin_inset Formula $S$
36034 unser normiertes Ausgangssignal und
36035 \begin_inset Formula $P$
36038 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36042 \begin_layout Plain Layout
36052 \begin_inset VSpace -6mm
36056 \begin_inset Formula
36058 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36067 \begin_layout Plain Layout
36071 begin{multicols}{2}
36077 \begin_inset Formula $S_{0}$
36080 das Signal ohne Gradient ist und die Normierungsbedingung
36081 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36085 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36087 \begin_inset Formula $\nicefrac{\pi}{2}$
36091 \begin_inset space \thinspace{}
36094 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36095 das Signal zusätzlich abschwächt.
36096 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36098 \begin_inset Formula $T_{2}$
36104 \begin_layout Standard
36110 \begin_layout Plain Layout
36122 \begin_layout Subsection
36123 Formulas with Description of Variables
36124 \begin_inset Index idx
36127 \begin_layout Plain Layout
36128 Formula ! with description of variables
36136 \begin_layout Standard
36137 To describe variables within a formula, like in formula
36138 \begin_inset CommandInset ref
36140 reference "eq:within"
36149 \begin_inset Formula $n$
36153 \begin_inset space ~
36156 matrix is used with left aligned columns for the
36157 \begin_inset Formula $n$
36164 \begin_layout Plain Layout
36166 \begin_inset CommandInset ref
36168 reference "sec:Matrices"
36177 To set the description in a smaller size, before the matrix e.
36178 \begin_inset space \thinspace{}
36182 \begin_inset space \space{}
36195 \begin_layout Plain Layout
36197 \begin_inset CommandInset ref
36199 reference "subsec:Font-Sizes"
36211 \begin_layout Standard
36212 When the formula style
36218 \begin_layout Plain Layout
36220 \begin_inset CommandInset ref
36222 reference "sec:Formula-Styles"
36243 \begin_layout Plain Layout
36250 only works in formulas with the style
36255 \begin_inset CommandInset ref
36257 reference "subsec:Variable-Space"
36266 is inserted before and after the matrix to have the same separation of
36267 the matrix from the equation and the side margin.
36270 \begin_layout Standard
36271 When the formula style
36275 is used, the method described in
36276 \begin_inset CommandInset ref
36278 reference "subsec:Flalign-Environment"
36282 is used to indent formulas.
36284 \begin_inset CommandInset ref
36286 reference "eq:within"
36290 consists of five columns where in the first two columns contain the equation,
36291 the third the matrix and the last one an empty \SpecialChar TeX
36293 \begin_inset Formula
36295 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36296 \rho & \textrm{density}\\
36297 V & \textrm{volume}\\
36298 g & \textrm{gravitational acceleration}
36299 \end{array} & & {}\label{eq:within}
36307 \begin_layout Subsection
36308 Upright small Greek Letters
36309 \begin_inset CommandInset label
36311 name "subsec:Upright-small-Greek"
36316 \begin_inset Index idx
36319 \begin_layout Plain Layout
36320 Greek letters ! upright
36328 \begin_layout Standard
36329 Most of the math fonts only provide italic small Greek letters.
36330 But for symbols of elementary particles like pions and neutrinos, upright
36331 Greek letters are needed.
36340 \begin_layout Plain Layout
36345 is part of the \SpecialChar LaTeX
36351 \begin_inset Index idx
36354 \begin_layout Plain Layout
36359 \begin_layout Plain Layout
36379 \begin_inset Index idx
36382 \begin_layout Plain Layout
36388 that is loaded with the \SpecialChar LaTeX
36392 \begin_layout Standard
36397 usepackage{upgreek}
36400 \begin_layout Standard
36406 \begin_layout Plain Layout
36416 \begin_inset Note Note
36419 \begin_layout Plain Layout
36420 The following table will only be displayed when the \SpecialChar LaTeX
36430 They are created when the command for a small Greek letter is started with
36436 For example the command
36443 \begin_inset Formula $\uptau$
36449 \begin_layout Standard
36450 With these commands reactions of elementary particles can be typeset:
36451 \begin_inset Formula
36453 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36461 \begin_layout Standard
36462 The upright letters are more bold and wider than the italic ones.
36463 They should therefore not be used for units like
36464 \begin_inset Quotes eld
36468 \begin_inset Quotes erd
36474 \begin_layout Standard
36478 \begin_layout Plain Layout
36488 \begin_inset Note Note
36491 \begin_layout Plain Layout
36492 The following will be displayed when the \SpecialChar LaTeX
36505 \begin_layout Standard
36506 You need to install the \SpecialChar LaTeX
36511 to see the rest of this subsection in the output.
