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 default
154 \bibtex_command default
155 \index_command default
159 \pdf_title "LyX's Math Manual"
160 \pdf_author "LyX Team, Uwe Stöhr"
161 \pdf_subject "LyX-documentation about math"
162 \pdf_keywords "LyX, Mathed"
164 \pdf_bookmarksnumbered true
165 \pdf_bookmarksopen true
166 \pdf_bookmarksopenlevel 1
167 \pdf_breaklinks false
171 \pdf_pdfusetitle false
172 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
175 \use_package amsmath 2
176 \use_package amssymb 2
177 \use_package cancel 0
179 \use_package mathdots 1
180 \use_package mathtools 2
181 \use_package mhchem 1
182 \use_package stackrel 0
183 \use_package stmaryrd 0
184 \use_package undertilde 0
186 \cite_engine_type default
190 \paperorientation portrait
194 \notefontcolor #0000ff
201 \paragraph_separation skip
203 \quotes_language english
206 \paperpagestyle plain
210 \tracking_changes false
211 \output_changes false
214 \html_be_strict false
221 's detailed Math manual
225 by the \SpecialChar LyX
230 \begin_layout Plain Layout
232 If you have comments or error corrections, please send them to the \SpecialChar LyX
237 \begin_inset CommandInset href
239 name "lyx-docs@lists.lyx.org"
240 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
251 \begin_inset Note Note
254 \begin_layout Plain Layout
261 \begin_inset Newline newline
265 \begin_inset Newline newline
273 \begin_layout Standard
274 \begin_inset CommandInset toc
275 LatexCommand tableofcontents
282 \begin_layout Standard
283 \begin_inset Note Note
286 \begin_layout Plain Layout
287 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
290 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
297 If they are not installed the document can be exported anyway but the sections
298 where the packages are required will not appear in the output.
303 ; if it is not installed, this file cannot be exported.
306 \begin_layout Plain Layout
307 The latest PDF-version of this document can be found here:
308 \begin_inset Newline newline
313 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
321 \begin_layout Standard
322 \begin_inset Newpage newpage
328 \begin_layout Section
332 \begin_layout Standard
333 This document explains \SpecialChar LyX
334 's math features and is furthermore a collection
335 of \SpecialChar LaTeX
336 -commands used for mathematical characters and constructs.
337 The explanations are designed for the usage of commands.
338 It is therefore required that you have read the section
349 \begin_layout Standard
350 Most of the characters and many constructs explained in this manual are
351 also accessible via the menu
355 \SpecialChar menuseparator
371 But everybody who has to write lots of formulas will notice that it is
372 much faster to use commands instead of the math toolbar.
373 Therefore this manual is focused on commands but also mentions the correspondin
374 g toolbar buttons when available.
377 \begin_layout Standard
378 If not specially mentioned the commands are only available within formulas.
379 To be able to use all commands explained in this document, the option
383 must be checked in the document settings (menu
385 Document\SpecialChar menuseparator
386 Settings\SpecialChar menuseparator
397 \begin_layout Plain Layout
400 Use AMS math package automatically
406 \begin_layout Plain Layout
415 -math when math constructs are found that are supported by \SpecialChar LyX
424 \begin_layout Standard
425 This document doesn't list all
429 \begin_layout Plain Layout
442 \begin_layout Plain Layout
447 \begin_layout Plain Layout
456 -math commands is in the file
459 \begin_inset CommandInset href
462 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
468 , which is part of every \SpecialChar LaTeX
469 standard installation.
474 for lucidity reasons.
477 \begin_layout Section
481 \begin_layout Standard
482 To create an inline formula
483 \begin_inset Index idx
486 \begin_layout Plain Layout
492 that is embedded into a text line, use one of the shortcuts
498 or the toolbar button
505 \begin_inset Newline newline
508 To create a display style formula
509 \begin_inset Index idx
512 \begin_layout Plain Layout
513 Formula ! display style
518 which will appear bigger, has a different format, and will be in a separate
519 paragraph, use one of these shortcuts:
528 \begin_layout Standard
529 To change a display style formula to an inline formula, set the cursor into
530 the formula and use one of the shortcuts
538 Edit\SpecialChar menuseparator
539 Math\SpecialChar menuseparator
543 The same way is used to change an inline formula to a display style formula.
546 \begin_layout Standard
547 To display parts of an inline formula in the size of a display style formula,
555 \begin_inset Index idx
558 \begin_layout Plain Layout
567 Then a new blue box appears in which the desired formula part is inserted.
570 \begin_layout Standard
571 Only inline formulas are allowed inside tables.
574 \begin_layout Standard
579 can be turned on in the menu
581 View\SpecialChar menuseparator
585 When you click there on
586 \begin_inset Quotes eld
590 \begin_inset Quotes erd
593 the toolbar will be shown permanently at the bottom; this state is visualized
598 menu with a checkmark.
599 When you click in this state again on
600 \begin_inset Quotes eld
604 \begin_inset Quotes erd
615 is only shown when the cursor is within a formula; this state is visualized
616 by the renaming of the menu entry from
617 \begin_inset Quotes eld
621 \begin_inset Quotes erd
625 \begin_inset Quotes eld
633 \begin_inset Quotes erd
639 \begin_layout Standard
642 \begin_inset Index idx
645 \begin_layout Plain Layout
652 is invoked by pressing the toolbar button
660 Insert\SpecialChar menuseparator
672 \begin_layout Standard
673 To change the \SpecialChar LaTeX
675 \begin_inset Index idx
678 \begin_layout Plain Layout
687 Document\SpecialChar menuseparator
688 Settings\SpecialChar menuseparator
698 \begin_layout Standard
699 To edit matrices, case differentiations and multiline formulas subsequently,
702 Edit\SpecialChar menuseparator
707 Edit\SpecialChar menuseparator
709 \begin_inset space \thinspace{}
713 \begin_inset space \thinspace{}
723 When lines and columns are swapped via the menu, the column or line where
724 the cursor is in is exchanged with the column to the right or the line
726 Is the cursor in the last column or row, the exchange is done with the
727 column to the left or the line above.
