1 #LyX 2.2 created this file. For more info see http://www.lyx.org/
8 % DO NOT ALTER THIS PREAMBLE!!!
10 % This preamble is designed to ensure that the file prints
11 % out as advertised. If you mess with this preamble,
12 % parts of this document may not print out as expected. If you
13 % have problems LaTeXing this file, please contact
14 % the documentation team
15 % email: lyx-docs@lists.lyx.org
17 % solves the following problem:
18 % If the dection number consits of too many numerals the section heading
19 % will be printed in the TOC without a space between it and the section number.
20 % As solution more space between the number and the heading is inserted:
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22 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
24 % increase link area for cross-references and autoname them,
25 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
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31 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
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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"
3406 that creates one or more phantom characters.
3413 a small blue box appears that is superposed with two red arrows.
3414 The arrows indicate that the complete width and height of the box content
3415 will be created as placeholder.
3416 Phantom characters are accordingly placeholders with the size of the characters.
3417 \begin_inset Separator parbreak
3423 \begin_layout Standard
3425 \begin_inset Tabular
3426 <lyxtabular version="3" rows="4" columns="2">
3427 <features booktabs="true" tabularvalignment="middle">
3428 <column alignment="center" valignment="top" width="0pt">
3429 <column alignment="center" valignment="top" width="0pt">
3431 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3434 \begin_layout Plain Layout
3440 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3443 \begin_layout Plain Layout
3450 <row topspace="1.5mm">
3451 <cell alignment="center" valignment="top" usebox="none">
3454 \begin_layout Plain Layout
3456 \begin_inset space \textvisiblespace{}
3462 \begin_inset space \textvisiblespace{}
3466 \begin_inset Formula $\to$
3470 \begin_inset space \textvisiblespace{}
3478 <cell alignment="center" valignment="top" usebox="none">
3481 \begin_layout Plain Layout
3482 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3491 <row topspace="1.5mm" bottomspace="0.5mm">
3492 <cell alignment="center" valignment="top" usebox="none">
3495 \begin_layout Plain Layout
3497 \begin_inset space \textvisiblespace{}
3503 \begin_inset space \textvisiblespace{}
3507 \begin_inset Formula $\to$
3511 \begin_inset space \textvisiblespace{}
3519 <cell alignment="center" valignment="top" usebox="none">
3522 \begin_layout Plain Layout
3523 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3532 <row topspace="1.5mm" bottomspace="0.5mm">
3533 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3536 \begin_layout Plain Layout
3540 \begin_inset space \textvisiblespace{}
3546 \begin_inset space \textvisiblespace{}
3550 \begin_inset Formula $\to$
3554 \begin_inset space \textvisiblespace{}
3562 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3565 \begin_layout Plain Layout
3566 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3582 \begin_layout Standard
3583 Furthermore there are the commands
3590 \begin_inset Index idx
3593 \begin_layout Plain Layout
3614 \begin_inset Index idx
3617 \begin_layout Plain Layout
3638 creates only space for the maximal height of the characters in the box
3639 but not for its width.
3646 creates only space for the width of the box content.
3647 Therefore the boxes of both commands have only one red arrow.
3650 \begin_layout Standard
3651 For example the command
3656 \begin_inset space \textvisiblespace{}
3663 creates space for the height of the integral sign,
3667 \begin_layout Plain Layout
3674 creates an integral sign, see
3675 \begin_inset CommandInset ref
3677 reference "subsec:Big-Operators"
3686 because this is the larger character.
3687 An example application is in
3688 \begin_inset CommandInset ref
3690 reference "subsec:Multiline-Brackets"
3697 \begin_layout Standard
3698 Placeholders can also be used for text when they are inserted via the menu
3701 Insert\SpecialChar menuseparator
3702 Formatting\SpecialChar menuseparator
3708 \begin_layout Standard
3710 \begin_inset Newline newline
3714 \begin_inset Phantom Phantom
3717 \begin_layout Plain Layout
3726 \begin_layout Subsection
3728 \begin_inset Index idx
3731 \begin_layout Plain Layout
3738 \begin_inset Index idx
3741 \begin_layout Plain Layout
3742 Formula ! underlined
3750 \begin_layout Standard
3752 \begin_inset Tabular
3753 <lyxtabular version="3" rows="4" columns="2">
3754 <features booktabs="true" tabularvalignment="middle">
3755 <column alignment="center" valignment="top" width="0pt">
3756 <column alignment="center" valignment="top" width="0pt">
3758 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3761 \begin_layout Plain Layout
3767 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3770 \begin_layout Plain Layout
3777 <row topspace="2mm">
3778 <cell alignment="center" valignment="top" usebox="none">
3781 \begin_layout Plain Layout
3785 \begin_inset space \textvisiblespace{}
3789 \begin_inset Index idx
3792 \begin_layout Plain Layout
3805 <cell alignment="center" valignment="top" usebox="none">
3808 \begin_layout Plain Layout
3809 \begin_inset Formula $\overline{A+B}$
3818 <row bottomspace="1mm">
3819 <cell alignment="center" valignment="top" usebox="none">
3822 \begin_layout Plain Layout
3826 \begin_inset space \textvisiblespace{}
3830 \begin_inset Index idx
3833 \begin_layout Plain Layout
3846 <cell alignment="center" valignment="top" usebox="none">
3849 \begin_layout Plain Layout
3850 \begin_inset Formula $\underline{A+B}$
3859 <row topspace="2mm" bottomspace="1mm">
3860 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3863 \begin_layout Plain Layout
3867 \begin_inset space \textvisiblespace{}
3873 \begin_inset space \textvisiblespace{}
3881 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3884 \begin_layout Plain Layout
3885 \begin_inset Formula $\overline{\underline{A+B}}$
3901 \begin_layout Standard
3902 In the last example it doesn't matter if first
3917 \begin_layout Standard
3918 To double underline use
3927 \begin_layout Standard
3928 It is possible to place up to 6 lines above or below characters.
3931 \begin_layout Standard
3932 \begin_inset VSpace bigskip
3935 Custom lines can be created using the command
3942 \begin_inset Index idx
3945 \begin_layout Plain Layout
3953 which has the following scheme:
3956 \begin_layout Standard
3961 rule[vertical offset]{length}{thickness}
3964 \begin_layout Standard
3965 The optional vertical offset shifts the line upwards (or downwards, when
3966 the value is negative).
3968 \begin_inset CommandInset ref
3970 reference "tab:Available-units"
3974 can be used for the values.
3975 Here are two example lines created with the commands
3976 \begin_inset Newline newline
3983 rule[-2ex]{3cm}{2pt}
3994 \begin_layout Standard
3996 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4002 \begin_layout Standard
4009 can also be used for text when a line is inserted via the menu
4011 Insert\SpecialChar menuseparator
4012 Formatting\SpecialChar menuseparator
4014 \begin_inset space ~
4022 \begin_layout Standard
4024 \begin_inset CommandInset line
4035 \begin_layout Subsection
4037 \begin_inset CommandInset label
4039 name "subsec:Ellipses"
4044 \begin_inset Index idx
4047 \begin_layout Plain Layout
4056 \begin_layout Standard
4057 There are different types of ellipses available.
4061 \begin_layout Plain Layout
4062 In the math toolbar in the submenu of the button
4065 arg "math-insert \\ldots"
4073 For listings dots at the baseline are used (
4080 \begin_inset Index idx
4083 \begin_layout Plain Layout
4091 ), while for operations dots are needed that are on the same height as the
4099 \begin_inset Index idx
4102 \begin_layout Plain Layout
4111 When using the command
4118 \begin_inset Index idx
4121 \begin_layout Plain Layout
4129 , \SpecialChar LaTeX
4130 decides on the basis of the next character what type is used.
4131 \begin_inset Separator parbreak
4137 \begin_layout Standard
4139 \begin_inset Tabular
4140 <lyxtabular version="3" rows="9" columns="2">
4141 <features booktabs="true" tabularvalignment="middle">
4142 <column alignment="center" valignment="top" width="0pt">
4143 <column alignment="center" valignment="top" width="0pt">
4145 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4148 \begin_layout Plain Layout
4154 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4157 \begin_layout Plain Layout
4165 <cell alignment="center" valignment="top" usebox="none">
4168 \begin_layout Plain Layout
4170 \begin_inset space \textvisiblespace{}
4176 \begin_inset space \textvisiblespace{}
4184 <cell alignment="center" valignment="top" usebox="none">
4187 \begin_layout Plain Layout
4188 \begin_inset Formula $A_{1},\dots,A_{n}$
4198 <cell alignment="center" valignment="top" usebox="none">
4201 \begin_layout Plain Layout
4203 \begin_inset space \textvisiblespace{}
4209 \begin_inset space \textvisiblespace{}
4217 <cell alignment="center" valignment="top" usebox="none">
4220 \begin_layout Plain Layout
4221 \begin_inset Formula $A_{1}+\dots+A_{n}$
4231 <cell alignment="center" valignment="top" usebox="none">
4234 \begin_layout Plain Layout
4236 \begin_inset space \textvisiblespace{}
4242 \begin_inset space \textvisiblespace{}
4250 <cell alignment="center" valignment="top" usebox="none">
4253 \begin_layout Plain Layout
4254 \begin_inset Formula $A_{1},\ldots,A_{n}$
4264 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4267 \begin_layout Plain Layout
4269 \begin_inset space \textvisiblespace{}
4275 \begin_inset space \textvisiblespace{}
4283 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4286 \begin_layout Plain Layout
4287 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4297 <cell alignment="center" valignment="top" usebox="none">
4300 \begin_layout Plain Layout
4308 <cell alignment="center" valignment="top" usebox="none">
4311 \begin_layout Plain Layout
4312 \begin_inset Formula $\vdots$
4322 <cell alignment="center" valignment="top" usebox="none">
4325 \begin_layout Plain Layout
4333 <cell alignment="center" valignment="top" usebox="none">
4336 \begin_layout Plain Layout
4337 \begin_inset Formula $\ddots$
4347 <cell alignment="center" valignment="top" usebox="none">
4350 \begin_layout Plain Layout
4358 <cell alignment="center" valignment="top" usebox="none">
4361 \begin_layout Plain Layout
4362 \begin_inset Formula $\iddots$
4372 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4375 \begin_layout Plain Layout
4377 \begin_inset space \thinspace{}
4380 matrix with the different dots
4385 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4388 \begin_layout Plain Layout
4389 \begin_inset Formula $\begin{array}{ccc}
4390 A_{11} & \cdots & A_{1m}\\
4391 \vdots & \ddots & \vdots\\
4392 A_{n1} & \cdots & A_{nm}
4409 \begin_layout Standard
4410 The ellipses available in menu
4412 Insert\SpecialChar menuseparator
4414 \begin_inset space ~
4428 \begin_layout Standard
4429 \begin_inset VSpace medskip
4438 , one of the options
4440 Use mathdots package (automatically)
4442 must be set in the document settings under
4445 \begin_inset space ~
4451 \begin_inset Newline newline
4456 Use mathdots package
4458 will improve the appearance of all dots in the documents if their font
4459 style or size is not the default.
4462 \begin_layout Standard
4463 \begin_inset VSpace medskip
4466 Specially for matrices there are ellipses that span over several columns.
4467 They are created with the command
4474 \begin_inset Index idx
4477 \begin_layout Plain Layout
4485 , that has the following scheme:
4488 \begin_layout Standard
4493 hdotsfor[distance]{number of columns}
4496 \begin_layout Standard
4497 The number of columns specifies how many columns should be spanned.
4498 Distance is a factor for the distance between the dots.
4501 \begin_layout Standard
4502 In the following matrix the command
4508 was inserted in the first box of the second line, to get an ellipsis with
4509 a dot distance twice as long as with the command
4516 \begin_inset Formula
4518 \left(\begin{array}{cccc}
4527 Note that the matrix fields that should be spanned must be empty, otherwise
4528 you get \SpecialChar LaTeX
4532 \begin_layout Standard
4533 \begin_inset VSpace bigskip
4536 Furthermore you can fill with the command
4543 \begin_inset Index idx
4546 \begin_layout Plain Layout
4554 the rest of a line with dots.
4555 The effect of these commands is the same as with
4562 \begin_inset CommandInset ref
4564 reference "subsec:Variable-Space"
4571 \begin_layout Standard
4572 For example the command
4577 \begin_inset space \textvisiblespace{}
4585 \begin_layout Standard
4586 \begin_inset Formula $A\dotfill B$
4592 \begin_layout Standard
4599 there is for a line the command
4606 \begin_inset Index idx
4609 \begin_layout Plain Layout
4620 \begin_layout Standard
4621 \begin_inset Formula $A\hrulefill B$
4627 \begin_layout Standard
4628 To use the commands for text, they have to be inserted in \SpecialChar TeX
4632 \begin_layout Section
4634 \begin_inset CommandInset label
4641 \begin_inset Index idx
4644 \begin_layout Plain Layout
4653 \begin_layout Standard
4654 Matrices can be inserted via the math toolbar button
4657 arg "dialog-show mathmatrix"
4662 Insert\SpecialChar menuseparator
4663 Math\SpecialChar menuseparator
4667 In the matrix dialog you can specify the number of columns and rows, the
4668 alignment and the decoration.
4669 The vertical alignment is only of importance for matrices in inline formulas:
4672 \begin_layout Standard
4673 The first matrix is top
4674 \begin_inset Formula $\begin{array}[t]{cccc}
4682 \begin_inset Formula $\begin{array}{cccc}
4689 and the third bottom
4690 \begin_inset Formula $\begin{array}[b]{cccc}
4700 \begin_layout Standard
4701 The horizontal alignment specifies how the column entries should be aligned.
4702 It is set by entering a letter for every column.
4707 denotes left aligned,
4716 To create for example a 4
4721 \begin_inset space ~
4724 matrix where the first column is left aligned, the second and third are
4725 centered and the last one is right aligned, one enters for the horizontal
4731 Normally in a matrix all columns are centered, therefore the default for
4739 \begin_layout Standard
4740 Horizontal alignment:
4743 \begin_layout Standard
4749 \begin_inset Formula $\begin{array}{lll}
4761 \begin_inset Formula $\begin{array}{ccc}
4773 \begin_inset Formula $\begin{array}{rrr}
4783 \begin_layout Standard
4784 To add or delete rows and columns subsequently, the math toolbar buttons
4788 arg "inset-modify tabular append-row"
4794 arg "inset-modify tabular delete-row"
4798 \begin_inset space \thinspace{}
4803 Edit\SpecialChar menuseparator
4807 New rows can also be created with
4810 arg "newline-insert newline"
4816 \begin_layout Standard
4817 \begin_inset VSpace bigskip
4824 adds parentheses in the selected style around the matrix.
4825 Alternatively, parentheses can can either be created with the commands
4833 \begin_inset Index idx
4836 \begin_layout Plain Layout
4851 \begin_inset Index idx
4854 \begin_layout Plain Layout
4865 \begin_inset space ~
4871 \begin_inset CommandInset ref
4873 reference "subsec:Automatic-Bracket-Size"
4877 , or by using the following commands:
4878 \begin_inset VSpace medskip
4884 \begin_layout Standard
4885 \begin_inset space \hfill{}
4889 \begin_inset Tabular
4890 <lyxtabular version="3" rows="4" columns="2">
4891 <features booktabs="true" tabularvalignment="middle">
4892 <column alignment="center" valignment="top" width="0pt">
4893 <column alignment="center" valignment="top">
4895 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4898 \begin_layout Plain Layout
4904 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4907 \begin_layout Plain Layout
4914 <row topspace="1.5mm">
4915 <cell alignment="center" valignment="top" usebox="none">
4918 \begin_layout Plain Layout
4922 \begin_inset space \textvisiblespace{}
4930 \begin_inset space \thinspace{}
4938 <cell alignment="center" valignment="top" usebox="none">
4941 \begin_layout Plain Layout
4942 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4943 0 & \textrm{-}\mathrm{i}\\
4945 \end{array}\end{bmatrix}$
4954 <row topspace="1.5mm" bottomspace="0.5mm">
4955 <cell alignment="center" valignment="top" usebox="none">
4958 \begin_layout Plain Layout
4962 \begin_inset space \textvisiblespace{}
4970 \begin_inset space \thinspace{}
4978 <cell alignment="center" valignment="top" usebox="none">
4981 \begin_layout Plain Layout
4982 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
4983 0 & \textrm{-}\mathrm{i}\\
4985 \end{array}\end{Bmatrix}$
4995 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4998 \begin_layout Plain Layout
5002 \begin_inset space \textvisiblespace{}
5010 \begin_inset space \thinspace{}
5018 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5021 \begin_layout Plain Layout
5022 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5023 0 & \textrm{-}\mathrm{i}\\
5025 \end{array}\end{pmatrix}$
5039 \begin_inset space \hfill{}
5043 \begin_inset Tabular
5044 <lyxtabular version="3" rows="4" columns="2">
5045 <features booktabs="true" tabularvalignment="middle">
5046 <column alignment="center" valignment="top" width="0pt">
5047 <column alignment="center" valignment="top">
5049 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5052 \begin_layout Plain Layout
5058 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5061 \begin_layout Plain Layout
5068 <row topspace="1.5mm">
5069 <cell alignment="center" valignment="top" usebox="none">
5072 \begin_layout Plain Layout
5076 \begin_inset space \textvisiblespace{}
5084 \begin_inset space \thinspace{}
5092 <cell alignment="center" valignment="top" usebox="none">
5095 \begin_layout Plain Layout
5096 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5097 0 & \textrm{-}\mathrm{i}\\
5099 \end{array}\end{vmatrix}$
5108 <row topspace="1.5mm" bottomspace="0.5mm">
5109 <cell alignment="center" valignment="top" usebox="none">
5112 \begin_layout Plain Layout
5116 \begin_inset space \textvisiblespace{}
5124 \begin_inset space \thinspace{}
5132 <cell alignment="center" valignment="top" usebox="none">
5135 \begin_layout Plain Layout
5136 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5137 0 & \textrm{-}\mathrm{i}\\
5139 \end{array}\end{Vmatrix}$
5149 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5152 \begin_layout Plain Layout
5156 \begin_inset space \textvisiblespace{}
5164 \begin_inset space \thinspace{}
5172 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5175 \begin_layout Plain Layout
5176 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5177 0 & \textrm{-}\mathrm{i}\\
5179 \end{array}\end{matrix}$
5193 \begin_inset space \hfill{}
5199 \begin_layout Standard
5200 \begin_inset VSpace medskip
5204 \begin_inset space \thinspace{}
5208 \begin_inset space \space{}
5217 is inserted, a blue box appears between two vertical lines where the matrix
5219 \begin_inset Newline newline
5222 Note that decorated matrices ignore the vertical alignment.
5225 \begin_layout Standard
5226 \begin_inset VSpace bigskip
5229 As all multiline formulas are matrices, the length
5236 \begin_inset Index idx
5239 \begin_layout Plain Layout
5247 that is described in
5248 \begin_inset CommandInset ref
5250 reference "subsec:Column-Separation"
5254 can also be used to change the column separation of matrices.
5257 \begin_layout Standard
5258 To change the row separation, the command
5265 \begin_inset Index idx
5268 \begin_layout Plain Layout
5277 It is used as follows:
5280 \begin_layout Standard
5287 arraystretch}{stretch factor}
5288 \begin_inset Index idx
5291 \begin_layout Plain Layout
5302 \begin_layout Standard
5309 assigns the stretch factor to the predefined command
5317 \begin_inset space \thinspace{}
5321 \begin_inset space \space{}
5324 the row separation, use the factor 2.
5325 This is then used for all following matrices.
5326 To go back to the original separation, assign the factor 1 to
5335 \begin_layout Standard
5336 To set matrices into a text line, the command
5343 \begin_inset Index idx
5346 \begin_layout Plain Layout
5355 When it is inserted a blue box with two dashed lines appears.
5356 In this box the matrix is inserted.
5359 \begin_layout Standard
5361 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5363 \end{smallmatrix}\right)$
5369 \begin_layout Section
5370 Brackets and Delimiters
5371 \begin_inset Index idx
5374 \begin_layout Plain Layout
5381 \begin_inset Index idx
5384 \begin_layout Plain Layout
5393 \begin_layout Subsection
5394 Vertical Brackets and Delimiters
5395 \begin_inset Index idx
5398 \begin_layout Plain Layout
5407 \begin_layout Standard
5408 \begin_inset space \hfill{}
5412 \begin_inset Tabular
5413 <lyxtabular version="3" rows="9" columns="2">
5414 <features booktabs="true" tabularvalignment="middle">
5415 <column alignment="center" valignment="top" width="0pt">
5416 <column alignment="center" valignment="top" width="0pt">
5418 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5421 \begin_layout Plain Layout
5427 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5430 \begin_layout Plain Layout
5438 <cell alignment="center" valignment="top" usebox="none">
5441 \begin_layout Plain Layout
5447 <cell alignment="center" valignment="top" usebox="none">
5450 \begin_layout Plain Layout
5451 \begin_inset Formula $($
5461 <cell alignment="center" valignment="top" usebox="none">
5464 \begin_layout Plain Layout
5470 <cell alignment="center" valignment="top" usebox="none">
5473 \begin_layout Plain Layout
5474 \begin_inset Formula $\{$
5484 <cell alignment="center" valignment="top" usebox="none">
5487 \begin_layout Plain Layout
5493 <cell alignment="center" valignment="top" usebox="none">
5496 \begin_layout Plain Layout
5497 \begin_inset Formula $[$
5507 <cell alignment="center" valignment="top" usebox="none">
5510 \begin_layout Plain Layout
5518 <cell alignment="center" valignment="top" usebox="none">
5521 \begin_layout Plain Layout
5522 \begin_inset Formula $\langle$
5532 <cell alignment="center" valignment="top" usebox="none">
5535 \begin_layout Plain Layout
5543 <cell alignment="center" valignment="top" usebox="none">
5546 \begin_layout Plain Layout
5547 \begin_inset Formula $\lceil$
5557 <cell alignment="center" valignment="top" usebox="none">
5560 \begin_layout Plain Layout
5568 <cell alignment="center" valignment="top" usebox="none">
5571 \begin_layout Plain Layout
5572 \begin_inset Formula $\lfloor$
5582 <cell alignment="center" valignment="top" usebox="none">
5585 \begin_layout Plain Layout
5591 <cell alignment="center" valignment="top" usebox="none">
5594 \begin_layout Plain Layout
5595 \begin_inset Formula $/$
5605 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5608 \begin_layout Plain Layout
5614 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5617 \begin_layout Plain Layout
5618 \begin_inset Formula $|$
5632 \begin_inset space \hfill{}
5636 \begin_inset Tabular
5637 <lyxtabular version="3" rows="9" columns="2">
5638 <features booktabs="true" tabularvalignment="middle">
5639 <column alignment="center" valignment="top" width="0pt">
5640 <column alignment="center" valignment="top" width="0pt">
5642 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5645 \begin_layout Plain Layout
5651 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5654 \begin_layout Plain Layout
5662 <cell alignment="center" valignment="top" usebox="none">
5665 \begin_layout Plain Layout
5671 <cell alignment="center" valignment="top" usebox="none">
5674 \begin_layout Plain Layout
5675 \begin_inset Formula $)$
5685 <cell alignment="center" valignment="top" usebox="none">
5688 \begin_layout Plain Layout
5694 <cell alignment="center" valignment="top" usebox="none">
5697 \begin_layout Plain Layout
5698 \begin_inset Formula $\}$
5708 <cell alignment="center" valignment="top" usebox="none">
5711 \begin_layout Plain Layout
5717 <cell alignment="center" valignment="top" usebox="none">
5720 \begin_layout Plain Layout
5721 \begin_inset Formula $]$
5731 <cell alignment="center" valignment="top" usebox="none">
5734 \begin_layout Plain Layout
5742 <cell alignment="center" valignment="top" usebox="none">
5745 \begin_layout Plain Layout
5746 \begin_inset Formula $\rangle$
5756 <cell alignment="center" valignment="top" usebox="none">
5759 \begin_layout Plain Layout
5767 <cell alignment="center" valignment="top" usebox="none">
5770 \begin_layout Plain Layout
5771 \begin_inset Formula $\rceil$
5781 <cell alignment="center" valignment="top" usebox="none">
5784 \begin_layout Plain Layout
5792 <cell alignment="center" valignment="top" usebox="none">
5795 \begin_layout Plain Layout
5796 \begin_inset Formula $\rfloor$
5806 <cell alignment="center" valignment="top" usebox="none">
5809 \begin_layout Plain Layout
5819 <cell alignment="center" valignment="top" usebox="none">
5822 \begin_layout Plain Layout
5823 \begin_inset Formula $\backslash$
5833 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5836 \begin_layout Plain Layout
5844 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5847 \begin_layout Plain Layout
5848 \begin_inset Formula $\|$
5862 \begin_inset space \hfill{}
5868 \begin_layout Standard
5871 \begin_inset Note Greyedout
5874 \begin_layout Plain Layout
5887 \begin_inset Index idx
5890 \begin_layout Plain Layout
5898 must be used for the backslash, because the command
5906 produces a line break there.
5914 \begin_layout Standard
5915 For all characters listed above the size can be adjusted with the commands
5916 described in the following two subsections.
5917 When using these commands, the characters < and > can directly be used
5918 instead of the commands
5933 \begin_layout Subsubsection
5935 \begin_inset CommandInset label
5937 name "subsec:Manual-Bracket-Size"
5942 \begin_inset Index idx
5945 \begin_layout Plain Layout
5946 Bracket size ! manual
5954 \begin_layout Standard
5955 The bracket size can be specified manually by the \SpecialChar LaTeX
5963 \begin_inset Index idx
5966 \begin_layout Plain Layout
5999 denotes the smallest and
6005 the largest bracket size.
6008 \begin_layout Standard
6009 These commands are used to emphasize levels of brackets:
6010 \begin_inset Separator parbreak
6016 \begin_layout Standard
6018 \begin_inset Tabular
6019 <lyxtabular version="3" rows="2" columns="2">
6020 <features booktabs="true" tabularvalignment="middle">
6021 <column alignment="center" valignment="top" width="0pt">
6022 <column alignment="center" valignment="top" width="0pt">
6024 <cell alignment="center" valignment="top" usebox="none">
6027 \begin_layout Plain Layout
6028 all brackets in the same size:
6033 <cell alignment="center" valignment="top" usebox="none">
6036 \begin_layout Plain Layout
6037 \begin_inset Formula $((A+B)(A-B))^{C}$
6046 <row topspace="2mm">
6047 <cell alignment="center" valignment="top" usebox="none">
6050 \begin_layout Plain Layout
6056 <cell alignment="center" valignment="top" usebox="none">
6059 \begin_layout Plain Layout
6060 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6076 \begin_layout Standard
6077 For the second formula the command
6084 \begin_inset space \textvisiblespace{}
6092 \begin_layout Standard
6093 Here is an overview about all bracket sizes:
6094 \begin_inset Separator parbreak
6100 \begin_layout Standard
6117 \begin_inset space \textvisiblespace{}
6125 \begin_inset space \textvisiblespace{}
6129 \begin_inset space \textvisiblespace{}
6139 \begin_layout Standard
6141 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6147 \begin_layout Standard
6154 -commands there is the variant
6161 \begin_inset Index idx
6164 \begin_layout Plain Layout
6172 that adds a bit more space between the bracket and its content, and the
6186 \begin_inset Index idx
6189 \begin_layout Plain Layout
6199 , that don't add additional space.
6204 at the end of the command
6210 is for a left bracket; for a right bracket this will be replaced by an
6216 A left or right bracket can each be an opening or closing bracket.
6219 \begin_layout Standard
6220 In the following table is a comparison of the variants:
6221 \begin_inset Separator parbreak
6227 \begin_layout Standard
6229 \begin_inset Tabular
6230 <lyxtabular version="3" rows="5" columns="2">
6231 <features booktabs="true" tabularvalignment="middle">
6232 <column alignment="center" valignment="top" width="0pt">
6233 <column alignment="center" valignment="middle">
6235 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6238 \begin_layout Plain Layout
6244 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6247 \begin_layout Plain Layout
6254 <row topspace="2mm">
6255 <cell alignment="center" valignment="top" usebox="none">
6258 \begin_layout Plain Layout
6268 \begin_inset space \textvisiblespace{}
6278 <cell alignment="center" valignment="top" usebox="none">
6281 \begin_layout Plain Layout
6282 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6291 <row topspace="2mm">
6292 <cell alignment="center" valignment="top" usebox="none">
6295 \begin_layout Plain Layout
6305 \begin_inset space \textvisiblespace{}
6315 <cell alignment="center" valignment="top" usebox="none">
6318 \begin_layout Plain Layout
6319 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6328 <row topspace="2mm" bottomspace="0.5mm">
6329 <cell alignment="center" valignment="top" usebox="none">
6332 \begin_layout Plain Layout
6342 \begin_inset space \textvisiblespace{}
6352 <cell alignment="center" valignment="top" usebox="none">
6355 \begin_layout Plain Layout
6356 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6365 <row topspace="1.5mm" bottomspace="0.5mm">
6366 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6369 \begin_layout Plain Layout
6381 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6384 \begin_layout Plain Layout
6385 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6401 \begin_layout Subsubsection
6402 Automatic Bracket Size
6403 \begin_inset CommandInset label
6405 name "subsec:Automatic-Bracket-Size"
6410 \begin_inset Index idx
6413 \begin_layout Plain Layout
6414 Bracket size ! automatic
6422 \begin_layout Standard
6423 Brackets with variable size can be inserted with the commands
6430 \begin_inset Index idx
6433 \begin_layout Plain Layout
6448 \begin_inset Index idx
6451 \begin_layout Plain Layout
6459 or via the math toolbar button
6462 arg "dialog-show mathdelimiter"
6478 the wanted bracket must be inserted.
6479 The bracket size will then automatically be calculated for the output.
6480 \begin_inset Separator parbreak
6486 \begin_layout Standard
6488 normal bracket: The command
6495 \begin_inset space \textvisiblespace{}
6499 \begin_inset Formula $\downarrow$
6503 \begin_inset space \textvisiblespace{}
6509 \begin_inset Formula
6519 \begin_layout Standard
6521 multiline bracket: The command
6530 \begin_inset space \textvisiblespace{}
6534 \begin_inset Formula $\downarrow$
6538 \begin_inset space \textvisiblespace{}
6546 \begin_inset Formula
6548 \ln\left(\frac{A}{C}\right)
6556 \begin_layout Standard
6572 \begin_inset space ~
6578 This has the advantage that you can see in \SpecialChar LyX
6579 immediately the real bracket
6580 size and that the matching right bracket will be created too.
6581 \begin_inset Newline newline
6584 The command for the last example would then be:
6595 \begin_inset space \textvisiblespace{}
6599 \begin_inset Formula $\downarrow$
6605 \begin_layout Standard
6606 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6607 For example the command
6614 \begin_inset space \textvisiblespace{}
6618 \begin_inset Formula $\downarrow$
6622 \begin_inset space \textvisiblespace{}
6632 \begin_inset Formula
6634 \left.\frac{A}{B}\right\}
6653 will be converted by \SpecialChar LyX
6654 to brackets in the right size when the document is
6655 reloaded and an omitted bracket will appear as dashed line.
6658 \begin_layout Standard
6659 \begin_inset VSpace bigskip
6662 Because all popular \SpecialChar LaTeX
6663 distributions use e\SpecialChar TeX
6664 , an extension to \SpecialChar LaTeX
6673 \begin_inset Index idx
6676 \begin_layout Plain Layout
6684 is additionally available for all brackets and limits.
6685 With this command the height of the following character is adapted to the
6686 one of the surrounding brackets, what is e.
6687 \begin_inset space \thinspace{}
6691 \begin_inset space \space{}
6694 needed for physical vectors:
6695 \begin_inset Formula
6697 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6702 For physical vectors there is a special \SpecialChar LaTeX
6703 -package, described in
6704 \begin_inset CommandInset ref
6706 reference "subsec:Physical-Vectors"
6713 \begin_layout Subsection
6715 \begin_inset Index idx
6718 \begin_layout Plain Layout
6719 Brackets ! horizontal
6727 \begin_layout Standard
6729 \begin_inset Tabular
6730 <lyxtabular version="3" rows="4" columns="2">
6731 <features booktabs="true" tabularvalignment="middle">
6732 <column alignment="center" valignment="top" width="0pt">
6733 <column alignment="center" valignment="top" width="0pt">
6735 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6738 \begin_layout Plain Layout
6744 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6747 \begin_layout Plain Layout
6755 <cell alignment="center" valignment="top" usebox="none">
6758 \begin_layout Plain Layout
6762 \begin_inset space \textvisiblespace{}
6766 \begin_inset space \textvisiblespace{}
6770 \begin_inset Index idx
6773 \begin_layout Plain Layout
6786 <cell alignment="center" valignment="top" usebox="none">
6789 \begin_layout Plain Layout
6790 \begin_inset Formula $\overbrace{A+B}^{3}$
6799 <row topspace="2mm">
6800 <cell alignment="center" valignment="top" usebox="none">
6803 \begin_layout Plain Layout
6807 \begin_inset space \textvisiblespace{}
6811 \begin_inset space \textvisiblespace{}
6815 \begin_inset Index idx
6818 \begin_layout Plain Layout
6831 <cell alignment="center" valignment="top" usebox="none">
6834 \begin_layout Plain Layout
6835 \begin_inset Formula $\underbrace{A+B}_{5}$
6845 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6848 \begin_layout Plain Layout
6852 \begin_inset space \textvisiblespace{}
6858 \begin_inset space \textvisiblespace{}
6862 \begin_inset space \textvisiblespace{}
6866 \begin_inset space \textvisiblespace{}
6870 \begin_inset space \textvisiblespace{}
6874 \begin_inset space \textvisiblespace{}
6878 \begin_inset space \textvisiblespace{}
6886 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6889 \begin_layout Plain Layout
6890 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6906 \begin_layout Standard
6907 In the last example it doesn't matter if
6919 is inserted at first.
6922 \begin_layout Standard
6923 \begin_inset VSpace medskip
6929 \begin_layout Standard
6930 If you set in the document settings under
6933 \begin_inset space ~
6943 \begin_inset Index idx
6946 \begin_layout Plain Layout
6947 Packages ! mathtools
6955 \begin_inset space ~
6960 , you have access to square backets:
6961 \begin_inset Separator parbreak
6967 \begin_layout Standard
6969 \begin_inset Tabular
6970 <lyxtabular version="3" rows="4" columns="2">
6971 <features booktabs="true" tabularvalignment="middle">
6972 <column alignment="center" valignment="top" width="0pt">
6973 <column alignment="center" valignment="top" width="0pt">
6975 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6978 \begin_layout Plain Layout
6984 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6987 \begin_layout Plain Layout
6995 <cell alignment="center" valignment="top" usebox="none">
6998 \begin_layout Plain Layout
7026 \begin_inset space \textvisiblespace{}
7030 \begin_inset Index idx
7033 \begin_layout Plain Layout
7046 <cell alignment="center" valignment="top" usebox="none">
7049 \begin_layout Plain Layout
7050 \begin_inset Formula $\overbracket{A+B}^{3}$
7059 <row topspace="2mm">
7060 <cell alignment="center" valignment="top" usebox="none">
7063 \begin_layout Plain Layout
7091 \begin_inset space \textvisiblespace{}
7095 \begin_inset Index idx
7098 \begin_layout Plain Layout
7123 <cell alignment="center" valignment="top" usebox="none">
7126 \begin_layout Plain Layout
7127 \begin_inset Formula $\underbracket{A+B}_{5}$
7137 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7140 \begin_layout Plain Layout
7146 \begin_inset space \textvisiblespace{}
7150 \begin_inset space \textvisiblespace{}
7154 \begin_inset space \textvisiblespace{}
7158 \begin_inset space \textvisiblespace{}
7162 \begin_inset space \textvisiblespace{}
7170 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7173 \begin_layout Plain Layout
7174 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7190 \begin_layout Standard
7203 you can change the thickness of the bracket's stroke by specifying the
7204 desired thickness in square brackets behind the command:
7205 \begin_inset Separator parbreak
7211 \begin_layout Standard
7213 \begin_inset Tabular
7214 <lyxtabular version="3" rows="3" columns="2">
7215 <features booktabs="true" tabularvalignment="middle">
7216 <column alignment="center" valignment="top" width="0pt">
7217 <column alignment="center" valignment="top" width="0pt">
7219 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7222 \begin_layout Plain Layout
7228 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7231 \begin_layout Plain Layout
7239 <cell alignment="center" valignment="top" usebox="none">
7242 \begin_layout Plain Layout
7272 \begin_inset space \textvisiblespace{}
7280 <cell alignment="center" valignment="top" usebox="none">
7283 \begin_layout Plain Layout
7284 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7293 <row topspace="2mm">
7294 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7297 \begin_layout Plain Layout
7327 \begin_inset space \textvisiblespace{}
7335 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7338 \begin_layout Plain Layout
7339 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7355 \begin_layout Standard
7356 \begin_inset VSpace bigskip
7359 When brackets should overlap each other, multiline formulas, as described
7361 \begin_inset CommandInset ref
7363 reference "sec:Multiline-Formulas"
7368 \begin_inset Formula
7370 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7371 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7376 In the first row the formula is inserted together with the first brace.