36514 \begin_layout Standard
36518 \begin_layout Plain Layout
36530 \begin_layout Subsection
36531 Text Characters in Formulas
36532 \begin_inset Index idx
36535 \begin_layout Plain Layout
36544 \begin_layout Standard
36545 In some cases you might want to insert text characters directly into formulas.
36546 When for example the centered dot · is often used in formulas like
36547 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36550 , one would have to insert the command
36560 \begin_layout Plain Layout
36562 \begin_inset CommandInset ref
36564 reference "subsec:Binary-Operators"
36573 all the time, because this character is defined in all encodings as text
36575 But the encoding can be changed by this \SpecialChar LaTeX
36579 \begin_layout Standard
36584 Declare Inputtext{183}{
36594 f\SpecialChar ligaturebreak
36598 \begin_layout Standard
36599 The character encoding (menu
36601 Document\SpecialChar menuseparator
36602 Settings\SpecialChar menuseparator
36605 ) specifies what character appears when a keyboard key is pressed.
36606 When the key for the character '·' is pressed, internally the command
36613 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36615 With the changed encoding the right command is chosen automatically, depending
36616 on if the character was inserted into a formula or not.
36619 \begin_layout Standard
36620 The encoding of several characters is saved in definition files.
36621 For example the encoding
36625 is defined in the file
36629 which is in the installation folder of \SpecialChar LaTeX
36631 Encodings should only be changed via the \SpecialChar LaTeX
36632 -preamble and not in the definition
36634 Otherwise documents could not be edited by other \SpecialChar LyX
36635 users working on other
36639 \begin_layout Standard
36640 \begin_inset VSpace medskip
36643 Besides the centered dot, in this document the degree sign ° is defined
36644 with the following \SpecialChar LaTeX
36645 -preamble line so that it can be directly inserted into
36649 \begin_layout Standard
36654 DeclareInputtext{176}{
36664 f\SpecialChar ligaturebreak
36668 \begin_layout Subsection
36670 -comments in formulas
36671 \begin_inset Index idx
36674 \begin_layout Plain Layout
36684 \begin_layout Standard
36685 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36687 code of your file with the menu
36689 Insert\SpecialChar menuseparator
36690 Note\SpecialChar menuseparator
36694 This is not possible in a formula but you can insert \SpecialChar LaTeX
36699 \begin_layout Standard
36707 \begin_layout Standard
36708 This creates a box in which you can write your comment.
36709 Due to a bug in \SpecialChar LyX
36714 \begin_layout Plain Layout
36715 \begin_inset CommandInset href
36717 name "LyX-bug #9002"
36718 target "http://www.lyx.org/trac/ticket/9002"
36727 you cannot write normal text inside the comment, even when you use mathematical
36728 text, you will see its \SpecialChar LaTeX
36729 -commands in the \SpecialChar LaTeX
36731 \begin_inset Newline newline
36734 This a formula with a \SpecialChar LaTeX
36736 \begin_inset Formula
36738 A=B%\text{This is the comment}
36746 \begin_layout Standard
36747 \begin_inset Newpage newpage
36753 \begin_layout Section
36756 \begin_inset Index idx
36759 \begin_layout Plain Layout
36768 \begin_layout Standard
36769 This section is a summary of the most important typographic rules, listed
36774 \begin_layout Plain Layout
36775 This collection was partly taken from the German semi-official dictionary
36777 \begin_inset Quotes eld
36781 \begin_inset Quotes erd
36785 \begin_inset CommandInset citation
36791 that lists some of the ISO rules.
36792 More rules are listed in
36793 \begin_inset CommandInset citation
36807 \begin_layout Itemize
36816 \begin_layout Plain Layout
36817 done with font styles, see
36818 \begin_inset CommandInset ref
36820 reference "subsec:Font-Styles"
36829 , no matter if they appear in italic text: 30
36830 \begin_inset space \thinspace{}
36834 \begin_inset Newline newline
36837 Between the value and the unit is the smallest space, see
36838 \begin_inset CommandInset ref
36840 reference "subsec:Predefined-Space"