730 \begin_layout Standard
731 To write text in formulas
735 \begin_layout Plain Layout
736 For multiline formulas the command
743 \begin_inset CommandInset ref
745 reference "subsec:Text-in-multiline"
759 \begin_inset Index idx
762 \begin_layout Plain Layout
769 \begin_inset Index idx
772 \begin_layout Plain Layout
779 This mode is invoked with the shortcut
785 or by the insertion of the command
792 \begin_inset Index idx
795 \begin_layout Plain Layout
804 The text appears black in \SpecialChar LyX
805 and can therefore be distinguished from the
806 other formula parts which appear blue.
807 In the output mathematical text is set upright, in contrary to other formula
811 \begin_layout Subsection*
815 \begin_layout Standard
816 Most of the \SpecialChar LaTeX
817 -commands for math constructs have the following scheme:
820 \begin_layout Standard
836 \begin_layout Standard
837 A command always starts with a backslash
838 \begin_inset Quotes gld
848 \begin_inset Quotes grd
852 To omit optional arguments, also omit the associated brackets.
853 The braces around the required arguments are named in this document as
856 \begin_inset Index idx
859 \begin_layout Plain Layout
867 If you add in a formula a left brace to a command name, \SpecialChar LyX
869 creates a \SpecialChar TeX
871 In all other cases \SpecialChar TeX
872 braces are created in formulas with the command
880 braces appear red in \SpecialChar LyX
881 , in contrary to normal braces which appear blue.
883 mode no command is needed to get \SpecialChar TeX
886 braces don't appear in the output.
889 \begin_layout Standard
890 When commands without arguments, like commands for symbols are entered in
892 mode, a space character must
896 be behind the command to end it.
897 This space doesn't appear in the output.
898 When the space should appear in the output, the space must be followed
899 by a protected space in normal text.
902 \begin_layout Standard
903 A protected space is inserted with
906 arg "command-alternatives space-insert protected ; math-space"
912 \begin_layout Subsection*
913 \begin_inset Newpage newpage
919 \begin_layout Itemize
921 \begin_inset space \textvisiblespace{}
924 denotes a space character to be input.
927 \begin_layout Itemize
929 \begin_inset Formula $\to$
932 denotes the usage of the corresponding arrow key on the keyboard.
937 key can often be used instead of
938 \begin_inset Formula $\to$
942 \begin_inset Formula $\downarrow$
950 \begin_inset Formula $\leftarrow$
954 \begin_inset Formula $\uparrow$
960 \begin_layout Subsection*
964 \begin_layout Standard
966 \begin_inset Float table
972 \begin_layout Plain Layout
974 \begin_inset Caption Standard
976 \begin_layout Plain Layout
977 \begin_inset CommandInset label
979 name "tab:Available-units"
991 \begin_layout Plain Layout
994 <lyxtabular version="3" rows="13" columns="2">
995 <features booktabs="true" tabularvalignment="middle">
996 <column alignment="center" valignment="top">
997 <column alignment="center" valignment="top" width="0pt">
999 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1002 \begin_layout Plain Layout
1008 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1011 \begin_layout Plain Layout
1019 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1022 \begin_layout Plain Layout
1028 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1031 \begin_layout Plain Layout
1039 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1042 \begin_layout Plain Layout
1048 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1051 \begin_layout Plain Layout
1059 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1062 \begin_layout Plain Layout
1068 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1071 \begin_layout Plain Layout
1073 \begin_inset space \thinspace{}
1077 \begin_inset space \thinspace{}
1087 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1090 \begin_layout Plain Layout
1096 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1099 \begin_layout Plain Layout
1101 \begin_inset space \thinspace{}
1105 \begin_inset space \thinspace{}
1115 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1118 \begin_layout Plain Layout
1124 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1127 \begin_layout Plain Layout
1129 \begin_inset space \thinspace{}
1133 \begin_inset space \thinspace{}
1143 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1146 \begin_layout Plain Layout
1152 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1155 \begin_layout Plain Layout
1157 \begin_inset space \thinspace{}
1161 \begin_inset space \thinspace{}
1171 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1174 \begin_layout Plain Layout
1180 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1183 \begin_layout Plain Layout
1185 \begin_inset space \thinspace{}
1189 \begin_inset space \thinspace{}
1199 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1202 \begin_layout Plain Layout
1208 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1211 \begin_layout Plain Layout
1213 \begin_inset space \thinspace{}
1217 \begin_inset Formula $\approx$
1221 \begin_inset space \thinspace{}
1231 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1234 \begin_layout Plain Layout
1240 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1243 \begin_layout Plain Layout
1245 \begin_inset space \thinspace{}
1249 \begin_inset space \thinspace{}
1259 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1262 \begin_layout Plain Layout
1268 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1271 \begin_layout Plain Layout
1275 \begin_inset Quotes eld
1281 \begin_inset Quotes erd
1291 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1294 \begin_layout Plain Layout
1300 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1303 \begin_layout Plain Layout
1305 \begin_inset Quotes eld
1313 \begin_inset Quotes erd
1323 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1326 \begin_layout Plain Layout
1332 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1335 \begin_layout Plain Layout
1337 \begin_inset space \thinspace{}
1341 \begin_inset Formula $\nicefrac{1}{18}$
1345 \begin_inset space \thinspace{}
1366 \begin_layout Standard