7377 It is hereby important that the space command
7381 \begin_layout Plain Layout
7382 Space commands are explained in
7383 \begin_inset CommandInset ref
7385 reference "subsec:Predefined-Space"
7400 is inserted before the first
7401 \begin_inset Formula $d$
7404 , because the brace that ends behind the
7405 \begin_inset Formula $q$
7408 prevents that the following
7409 \begin_inset Quotes eld
7413 \begin_inset Quotes erd
7416 is surrounded by space.
7420 \begin_layout Plain Layout
7421 because a bracket is not handled as a character, see
7422 \begin_inset CommandInset ref
7424 reference "subsec:Binary-Operators"
7433 In the second row the second brace is inserted.
7434 As it should begin before the
7435 \begin_inset Formula $b$
7450 \begin_layout Plain Layout
7458 \begin_inset CommandInset ref
7460 reference "subsec:Placeholders"
7469 This space is needed because the
7470 \begin_inset Quotes eld
7474 \begin_inset Quotes erd
7477 is also surrounded by space in the formula.
7478 The brace is placed under the command
7487 \begin_layout Standard
7488 It gets more complicated when brackets overlap each other above and under
7489 the formula, like in the following example:
7493 \begin_layout Plain Layout
7505 \begin_inset Formula
7507 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7508 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7517 \begin_layout Plain Layout
7528 The first formula row is the same as the second row of the previous example,
7529 with the difference that the brace is above.
7530 The second row contains the formula together with the second brace.
7531 To avoid that there is space between the upper brace in the first row and
7532 the formula, the row spacing needs to be reduced.
7533 This is not easily possible due to a bug in \SpecialChar LyX
7538 \begin_layout Plain Layout
7539 \begin_inset CommandInset href
7541 name "LyX-bug #1505"
7542 target "http://www.lyx.org/trac/ticket/1505"
7551 As a solution for the problem, the global formula row separation
7558 \begin_inset Index idx
7561 \begin_layout Plain Layout
7569 must be changed to -6
7570 \begin_inset space \thinspace{}
7573 pt before the formula with the command
7589 is set back after the formula to the standard value of 3
7590 \begin_inset space \thinspace{}
7593 pt using the same command.
7594 More about the row separation in formulas is explained in
7595 \begin_inset CommandInset ref
7597 reference "subsec:Line-Separation"
7604 \begin_layout Section
7606 \begin_inset Index idx
7609 \begin_layout Plain Layout
7618 \begin_layout Standard
7619 Arrows can be inserted via the math toolbar button
7622 arg "math-insert \\leftarrow"
7625 or the commands listed in the following subsections.
7628 \begin_layout Subsection
7630 \begin_inset Index idx
7633 \begin_layout Plain Layout
7642 \begin_layout Standard
7643 \begin_inset space \hfill{}
7647 \begin_inset Tabular
7648 <lyxtabular version="3" rows="8" columns="2">
7649 <features booktabs="true" tabularvalignment="middle">
7650 <column alignment="center" valignment="top" width="0pt">
7651 <column alignment="center" valignment="top" width="0pt">
7653 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7656 \begin_layout Plain Layout
7662 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7665 \begin_layout Plain Layout
7673 <cell alignment="center" valignment="top" usebox="none">
7676 \begin_layout Plain Layout
7684 <cell alignment="center" valignment="top" usebox="none">
7687 \begin_layout Plain Layout
7688 \begin_inset Formula $\gets$
7698 <cell alignment="center" valignment="top" usebox="none">
7701 \begin_layout Plain Layout
7709 <cell alignment="center" valignment="top" usebox="none">
7712 \begin_layout Plain Layout
7713 \begin_inset Formula $\Leftarrow$
7723 <cell alignment="center" valignment="top" usebox="none">
7726 \begin_layout Plain Layout
7734 <cell alignment="center" valignment="top" usebox="none">
7737 \begin_layout Plain Layout
7738 \begin_inset Formula $\longleftarrow$
7748 <cell alignment="center" valignment="top" usebox="none">
7751 \begin_layout Plain Layout
7759 <cell alignment="center" valignment="top" usebox="none">
7762 \begin_layout Plain Layout
7763 \begin_inset Formula $\Longleftarrow$
7773 <cell alignment="center" valignment="top" usebox="none">
7776 \begin_layout Plain Layout
7784 <cell alignment="center" valignment="top" usebox="none">
7787 \begin_layout Plain Layout
7788 \begin_inset Formula $\leftharpoonup$
7798 <cell alignment="center" valignment="top" usebox="none">
7801 \begin_layout Plain Layout
7809 <cell alignment="center" valignment="top" usebox="none">
7812 \begin_layout Plain Layout
7813 \begin_inset Formula $\leftharpoondown$
7823 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7826 \begin_layout Plain Layout
7834 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7837 \begin_layout Plain Layout
7838 \begin_inset Formula $\hookleftarrow$
7852 \begin_inset space \hfill{}
7856 \begin_inset Tabular
7857 <lyxtabular version="3" rows="8" columns="2">
7858 <features booktabs="true" tabularvalignment="middle">
7859 <column alignment="center" valignment="top" width="0pt">
7860 <column alignment="center" valignment="top" width="0pt">
7862 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7865 \begin_layout Plain Layout
7871 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7874 \begin_layout Plain Layout
7882 <cell alignment="center" valignment="top" usebox="none">
7885 \begin_layout Plain Layout
7893 <cell alignment="center" valignment="top" usebox="none">
7896 \begin_layout Plain Layout
7897 \begin_inset Formula $\to$
7907 <cell alignment="center" valignment="top" usebox="none">
7910 \begin_layout Plain Layout
7918 <cell alignment="center" valignment="top" usebox="none">
7921 \begin_layout Plain Layout
7922 \begin_inset Formula $\Rightarrow$
7932 <cell alignment="center" valignment="top" usebox="none">
7935 \begin_layout Plain Layout
7943 <cell alignment="center" valignment="top" usebox="none">
7946 \begin_layout Plain Layout
7947 \begin_inset Formula $\longrightarrow$
7957 <cell alignment="center" valignment="top" usebox="none">
7960 \begin_layout Plain Layout
7968 <cell alignment="center" valignment="top" usebox="none">
7971 \begin_layout Plain Layout
7972 \begin_inset Formula $\Longrightarrow$
7982 <cell alignment="center" valignment="top" usebox="none">
7985 \begin_layout Plain Layout
7993 <cell alignment="center" valignment="top" usebox="none">
7996 \begin_layout Plain Layout
7997 \begin_inset Formula $\rightharpoonup$
8007 <cell alignment="center" valignment="top" usebox="none">
8010 \begin_layout Plain Layout
8018 <cell alignment="center" valignment="top" usebox="none">
8021 \begin_layout Plain Layout
8022 \begin_inset Formula $\rightharpoondown$
8032 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8035 \begin_layout Plain Layout
8043 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8046 \begin_layout Plain Layout
8047 \begin_inset Formula $\hookrightarrow$
8061 \begin_inset space \hfill{}
8067 \begin_layout Standard
8068 \begin_inset space \hfill{}
8072 \begin_inset Tabular
8073 <lyxtabular version="3" rows="6" columns="2">
8074 <features booktabs="true" tabularvalignment="middle">
8075 <column alignment="center" valignment="top" width="0pt">
8076 <column alignment="center" valignment="top" width="0pt">
8078 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8081 \begin_layout Plain Layout
8087 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8090 \begin_layout Plain Layout
8098 <cell alignment="center" valignment="top" usebox="none">
8101 \begin_layout Plain Layout
8109 <cell alignment="center" valignment="top" usebox="none">
8112 \begin_layout Plain Layout
8113 \begin_inset Formula $\leftrightarrow$
8123 <cell alignment="center" valignment="top" usebox="none">
8126 \begin_layout Plain Layout
8134 <cell alignment="center" valignment="top" usebox="none">
8137 \begin_layout Plain Layout
8138 \begin_inset Formula $\Leftrightarrow$
8148 <cell alignment="center" valignment="top" usebox="none">
8151 \begin_layout Plain Layout
8159 <cell alignment="center" valignment="top" usebox="none">
8162 \begin_layout Plain Layout
8163 \begin_inset Formula $\longleftrightarrow$
8173 <cell alignment="center" valignment="top" usebox="none">
8176 \begin_layout Plain Layout
8184 <cell alignment="center" valignment="top" usebox="none">
8187 \begin_layout Plain Layout
8188 \begin_inset Formula $\Longleftrightarrow$
8198 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8201 \begin_layout Plain Layout
8209 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8212 \begin_layout Plain Layout
8213 \begin_inset Formula $\rightleftharpoons$
8227 \begin_inset space \hspace{}
8232 \begin_inset space \hfill{}
8236 \begin_inset Tabular
8237 <lyxtabular version="3" rows="5" columns="2">
8238 <features booktabs="true" tabularvalignment="middle">
8239 <column alignment="center" valignment="top" width="0pt">
8240 <column alignment="center" valignment="top" width="0pt">
8242 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8245 \begin_layout Plain Layout
8251 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8254 \begin_layout Plain Layout
8262 <cell alignment="center" valignment="top" usebox="none">
8265 \begin_layout Plain Layout
8273 <cell alignment="center" valignment="top" usebox="none">
8276 \begin_layout Plain Layout
8277 \begin_inset Formula $\mapsto$
8287 <cell alignment="center" valignment="top" usebox="none">
8290 \begin_layout Plain Layout
8298 <cell alignment="center" valignment="top" usebox="none">
8301 \begin_layout Plain Layout
8302 \begin_inset Formula $\longmapsto$
8312 <cell alignment="center" valignment="top" usebox="none">
8315 \begin_layout Plain Layout
8323 <cell alignment="center" valignment="top" usebox="none">
8326 \begin_layout Plain Layout
8327 \begin_inset Formula $\leadsto$
8337 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8340 \begin_layout Plain Layout
8348 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8351 \begin_layout Plain Layout
8352 \begin_inset Formula $\dasharrow$
8366 \begin_inset space \hfill{}
8372 \begin_layout Standard
8373 \begin_inset VSpace medskip
8376 Arrows used as accents like e.
8377 \begin_inset space \thinspace{}
8381 \begin_inset space \space{}
8384 vector arrows are listed in
8385 \begin_inset CommandInset ref
8387 reference "sec:Accents"
8394 \begin_layout Standard
8395 \begin_inset VSpace bigskip
8398 Furthermore there are the labeled arrows
8399 \begin_inset Index idx
8402 \begin_layout Plain Layout
8415 \begin_inset Index idx
8418 \begin_layout Plain Layout
8433 \begin_inset Index idx
8436 \begin_layout Plain Layout
8443 \begin_layout Plain Layout
8458 When inserting one of these commands in a formula, an arrow with two blue
8459 boxes appear where the label can be inserted.
8460 The length of the arrow adapts to the label width.
8463 \begin_layout Standard
8465 \begin_inset Tabular
8466 <lyxtabular version="3" rows="3" columns="2">
8467 <features booktabs="true" tabularvalignment="middle">
8468 <column alignment="center" valignment="top" width="0pt">
8469 <column alignment="center" valignment="top" width="0pt">
8471 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8474 \begin_layout Plain Layout
8480 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8483 \begin_layout Plain Layout
8491 <cell alignment="center" valignment="top" usebox="none">
8494 \begin_layout Plain Layout
8498 \begin_inset space \textvisiblespace{}
8502 \begin_inset Formula $\downarrow$
8506 \begin_inset Formula $\to$
8514 <cell alignment="center" valignment="top" usebox="none">
8517 \begin_layout Plain Layout
8518 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8527 <row topspace="2mm">
8528 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8531 \begin_layout Plain Layout
8535 \begin_inset space \textvisiblespace{}
8539 \begin_inset Formula $\downarrow$
8543 \begin_inset Formula $\to$
8551 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8554 \begin_layout Plain Layout
8555 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8571 \begin_layout Standard
8572 \begin_inset VSpace medskip
8578 \begin_layout Standard
8579 If you set in the document settings under
8582 \begin_inset space ~
8592 \begin_inset Index idx
8595 \begin_layout Plain Layout
8596 Packages ! mathtools
8604 \begin_inset space ~
8609 , you have access to the following labeled arrows:
8612 \begin_layout Standard
8613 \begin_inset Newpage newpage
8617 \begin_inset Separator parbreak
8623 \begin_layout Standard
8625 \begin_inset space \hspace*{\fill}
8629 \begin_inset Tabular
8630 <lyxtabular version="3" rows="7" columns="2">
8631 <features booktabs="true" tabularvalignment="middle">
8632 <column alignment="center" valignment="top" width="0pt">
8633 <column alignment="center" valignment="top" width="0pt">
8635 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8638 \begin_layout Plain Layout
8644 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8647 \begin_layout Plain Layout
8655 <cell alignment="center" valignment="top" usebox="none">
8658 \begin_layout Plain Layout
8678 <cell alignment="center" valignment="top" usebox="none">
8681 \begin_layout Plain Layout
8682 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8691 <row topspace="2mm">
8692 <cell alignment="center" valignment="top" usebox="none">
8695 \begin_layout Plain Layout
8715 <cell alignment="center" valignment="top" usebox="none">
8718 \begin_layout Plain Layout
8719 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8728 <row topspace="2mm">
8729 <cell alignment="center" valignment="top" usebox="none">
8732 \begin_layout Plain Layout
8752 <cell alignment="center" valignment="top" usebox="none">
8755 \begin_layout Plain Layout
8756 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8765 <row topspace="2mm">
8766 <cell alignment="center" valignment="top" usebox="none">
8769 \begin_layout Plain Layout
8789 <cell alignment="center" valignment="top" usebox="none">
8792 \begin_layout Plain Layout
8793 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8802 <row topspace="2mm">
8803 <cell alignment="center" valignment="top" usebox="none">
8806 \begin_layout Plain Layout
8826 <cell alignment="center" valignment="top" usebox="none">
8829 \begin_layout Plain Layout
8830 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8839 <row topspace="2mm">
8840 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8843 \begin_layout Plain Layout
8863 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8866 \begin_layout Plain Layout
8867 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8881 \begin_inset space \hspace*{\fill}
8885 \begin_inset Tabular
8886 <lyxtabular version="3" rows="7" columns="2">
8887 <features booktabs="true" tabularvalignment="middle">
8888 <column alignment="center" valignment="top" width="0pt">
8889 <column alignment="center" valignment="top" width="0pt">
8891 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8894 \begin_layout Plain Layout
8900 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8903 \begin_layout Plain Layout
8911 <cell alignment="center" valignment="top" usebox="none">
8914 \begin_layout Plain Layout
8934 <cell alignment="center" valignment="top" usebox="none">
8937 \begin_layout Plain Layout
8938 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8947 <row topspace="2mm">
8948 <cell alignment="center" valignment="top" usebox="none">
8951 \begin_layout Plain Layout
8971 <cell alignment="center" valignment="top" usebox="none">
8974 \begin_layout Plain Layout
8975 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8984 <row topspace="2mm">
8985 <cell alignment="center" valignment="top" usebox="none">
8988 \begin_layout Plain Layout
9008 <cell alignment="center" valignment="top" usebox="none">
9011 \begin_layout Plain Layout
9012 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
9021 <row topspace="2mm">
9022 <cell alignment="center" valignment="top" usebox="none">
9025 \begin_layout Plain Layout
9045 <cell alignment="center" valignment="top" usebox="none">
9048 \begin_layout Plain Layout
9049 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9058 <row topspace="2mm">
9059 <cell alignment="center" valignment="top" usebox="none">
9062 \begin_layout Plain Layout
9082 <cell alignment="center" valignment="top" usebox="none">
9085 \begin_layout Plain Layout
9086 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9095 <row topspace="2mm">
9096 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9099 \begin_layout Plain Layout
9119 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9122 \begin_layout Plain Layout
9123 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9137 \begin_inset space \hspace*{\fill}
9143 \begin_layout Standard
9144 The command scheme is for all these arrows:
9145 \begin_inset Separator parbreak
9151 \begin_layout Standard
9153 \begin_inset Tabular
9154 <lyxtabular version="3" rows="2" columns="2">
9155 <features booktabs="true" tabularvalignment="middle">
9156 <column alignment="center" valignment="top" width="0pt">
9157 <column alignment="center" valignment="top" width="0pt">
9159 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9162 \begin_layout Plain Layout
9168 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9171 \begin_layout Plain Layout
9178 <row bottomspace="0.5mm">
9179 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9182 \begin_layout Plain Layout
9185 xleftrightarrow[x=a]
9188 \begin_inset Formula $\to$
9196 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9199 \begin_layout Plain Layout
9200 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9216 \begin_layout Subsection
9217 Vertical and diagonal Arrows
9218 \begin_inset Index idx
9221 \begin_layout Plain Layout
9228 \begin_inset Index idx
9231 \begin_layout Plain Layout
9240 \begin_layout Standard
9241 \begin_inset space \hfill{}
9245 \begin_inset Tabular
9246 <lyxtabular version="3" rows="7" columns="2">
9247 <features booktabs="true" tabularvalignment="middle">
9248 <column alignment="center" valignment="top" width="0pt">
9249 <column alignment="center" valignment="top" width="0pt">
9251 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9254 \begin_layout Plain Layout
9260 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9263 \begin_layout Plain Layout
9271 <cell alignment="center" valignment="top" usebox="none">
9274 \begin_layout Plain Layout
9282 <cell alignment="center" valignment="top" usebox="none">
9285 \begin_layout Plain Layout
9286 \begin_inset Formula $\uparrow$
9296 <cell alignment="center" valignment="top" usebox="none">
9299 \begin_layout Plain Layout
9307 <cell alignment="center" valignment="top" usebox="none">
9310 \begin_layout Plain Layout
9311 \begin_inset Formula $\Uparrow$
9321 <cell alignment="center" valignment="top" usebox="none">
9324 \begin_layout Plain Layout
9332 <cell alignment="center" valignment="top" usebox="none">
9335 \begin_layout Plain Layout
9336 \begin_inset Formula $\updownarrow$
9346 <cell alignment="center" valignment="top" usebox="none">
9349 \begin_layout Plain Layout
9357 <cell alignment="center" valignment="top" usebox="none">
9360 \begin_layout Plain Layout
9361 \begin_inset Formula $\Updownarrow$
9371 <cell alignment="center" valignment="top" usebox="none">
9374 \begin_layout Plain Layout
9382 <cell alignment="center" valignment="top" usebox="none">
9385 \begin_layout Plain Layout
9386 \begin_inset Formula $\Downarrow$
9396 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9399 \begin_layout Plain Layout
9407 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9410 \begin_layout Plain Layout
9411 \begin_inset Formula $\downarrow$
9425 \begin_inset space \hfill{}
9429 \begin_inset Tabular
9430 <lyxtabular version="3" rows="5" columns="2">
9431 <features booktabs="true" tabularvalignment="middle">
9432 <column alignment="center" valignment="top" width="0pt">
9433 <column alignment="center" valignment="top" width="0pt">
9435 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9438 \begin_layout Plain Layout
9444 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9447 \begin_layout Plain Layout
9455 <cell alignment="center" valignment="top" usebox="none">
9458 \begin_layout Plain Layout
9466 <cell alignment="center" valignment="top" usebox="none">
9469 \begin_layout Plain Layout
9470 \begin_inset Formula $\nearrow$
9480 <cell alignment="center" valignment="top" usebox="none">
9483 \begin_layout Plain Layout
9491 <cell alignment="center" valignment="top" usebox="none">
9494 \begin_layout Plain Layout
9495 \begin_inset Formula $\searrow$
9505 <cell alignment="center" valignment="top" usebox="none">
9508 \begin_layout Plain Layout
9516 <cell alignment="center" valignment="top" usebox="none">
9519 \begin_layout Plain Layout
9520 \begin_inset Formula $\swarrow$
9530 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9533 \begin_layout Plain Layout
9541 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9544 \begin_layout Plain Layout
9545 \begin_inset Formula $\nwarrow$
9559 \begin_inset space \hfill{}
9565 \begin_layout Standard
9566 \begin_inset VSpace medskip
9569 Vertical arrows can be used also as delimiters together with the commands
9571 \begin_inset CommandInset ref
9573 reference "subsec:Manual-Bracket-Size"
9578 \begin_inset CommandInset ref
9580 reference "subsec:Automatic-Bracket-Size"
9587 \begin_layout Section
9589 \begin_inset CommandInset label
9596 \begin_inset Index idx
9599 \begin_layout Plain Layout
9608 \begin_layout Standard
9609 Accents can be inserted via the math toolbar button
9612 arg "math-insert \\hat"
9615 or the commands listed in the following subsections.
9618 \begin_layout Subsection
9619 Accents for one Character
9623 \begin_layout Plain Layout
9636 \begin_layout Plain Layout
9638 \begin_inset CommandInset ref
9640 reference "subsec:Accents-in-Text"
9653 \begin_layout Plain Layout
9661 \begin_inset Note Note
9664 \begin_layout Plain Layout
9671 is used to avoid that the footnote appears in the PDF-bookmark.
9674 \begin_layout Plain Layout
9682 \begin_inset CommandInset ref
9684 reference "subsec:Formulas-in-Section"
9694 \begin_inset CommandInset label
9696 name "subsec:Accents-for-one"
9701 \begin_inset Index idx
9704 \begin_layout Plain Layout
9705 Accents ! for one character
9713 \begin_layout Standard
9714 \begin_inset space \hfill{}
9718 \begin_inset Tabular
9719 <lyxtabular version="3" rows="8" columns="2">
9720 <features booktabs="true" tabularvalignment="middle">
9721 <column alignment="center" valignment="top" width="0pt">
9722 <column alignment="center" valignment="top" width="0pt">
9724 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9727 \begin_layout Plain Layout
9733 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9736 \begin_layout Plain Layout
9743 <row topspace="1.5mm">
9744 <cell alignment="center" valignment="top" usebox="none">
9747 \begin_layout Plain Layout
9751 \begin_inset space \textvisiblespace{}
9759 <cell alignment="center" valignment="top" usebox="none">
9762 \begin_layout Plain Layout
9763 \begin_inset Formula $\dot{A}$
9772 <row topspace="1.5mm">
9773 <cell alignment="center" valignment="top" usebox="none">
9776 \begin_layout Plain Layout
9780 \begin_inset space \textvisiblespace{}
9788 <cell alignment="center" valignment="top" usebox="none">
9791 \begin_layout Plain Layout
9792 \begin_inset Formula $\ddot{A}$
9801 <row topspace="1.5mm">
9802 <cell alignment="center" valignment="top" usebox="none">
9805 \begin_layout Plain Layout
9809 \begin_inset space \textvisiblespace{}
9817 <cell alignment="center" valignment="top" usebox="none">
9820 \begin_layout Plain Layout
9821 \begin_inset Formula $\dddot{A}$
9830 <row topspace="1.5mm">
9831 <cell alignment="center" valignment="top" usebox="none">
9834 \begin_layout Plain Layout
9838 \begin_inset space \textvisiblespace{}
9846 <cell alignment="center" valignment="top" usebox="none">
9849 \begin_layout Plain Layout
9850 \begin_inset Formula $\ddddot{A}$
9859 <row topspace="1.5mm">
9860 <cell alignment="center" valignment="top" usebox="none">
9863 \begin_layout Plain Layout
9867 \begin_inset space \textvisiblespace{}
9871 \begin_inset Index idx
9874 \begin_layout Plain Layout
9885 <cell alignment="center" valignment="top" usebox="none">
9888 \begin_layout Plain Layout
9889 \begin_inset Formula $\vec{A}$
9898 <row topspace="1.5mm">
9899 <cell alignment="center" valignment="top" usebox="none">
9902 \begin_layout Plain Layout
9906 \begin_inset space \textvisiblespace{}
9914 <cell alignment="center" valignment="top" usebox="none">
9917 \begin_layout Plain Layout
9918 \begin_inset Formula $\bar{A}$
9927 <row topspace="1.5mm">
9928 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9931 \begin_layout Plain Layout
9935 \begin_inset space \textvisiblespace{}
9943 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9946 \begin_layout Plain Layout
9947 \begin_inset Formula $\mathring{A}$
9961 \begin_inset space \hfill{}
9965 \begin_inset Tabular
9966 <lyxtabular version="3" rows="7" columns="2">
9967 <features booktabs="true" tabularvalignment="middle">
9968 <column alignment="center" valignment="top" width="0pt">
9969 <column alignment="center" valignment="top" width="0pt">
9971 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9974 \begin_layout Plain Layout
9980 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9983 \begin_layout Plain Layout
9990 <row topspace="1.5mm">
9991 <cell alignment="center" valignment="top" usebox="none">
9994 \begin_layout Plain Layout
9998 \begin_inset space \textvisiblespace{}
10006 <cell alignment="center" valignment="top" usebox="none">
10009 \begin_layout Plain Layout
10010 \begin_inset Formula $\tilde{A}$
10019 <row topspace="1.5mm">
10020 <cell alignment="center" valignment="top" usebox="none">
10023 \begin_layout Plain Layout
10027 \begin_inset space \textvisiblespace{}
10035 <cell alignment="center" valignment="top" usebox="none">
10038 \begin_layout Plain Layout
10039 \begin_inset Formula $\hat{A}$
10048 <row topspace="1.5mm">
10049 <cell alignment="center" valignment="top" usebox="none">
10052 \begin_layout Plain Layout
10056 \begin_inset space \textvisiblespace{}
10064 <cell alignment="center" valignment="top" usebox="none">
10067 \begin_layout Plain Layout
10068 \begin_inset Formula $\check{A}$
10077 <row topspace="1.5mm">
10078 <cell alignment="center" valignment="top" usebox="none">
10081 \begin_layout Plain Layout
10085 \begin_inset space \textvisiblespace{}
10093 <cell alignment="center" valignment="top" usebox="none">
10096 \begin_layout Plain Layout
10097 \begin_inset Formula $\acute{A}$
10106 <row topspace="1.5mm">
10107 <cell alignment="center" valignment="top" usebox="none">
10110 \begin_layout Plain Layout
10114 \begin_inset space \textvisiblespace{}
10122 <cell alignment="center" valignment="top" usebox="none">
10125 \begin_layout Plain Layout
10126 \begin_inset Formula $\grave{A}$
10135 <row topspace="1.5mm">
10136 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10139 \begin_layout Plain Layout
10143 \begin_inset space \textvisiblespace{}
10151 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10154 \begin_layout Plain Layout
10155 \begin_inset Formula $\breve{A}$
10169 \begin_inset space \hfill{}
10175 \begin_layout Standard
10176 \begin_inset VSpace bigskip
10182 \begin_layout Standard
10183 You can directly insert accents like é to formulas.
10185 will transform them to the corresponding accent command.
10187 \begin_inset Index idx
10190 \begin_layout Plain Layout
10196 it is better to insert a quotation mark before the vowel.
10197 These two characters are then treated by \SpecialChar LaTeX
10202 character when the formula part with the umlaut is marked as German.
10210 \begin_inset Quotes eld
10214 \begin_inset Quotes erd
10217 umlauts are created as demonstrated in the following example:
10220 \begin_layout Standard
10221 \begin_inset VSpace -2mm
10227 \begin_layout Standard
10229 \begin_inset Tabular
10230 <lyxtabular version="3" rows="3" columns="2">
10231 <features booktabs="true" tabularvalignment="middle">
10232 <column alignment="center" valignment="top" width="0pt">
10233 <column alignment="center" valignment="top">
10235 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10238 \begin_layout Plain Layout
10244 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10247 \begin_layout Plain Layout
10255 <cell alignment="center" valignment="top" usebox="none">
10258 \begin_layout Plain Layout
10259 \begin_inset Quotes grd
10267 <cell alignment="center" valignment="top" usebox="none">
10270 \begin_layout Plain Layout
10271 \begin_inset space \hspace{}
10278 \begin_inset Formula $"i$
10287 <row topspace="1.5mm">
10288 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10291 \begin_layout Plain Layout
10295 \begin_inset space \textvisiblespace{}
10303 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10306 \begin_layout Plain Layout
10307 \begin_inset Formula $\ddot{i}$
10323 \begin_layout Standard
10324 Another advantage to
10330 is that umlauts can directly be converted to mathematical text because
10331 the accent commands above are
10337 in mathematical text
10340 To convert an accented character to mathematical text, only the character
10341 under the accent may be converted.
10342 This applies also for all other conversions, e.
10343 \begin_inset space \thinspace{}
10347 \begin_inset space \space{}
10353 \begin_layout Standard
10354 In mathematical text, umlauts and other accented characters can directly
10358 \begin_layout Standard
10359 \begin_inset VSpace bigskip
10365 \begin_layout Standard
10367 also supports a tilde under the character if the \SpecialChar LaTeX
10373 \begin_inset Index idx
10376 \begin_layout Plain Layout
10377 Packages ! undertilde
10382 is installed on your system:
10385 \begin_layout Standard
10389 \begin_layout Plain Layout
10399 \begin_inset Note Note
10402 \begin_layout Plain Layout
10403 The following table will only be displayed when the \SpecialChar LaTeX
10414 \begin_inset Separator parbreak
10420 \begin_layout Standard
10423 \begin_inset Tabular
10424 <lyxtabular version="3" rows="2" columns="2">
10425 <features booktabs="true" tabularvalignment="middle">
10426 <column alignment="center" valignment="top" width="0pt">
10427 <column alignment="center" valignment="top" width="0pt">
10429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10432 \begin_layout Plain Layout
10438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10441 \begin_layout Plain Layout
10449 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10452 \begin_layout Plain Layout
10456 \begin_inset space \textvisiblespace{}
10464 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10467 \begin_layout Plain Layout
10468 \begin_inset Formula $\utilde{A}$
10484 \begin_layout Standard
10488 \begin_layout Plain Layout
10498 \begin_inset Note Note
10501 \begin_layout Plain Layout
10502 The following will be displayed when the \SpecialChar LaTeX
10515 \begin_layout Standard
10516 You need to install the \SpecialChar LaTeX
10521 to see the rest of this subsection in the output.
10524 \begin_layout Standard
10528 \begin_layout Plain Layout
10540 \begin_layout Standard
10541 \begin_inset Newpage newpage
10547 \begin_layout Subsection
10548 Accents for several Characters
10549 \begin_inset Index idx
10552 \begin_layout Plain Layout
10553 Accents ! for several characters
10561 \begin_layout Standard
10562 \begin_inset space \hfill{}
10566 \begin_inset Tabular
10567 <lyxtabular version="3" rows="5" columns="2">
10568 <features booktabs="true" tabularvalignment="middle">
10569 <column alignment="center" valignment="top" width="0pt">
10570 <column alignment="center" valignment="top" width="0pt">
10572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10575 \begin_layout Plain Layout
10581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10584 \begin_layout Plain Layout
10591 <row topspace="1.5mm">
10592 <cell alignment="center" valignment="top" usebox="none">
10595 \begin_layout Plain Layout
10599 \begin_inset space \textvisiblespace{}
10607 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10610 \begin_layout Plain Layout
10611 \begin_inset Formula $\overleftarrow{A=B}$
10620 <row topspace="1.5mm">
10621 <cell alignment="center" valignment="top" usebox="none">
10624 \begin_layout Plain Layout
10628 \begin_inset space \textvisiblespace{}
10636 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10639 \begin_layout Plain Layout
10640 \begin_inset Formula $\underleftarrow{A=B}$
10649 <row topspace="1.5mm">
10650 <cell alignment="center" valignment="top" usebox="none">
10653 \begin_layout Plain Layout
10657 \begin_inset space \textvisiblespace{}
10665 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10668 \begin_layout Plain Layout
10669 \begin_inset Formula $\overleftrightarrow{A=B}$
10678 <row topspace="1.5mm" bottomspace="1mm">
10679 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10682 \begin_layout Plain Layout
10685 underleftrightarrow
10686 \begin_inset space \textvisiblespace{}
10694 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10697 \begin_layout Plain Layout
10698 \begin_inset Formula $\underleftrightarrow{A=B}$
10712 \begin_inset space \hfill{}
10716 \begin_inset Tabular
10717 <lyxtabular version="3" rows="5" columns="2">
10718 <features booktabs="true" tabularvalignment="middle">
10719 <column alignment="center" valignment="top" width="0pt">
10720 <column alignment="center" valignment="top" width="0pt">
10722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10725 \begin_layout Plain Layout
10731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10734 \begin_layout Plain Layout
10741 <row topspace="1.5mm">
10742 <cell alignment="center" valignment="top" usebox="none">
10745 \begin_layout Plain Layout
10749 \begin_inset space \textvisiblespace{}
10757 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10760 \begin_layout Plain Layout
10761 \begin_inset Formula $\overrightarrow{A=B}$
10770 <row topspace="1.5mm">
10771 <cell alignment="center" valignment="top" usebox="none">
10774 \begin_layout Plain Layout
10778 \begin_inset space \textvisiblespace{}
10786 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10789 \begin_layout Plain Layout
10790 \begin_inset Formula $\underrightarrow{A=B}$
10799 <row topspace="1.5mm">
10800 <cell alignment="center" valignment="top" usebox="none">
10803 \begin_layout Plain Layout
10807 \begin_inset space \textvisiblespace{}
10815 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10818 \begin_layout Plain Layout
10819 \begin_inset Formula $\widetilde{A=B}$
10828 <row topspace="1.5mm" bottomspace="1mm">
10829 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10832 \begin_layout Plain Layout
10836 \begin_inset space \textvisiblespace{}
10844 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10847 \begin_layout Plain Layout
10848 \begin_inset Formula $\widehat{A=B}$
10862 \begin_inset space \hfill{}
10868 \begin_layout Standard
10869 \begin_inset VSpace medskip
10872 With these commands as many characters as you like can be accented.
10885 will only be set in the output with a length of three characters, as shown
10886 in the following example:
10887 \begin_inset Formula
10889 \widetilde{A+B=C-D}
10897 \begin_layout Standard
10905 \begin_inset Index idx
10908 \begin_layout Plain Layout
10923 \begin_inset Index idx
10926 \begin_layout Plain Layout
10934 described in the previous subsection it is also possible to accent several
10941 \begin_inset space \textvisiblespace{}
10945 \begin_inset Formula $\downarrow$
10951 \begin_inset Formula
10953 \underset{***}{A=B}
10961 \begin_layout Section
10963 \begin_inset CommandInset label
10965 name "subsec:Space"
10970 \begin_inset Index idx
10973 \begin_layout Plain Layout
10982 \begin_layout Subsection
10984 \begin_inset CommandInset label
10986 name "subsec:Predefined-Space"
10991 \begin_inset Index idx
10994 \begin_layout Plain Layout
10995 Space ! horizontal ! predefined
11003 \begin_layout Standard
11004 Sometimes it is necessary to insert horizontal space into a formula.
11005 This is done by inserting a protected space (shortcut
11008 arg "command-alternatives space-insert protected ; math-space"
11013 \begin_inset Quotes eld
11019 \begin_inset space \textvisiblespace{}
11025 \begin_inset Quotes erd
11028 appears and by pressing
11032 several times one can select one of eight different space sizes.
11033 The spaces can also be inserted using the math toolbar button
11036 arg "math-insert \\space"
11039 or special commands.
11040 Independent from the inserted command, one can select the size again by
11046 \begin_inset Separator parbreak
11052 \begin_layout Standard
11055 \begin_inset Tabular
11056 <lyxtabular version="3" rows="6" columns="3">
11057 <features booktabs="true" tabularvalignment="middle">
11058 <column alignment="center" valignment="top">
11059 <column alignment="center" valignment="top" width="15col%">
11060 <column alignment="center" valignment="top">
11062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11065 \begin_layout Plain Layout
11071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11074 \begin_layout Plain Layout
11084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11087 \begin_layout Plain Layout
11095 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11098 \begin_layout Plain Layout
11106 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11109 \begin_layout Plain Layout
11115 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11118 \begin_layout Plain Layout
11119 \begin_inset Formula $A\,B$
11129 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11132 \begin_layout Plain Layout
11140 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11143 \begin_layout Plain Layout
11149 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11152 \begin_layout Plain Layout
11153 \begin_inset Formula $A\:B$
11163 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11166 \begin_layout Plain Layout
11174 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11177 \begin_layout Plain Layout
11183 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11186 \begin_layout Plain Layout
11187 \begin_inset Formula $A\;B$
11197 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11200 \begin_layout Plain Layout
11208 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11211 \begin_layout Plain Layout
11217 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11220 \begin_layout Plain Layout
11221 \begin_inset Formula $A\quad B$
11231 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11234 \begin_layout Plain Layout
11242 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11245 \begin_layout Plain Layout
11251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11254 \begin_layout Plain Layout
11255 \begin_inset Formula $A\qquad B$
11269 \begin_inset space \hfill{}
11273 \begin_inset Tabular
11274 <lyxtabular version="3" rows="6" columns="3">
11275 <features booktabs="true" tabularvalignment="middle">
11276 <column alignment="center" valignment="top">
11277 <column alignment="center" valignment="top" width="15col%">
11278 <column alignment="center" valignment="top">
11280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11283 \begin_layout Plain Layout
11289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11292 \begin_layout Plain Layout
11302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11305 \begin_layout Plain Layout
11313 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11316 \begin_layout Plain Layout
11324 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11327 \begin_layout Plain Layout
11333 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11336 \begin_layout Plain Layout
11337 \begin_inset Formula $A\hfill B$
11347 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11350 \begin_layout Plain Layout
11358 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11361 \begin_layout Plain Layout
11367 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11370 \begin_layout Plain Layout
11371 \begin_inset Formula $A\hspace*{1em}B$
11381 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11384 \begin_layout Plain Layout
11392 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11395 \begin_layout Plain Layout
11401 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11404 \begin_layout Plain Layout
11405 \begin_inset Formula $A\hspace{1em}B$
11415 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11418 \begin_layout Plain Layout
11422 \begin_inset space \textvisiblespace{}
11430 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11433 \begin_layout Plain Layout
11439 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11442 \begin_layout Plain Layout
11443 \begin_inset Formula $A\ B$
11453 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11456 \begin_layout Plain Layout
11464 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11467 \begin_layout Plain Layout
11473 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11476 \begin_layout Plain Layout
11477 \begin_inset Formula $A\!B$
11493 \begin_layout Standard
11495 \begin_inset space ~
11499 \begin_inset space \thinspace{}
11503 \begin_inset space \thinspace{}
11506 7 are variable spaces which are explained in
11507 \begin_inset CommandInset ref
11509 reference "subsec:Variable-Space"
11515 \begin_inset space ~
11518 9 seems to produce no space.