36845 \begin_inset Newline newline
36848 This convention is automatically fulfilled when the command
36855 When it is entered to a formula, two boxes appear.
36856 In the first one the value is inserted, in the second one the unit, and
36858 \begin_inset Formula $\unit[30]{km/h}$
36862 \begin_inset space \thinspace{}
36872 is not a real \SpecialChar LaTeX
36873 command but the command
36879 , therefore you cannot use it in \SpecialChar TeX
36883 \begin_layout Itemize
36884 Percent and perthousand signs are set like physical units:
36885 \begin_inset Newline newline
36889 \begin_inset space \thinspace{}
36895 \begin_layout Itemize
36896 The degree sign follows directly on the value: 15°, but not when it is used
36898 \begin_inset space \thinspace{}
36904 \begin_layout Itemize
36905 In numbers with more than four digits the smallest space is inserted before
36906 every third digit to group them:
36916 \begin_inset space \thinspace{}
36920 \begin_inset space \thinspace{}
36926 \begin_layout Itemize
36927 For dimensions like 120×90×40
36928 \begin_inset space \thinspace{}
36931 cm the multiplication sign
36932 \begin_inset Quotes eld
36936 \begin_inset Quotes erd
36940 It is available either via the command
36948 Insert\SpecialChar menuseparator
36949 Special Character\SpecialChar menuseparator
36955 \begin_layout Itemize
36956 Functions with names consisting of several letters are set upright to avoid
36958 \begin_inset CommandInset ref
36960 reference "subsec:Predefined-Functions"
36967 \begin_layout Itemize
36968 Indices consisting of several letters, are set upright:
36969 \begin_inset Formula $E_{\mathrm{kin}}$
36973 \begin_inset Newline newline
36976 Components of matrices are set italic:
36977 \begin_inset Formula $\hat{H}_{kl}$
36983 \begin_layout Itemize
36984 The differentiation/integration operator 'd', the Euler's number 'e' and
36985 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36989 \begin_layout Itemize
36990 The character that denotes a
36994 transformation is inserted either by the command
36999 \begin_inset space \textvisiblespace{}
37006 Insert\SpecialChar menuseparator
37007 Special Character\SpecialChar menuseparator
37008 Symbols\SpecialChar menuseparator
37010 \begin_inset space ~
37016 \begin_inset Formula $\mathscr{F}$
37022 \begin_layout Standard
37023 \begin_inset Newpage newpage
37029 \begin_layout Section
37031 \begin_inset Index idx
37034 \begin_layout Plain Layout
37043 \begin_layout Standard
37044 Some characters and symbols can be created with several commands.
37045 Here is a list of the synonym commands:
37048 \begin_layout Standard
37049 \begin_inset VSpace bigskip
37053 \begin_inset space \hfill{}
37057 \begin_inset Tabular
37058 <lyxtabular version="3" rows="12" columns="2">
37059 <features booktabs="true" tabularvalignment="middle">
37060 <column alignment="center" valignment="top" width="0pt">
37061 <column alignment="center" valignment="top" width="0pt">
37063 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37066 \begin_layout Plain Layout
37072 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37075 \begin_layout Plain Layout
37083 <cell alignment="center" valignment="top" usebox="none">
37086 \begin_layout Plain Layout
37094 <cell alignment="center" valignment="top" usebox="none">
37097 \begin_layout Plain Layout
37105 <cell alignment="center" valignment="top" usebox="none">
37108 \begin_layout Plain Layout
37116 <cell alignment="center" valignment="top" usebox="none">
37119 \begin_layout Plain Layout
37129 <cell alignment="center" valignment="top" usebox="none">
37132 \begin_layout Plain Layout
37140 <cell alignment="center" valignment="top" usebox="none">
37143 \begin_layout Plain Layout
37153 <cell alignment="center" valignment="top" usebox="none">
37156 \begin_layout Plain Layout
37164 <cell alignment="center" valignment="top" usebox="none">
37167 \begin_layout Plain Layout
37175 <cell alignment="center" valignment="top" usebox="none">
37178 \begin_layout Plain Layout
37186 <cell alignment="center" valignment="top" usebox="none">
37189 \begin_layout Plain Layout
37197 <cell alignment="center" valignment="top" usebox="none">
37200 \begin_layout Plain Layout
37208 <cell alignment="center" valignment="top" usebox="none">
37211 \begin_layout Plain Layout
37221 <cell alignment="center" valignment="top" usebox="none">
37224 \begin_layout Plain Layout
37232 <cell alignment="center" valignment="top" usebox="none">
37235 \begin_layout Plain Layout
37245 <cell alignment="center" valignment="top" usebox="none">
37248 \begin_layout Plain Layout
37256 <cell alignment="center" valignment="top" usebox="none">
37259 \begin_layout Plain Layout
37269 <cell alignment="center" valignment="top" usebox="none">
37272 \begin_layout Plain Layout
37280 <cell alignment="center" valignment="top" usebox="none">
37283 \begin_layout Plain Layout
37293 <cell alignment="center" valignment="top" usebox="none">
37296 \begin_layout Plain Layout
37304 <cell alignment="center" valignment="top" usebox="none">
37307 \begin_layout Plain Layout
37315 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37318 \begin_layout Plain Layout