1367 \begin_inset Newpage newpage
1373 \begin_layout Section
1377 \begin_layout Subsection
1379 \begin_inset Index idx
1382 \begin_layout Plain Layout
1389 \begin_inset Index idx
1392 \begin_layout Plain Layout
1399 \begin_inset Index idx
1402 \begin_layout Plain Layout
1407 \begin_layout Plain Layout
1418 \begin_layout Plain Layout
1431 \begin_inset Index idx
1434 \begin_layout Plain Layout
1439 \begin_layout Plain Layout
1450 \begin_layout Plain Layout
1465 \begin_layout Standard
1466 Indices are created with an underscore
1467 \begin_inset Quotes eld
1471 \begin_inset Quotes erd
1474 or via the math toolbar button
1477 arg "math-subscript"
1480 , exponents with a caret
1481 \begin_inset Quotes eld
1485 \begin_inset Quotes erd
1488 or via the math toolbar button
1491 arg "math-superscript"
1495 \begin_inset Separator parbreak
1501 \begin_layout Standard
1503 \begin_inset Tabular
1504 <lyxtabular version="3" rows="4" columns="2">
1505 <features booktabs="true" tabularvalignment="middle">
1506 <column alignment="center" valignment="top" width="0pt">
1507 <column alignment="center" valignment="top" width="0pt">
1509 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1512 \begin_layout Plain Layout
1518 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1521 \begin_layout Plain Layout
1529 <cell alignment="center" valignment="top" usebox="none">
1532 \begin_layout Plain Layout
1538 <cell alignment="center" valignment="top" usebox="none">
1541 \begin_layout Plain Layout
1542 \begin_inset Formula $B_{V}$
1551 <row topspace="1.5mm">
1552 <cell alignment="center" valignment="top" usebox="none">
1555 \begin_layout Plain Layout
1561 <cell alignment="center" valignment="top" usebox="none">
1564 \begin_layout Plain Layout
1565 \begin_inset Formula $B^{V}$
1574 <row topspace="1.5mm">
1575 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1578 \begin_layout Plain Layout
1580 \begin_inset space \textvisiblespace{}
1588 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1591 \begin_layout Plain Layout
1592 \begin_inset Formula $B^{A}$
1608 \begin_layout Standard
1609 As the caret is in some languages an accent, vowels will be accentuated
1610 in this case and not set as exponents
1614 \begin_layout Plain Layout
1615 Depending on the used keyboard settings this can also happen for characters
1622 To get exponents in this case, press
1626 after the caret as in the last example.
1629 \begin_layout Subsection
1631 \begin_inset CommandInset label
1633 name "subsec:Fractions"
1638 \begin_inset Index idx
1641 \begin_layout Plain Layout
1650 \begin_layout Standard
1651 Fractions are generated with the command
1658 \begin_inset Index idx
1661 \begin_layout Plain Layout
1669 or via the math toolbar button
1672 arg "math-insert \\frac"
1676 The font size is adjusted automatically, depending on whether the fraction
1677 is in an inline or display style formula.
1678 With the math toolbar button
1681 arg "math-insert \\frac-square"
1684 you can select different fraction types.
1687 \begin_layout Standard
1695 \begin_inset Index idx
1698 \begin_layout Plain Layout
1706 a fraction can be created that always has the size of a display style formula.
1714 \begin_inset Index idx
1717 \begin_layout Plain Layout
1725 the fraction appears always with the size of an inline formula.
1729 \begin_layout Standard
1730 A line with the fraction
1731 \begin_inset Formula $\frac{1}{2}$
1734 that was created with the command
1743 \begin_layout Standard
1744 A line with the fraction
1745 \begin_inset Formula $\dfrac{1}{2}$
1748 that was created with the command
1755 \begin_inset Separator parbreak
1761 \begin_layout Standard
1763 \begin_inset Tabular
1764 <lyxtabular version="3" rows="4" columns="2">
1765 <features booktabs="true" tabularvalignment="middle">
1766 <column alignment="center" valignment="top" width="0pt">
1767 <column alignment="center" valignment="top" width="0pt">
1769 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1772 \begin_layout Plain Layout
1778 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1781 \begin_layout Plain Layout
1788 <row topspace="1.5mm">
1789 <cell alignment="center" valignment="top" usebox="none">
1792 \begin_layout Plain Layout
1796 \begin_inset space \textvisiblespace{}
1800 \begin_inset Formula $\downarrow$
1808 <cell alignment="center" valignment="top" usebox="none">
1811 \begin_layout Plain Layout
1812 \begin_inset Formula $\frac{A}{B}$
1821 <row topspace="2mm">
1822 <cell alignment="center" valignment="top" usebox="none">
1825 \begin_layout Plain Layout
1829 \begin_inset space \textvisiblespace{}
1833 \begin_inset Formula $\downarrow$
1841 <cell alignment="center" valignment="top" usebox="none">
1844 \begin_layout Plain Layout
1845 \begin_inset Formula $\dfrac{A}{B}$
1854 <row topspace="2mm" bottomspace="1mm">
1855 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1858 \begin_layout Plain Layout
1862 \begin_inset space \textvisiblespace{}
1868 \begin_inset space \textvisiblespace{}
1872 \begin_inset Formula $\downarrow$
1876 \begin_inset Formula $\downarrow\downarrow$
1884 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1887 \begin_layout Plain Layout
1888 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1904 \begin_layout Standard
1905 \begin_inset VSpace bigskip
1909 \begin_inset Newpage newpage
1912 For nested fractions the command
1919 \begin_inset Index idx
1922 \begin_layout Plain Layout
1932 \begin_inset VSpace -3mm
1938 \begin_layout Standard
1939 \begin_inset Formula
1941 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1942 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1950 \begin_layout Standard
1951 The command for the example above is:
1954 \begin_layout Standard
1960 \begin_inset space \textvisiblespace{}
1964 \begin_inset Formula $\downarrow$
1970 \begin_inset space \textvisiblespace{}
1976 \begin_inset space \textvisiblespace{}
1980 \begin_inset Formula $\downarrow$
1984 \begin_inset Formula $\downarrow$
1990 \begin_layout Standard
1991 \begin_inset VSpace medskip
1997 \begin_layout Standard
2004 sets the fraction always in the size of a displayed formula, also when
2005 it is part of another fraction.