11519 It is displayed red in \SpecialChar LyX
11520 contrary to the other sizes, because it is a negative
11522 There are two more negative spaces:
11523 \begin_inset Separator parbreak
11529 \begin_layout Standard
11531 \begin_inset Tabular
11532 <lyxtabular version="3" rows="3" columns="3">
11533 <features booktabs="true" tabularvalignment="middle">
11534 <column alignment="center" valignment="middle" width="6.8cm">
11535 <column alignment="center" valignment="top" width="0pt">
11536 <column alignment="center" valignment="top" width="0pt">
11538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11541 \begin_layout Plain Layout
11547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11550 \begin_layout Plain Layout
11558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11561 \begin_layout Plain Layout
11571 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11574 \begin_layout Plain Layout
11579 keystrokes after inserting the protected space
11584 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11587 \begin_layout Plain Layout
11593 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11596 \begin_layout Plain Layout
11604 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11607 \begin_layout Plain Layout
11613 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11616 \begin_layout Plain Layout
11617 \begin_inset Formula $A\negmedspace B$
11625 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11628 \begin_layout Plain Layout
11629 \begin_inset Formula $A\negthickspace B$
11645 \begin_layout Standard
11646 Negative spaces can lead to characters overlapping each other.
11647 Thus they can be used to enforce ligatures, which are e.
11648 \begin_inset space \thinspace{}
11652 \begin_inset space \space{}
11655 useful for summation operators:
11656 \begin_inset Separator parbreak
11662 \begin_layout Standard
11664 \begin_inset Tabular
11665 <lyxtabular version="3" rows="3" columns="2">
11666 <features booktabs="true" tabularvalignment="middle">
11667 <column alignment="center" valignment="top" width="0pt">
11668 <column alignment="center" valignment="top">
11670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11673 \begin_layout Plain Layout
11679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11682 \begin_layout Plain Layout
11690 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11693 \begin_layout Plain Layout
11699 \begin_inset space \textvisiblespace{}
11707 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11710 \begin_layout Plain Layout
11711 \begin_inset Formula $\sum\sum f_{kl}$
11721 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11724 \begin_layout Plain Layout
11732 \begin_inset space \textvisiblespace{}
11740 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11743 \begin_layout Plain Layout
11744 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11760 \begin_layout Standard
11762 \begin_inset VSpace medskip
11768 \begin_layout Standard
11770 Relations like for example equal signs, are always surrounded by space.
11771 To suppress this, the equal sign is placed into a \SpecialChar TeX
11773 The following example demonstrates this:
11774 \begin_inset Separator parbreak
11780 \begin_layout Standard
11782 \begin_inset Tabular
11783 <lyxtabular version="3" rows="2" columns="2">
11784 <features tabularvalignment="middle">
11785 <column alignment="center" valignment="top" width="0pt">
11786 <column alignment="center" valignment="top" width="0pt">
11788 <cell alignment="center" valignment="top" usebox="none">
11791 \begin_layout Plain Layout
11797 <cell alignment="center" valignment="top" usebox="none">
11800 \begin_layout Plain Layout
11801 \begin_inset Formula $A=B$
11811 <cell alignment="center" valignment="top" usebox="none">
11814 \begin_layout Plain Layout
11815 equation without space
11820 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11823 \begin_layout Plain Layout
11824 \begin_inset Formula $A{=}B$
11840 \begin_layout Standard
11842 The command for the last formula is:
11847 \begin_inset Formula $\to$
11853 \begin_layout Standard
11854 \begin_inset VSpace bigskip
11860 \begin_layout Standard
11861 Spaces are needed for physical units, because the space between the value
11862 and the unit is the smallest one and not a normal space.
11863 For units in text, the smallest space is inserted via the menu
11865 Insert\SpecialChar menuseparator
11866 Formatting\SpecialChar menuseparator
11868 \begin_inset space ~
11876 arg "space-insert thin"
11882 \begin_layout Standard
11883 An example to visualize the difference:
11886 \begin_layout Standard
11887 \begin_inset Tabular
11888 <lyxtabular version="3" rows="2" columns="2">
11889 <features tabularvalignment="middle">
11890 <column alignment="left" valignment="top">
11891 <column alignment="left" valignment="top">
11893 <cell alignment="center" valignment="top" usebox="none">
11896 \begin_layout Plain Layout
11898 \begin_inset Formula $\cdot$
11906 <cell alignment="center" valignment="top" usebox="none">
11909 \begin_layout Plain Layout
11910 space between value and unit
11917 <cell alignment="center" valignment="top" usebox="none">
11920 \begin_layout Plain Layout
11922 \begin_inset space \thinspace{}
11926 \begin_inset Formula $\cdot$
11934 <cell alignment="center" valignment="top" usebox="none">
11937 \begin_layout Plain Layout
11938 smallest space between value and unit
11951 \begin_layout Subsection
11956 \begin_layout Plain Layout
11969 \begin_layout Plain Layout
11970 for vertical space in formulas see
11971 \begin_inset CommandInset ref
11973 reference "subsec:Line-Separation"
11986 \begin_layout Plain Layout
11994 \begin_inset Note Note
11997 \begin_layout Plain Layout
12000 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12003 \begin_layout Plain Layout
12006 texorpdfstring is in section
12007 \begin_inset CommandInset ref
12009 reference "subsec:Formulas-in-Section"
12019 \begin_inset CommandInset label
12021 name "subsec:Variable-Space"
12026 \begin_inset Index idx
12029 \begin_layout Plain Layout
12030 Space ! horizontal ! variable
12038 \begin_layout Standard
12039 Space with a defined length can be inserted with the command
12046 \begin_inset Index idx
12049 \begin_layout Plain Layout
12059 \begin_inset Quotes eld
12065 \begin_inset space \textvisiblespace{}
12071 \begin_inset Quotes erd
12075 The length can be specified by left-clicking on the
12076 \begin_inset Quotes eld
12082 \begin_inset space \textvisiblespace{}
12088 \begin_inset Quotes erd
12092 The length may also be negative.
12093 When a space would be the first character in a line it would be omitted.
12094 To force its output use the command
12106 or left-click on the
12107 \begin_inset Quotes eld
12113 \begin_inset space \textvisiblespace{}
12119 \begin_inset Quotes erd
12122 and check the option
12127 \begin_inset Newline newline
12130 To insert as much space as is available, the command
12137 \begin_inset Index idx
12140 \begin_layout Plain Layout
12151 \begin_layout Standard
12153 \begin_inset Tabular
12154 <lyxtabular version="3" rows="4" columns="2">
12155 <features booktabs="true" tabularvalignment="middle">
12156 <column alignment="center" valignment="top" width="0pt">
12157 <column alignment="center" valignment="top">
12159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12162 \begin_layout Plain Layout
12170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12173 \begin_layout Plain Layout
12181 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12184 \begin_layout Plain Layout
12188 \begin_inset space \textvisiblespace{}
12194 \begin_inset space \thinspace{}
12202 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12205 \begin_layout Plain Layout
12206 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12216 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12219 \begin_layout Plain Layout
12223 \begin_inset space \textvisiblespace{}
12229 \begin_inset space \thinspace{}
12237 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12240 \begin_layout Plain Layout
12241 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12254 \begin_layout Plain Layout
12258 \begin_inset space \textvisiblespace{}
12266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12269 \begin_layout Plain Layout
12270 \begin_inset Formula $A=A\hfill B=B$
12286 \begin_layout Standard
12287 In the last example the available space is given by the longest column entry
12289 In an inline formula the space depends on the length of the line in which
12297 Thus, when the line uses the full width, no space will be created.
12304 only has an effect on displayed formulas when the formula style
12309 (Formula styles are explained in
12310 \begin_inset CommandInset ref
12312 reference "sec:Formula-Styles"
12319 \begin_layout Standard
12326 , there are the commands
12338 that fill the space with a pattern, see
12339 \begin_inset CommandInset ref
12341 reference "subsec:Ellipses"
12348 \begin_layout Standard
12349 For text, variable space can be inserted via the menu
12351 Insert\SpecialChar menuseparator
12352 Formatting\SpecialChar menuseparator
12354 \begin_inset space ~
12362 \begin_layout Standard
12363 This is a line with
12364 \begin_inset space \hspace{}
12369 \begin_inset space \thinspace{}
12375 \begin_layout Standard
12376 This is a line with
12377 \begin_inset space \hfill{}
12383 \begin_layout Subsection
12384 Space besides inline Formulas
12385 \begin_inset Index idx
12388 \begin_layout Plain Layout
12389 Space ! besides inline formulas
12397 \begin_layout Standard
12398 The space that surrounds inline formulas can be adjusted with the length
12406 \begin_inset Index idx
12409 \begin_layout Plain Layout
12418 The value of a length is set with the command
12425 \begin_inset Index idx
12428 \begin_layout Plain Layout
12436 which has the following scheme:
12439 \begin_layout Standard
12444 setlength{length name}{value}
12447 \begin_layout Standard
12455 \begin_inset space \thinspace{}
12461 \begin_layout Standard
12471 \begin_layout Standard
12472 is inserted in \SpecialChar TeX
12475 \begin_inset space \thinspace{}
12478 mm space will now be set around all inline formulas:
12482 \begin_layout Plain Layout
12496 \begin_layout Standard
12497 This is a line with an inline formula
12498 \begin_inset Formula $A=B$
12502 \begin_inset space \thinspace{}
12505 mm surrounding space.
12509 \begin_layout Plain Layout
12523 \begin_layout Standard
12524 To return to the predefined value,
12530 is set to the value 0
12531 \begin_inset space \thinspace{}
12537 \begin_layout Standard
12538 \begin_inset Newpage newpage
12544 \begin_layout Section
12546 \begin_inset Index idx
12549 \begin_layout Plain Layout
12556 \begin_inset Index idx
12559 \begin_layout Plain Layout
12564 \begin_layout Plain Layout
12575 \begin_layout Plain Layout
12590 \begin_layout Standard
12591 Boxes for text are described in chapter
12598 \begin_inset space ~
12606 \begin_layout Subsection
12608 \begin_inset CommandInset label
12610 name "subsec:Boxes-with-Frame"
12615 \begin_inset Index idx
12618 \begin_layout Plain Layout
12627 \begin_layout Standard
12628 It is possible to frame a formula or part of one with the commands
12635 \begin_inset Index idx
12638 \begin_layout Plain Layout
12653 \begin_inset Index idx
12656 \begin_layout Plain Layout
12667 \begin_layout Standard
12668 When one of these commands is inserted in a formula, a blue box appears
12669 within a frame to enter formula parts.
12676 an additional formula has to be created by
12680 within this box, because the box content will otherwise be treated as mathemati
12688 is used, a new formula is automatically created inside the frame.
12691 \begin_layout Standard
12698 is not suitable to frame displayed formulas because the formula will always
12699 be set in the size of the text.
12706 is in contrary not suitable to frame inline formulas, because the formula
12707 will always be set in the size of a displayed formula.
12710 \begin_layout Standard
12724 \begin_inset Index idx
12727 \begin_layout Plain Layout
12735 where additionally the frame width and the alignment can be specified.
12742 is used in the following scheme:
12745 \begin_layout Standard
12750 framebox[frame width][position]{box content}
12753 \begin_layout Standard
12754 The position can either be
12771 right aligns the formula in the box.
12772 When no position is given, the formula will be centered.
12773 \begin_inset Newline newline
12776 If no width is given, also no position can be given.
12777 In this case the frame width is adjusted to the box content like for
12786 \begin_layout Standard
12793 is inserted, a box appears containing three blue boxes.
12794 The first two boxes are surrounded by brackets and denote the two optional
12796 The third box is for formula parts like for
12803 \begin_inset Separator parbreak
12809 \begin_layout Standard
12811 \begin_inset Tabular
12812 <lyxtabular version="3" rows="5" columns="2">
12813 <features booktabs="true" tabularvalignment="middle">
12814 <column alignment="center" valignment="top" width="0pt">
12815 <column alignment="center" valignment="top">
12817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12820 \begin_layout Plain Layout
12826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12829 \begin_layout Plain Layout
12836 <row topspace="1.5mm">
12837 <cell alignment="center" valignment="top" usebox="none">
12840 \begin_layout Plain Layout
12844 \begin_inset space \textvisiblespace{}
12854 \begin_inset space \textvisiblespace{}
12862 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12865 \begin_layout Plain Layout
12866 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12875 <row topspace="1.5mm">
12876 <cell alignment="center" valignment="top" usebox="none">
12879 \begin_layout Plain Layout
12883 \begin_inset space \textvisiblespace{}
12889 \begin_inset space \textvisiblespace{}
12897 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12900 \begin_layout Plain Layout
12901 \begin_inset Formula $\boxed{\int A=B}$
12910 <row topspace="1.5mm">
12911 <cell alignment="center" valignment="top" usebox="none">
12914 \begin_layout Plain Layout
12918 \begin_inset space \textvisiblespace{}
12926 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12929 \begin_layout Plain Layout
12930 \begin_inset Formula $A+\fbox{B}$
12939 <row topspace="1.5mm" bottomspace="1mm">
12940 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12943 \begin_layout Plain Layout
12947 \begin_inset space \textvisiblespace{}
12951 \begin_inset Formula $\to$
12955 \begin_inset Formula $\to$
12965 \begin_inset space \textvisiblespace{}
12969 \begin_inset Formula $\downarrow$
12977 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12980 \begin_layout Plain Layout
12981 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12997 \begin_layout Standard
12998 The frame thickness can also be adjusted.
12999 To do this the following commands have to be inserted in \SpecialChar TeX
13004 \begin_layout Standard
13014 \begin_inset Quotes eld
13018 \begin_inset Quotes erd
13032 \begin_inset Quotes eld
13036 \begin_inset Quotes erd
13042 \begin_layout Standard
13043 \begin_inset Quotes eld
13047 \begin_inset Quotes erd
13050 specifies the minimal distance between the frame and the first character
13052 An example for this is the following framed formula:
13056 \begin_layout Plain Layout
13068 \begin_inset Formula
13075 Before this formula the commands
13078 \begin_layout Standard
13100 \begin_layout Standard
13101 were inserted in \SpecialChar TeX
13103 The given values are used for all following boxes.
13106 \begin_layout Standard
13107 To return to the standard frame size, the command
13110 \begin_layout Standard
13135 \begin_layout Plain Layout
13149 \begin_layout Standard
13150 is inserted in \SpecialChar TeX
13151 mode before the next formula.
13154 \begin_layout Subsection
13155 Boxes without Frame
13156 \begin_inset CommandInset label
13158 name "subsec:Boxes-without-Frame"
13163 \begin_inset Index idx
13166 \begin_layout Plain Layout
13167 Boxes ! without frame
13175 \begin_layout Standard
13176 For boxes without a frame there are the following box commands:
13183 \begin_inset Index idx
13186 \begin_layout Plain Layout
13201 \begin_inset Index idx
13204 \begin_layout Plain Layout
13219 \begin_inset Index idx
13222 \begin_layout Plain Layout
13233 \begin_layout Standard
13240 a box can be super- or subscripted.
13241 But in contrary to normal super- and subscripting, the characters in the
13242 box keep their font size.
13249 is used in the following scheme:
13252 \begin_layout Standard
13257 raisebox{height}{box content}
13260 \begin_layout Standard
13261 When the box should contain a formula, an extra formula is needed like for
13272 \begin_inset Note Greyedout
13275 \begin_layout Plain Layout
13286 this extra formula is created by pressing
13290 twice instead of once because \SpecialChar LyX
13291 doesn't yet support
13305 \begin_inset Separator parbreak
13311 \begin_layout Standard
13313 \begin_inset Tabular
13314 <lyxtabular version="3" rows="4" columns="2">
13315 <features booktabs="true" tabularvalignment="middle">
13316 <column alignment="center" valignment="top" width="0pt">
13317 <column alignment="center" valignment="top">
13319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13322 \begin_layout Plain Layout
13328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13331 \begin_layout Plain Layout
13339 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13342 \begin_layout Plain Layout
13346 \begin_inset Formula $\to$
13352 \begin_inset Formula $\to$
13360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13363 \begin_layout Plain Layout
13364 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13374 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13377 \begin_layout Plain Layout
13381 \begin_inset Formula $\to$
13387 \begin_inset Formula $\to$
13395 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13398 \begin_layout Plain Layout
13399 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13412 \begin_layout Plain Layout
13416 \begin_inset Formula $\to$
13432 \begin_inset space \textvisiblespace{}
13440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13443 \begin_layout Plain Layout
13444 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13460 \begin_layout Standard
13485 , with the difference that there is no frame.
13488 \begin_layout Subsection
13490 \begin_inset CommandInset label
13492 name "subsec:Colored-Boxes"
13497 \begin_inset Index idx
13500 \begin_layout Plain Layout
13509 \begin_layout Standard
13510 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13519 \begin_layout Plain Layout
13520 The \SpecialChar LaTeX
13525 is part of every \SpecialChar LaTeX
13526 standard installation.
13532 \begin_inset Index idx
13535 \begin_layout Plain Layout
13541 has to be loaded in the \SpecialChar LaTeX
13542 -preamble with the line
13546 \begin_layout Plain Layout
13547 When text is colored somewhere in the document with a predefined color,
13549 loads the \SpecialChar LaTeX
13555 Thus it is possible that the package is loaded twice, but this does not
13562 \begin_inset Note Note
13565 \begin_layout Plain Layout
13566 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13575 \begin_layout Standard
13583 \begin_layout Standard
13584 \begin_inset VSpace medskip
13587 To color boxes, the command
13594 \begin_inset Index idx
13597 \begin_layout Plain Layout
13605 is used in the following scheme:
13608 \begin_layout Standard
13613 colorbox{color}{box content}
13616 \begin_layout Standard
13617 The box content can also be a box and a
13623 can also be part of another box (see the 2nd and 3rd example).
13624 When the box should contain a formula, an extra formula has to be created,
13625 the same way as for
13635 \begin_layout Plain Layout
13636 This also applies for the command
13650 \begin_layout Standard
13651 One of the following predefined colors can be chosen:
13654 \begin_layout Standard
13688 \begin_inset Separator parbreak
13694 \begin_layout Standard
13696 \begin_inset Tabular
13697 <lyxtabular version="3" rows="4" columns="2">
13698 <features booktabs="true" tabularvalignment="middle">
13699 <column alignment="center" valignment="top" width="0pt">
13700 <column alignment="center" valignment="top">
13702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13705 \begin_layout Plain Layout
13711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13714 \begin_layout Plain Layout
13722 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13725 \begin_layout Plain Layout
13729 \begin_inset Formula $\to$
13739 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13742 \begin_layout Plain Layout
13743 \begin_inset Formula $\colorbox{yellow}{A=B}$
13752 <row topspace="1.5mm">
13753 <cell alignment="center" valignment="top" usebox="none">
13756 \begin_layout Plain Layout
13760 \begin_inset Formula $\to$
13768 \begin_inset space \textvisiblespace{}
13776 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13779 \begin_layout Plain Layout
13780 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13789 <row topspace="1.5mm" bottomspace="1mm">
13790 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13793 \begin_layout Plain Layout
13797 \begin_inset space \textvisiblespace{}
13803 \begin_inset Formula $\to$
13819 \begin_inset space \textvisiblespace{}
13827 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13830 \begin_layout Plain Layout
13831 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13847 \begin_layout Standard
13854 only colors the box but not the characters in the box.
13855 To color all characters, the whole formula is highlighted and the desired
13856 color is chosen in the
13859 \begin_inset space ~
13865 The dialog can be called with the toolbar button
13868 arg "dialog-show character"
13873 Edit\SpecialChar menuseparator
13875 \begin_inset space ~
13878 Style\SpecialChar menuseparator
13882 The formula number then has the same color as the formula.
13883 When the formula number should get another color than the formula characters,
13884 the color must be changed within the formula.
13887 \begin_layout Standard
13891 \begin_layout Standard
13894 \begin_inset Formula
13896 \int A=B\label{eq:red}
13904 \begin_inset Formula
13906 \textcolor{red}{\int A=B}\label{eq:redgreen}
13914 \begin_layout Standard
13916 \begin_inset CommandInset ref
13922 is completely colored red.
13923 \begin_inset Newline newline
13927 \begin_inset CommandInset ref
13929 reference "eq:redgreen"
13933 was first completely colored green to set the color for the formula number.
13934 Subsequently the formula characters were colored red.
13937 \begin_layout Standard
13938 \begin_inset VSpace bigskip
13941 To color the frame different than the rest of the box, the command
13948 \begin_inset Index idx
13951 \begin_layout Plain Layout
13959 is used in the following scheme:
13962 \begin_layout Standard
13967 fcolorbox{frame color}{color}{box content}
13970 \begin_layout Standard
13977 is an extension of the command
13984 The frame width is set, like for
14007 \begin_layout Plain Layout
14019 \begin_inset Formula
14021 \fcolorbox{cyan}{magenta}{A=B}
14030 \begin_layout Plain Layout
14044 \begin_layout Standard
14045 This formula was created with the command
14046 \begin_inset Newline newline
14054 \begin_inset Formula $\to$
14060 \begin_inset Formula $\to$
14070 \begin_layout Standard
14071 \begin_inset VSpace bigskip
14074 To use other colors than the predefined ones, they have to be defined first.
14077 \begin_layout Standard
14078 One can for example define the color
14079 \begin_inset Quotes eld
14087 \begin_inset Quotes erd
14090 with the \SpecialChar LaTeX
14094 \begin_layout Standard
14099 definecolor{darkgreen}{cmyk}{0.5,
14114 \begin_inset Index idx
14117 \begin_layout Plain Layout
14128 \begin_layout Standard
14133 is the color space that denotes the colors
14150 The four comma separated numbers are the portion factor for the corresponding
14151 colors of the color space.
14152 The factors can be in the range of 0
14153 \begin_inset space \thinspace{}
14157 \begin_inset space \thinspace{}
14165 also the color space
14169 can be used for definitions.
14186 , so that there are in this case three portion factors for the corresponding
14188 Furthermore there is the color space
14192 with one portion factor for the gray value.
14195 \begin_layout Standard
14196 As example a framed box with the new defined color
14200 where the characters have been colored
14205 \begin_inset Formula
14207 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14215 \begin_layout Standard
14216 Self-defined colors can also be used for text with the help of the command
14224 \begin_inset Index idx
14227 \begin_layout Plain Layout
14236 \begin_layout Standard
14240 \begin_layout Plain Layout
14244 textcolor{darkgreen}{
14250 \begin_inset Quotes eld
14254 \begin_inset Quotes erd
14261 \begin_layout Plain Layout
14271 \begin_layout Standard
14279 \begin_inset Index idx
14282 \begin_layout Plain Layout
14290 is used in the scheme
14294 textcolor{color}{characters to color}
14299 \begin_layout Subsection
14301 \begin_inset CommandInset label
14303 name "subsec:Paragraph-Boxes"
14308 \begin_inset Index idx
14311 \begin_layout Plain Layout
14312 Boxes ! as paragraph
14320 \begin_layout Standard
14321 A box that can contain several lines and paragraphs, a so-called paragraph
14322 box (parbox), can be created with the menu
14324 Insert\SpecialChar menuseparator
14327 or the toolbar button
14336 \begin_layout Standard
14337 The following example shows a framed parbox in a line:
14340 \begin_layout Standard
14341 \begin_inset VSpace medskip
14345 \begin_inset Box Boxed
14355 height_special "totalheight"
14360 backgroundcolor "none"
14363 \begin_layout Plain Layout
14364 This is a paragraph box.
14366 \begin_inset space \thinspace{}
14369 cm long and can also contain formulas:
14370 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14381 \begin_layout Standard
14382 \begin_inset VSpace medskip
14388 \begin_layout Standard
14389 Such a box is created by right-clicking on the gray box inset.
14390 A dialog pops up showing the box properties.
14404 \begin_inset space \thinspace{}
14409 Vertical Box Alignment
14414 \begin_layout Standard
14415 \begin_inset VSpace medskip
14418 In \SpecialChar LaTeX
14419 a parbox is created with the command
14426 \begin_inset Index idx
14429 \begin_layout Plain Layout
14437 which has the following scheme:
14440 \begin_layout Standard
14445 parbox[position]{width}{box content}
14448 \begin_layout Standard
14463 \begin_inset Quotes eld
14467 \begin_inset Quotes erd
14470 means that the box is aligned within the surrounding text with its last
14477 \begin_inset Quotes eld
14481 \begin_inset Quotes erd
14484 this is done with the first line.
14485 When no position is given, the box will be vertically centered, see section
14493 \begin_inset space ~
14498 manual for examples.
14501 \begin_layout Standard
14502 \begin_inset VSpace bigskip
14505 To frame formulas completely, including the formula number, the formula
14506 must be set into a parbox.
14507 To do this, the command
14521 is inserted in \SpecialChar TeX
14522 mode before the formula.
14530 \begin_inset Index idx
14533 \begin_layout Plain Layout
14541 is hereby the line width set for the document.
14542 Because the frame is outside the parbox, 2
14543 \begin_inset space \thinspace{}
14546 times the frame separation and the frame thickness must be subtracted from
14548 As this is not automatically done by \SpecialChar LyX
14553 \begin_layout Plain Layout
14554 \begin_inset CommandInset href
14556 name "LyX-bug #4483"
14557 target "http://www.lyx.org/trac/ticket/4483"
14567 mode has to be used.
14568 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14577 \begin_layout Plain Layout
14582 is part of every \SpecialChar LaTeX
14583 standard installation.
14589 \begin_inset Index idx
14592 \begin_layout Plain Layout
14598 must be loaded in the \SpecialChar LaTeX
14599 -preamble with the line
14602 \begin_layout Standard
14610 \begin_layout Standard
14611 Behind the formula both boxes are closed by entering
14615 in \SpecialChar TeX
14617 Here is an example:
14621 \begin_layout Plain Layout
14635 \begin_layout Standard
14639 \begin_layout Plain Layout
14657 \begin_inset Formula
14659 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14668 \begin_layout Plain Layout
14679 \begin_layout Plain Layout
14693 \begin_layout Standard
14694 \begin_inset VSpace medskip
14697 As a parbox is used as the argument of
14703 , there is in this case no difference between
14718 \begin_layout Standard
14719 \begin_inset VSpace bigskip
14722 Paragraph boxes are very useful to comment formulas directly.
14729 is used in combination with the command
14743 \begin_inset CommandInset ref
14745 reference "subsec:User-defined-Numbering"
14752 \begin_layout Standard
14753 An example of a formula commented with
14762 \begin_layout Standard
14766 \begin_layout Plain Layout
14779 This is a description.
14780 It is distinctly separated from the formula and multiline.
14784 \begin_layout Plain Layout
14796 \begin_layout Standard
14797 Such a formula must be inserted completely in \SpecialChar TeX
14798 mode because \SpecialChar LyX
14800 support the command
14807 The formula is created with the following command sequence:
14810 \begin_layout Standard
14823 is inserted in \SpecialChar TeX
14828 \begin_layout Plain Layout
14829 When the formula style
14841 can also be replaced by
14848 (formula styles see
14849 \begin_inset CommandInset ref
14851 reference "sec:Formula-Styles"
14860 Then the description follows as normal text and finally
14866 is inserted in \SpecialChar TeX
14880 hereby create a displayed formula.
14883 \begin_layout Standard
14890 can be seen in this example that was
14891 \begin_inset Quotes eld
14895 \begin_inset Quotes erd
14898 using the mathematical textmode:
14899 \begin_inset Formula
14901 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14909 \begin_layout Section
14911 \begin_inset Index idx
14914 \begin_layout Plain Layout
14923 \begin_layout Subsection
14925 \begin_inset CommandInset label
14927 name "subsec:Big-Operators"
14932 \begin_inset Index idx
14935 \begin_layout Plain Layout
14942 \begin_inset Index idx
14945 \begin_layout Plain Layout
14952 \begin_inset Index idx
14955 \begin_layout Plain Layout
14964 \begin_layout Standard
14965 To be able to use all integral operators listed here, the option
14967 Use esint package automatically
14969 must be set in the document settings under
14972 \begin_inset space ~
14980 \begin_layout Standard
14981 \begin_inset space \hfill{}
14985 \begin_inset Tabular
14986 <lyxtabular version="3" rows="11" columns="2">
14987 <features booktabs="true" tabularvalignment="middle">
14988 <column alignment="center" valignment="top" width="0pt">
14989 <column alignment="center" valignment="top" width="0pt">
14991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14994 \begin_layout Plain Layout
15000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15003 \begin_layout Plain Layout
15011 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15014 \begin_layout Plain Layout
15018 \begin_inset Index idx
15021 \begin_layout Plain Layout
15034 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15037 \begin_layout Plain Layout
15038 \begin_inset Formula $\int$
15048 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15051 \begin_layout Plain Layout
15059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15062 \begin_layout Plain Layout
15063 \begin_inset Formula $\oint$
15073 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15076 \begin_layout Plain Layout
15084 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15087 \begin_layout Plain Layout
15088 \begin_inset Formula $\ointctrclockwise$
15098 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15101 \begin_layout Plain Layout
15109 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15112 \begin_layout Plain Layout
15113 \begin_inset Formula $\ointclockwise$
15123 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15126 \begin_layout Plain Layout
15134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15137 \begin_layout Plain Layout
15138 \begin_inset Formula $\sqint$
15148 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15151 \begin_layout Plain Layout
15159 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15162 \begin_layout Plain Layout
15164 \begin_inset Formula $\fint$
15174 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15177 \begin_layout Plain Layout
15185 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15188 \begin_layout Plain Layout
15190 \begin_inset Formula $\landupint$
15200 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15203 \begin_layout Plain Layout
15211 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15214 \begin_layout Plain Layout
15216 \begin_inset Formula $\landdownint$
15226 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15229 \begin_layout Plain Layout
15237 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15240 \begin_layout Plain Layout
15241 \begin_inset Formula $\bigcap$
15251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15254 \begin_layout Plain Layout
15262 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15265 \begin_layout Plain Layout
15266 \begin_inset Formula $\bigcup$
15280 \begin_inset space \hfill{}
15284 \begin_inset Tabular
15285 <lyxtabular version="3" rows="11" columns="2">
15286 <features booktabs="true" tabularvalignment="middle">
15287 <column alignment="center" valignment="top" width="0pt">
15288 <column alignment="center" valignment="top" width="0pt">
15290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15293 \begin_layout Plain Layout
15299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15302 \begin_layout Plain Layout
15310 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15313 \begin_layout Plain Layout
15317 \begin_inset Index idx
15320 \begin_layout Plain Layout
15333 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15336 \begin_layout Plain Layout
15337 \begin_inset Formula $\sum$
15347 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15350 \begin_layout Plain Layout
15354 \begin_inset Index idx
15357 \begin_layout Plain Layout
15364 \begin_layout Plain Layout
15383 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15386 \begin_layout Plain Layout
15387 \begin_inset Formula $\prod$
15397 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15400 \begin_layout Plain Layout
15408 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15411 \begin_layout Plain Layout
15412 \begin_inset Formula $\coprod$
15422 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15425 \begin_layout Plain Layout
15433 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15436 \begin_layout Plain Layout
15437 \begin_inset Formula $\bigodot$
15447 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15450 \begin_layout Plain Layout
15458 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15461 \begin_layout Plain Layout
15462 \begin_inset Formula $\bigotimes$
15472 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15475 \begin_layout Plain Layout
15483 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15486 \begin_layout Plain Layout
15487 \begin_inset Formula $\bigoplus$
15497 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15500 \begin_layout Plain Layout
15508 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15511 \begin_layout Plain Layout
15512 \begin_inset Formula $\bigwedge$
15522 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15525 \begin_layout Plain Layout
15533 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15536 \begin_layout Plain Layout
15537 \begin_inset Formula $\bigvee$
15547 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15550 \begin_layout Plain Layout
15558 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15561 \begin_layout Plain Layout
15562 \begin_inset Formula $\bigsqcup$
15572 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15575 \begin_layout Plain Layout
15583 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15586 \begin_layout Plain Layout
15587 \begin_inset Formula $\biguplus$
15601 \begin_inset space \hfill{}
15607 \begin_layout Standard
15608 All big operators can also be inserted via the math toolbar button
15611 arg "math-insert \\intop"
15617 \begin_layout Standard
15618 The operators are called big because they are bigger than the sometimes
15619 equal looking binary operators.
15620 All big operators can have limits as described in the next subsection.
15623 \begin_layout Standard
15624 For all integral operators there is a second version available, ending in
15642 These operators are different from
15649 \begin_inset space \space{}
15652 in the style the operator limits are displayed, see
15653 \begin_inset CommandInset ref
15655 reference "subsec:Operator-Limits"
15663 \begin_layout Subsubsection*
15664 Advice for Integrals
15667 \begin_layout Standard
15672 in an integral is an operator, that therefore has to be set upright.
15673 This is done by highlighting the
15677 and using the keyboard shortcut
15687 \begin_layout Plain Layout
15693 \begin_inset CommandInset ref
15695 reference "subsec:Font-Styles"
15705 Finally the smallest space is inserted before the
15709 , as this is usual for operators.
15713 \begin_layout Standard
15715 \begin_inset Formula $\int A(x)dx$
15719 \begin_inset Newline newline
15723 \begin_inset Phantom HPhantom
15726 \begin_layout Plain Layout
15733 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15739 \begin_layout Standard
15740 For multiple integrals there are the following commands:
15741 \begin_inset VSpace medskip
15747 \begin_layout Standard
15748 \begin_inset space \hfill{}
15752 \begin_inset Tabular
15753 <lyxtabular version="3" rows="4" columns="2">
15754 <features booktabs="true" tabularvalignment="middle">
15755 <column alignment="center" valignment="top" width="0pt">
15756 <column alignment="center" valignment="top" width="0pt">
15758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15761 \begin_layout Plain Layout
15767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15770 \begin_layout Plain Layout
15777 <row bottomspace="1mm">
15778 <cell alignment="center" valignment="top" usebox="none">
15781 \begin_layout Plain Layout
15789 <cell alignment="center" valignment="top" usebox="none">
15792 \begin_layout Plain Layout
15793 \begin_inset Formula $\iint$
15802 <row bottomspace="1mm">
15803 <cell alignment="center" valignment="top" usebox="none">
15806 \begin_layout Plain Layout
15814 <cell alignment="center" valignment="top" usebox="none">
15817 \begin_layout Plain Layout
15818 \begin_inset Formula $\oiint$
15827 <row bottomspace="1mm">
15828 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15831 \begin_layout Plain Layout
15839 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15842 \begin_layout Plain Layout
15843 \begin_inset Formula $\sqiint$
15857 \begin_inset space \hfill{}
15861 \begin_inset Tabular
15862 <lyxtabular version="3" rows="4" columns="2">
15863 <features booktabs="true" tabularvalignment="middle">
15864 <column alignment="center" valignment="top" width="0pt">
15865 <column alignment="center" valignment="top" width="0pt">
15867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15870 \begin_layout Plain Layout
15876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15879 \begin_layout Plain Layout
15886 <row bottomspace="1mm">
15887 <cell alignment="center" valignment="top" usebox="none">
15890 \begin_layout Plain Layout
15898 <cell alignment="center" valignment="top" usebox="none">
15901 \begin_layout Plain Layout
15902 \begin_inset Formula $\iiint$
15911 <row bottomspace="1mm">
15912 <cell alignment="center" valignment="top" usebox="none">
15915 \begin_layout Plain Layout
15923 <cell alignment="center" valignment="top" usebox="none">
15926 \begin_layout Plain Layout
15927 \begin_inset Formula $\iiiint$
15936 <row bottomspace="1mm">
15937 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15940 \begin_layout Plain Layout
15948 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15951 \begin_layout Plain Layout
15952 \begin_inset Formula $\dotsint$
15966 \begin_inset space \hfill{}
15972 \begin_layout Subsection
15974 \begin_inset CommandInset label
15976 name "subsec:Operator-Limits"
15981 \begin_inset Index idx
15984 \begin_layout Plain Layout
15993 \begin_layout Standard
15994 Limits are created by super- and subscripts:
15995 \begin_inset Separator parbreak
16001 \begin_layout Standard
16003 \begin_inset Tabular
16004 <lyxtabular version="3" rows="2" columns="2">
16005 <features booktabs="true" tabularvalignment="middle">
16006 <column alignment="center" valignment="top" width="0pt">
16007 <column alignment="center" valignment="top" width="0pt">
16009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16012 \begin_layout Plain Layout
16018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16021 \begin_layout Plain Layout
16029 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16032 \begin_layout Plain Layout
16038 \begin_inset space \textvisiblespace{}
16042 \begin_inset Formula $\to$
16046 \begin_inset Formula $\to$
16054 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16057 \begin_layout Plain Layout
16058 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
16074 \begin_layout Standard
16075 Limits of inline formulas are set right beside the operator.
16076 Limits in displayed formulas are set above or below the operator, except
16077 for integral limits.