37326 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37329 \begin_layout Plain Layout
37341 \begin_inset space \hfill{}
37345 \begin_inset Tabular
37346 <lyxtabular version="3" rows="12" columns="2">
37347 <features booktabs="true" tabularvalignment="middle">
37348 <column alignment="center" valignment="top" width="0pt">
37349 <column alignment="center" valignment="top" width="0pt">
37351 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37354 \begin_layout Plain Layout
37360 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37363 \begin_layout Plain Layout
37371 <cell alignment="center" valignment="top" usebox="none">
37374 \begin_layout Plain Layout
37382 <cell alignment="center" valignment="top" usebox="none">
37385 \begin_layout Plain Layout
37397 <cell alignment="center" valignment="top" usebox="none">
37400 \begin_layout Plain Layout
37408 <cell alignment="center" valignment="top" usebox="none">
37411 \begin_layout Plain Layout
37421 <cell alignment="center" valignment="top" usebox="none">
37424 \begin_layout Plain Layout
37432 <cell alignment="center" valignment="top" usebox="none">
37435 \begin_layout Plain Layout
37445 <cell alignment="center" valignment="top" usebox="none">
37448 \begin_layout Plain Layout
37456 <cell alignment="center" valignment="top" usebox="none">
37459 \begin_layout Plain Layout
37467 <cell alignment="center" valignment="top" usebox="none">
37470 \begin_layout Plain Layout
37478 <cell alignment="center" valignment="top" usebox="none">
37481 \begin_layout Plain Layout
37489 <cell alignment="center" valignment="top" usebox="none">
37492 \begin_layout Plain Layout
37500 <cell alignment="center" valignment="top" usebox="none">
37503 \begin_layout Plain Layout
37513 <cell alignment="center" valignment="top" usebox="none">
37516 \begin_layout Plain Layout
37524 <cell alignment="center" valignment="top" usebox="none">
37527 \begin_layout Plain Layout
37537 <cell alignment="center" valignment="top" usebox="none">
37540 \begin_layout Plain Layout
37548 <cell alignment="center" valignment="top" usebox="none">
37551 \begin_layout Plain Layout
37561 <cell alignment="center" valignment="top" usebox="none">
37564 \begin_layout Plain Layout
37572 <cell alignment="center" valignment="top" usebox="none">
37575 \begin_layout Plain Layout
37585 <cell alignment="center" valignment="top" usebox="none">
37588 \begin_layout Plain Layout
37596 <cell alignment="center" valignment="top" usebox="none">
37599 \begin_layout Plain Layout
37609 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37612 \begin_layout Plain Layout
37620 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37623 \begin_layout Plain Layout
37637 \begin_inset space \hfill{}
37643 \begin_layout Standard
37644 \begin_inset Newpage newpage
37650 \begin_layout Bibliography
37651 \begin_inset CommandInset bibitem
37652 LatexCommand bibitem
37664 The \SpecialChar LaTeX
37668 Addison Wesley, 2004
37671 \begin_layout Bibliography
37672 \begin_inset CommandInset bibitem
37673 LatexCommand bibitem
37679 \begin_inset CommandInset href
37682 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37686 of \SpecialChar LaTeX
37690 \begin_layout Bibliography
37691 \begin_inset CommandInset bibitem
37692 LatexCommand bibitem
37698 \begin_inset CommandInset href
37701 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37709 \begin_layout Plain Layout
37718 -\SpecialChar LaTeX
37722 \begin_layout Bibliography
37723 \begin_inset CommandInset bibitem
37724 LatexCommand bibitem
37730 \begin_inset CommandInset href
37733 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37737 of all symbols available with \SpecialChar LaTeX
37741 \begin_layout Bibliography
37742 \begin_inset CommandInset bibitem
37743 LatexCommand bibitem
37749 \begin_inset CommandInset href
37751 name "Documentation"
37752 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37756 of the \SpecialChar LaTeX
37762 \begin_inset Index idx
37765 \begin_layout Plain Layout
37774 \begin_layout Bibliography
37775 \begin_inset CommandInset bibitem
37776 LatexCommand bibitem
37782 \begin_inset CommandInset href
37784 name "Documentation"
37785 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37789 of the \SpecialChar LaTeX
37795 \begin_inset Index idx
37798 \begin_layout Plain Layout
37799 Packages ! hyperref
37807 \begin_layout Bibliography
37808 \begin_inset CommandInset bibitem
37809 LatexCommand bibitem
37815 \begin_inset CommandInset href
37817 name "Documentation"
37818 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37822 of the \SpecialChar LaTeX
37828 \begin_inset Index idx
37831 \begin_layout Plain Layout
37840 \begin_layout Bibliography
37841 \begin_inset CommandInset bibitem
37842 LatexCommand bibitem
37853 Auflage, Duden 2001
37856 \begin_layout Bibliography
37857 \begin_inset CommandInset bibitem
37858 LatexCommand bibitem
37864 \begin_inset CommandInset href
37867 target "http://physics.nist.gov/Document/checklist.pdf"
37871 for reviewing manuscripts
37874 \begin_layout Standard
37875 \begin_inset CommandInset index_print
37876 LatexCommand printindex