2008 \begin_layout Standard
2009 It is possible to specify the alignment of the numerator.
2016 is used to left align it, the command
2029 centers the numerator.
2030 These fractions demonstrate the different alignments:
2033 \begin_layout Standard
2036 \begin_inset Formula
2038 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2046 \begin_layout Standard
2047 \begin_inset Note Greyedout
2050 \begin_layout Plain Layout
2067 are no real \SpecialChar LaTeX
2068 commands but represent the command
2072 cfrac[alignment]{numerator}{denominator}
2075 Therefore you cannot use them in \SpecialChar TeX
2084 \begin_layout Standard
2085 \begin_inset VSpace medskip
2088 It is often advantageous to combine
2101 \begin_inset Formula
2103 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2111 \begin_layout Standard
2112 For inline fractions with a sloped fraction stroke you can use the command
2120 \begin_inset Index idx
2123 \begin_layout Plain Layout
2132 \begin_inset Formula $\nicefrac{5}{31}$
2142 \begin_inset Index idx
2145 \begin_layout Plain Layout
2154 \begin_inset Formula $\unitfrac{5}{31}$
2157 There is furthermore the command
2163 that offers to write a fraction in combination with a number:
2164 \begin_inset Formula $\unitfrac[2]{1}{3}$
2170 \begin_layout Standard
2171 \begin_inset Note Greyedout
2174 \begin_layout Plain Layout
2185 is not a real \SpecialChar LaTeX
2186 command but the command
2187 \begin_inset Newline newline
2194 unitfrac[number]{numerator}{denominator}
2197 Therefore you cannot use it in \SpecialChar TeX
2206 \begin_layout Standard
2207 How to define own fractions where the fraction stroke can be changed, is
2209 \begin_inset CommandInset ref
2211 reference "subsec:Self-defined-Fractions"
2218 \begin_layout Standard
2219 Multiline fractions are explained in
2220 \begin_inset CommandInset ref
2222 reference "subsec:Multiline-Fractions"
2229 \begin_layout Subsection
2231 \begin_inset Index idx
2234 \begin_layout Plain Layout
2243 \begin_layout Standard
2244 Square roots are created with
2251 \begin_inset Index idx
2254 \begin_layout Plain Layout
2262 or the math toolbar button
2265 arg "math-insert \\sqrt"
2268 , all other roots with the command
2275 \begin_inset Index idx
2278 \begin_layout Plain Layout
2286 or with the math toolbar button
2289 arg "math-insert \\root"
2293 \begin_inset Separator parbreak
2299 \begin_layout Standard
2301 \begin_inset Tabular
2302 <lyxtabular version="3" rows="3" columns="2">
2303 <features booktabs="true" tabularvalignment="middle">
2304 <column alignment="center" valignment="top" width="0pt">
2305 <column alignment="center" valignment="top" width="0pt">
2307 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2310 \begin_layout Plain Layout
2316 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2319 \begin_layout Plain Layout
2326 <row topspace="1mm">
2327 <cell alignment="center" valignment="top" usebox="none">
2330 \begin_layout Plain Layout
2334 \begin_inset space \textvisiblespace{}
2342 <cell alignment="center" valignment="top" usebox="none">
2345 \begin_layout Plain Layout
2346 \begin_inset Formula $\sqrt{A-B}$
2355 <row topspace="1mm">
2356 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2359 \begin_layout Plain Layout
2363 \begin_inset space \textvisiblespace{}
2367 \begin_inset Formula $\downarrow$
2375 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2378 \begin_layout Plain Layout
2379 \begin_inset Formula $\sqrt[3]{A-B}$
2395 \begin_layout Standard
2396 A square root can also be created with
2402 when the root index field is left empty.
2405 \begin_layout Standard
2406 With certain indices the distance to the root is too small, like in this
2408 \begin_inset Formula $\sqrt[\beta]{B}$
2412 \begin_inset Newline newline
2416 \begin_inset Formula $\beta$
2420 To avoid this, the commands
2427 \begin_inset Index idx
2430 \begin_layout Plain Layout
2445 \begin_inset Index idx
2448 \begin_layout Plain Layout
2456 are used with the following scheme:
2459 \begin_layout Standard
2473 \begin_layout Standard
2474 Distance is the number of Big Points (unit bp;
2475 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2478 ), that the index should be moved to the left or top, resp..