16080 \begin_layout Standard
16081 To force that the limits are set beside the operator, the cursor is set
16082 directly behind the operator and the limits type is changed with the menu
16085 Edit\SpecialChar menuseparator
16086 Math\SpecialChar menuseparator
16105 \begin_layout Standard
16106 The default limits type is this:
16107 \begin_inset Formula
16109 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16114 This is how it looks when the limits type was changed to
16121 \begin_inset Formula
16123 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16128 For integrals, except those ending with
16144 etc., the limits are by default set beside the operator.
16145 But for multiple integrals the limits are often set below the operator.
16146 In the following example the limits type was therefore set to
16150 and so set below the integrals:
16151 \begin_inset Formula
16153 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16161 \begin_layout Standard
16162 \begin_inset VSpace medskip
16165 To specify conditions for limits, the commands
16172 \begin_inset Index idx
16175 \begin_layout Plain Layout
16190 \begin_inset Index idx
16193 \begin_layout Plain Layout
16202 To create for example this expression
16203 \begin_inset Formula
16205 \sum_{\begin{subarray}{c}
16209 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16217 \begin_layout Standard
16218 the following has to be done:
16219 \begin_inset Newline newline
16231 \begin_inset space \textvisiblespace{}
16237 One is now in a blue box under the summation operator and insert there
16243 \begin_inset space \textvisiblespace{}
16249 The blue box is now within a purple box and now several lines can be written
16251 A new line is created by inserting a line break (
16254 arg "newline-insert newline"
16259 \begin_inset Newline newline
16264 0<k<1000 Ctrl+Return
16265 \begin_inset Newline newline
16270 is typed in, a new box appears below for the new line.
16273 \begin_layout Standard
16274 The alignment of the lines can be changed to left aligned with the
16284 Edit\SpecialChar menuseparator
16288 To get right alignment,
16293 \begin_inset space \textvisiblespace{}
16298 is inserted at the beginning of the line.
16301 \begin_layout Standard
16314 with the difference that the lines are always centered.
16317 \begin_layout Standard
16318 \begin_inset VSpace bigskip
16322 \begin_inset CommandInset ref
16324 reference "eq:substack"
16328 there can be too much space beside an operator, because the characters
16329 following the operator are set beside the limits.
16330 To avoid this the command
16337 \begin_inset Index idx
16340 \begin_layout Plain Layout
16349 To activate it, set in the document settings under
16352 \begin_inset space ~
16362 \begin_inset Index idx
16365 \begin_layout Plain Layout
16366 Packages ! mathtools
16374 \begin_inset space ~
16386 sets the space besides the operator to 0
16387 \begin_inset space \thinspace{}
16391 \begin_inset Newline newline
16395 \begin_inset CommandInset ref
16397 reference "eq:substack"
16401 , one uses the command
16404 \begin_layout Standard
16412 \begin_layout Standard
16413 and inserts the operator with its limits into the braces.
16414 Behind the brace one continues the formula:
16415 \begin_inset Formula
16417 \smashoperator{\sum_{\begin{subarray}{c}
16421 \end{subarray}}^{n}}k^{-2}
16429 \begin_layout Standard
16430 It is possible to set the space of only one side of the operator to 0
16431 \begin_inset space \thinspace{}
16435 To do this write either
16454 stands for the left and
16458 for the right side of the operator.
16459 Here is an example of the possible
16468 \begin_layout Standard
16469 \begin_inset Formula
16471 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}
16479 \begin_layout Standard
16480 \begin_inset VSpace bigskip
16486 \begin_layout Standard
16487 When several consecutive operators have limits the typesetting of the limits
16488 looks often imperfect in the output, see this example:
16489 \begin_inset Formula
16491 \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}
16496 To improve the typesetting set in the document settings under
16499 \begin_inset space ~
16509 \begin_inset Index idx
16512 \begin_layout Plain Layout
16513 Packages ! mathtools
16521 \begin_inset space ~
16527 Then insert into your formula the command
16534 \begin_inset Index idx
16537 \begin_layout Plain Layout
16545 directly before the first operator.
16546 The example will then look like this:
16547 \begin_inset Formula
16549 \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}
16557 \begin_layout Standard
16558 \begin_inset VSpace bigskip
16561 How to use one limit for several operators is described in
16562 \begin_inset CommandInset ref
16564 reference "subsec:Self-defined-Operators"
16571 \begin_layout Subsection
16572 Decoration for Operators
16573 \begin_inset Index idx
16576 \begin_layout Plain Layout
16577 Operators ! Decoration
16585 \begin_layout Standard
16593 \begin_inset Index idx
16596 \begin_layout Plain Layout
16611 \begin_inset Index idx
16614 \begin_layout Plain Layout
16622 characters can be placed above or below an operator, respectively.
16630 \begin_inset Index idx
16633 \begin_layout Plain Layout
16641 characters can be set before and behind a big operator.
16644 \begin_layout Standard
16646 \begin_inset space ~
16658 \begin_layout Itemize
16665 is used to set characters at the corners of the operator
16668 \begin_layout Itemize
16675 is used to set characters before and/or behind the operator (this variant
16676 represents \SpecialChar LaTeX
16686 \begin_layout Itemize
16693 is used to set characters at the left corners and/or behind the operator
16696 \begin_layout Itemize
16703 is used to set characters at the right corners and/or before the operator
16706 \begin_layout Standard
16707 For example the command
16712 \begin_inset space \textvisiblespace{}
16718 \begin_inset space \textvisiblespace{}
16722 \begin_inset Formula $\to$
16726 \begin_inset Formula $\to$
16730 \begin_inset space \textvisiblespace{}
16740 \begin_inset Formula
16742 \sideset{}{'}\sum_{k=1}^{n}
16750 \begin_layout Standard
16751 \begin_inset Note Greyedout
16754 \begin_layout Plain Layout
16761 can only be used to decorate big operators, binary operators are not allowed.
16769 \begin_layout Standard
16782 can also be used to decorate symbols and characters.
16783 For example, the command
16788 \begin_inset space \textvisiblespace{}
16794 \begin_inset space \textvisiblespace{}
16800 \begin_inset Formula $\uparrow$
16808 \begin_inset Formula
16810 \overset{a}{\maltese}
16818 \begin_layout Subsection
16820 \begin_inset CommandInset label
16822 name "subsec:Binary-Operators"
16827 \begin_inset Index idx
16830 \begin_layout Plain Layout
16839 \begin_layout Standard
16840 Binary operators are surrounded by space when there is a character before
16842 \begin_inset VSpace medskip
16848 \begin_layout Standard
16849 \begin_inset Tabular
16850 <lyxtabular version="3" rows="13" columns="2">
16851 <features booktabs="true" tabularvalignment="middle">
16852 <column alignment="center" valignment="top" width="0pt">
16853 <column alignment="center" valignment="top" width="0pt">
16855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16858 \begin_layout Plain Layout
16860 \begin_inset Note Note
16863 \begin_layout Plain Layout
16870 is only used as spacer.
16880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16883 \begin_layout Plain Layout
16891 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16894 \begin_layout Plain Layout
16900 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16903 \begin_layout Plain Layout
16904 \begin_inset Formula $+$
16914 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16917 \begin_layout Plain Layout
16923 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16926 \begin_layout Plain Layout
16927 \begin_inset Formula $-$
16937 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16940 \begin_layout Plain Layout
16948 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16951 \begin_layout Plain Layout
16952 \begin_inset Formula $\pm$
16962 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16965 \begin_layout Plain Layout
16973 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16976 \begin_layout Plain Layout
16977 \begin_inset Formula $\mp$
16987 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16990 \begin_layout Plain Layout
16998 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17001 \begin_layout Plain Layout
17002 \begin_inset Formula $\cdot$
17012 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17015 \begin_layout Plain Layout
17023 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17026 \begin_layout Plain Layout
17027 \begin_inset Formula $\times$
17037 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17040 \begin_layout Plain Layout
17048 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17051 \begin_layout Plain Layout
17052 \begin_inset Formula $\div$
17062 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17065 \begin_layout Plain Layout
17069 \begin_layout Plain Layout
17082 \begin_layout Plain Layout
17094 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17097 \begin_layout Plain Layout
17098 \begin_inset Formula $*$
17108 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17111 \begin_layout Plain Layout
17119 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17122 \begin_layout Plain Layout
17123 \begin_inset Formula $\star$
17133 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17136 \begin_layout Plain Layout
17144 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17147 \begin_layout Plain Layout
17148 \begin_inset Formula $\circ$
17158 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17161 \begin_layout Plain Layout
17169 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17172 \begin_layout Plain Layout
17173 \begin_inset Formula $\diamond$
17183 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17186 \begin_layout Plain Layout
17194 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17197 \begin_layout Plain Layout
17198 \begin_inset Formula $\bullet$
17212 \begin_inset space \hfill{}
17216 \begin_inset Tabular
17217 <lyxtabular version="3" rows="13" columns="2">
17218 <features booktabs="true" tabularvalignment="middle">
17219 <column alignment="center" valignment="top" width="0pt">
17220 <column alignment="center" valignment="top" width="0pt">
17222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17225 \begin_layout Plain Layout
17231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17234 \begin_layout Plain Layout
17242 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17245 \begin_layout Plain Layout
17253 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17256 \begin_layout Plain Layout
17257 \begin_inset Formula $\nabla$
17267 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17270 \begin_layout Plain Layout
17278 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17281 \begin_layout Plain Layout
17282 \begin_inset Formula $\bigtriangledown$
17292 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17295 \begin_layout Plain Layout
17303 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17306 \begin_layout Plain Layout
17307 \begin_inset Formula $\bigtriangleup$
17317 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17320 \begin_layout Plain Layout
17328 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17331 \begin_layout Plain Layout
17332 \begin_inset Formula $\Box$
17342 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17345 \begin_layout Plain Layout
17353 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17356 \begin_layout Plain Layout
17357 \begin_inset Formula $\cap$
17367 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17370 \begin_layout Plain Layout
17378 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17381 \begin_layout Plain Layout
17382 \begin_inset Formula $\cup$
17392 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17395 \begin_layout Plain Layout
17403 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17406 \begin_layout Plain Layout
17407 \begin_inset Formula $\dagger$
17417 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17420 \begin_layout Plain Layout
17428 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17431 \begin_layout Plain Layout
17432 \begin_inset Formula $\ddagger$
17442 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17445 \begin_layout Plain Layout
17453 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17456 \begin_layout Plain Layout
17457 \begin_inset Formula $\wr$
17467 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17470 \begin_layout Plain Layout
17478 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17481 \begin_layout Plain Layout
17482 \begin_inset Formula $\bigcirc$
17492 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17495 \begin_layout Plain Layout
17503 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17506 \begin_layout Plain Layout
17507 \begin_inset Formula $\wedge$
17517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17520 \begin_layout Plain Layout
17528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17531 \begin_layout Plain Layout
17532 \begin_inset Formula $\vee$
17546 \begin_inset space \hfill{}
17550 \begin_inset Tabular
17551 <lyxtabular version="3" rows="13" columns="2">
17552 <features booktabs="true" tabularvalignment="middle">
17553 <column alignment="center" valignment="top" width="0pt">
17554 <column alignment="center" valignment="top" width="0pt">
17556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17559 \begin_layout Plain Layout
17565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17568 \begin_layout Plain Layout
17576 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17579 \begin_layout Plain Layout
17587 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17590 \begin_layout Plain Layout
17591 \begin_inset Formula $\oplus$
17601 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17604 \begin_layout Plain Layout
17612 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17615 \begin_layout Plain Layout
17616 \begin_inset Formula $\ominus$
17626 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17629 \begin_layout Plain Layout
17637 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17640 \begin_layout Plain Layout
17641 \begin_inset Formula $\otimes$
17651 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17654 \begin_layout Plain Layout
17662 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17665 \begin_layout Plain Layout
17666 \begin_inset Formula $\oslash$
17676 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17679 \begin_layout Plain Layout
17687 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17690 \begin_layout Plain Layout
17691 \begin_inset Formula $\odot$
17701 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17704 \begin_layout Plain Layout
17712 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17715 \begin_layout Plain Layout
17716 \begin_inset Formula $\amalg$
17726 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17729 \begin_layout Plain Layout
17737 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17740 \begin_layout Plain Layout
17741 \begin_inset Formula $\uplus$
17751 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17754 \begin_layout Plain Layout
17762 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17765 \begin_layout Plain Layout
17766 \begin_inset Formula $\setminus$
17776 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17779 \begin_layout Plain Layout
17787 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17790 \begin_layout Plain Layout
17791 \begin_inset Formula $\sqcap$
17801 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17804 \begin_layout Plain Layout
17812 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17815 \begin_layout Plain Layout
17816 \begin_inset Formula $\sqcup$
17826 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17829 \begin_layout Plain Layout
17837 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17840 \begin_layout Plain Layout
17841 \begin_inset Formula $\triangleleft$
17851 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17854 \begin_layout Plain Layout
17862 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17865 \begin_layout Plain Layout
17866 \begin_inset Formula $\triangleright$
17882 \begin_layout Standard
17883 All binary operators can also be inserted via the math toolbar button
17886 arg "math-insert \\pm"
17892 \begin_layout Standard
17893 To typeset the Laplace operator also
17910 \begin_inset Formula $\nabla^{2}$
17913 ) can be used instead of
17922 \begin_layout Standard
17929 Insert\SpecialChar menuseparator
17941 \begin_layout Subsection
17942 Self-defined Operators
17943 \begin_inset CommandInset label
17945 name "subsec:Self-defined-Operators"
17950 \begin_inset Index idx
17953 \begin_layout Plain Layout
17954 Operators ! self-defined
17962 \begin_layout Standard
17963 With the help of the command
17967 DeclareMathOperator
17970 \begin_inset Index idx
17973 \begin_layout Plain Layout
17978 DeclareMathOperator
17983 custom operators can be defined in the \SpecialChar LaTeX
17985 Its command scheme is:
17988 \begin_layout Standard
17993 DeclareMathOperator{new command}{display}
17996 \begin_layout Standard
17997 Display can be characters or symbols that define how the operator looks
17999 To define a big operator a * is set behind the command.
18000 All self-defined big operators can have limits as described in
18001 \begin_inset CommandInset ref
18003 reference "subsec:Operator-Limits"
18010 \begin_layout Standard
18011 For example the \SpecialChar LaTeX
18015 \begin_layout Standard
18020 DeclareMathOperator*{
18027 \begin_layout Standard
18028 defines the command
18034 , that inserts a big operator consisting of the lozenge symbol from
18035 \begin_inset CommandInset ref
18037 reference "subsec:Miscellaneous-Symbols"
18042 \begin_inset Formula
18044 \Lozenge_{n=1}^{\infty}
18049 The command for this formula is:
18060 \begin_inset Formula $\to$
18066 \begin_layout Standard
18067 \begin_inset VSpace bigskip
18070 When self-defined operators are not used several times in the document,
18071 they can also be defined with the commands
18078 \begin_inset Index idx
18081 \begin_layout Plain Layout
18096 \begin_inset Index idx
18099 \begin_layout Plain Layout
18107 , which have the following scheme:
18110 \begin_layout Standard
18124 \begin_layout Standard
18131 defines big operators,
18140 \begin_layout Standard
18148 \begin_inset space \thinspace{}
18152 \begin_inset space \space{}
18155 be used to use one limit for several operators:
18158 \begin_layout Standard
18159 \begin_inset Formula
18161 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18169 \begin_layout Standard
18170 The command for the formula above is:
18171 \begin_inset Newline newline
18187 \begin_inset space \textvisiblespace{}
18193 \begin_inset Formula $\to$
18199 \begin_inset space \textvisiblespace{}
18207 \begin_layout Section
18209 \begin_inset Index idx
18212 \begin_layout Plain Layout
18221 \begin_layout Subsection
18223 \begin_inset CommandInset label
18225 name "subsec:Font-Styles"
18230 \begin_inset Index idx
18233 \begin_layout Plain Layout
18242 \begin_layout Standard
18243 Latin letters in formulas can be set in one of the following font styles:
18246 \begin_layout Standard
18248 \begin_inset space \hfill{}
18252 \begin_inset Tabular
18253 <lyxtabular version="3" rows="6" columns="2">
18254 <features booktabs="true" tabularvalignment="middle">
18255 <column alignment="center" valignment="top" width="0pt">
18256 <column alignment="center" valignment="top">
18258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18261 \begin_layout Plain Layout
18267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18270 \begin_layout Plain Layout
18278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18281 \begin_layout Plain Layout
18287 \begin_inset space \textvisiblespace{}
18297 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18300 \begin_layout Plain Layout
18301 \begin_inset Formula $\mathbb{ABC}$
18311 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18314 \begin_layout Plain Layout
18320 \begin_inset space \textvisiblespace{}
18330 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18333 \begin_layout Plain Layout
18334 \begin_inset Formula $\mathbf{AbC}$
18344 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18347 \begin_layout Plain Layout
18353 \begin_inset space \textvisiblespace{}
18363 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18366 \begin_layout Plain Layout
18367 \begin_inset Formula $\boldsymbol{AbC}$
18377 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18380 \begin_layout Plain Layout
18386 \begin_inset space \textvisiblespace{}
18396 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18399 \begin_layout Plain Layout
18400 \begin_inset Formula $\mathcal{ABC}$
18410 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18413 \begin_layout Plain Layout
18419 \begin_inset space \textvisiblespace{}
18429 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18432 \begin_layout Plain Layout
18433 \begin_inset Formula $\mathfrak{AbC}$
18447 \begin_inset space \hfill{}
18451 \begin_inset Tabular
18452 <lyxtabular version="3" rows="6" columns="2">
18453 <features booktabs="true" tabularvalignment="middle">
18454 <column alignment="center" valignment="top" width="0pt">
18455 <column alignment="center" valignment="top">
18457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18460 \begin_layout Plain Layout
18466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18469 \begin_layout Plain Layout
18477 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18480 \begin_layout Plain Layout
18486 \begin_inset space \textvisiblespace{}
18496 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18499 \begin_layout Plain Layout
18500 \begin_inset Formula $\mathit{AbC}$
18510 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18513 \begin_layout Plain Layout
18519 \begin_inset space \textvisiblespace{}
18529 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18532 \begin_layout Plain Layout
18533 \begin_inset Formula $\mathrm{AbC}$
18543 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18546 \begin_layout Plain Layout
18552 \begin_inset space \textvisiblespace{}
18562 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18565 \begin_layout Plain Layout
18566 \begin_inset Formula $\mathsf{AbC}$
18576 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18579 \begin_layout Plain Layout
18585 \begin_inset space \textvisiblespace{}
18595 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18598 \begin_layout Plain Layout
18599 \begin_inset Formula $\mathtt{AbC}$
18609 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18612 \begin_layout Plain Layout
18618 \begin_inset space \textvisiblespace{}
18628 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18631 \begin_layout Plain Layout
18632 \begin_inset Formula $\mathscr{ABC}$
18646 \begin_inset space \hfill{}
18652 \begin_layout Standard
18653 \begin_inset Note Greyedout
18656 \begin_layout Plain Layout
18679 can only be used for big letters.
18687 \begin_layout Standard
18688 Predefined is the style
18697 \begin_layout Standard
18698 The style commands work also for letters in mathematical constructs:
18699 \begin_inset Formula
18701 \mathfrak{A=\frac{b}{C}}
18709 \begin_layout Standard
18710 Characters in mathematical text don't appear in a math font style but in
18711 the text font style
18718 That their style can't be set correctly via the text style dialog is a
18719 bug in \SpecialChar LyX
18724 \begin_layout Plain Layout
18725 \begin_inset CommandInset href
18727 name "LyX-bug #4629"
18728 target "http://www.lyx.org/trac/ticket/4629"
18740 \begin_layout Standard
18741 Instead of the style commands the dialog
18743 Edit\SpecialChar menuseparator
18744 Math\SpecialChar menuseparator
18747 or the toolbar button
18750 arg "math-insert \\font"
18756 \begin_layout Subsection
18758 \begin_inset CommandInset label
18760 name "subsec:Bold-Formulas"
18765 \begin_inset Index idx
18768 \begin_layout Plain Layout
18777 \begin_layout Standard
18778 To make a complete formula bold, the command
18784 from the previous subsection cannot be used, because it doesn't work for
18785 small Greek letters.
18786 Furthermore it prints Latin letters always upright, like in the following
18790 \begin_layout Standard
18791 \begin_inset Formula
18793 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18801 \begin_layout Standard
18802 To display the formula correctly, the command
18809 \begin_inset Formula
18811 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18816 It is also possible to set the formula in a
18818 boldmath environment
18821 This environment is created by inserting the command
18828 \begin_inset Index idx
18831 \begin_layout Plain Layout
18839 in \SpecialChar TeX
18841 To end the environment, the command
18848 \begin_inset Index idx
18851 \begin_layout Plain Layout
18859 is inserted in \SpecialChar TeX
18864 \begin_layout Plain Layout
18874 \begin_inset Formula
18876 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18885 \begin_layout Plain Layout
18897 \begin_layout Subsection
18899 \begin_inset Index idx
18902 \begin_layout Plain Layout
18911 \begin_layout Standard
18912 Formulas can be colored like normal text: Highlight a formula or a formula
18918 Here is a formula in magenta:
18919 \begin_inset Formula
18921 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18929 \begin_layout Standard
18930 You can also define your own colors as described in
18931 \begin_inset CommandInset ref
18933 reference "subsec:Colored-Boxes"
18938 They can be used with the \SpecialChar TeX
18946 \begin_inset Index idx
18949 \begin_layout Plain Layout
18960 \begin_layout Standard
18965 textcolor{color}{characters or formula}
18968 \begin_layout Standard
18969 The following example was colored completely dark green and partly red:
18972 \begin_layout Standard
18976 \begin_layout Plain Layout
18980 textcolor{darkgreen}{
18986 \begin_inset Formula
18988 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
18997 \begin_layout Plain Layout
19007 \begin_layout Standard
19008 Due to a bug in \SpecialChar LyX
19009 only complete formulas can be colored with self-defined
19014 \begin_layout Plain Layout
19015 \begin_inset CommandInset href
19017 name "LyX-bug #5269"
19018 target "http://www.lyx.org/trac/ticket/5269"
19030 \begin_layout Subsection
19032 \begin_inset CommandInset label
19034 name "subsec:Font-Sizes"
19039 \begin_inset Index idx
19042 \begin_layout Plain Layout
19051 \begin_layout Standard
19052 For characters in formulas there are, analog to characters in text, the
19053 following size commands:
19056 \begin_layout Standard
19100 \begin_inset Newline newline
19122 \begin_layout Standard
19123 The size produced by the commands depends on the document font size, which
19124 corresponds to the command
19131 The other commands produce smaller or larger sizes than
19138 The font size can however not exceed a certain value.
19139 Is for example the document font size 12
19140 \begin_inset space \thinspace{}
19149 switches to the same size as
19159 \begin_layout Standard
19160 A size command is inserted in \SpecialChar TeX
19161 mode before the formula and sets the size
19162 for all following formula and text characters.
19163 To switch back to the initial size, the command
19169 is inserted behind the formula in \SpecialChar TeX
19173 \begin_layout Standard
19174 Within a formula the size can be changed using the following size commands
19175 or the toolbar button
19178 arg "math-insert \\style"
19182 \begin_inset Separator parbreak
19188 \begin_layout Standard
19191 \begin_inset Tabular
19192 <lyxtabular version="3" rows="5" columns="2">
19193 <features booktabs="true" tabularvalignment="middle">
19194 <column alignment="center" valignment="top" width="0pt">
19195 <column alignment="center" valignment="top">
19197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19200 \begin_layout Plain Layout
19206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19209 \begin_layout Plain Layout
19217 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19220 \begin_layout Plain Layout
19224 \begin_inset Index idx
19227 \begin_layout Plain Layout
19240 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19243 \begin_layout Plain Layout
19244 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19253 <row topspace="1mm">
19254 <cell alignment="center" valignment="top" usebox="none">
19257 \begin_layout Plain Layout
19265 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19268 \begin_layout Plain Layout
19269 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19279 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19282 \begin_layout Plain Layout
19290 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19293 \begin_layout Plain Layout
19294 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19304 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19307 \begin_layout Plain Layout
19315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19318 \begin_layout Plain Layout
19319 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19335 \begin_layout Standard
19336 After entering these commands, a blue box appears in which the formula parts
19340 \begin_layout Standard
19341 There is a further method to change the font size, that though only works
19342 for symbols or letters in mathematical text.
19343 To use it, one of the above text size commands is inserted in mathematical
19345 All following characters until the end of the mathematical text or until
19346 another size command will have the selected size.
19348 \begin_inset VSpace -2mm
19354 \begin_layout Standard
19358 \begin_layout Plain Layout
19368 \begin_inset Formula
19370 A=\frac{B}{c}\cdot\maltese
19376 \begin_inset Formula
19378 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19387 \begin_layout Plain Layout
19399 \begin_layout Standard
19400 \begin_inset VSpace medskip
19403 Before both formulas the command
19410 The command for the second formula is:
19411 \begin_inset Newline newline
19419 \begin_inset space \textvisiblespace{}
19425 \begin_inset space \textvisiblespace{}
19431 \begin_inset space \textvisiblespace{}
19437 \begin_inset space \textvisiblespace{}
19441 \begin_inset Formula $\to$
19445 \begin_inset Formula $\to$
19449 \begin_inset Newline newline
19453 \begin_inset space \hspace*{}
19464 \begin_inset space \textvisiblespace{}
19470 \begin_inset space \textvisiblespace{}
19476 \begin_inset space \textvisiblespace{}
19482 \begin_layout Standard
19483 If a symbol cannot be displayed in different sizes, it will always be displayed
19484 in the default size.
19487 \begin_layout Section
19489 \begin_inset Index idx
19492 \begin_layout Plain Layout
19501 \begin_layout Standard
19502 Greek letters can also be inserted via the toolbar button
19505 arg "math-insert \\alpha"
19509 All international typesetting norms purport that Greek letters in math
19510 have to be typeset italic/slanted.
19511 In some languages, like French or Russian, they are nevertheless sometimes
19515 \begin_layout Subsection
19517 \begin_inset Index idx
19520 \begin_layout Plain Layout
19521 Greek letters ! small
19529 \begin_layout Standard
19530 \begin_inset space \hfill{}
19534 \begin_inset Tabular
19535 <lyxtabular version="3" rows="11" columns="2">
19536 <features booktabs="true" tabularvalignment="middle">
19537 <column alignment="center" valignment="top" width="0pt">
19538 <column alignment="center" valignment="top" width="0pt">
19540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19543 \begin_layout Plain Layout
19549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19552 \begin_layout Plain Layout
19560 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19563 \begin_layout Plain Layout
19571 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19574 \begin_layout Plain Layout
19575 \begin_inset Formula $\alpha$
19585 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19588 \begin_layout Plain Layout
19596 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19599 \begin_layout Plain Layout
19600 \begin_inset Formula $\beta$
19610 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19613 \begin_layout Plain Layout
19621 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19624 \begin_layout Plain Layout
19625 \begin_inset Formula $\gamma$
19635 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19638 \begin_layout Plain Layout
19646 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19649 \begin_layout Plain Layout
19650 \begin_inset Formula $\delta$
19660 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19663 \begin_layout Plain Layout
19671 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19674 \begin_layout Plain Layout
19675 \begin_inset Formula $\epsilon$
19685 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19688 \begin_layout Plain Layout
19696 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19699 \begin_layout Plain Layout
19700 \begin_inset Formula $\varepsilon$
19710 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19713 \begin_layout Plain Layout
19721 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19724 \begin_layout Plain Layout
19725 \begin_inset Formula $\zeta$
19735 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19738 \begin_layout Plain Layout
19746 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19749 \begin_layout Plain Layout
19750 \begin_inset Formula $\eta$
19760 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19763 \begin_layout Plain Layout
19771 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19774 \begin_layout Plain Layout
19775 \begin_inset Formula $\theta$
19785 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19788 \begin_layout Plain Layout
19796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19799 \begin_layout Plain Layout
19800 \begin_inset Formula $\vartheta$
19814 \begin_inset space \hfill{}
19818 \begin_inset Tabular
19819 <lyxtabular version="3" rows="12" columns="2">
19820 <features booktabs="true" tabularvalignment="middle">
19821 <column alignment="center" valignment="top" width="0pt">
19822 <column alignment="center" valignment="top" width="0pt">
19824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19827 \begin_layout Plain Layout
19833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19836 \begin_layout Plain Layout
19844 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19847 \begin_layout Plain Layout
19855 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19858 \begin_layout Plain Layout
19859 \begin_inset Formula $\iota$
19869 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19872 \begin_layout Plain Layout
19880 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19883 \begin_layout Plain Layout
19884 \begin_inset Formula $\kappa$
19894 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19897 \begin_layout Plain Layout
19905 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19908 \begin_layout Plain Layout
19909 \begin_inset Formula $\varkappa$
19919 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19922 \begin_layout Plain Layout
19930 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19933 \begin_layout Plain Layout
19934 \begin_inset Formula $\lambda$
19944 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19947 \begin_layout Plain Layout
19955 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19958 \begin_layout Plain Layout
19959 \begin_inset Formula $\mu$
19969 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19972 \begin_layout Plain Layout
19980 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19983 \begin_layout Plain Layout
19984 \begin_inset Formula $\nu$
19994 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19997 \begin_layout Plain Layout
20005 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20008 \begin_layout Plain Layout
20009 \begin_inset Formula $\xi$
20019 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20022 \begin_layout Plain Layout
20028 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20031 \begin_layout Plain Layout
20032 \begin_inset Formula $o$
20042 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20045 \begin_layout Plain Layout
20053 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20056 \begin_layout Plain Layout
20057 \begin_inset Formula $\pi$
20067 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20070 \begin_layout Plain Layout
20078 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20081 \begin_layout Plain Layout
20082 \begin_inset Formula $\varpi$
20092 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20095 \begin_layout Plain Layout
20103 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20106 \begin_layout Plain Layout
20107 \begin_inset Formula $\rho$
20121 \begin_inset space \hfill{}
20125 \begin_inset Tabular
20126 <lyxtabular version="3" rows="11" columns="2">
20127 <features booktabs="true" tabularvalignment="middle">
20128 <column alignment="center" valignment="top" width="0pt">
20129 <column alignment="center" valignment="top" width="0pt">
20131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20134 \begin_layout Plain Layout
20140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20143 \begin_layout Plain Layout
20151 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20154 \begin_layout Plain Layout
20162 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20165 \begin_layout Plain Layout
20166 \begin_inset Formula $\varrho$
20176 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20179 \begin_layout Plain Layout
20187 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20190 \begin_layout Plain Layout
20191 \begin_inset Formula $\sigma$
20201 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20204 \begin_layout Plain Layout
20212 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20215 \begin_layout Plain Layout
20216 \begin_inset Formula $\varsigma$
20226 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20229 \begin_layout Plain Layout
20237 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20240 \begin_layout Plain Layout
20241 \begin_inset Formula $\tau$
20251 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20254 \begin_layout Plain Layout
20262 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20265 \begin_layout Plain Layout
20266 \begin_inset Formula $\upsilon$
20276 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20279 \begin_layout Plain Layout
20287 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20290 \begin_layout Plain Layout
20291 \begin_inset Formula $\phi$
20301 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20304 \begin_layout Plain Layout
20312 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20315 \begin_layout Plain Layout
20316 \begin_inset Formula $\varphi$
20326 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20329 \begin_layout Plain Layout
20337 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20340 \begin_layout Plain Layout
20341 \begin_inset Formula $\chi$
20351 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20354 \begin_layout Plain Layout
20362 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20365 \begin_layout Plain Layout
20366 \begin_inset Formula $\psi$
20376 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20379 \begin_layout Plain Layout
20387 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20390 \begin_layout Plain Layout
20391 \begin_inset Formula $\omega$
20405 \begin_inset space \hfill{}
20411 \begin_layout Standard
20412 \begin_inset VSpace medskip
20418 \begin_layout Standard
20419 How to create special upright Greek letters is explained in
20420 \begin_inset CommandInset ref
20422 reference "subsec:Upright-small-Greek"
20429 \begin_layout Subsection
20431 \begin_inset Index idx
20434 \begin_layout Plain Layout
20435 Greek letters ! big
20443 \begin_layout Standard
20444 \begin_inset space \hfill{}
20448 \begin_inset Tabular
20449 <lyxtabular version="3" rows="7" columns="2">
20450 <features booktabs="true" tabularvalignment="middle">
20451 <column alignment="center" valignment="top" width="0pt">
20452 <column alignment="center" valignment="top" width="0pt">
20454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20457 \begin_layout Plain Layout
20463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20466 \begin_layout Plain Layout
20474 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20477 \begin_layout Plain Layout
20485 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20488 \begin_layout Plain Layout
20489 \begin_inset Formula $\Gamma$
20499 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20502 \begin_layout Plain Layout
20510 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20513 \begin_layout Plain Layout
20514 \begin_inset Formula $\Delta$
20524 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20527 \begin_layout Plain Layout
20535 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20538 \begin_layout Plain Layout
20539 \begin_inset Formula $\Theta$
20549 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20552 \begin_layout Plain Layout
20560 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20563 \begin_layout Plain Layout
20564 \begin_inset Formula $\Lambda$
20574 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20577 \begin_layout Plain Layout
20585 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20588 \begin_layout Plain Layout
20589 \begin_inset Formula $\Xi$
20599 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20602 \begin_layout Plain Layout
20610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20613 \begin_layout Plain Layout
20614 \begin_inset Formula $\Pi$
20628 \begin_inset space \hfill{}
20632 \begin_inset Tabular
20633 <lyxtabular version="3" rows="6" columns="2">
20634 <features booktabs="true" tabularvalignment="middle">
20635 <column alignment="center" valignment="top" width="0pt">
20636 <column alignment="center" valignment="top" width="0pt">
20638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20641 \begin_layout Plain Layout
20647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20650 \begin_layout Plain Layout
20658 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20661 \begin_layout Plain Layout
20669 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20672 \begin_layout Plain Layout
20673 \begin_inset Formula $\Sigma$
20683 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20686 \begin_layout Plain Layout
20694 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20697 \begin_layout Plain Layout
20698 \begin_inset Formula $\Upsilon$
20708 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20711 \begin_layout Plain Layout
20719 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20722 \begin_layout Plain Layout
20723 \begin_inset Formula $\Phi$
20733 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20736 \begin_layout Plain Layout
20744 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20747 \begin_layout Plain Layout
20748 \begin_inset Formula $\Psi$
20758 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20761 \begin_layout Plain Layout
20769 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20772 \begin_layout Plain Layout
20773 \begin_inset Formula $\Omega$
20787 \begin_inset space \hfill{}
20793 \begin_layout Standard
20794 \begin_inset VSpace medskip
20797 That the big Greek letters appear upright is caused by a design bug when
20800 To get correct italic big letters, begin every command with
20805 For example the command
20812 \begin_inset Formula $\varGamma$
20816 Another way is to load the package
20824 \begin_layout Plain Layout
20829 is part of the \SpecialChar LaTeX
20835 \begin_inset Index idx
20838 \begin_layout Plain Layout
20843 \begin_layout Plain Layout
20863 \begin_inset Index idx
20866 \begin_layout Plain Layout
20872 with the \SpecialChar LaTeX
20876 \begin_layout Standard
20881 usepackage{fixmath}
20884 \begin_layout Standard
20885 Then all big Greek letters in a document will automatically be typeset italic.
20888 \begin_layout Subsection
20890 \begin_inset Index idx
20893 \begin_layout Plain Layout
20894 Greek letters ! bold
20902 \begin_layout Standard
20903 Greek letters cannot be set with different font styles like Latin letters.
20904 They can only be made bold with the command
20911 \begin_inset Index idx
20914 \begin_layout Plain Layout
20923 \begin_inset Separator parbreak
20929 \begin_layout Standard
20931 \begin_inset Tabular
20932 <lyxtabular version="3" rows="3" columns="2">
20933 <features booktabs="true" tabularvalignment="middle">
20934 <column alignment="center" valignment="top" width="0pt">
20935 <column alignment="center" valignment="top">
20937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20940 \begin_layout Plain Layout
20946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20949 \begin_layout Plain Layout
20957 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20960 \begin_layout Plain Layout
20972 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20975 \begin_layout Plain Layout
20976 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20986 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20989 \begin_layout Plain Layout
21001 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21004 \begin_layout Plain Layout
21005 \begin_inset Formula $\theta\boldsymbol{\theta}$
21021 \begin_layout Section
21026 \begin_layout Plain Layout
21039 \begin_layout Plain Layout
21040 A list with all symbols of most of the \SpecialChar LaTeX
21041 -packages can be found in
21042 \begin_inset CommandInset citation
21057 \begin_layout Plain Layout
21065 \begin_inset Note Note
21068 \begin_layout Plain Layout
21071 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21074 \begin_layout Plain Layout
21077 texorpdfstring is in section
21078 \begin_inset CommandInset ref
21080 reference "subsec:Formulas-in-Section"
21090 \begin_inset Index idx
21093 \begin_layout Plain Layout
21102 \begin_layout Standard
21103 Many of the symbols listed in this section can also be inserted via the
21107 arg "math-insert \\nabla"
21113 arg "math-insert \\digamma"
21119 \begin_layout Subsection
21120 Mathematical Symbols
21121 \begin_inset CommandInset label
21123 name "subsec:Mathematical-Symbols"
21128 \begin_inset Index idx
21131 \begin_layout Plain Layout
21132 Symbols ! mathematical
21140 \begin_layout Standard
21141 \begin_inset Tabular
21142 <lyxtabular version="3" rows="10" columns="2">
21143 <features booktabs="true" tabularvalignment="middle">
21144 <column alignment="center" valignment="top" width="0pt">
21145 <column alignment="center" valignment="top" width="0pt">
21147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21150 \begin_layout Plain Layout
21156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21159 \begin_layout Plain Layout
21167 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21170 \begin_layout Plain Layout
21178 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21181 \begin_layout Plain Layout
21182 \begin_inset Formula $\neg$
21192 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21195 \begin_layout Plain Layout
21203 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21206 \begin_layout Plain Layout
21207 \begin_inset Formula $\Im$
21217 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21220 \begin_layout Plain Layout
21228 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21231 \begin_layout Plain Layout
21232 \begin_inset Formula $\Re$
21242 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21245 \begin_layout Plain Layout
21253 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21256 \begin_layout Plain Layout
21257 \begin_inset Formula $\aleph$
21267 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21270 \begin_layout Plain Layout
21278 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21281 \begin_layout Plain Layout
21282 \begin_inset Formula $\partial$
21292 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21295 \begin_layout Plain Layout
21303 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21306 \begin_layout Plain Layout
21307 \begin_inset Formula $\infty$
21317 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21320 \begin_layout Plain Layout
21328 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21331 \begin_layout Plain Layout
21332 \begin_inset Formula $\wp$
21342 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21345 \begin_layout Plain Layout
21353 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21356 \begin_layout Plain Layout
21357 \begin_inset Formula $\imath$
21367 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21370 \begin_layout Plain Layout
21378 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21381 \begin_layout Plain Layout
21382 \begin_inset Formula $\jmath$
21396 \begin_inset space \hfill{}
21400 \begin_inset Tabular
21401 <lyxtabular version="3" rows="10" columns="2">
21402 <features booktabs="true" tabularvalignment="middle">
21403 <column alignment="center" valignment="top" width="0pt">
21404 <column alignment="center" valignment="top" width="0pt">
21406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21409 \begin_layout Plain Layout
21415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21418 \begin_layout Plain Layout
21420 \begin_inset Note Note
21423 \begin_layout Plain Layout
21430 is only used as spacer.