2479 The commands are written to the index.
2480 This way the command
2481 \begin_inset Newline newline
2491 \begin_inset Formula $\to$
2497 \begin_inset Formula $\to$
2503 \begin_inset space \textvisiblespace{}
2507 \begin_inset Formula $\to$
2511 \begin_inset Newline newline
2516 produces a correct typeset formula:
2517 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2523 \begin_layout Subsection
2524 Binomial Coefficients
2525 \begin_inset Index idx
2528 \begin_layout Plain Layout
2529 Binomial coefficients
2537 \begin_layout Standard
2538 Binomial coefficients are inserted with the command
2545 \begin_inset Index idx
2548 \begin_layout Plain Layout
2556 or with the submenu of the math toolbar button
2559 arg "math-insert \\frac-square"
2575 there are the commands
2582 \begin_inset Index idx
2585 \begin_layout Plain Layout
2600 \begin_inset Index idx
2603 \begin_layout Plain Layout
2612 For other brackets around binomial coeficients there are the commands
2619 \begin_inset Index idx
2622 \begin_layout Plain Layout
2637 \begin_inset Index idx
2640 \begin_layout Plain Layout
2649 \begin_inset Separator parbreak
2655 \begin_layout Standard
2657 \begin_inset Tabular
2658 <lyxtabular version="3" rows="6" columns="2">
2659 <features booktabs="true" tabularvalignment="middle">
2660 <column alignment="center" valignment="top" width="0pt">
2661 <column alignment="center" valignment="top" width="0pt">
2663 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2666 \begin_layout Plain Layout
2672 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2675 \begin_layout Plain Layout
2682 <row topspace="1mm">
2683 <cell alignment="center" valignment="top" usebox="none">
2686 \begin_layout Plain Layout
2690 \begin_inset space \textvisiblespace{}
2694 \begin_inset Formula $\downarrow$
2702 <cell alignment="center" valignment="top" usebox="none">
2705 \begin_layout Plain Layout
2706 \begin_inset Formula $\binom{A}{B}$
2715 <row topspace="2mm">
2716 <cell alignment="center" valignment="top" usebox="none">
2719 \begin_layout Plain Layout
2723 \begin_inset space \textvisiblespace{}
2727 \begin_inset Formula $\downarrow$
2735 <cell alignment="center" valignment="top" usebox="none">
2738 \begin_layout Plain Layout
2739 \begin_inset Formula $\dbinom{A}{B}$
2748 <row topspace="2mm" bottomspace="0.5mm">
2749 <cell alignment="center" valignment="top" usebox="none">
2752 \begin_layout Plain Layout
2756 \begin_inset space \textvisiblespace{}
2760 \begin_inset Formula $\downarrow$
2768 <cell alignment="center" valignment="top" usebox="none">
2771 \begin_layout Plain Layout
2772 \begin_inset Formula $\tbinom{A}{B}$
2781 <row topspace="1mm">
2782 <cell alignment="center" valignment="top" topline="true" usebox="none">
2785 \begin_layout Plain Layout
2789 \begin_inset space \textvisiblespace{}
2793 \begin_inset Formula $\downarrow$
2801 <cell alignment="center" valignment="top" topline="true" usebox="none">
2804 \begin_layout Plain Layout
2805 \begin_inset Formula ${A \brack B}$
2814 <row topspace="2mm" bottomspace="0.5mm">
2815 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2818 \begin_layout Plain Layout
2822 \begin_inset space \textvisiblespace{}
2826 \begin_inset Formula $\downarrow$
2834 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2837 \begin_layout Plain Layout
2838 \begin_inset Formula ${A \brace B}$
2854 \begin_layout Subsection
2855 Case Differentiations
2856 \begin_inset Index idx
2859 \begin_layout Plain Layout
2860 Case differentiations
2868 \begin_layout Standard
2870 \begin_inset Tabular
2871 <lyxtabular version="3" rows="3" columns="2">
2872 <features booktabs="true" tabularvalignment="middle">
2873 <column alignment="center" valignment="top" width="0pt">
2874 <column alignment="center" valignment="top" width="0pt">
2876 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2879 \begin_layout Plain Layout
2885 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2888 \begin_layout Plain Layout
2896 <cell alignment="center" valignment="top" usebox="none">
2899 \begin_layout Plain Layout
2903 \begin_inset space \textvisiblespace{}
2907 \begin_inset Formula $\to$
2911 \begin_inset Index idx
2914 \begin_layout Plain Layout
2927 <cell alignment="center" valignment="top" usebox="none">
2930 \begin_layout Plain Layout
2931 \begin_inset Formula $\begin{cases}
2941 <row topspace="1.5mm">
2942 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2945 \begin_layout Plain Layout
2949 \begin_inset space \textvisiblespace{}
2955 arg "newline-insert newline"
2963 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2966 \begin_layout Plain Layout
2967 \begin_inset Formula $\begin{cases}
2968 A & \textrm{for }x>0\\
2969 B & \textrm{for }x=0
2986 \begin_layout Standard
2993 or pressing the math toolbar button
2996 arg "math-insert \\cases"
2999 you can create new lines with the shortcut
3002 arg "newline-insert newline"
3005 or the table toolbar button
3008 arg "inset-modify tabular append-row"
3014 \begin_layout Standard
3021 is also available via the menu
3023 Insert\SpecialChar menuseparator
3024 Math\SpecialChar menuseparator
3030 \begin_layout Subsection
3032 \begin_inset Index idx
3035 \begin_layout Plain Layout
3044 \begin_layout Standard
3052 \begin_inset Index idx
3055 \begin_layout Plain Layout
3063 every character can be displayed canceled.
3064 The characters are quasi accentuated by a slash.
3065 \begin_inset Separator parbreak
3071 \begin_layout Standard
3073 \begin_inset Tabular
3074 <lyxtabular version="3" rows="4" columns="2">
3075 <features booktabs="true" tabularvalignment="middle">
3076 <column alignment="center" valignment="top" width="0pt">
3077 <column alignment="center" valignment="top" width="0pt">
3079 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3082 \begin_layout Plain Layout
3088 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3091 \begin_layout Plain Layout
3099 <cell alignment="center" valignment="top" usebox="none">
3102 \begin_layout Plain Layout
3110 <cell alignment="center" valignment="top" usebox="none">
3113 \begin_layout Plain Layout
3114 \begin_inset Formula $\not=$
3124 <cell alignment="center" valignment="top" usebox="none">
3127 \begin_layout Plain Layout
3137 <cell alignment="center" valignment="top" usebox="none">
3140 \begin_layout Plain Layout
3141 \begin_inset Formula $\not\le$
3151 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3154 \begin_layout Plain Layout
3164 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3167 \begin_layout Plain Layout
3168 \begin_inset Formula $\not\parallel$
3184 \begin_layout Standard
3185 The last example shows that not all negations look good.
3186 Therefore there are special commands for some negations (see
3187 \begin_inset CommandInset ref
3189 reference "subsec:Mathematical-Symbols"
3194 \begin_inset CommandInset ref
3196 reference "sec:Relations"
3203 \begin_layout Subsection
3205 \begin_inset CommandInset label
3207 name "subsec:Placeholders"
3212 \begin_inset Index idx
3215 \begin_layout Plain Layout
3222 \begin_inset Index idx
3225 \begin_layout Plain Layout
3226 Chemical characters ! Isotopes
3232 \begin_inset Index idx
3235 \begin_layout Plain Layout
3240 \begin_layout Plain Layout
3251 \begin_layout Plain Layout
3266 \begin_layout Standard
3268 \begin_inset space \thinspace{}
3272 \begin_inset space \space{}
3279 \begin_layout Plain Layout
3280 Typesetting isotopes and chemical symbols is described in
3281 \begin_inset CommandInset ref
3283 reference "subsec:Chemical-Symbols-and"
3292 the following problem occurs:
3293 \begin_inset Separator parbreak
3299 \begin_layout Standard
3301 \begin_inset Tabular
3302 <lyxtabular version="3" rows="2" columns="2">
3303 <features booktabs="true" tabularvalignment="middle">
3304 <column alignment="center" valignment="top" width="0pt">
3305 <column alignment="center" valignment="top" width="0pt">
3307 <cell alignment="center" valignment="top" usebox="none">
3310 \begin_layout Plain Layout
3311 Indices created with sub- and superscripts:
3316 <cell alignment="center" valignment="top" usebox="none">
3319 \begin_layout Plain Layout
3320 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3329 <row topspace="1.5mm">
3330 <cell alignment="center" valignment="top" usebox="none">
3333 \begin_layout Plain Layout
3339 <cell alignment="center" valignment="top" usebox="none">
3342 \begin_layout Plain Layout
3343 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3359 \begin_layout Standard
3360 The shorter index is by default placed below or above the first character
3361 of the longer index.
3362 To avoid this there is the command
3369 \begin_inset Index idx
3372 \begin_layout Plain Layout
3380 or the math toolbar button
3381 \begin_inset space \thinspace{}
3388 \begin_layout Plain Layout
3389 can be found in the submenu of the toolbar button
3392 arg "math-insert \\space"
3401 \begin_inset Graphics
3402 filename ../images/math/phantom.png
3407 that creates one or more phantom characters.
3414 a small blue box appears that is superposed with two red arrows.
3415 The arrows indicate that the complete width and height of the box content
3416 will be created as placeholder.
3417 Phantom characters are accordingly placeholders with the size of the characters.
3418 \begin_inset Separator parbreak
3424 \begin_layout Standard
3426 \begin_inset Tabular
3427 <lyxtabular version="3" rows="4" columns="2">
3428 <features booktabs="true" tabularvalignment="middle">
3429 <column alignment="center" valignment="top" width="0pt">
3430 <column alignment="center" valignment="top" width="0pt">
3432 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3435 \begin_layout Plain Layout
3441 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3444 \begin_layout Plain Layout
3451 <row topspace="1.5mm">
3452 <cell alignment="center" valignment="top" usebox="none">
3455 \begin_layout Plain Layout
3457 \begin_inset space \textvisiblespace{}
3463 \begin_inset space \textvisiblespace{}
3467 \begin_inset Formula $\to$
3471 \begin_inset space \textvisiblespace{}
3479 <cell alignment="center" valignment="top" usebox="none">
3482 \begin_layout Plain Layout
3483 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3492 <row topspace="1.5mm" bottomspace="0.5mm">
3493 <cell alignment="center" valignment="top" usebox="none">
3496 \begin_layout Plain Layout
3498 \begin_inset space \textvisiblespace{}
3504 \begin_inset space \textvisiblespace{}
3508 \begin_inset Formula $\to$
3512 \begin_inset space \textvisiblespace{}
3520 <cell alignment="center" valignment="top" usebox="none">
3523 \begin_layout Plain Layout
3524 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3533 <row topspace="1.5mm" bottomspace="0.5mm">
3534 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3537 \begin_layout Plain Layout
3541 \begin_inset space \textvisiblespace{}
3547 \begin_inset space \textvisiblespace{}
3551 \begin_inset Formula $\to$
3555 \begin_inset space \textvisiblespace{}
3563 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3566 \begin_layout Plain Layout
3567 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3583 \begin_layout Standard
3584 Furthermore there are the commands
3591 \begin_inset Index idx
3594 \begin_layout Plain Layout
3603 \begin_inset space ~
3607 \begin_inset Graphics
3608 filename ../images/math/vphantom.png
3620 \begin_inset Index idx
3623 \begin_layout Plain Layout
3632 \begin_inset space ~
3636 \begin_inset Graphics
3637 filename ../images/math/hphantom.png
3649 creates only space for the maximal height of the characters in the box
3650 but not for its width.
3657 creates only space for the width of the box content.
3658 Therefore the boxes of both commands have only one red arrow.
3661 \begin_layout Standard
3662 For example the command
3667 \begin_inset space \textvisiblespace{}
3674 creates space for the height of the integral sign,
3678 \begin_layout Plain Layout
3685 creates an integral sign, see
3686 \begin_inset CommandInset ref
3688 reference "subsec:Big-Operators"
3697 because this is the larger character.