21442 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21445 \begin_layout Plain Layout
21453 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21456 \begin_layout Plain Layout
21457 \begin_inset Formula $\forall$
21467 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21470 \begin_layout Plain Layout
21478 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21481 \begin_layout Plain Layout
21482 \begin_inset Formula $\exists$
21492 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21495 \begin_layout Plain Layout
21503 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21506 \begin_layout Plain Layout
21507 \begin_inset Formula $\nexists$
21517 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21520 \begin_layout Plain Layout
21528 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21531 \begin_layout Plain Layout
21532 \begin_inset Formula $\emptyset$
21542 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21545 \begin_layout Plain Layout
21553 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21556 \begin_layout Plain Layout
21557 \begin_inset Formula $\varnothing$
21567 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21570 \begin_layout Plain Layout
21578 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21581 \begin_layout Plain Layout
21582 \begin_inset Formula $\dag$
21592 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21595 \begin_layout Plain Layout
21603 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21606 \begin_layout Plain Layout
21607 \begin_inset Formula $\ddag$
21617 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21620 \begin_layout Plain Layout
21628 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21631 \begin_layout Plain Layout
21635 \begin_layout Plain Layout
21645 \begin_inset Formula $\complement$
21652 \begin_layout Plain Layout
21666 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21669 \begin_layout Plain Layout
21677 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21680 \begin_layout Plain Layout
21681 \begin_inset Formula $\Bbbk$
21695 \begin_inset space \hfill{}
21699 \begin_inset Tabular
21700 <lyxtabular version="3" rows="10" columns="2">
21701 <features booktabs="true" tabularvalignment="middle">
21702 <column alignment="center" valignment="top" width="0pt">
21703 <column alignment="center" valignment="top" width="0pt">
21705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21708 \begin_layout Plain Layout
21714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21717 \begin_layout Plain Layout
21725 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21728 \begin_layout Plain Layout
21736 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21739 \begin_layout Plain Layout
21740 \begin_inset Formula $\prime$
21750 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21753 \begin_layout Plain Layout
21761 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21764 \begin_layout Plain Layout
21765 \begin_inset Formula $\backprime$
21775 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21778 \begin_layout Plain Layout
21786 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21789 \begin_layout Plain Layout
21790 \begin_inset Formula $\mho$
21800 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21803 \begin_layout Plain Layout
21811 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21814 \begin_layout Plain Layout
21815 \begin_inset Formula $\triangle$
21825 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21828 \begin_layout Plain Layout
21836 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21839 \begin_layout Plain Layout
21840 \begin_inset Formula $\angle$
21850 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21853 \begin_layout Plain Layout
21861 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21864 \begin_layout Plain Layout
21865 \begin_inset Formula $\measuredangle$
21875 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21878 \begin_layout Plain Layout
21886 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21889 \begin_layout Plain Layout
21890 \begin_inset Formula $\sphericalangle$
21900 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21903 \begin_layout Plain Layout
21911 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21914 \begin_layout Plain Layout
21915 \begin_inset Formula $\top$
21925 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21928 \begin_layout Plain Layout
21936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21939 \begin_layout Plain Layout
21940 \begin_inset Formula $\bot$
21956 \begin_layout Standard
21957 \begin_inset Newpage newpage
21963 \begin_layout Subsection
21964 Miscellaneous Symbols
21965 \begin_inset CommandInset label
21967 name "subsec:Miscellaneous-Symbols"
21972 \begin_inset Index idx
21975 \begin_layout Plain Layout
21976 Symbols ! miscellaneous
21984 \begin_layout Standard
21987 \begin_inset Tabular
21988 <lyxtabular version="3" rows="10" columns="2">
21989 <features booktabs="true" tabularvalignment="middle">
21990 <column alignment="center" valignment="top" width="0pt">
21991 <column alignment="center" valignment="top" width="0pt">
21993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21996 \begin_layout Plain Layout
22002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22005 \begin_layout Plain Layout
22013 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22016 \begin_layout Plain Layout
22024 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22027 \begin_layout Plain Layout
22028 \begin_inset Formula $\flat$
22038 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22041 \begin_layout Plain Layout
22049 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22052 \begin_layout Plain Layout
22053 \begin_inset Formula $\natural$
22063 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22066 \begin_layout Plain Layout
22074 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22077 \begin_layout Plain Layout
22078 \begin_inset Formula $\sharp$
22088 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22091 \begin_layout Plain Layout
22099 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22102 \begin_layout Plain Layout
22103 \begin_inset Formula $\surd$
22113 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22116 \begin_layout Plain Layout
22124 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22127 \begin_layout Plain Layout
22128 \begin_inset Formula $\checkmark$
22138 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22141 \begin_layout Plain Layout
22149 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22152 \begin_layout Plain Layout
22153 \begin_inset Formula $\yen$
22163 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22166 \begin_layout Plain Layout
22174 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22177 \begin_layout Plain Layout
22178 \begin_inset Formula $\pounds$
22188 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22191 \begin_layout Plain Layout
22197 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22200 \begin_layout Plain Layout
22201 \begin_inset Formula $\$$
22211 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22214 \begin_layout Plain Layout
22220 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22223 \begin_layout Plain Layout
22224 \begin_inset Formula $§$
22238 \begin_inset space \hfill{}
22242 \begin_inset Tabular
22243 <lyxtabular version="3" rows="10" columns="2">
22244 <features booktabs="true" tabularvalignment="middle">
22245 <column alignment="center" valignment="top" width="0pt">
22246 <column alignment="center" valignment="top">
22248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22251 \begin_layout Plain Layout
22257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22260 \begin_layout Plain Layout
22268 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22271 \begin_layout Plain Layout
22279 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22282 \begin_layout Plain Layout
22283 \begin_inset Formula $\hbar$
22293 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22296 \begin_layout Plain Layout
22304 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22307 \begin_layout Plain Layout
22308 \begin_inset Formula $\hslash$
22318 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22321 \begin_layout Plain Layout
22329 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22332 \begin_layout Plain Layout
22333 \begin_inset Formula $\clubsuit$
22343 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22346 \begin_layout Plain Layout
22354 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22357 \begin_layout Plain Layout
22358 \begin_inset Formula $\spadesuit$
22368 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22371 \begin_layout Plain Layout
22379 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22382 \begin_layout Plain Layout
22383 \begin_inset Formula $\bigstar$
22393 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22396 \begin_layout Plain Layout
22404 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22407 \begin_layout Plain Layout
22408 \begin_inset Formula $\blacklozenge$
22418 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22421 \begin_layout Plain Layout
22429 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22432 \begin_layout Plain Layout
22433 \begin_inset Formula $\blacktriangle$
22443 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22446 \begin_layout Plain Layout
22454 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22457 \begin_layout Plain Layout
22458 \begin_inset Formula $\blacktriangledown$
22468 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22471 \begin_layout Plain Layout
22479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22482 \begin_layout Plain Layout
22483 \begin_inset Formula $\bullet$
22497 \begin_inset space \hfill{}
22501 \begin_inset Tabular
22502 <lyxtabular version="3" rows="10" columns="2">
22503 <features booktabs="true" tabularvalignment="middle">
22504 <column alignment="center" valignment="top" width="0pt">
22505 <column alignment="center" valignment="top" width="0pt">
22507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22510 \begin_layout Plain Layout
22516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22519 \begin_layout Plain Layout
22527 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22530 \begin_layout Plain Layout
22538 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22541 \begin_layout Plain Layout
22542 \begin_inset Formula $\diamondsuit$
22552 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22555 \begin_layout Plain Layout
22563 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22566 \begin_layout Plain Layout
22567 \begin_inset Formula $\Diamond$
22577 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22580 \begin_layout Plain Layout
22588 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22591 \begin_layout Plain Layout
22592 \begin_inset Formula $\heartsuit$
22602 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22605 \begin_layout Plain Layout
22613 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22616 \begin_layout Plain Layout
22617 \begin_inset Formula $\P$
22627 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22630 \begin_layout Plain Layout
22638 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22641 \begin_layout Plain Layout
22642 \begin_inset Formula $\copyright$
22652 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22655 \begin_layout Plain Layout
22663 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22666 \begin_layout Plain Layout
22667 \begin_inset Formula $\circledR$
22677 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22680 \begin_layout Plain Layout
22688 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22691 \begin_layout Plain Layout
22692 \begin_inset Formula $\maltese$
22702 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22705 \begin_layout Plain Layout
22713 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22716 \begin_layout Plain Layout
22717 \begin_inset Formula $\diagup$
22727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22730 \begin_layout Plain Layout
22738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22741 \begin_layout Plain Layout
22742 \begin_inset Formula $\diagdown$
22758 \begin_layout Standard
22759 \begin_inset VSpace medskip
22765 \begin_layout Standard
22766 Some symbols can be displayed in different sizes, see
22767 \begin_inset CommandInset ref
22769 reference "subsec:Font-Sizes"
22776 \begin_layout Subsection
22778 \begin_inset Index idx
22781 \begin_layout Plain Layout
22782 Symbols ! Euro-symbol
22788 \begin_inset Index idx
22791 \begin_layout Plain Layout
22798 \begin_layout Plain Layout
22815 \begin_layout Standard
22816 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22822 \begin_inset Index idx
22825 \begin_layout Plain Layout
22831 must be installed and loaded with the \SpecialChar LaTeX
22835 \begin_layout Standard
22840 usepackage[gennarrow]{eurosym}
22843 \begin_layout Standard
22844 The Euro symbol can now be inserted with the command
22851 \begin_inset Index idx
22854 \begin_layout Plain Layout
22865 \begin_layout Standard
22866 The Euro symbol can directly be inserted with the € key in mathematical
22867 text, without having
22882 can also be inserted in \SpecialChar TeX
22884 The official currency symbol can then be inserted with the command
22891 \begin_inset Index idx
22894 \begin_layout Plain Layout
22902 , that is only available in \SpecialChar TeX
22906 \begin_layout Standard
22910 \begin_layout Plain Layout
22920 \begin_inset Note Note
22923 \begin_layout Plain Layout
22924 The following table will only be displayed when the \SpecialChar LaTeX
22937 \begin_layout Standard
22938 An overview about the different Euro symbols:
22939 \begin_inset Separator parbreak
22945 \begin_layout Standard
22947 \begin_inset Tabular
22948 <lyxtabular version="3" rows="4" columns="3">
22949 <features booktabs="true" tabularvalignment="middle">
22950 <column alignment="center" valignment="top" width="0pt">
22951 <column alignment="center" valignment="top" width="0pt">
22952 <column alignment="center" valignment="top" width="0pt">
22954 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22957 \begin_layout Plain Layout
22961 \begin_layout Plain Layout
22965 cmidrule[0.08em]{2-3}
22975 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22978 \begin_layout Plain Layout
22984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22987 \begin_layout Plain Layout
22995 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22998 \begin_layout Plain Layout
23004 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23007 \begin_layout Plain Layout
23015 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23018 \begin_layout Plain Layout
23019 \begin_inset Formula $\euro$
23029 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23032 \begin_layout Plain Layout
23038 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23041 \begin_layout Plain Layout
23047 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23050 \begin_layout Plain Layout
23051 \begin_inset Formula $\mbox{€}$
23061 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23064 \begin_layout Plain Layout
23071 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23074 \begin_layout Plain Layout
23082 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23085 \begin_layout Plain Layout
23089 \begin_layout Plain Layout
23109 \begin_inset Note Note
23112 \begin_layout Plain Layout
23119 is used here only for table borders.
23129 manual for details.
23137 \begin_layout Standard
23141 \begin_layout Plain Layout
23151 \begin_inset Note Note
23154 \begin_layout Plain Layout
23155 The following will be displayed when the \SpecialChar LaTeX
23168 \begin_layout Standard
23169 You need to install the \SpecialChar LaTeX
23174 to see the rest of this subsection in the output.
23177 \begin_layout Standard
23181 \begin_layout Plain Layout
23193 \begin_layout Standard
23194 \begin_inset Newpage newpage
23200 \begin_layout Section
23202 \begin_inset CommandInset label
23204 name "sec:Relations"
23209 \begin_inset Index idx
23212 \begin_layout Plain Layout
23219 \begin_inset Index idx
23222 \begin_layout Plain Layout
23227 \begin_layout Plain Layout
23238 \begin_layout Plain Layout
23253 \begin_layout Standard
23254 All following relations can also be inserted via the toolbar button
23257 arg "math-insert \\leq"
23263 \begin_layout Standard
23264 \begin_inset Tabular
23265 <lyxtabular version="3" rows="17" columns="2">
23266 <features booktabs="true" tabularvalignment="middle">
23267 <column alignment="center" valignment="top" width="0pt">
23268 <column alignment="center" valignment="top" width="0pt">
23270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23273 \begin_layout Plain Layout
23279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23282 \begin_layout Plain Layout
23290 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23293 \begin_layout Plain Layout
23299 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23302 \begin_layout Plain Layout
23303 \begin_inset Formula $<$
23313 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23316 \begin_layout Plain Layout
23324 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23327 \begin_layout Plain Layout
23328 \begin_inset Formula $\le$
23338 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23341 \begin_layout Plain Layout
23349 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23352 \begin_layout Plain Layout
23353 \begin_inset Formula $\ll$
23363 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23366 \begin_layout Plain Layout
23374 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23377 \begin_layout Plain Layout
23378 \begin_inset Formula $\prec$
23388 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23391 \begin_layout Plain Layout
23399 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23402 \begin_layout Plain Layout
23403 \begin_inset Formula $\preceq$
23413 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23416 \begin_layout Plain Layout
23424 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23427 \begin_layout Plain Layout
23428 \begin_inset Formula $\subset$
23438 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23441 \begin_layout Plain Layout
23449 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23452 \begin_layout Plain Layout
23453 \begin_inset Formula $\subseteq$
23463 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23466 \begin_layout Plain Layout
23474 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23477 \begin_layout Plain Layout
23478 \begin_inset Formula $\sqsubseteq$
23488 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23491 \begin_layout Plain Layout
23499 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23502 \begin_layout Plain Layout
23503 \begin_inset Formula $\in$
23513 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23516 \begin_layout Plain Layout
23524 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23527 \begin_layout Plain Layout
23528 \begin_inset Formula $\vdash$
23538 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23541 \begin_layout Plain Layout
23549 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23552 \begin_layout Plain Layout
23553 \begin_inset Formula $\smile$
23563 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23566 \begin_layout Plain Layout
23574 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23577 \begin_layout Plain Layout
23578 \begin_inset Formula $\lhd$
23588 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23591 \begin_layout Plain Layout
23599 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23602 \begin_layout Plain Layout
23603 \begin_inset Formula $\unlhd$
23613 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23616 \begin_layout Plain Layout
23624 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23627 \begin_layout Plain Layout
23628 \begin_inset Formula $\gtrless$
23638 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23641 \begin_layout Plain Layout
23649 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23652 \begin_layout Plain Layout
23653 \begin_inset Formula $\mid$
23663 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23666 \begin_layout Plain Layout
23674 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23677 \begin_layout Plain Layout
23678 \begin_inset Formula $\nmid$
23692 \begin_inset space \hfill{}
23696 \begin_inset Tabular
23697 <lyxtabular version="3" rows="17" columns="2">
23698 <features booktabs="true" tabularvalignment="middle">
23699 <column alignment="center" valignment="top" width="0pt">
23700 <column alignment="center" valignment="top" width="0pt">
23702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23705 \begin_layout Plain Layout
23711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23714 \begin_layout Plain Layout
23722 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23725 \begin_layout Plain Layout
23731 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23734 \begin_layout Plain Layout
23735 \begin_inset Formula $=$
23745 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23748 \begin_layout Plain Layout
23756 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23759 \begin_layout Plain Layout
23760 \begin_inset Formula $\not=$
23770 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23773 \begin_layout Plain Layout
23781 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23784 \begin_layout Plain Layout
23785 \begin_inset Formula $\equiv$
23795 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23798 \begin_layout Plain Layout
23806 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23809 \begin_layout Plain Layout
23810 \begin_inset Formula $\sim$
23820 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23823 \begin_layout Plain Layout
23831 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23834 \begin_layout Plain Layout
23835 \begin_inset Formula $\simeq$
23845 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23848 \begin_layout Plain Layout
23856 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23859 \begin_layout Plain Layout
23860 \begin_inset Formula $\approx$
23870 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23873 \begin_layout Plain Layout
23881 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23884 \begin_layout Plain Layout
23885 \begin_inset Formula $\cong$
23895 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23898 \begin_layout Plain Layout
23906 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23909 \begin_layout Plain Layout
23910 \begin_inset Formula $\bowtie$
23920 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23923 \begin_layout Plain Layout
23931 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23934 \begin_layout Plain Layout
23935 \begin_inset Formula $\notin$
23945 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23948 \begin_layout Plain Layout
23956 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23959 \begin_layout Plain Layout
23960 \begin_inset Formula $\perp$
23970 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23973 \begin_layout Plain Layout
23981 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23984 \begin_layout Plain Layout
23985 \begin_inset Formula $\propto$
23995 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23998 \begin_layout Plain Layout
24006 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24009 \begin_layout Plain Layout
24010 \begin_inset Formula $\asymp$
24020 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24023 \begin_layout Plain Layout
24031 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24034 \begin_layout Plain Layout
24035 \begin_inset Formula $\doteq$
24045 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24048 \begin_layout Plain Layout
24056 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24059 \begin_layout Plain Layout
24060 \begin_inset Formula $\circeq$
24070 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24073 \begin_layout Plain Layout
24081 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24084 \begin_layout Plain Layout
24085 \begin_inset Formula $\models$
24095 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24098 \begin_layout Plain Layout
24106 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24109 \begin_layout Plain Layout
24110 \begin_inset Formula $\widehat{=}$
24124 \begin_inset space \hfill{}
24128 \begin_inset Tabular
24129 <lyxtabular version="3" rows="17" columns="2">
24130 <features booktabs="true" tabularvalignment="middle">
24131 <column alignment="center" valignment="top" width="0pt">
24132 <column alignment="center" valignment="top" width="0pt">
24134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24137 \begin_layout Plain Layout
24143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24146 \begin_layout Plain Layout
24154 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24157 \begin_layout Plain Layout
24163 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24166 \begin_layout Plain Layout
24167 \begin_inset Formula $>$
24177 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24180 \begin_layout Plain Layout
24188 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24191 \begin_layout Plain Layout
24192 \begin_inset Formula $\ge$
24202 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24205 \begin_layout Plain Layout
24213 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24216 \begin_layout Plain Layout
24217 \begin_inset Formula $\gg$
24227 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24230 \begin_layout Plain Layout
24238 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24241 \begin_layout Plain Layout
24242 \begin_inset Formula $\succ$
24252 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24255 \begin_layout Plain Layout
24263 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24266 \begin_layout Plain Layout
24267 \begin_inset Formula $\succeq$
24277 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24280 \begin_layout Plain Layout
24288 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24291 \begin_layout Plain Layout
24292 \begin_inset Formula $\supset$
24302 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24305 \begin_layout Plain Layout
24313 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24316 \begin_layout Plain Layout
24317 \begin_inset Formula $\supseteq$
24327 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24330 \begin_layout Plain Layout
24338 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24341 \begin_layout Plain Layout
24342 \begin_inset Formula $\sqsupseteq$
24352 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24355 \begin_layout Plain Layout
24363 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24366 \begin_layout Plain Layout
24367 \begin_inset Formula $\ni$
24377 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24380 \begin_layout Plain Layout
24388 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24391 \begin_layout Plain Layout
24392 \begin_inset Formula $\dashv$
24402 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24405 \begin_layout Plain Layout
24413 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24416 \begin_layout Plain Layout
24417 \begin_inset Formula $\frown$
24427 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24430 \begin_layout Plain Layout
24438 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24441 \begin_layout Plain Layout
24442 \begin_inset Formula $\rhd$
24452 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24455 \begin_layout Plain Layout
24463 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24466 \begin_layout Plain Layout
24467 \begin_inset Formula $\unrhd$
24477 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24480 \begin_layout Plain Layout
24488 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24491 \begin_layout Plain Layout
24492 \begin_inset Formula $\lessgtr$
24502 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24505 \begin_layout Plain Layout
24513 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24516 \begin_layout Plain Layout
24517 \begin_inset Formula $\parallel$
24527 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24530 \begin_layout Plain Layout
24538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24541 \begin_layout Plain Layout
24542 \begin_inset Formula $\nparallel$
24558 \begin_layout Standard
24559 \begin_inset VSpace medskip
24574 are bigger than the equal looking operators
24589 \begin_layout Standard
24591 supports also many special relations.
24592 Use the toolbar button
24595 arg "math-insert \\leqq"
24598 to see a list of these relations.
24601 \begin_layout Standard
24602 Relations are, in contrary to symbols, always surrounded by space.
24605 \begin_layout Standard
24606 Relations with labels can be created with the command
24613 \begin_inset Index idx
24616 \begin_layout Plain Layout
24625 \begin_inset Separator parbreak
24631 \begin_layout Standard
24633 \begin_inset Tabular
24634 <lyxtabular version="3" rows="2" columns="2">
24635 <features booktabs="true" tabularvalignment="middle">
24636 <column alignment="center" valignment="top" width="0pt">
24637 <column alignment="center" valignment="top">
24639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24642 \begin_layout Plain Layout
24648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24651 \begin_layout Plain Layout
24658 <row topspace="1.5mm">
24659 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24662 \begin_layout Plain Layout
24666 \begin_inset space \textvisiblespace{}
24674 \begin_inset space \textvisiblespace{}
24678 \begin_inset Formula $\downarrow$
24684 \begin_inset space \textvisiblespace{}
24688 \begin_inset space \textvisiblespace{}
24696 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24699 \begin_layout Plain Layout
24700 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24716 \begin_layout Section
24720 \begin_layout Subsection
24721 Predefined Functions
24722 \begin_inset CommandInset label
24724 name "subsec:Predefined-Functions"
24729 \begin_inset Index idx
24732 \begin_layout Plain Layout
24733 Functions ! predefined
24741 \begin_layout Standard
24742 In general, variables are set
24746 in mathematical expressions, but not function names, because
24747 \begin_inset Formula $sin$
24750 could be misunderstood as
24751 \begin_inset Formula $s\cdot i\cdot n$
24755 Therefore there are predefined functionswhich are additionally a bit separated
24757 They are inserted as commands starting with a backslash before their name.
24758 \begin_inset Separator parbreak
24764 \begin_layout Standard
24766 \begin_inset Tabular
24767 <lyxtabular version="3" rows="2" columns="2">
24768 <features booktabs="true" tabularvalignment="middle">
24769 <column alignment="center" valignment="top" width="0pt">
24770 <column alignment="center" valignment="top" width="0pt">
24772 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24775 \begin_layout Plain Layout
24781 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24784 \begin_layout Plain Layout
24792 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24795 \begin_layout Plain Layout
24801 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24804 \begin_layout Plain Layout
24805 \begin_inset Formula $Asin(x)+B$
24819 \begin_inset space \quad{}
24823 \begin_inset Tabular
24824 <lyxtabular version="3" rows="2" columns="2">
24825 <features booktabs="true" tabularvalignment="middle">
24826 <column alignment="center" valignment="top" width="0pt">
24827 <column alignment="center" valignment="top" width="0pt">
24829 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24832 \begin_layout Plain Layout
24838 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24841 \begin_layout Plain Layout
24849 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24852 \begin_layout Plain Layout
24860 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24863 \begin_layout Plain Layout
24864 \begin_inset Formula $A\sin(x)+B$
24880 \begin_layout Standard
24881 The following functions are predefined:
24884 \begin_layout Standard
24885 \begin_inset VSpace -2mm
24891 \begin_layout Standard
24893 \begin_inset Tabular
24894 <lyxtabular version="3" rows="9" columns="4">
24895 <features booktabs="true" tabularvalignment="middle">
24896 <column alignment="center" valignment="top" width="0pt">
24897 <column alignment="center" valignment="top" width="0pt">
24898 <column alignment="center" valignment="top" width="0pt">
24899 <column alignment="center" valignment="top" width="0pt">
24901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24904 \begin_layout Plain Layout
24910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24913 \begin_layout Plain Layout
24919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24922 \begin_layout Plain Layout
24928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24931 \begin_layout Plain Layout
24939 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24942 \begin_layout Plain Layout
24950 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24953 \begin_layout Plain Layout
24961 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24964 \begin_layout Plain Layout
24972 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24975 \begin_layout Plain Layout
24985 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24988 \begin_layout Plain Layout
24996 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24999 \begin_layout Plain Layout
25007 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25010 \begin_layout Plain Layout
25018 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25021 \begin_layout Plain Layout
25031 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25034 \begin_layout Plain Layout
25042 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25045 \begin_layout Plain Layout
25053 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25056 \begin_layout Plain Layout
25064 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25067 \begin_layout Plain Layout
25077 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25080 \begin_layout Plain Layout
25088 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25091 \begin_layout Plain Layout
25099 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25102 \begin_layout Plain Layout
25110 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25113 \begin_layout Plain Layout
25123 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25126 \begin_layout Plain Layout
25134 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25137 \begin_layout Plain Layout
25145 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25148 \begin_layout Plain Layout
25156 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25159 \begin_layout Plain Layout
25169 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25172 \begin_layout Plain Layout
25180 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25183 \begin_layout Plain Layout
25191 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25194 \begin_layout Plain Layout
25202 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25205 \begin_layout Plain Layout
25215 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25218 \begin_layout Plain Layout
25226 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25229 \begin_layout Plain Layout
25237 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25240 \begin_layout Plain Layout
25248 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25251 \begin_layout Plain Layout
25261 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25264 \begin_layout Plain Layout
25272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25275 \begin_layout Plain Layout
25283 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25286 \begin_layout Plain Layout
25294 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25297 \begin_layout Plain Layout
25313 \begin_layout Standard
25314 They can also be inserted with the math toolbar button
25317 arg "math-insert \\functions"
25323 \begin_layout Subsection
25324 Self-defined Functions
25325 \begin_inset Index idx
25328 \begin_layout Plain Layout
25329 Functions ! self-defined
25337 \begin_layout Standard
25338 To use a function that is not predefined, like for example the sign function
25339 sgn(x), there are two possibilities:
25342 \begin_layout Itemize
25343 Define the function by inserting the following line to the \SpecialChar LaTeX
25348 \begin_layout Plain Layout
25353 DeclareMathOperator
25356 \begin_inset CommandInset ref
25358 reference "subsec:Self-defined-Operators"
25368 \begin_inset Newline newline
25372 \begin_inset VSpace -3mm
25376 \begin_inset Newline newline
25383 DeclareMathOperator{
25388 \begin_inset Index idx
25391 \begin_layout Plain Layout
25396 DeclareMathOperator
25402 \begin_inset Newline newline
25406 \begin_inset VSpace -2mm
25410 \begin_inset Newline newline
25413 Now the new defined function can be called with the command
25422 \begin_layout Itemize
25423 Write the formula as usual, mark the formula name, in our example the letters
25428 , and change it to mathematical text.
25429 Finally, a space is inserted between prefactor and function.
25432 \begin_layout Standard
25433 The result is the same with both methods as with a predefined function
25437 \begin_layout Plain Layout
25438 In \SpecialChar LyX
25439 self-defined functions are displayed red, predefined ones black.
25445 \begin_inset Separator parbreak
25451 \begin_layout Standard
25453 \begin_inset Tabular
25454 <lyxtabular version="3" rows="3" columns="2">
25455 <features booktabs="true" tabularvalignment="middle">
25456 <column alignment="center" valignment="top" width="0pt">
25457 <column alignment="center" valignment="top" width="0pt">
25459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25462 \begin_layout Plain Layout
25468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25471 \begin_layout Plain Layout
25479 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25482 \begin_layout Plain Layout
25490 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25493 \begin_layout Plain Layout
25494 \begin_inset Formula $A\sgn(x)+B$
25504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25507 \begin_layout Plain Layout
25511 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25522 \begin_layout Plain Layout
25523 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25539 \begin_layout Standard
25540 The first method is more suitable when the self-defined function should
25541 be used several times.