3698 An example application is in
3699 \begin_inset CommandInset ref
3701 reference "subsec:Multiline-Brackets"
3708 \begin_layout Standard
3709 Placeholders can also be used for text when they are inserted via the menu
3712 Insert\SpecialChar menuseparator
3713 Formatting\SpecialChar menuseparator
3719 \begin_layout Standard
3721 \begin_inset Newline newline
3725 \begin_inset Phantom Phantom
3728 \begin_layout Plain Layout
3737 \begin_layout Subsection
3739 \begin_inset Index idx
3742 \begin_layout Plain Layout
3749 \begin_inset Index idx
3752 \begin_layout Plain Layout
3753 Formula ! underlined
3761 \begin_layout Standard
3763 \begin_inset Tabular
3764 <lyxtabular version="3" rows="4" columns="2">
3765 <features booktabs="true" tabularvalignment="middle">
3766 <column alignment="center" valignment="top" width="0pt">
3767 <column alignment="center" valignment="top" width="0pt">
3769 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3772 \begin_layout Plain Layout
3778 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3781 \begin_layout Plain Layout
3788 <row topspace="2mm">
3789 <cell alignment="center" valignment="top" usebox="none">
3792 \begin_layout Plain Layout
3796 \begin_inset space \textvisiblespace{}
3800 \begin_inset Index idx
3803 \begin_layout Plain Layout
3816 <cell alignment="center" valignment="top" usebox="none">
3819 \begin_layout Plain Layout
3820 \begin_inset Formula $\overline{A+B}$
3829 <row bottomspace="1mm">
3830 <cell alignment="center" valignment="top" usebox="none">
3833 \begin_layout Plain Layout
3837 \begin_inset space \textvisiblespace{}
3841 \begin_inset Index idx
3844 \begin_layout Plain Layout
3857 <cell alignment="center" valignment="top" usebox="none">
3860 \begin_layout Plain Layout
3861 \begin_inset Formula $\underline{A+B}$
3870 <row topspace="2mm" bottomspace="1mm">
3871 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3874 \begin_layout Plain Layout
3878 \begin_inset space \textvisiblespace{}
3884 \begin_inset space \textvisiblespace{}
3892 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3895 \begin_layout Plain Layout
3896 \begin_inset Formula $\overline{\underline{A+B}}$
3912 \begin_layout Standard
3913 In the last example it doesn't matter if first
3928 \begin_layout Standard
3929 To double underline use
3938 \begin_layout Standard
3939 It is possible to place up to 6 lines above or below characters.
3942 \begin_layout Standard
3943 \begin_inset VSpace bigskip
3946 Custom lines can be created using the command
3953 \begin_inset Index idx
3956 \begin_layout Plain Layout
3964 which has the following scheme:
3967 \begin_layout Standard
3972 rule[vertical offset]{length}{thickness}
3975 \begin_layout Standard
3976 The optional vertical offset shifts the line upwards (or downwards, when
3977 the value is negative).
3979 \begin_inset CommandInset ref
3981 reference "tab:Available-units"
3985 can be used for the values.
3986 Here are two example lines created with the commands
3987 \begin_inset Newline newline
3994 rule[-2ex]{3cm}{2pt}
4005 \begin_layout Standard
4007 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4013 \begin_layout Standard
4020 can also be used for text when a line is inserted via the menu
4022 Insert\SpecialChar menuseparator
4023 Formatting\SpecialChar menuseparator
4025 \begin_inset space ~
4033 \begin_layout Standard
4035 \begin_inset CommandInset line
4046 \begin_layout Subsection
4048 \begin_inset CommandInset label
4050 name "subsec:Ellipses"
4055 \begin_inset Index idx
4058 \begin_layout Plain Layout
4067 \begin_layout Standard
4068 There are different types of ellipses available.
4072 \begin_layout Plain Layout
4073 In the math toolbar in the submenu of the button
4076 arg "math-insert \\ldots"
4084 For listings dots at the baseline are used (
4091 \begin_inset Index idx
4094 \begin_layout Plain Layout
4102 ), while for operations dots are needed that are on the same height as the
4110 \begin_inset Index idx
4113 \begin_layout Plain Layout
4122 When using the command
4129 \begin_inset Index idx
4132 \begin_layout Plain Layout
4140 , \SpecialChar LaTeX
4141 decides on the basis of the next character what type is used.
4142 \begin_inset Separator parbreak
4148 \begin_layout Standard
4150 \begin_inset Tabular
4151 <lyxtabular version="3" rows="9" columns="2">
4152 <features booktabs="true" tabularvalignment="middle">
4153 <column alignment="center" valignment="top" width="0pt">
4154 <column alignment="center" valignment="top" width="0pt">
4156 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4159 \begin_layout Plain Layout
4165 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4168 \begin_layout Plain Layout
4176 <cell alignment="center" valignment="top" usebox="none">
4179 \begin_layout Plain Layout
4181 \begin_inset space \textvisiblespace{}
4187 \begin_inset space \textvisiblespace{}
4195 <cell alignment="center" valignment="top" usebox="none">
4198 \begin_layout Plain Layout
4199 \begin_inset Formula $A_{1},\dots,A_{n}$
4209 <cell alignment="center" valignment="top" usebox="none">
4212 \begin_layout Plain Layout
4214 \begin_inset space \textvisiblespace{}
4220 \begin_inset space \textvisiblespace{}
4228 <cell alignment="center" valignment="top" usebox="none">
4231 \begin_layout Plain Layout
4232 \begin_inset Formula $A_{1}+\dots+A_{n}$
4242 <cell alignment="center" valignment="top" usebox="none">
4245 \begin_layout Plain Layout
4247 \begin_inset space \textvisiblespace{}
4253 \begin_inset space \textvisiblespace{}
4261 <cell alignment="center" valignment="top" usebox="none">
4264 \begin_layout Plain Layout
4265 \begin_inset Formula $A_{1},\ldots,A_{n}$
4275 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4278 \begin_layout Plain Layout
4280 \begin_inset space \textvisiblespace{}
4286 \begin_inset space \textvisiblespace{}
4294 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4297 \begin_layout Plain Layout
4298 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4308 <cell alignment="center" valignment="top" usebox="none">
4311 \begin_layout Plain Layout
4319 <cell alignment="center" valignment="top" usebox="none">
4322 \begin_layout Plain Layout
4323 \begin_inset Formula $\vdots$
4333 <cell alignment="center" valignment="top" usebox="none">
4336 \begin_layout Plain Layout
4344 <cell alignment="center" valignment="top" usebox="none">
4347 \begin_layout Plain Layout
4348 \begin_inset Formula $\ddots$
4358 <cell alignment="center" valignment="top" usebox="none">
4361 \begin_layout Plain Layout
4369 <cell alignment="center" valignment="top" usebox="none">
4372 \begin_layout Plain Layout
4373 \begin_inset Formula $\iddots$
4383 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4386 \begin_layout Plain Layout
4388 \begin_inset space \thinspace{}
4391 matrix with the different dots
4396 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4399 \begin_layout Plain Layout
4400 \begin_inset Formula $\begin{array}{ccc}
4401 A_{11} & \cdots & A_{1m}\\
4402 \vdots & \ddots & \vdots\\
4403 A_{n1} & \cdots & A_{nm}
4420 \begin_layout Standard
4421 The ellipses available in menu
4423 Insert\SpecialChar menuseparator
4425 \begin_inset space ~
4439 \begin_layout Standard
4440 \begin_inset VSpace medskip
4449 , one of the options
4451 Use mathdots package (automatically)
4453 must be set in the document settings under
4456 \begin_inset space ~
4462 \begin_inset Newline newline
4467 Use mathdots package
4469 will improve the appearance of all dots in the documents if their font
4470 style or size is not the default.