25544 \begin_layout Subsection
25546 \begin_inset Index idx
25549 \begin_layout Plain Layout
25558 \begin_layout Standard
25559 For limits, in addition to the commands
25566 \begin_inset Index idx
25569 \begin_layout Plain Layout
25589 the following functions are defined:
25590 \begin_inset Separator parbreak
25596 \begin_layout Standard
25598 \begin_inset Tabular
25599 <lyxtabular version="3" rows="5" columns="2">
25600 <features booktabs="true" tabularvalignment="middle">
25601 <column alignment="center" valignment="top" width="0pt">
25602 <column alignment="center" valignment="top" width="0pt">
25604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25607 \begin_layout Plain Layout
25613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25616 \begin_layout Plain Layout
25624 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25627 \begin_layout Plain Layout
25635 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25638 \begin_layout Plain Layout
25639 \begin_inset Formula $\varliminf$
25648 <row topspace="1.5mm">
25649 <cell alignment="center" valignment="top" usebox="none">
25652 \begin_layout Plain Layout
25660 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25663 \begin_layout Plain Layout
25664 \begin_inset Formula $\varlimsup$
25673 <row topspace="1.5mm">
25674 <cell alignment="center" valignment="top" usebox="none">
25677 \begin_layout Plain Layout
25685 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25688 \begin_layout Plain Layout
25689 \begin_inset Formula $\varprojlim$
25698 <row topspace="1.5mm" bottomspace="1mm">
25699 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25702 \begin_layout Plain Layout
25710 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25713 \begin_layout Plain Layout
25714 \begin_inset Formula $\varinjlim$
25730 \begin_layout Standard
25731 \begin_inset VSpace medskip
25734 The limit is created by inserting a subscript.
25735 It is set right beside the function in an inline formula:
25738 \begin_layout Standard
25740 \begin_inset Tabular
25741 <lyxtabular version="3" rows="2" columns="2">
25742 <features booktabs="true" tabularvalignment="middle">
25743 <column alignment="center" valignment="top" width="0pt">
25744 <column alignment="center" valignment="top" width="0pt">
25746 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25749 \begin_layout Plain Layout
25755 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25758 \begin_layout Plain Layout
25766 <cell alignment="center" valignment="top" usebox="none">
25769 \begin_layout Plain Layout
25775 \begin_inset space \textvisiblespace{}
25779 \begin_inset space \textvisiblespace{}
25787 <cell alignment="center" valignment="top" usebox="none">
25790 \begin_layout Plain Layout
25791 \begin_inset Formula $\lim_{x\to A}x=B$
25807 \begin_layout Standard
25808 In a displayed formula the limit is set below the formula, as usual:
25809 \begin_inset Formula
25819 \begin_layout Standard
25820 \begin_inset VSpace medskip
25826 \begin_layout Standard
25827 How to adjust the typesetting of the limits see
25828 \begin_inset CommandInset ref
25830 reference "subsec:Operator-Limits"
25837 \begin_layout Subsection
25839 \begin_inset Index idx
25842 \begin_layout Plain Layout
25843 Functions ! modulo-
25851 \begin_layout Standard
25852 The modulo-function is special, because it exists in four variants.
25853 The variants in a displayed formula are:
25854 \begin_inset Formula
25856 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25857 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25858 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25859 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25860 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25868 \begin_layout Standard
25869 In an inline formula less space is set before the function names for all
25871 By default the modulo-functions take only the first following character
25873 To use more than one character, one has to put them into \SpecialChar TeX
25875 \begin_inset Formula
25877 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25878 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25879 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25887 \begin_layout Section
25889 \begin_inset Index idx
25892 \begin_layout Plain Layout
25901 \begin_layout Standard
25902 The characters ^ and _ would normally create a superscript and subscript,
25904 To get these characters you have to insert them with a leading
25907 \begin_inset Separator parbreak
25913 \begin_layout Standard
25916 \begin_inset Tabular
25917 <lyxtabular version="3" rows="3" columns="2">
25918 <features booktabs="true" tabularvalignment="middle">
25919 <column alignment="left" valignment="top" width="0pt">
25920 <column alignment="block" valignment="top">
25922 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25925 \begin_layout Plain Layout
25931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25934 \begin_layout Plain Layout
25942 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25945 \begin_layout Plain Layout
25949 \begin_inset space \textvisiblespace{}
25957 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25960 \begin_layout Plain Layout
25961 \begin_inset Formula $\mathcircumflex$
25971 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25974 \begin_layout Plain Layout
25982 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25985 \begin_layout Plain Layout
25986 \begin_inset Formula $\_$
26002 \begin_layout Subsection
26003 Special Characters in Mathematical Text
26006 \begin_layout Standard
26007 The following commands can only be used in mathematical text or in \SpecialChar TeX
26011 \begin_layout Standard
26012 \begin_inset space \hfill{}
26016 \begin_inset Tabular
26017 <lyxtabular version="3" rows="8" columns="2">
26018 <features booktabs="true" tabularvalignment="middle">
26019 <column alignment="left" valignment="top" width="0pt">
26020 <column alignment="block" valignment="top">
26022 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26025 \begin_layout Plain Layout
26031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26034 \begin_layout Plain Layout
26042 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26045 \begin_layout Plain Layout
26053 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26056 \begin_layout Plain Layout
26057 \begin_inset Formula $\textrm{œ}$
26067 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26070 \begin_layout Plain Layout
26078 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26081 \begin_layout Plain Layout
26082 \begin_inset Formula $\textrm{Œ}$
26092 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26095 \begin_layout Plain Layout
26103 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26106 \begin_layout Plain Layout
26107 \begin_inset Formula $\textrm{æ}$
26117 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26120 \begin_layout Plain Layout
26128 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26131 \begin_layout Plain Layout
26132 \begin_inset Formula $\textrm{Æ}$
26142 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26145 \begin_layout Plain Layout
26153 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26156 \begin_layout Plain Layout
26157 \begin_inset Formula $\textrm{\aa}$
26167 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26170 \begin_layout Plain Layout
26174 \begin_inset Index idx
26177 \begin_layout Plain Layout
26184 \begin_layout Plain Layout
26205 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26208 \begin_layout Plain Layout
26209 \begin_inset Formula $\textrm{Å}$
26219 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26222 \begin_layout Plain Layout
26230 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26233 \begin_layout Plain Layout
26234 \begin_inset Formula $\textrm{ı}$
26248 \begin_inset space \hfill{}
26252 \begin_inset Tabular
26253 <lyxtabular version="3" rows="8" columns="2">
26254 <features booktabs="true" tabularvalignment="middle">
26255 <column alignment="left" valignment="top" width="0pt">
26256 <column alignment="center" valignment="top">
26258 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26261 \begin_layout Plain Layout
26263 \begin_inset Note Note
26266 \begin_layout Plain Layout
26268 \begin_inset space \thinspace{}
26271 mm is used for separation, because otherwise the output will be ¡ and ¿
26282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26285 \begin_layout Plain Layout
26293 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26296 \begin_layout Plain Layout
26304 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26307 \begin_layout Plain Layout
26308 \begin_inset Formula $\textrm{ø}$
26318 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26321 \begin_layout Plain Layout
26329 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26332 \begin_layout Plain Layout
26333 \begin_inset Formula $\textrm{Ø}$
26343 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26346 \begin_layout Plain Layout
26354 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26357 \begin_layout Plain Layout
26358 \begin_inset Formula $\textrm{ł}$
26368 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26371 \begin_layout Plain Layout
26379 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26382 \begin_layout Plain Layout
26383 \begin_inset Formula $\textrm{Ł}$
26393 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26396 \begin_layout Plain Layout
26398 \begin_inset space \hspace{}
26403 \begin_inset space \textvisiblespace{}
26411 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26414 \begin_layout Plain Layout
26415 \begin_inset Formula $\textrm{!`}$
26425 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26428 \begin_layout Plain Layout
26430 \begin_inset space \hspace{}
26435 \begin_inset space \textvisiblespace{}
26443 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26446 \begin_layout Plain Layout
26447 \begin_inset Formula $\textrm{?`}$
26457 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26460 \begin_layout Plain Layout
26468 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26471 \begin_layout Plain Layout
26472 \begin_inset Formula $\textrm{ȷ}$
26486 \begin_inset space \hfill{}
26492 \begin_layout Standard
26494 \begin_inset Formula $\textrm{\textrm{Å}}$
26498 \begin_inset Formula $\textrm{\textrm{Ø}}$
26501 can also be inserted via the math toolbar button
26504 arg "math-insert \\digamma"
26510 \begin_layout Standard
26511 An exception are the commands
26514 \begin_inset space \hspace{}
26523 \begin_inset space \hspace{}
26529 , because they can be inserted in \SpecialChar LyX
26533 \begin_layout Subsection
26535 \begin_inset CommandInset label
26537 name "subsec:Accents-in-Text"
26542 \begin_inset Index idx
26545 \begin_layout Plain Layout
26554 \begin_layout Standard
26555 With the following commands all letters can be accented.
26556 The commands must be inserted in \SpecialChar TeX
26560 \begin_layout Standard
26561 \begin_inset space \hfill{}
26565 \begin_inset Tabular
26566 <lyxtabular version="3" rows="8" columns="2">
26567 <features booktabs="true" tabularvalignment="middle">
26568 <column alignment="left" valignment="top" width="0pt">
26569 <column alignment="block" valignment="top">
26571 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26574 \begin_layout Plain Layout
26580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26583 \begin_layout Plain Layout
26591 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26594 \begin_layout Plain Layout
26598 \begin_inset Quotes grd
26606 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26609 \begin_layout Plain Layout
26613 \begin_layout Plain Layout
26629 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26632 \begin_layout Plain Layout
26640 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26643 \begin_layout Plain Layout
26647 \begin_layout Plain Layout
26663 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26666 \begin_layout Plain Layout
26670 \begin_inset space \textvisiblespace{}
26678 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26681 \begin_layout Plain Layout
26685 \begin_layout Plain Layout
26701 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26704 \begin_layout Plain Layout
26712 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26715 \begin_layout Plain Layout
26719 \begin_layout Plain Layout
26735 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26738 \begin_layout Plain Layout
26742 \begin_inset space \textvisiblespace{}
26750 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26753 \begin_layout Plain Layout
26757 \begin_layout Plain Layout
26773 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26776 \begin_layout Plain Layout
26780 \begin_inset space \textvisiblespace{}
26788 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26791 \begin_layout Plain Layout
26795 \begin_layout Plain Layout
26811 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26814 \begin_layout Plain Layout
26818 \begin_inset space \textvisiblespace{}
26826 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26829 \begin_layout Plain Layout
26833 \begin_layout Plain Layout
26853 \begin_inset space \hfill{}
26857 \begin_inset Tabular
26858 <lyxtabular version="3" rows="8" columns="2">
26859 <features booktabs="true" tabularvalignment="middle">
26860 <column alignment="left" valignment="top" width="0pt">
26861 <column alignment="center" valignment="top">
26863 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26866 \begin_layout Plain Layout
26872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26875 \begin_layout Plain Layout
26883 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26886 \begin_layout Plain Layout
26890 \begin_inset space \textvisiblespace{}
26898 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26901 \begin_layout Plain Layout
26905 \begin_layout Plain Layout
26921 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26924 \begin_layout Plain Layout
26932 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26935 \begin_layout Plain Layout
26939 \begin_layout Plain Layout
26955 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26958 \begin_layout Plain Layout
26962 \begin_inset Index idx
26965 \begin_layout Plain Layout
26976 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26979 \begin_layout Plain Layout
26983 \begin_layout Plain Layout
26999 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27002 \begin_layout Plain Layout
27010 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27013 \begin_layout Plain Layout
27017 \begin_layout Plain Layout
27033 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27036 \begin_layout Plain Layout
27040 \begin_inset space \textvisiblespace{}
27048 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27051 \begin_layout Plain Layout
27055 \begin_layout Plain Layout
27071 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27074 \begin_layout Plain Layout
27078 \begin_inset space \textvisiblespace{}
27086 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27089 \begin_layout Plain Layout
27093 \begin_layout Plain Layout
27109 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27112 \begin_layout Plain Layout
27116 \begin_inset space \textvisiblespace{}
27124 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27127 \begin_layout Plain Layout
27131 \begin_layout Plain Layout
27151 \begin_inset space \hfill{}
27157 \begin_layout Standard
27158 \begin_inset VSpace medskip
27167 also two different characters can be accented.
27173 \begin_inset space \textvisiblespace{}
27182 \begin_layout Plain Layout
27194 \begin_layout Standard
27207 can in combination with vowels directly be inserted with the keyboard without
27208 using \SpecialChar TeX
27210 The same applies for the tilde
27214 \begin_layout Plain Layout
27215 This only applies for keyboards where the tilde is defined as accent.
27224 in combination with
27239 \begin_layout Standard
27282 and accents that are inserted directly with the keyboard are also available
27283 in mathematical text.
27284 For the other accents there are special math commands to be used in formulas,
27286 \begin_inset CommandInset ref
27288 reference "subsec:Accents-for-one"
27295 \begin_layout Standard
27296 \begin_inset VSpace bigskip
27299 Furthermore, with the command
27306 \begin_inset Index idx
27309 \begin_layout Plain Layout
27317 all numbers and letters can be set into a circle, quasi accented with a
27318 circle, similar to the copyright symbol.
27321 \begin_layout Standard
27323 \begin_inset Tabular
27324 <lyxtabular version="3" rows="3" columns="2">
27325 <features booktabs="true" tabularvalignment="middle">
27326 <column alignment="center" valignment="top" width="0pt">
27327 <column alignment="center" valignment="top">
27329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27332 \begin_layout Plain Layout
27338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27341 \begin_layout Plain Layout
27349 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27352 \begin_layout Plain Layout
27360 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27363 \begin_layout Plain Layout
27367 \begin_layout Plain Layout
27382 <row topspace="1mm">
27383 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27386 \begin_layout Plain Layout
27397 raisebox{-1.5pt}{W}}
27402 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27405 \begin_layout Plain Layout
27409 \begin_layout Plain Layout
27439 \begin_layout Standard
27440 One has to take care that the character fits in the circle.
27451 \begin_layout Plain Layout
27453 \begin_inset CommandInset ref
27455 reference "subsec:Font-Sizes"
27464 specifies thereby the size of the circle.
27475 \begin_layout Plain Layout
27477 \begin_inset CommandInset ref
27479 reference "subsec:Boxes-without-Frame"
27488 the character can be centered.
27491 \begin_layout Subsection
27493 \begin_inset Index idx
27496 \begin_layout Plain Layout
27505 \begin_layout Standard
27506 Old-style figures (also known as old-style numerals) are created with the
27514 \begin_inset Index idx
27517 \begin_layout Plain Layout
27526 The command can be used in formulas and in \SpecialChar TeX
27528 The command scheme is:
27531 \begin_layout Standard
27536 oldstylenums{number}
27539 \begin_layout Standard
27544 oldstylenums{0123456789
27547 \begin_inset Formula $\oldstylenums{0123456789}$
27553 \begin_layout Section
27555 \begin_inset CommandInset label
27557 name "sec:Formula-Styles"
27562 \begin_inset Index idx
27565 \begin_layout Plain Layout
27574 \begin_layout Itemize
27575 There are two different alignment styles:
27576 \begin_inset Separator parbreak
27583 \begin_layout Description
27584 Centered is the predefined standard
27587 \begin_layout Description
27588 Indented for this the option
27592 must be inserted in the menu
27594 Document\SpecialChar menuseparator
27600 \begin_inset space ~
27606 \begin_layout Standard
27611 is used, the indentation can be adjusted with the length
27618 \begin_inset Index idx
27621 \begin_layout Plain Layout
27630 Should the distance be 15
27631 \begin_inset space \thinspace{}
27634 mm, the following command line is inserted in the \SpecialChar LaTeX
27638 \begin_layout Standard
27648 \begin_layout Standard
27649 When no length is specified, the predefined value of 30
27650 \begin_inset space \thinspace{}
27657 \begin_layout Itemize
27658 And two different numbering styles:
27659 \begin_inset Separator parbreak
27666 \begin_layout Description
27667 Right is the predefined standard
27670 \begin_layout Description
27671 Left for this the option
27675 must be inserted in the menu
27677 Document\SpecialChar menuseparator
27683 \begin_inset space ~
27690 \begin_layout Standard
27699 can also be used together.
27700 In this case both options are inserted, separated by a comma.
27703 \begin_layout Standard
27704 The chosen styles are used for all displayed formulas of the document.
27705 When both, centered and indented formulas should be created in a document,
27711 The indented formulas are then set in a flalign environment, see
27712 \begin_inset CommandInset ref
27714 reference "subsec:Flalign-Environment"
27721 \begin_layout Section
27723 \begin_inset CommandInset label
27725 name "sec:Multiline-Formulas"
27730 \begin_inset Index idx
27733 \begin_layout Plain Layout
27734 Formula ! multiline
27742 \begin_layout Subsection
27746 \begin_layout Standard
27747 In \SpecialChar LyX
27748 multiline formulas are created by pressing
27751 arg "newline-insert newline"
27755 This creates either an
27759 that is described in
27760 \begin_inset CommandInset ref
27762 reference "subsec:Standard-align-Environment"
27766 or, when automatically loading the package
27770 is disabled in the document settings, an
27772 eqnarray environment
27774 that is described in
27775 \begin_inset CommandInset ref
27777 reference "subsec:Eqnarray-Environment"
27782 The align environment is recommended because it provides in any case a
27783 typographically correct output.
27786 \begin_layout Standard
27787 There are other multiline formula environments that can be created via the
27790 Insert\SpecialChar menuseparator
27794 These environments are described in the following sections.
27797 \begin_layout Standard
27798 In all multiline formula environments a new line is created by pressing
27802 arg "newline-insert newline"
27806 To add or delete lines, the math toolbar buttons
27809 arg "inset-modify tabular append-row"
27815 arg "inset-modify tabular delete-row"
27818 , respectively, or the menu
27820 Edit\SpecialChar menuseparator
27826 \begin_layout Subsubsection
27828 \begin_inset CommandInset label
27830 name "subsec:Line-Separation"
27835 \begin_inset Index idx
27838 \begin_layout Plain Layout
27839 Formula ! multiline ! Line separation
27847 \begin_layout Standard
27848 There is sometimes not enough space in multiline formulas between the lines:
27849 \begin_inset Formula
27851 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}\\
27852 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
27860 \begin_layout Standard
27861 In \SpecialChar LaTeX
27862 additional line space is specified as optional argument of the new line
27864 This is not yet possible in \SpecialChar LyX
27869 \begin_layout Plain Layout
27871 \begin_inset CommandInset href
27873 name "LyX-bug #1505"
27874 target "http://www.lyx.org/trac/ticket/1505"
27883 , therefore the whole formula must be inserted in \SpecialChar TeX
27885 To add in our example space, the command
27893 is inserted at the end of the first line.
27898 \begin_layout Plain Layout
27905 \begin_layout Plain Layout
27907 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27910 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27917 \begin_layout Plain Layout
27921 left(B^{2}+x_{0}^{2}
27929 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27934 \begin_layout Plain Layout
27946 \begin_layout Standard
27947 \begin_inset VSpace bigskip
27950 To set the line separation for all lines in a formula, the length
27957 \begin_inset Index idx
27960 \begin_layout Plain Layout
27970 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27981 \begin_inset space \thinspace{}
27986 \begin_inset space \thinspace{}
27989 mm additional line separation as in the previous example, the command
27992 \begin_layout Standard
28002 \begin_layout Standard
28003 is inserted in \SpecialChar TeX
28004 mode before the formula.
28005 This requires that the \SpecialChar LaTeX
28014 \begin_layout Plain Layout
28019 is part of every \SpecialChar LaTeX
28020 standard installation.
28026 \begin_inset Index idx
28029 \begin_layout Plain Layout
28035 was loaded in \SpecialChar LaTeX
28036 -preamble with the line
28039 \begin_layout Standard
28047 \begin_layout Standard
28052 \begin_layout Plain Layout
28064 \begin_inset Formula
28066 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}\\
28067 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
28075 \begin_layout Standard
28079 \begin_layout Plain Layout
28090 To get back to the predefined distance,
28096 is set to the value 3
28097 \begin_inset space \thinspace{}
28103 \begin_layout Subsubsection
28105 \begin_inset CommandInset label
28107 name "subsec:Column-Separation"
28112 \begin_inset Index idx
28115 \begin_layout Plain Layout
28116 Formula ! multiline ! Column separation
28124 \begin_layout Standard
28125 Multiline formulas form a matrix.
28126 A formula in the eqnarray environment is for example a matrix with three
28128 By changing the column separation in this environment, the space beside
28129 the relation sign can be changed.
28132 \begin_layout Standard
28133 The column separation is specified with the length
28140 \begin_inset Index idx
28143 \begin_layout Plain Layout
28152 \begin_inset Newline newline
28155 column separation = 2
28156 \begin_inset space \thinspace{}
28166 \begin_inset Newline newline
28172 \begin_layout Standard
28182 \begin_layout Standard
28183 inserted in \SpecialChar TeX
28184 mode, sets for all following formulas a column separation of
28186 \begin_inset space \thinspace{}
28190 To get back to the predefined distance,
28197 \begin_inset space \thinspace{}
28203 \begin_layout Standard
28205 \begin_inset space \thinspace{}
28208 cm column separation:
28212 \begin_layout Plain Layout
28224 \begin_inset Formula
28232 A formula with the predefined column separation for matrices of 10
28233 \begin_inset space \thinspace{}
28240 \begin_layout Plain Layout
28252 \begin_inset Formula
28263 \begin_layout Subsubsection
28265 \begin_inset Index idx
28268 \begin_layout Plain Layout
28277 \begin_layout Standard
28278 Long formulas can be typeset using these methods:
28281 \begin_layout Itemize
28282 When one side of the equation is much shorter than the line width, this
28283 one is chosen for the left side and the right side is typeset over two
28285 \begin_inset Formula
28287 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 \\
28288 & & -\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}
28293 The minus sign at the beginning of the second line does normally not appear
28294 as an operator because it is the first character of the line.
28295 Thus it would not be surrounded by space and could not be distinguished
28296 from the fraction bar.
28298 \begin_inset space \thinspace{}
28301 pt space was inserted behind the minus sign with the command
28311 \begin_layout Plain Layout
28319 \begin_inset CommandInset ref
28321 reference "subsec:Variable-Space"
28331 \begin_inset Index idx
28334 \begin_layout Plain Layout
28345 \begin_layout Itemize
28346 When both sides of the equation are too long, the command
28353 \begin_inset Index idx
28356 \begin_layout Plain Layout
28365 It is inserted in the first column of the first line and causes all further
28366 insertions to overwrite the following columns:
28367 \begin_inset Formula
28369 \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 \\
28370 & & -\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 \\
28371 & & =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}
28376 After the insertion of
28382 , the cursor is in a purple box that is a bit shifted to the left from the
28384 In this the formula is inserted.
28385 \begin_inset Newline newline
28388 The content of the further lines is inserted to the second or another formula
28390 The greater the column number where it was inserted, the larger the indentation.
28391 \begin_inset VSpace medskip
28395 \begin_inset Newline newline
28399 \begin_inset Note Greyedout
28402 \begin_layout Plain Layout
28403 Note the following when using
28412 \begin_layout Itemize
28413 The formula doesn't use the full page width.
28415 \begin_inset space \thinspace{}
28419 \begin_inset space \space{}
28423 \begin_inset Formula $-B^{2}$
28426 is added to the first line in the above example, it would have been outside
28428 To better use the width, negative space can be inserted at the beginning
28432 \begin_layout Itemize
28433 Due to a bug in \SpecialChar LyX
28434 the cursor cannot be set with the mouse into the first
28439 \begin_layout Plain Layout
28440 \begin_inset CommandInset href
28442 name "LyX-bug #1429"
28443 target "http://www.lyx.org/trac/ticket/1429"
28452 One can only set the cursor at the beginning of the line and move it with
28461 \begin_layout Itemize
28462 Other methods to set long formulas are offered by the environments described
28464 \begin_inset CommandInset ref
28466 reference "subsec:Multline-Environment"
28471 \begin_inset CommandInset ref
28473 reference "subsec:Multiline-Formula-Parts"
28480 \begin_layout Subsubsection
28481 Multiline Fractions
28482 \begin_inset CommandInset label
28484 name "subsec:Multiline-Fractions"
28489 \begin_inset Index idx
28492 \begin_layout Plain Layout
28493 Fractions ! multiline
28501 \begin_layout Standard
28502 There are cases where the denominator and/or the numerator of a fraction
28503 is so long that the fraction does not fit into one line.
28504 It is then necessary to add a line break within the fraction.
28505 This can be done using the command
28512 \begin_inset Index idx
28515 \begin_layout Plain Layout
28524 To activate it, set in the document settings under
28527 \begin_inset space ~
28537 \begin_inset Index idx
28540 \begin_layout Plain Layout
28541 Packages ! mathtools
28549 \begin_inset space ~
28564 \begin_layout Standard
28569 splitfrac{first line}{second line}
28572 \begin_layout Standard
28573 and is used as denominator and/or numerator:
28576 \begin_layout Standard
28577 \begin_inset Formula
28579 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}
28584 The command for the first numerator above is:
28587 \begin_layout Standard
28592 splitfrac{xy+xy+xy+xy+xy
28593 \begin_inset space \textvisiblespace{}
28601 \begin_layout Subsubsection
28603 \begin_inset CommandInset label
28605 name "subsec:Multiline-Brackets"
28610 \begin_inset Index idx
28613 \begin_layout Plain Layout
28614 Brackets ! for multiline expressions
28622 \begin_layout Standard
28623 For brackets spanning multiple lines the following problem occurs:
28624 \begin_inset Formula
28626 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28627 & & \left.\cdots+B-D\right]
28635 \begin_layout Standard
28636 The closing bracket is smaller than the opening bracket because brackets
28637 with variable size may not span multiple lines.
28640 \begin_layout Standard
28641 To set the bracket size for the second line correctly, the first line is
28649 \begin_inset Index idx
28652 \begin_layout Plain Layout
28660 and the second line with
28668 \begin_layout Plain Layout
28682 \begin_inset CommandInset ref
28684 reference "subsec:Automatic-Bracket-Size"
28696 \begin_inset Index idx
28699 \begin_layout Plain Layout
28722 \begin_inset space \textvisiblespace{}
28732 \begin_inset space \textvisiblespace{}
28742 \begin_inset space \textvisiblespace{}
28748 \begin_inset Formula $\downarrow$
28754 \begin_inset Index idx
28757 \begin_layout Plain Layout
28765 is inserted, because the multiplication operator with its limits is the
28766 largest symbol in the first line and this should be the size for the bracket
28767 in the second line.
28770 \begin_layout Standard
28771 The result is this:
28772 \begin_inset Formula
28774 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28775 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28783 \begin_layout Subsection
28787 \begin_layout Standard
28788 Align environments can be used for every kind of multiline formulas.
28789 They are especially useful to set several formulas side by side.
28792 \begin_layout Standard
28793 Align environments consist of columns.
28794 The odd columns are right aligned, the even ones left aligned.
28795 Every line in an Align environment can be numbered.
28798 \begin_layout Standard
28799 Align environments are created via the menu
28801 Insert\SpecialChar menuseparator
28807 Edit\SpecialChar menuseparator
28808 Math\SpecialChar menuseparator
28809 Change Formula Type
28811 already existing formulas can be converted to Align environments.
28814 \begin_layout Standard
28815 To add or delete columns, the math toolbar buttons
28818 arg "inset-modify tabular append-column"
28824 arg "inset-modify tabular delete-column"
28827 , respectively, or the menu
28829 Edit\SpecialChar menuseparator
28835 \begin_layout Subsubsection
28836 Standard align Environment
28837 \begin_inset CommandInset label
28839 name "subsec:Standard-align-Environment"
28844 \begin_inset Index idx
28847 \begin_layout Plain Layout
28848 Formula ! multiline ! align environment
28856 \begin_layout Standard
28857 This Align environment is created by pressing
28860 arg "newline-insert newline"
28863 in a formula or by the menu
28865 Insert\SpecialChar menuseparator
28866 Math\SpecialChar menuseparator
28867 AMS align Environment
28872 \begin_layout Standard
28873 An example for two formulas set side by side, that are created with a four
28874 column align environment:
28875 \begin_inset Formula
28877 A & =\sin(B) & C & =D\\
28878 C & \ne A & B & \ne D
28883 As it can be seen, the formulas in this environment are placed so as if
28892 \begin_layout Plain Layout
28900 \begin_inset CommandInset ref
28902 reference "subsec:Variable-Space"
28913 before the first and after every even column.
28914 When the formula style
28920 \begin_layout Plain Layout
28922 \begin_inset CommandInset ref
28924 reference "sec:Formula-Styles"
28935 is used, the formula is set without the
28941 before the first column.
28944 \begin_layout Subsubsection
28945 Alignat Environment
28946 \begin_inset Index idx
28949 \begin_layout Plain Layout
28950 Formula ! multiline ! alignat environment
28958 \begin_layout Standard
28959 The alignat environment has no predefined column separation.
28960 It can be inserted manually with the spaces that are described
28961 \begin_inset CommandInset ref
28963 reference "subsec:Space"
28970 \begin_layout Standard
28971 The above example in the alignat environment where 1
28972 \begin_inset space \thinspace{}
28975 cm space was inserted at the beginning of the second formula:
28976 \begin_inset Formula
28977 \begin{alignat*}{2}
28978 A & =\sin(B) & \hspace{1cm}C & =D\\
28979 C & \ne A & B & \ne D
28984 Because the column separation can be set separately for every column, this
28985 environment is especially suitable to set three and more formulas side
28989 \begin_layout Subsubsection
28990 Flalign Environment
28991 \begin_inset CommandInset label
28993 name "subsec:Flalign-Environment"
28998 \begin_inset Index idx
29001 \begin_layout Plain Layout
29002 Formula ! multiline ! flalign environment
29010 \begin_layout Standard
29011 In this environment the first two columns are always set as much as possible
29012 to the left and the last two ones to the right.
29014 \begin_inset Formula
29016 A & =1 & B & =2 & C & =3\\
29017 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29025 \begin_layout Standard
29026 By creating a flalign environment with an odd number of columns where an
29027 empty \SpecialChar TeX
29028 brace is inserted to the last column, several formulas in a document
29029 can be set to the left, although the formula style
29034 As example the indented formula
29035 \begin_inset CommandInset ref
29037 reference "eq:VolInt"
29042 \begin_inset Formula
29044 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29049 The first two columns contain the formula.
29050 To indent it as with the formula style
29055 \begin_inset space \thinspace{}
29058 pt space was inserted at the beginning of the first column.
29061 \begin_layout Subsection
29062 Eqnarray Environment
29063 \begin_inset CommandInset label
29065 name "subsec:Eqnarray-Environment"
29070 \begin_inset Index idx
29073 \begin_layout Plain Layout
29074 Formula ! multiline ! eqnarray environment
29082 \begin_layout Standard
29083 When this environment has been created, three blue boxes appear.
29084 The content of the first box is right aligned, the content of the last
29086 The content of the middle box appears centered and a bit smaller, because
29087 it is designed to insert there only relation characters.
29088 \begin_inset Formula
29090 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29100 \begin_layout Subsection
29102 \begin_inset Index idx
29105 \begin_layout Plain Layout
29106 Formula ! multiline ! gather environment
29114 \begin_layout Standard
29115 This environment consists of only one centered column.
29116 Every line can be numbered.
29117 \begin_inset Formula
29128 \begin_layout Subsection
29129 Multline Environment
29130 \begin_inset CommandInset label
29132 name "subsec:Multline-Environment"
29137 \begin_inset Index idx
29140 \begin_layout Plain Layout
29141 Formula ! multiline ! multline environment
29149 \begin_layout Standard
29150 The multline environment consists, like the gather environment, of only
29152 But the first line is left aligned, the last one right aligned.
29153 All other lines are centered.
29154 Therefore this environment is suitable for long formulas.
29156 \begin_inset CommandInset ref
29158 reference "eq:lefteqn"
29162 in the multline environment:
29163 \begin_inset Formula
29165 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}\\
29166 -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}\\
29167 =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}}
29175 \begin_layout Standard
29176 In the output only the last (first) line of a multline environment appears
29177 numbered when the document numbering is right (left).
29181 \begin_layout Plain Layout
29182 numbering styles see
29183 \begin_inset CommandInset ref
29185 reference "sec:Formula-Styles"
29197 \begin_layout Standard
29205 \begin_inset Index idx
29208 \begin_layout Plain Layout
29223 \begin_inset Index idx
29226 \begin_layout Plain Layout
29234 a centered line can be right or left aligned, respectively.
29235 The commands are used as follows:
29238 \begin_layout Standard
29243 shoveright{line content}
29249 shoveleft{line content}
29252 \begin_layout Standard
29253 \begin_inset VSpace medskip
29263 \begin_inset Index idx
29266 \begin_layout Plain Layout
29274 specifies the distance of the first line from the left page margin.
29275 Predefined is the length 0
29276 \begin_inset space \thinspace{}
29282 \begin_layout Standard
29283 As example the above formula where the command
29286 \begin_layout Standard
29296 \begin_layout Standard
29297 was inserted in \SpecialChar TeX
29302 \begin_layout Plain Layout
29314 \begin_inset Formula
29316 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}\\
29317 \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}}\\
29318 =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}}
29327 \begin_layout Plain Layout
29338 The second line was left aligned using
29347 \begin_layout Subsection
29348 Multiline Formula Parts
29349 \begin_inset CommandInset label
29351 name "subsec:Multiline-Formula-Parts"
29356 \begin_inset Index idx
29359 \begin_layout Plain Layout
29360 Formula ! multiline ! formula parts
29368 \begin_layout Standard
29369 To display only parts of a formula with multiple lines, one of the following
29370 environments is used:
29387 They can be inserted via the menu
29389 Insert\SpecialChar menuseparator
29392 or by using the commands described in this section.
29395 \begin_layout Standard
29396 The first three have the same properties as the corresponding multiline
29397 formula environments, but it is possible to set further formula parts beside
29400 \begin_inset Formula
29402 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29403 \Delta E\Delta t & \ge\frac{\hbar}{2}
29405 \right\} \textrm{Uncertainty relations}
29413 \begin_layout Standard
29414 To get this formula, a displayed formula is created where the command
29421 \begin_inset Index idx
29424 \begin_layout Plain Layout
29433 A purple box appears around the blue formula box where now columns and
29434 lines can be added.
29435 Outside the multiline environment other formula parts can be set, like
29439 \begin_layout Standard
29440 The aligned environment is also suitable for long formulas whose lines are
29441 horizontally aligned.
29442 Using aligned in a displayed formula has the advantage that the formula
29443 number is vertically centered behind the lines.
29445 \begin_inset CommandInset ref
29447 reference "eq:shortlong"
29451 in the aligned environment:
29452 \begin_inset Formula
29454 \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}|}\\
29455 & -\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}|}
29464 \begin_layout Standard
29465 To use the environments
29484 \begin_inset Index idx
29487 \begin_layout Plain Layout
29502 \begin_inset Index idx
29505 \begin_layout Plain Layout
29520 \begin_inset Index idx
29523 \begin_layout Plain Layout
29531 are inserted, respectively.
29532 The split environment has the same properties as the aligned environment
29533 but it can only have two columns.
29536 \begin_layout Subsection
29537 Text in multiline Formulas
29538 \begin_inset CommandInset label
29540 name "subsec:Text-in-multiline"
29545 \begin_inset Index idx
29548 \begin_layout Plain Layout
29555 \begin_inset Index idx
29558 \begin_layout Plain Layout
29559 Formula ! multiline ! text
29567 \begin_layout Standard
29568 In the Align environments, and the multline and gather environment, text
29569 can be inserted that will appear in a separate line and doesn't affect
29570 the column alignment.
29571 To do this, the command
29578 \begin_inset Index idx
29581 \begin_layout Plain Layout
29589 is used in the following scheme:
29592 \begin_layout Standard
29600 \begin_layout Standard
29601 The text should not be longer than a line because it cannot be hyphenated.
29602 As \SpecialChar LyX
29603 doesn't yet support
29609 directly, the text is written as mathematical text.
29616 must hereby be at the beginning of a line and appears in the output above
29618 An example where the text was inserted at the beginning of the second line:
29619 \begin_inset Formula
29621 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29622 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29630 \begin_layout Standard
29637 always creates some vertical space between the text and the formula lines.
29638 To avoid this space, set in the document settings under
29641 \begin_inset space ~
29651 \begin_inset Index idx
29654 \begin_layout Plain Layout
29655 Packages ! mathtools
29663 \begin_inset space ~
29669 Then you can use the command
29676 \begin_inset Index idx
29679 \begin_layout Plain Layout
29696 \begin_layout Standard
29697 \begin_inset Formula
29699 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29700 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29708 \begin_layout Section
29710 \begin_inset Index idx
29713 \begin_layout Plain Layout
29720 \begin_inset Index idx
29723 \begin_layout Plain Layout
29724 Formula ! numbering|see
29728 \begin_layout Plain Layout
29739 \begin_layout Plain Layout
29754 \begin_layout Subsection
29758 \begin_layout Standard
29759 Numbered formulas can be created with the menu
29761 Insert\SpecialChar menuseparator
29762 Math\SpecialChar menuseparator
29764 \begin_inset space ~
29772 \begin_inset space ~
29778 Existing formulas can be numbered with the menu
29780 Edit\SpecialChar menuseparator
29781 Math\SpecialChar menuseparator
29783 \begin_inset space ~
29791 arg "math-number-toggle"
29795 The formula number is displayed in \SpecialChar LyX
29796 behind the formula as a number sign
29798 The number sign is replaced in the output by the formula number.
29801 \begin_layout Standard
29802 When numbering is turned on in multiline formulas, all lines will be numbered.
29803 But the numbering can be controlled with the menu
29805 Edit\SpecialChar menuseparator
29806 Math\SpecialChar menuseparator
29808 \begin_inset space ~
29812 \begin_inset space ~
29816 \begin_inset space ~
29824 arg "math-number-line-toggle"
29830 \begin_layout Standard
29831 Except for inline formulas, all formulas can be numbered with two different
29833 \begin_inset CommandInset ref
29835 reference "sec:Formula-Styles"
29842 \begin_layout Subsection
29844 \begin_inset Index idx
29847 \begin_layout Plain Layout
29848 Cross-references ! to formulas
29856 \begin_layout Standard
29857 All labeled formulas can be cross-referenced.
29858 A label is added by the menu
29860 Insert\SpecialChar menuseparator
29863 or the toolbar button
29870 The cursor must hereby be inside a displayed formula.
29871 Alternatively you can right-click on the formula and choose
29876 A dialog pops up displaying the prefix
29881 The label is inserted there behind the prefix.
29882 The predefined prefix means
29883 \begin_inset Quotes eld
29887 \begin_inset Quotes erd
29890 and makes it easier to find labels in large documents because it marks
29891 it as formula label to divide it from e.
29892 \begin_inset space \thinspace{}
29896 \begin_inset space \space{}
29900 To change a label, the menu
29902 Insert\SpecialChar menuseparator
29905 is used again or you right-click on a formula and then on
29912 \begin_layout Standard
29913 The name of the label is displayed in \SpecialChar LyX
29914 within two parentheses behind formula.
29915 A formula with a label is always numbered.
29918 \begin_layout Standard
29919 Cross-references are inserted via the menu
29921 Insert\SpecialChar menuseparator
29924 or with the toolbar button
29927 arg "dialog-show-new-inset ref"
29931 A formula cross-reference appears in the output as formula number.
29932 When in the cross-reference dialog window the format
29936 is chosen, the cross-reference appears in the output as formula number
29938 \begin_inset Newline newline
29941 By right-clicking on a cross-reference in \SpecialChar LyX
29942 , one jumps to the formula that
29946 \begin_layout Standard
29947 Here are as examples cross-references to formulas of the following subsections:
29948 \begin_inset Note Note
29951 \begin_layout Plain Layout
29952 Note the different cross-reference types.
29960 \begin_layout Standard
29962 \begin_inset CommandInset ref
29969 \begin_inset CommandInset ref
29977 \begin_inset CommandInset ref
29983 ) big Latin letters are used for the numbering in contrary to (
29984 \begin_inset CommandInset ref
29993 \begin_layout Standard
29994 \begin_inset VSpace medskip
29997 When the argument of
30005 \begin_layout Plain Layout
30013 \begin_inset CommandInset ref
30015 reference "subsec:User-defined-Numbering"
30026 contains a box like in
30027 \begin_inset CommandInset ref
30029 reference "subsec:Paragraph-Boxes"
30033 , the formula cannot be referenced.
30036 \begin_layout Subsection
30038 \begin_inset Index idx
30041 \begin_layout Plain Layout
30042 Formula numbering ! subnumbering
30050 \begin_layout Standard
30051 With the help of the commands
30055 begin{subequations}
30063 formulas can be subnumbered.
30064 Both commands are inserted in \SpecialChar TeX
30068 \begin_layout Standard
30070 \begin_inset Formula
30081 \begin_layout Plain Layout
30085 addtocounter{equation}{-1}
30094 \begin_layout Plain Layout
30098 begin{subequations}
30104 \begin_inset VSpace -5mm
30108 \begin_inset Formula
30116 \begin_inset Formula
30126 \begin_layout Standard
30130 \begin_layout Plain Layout
30142 \begin_layout Standard
30143 To create the example, the following is done:
30146 \begin_layout Enumerate
30147 first formula is inserted
30150 \begin_layout Enumerate
30155 addtocounter{equation}{-1}
30157 begin{subequations}
30158 \begin_inset Index idx
30161 \begin_layout Plain Layout
30170 \begin_inset Newline newline
30175 is inserted after the first formula
30178 \begin_layout Enumerate
30179 second formula is inserted
30182 \begin_layout Enumerate
30183 third formula is inserted
30186 \begin_layout Enumerate
30193 is inserted after the third formula
30196 \begin_layout Standard
30197 Every formula between the commands
30209 is subnumbered as a, b,
30210 \begin_inset Newline linebreak
30213 c, \SpecialChar ldots
30214 For multiline formulas every line will be subnumbered.
30215 All subnumbered formulas are treated as
30220 But as every numbered formula increases the counter
30224 by one, the command
30230 is needed to decrease it.
30231 Otherwise the formulas
30232 \begin_inset CommandInset ref
30239 \begin_inset CommandInset ref
30246 \begin_inset CommandInset ref
30252 would be numbered as
30253 \begin_inset CommandInset ref
30260 \begin_inset CommandInset ref
30267 \begin_inset CommandInset ref
30276 \begin_layout Standard
30277 By inserting the commands in \SpecialChar TeX
30278 mode, a space is created between the first
30281 \begin_inset space \thinspace{}
30284 mm vertical space is inserted after the command
30288 begin{subequations}
30291 When the formula style
30297 \begin_layout Plain Layout
30299 \begin_inset CommandInset ref
30301 reference "sec:Formula-Styles"
30313 \begin_inset space \thinspace{}
30316 mm space is inserted instead.
30319 \begin_layout Standard
30320 Here is an example for a multiline formula where the numbering was turned
30321 off for the second line:
30325 \begin_layout Plain Layout
30329 begin{subequations}
30335 \begin_inset Formula
30337 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30338 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30339 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30348 \begin_layout Plain Layout
30360 \begin_layout Subsection
30361 User-defined Numbering
30362 \begin_inset CommandInset label
30364 name "subsec:User-defined-Numbering"
30369 \begin_inset Index idx
30372 \begin_layout Plain Layout
30373 Formula numbering ! user-defined
30381 \begin_layout Standard
30382 \begin_inset Index idx
30385 \begin_layout Plain Layout
30386 Formula numbering ! self-defined delimiters
30391 With the standard numbering parentheses are set around the formula number.
30392 To replace the parentheses for example by vertical bars, the following
30393 line is added to the \SpecialChar LaTeX
30397 \begin_layout Standard
30409 \begin_inset Note Note
30412 \begin_layout Plain Layout
30413 This macro is already declared in the \SpecialChar LaTeX
30414 -preamble for testing.
30415 To activate it, remove the percent sign at the beginning.
30423 \begin_layout Standard
30424 To use other characters, the vertical bars besides the
30428 are replaced by one ore more characters.
30429 To get only the formula number the vertical bars are omitted.
30432 \begin_layout Standard
30433 \begin_inset VSpace bigskip
30436 When there should be an expression of your choice instead of the consecutive
30437 formula number in parentheses behind the formula, the command
30444 \begin_inset Index idx
30447 \begin_layout Plain Layout
30456 \begin_inset Formula
30458 A+B=C\tag{something}\label{eq:tag}
30463 In this example the command
30468 \begin_inset space \textvisiblespace{}
30473 was inserted in the formula.
30476 \begin_layout Standard
30482 \begin_inset space \textvisiblespace{}
30487 is inserted instead, the star prevents the parentheses around the expression:
30488 \begin_inset Formula
30490 A+B=C\tag*{something}
30498 \begin_layout Standard
30499 \begin_inset VSpace bigskip
30502 To restart the formula numbering with new document parts or sections, the
30503 following command is used:
30506 \begin_layout Standard
30511 @addtoreset{equation}{part}
30514 \begin_inset Index idx
30517 \begin_layout Plain Layout
30522 \begin_layout Plain Layout
30533 \begin_layout Plain Layout
30546 \begin_layout Plain Layout
30557 \begin_layout Plain Layout
30570 \begin_inset Newline newline
30574 \begin_inset Newline newline
30581 @addtoreset{equation}{section}
30584 \begin_layout Standard
30585 To be able to use these commands in \SpecialChar TeX
30587 \begin_inset Quotes eld
30591 \begin_inset Quotes erd
30594 character has to be made
30595 \begin_inset Quotes eld
30599 \begin_inset Quotes erd
30602 for \SpecialChar LaTeX
30617 So the command sequence in \SpecialChar TeX
30621 \begin_layout Standard
30627 \begin_inset Newline newline
30632 @addtoreset{equation}{section}
30633 \begin_inset Newline newline
30641 \begin_layout Standard
30642 In the \SpecialChar LaTeX
30655 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30659 \begin_layout Standard
30674 \begin_layout Plain Layout
30679 is part of the \SpecialChar LaTeX
30685 \begin_inset Index idx
30688 \begin_layout Plain Layout
30689 Packages ! carlisle
30694 that is part of every \SpecialChar LaTeX
30695 standard installation.
30701 \begin_inset Index idx
30704 \begin_layout Plain Layout
30705 Packages ! remreset
30710 has to be loaded in the \SpecialChar LaTeX
30711 -preamble with the line
30714 \begin_layout Standard
30719 usepackage{remreset}
30722 \begin_layout Standard
30730 \begin_inset Index idx
30733 \begin_layout Plain Layout
30738 \begin_layout Plain Layout
30749 \begin_layout Plain Layout
30762 \begin_layout Plain Layout
30773 \begin_layout Plain Layout
30785 can be used with the same scheme as
30794 \begin_layout Standard
30795 \begin_inset VSpace bigskip
30798 Sometimes formulas should be numbered in the following form:
30801 \begin_layout Standard
30804 (section number.formula number)
30807 \begin_layout Standard
30808 The formula number should start with every section with
30809 \begin_inset Quotes eld
30813 \begin_inset Quotes erd
30819 \begin_layout Standard
30820 For this case there is the command
30827 \begin_inset Index idx
30830 \begin_layout Plain Layout
30838 , which is used with the following scheme:
30841 \begin_layout Standard
30846 numberwithin{counter}{sectioning}
30849 \begin_layout Standard
30850 Counter denotes what kind of numbering is affected, sectioning denotes what
30851 number is before the dot.
30854 \begin_layout Standard
30855 Thus in our case the following \SpecialChar LaTeX
30856 preamble or \SpecialChar TeX
30860 \begin_layout Standard
30865 numberwithin{equation}{section}
30868 \begin_layout Standard
30869 This is the result:
30873 \begin_layout Plain Layout
30877 numberwithin{equation}{section}
30883 \begin_inset Formula
30893 \begin_layout Standard
30895 \begin_inset space \thinspace{}
30899 \begin_inset space \space{}
30902 tables so that the number of the part is the sectioning,
30903 \begin_inset Newline newline
30910 numberwithin{table}{part}
30915 \begin_layout Standard
30916 To go back to the standard numbering or to prevent this kind of numbering
30917 when it is defined by the document class, the following command is inserted
30918 as \SpecialChar TeX
30919 code or to the \SpecialChar LaTeX
30923 \begin_layout Standard
30933 \begin_inset Index idx
30936 \begin_layout Plain Layout
30950 \begin_layout Plain Layout
30966 \begin_inset Newline newline
30974 \begin_inset Newline newline
30986 \begin_layout Standard
30993 uses internally the command
30999 , described above, that also needs to be reverted.
31003 \begin_layout Plain Layout
31010 \begin_layout Plain Layout
31014 @removefromreset{equation}{section}
31017 \begin_layout Plain Layout
31029 \begin_layout Subsection
31030 Numbering with Roman Numbers and Letters
31031 \begin_inset Index idx
31034 \begin_layout Plain Layout
31035 Formula numbering ! with letters
31041 \begin_inset Index idx
31044 \begin_layout Plain Layout
31045 Formula numbering ! with Roman numbers
31053 \begin_layout Standard
31054 Formulas can also be numbered with Roman numbers and Latin letters.
31055 To number for example with small Roman numbers, the command
31058 \begin_layout Standard
31070 \begin_layout Standard
31071 is inserted before the formula in \SpecialChar TeX
31080 \begin_inset Index idx
31083 \begin_layout Plain Layout
31091 redefines the predefined command
31107 \begin_layout Plain Layout
31114 has the same scheme like the command
31120 that is described in
31121 \begin_inset CommandInset ref
31123 reference "subsec:The-Command-newcommand"
31136 is the formula counter.
31143 is used as prefix for a counter, the value of the counter is output as
31145 When a formula is numbered, \SpecialChar LaTeX
31146 sets internally the command
31152 behind the formula.
31158 \begin_inset Index idx
31161 \begin_layout Plain Layout
31171 outputs the counter as small Roman number.
31174 \begin_layout Standard
31175 All formulas behind the command
31185 are now numbered Roman.
31186 To switch to numbering with big Roman numbers, the command is inserted
31200 \begin_inset Index idx
31203 \begin_layout Plain Layout
31215 \begin_inset Quotes eld
31219 \begin_inset Quotes erd
31222 with small Latin letters there is the command
31229 \begin_inset Index idx
31232 \begin_layout Plain Layout
31240 , for big ones there is the command
31247 \begin_inset Index idx
31250 \begin_layout Plain Layout
31263 \begin_layout Standard
31264 \begin_inset Note Greyedout
31267 \begin_layout Plain Layout
31274 \begin_inset space ~
31277 formulas can be numbered with Latin letters in one document.
31285 \begin_layout Standard
31289 \begin_layout Plain Layout
31305 \begin_layout Standard
31306 \begin_inset Formula
31308 A=\textrm{small roman}
31317 \begin_layout Plain Layout
31331 \begin_inset Formula
31333 B=\textrm{big Roman}\label{eq:Rom}
31342 \begin_layout Plain Layout
31356 \begin_inset Formula
31358 C=\textrm{small Latin}
31367 \begin_layout Plain Layout
31381 \begin_inset Formula
31383 D=\textrm{big Latin}\label{eq:Lat}
31391 \begin_layout Standard
31392 To switch back to the default numbering, insert the command:
31395 \begin_layout Standard
31405 \begin_inset Index idx
31408 \begin_layout Plain Layout
31419 \begin_layout Standard
31423 \begin_layout Plain Layout
31437 \begin_inset Formula
31447 \begin_layout Standard
31448 \begin_inset VSpace medskip
31451 As you see, formulas are numbered serially independent from the numbering
31453 When then numbering should start with
31454 \begin_inset Quotes eld
31458 \begin_inset Quotes erd
31461 when the style is changed, new equation counters have to be defined.
31462 A description about this can be found in the file
31463 \begin_inset CommandInset href
31465 name "Formula-numbering.lyx"
31466 target "run:Formula-numbering.lyx"
31473 \begin_layout Section
31474 Chemical Symbols and Equations
31475 \begin_inset CommandInset label
31477 name "subsec:Chemical-Symbols-and"
31482 \begin_inset Index idx
31485 \begin_layout Plain Layout
31486 Chemical characters ! Symbols
31492 \begin_inset Index idx
31495 \begin_layout Plain Layout
31502 \begin_inset Index idx
31505 \begin_layout Plain Layout
31514 \begin_layout Standard
31515 An example text from chemistry:
31518 \begin_layout Quote
31520 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31523 -ion reacts with two
31524 \begin_inset Formula $\mathrm{Na^{+}}$
31527 -ions to sodium sulfate
31528 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31532 The chemical equation for this is:
31533 \begin_inset Formula
31535 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31543 \begin_layout Standard
31544 This chemical equation can directly be created as formula.
31545 To avoid that the symbols appear italic, everything is highlighted and
31546 changed by the shortcut
31552 to the upright font style.
31556 \begin_layout Plain Layout
31562 \begin_inset CommandInset ref
31564 reference "subsec:Font-Styles"
31576 \begin_layout Standard
31577 A more convenient way to typeset chemical formulas is to use the command
31585 \begin_inset Index idx
31588 \begin_layout Plain Layout
31596 that is available when the \SpecialChar LaTeX
31602 \begin_inset Index idx
31605 \begin_layout Plain Layout
31618 to a formula a new blue box appears where chemical formulas can be inserted
31619 in an intuitive way.
31620 \begin_inset Separator parbreak
31626 \begin_layout Standard
31628 \begin_inset Tabular
31629 <lyxtabular version="3" rows="10" columns="2">
31630 <features booktabs="true" tabularvalignment="middle">
31631 <column alignment="center" valignment="top" width="0pt">
31632 <column alignment="center" valignment="top">
31634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31637 \begin_layout Plain Layout
31643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31646 \begin_layout Plain Layout
31654 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31657 \begin_layout Plain Layout
31661 \begin_inset space \textvisiblespace{}
31669 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31672 \begin_layout Plain Layout
31673 \begin_inset Formula $\ce{H2CO3}$
31682 <row topspace="1.5mm">
31683 <cell alignment="center" valignment="top" usebox="none">
31686 \begin_layout Plain Layout
31690 \begin_inset space \textvisiblespace{}
31698 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31701 \begin_layout Plain Layout
31702 \begin_inset Formula $\ce{SO4^{2-}}$
31711 <row topspace="1.5mm">
31712 <cell alignment="center" valignment="top" usebox="none">
31715 \begin_layout Plain Layout
31719 \begin_inset space \textvisiblespace{}
31727 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31730 \begin_layout Plain Layout
31731 \begin_inset Formula $\ce{(NH4)2S}$
31740 <row topspace="1.5mm">
31741 <cell alignment="center" valignment="top" usebox="none">
31744 \begin_layout Plain Layout
31748 \begin_inset space \textvisiblespace{}
31756 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31759 \begin_layout Plain Layout
31760 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31769 <row topspace="1.5mm">
31770 <cell alignment="center" valignment="top" usebox="none">
31773 \begin_layout Plain Layout
31777 \begin_inset space \textvisiblespace{}
31783 \begin_inset space \textvisiblespace{}
31789 \begin_inset space \textvisiblespace{}
31797 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31800 \begin_layout Plain Layout
31801 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31810 <row topspace="1.5mm">
31811 <cell alignment="center" valignment="top" usebox="none">
31814 \begin_layout Plain Layout
31818 \begin_inset space \textvisiblespace{}
31822 \begin_inset Formula $\downarrow$
31826 \begin_inset Formula $\to$
31834 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31837 \begin_layout Plain Layout
31838 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31848 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31851 \begin_layout Plain Layout
31855 \begin_inset space \textvisiblespace{}
31861 \begin_inset space \textvisiblespace{}
31867 \begin_inset space \textvisiblespace{}
31875 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31878 \begin_layout Plain Layout
31879 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31892 \begin_layout Plain Layout
31896 \begin_inset space \textvisiblespace{}
31900 \begin_inset space \textvisiblespace{}
31904 \begin_inset space \textvisiblespace{}
31908 \begin_inset space \textvisiblespace{}
31912 \begin_inset space \textvisiblespace{}
31920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31923 \begin_layout Plain Layout
31924 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31933 <row topspace="1.5mm">
31934 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31937 \begin_layout Plain Layout
31941 \begin_inset space \textvisiblespace{}
31945 \begin_inset space \textvisiblespace{}
31949 \begin_inset space \textvisiblespace{}
31953 \begin_inset space \textvisiblespace{}
31961 \begin_inset space \textvisiblespace{}
31969 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31972 \begin_layout Plain Layout
31973 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
31989 \begin_layout Standard
31990 \begin_inset Note Greyedout
31993 \begin_layout Plain Layout
31999 It is not possible in \SpecialChar LyX
32000 to use the character ^ to get an up-arrow as described
32006 One instead uses a negative thin space followed by the command
32013 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32024 \begin_layout Standard
32031 the command for equation
32032 \begin_inset space ~
32036 \begin_inset CommandInset ref
32038 reference "eq:chem-reaction"
32043 \begin_inset Newline newline
32051 \begin_inset space \textvisiblespace{}
32055 \begin_inset space \textvisiblespace{}
32059 \begin_inset space \textvisiblespace{}
32063 \begin_inset space \textvisiblespace{}
32067 \begin_inset space \textvisiblespace{}
32071 \begin_inset space \textvisiblespace{}
32077 \begin_layout Standard
32078 To create multiline chemical equations first a multiline formula is created
32080 \begin_inset CommandInset ref
32082 reference "sec:Multiline-Formulas"
32087 Afterwards the command
32093 is used in every small blue box of the formula.
32095 \begin_inset CommandInset ref
32097 reference "eq:TEOS-reaction-1"
32102 \begin_inset CommandInset ref
32104 reference "eq:TEOS-reaction-2"
32108 are an example of a multi-stage chemical reaction where every equation
32109 has its own number.
32110 \begin_inset Formula
32112 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32113 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32121 \begin_layout Standard
32132 package provides the command
32139 \begin_inset Index idx
32142 \begin_layout Plain Layout
32150 that has to be used for special cases.
32151 For more information about
32157 and more examples have a look at the documentation of
32162 \begin_inset CommandInset citation
32171 \begin_layout Section
32175 \begin_layout Standard
32177 supports two types of commutative diagrams:
32185 that are explained in the following.
32188 \begin_layout Subsection
32190 \begin_inset Index idx
32193 \begin_layout Plain Layout
32202 \begin_layout Standard
32203 Diagrams of this type visualize relations by vertical and horizontal lines
32205 \begin_inset Formula
32207 \begin{CD}A@>>>B@>>>C\\
32218 \begin_layout Standard
32219 To get them, the command
32224 \begin_inset Index idx
32227 \begin_layout Plain Layout
32237 is inserted to a formula.
32238 A blue box appears with two dashed lines where further commands can be
32243 arg "newline-insert newline"
32246 a new line is created.
32247 Horizontal relations are inserted in odd, vertical in even formula lines.
32250 \begin_layout Standard
32251 To create the relations there are the following commands:
32254 \begin_layout Itemize
32259 creates a left arrow,
32270 \begin_layout Itemize
32275 creates an up arrow,
32283 a vertical equal sign
32286 \begin_layout Itemize
32292 is a placeholder for non-existent relations
32295 \begin_layout Standard
32296 All arrows can be labeled as follows:
32299 \begin_layout Itemize
32300 If text inserted between the first and second < or >, resp., it is placed
32302 When it is inserted between the second and third one, it appears under
32306 \begin_layout Itemize
32307 When text for vertical arrows is inserted between the first and second A
32308 or V, resp., it is placed left beside the arrow.
32309 When it is inserted between the second and third one, it appears right
32311 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32315 \begin_layout Standard
32316 As example a diagram with all possible relations:
32319 \begin_layout Standard
32320 \begin_inset Formula
32322 \begin{CD}A@>j>>B@>>k>C@=F\\
32333 \begin_layout Standard
32334 The command for this is:
32335 \begin_inset Newline newline
32343 \begin_inset space \textvisiblespace{}
32346 A@>j>>B@>>k>C@=F Ctrl+Return
32347 \begin_inset Newline newline
32351 \begin_inset Phantom HPhantom
32354 \begin_layout Plain Layout
32360 \begin_inset space \textvisiblespace{}
32373 \begin_inset Formula $\to$
32379 \begin_inset Newline newline
32383 \begin_inset Phantom HPhantom
32386 \begin_layout Plain Layout
32392 \begin_inset space \textvisiblespace{}
32403 \begin_layout Subsection
32405 \begin_inset Index idx
32408 \begin_layout Plain Layout
32409 Diagrams ! xymatrix
32417 \begin_layout Standard
32418 To be able to use xymatrices, the \SpecialChar LaTeX
32424 A xymatrix is created by inserting the command
32431 Then you are able to add new matrix columns and rows like for normal matrices,
32433 \begin_inset CommandInset ref
32435 reference "sec:Matrices"
32442 \begin_layout Standard
32443 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32445 All possibilities to create commutative diagrams and decorations are explained
32450 that you find in the menu
32452 Help\SpecialChar menuseparator
32454 \begin_inset space ~
32462 \begin_layout Subsection
32468 \begin_inset Index idx
32471 \begin_layout Plain Layout
32480 \begin_layout Standard
32485 -diagrams, the \SpecialChar LaTeX
32495 -diagram is created by inserting the command
32502 Then you are able to add new matrix columns and rows like for normal matrices,
32504 \begin_inset CommandInset ref
32506 reference "sec:Matrices"
32513 \begin_layout Standard
32514 Examples how to create
32518 diagrams in \SpecialChar LyX
32521 Feynman-diagram manual
32523 that you find in the menu
32525 Help\SpecialChar menuseparator
32527 \begin_inset space ~
32535 \begin_layout Standard
32536 \begin_inset Newpage newpage
32542 \begin_layout Section
32543 User-defined Commands
32544 \begin_inset Index idx
32547 \begin_layout Plain Layout
32548 User-defined commands
32556 \begin_layout Standard
32557 \begin_inset Note Greyedout
32560 \begin_layout Plain Layout
32565 The names of user-defined commands and macros may only consist of Latin
32574 \begin_layout Subsection
32578 \begin_inset CommandInset label
32580 name "subsec:The-Command-newcommand"
32585 \begin_inset Index idx
32588 \begin_layout Plain Layout
32589 User-defined commands !
32597 \begin_inset Index idx
32600 \begin_layout Plain Layout
32611 \begin_layout Standard
32612 Many \SpecialChar LaTeX
32613 -commands are too long to be used frequently.
32614 But it is possible to define with the command
32620 new shorter commands.
32623 \begin_layout Standard
32624 The command scheme of
32633 \begin_layout Standard
32638 newcommand{new command name}[number of arguments][optional
32643 \begin_inset Newline newline
32647 \begin_inset Phantom HPhantom
32650 \begin_layout Plain Layout
32660 {command definition}
32663 \begin_layout Standard
32664 \begin_inset Note Greyedout
32667 \begin_layout Plain Layout
32672 Assure that the name of the new command is not already used in your document
32673 or by \SpecialChar LaTeX
32674 -packages that you use.
32675 When you for example define the command
32687 , you get an error message because
32693 is already defined as command for
32694 \begin_inset Quotes eld
32698 \begin_inset Formula $\le$
32702 \begin_inset Quotes erd
32713 \begin_layout Standard
32714 The number of arguments is an integer in the range 0
32715 \begin_inset space \thinspace{}
32719 \begin_inset space \thinspace{}
32722 9 and specifies how many arguments the new command should have.
32723 With the optional value a value for an optional argument can be predefined.
32724 When this is done, the
32732 rgument of the new command is automatically an optional one.
32735 \begin_layout Standard
32736 Here are some examples:
32739 \begin_layout Itemize
32740 To define the command
32752 , the \SpecialChar LaTeX
32754 \begin_inset VSpace medskip
32758 \begin_inset Newline newline
32772 \begin_layout Itemize
32773 To define the command
32785 , the argument (that should be underlined) must be taken into account.
32786 For this the preamble line is:
32787 \begin_inset VSpace medskip
32791 \begin_inset Newline newline
32805 \begin_inset VSpace medskip
32809 \begin_inset Newline newline
32816 acts as argument placeholder, the
32820 behind it denotes that it is the placeholder for the first argument.
32823 \begin_layout Itemize
32831 \begin_inset space \thinspace{}
32835 \begin_inset space \space{}
32845 \begin_inset VSpace medskip
32849 \begin_inset Newline newline
32860 framebox#1#2{$#3$}}
32863 \begin_inset VSpace medskip
32867 \begin_inset Newline newline
32870 The two Dollar signs creates the extra formula needed for
32877 \begin_inset CommandInset ref
32879 reference "subsec:Boxes-with-Frame"
32886 \begin_layout Itemize
32887 To create a new command for
32893 where the color for the box need not be specified, the argument for the
32894 color is defined optional:
32895 \begin_inset VSpace medskip
32899 \begin_inset Newline newline
32910 fcolorbox{#2}{#1}{$#3$}}
32913 \begin_inset VSpace medskip
32917 \begin_inset Newline newline
32920 When the color is not specified when using
32926 , the predefined color
32933 \begin_layout Standard
32934 A test of the new defined commands:
32935 \begin_inset Separator parbreak
32941 \begin_layout Standard
32943 \begin_inset Tabular
32944 <lyxtabular version="3" rows="6" columns="2">
32945 <features booktabs="true" tabularvalignment="middle">
32946 <column alignment="center" valignment="top" width="0pt">
32947 <column alignment="center" valignment="top">
32949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32952 \begin_layout Plain Layout
32958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32961 \begin_layout Plain Layout
32969 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32972 \begin_layout Plain Layout
32976 \begin_inset space \textvisiblespace{}
32984 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32987 \begin_layout Plain Layout
32988 \begin_inset Formula $A\gr B$
32998 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33001 \begin_layout Plain Layout
33009 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33012 \begin_layout Plain Layout
33013 \begin_inset Formula $\us{ABcd}$
33022 <row topspace="1mm">
33023 <cell alignment="center" valignment="top" usebox="none">
33026 \begin_layout Plain Layout
33030 \begin_inset Formula $\to$
33036 \begin_inset Formula $\to$
33044 \begin_inset space \textvisiblespace{}
33052 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33055 \begin_layout Plain Layout
33056 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33065 <row topspace="1.5mm">
33066 <cell alignment="center" valignment="top" usebox="none">
33069 \begin_layout Plain Layout
33073 \begin_inset Formula $\to$
33081 \begin_inset space \textvisiblespace{}
33089 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33092 \begin_layout Plain Layout
33093 \begin_inset Formula $\cb{red}{\int A=B}$
33102 <row topspace="1.5mm" bottomspace="1mm">
33103 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33106 \begin_layout Plain Layout
33112 \begin_inset Formula $\to$
33120 \begin_inset space \textvisiblespace{}
33128 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33131 \begin_layout Plain Layout
33132 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33148 \begin_layout Subsection
33150 \begin_inset Index idx
33153 \begin_layout Plain Layout
33154 User-defined commands! Math macros
33160 \begin_inset Index idx
33163 \begin_layout Plain Layout
33172 \begin_layout Standard
33173 User-defined commands are especially convenient for complex expressions.
33174 When you are for example dealing with a document that has quadratic equations,
33175 the same solution type occurs several times.
33176 The general form of a quadratic equation is
33177 \begin_inset Formula
33179 0=\lambda^{2}+p\lambda+q
33184 The general form of the solution is
33185 \begin_inset Formula
33187 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33195 \begin_layout Standard
33196 To define a command for the solution formula where only the three parameters
33198 \begin_inset Formula $\lambda$
33202 \begin_inset Formula $p$
33206 \begin_inset Formula $q$
33209 need to be specified and the index of
33210 \begin_inset Formula $\lambda$
33213 can be given optionally, the \SpecialChar LaTeX
33215 \begin_inset Newline newline
33231 \begin_inset Newline newline
33235 \begin_inset Phantom HPhantom
33238 \begin_layout Plain Layout
33252 frac{#3^{2}}{4}-#4}}
33255 \begin_layout Standard
33256 To create with this the solution formula, the command
33257 \begin_inset Newline newline
33267 \begin_inset Formula $\to$
33273 \begin_inset Formula $\to$
33280 is inserted to a formula
33285 \begin_layout Standard
33286 The definition of the new command is unintuitive because one has to know
33287 the schemes of all used \SpecialChar LaTeX
33289 \begin_inset space \thinspace{}
33293 \begin_inset space \space{}
33296 that a fraction is inserted in \SpecialChar LaTeX
33301 frac{numerator}{denominator}
33304 Furthermore one can easily forget a brace in the definition and cannot
33305 see in \SpecialChar LyX
33306 what the new command is doing.
33307 To avoid these problems \SpecialChar LyX
33308 offers the possibility to use math macros instead
33318 \begin_layout Standard
33319 A math macro is created by using the menu
33321 Insert\SpecialChar menuseparator
33322 Math\SpecialChar menuseparator
33325 or the toolbar button
33328 arg "math-macro newmacroname_newcommand"
33332 The math macro toolbar appears together with the following box where the
33334 \begin_inset Newline newline
33338 \begin_inset space \hspace*{\fill}
33342 \begin_inset Graphics
33343 filename clipart/macrobox.png
33349 \begin_inset space \hspace*{\fill}
33353 \begin_inset Newline newline
33357 \begin_inset FormulaMacro
33358 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33363 newmacroname is the default name of the macro that should be changed to
33364 something sensible.
33365 The wanted formula is inserted in the first blue box.
33366 An argument placeholder is inserted with the command
33373 \begin_inset space \thinspace{}
33377 \begin_inset space \space{}
33386 or by using the macro toolbar button
33389 arg "math-macro-add-param"
33393 Argument placeholders are displayed red.
33395 \begin_inset space ~
33398 arguments are possible.
33399 Optional arguments are created with the toolbar button
33402 arg "math-macro-add-optional-param"
33406 The first non-optional argument can be transformed to an optional one with
33410 arg "math-macro-make-optional"
33414 In the second blue box the appearance of the macro in \SpecialChar LyX
33416 Normally you want to see it as it is defined, so the box is kept empty.
33417 But when you have created a macro that needs lot of space on the screen,
33418 you can insert in the box for example
33419 \begin_inset Newline newline
33449 \begin_inset Newline newline
33454 For the macro only the arguments with the macro name in front of them will
33455 then be displayed in \SpecialChar LyX
33456 , leading to a better overview.
33457 The formula appears in the output as defined in the first box.
33458 \begin_inset Newline newline
33461 The appearance of macros in formulas can furthermore be changed for single
33462 macros by setting the cursor in the macro and using the menu
33464 View\SpecialChar menuseparator
33466 \begin_inset space ~
33470 \begin_inset space ~
33478 \begin_layout Standard
33479 To use a macro, the macro name is inserted as command to a formula, in our
33487 Our macro looks in \SpecialChar LyX
33489 \begin_inset Newline newline
33493 \begin_inset space \hspace*{\fill}
33497 \begin_inset Graphics
33498 filename clipart/macrouse.png
33504 \begin_inset space \hspace*{\fill}
33508 \begin_inset Newline newline
33511 Here is our macro example with the arguments
33512 \begin_inset Formula $x$
33516 \begin_inset Formula $\ln(x)$
33520 \begin_inset Formula $B$
33526 \begin_layout Standard
33527 \begin_inset Formula
33537 \begin_layout Standard
33541 Tools\SpecialChar menuseparator
33542 Preferences\SpecialChar menuseparator
33543 Editing\SpecialChar menuseparator
33546 different styles to edit macros.
33547 To find the style that suits you the most, choose a style and set the cursor
33548 in a macro formula to see the difference.
33551 \begin_layout Standard
33552 A math macro is transformed internally to a
33558 command when exporting the document.
33565 command is not placed in the \SpecialChar LaTeX
33566 -preamble, therefore macros can only be used
33567 in formulas that are in the document below the macro definition box.
33570 \begin_layout Standard
33571 Math macros can also be directly created from a
33578 When writing for example the command
33581 \begin_inset Newline newline
33590 xleftarrow[#2]{#1}}
33591 \begin_inset Newline newline
33596 in \SpecialChar LyX
33597 as normal text, highlighting it completely and using then the shortcut
33602 , the command will be transformed to a math macro.
33603 Using this method you need to be careful that the
33609 command is typed correctly, otherwise you get a faulty macro leading to
33614 \begin_layout Standard
33615 Math macros currently have the problem that further formulas in macro definition
33616 s are handled wrongly.
33617 Therefore the example
33624 \begin_inset CommandInset ref
33626 reference "subsec:The-Command-newcommand"
33630 cannot be created as macro.
33633 \begin_layout Standard
33634 When the cursor is in a macro definition box, you will see the macro toolbar
33635 in \SpecialChar LyX
33639 \begin_layout Standard
33640 \begin_inset VSpace defskip
33646 \begin_layout Standard
33647 \begin_inset Graphics
33648 filename clipart/MacroToolbar.png
33653 \begin_inset Index idx
33656 \begin_layout Plain Layout
33665 \begin_layout Standard
33666 \begin_inset VSpace defskip
33672 \begin_layout Standard
33673 The macro toolbar contains from left to right the following buttons:
33676 \begin_layout Standard
33677 \begin_inset VSpace defskip
33683 \begin_layout Standard
33684 \begin_inset Tabular
33685 <lyxtabular version="3" rows="9" columns="2">
33686 <features islongtable="true" longtabularalignment="center">
33687 <column alignment="left" valignment="top">
33688 <column alignment="left" valignment="top" width="85col%">
33689 <row interlinespace="2.5mm">
33690 <cell alignment="center" valignment="top" usebox="none">
33693 \begin_layout Plain Layout
33696 arg "math-macro-remove-param"
33704 <cell alignment="center" valignment="top" usebox="none">
33707 \begin_layout Plain Layout
33710 Edit\SpecialChar menuseparator
33711 Math\SpecialChar menuseparator
33713 \begin_inset space ~
33716 Definition\SpecialChar menuseparator
33717 Remove Last Argument
33723 <row interlinespace="2.5mm">
33724 <cell alignment="center" valignment="top" usebox="none">
33727 \begin_layout Plain Layout
33730 arg "math-macro-add-param"
33738 <cell alignment="center" valignment="top" usebox="none">
33741 \begin_layout Plain Layout
33744 Edit\SpecialChar menuseparator
33745 Math\SpecialChar menuseparator
33747 \begin_inset space ~
33750 Definition\SpecialChar menuseparator
33757 <row interlinespace="2.5mm">
33758 <cell alignment="center" valignment="top" usebox="none">
33761 \begin_layout Plain Layout
33764 arg "math-macro-make-optional"
33772 <cell alignment="center" valignment="top" usebox="none">
33775 \begin_layout Plain Layout
33778 Edit\SpecialChar menuseparator
33779 Math\SpecialChar menuseparator
33781 \begin_inset space ~
33784 Definition\SpecialChar menuseparator
33785 Transform First Non-Optional to
33786 \begin_inset Newline newline
33790 \begin_inset Phantom HPhantom
33793 \begin_layout Plain Layout
33796 Edit\SpecialChar menuseparator
33797 Math\SpecialChar menuseparator
33799 \begin_inset space ~
33802 Definition\SpecialChar menuseparator
33814 <row interlinespace="2.5mm">
33815 <cell alignment="center" valignment="top" usebox="none">
33818 \begin_layout Plain Layout
33821 arg "math-macro-make-nonoptional"
33829 <cell alignment="center" valignment="top" usebox="none">
33832 \begin_layout Plain Layout
33835 Edit\SpecialChar menuseparator
33836 Math\SpecialChar menuseparator
33838 \begin_inset space ~
33841 Definition\SpecialChar menuseparator
33842 Transform Last Optional to
33843 \begin_inset Newline newline
33847 \begin_inset Phantom HPhantom
33850 \begin_layout Plain Layout
33853 Edit\SpecialChar menuseparator
33854 Math\SpecialChar menuseparator
33856 \begin_inset space ~
33859 Definition\SpecialChar menuseparator
33865 Non-Optional Argument
33871 <row interlinespace="2.5mm">
33872 <cell alignment="center" valignment="top" usebox="none">
33875 \begin_layout Plain Layout
33878 arg "math-macro-remove-optional-param"
33886 <cell alignment="center" valignment="top" usebox="none">
33889 \begin_layout Plain Layout
33892 Edit\SpecialChar menuseparator
33893 Math\SpecialChar menuseparator
33895 \begin_inset space ~
33898 Definition\SpecialChar menuseparator
33899 Remove Optional Argument
33905 <row interlinespace="2.5mm">
33906 <cell alignment="center" valignment="top" usebox="none">
33909 \begin_layout Plain Layout
33912 arg "math-macro-add-optional-param"
33920 <cell alignment="center" valignment="top" usebox="none">
33923 \begin_layout Plain Layout
33926 Edit\SpecialChar menuseparator
33927 Math\SpecialChar menuseparator
33929 \begin_inset space ~
33932 Definition\SpecialChar menuseparator
33933 Insert Optional Argument
33939 <row interlinespace="2.5mm">
33940 <cell alignment="center" valignment="top" usebox="none">
33943 \begin_layout Plain Layout
33946 arg "math-macro-remove-greedy-param"
33954 <cell alignment="center" valignment="top" usebox="none">
33957 \begin_layout Plain Layout
33960 Edit\SpecialChar menuseparator
33961 Math\SpecialChar menuseparator
33963 \begin_inset space ~
33966 Definition\SpecialChar menuseparator
33967 Remove Last Argument
33968 \begin_inset Newline newline
33972 \begin_inset Phantom HPhantom
33975 \begin_layout Plain Layout
33978 Edit\SpecialChar menuseparator
33979 Math\SpecialChar menuseparator
33981 \begin_inset space ~
33984 Definition\SpecialChar menuseparator
33990 Spitting Out To The Right
33996 <row interlinespace="2.5mm">
33997 <cell alignment="center" valignment="top" usebox="none">
34000 \begin_layout Plain Layout
34003 arg "math-macro-append-greedy-param"
34011 <cell alignment="center" valignment="top" usebox="none">
34014 \begin_layout Plain Layout
34017 Edit\SpecialChar menuseparator
34018 Math\SpecialChar menuseparator
34020 \begin_inset space ~
34023 Definition\SpecialChar menuseparator
34025 \begin_inset Newline newline
34029 \begin_inset Phantom HPhantom
34032 \begin_layout Plain Layout
34035 Edit\SpecialChar menuseparator
34036 Math\SpecialChar menuseparator
34038 \begin_inset space ~
34041 Definition\SpecialChar menuseparator
34047 Eating From The Right
34053 <row interlinespace="2.5mm">
34054 <cell alignment="center" valignment="top" usebox="none">
34057 \begin_layout Plain Layout
34060 arg "math-macro-add-greedy-optional-param"
34068 <cell alignment="center" valignment="top" usebox="none">
34071 \begin_layout Plain Layout
34074 Edit\SpecialChar menuseparator
34075 Math\SpecialChar menuseparator
34077 \begin_inset space ~
34080 Definition\SpecialChar menuseparator
34081 Append Optional Argument
34082 \begin_inset Newline newline
34086 \begin_inset Phantom HPhantom
34089 \begin_layout Plain Layout
34092 Edit\SpecialChar menuseparator
34093 Math\SpecialChar menuseparator
34095 \begin_inset space ~
34098 Definition\SpecialChar menuseparator
34104 Eating From The Right
34117 \begin_layout Section
34118 Computer Algebra Systems
34121 \begin_layout Standard
34123 offers the exchange between mathematical expressions written in \SpecialChar LyX
34125 editor and external applications or user defined scripts.
34126 Currently supported applications are
34143 Note that the set of supported mathematical constructs is limited only
34144 to very simple cases.
34147 \begin_layout Subsection
34151 \begin_layout Standard
34152 Write some expression in a formula, go to the
34154 Edit\SpecialChar menuseparator
34155 Math\SpecialChar menuseparator
34156 Use Computer Algebra System
34158 menu and choose the application you have installed on the computer.
34159 After that the result of computation should show on the right side of the
34160 expression together with the
34161 \begin_inset Quotes eld
34165 \begin_inset Quotes erd
34171 \begin_layout Standard
34172 Here are few simple examples (with results from
34176 ) to show what kind of computations can be performed:
34179 \begin_layout Itemize
34180 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34186 \begin_layout Itemize
34187 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34193 \begin_layout Itemize
34194 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34200 \begin_layout Itemize
34201 \begin_inset Formula $\det\left[\begin{array}{ccc}
34205 \end{array}\right]=-56$
34211 \begin_layout Itemize
34212 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34218 \begin_layout Subsection
34222 \begin_layout Standard
34223 Currently there is no keyboard shortcut for calling the algebra applications.
34224 One can easily bind a shortcut to the
34238 \begin_inset space \thinspace{}
34242 \begin_inset space \space{}
34249 key inside the math editor.
34254 one would use this shortcut definition command:
34257 \begin_layout Standard
34260 command-alternatives paragraph-break;math-extern maxima
34263 \begin_layout Section
34265 \begin_inset Index idx
34268 \begin_layout Plain Layout
34277 \begin_layout Subsection
34279 \begin_inset Index idx
34282 \begin_layout Plain Layout
34291 \begin_layout Standard
34292 Negative numbers often look ugly in formulas because the minus sign before
34293 the number is set with the same length as the minus operator sign.
34294 When writing the negative number in normal text, the minus sign appears
34298 \begin_layout Standard
34299 Thus, the problem disappears when converting the minus sign to mathematical
34303 \begin_layout Standard
34304 An example to visualize the problem:
34305 \begin_inset Separator parbreak
34311 \begin_layout Standard
34313 \begin_inset Tabular
34314 <lyxtabular version="3" rows="3" columns="2">
34315 <features booktabs="true" tabularvalignment="middle">
34316 <column alignment="right" valignment="top" width="0pt">
34317 <column alignment="left" valignment="top">
34319 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34322 \begin_layout Plain Layout
34328 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34331 \begin_layout Plain Layout
34339 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34342 \begin_layout Plain Layout
34348 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34351 \begin_layout Plain Layout
34352 \begin_inset Formula $x=-2$
34362 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34365 \begin_layout Plain Layout
34371 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34374 \begin_layout Plain Layout
34375 \begin_inset Formula $x=\textrm{-}2$
34391 \begin_layout Subsection
34392 Comma as decimal Separator
34393 \begin_inset Index idx
34396 \begin_layout Plain Layout
34405 \begin_layout Standard
34406 In \SpecialChar LaTeX
34407 a comma inside a formula is used, according to the English convention,
34408 as number group separator.
34409 So there will be space added behind all commas in formulas.
34412 \begin_layout Standard
34413 To avoid this, the comma is highlighted and changed to mathematical text
34423 \begin_layout Standard
34424 To use all formula commas in the document as decimal separator, the file
34433 \begin_layout Plain Layout
34438 is part of the \SpecialChar LaTeX
34444 \begin_inset Index idx
34447 \begin_layout Plain Layout
34452 \begin_layout Plain Layout
34472 \begin_inset Index idx
34475 \begin_layout Plain Layout
34481 is loaded with the \SpecialChar LaTeX
34485 \begin_layout Standard
34493 \begin_layout Subsection
34495 \begin_inset CommandInset label
34497 name "subsec:Physical-Vectors"
34502 \begin_inset Index idx
34505 \begin_layout Plain Layout
34514 \begin_layout Standard
34515 Predefined vectors are offered by the \SpecialChar LaTeX
34521 \begin_inset Index idx
34524 \begin_layout Plain Layout
34530 that is loaded with the \SpecialChar LaTeX
34534 \begin_layout Standard
34542 \begin_layout Standard
34546 \begin_layout Plain Layout
34556 \begin_inset Note Note
34559 \begin_layout Plain Layout
34560 The following table will only be displayed when the \SpecialChar LaTeX
34573 \begin_layout Standard
34574 The following commands are defined:
34575 \begin_inset Separator parbreak
34581 \begin_layout Standard
34583 \begin_inset Tabular
34584 <lyxtabular version="3" rows="4" columns="2">
34585 <features booktabs="true" tabularvalignment="middle">
34586 <column alignment="center" valignment="top" width="0pt">
34587 <column alignment="center" valignment="top">
34589 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34592 \begin_layout Plain Layout
34598 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34601 \begin_layout Plain Layout
34609 <cell alignment="center" valignment="top" usebox="none">
34612 \begin_layout Plain Layout
34622 <cell alignment="center" valignment="top" usebox="none">
34625 \begin_layout Plain Layout
34626 \begin_inset Formula $\Bra{\psi}$
34636 <cell alignment="center" valignment="top" usebox="none">
34639 \begin_layout Plain Layout
34649 <cell alignment="center" valignment="top" usebox="none">
34652 \begin_layout Plain Layout
34653 \begin_inset Formula $\Ket{\psi}$
34663 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34666 \begin_layout Plain Layout
34678 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34681 \begin_layout Plain Layout
34682 \begin_inset Formula $\Braket{\psi|\phi}$
34698 \begin_layout Standard
34705 assures that all vertical bars are set in the size of the surrounding brackets:
34706 \begin_inset Formula
34708 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34717 \begin_layout Plain Layout
34727 \begin_inset Note Note
34730 \begin_layout Plain Layout
34731 The following will be displayed when the \SpecialChar LaTeX
34744 \begin_layout Standard
34745 You need to install the \SpecialChar LaTeX
34750 to see the rest of this subsection in the output.
34753 \begin_layout Standard
34757 \begin_layout Plain Layout
34769 \begin_layout Standard
34776 can also be achieved using the command
34782 , that is described in
34783 \begin_inset CommandInset ref
34785 reference "subsec:Automatic-Bracket-Size"
34792 \begin_layout Subsection
34793 Self-defined Fractions
34794 \begin_inset CommandInset label
34796 name "subsec:Self-defined-Fractions"
34801 \begin_inset Index idx
34804 \begin_layout Plain Layout
34805 Fractions ! self-defined
34813 \begin_layout Standard
34814 To define custom commands for fractions, the command
34821 \begin_inset Index idx
34824 \begin_layout Plain Layout
34831 \begin_layout Plain Layout
34845 is used in the following scheme:
34848 \begin_layout Standard
34861 bracket}{fraction bar thickness}{style}
34862 \begin_inset Newline newline
34866 \begin_inset Phantom HPhantom
34869 \begin_layout Plain Layout
34879 {numerator}{denominator}
34882 \begin_layout Standard
34883 The style is a number in the range of 0
34884 \begin_inset space \thinspace{}
34888 \begin_inset space \thinspace{}
34892 \begin_inset Separator parbreak
34898 \begin_layout Standard
34900 \begin_inset Tabular
34901 <lyxtabular version="3" rows="5" columns="2">
34902 <features booktabs="true" tabularvalignment="middle">
34903 <column alignment="center" valignment="top" width="0pt">
34904 <column alignment="center" valignment="top">
34906 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34909 \begin_layout Plain Layout
34915 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34918 \begin_layout Plain Layout
34926 <cell alignment="center" valignment="top" usebox="none">
34929 \begin_layout Plain Layout
34935 <cell alignment="center" valignment="top" usebox="none">
34938 \begin_layout Plain Layout
34939 display style formula
34946 <cell alignment="center" valignment="top" usebox="none">
34949 \begin_layout Plain Layout
34955 <cell alignment="center" valignment="top" usebox="none">
34958 \begin_layout Plain Layout
34966 <cell alignment="center" valignment="top" usebox="none">
34969 \begin_layout Plain Layout
34975 <cell alignment="center" valignment="top" usebox="none">
34978 \begin_layout Plain Layout
34986 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34989 \begin_layout Plain Layout
34995 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34998 \begin_layout Plain Layout
35012 \begin_layout Standard
35013 When no style is given, the size is adjusted to the surrounding environment
35014 like for the command
35023 \begin_layout Standard
35024 When no fraction bar thickness is given, the predefined value of 0.4
35025 \begin_inset space \thinspace{}
35031 \begin_layout Standard
35032 \begin_inset VSpace medskip
35035 For example, the commands
35048 \begin_inset CommandInset ref
35050 reference "subsec:Fractions"
35054 are defined with the commands
35057 \begin_layout Standard
35066 genfrac{}{}{}{0}{#1}{#2}}
35069 \begin_layout Standard
35073 \begin_layout Standard
35082 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35085 \begin_layout Standard
35086 \begin_inset VSpace medskip
35089 To define a fraction where the fraction bar thickness can be given as optional
35090 argument, the following line is inserted to the \SpecialChar LaTeX
35094 \begin_layout Standard
35103 genfrac{}{}{#1}{}{#2}{#3}}
35106 \begin_layout Standard
35108 \begin_inset Formula
35110 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35111 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35116 As one can see, the distance of the numerator and the denominator to the
35117 fraction bar is round about three times the bar thickness.
35120 \begin_layout Subsection
35122 \begin_inset Index idx
35125 \begin_layout Plain Layout
35134 \begin_layout Standard
35135 There are four ways to cancel formulas or parts of formulas:
35138 \begin_layout Standard
35142 \begin_layout Plain Layout
35152 \begin_inset Note Note
35155 \begin_layout Plain Layout
35156 The following table will only be displayed when the \SpecialChar LaTeX
35167 \begin_inset Separator parbreak
35173 \begin_layout Standard
35175 \begin_inset Tabular
35176 <lyxtabular version="3" rows="5" columns="2">
35177 <features booktabs="true" tabularvalignment="middle">
35178 <column alignment="center" valignment="top" width="0pt">
35179 <column alignment="center" valignment="top">
35181 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35184 \begin_layout Plain Layout
35190 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35193 \begin_layout Plain Layout
35201 <cell alignment="center" valignment="top" usebox="none">
35204 \begin_layout Plain Layout
35208 \begin_inset space \textvisiblespace{}
35214 \begin_inset space \textvisiblespace{}
35222 <cell alignment="center" valignment="top" usebox="none">
35225 \begin_layout Plain Layout
35226 \begin_inset Formula $\cancel{\int A=B}$
35235 <row topspace="1.5mm">
35236 <cell alignment="center" valignment="top" usebox="none">
35239 \begin_layout Plain Layout
35243 \begin_inset space \textvisiblespace{}
35249 \begin_inset space \textvisiblespace{}
35257 <cell alignment="center" valignment="top" usebox="none">
35260 \begin_layout Plain Layout
35261 \begin_inset Formula $\bcancel{\int A=B}$
35270 <row topspace="1.5mm">
35271 <cell alignment="center" valignment="top" usebox="none">
35274 \begin_layout Plain Layout
35278 \begin_inset space \textvisiblespace{}
35284 \begin_inset space \textvisiblespace{}
35292 <cell alignment="center" valignment="top" usebox="none">
35295 \begin_layout Plain Layout
35296 \begin_inset Formula $\xcancel{\int A=B}$
35306 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35309 \begin_layout Plain Layout
35313 \begin_inset space \textvisiblespace{}
35319 \begin_inset space \textvisiblespace{}
35323 \begin_inset Formula $\to$
35331 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35334 \begin_layout Plain Layout
35335 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35351 \begin_layout Standard
35358 is especially suitable to visualize the reduction of fractions within formulas:
35359 \begin_inset Formula
35361 \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}}}
35369 \begin_layout Standard
35370 To change the size of
35377 \begin_inset Quotes eld
35381 \begin_inset Quotes erd
35384 value one can add the \SpecialChar LaTeX
35388 \begin_layout Standard
35393 PassOptionsToPackage{option}{cancel}
35396 \begin_layout Standard
35405 which leads to the same size as for the canceled value, or
35409 which makes is it a bit smaller than normal.
35412 \begin_layout Standard
35413 To color the cancellation bar one adds this command as \SpecialChar TeX
35417 \begin_layout Standard
35429 \begin_layout Standard
35434 can be replaced by a color of your choice.
35437 \begin_layout Standard
35441 \begin_layout Plain Layout
35457 \begin_layout Standard
35458 \begin_inset Formula
35460 \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}}}
35468 \begin_layout Standard
35472 \begin_layout Plain Layout
35486 \begin_inset Note Note
35489 \begin_layout Plain Layout
35498 \begin_layout Standard
35499 For further customizations, see the documentation of the package
35504 \begin_inset CommandInset citation
35511 \begin_inset Index idx
35514 \begin_layout Plain Layout
35523 \begin_layout Standard
35527 \begin_layout Plain Layout
35537 \begin_inset Note Note
35540 \begin_layout Plain Layout
35541 The following will be displayed when the \SpecialChar LaTeX
35554 \begin_layout Standard
35555 You need to install the \SpecialChar LaTeX
35560 to see the rest of this subsection in the output.
35563 \begin_layout Standard
35567 \begin_layout Plain Layout
35579 \begin_layout Subsection
35580 Formulas in Section Headings
35581 \begin_inset CommandInset label
35583 name "subsec:Formulas-in-Section"
35588 \begin_inset Index idx
35591 \begin_layout Plain Layout
35592 Formula ! in section headings
35600 \begin_layout Standard
35601 When formulas are used in section headings, the following has to be taken
35605 \begin_layout Standard
35606 \begin_inset Note Greyedout
35609 \begin_layout Plain Layout
35615 \begin_inset Index idx
35618 \begin_layout Plain Layout
35619 Packages ! hyperref
35624 support is enabled in the document settings dialog under
35627 \begin_inset space ~
35632 , PDF-bookmarks are created for every section heading in the table of contents.
35633 If a section heading contains formulas, they are incorrectly displayed
35634 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35643 \begin_layout Standard
35644 Both problems can be solved by inserting at the end of the section heading
35645 a short title with the menu
35647 Insert\SpecialChar menuseparator
35649 \begin_inset space ~
35655 Short titles are used as alternative for multiline section headings to
35656 keep the table of contents clearly arranged.
35657 Only the short title appears in the table of contents and therefore also
35658 in the PDF-bookmark.
35661 \begin_layout Standard
35662 When formulas should be used in the table of contents but
35666 is used, one can use the following command in \SpecialChar TeX
35670 \begin_layout Standard
35675 texorpdfstring{part}{alternative}
35676 \begin_inset Index idx
35679 \begin_layout Plain Layout
35690 \begin_layout Standard
35691 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35692 This can be characters, formulas, footnotes, but also cross-references.
35693 The alternative is used instead of the part for the bookmark.
35696 \begin_layout Standard
35697 Here are two example headings:
35698 \begin_inset VSpace -3mm
35705 \begin_layout Plain Layout
35717 \begin_layout Subsubsection
35718 Heading without formula in table of contents
35719 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35723 \begin_inset Argument 1
35726 \begin_layout Plain Layout
35727 Heading without formula in table of contents
35735 \begin_layout Subsubsection
35736 Heading with formula in table of contents
35740 \begin_layout Plain Layout
35750 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35757 \begin_layout Plain Layout
35767 \begin_layout Standard
35771 \begin_layout Plain Layout
35780 In the first heading a short title was used, in the second one
35789 \begin_layout Standard
35790 To get the same formatting as for the other headings, the complete heading
35799 \begin_layout Plain Layout
35801 \begin_inset CommandInset ref
35803 reference "subsec:Bold-Formulas"
35815 \begin_layout Subsection
35816 Formulas in multi-column Text
35817 \begin_inset Index idx
35820 \begin_layout Plain Layout
35821 Formula ! in multi-column text
35829 \begin_layout Standard
35830 Formulas in multi-column text are often too wide to fit into a column and
35831 thus need to be set over the whole page width.
35832 This is done by using the \SpecialChar LaTeX
35841 \begin_layout Plain Layout
35846 is part of every \SpecialChar LaTeX
35847 standard installation.
35853 \begin_inset Index idx
35856 \begin_layout Plain Layout
35857 Packages ! multicol
35862 , that is loaded with the \SpecialChar LaTeX
35866 \begin_layout Standard
35871 usepackage{multicol}
35874 \begin_layout Standard
35875 \begin_inset Note Greyedout
35878 \begin_layout Plain Layout
35879 Note that in this case the setting
35882 \begin_inset space ~
35889 Document\SpecialChar menuseparator
35895 \begin_inset space ~
35915 \begin_layout Standard
35916 Before the multi-column text the command
35919 \begin_layout Standard
35924 begin{multicols}{column number}
35927 \begin_layout Standard
35928 is written in \SpecialChar TeX
35930 The column number is a number in the range of 2
35931 \begin_inset space \thinspace{}
35935 \begin_inset space \thinspace{}
35939 Before the formula the multi-column text is ended by inserting the command
35942 \begin_layout Standard
35950 \begin_layout Standard
35951 in \SpecialChar TeX
35955 \begin_layout Standard
35956 Due to the command some space is automatically added before the formula.
35958 \begin_inset space \thinspace{}
35961 mm vertical space is inserted before the formula.
35962 When the formula style
35968 \begin_layout Plain Layout
35970 \begin_inset CommandInset ref
35972 reference "sec:Formula-Styles"
35984 \begin_inset space \thinspace{}
35987 mm space is inserted instead.
35990 \begin_layout Standard
35991 As example a multi-column text with a displayed formula:
35994 \begin_layout Standard
36000 \begin_layout Plain Layout
36004 begin{multicols}{2}
36009 Das Spektrum wird fouriertransformiert.
36010 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36011 , Lösungsmittel) zu trennen.
36012 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36013 nun das Aussehen des Ausgangssignals.
36014 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36015 über alle Phasen integrieren muss.
36017 \begin_inset Formula $S$
36020 unser normiertes Ausgangssignal und
36021 \begin_inset Formula $P$
36024 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36028 \begin_layout Plain Layout
36038 \begin_inset VSpace -6mm
36042 \begin_inset Formula
36044 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36053 \begin_layout Plain Layout
36057 begin{multicols}{2}
36063 \begin_inset Formula $S_{0}$
36066 das Signal ohne Gradient ist und die Normierungsbedingung
36067 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36071 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36073 \begin_inset Formula $\nicefrac{\pi}{2}$
36077 \begin_inset space \thinspace{}
36080 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36081 das Signal zusätzlich abschwächt.
36082 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36084 \begin_inset Formula $T_{2}$
36090 \begin_layout Standard
36096 \begin_layout Plain Layout
36108 \begin_layout Subsection
36109 Formulas with Description of Variables
36110 \begin_inset Index idx
36113 \begin_layout Plain Layout
36114 Formula ! with description of variables
36122 \begin_layout Standard
36123 To describe variables within a formula, like in formula
36124 \begin_inset CommandInset ref
36126 reference "eq:within"
36135 \begin_inset Formula $n$
36139 \begin_inset space ~
36142 matrix is used with left aligned columns for the
36143 \begin_inset Formula $n$
36150 \begin_layout Plain Layout
36152 \begin_inset CommandInset ref
36154 reference "sec:Matrices"
36163 To set the description in a smaller size, before the matrix e.
36164 \begin_inset space \thinspace{}
36168 \begin_inset space \space{}
36181 \begin_layout Plain Layout
36183 \begin_inset CommandInset ref
36185 reference "subsec:Font-Sizes"
36197 \begin_layout Standard
36198 When the formula style
36204 \begin_layout Plain Layout
36206 \begin_inset CommandInset ref
36208 reference "sec:Formula-Styles"
36229 \begin_layout Plain Layout
36236 only works in formulas with the style
36241 \begin_inset CommandInset ref
36243 reference "subsec:Variable-Space"
36252 is inserted before and after the matrix to have the same separation of
36253 the matrix from the equation and the side margin.
36256 \begin_layout Standard
36257 When the formula style
36261 is used, the method described in
36262 \begin_inset CommandInset ref
36264 reference "subsec:Flalign-Environment"
36268 is used to indent formulas.
36270 \begin_inset CommandInset ref
36272 reference "eq:within"
36276 consists of five columns where in the first two columns contain the equation,
36277 the third the matrix and the last one an empty \SpecialChar TeX
36279 \begin_inset Formula
36281 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36282 \rho & \textrm{density}\\
36283 V & \textrm{volume}\\
36284 g & \textrm{gravitational acceleration}
36285 \end{array} & & {}\label{eq:within}
36293 \begin_layout Subsection
36294 Upright small Greek Letters
36295 \begin_inset CommandInset label
36297 name "subsec:Upright-small-Greek"
36302 \begin_inset Index idx
36305 \begin_layout Plain Layout
36306 Greek letters ! upright
36314 \begin_layout Standard
36315 Most of the math fonts only provide italic small Greek letters.
36316 But for symbols of elementary particles like pions and neutrinos, upright
36317 Greek letters are needed.
36326 \begin_layout Plain Layout
36331 is part of the \SpecialChar LaTeX
36337 \begin_inset Index idx
36340 \begin_layout Plain Layout
36345 \begin_layout Plain Layout
36365 \begin_inset Index idx
36368 \begin_layout Plain Layout
36374 that is loaded with the \SpecialChar LaTeX
36378 \begin_layout Standard
36383 usepackage{upgreek}
36386 \begin_layout Standard
36392 \begin_layout Plain Layout
36402 \begin_inset Note Note
36405 \begin_layout Plain Layout
36406 The following table will only be displayed when the \SpecialChar LaTeX
36416 They are created when the command for a small Greek letter is started with
36422 For example the command
36429 \begin_inset Formula $\uptau$
36435 \begin_layout Standard
36436 With these commands reactions of elementary particles can be typeset:
36437 \begin_inset Formula
36439 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36447 \begin_layout Standard
36448 The upright letters are more bold and wider than the italic ones.
36449 They should therefore not be used for units like
36450 \begin_inset Quotes eld
36454 \begin_inset Quotes erd
36460 \begin_layout Standard
36464 \begin_layout Plain Layout
36474 \begin_inset Note Note
36477 \begin_layout Plain Layout
36478 The following will be displayed when the \SpecialChar LaTeX
36491 \begin_layout Standard
36492 You need to install the \SpecialChar LaTeX
36497 to see the rest of this subsection in the output.
36500 \begin_layout Standard
36504 \begin_layout Plain Layout
36516 \begin_layout Subsection
36517 Text Characters in Formulas
36518 \begin_inset Index idx
36521 \begin_layout Plain Layout
36530 \begin_layout Standard
36531 In some cases you might want to insert text characters directly into formulas.
36532 When for example the centered dot · is often used in formulas like
36533 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36536 , one would have to insert the command
36546 \begin_layout Plain Layout
36548 \begin_inset CommandInset ref
36550 reference "subsec:Binary-Operators"
36559 all the time, because this character is defined in all encodings as text
36561 But the encoding can be changed by this \SpecialChar LaTeX
36565 \begin_layout Standard
36570 Declare Inputtext{183}{
36580 f\SpecialChar ligaturebreak
36584 \begin_layout Standard
36585 The character encoding (menu
36587 Document\SpecialChar menuseparator
36588 Settings\SpecialChar menuseparator
36591 ) specifies what character appears when a keyboard key is pressed.
36592 When the key for the character '·' is pressed, internally the command
36599 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36601 With the changed encoding the right command is chosen automatically, depending
36602 on if the character was inserted into a formula or not.
36605 \begin_layout Standard
36606 The encoding of several characters is saved in definition files.
36607 For example the encoding
36611 is defined in the file
36615 which is in the installation folder of \SpecialChar LaTeX
36617 Encodings should only be changed via the \SpecialChar LaTeX
36618 -preamble and not in the definition
36620 Otherwise documents could not be edited by other \SpecialChar LyX
36621 users working on other
36625 \begin_layout Standard
36626 \begin_inset VSpace medskip
36629 Besides the centered dot, in this document the degree sign ° is defined
36630 with the following \SpecialChar LaTeX
36631 -preamble line so that it can be directly inserted into
36635 \begin_layout Standard
36640 DeclareInputtext{176}{
36650 f\SpecialChar ligaturebreak
36654 \begin_layout Subsection
36656 -comments in formulas
36657 \begin_inset Index idx
36660 \begin_layout Plain Layout
36670 \begin_layout Standard
36671 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36673 code of your file with the menu
36675 Insert\SpecialChar menuseparator
36676 Note\SpecialChar menuseparator
36680 This is not possible in a formula but you can insert \SpecialChar LaTeX
36685 \begin_layout Standard
36693 \begin_layout Standard
36694 This creates a box in which you can write your comment.
36695 Due to a bug in \SpecialChar LyX
36700 \begin_layout Plain Layout
36701 \begin_inset CommandInset href
36703 name "LyX-bug #9002"
36704 target "http://www.lyx.org/trac/ticket/9002"
36713 you cannot write normal text inside the comment, even when you use mathematical
36714 text, you will see its \SpecialChar LaTeX
36715 -commands in the \SpecialChar LaTeX
36717 \begin_inset Newline newline
36720 This a formula with a \SpecialChar LaTeX
36722 \begin_inset Formula
36724 A=B%\text{This is the comment}
36732 \begin_layout Standard
36733 \begin_inset Newpage newpage
36739 \begin_layout Section
36742 \begin_inset Index idx
36745 \begin_layout Plain Layout
36754 \begin_layout Standard
36755 This section is a summary of the most important typographic rules, listed
36760 \begin_layout Plain Layout
36761 This collection was partly taken from the German semi-official dictionary
36763 \begin_inset Quotes eld
36767 \begin_inset Quotes erd
36771 \begin_inset CommandInset citation
36777 that lists some of the ISO rules.
36778 More rules are listed in
36779 \begin_inset CommandInset citation
36793 \begin_layout Itemize
36802 \begin_layout Plain Layout
36803 done with font styles, see
36804 \begin_inset CommandInset ref
36806 reference "subsec:Font-Styles"
36815 , no matter if they appear in italic text: 30
36816 \begin_inset space \thinspace{}
36820 \begin_inset Newline newline
36823 Between the value and the unit is the smallest space, see
36824 \begin_inset CommandInset ref
36826 reference "subsec:Predefined-Space"
36831 \begin_inset Newline newline
36834 This convention is automatically fulfilled when the command
36841 When it is entered to a formula, two boxes appear.
36842 In the first one the value is inserted, in the second one the unit, and
36844 \begin_inset Formula $\unit[30]{km/h}$
36848 \begin_inset space \thinspace{}
36858 is not a real \SpecialChar LaTeX
36859 command but the command
36865 , therefore you cannot use it in \SpecialChar TeX
36869 \begin_layout Itemize
36870 Percent and perthousand signs are set like physical units:
36871 \begin_inset Newline newline
36875 \begin_inset space \thinspace{}
36881 \begin_layout Itemize
36882 The degree sign follows directly on the value: 15°, but not when it is used
36884 \begin_inset space \thinspace{}
36890 \begin_layout Itemize
36891 In numbers with more than four digits the smallest space is inserted before
36892 every third digit to group them:
36902 \begin_inset space \thinspace{}
36906 \begin_inset space \thinspace{}
36912 \begin_layout Itemize
36913 For dimensions like 120×90×40
36914 \begin_inset space \thinspace{}
36917 cm the multiplication sign
36918 \begin_inset Quotes eld
36922 \begin_inset Quotes erd
36926 It is available either via the command
36934 Insert\SpecialChar menuseparator
36935 Special Character\SpecialChar menuseparator
36941 \begin_layout Itemize
36942 Functions with names consisting of several letters are set upright to avoid
36944 \begin_inset CommandInset ref
36946 reference "subsec:Predefined-Functions"
36953 \begin_layout Itemize
36954 Indices consisting of several letters, are set upright:
36955 \begin_inset Formula $E_{\mathrm{kin}}$
36959 \begin_inset Newline newline
36962 Components of matrices are set italic:
36963 \begin_inset Formula $\hat{H}_{kl}$
36969 \begin_layout Itemize
36970 The differentiation/integration operator 'd', the Euler's number 'e' and
36971 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36975 \begin_layout Itemize
36976 The character that denotes a
36980 transformation is inserted either by the command
36985 \begin_inset space \textvisiblespace{}
36992 Insert\SpecialChar menuseparator
36993 Special Character\SpecialChar menuseparator
36994 Symbols\SpecialChar menuseparator
36996 \begin_inset space ~
37002 \begin_inset Formula $\mathscr{F}$
37008 \begin_layout Standard
37009 \begin_inset Newpage newpage
37015 \begin_layout Section
37017 \begin_inset Index idx
37020 \begin_layout Plain Layout
37029 \begin_layout Standard
37030 Some characters and symbols can be created with several commands.
37031 Here is a list of the synonym commands:
37034 \begin_layout Standard
37035 \begin_inset VSpace bigskip
37039 \begin_inset space \hfill{}
37043 \begin_inset Tabular
37044 <lyxtabular version="3" rows="12" columns="2">
37045 <features booktabs="true" tabularvalignment="middle">
37046 <column alignment="center" valignment="top" width="0pt">
37047 <column alignment="center" valignment="top" width="0pt">
37049 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37052 \begin_layout Plain Layout
37058 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37061 \begin_layout Plain Layout
37069 <cell alignment="center" valignment="top" usebox="none">
37072 \begin_layout Plain Layout
37080 <cell alignment="center" valignment="top" usebox="none">
37083 \begin_layout Plain Layout
37091 <cell alignment="center" valignment="top" usebox="none">
37094 \begin_layout Plain Layout
37102 <cell alignment="center" valignment="top" usebox="none">
37105 \begin_layout Plain Layout
37115 <cell alignment="center" valignment="top" usebox="none">
37118 \begin_layout Plain Layout
37126 <cell alignment="center" valignment="top" usebox="none">
37129 \begin_layout Plain Layout
37139 <cell alignment="center" valignment="top" usebox="none">
37142 \begin_layout Plain Layout
37150 <cell alignment="center" valignment="top" usebox="none">
37153 \begin_layout Plain Layout
37161 <cell alignment="center" valignment="top" usebox="none">
37164 \begin_layout Plain Layout
37172 <cell alignment="center" valignment="top" usebox="none">
37175 \begin_layout Plain Layout
37183 <cell alignment="center" valignment="top" usebox="none">
37186 \begin_layout Plain Layout
37194 <cell alignment="center" valignment="top" usebox="none">
37197 \begin_layout Plain Layout
37207 <cell alignment="center" valignment="top" usebox="none">
37210 \begin_layout Plain Layout
37218 <cell alignment="center" valignment="top" usebox="none">
37221 \begin_layout Plain Layout
37231 <cell alignment="center" valignment="top" usebox="none">
37234 \begin_layout Plain Layout
37242 <cell alignment="center" valignment="top" usebox="none">
37245 \begin_layout Plain Layout
37255 <cell alignment="center" valignment="top" usebox="none">
37258 \begin_layout Plain Layout
37266 <cell alignment="center" valignment="top" usebox="none">
37269 \begin_layout Plain Layout
37279 <cell alignment="center" valignment="top" usebox="none">
37282 \begin_layout Plain Layout
37290 <cell alignment="center" valignment="top" usebox="none">
37293 \begin_layout Plain Layout
37301 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37304 \begin_layout Plain Layout
37312 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37315 \begin_layout Plain Layout
37327 \begin_inset space \hfill{}
37331 \begin_inset Tabular
37332 <lyxtabular version="3" rows="12" columns="2">
37333 <features booktabs="true" tabularvalignment="middle">
37334 <column alignment="center" valignment="top" width="0pt">
37335 <column alignment="center" valignment="top" width="0pt">
37337 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37340 \begin_layout Plain Layout
37346 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37349 \begin_layout Plain Layout
37357 <cell alignment="center" valignment="top" usebox="none">
37360 \begin_layout Plain Layout
37368 <cell alignment="center" valignment="top" usebox="none">
37371 \begin_layout Plain Layout
37383 <cell alignment="center" valignment="top" usebox="none">
37386 \begin_layout Plain Layout
37394 <cell alignment="center" valignment="top" usebox="none">
37397 \begin_layout Plain Layout
37407 <cell alignment="center" valignment="top" usebox="none">
37410 \begin_layout Plain Layout
37418 <cell alignment="center" valignment="top" usebox="none">
37421 \begin_layout Plain Layout
37431 <cell alignment="center" valignment="top" usebox="none">
37434 \begin_layout Plain Layout
37442 <cell alignment="center" valignment="top" usebox="none">
37445 \begin_layout Plain Layout
37453 <cell alignment="center" valignment="top" usebox="none">
37456 \begin_layout Plain Layout
37464 <cell alignment="center" valignment="top" usebox="none">
37467 \begin_layout Plain Layout
37475 <cell alignment="center" valignment="top" usebox="none">
37478 \begin_layout Plain Layout
37486 <cell alignment="center" valignment="top" usebox="none">
37489 \begin_layout Plain Layout
37499 <cell alignment="center" valignment="top" usebox="none">
37502 \begin_layout Plain Layout
37510 <cell alignment="center" valignment="top" usebox="none">
37513 \begin_layout Plain Layout
37523 <cell alignment="center" valignment="top" usebox="none">
37526 \begin_layout Plain Layout
37534 <cell alignment="center" valignment="top" usebox="none">
37537 \begin_layout Plain Layout
37547 <cell alignment="center" valignment="top" usebox="none">
37550 \begin_layout Plain Layout
37558 <cell alignment="center" valignment="top" usebox="none">
37561 \begin_layout Plain Layout
37571 <cell alignment="center" valignment="top" usebox="none">
37574 \begin_layout Plain Layout
37582 <cell alignment="center" valignment="top" usebox="none">
37585 \begin_layout Plain Layout
37595 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37598 \begin_layout Plain Layout
37606 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37609 \begin_layout Plain Layout
37623 \begin_inset space \hfill{}
37629 \begin_layout Standard
37630 \begin_inset Newpage newpage
37636 \begin_layout Bibliography
37637 \begin_inset CommandInset bibitem
37638 LatexCommand bibitem
37650 The \SpecialChar LaTeX
37654 Addison Wesley, 2004
37657 \begin_layout Bibliography
37658 \begin_inset CommandInset bibitem
37659 LatexCommand bibitem
37665 \begin_inset CommandInset href
37668 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37672 of \SpecialChar LaTeX
37676 \begin_layout Bibliography
37677 \begin_inset CommandInset bibitem
37678 LatexCommand bibitem
37684 \begin_inset CommandInset href
37687 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37695 \begin_layout Plain Layout
37704 -\SpecialChar LaTeX
37708 \begin_layout Bibliography
37709 \begin_inset CommandInset bibitem
37710 LatexCommand bibitem
37716 \begin_inset CommandInset href
37719 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37723 of all symbols available with \SpecialChar LaTeX
37727 \begin_layout Bibliography
37728 \begin_inset CommandInset bibitem
37729 LatexCommand bibitem
37735 \begin_inset CommandInset href
37737 name "Documentation"
37738 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37742 of the \SpecialChar LaTeX
37748 \begin_inset Index idx
37751 \begin_layout Plain Layout
37760 \begin_layout Bibliography
37761 \begin_inset CommandInset bibitem
37762 LatexCommand bibitem
37768 \begin_inset CommandInset href
37770 name "Documentation"
37771 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37775 of the \SpecialChar LaTeX
37781 \begin_inset Index idx
37784 \begin_layout Plain Layout
37785 Packages ! hyperref
37793 \begin_layout Bibliography
37794 \begin_inset CommandInset bibitem
37795 LatexCommand bibitem
37801 \begin_inset CommandInset href
37803 name "Documentation"
37804 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37808 of the \SpecialChar LaTeX
37814 \begin_inset Index idx
37817 \begin_layout Plain Layout
37826 \begin_layout Bibliography
37827 \begin_inset CommandInset bibitem
37828 LatexCommand bibitem
37839 Auflage, Duden 2001
37842 \begin_layout Bibliography
37843 \begin_inset CommandInset bibitem
37844 LatexCommand bibitem
37850 \begin_inset CommandInset href
37853 target "http://physics.nist.gov/Document/checklist.pdf"
37857 for reviewing manuscripts
37860 \begin_layout Standard
37861 \begin_inset CommandInset index_print
37862 LatexCommand printindex