4473 \begin_layout Standard
4474 \begin_inset VSpace medskip
4477 Specially for matrices there are ellipses that span over several columns.
4478 They are created with the command
4485 \begin_inset Index idx
4488 \begin_layout Plain Layout
4496 , that has the following scheme:
4499 \begin_layout Standard
4504 hdotsfor[distance]{number of columns}
4507 \begin_layout Standard
4508 The number of columns specifies how many columns should be spanned.
4509 Distance is a factor for the distance between the dots.
4512 \begin_layout Standard
4513 In the following matrix the command
4519 was inserted in the first box of the second line, to get an ellipsis with
4520 a dot distance twice as long as with the command
4527 \begin_inset Formula
4529 \left(\begin{array}{cccc}
4538 Note that the matrix fields that should be spanned must be empty, otherwise
4539 you get \SpecialChar LaTeX
4543 \begin_layout Standard
4544 \begin_inset VSpace bigskip
4547 Furthermore you can fill with the command
4554 \begin_inset Index idx
4557 \begin_layout Plain Layout
4565 the rest of a line with dots.
4566 The effect of these commands is the same as with
4573 \begin_inset CommandInset ref
4575 reference "subsec:Variable-Space"
4582 \begin_layout Standard
4583 For example the command
4588 \begin_inset space \textvisiblespace{}
4596 \begin_layout Standard
4597 \begin_inset Formula $A\dotfill B$
4603 \begin_layout Standard
4610 there is for a line the command
4617 \begin_inset Index idx
4620 \begin_layout Plain Layout
4631 \begin_layout Standard
4632 \begin_inset Formula $A\hrulefill B$
4638 \begin_layout Standard
4639 To use the commands for text, they have to be inserted in \SpecialChar TeX
4643 \begin_layout Section
4645 \begin_inset CommandInset label
4652 \begin_inset Index idx
4655 \begin_layout Plain Layout
4664 \begin_layout Standard
4665 Matrices can be inserted via the math toolbar button
4668 arg "dialog-show mathmatrix"
4673 Insert\SpecialChar menuseparator
4674 Math\SpecialChar menuseparator
4678 In the matrix dialog you can specify the number of columns and rows, the
4679 alignment and the decoration.
4680 The vertical alignment is only of importance for matrices in inline formulas:
4683 \begin_layout Standard
4684 The first matrix is top
4685 \begin_inset Formula $\begin{array}[t]{cccc}
4693 \begin_inset Formula $\begin{array}{cccc}
4700 and the third bottom
4701 \begin_inset Formula $\begin{array}[b]{cccc}
4711 \begin_layout Standard
4712 The horizontal alignment specifies how the column entries should be aligned.
4713 It is set by entering a letter for every column.
4718 denotes left aligned,
4727 To create for example a 4
4732 \begin_inset space ~
4735 matrix where the first column is left aligned, the second and third are
4736 centered and the last one is right aligned, one enters for the horizontal
4742 Normally in a matrix all columns are centered, therefore the default for
4750 \begin_layout Standard
4751 Horizontal alignment:
4754 \begin_layout Standard
4760 \begin_inset Formula $\begin{array}{lll}
4772 \begin_inset Formula $\begin{array}{ccc}
4784 \begin_inset Formula $\begin{array}{rrr}
4794 \begin_layout Standard
4795 To add or delete rows and columns subsequently, the math toolbar buttons
4799 arg "inset-modify tabular append-row"
4805 arg "inset-modify tabular delete-row"
4809 \begin_inset space \thinspace{}
4814 Edit\SpecialChar menuseparator
4818 New rows can also be created with
4821 arg "newline-insert newline"
4827 \begin_layout Standard
4828 \begin_inset VSpace bigskip
4835 adds parentheses in the selected style around the matrix.
4836 Alternatively, parentheses can can either be created with the commands
4844 \begin_inset Index idx
4847 \begin_layout Plain Layout
4862 \begin_inset Index idx
4865 \begin_layout Plain Layout
4876 \begin_inset space ~
4882 \begin_inset CommandInset ref
4884 reference "subsec:Automatic-Bracket-Size"
4888 , or by using the following commands:
4889 \begin_inset VSpace medskip
4895 \begin_layout Standard
4896 \begin_inset space \hfill{}
4900 \begin_inset Tabular
4901 <lyxtabular version="3" rows="4" columns="2">
4902 <features booktabs="true" tabularvalignment="middle">
4903 <column alignment="center" valignment="top" width="0pt">
4904 <column alignment="center" valignment="top">
4906 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4909 \begin_layout Plain Layout
4915 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4918 \begin_layout Plain Layout
4925 <row topspace="1.5mm">
4926 <cell alignment="center" valignment="top" usebox="none">
4929 \begin_layout Plain Layout
4933 \begin_inset space \textvisiblespace{}
4941 \begin_inset space \thinspace{}
4949 <cell alignment="center" valignment="top" usebox="none">
4952 \begin_layout Plain Layout
4953 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4954 0 & \textrm{-}\mathrm{i}\\
4956 \end{array}\end{bmatrix}$
4965 <row topspace="1.5mm" bottomspace="0.5mm">
4966 <cell alignment="center" valignment="top" usebox="none">
4969 \begin_layout Plain Layout
4973 \begin_inset space \textvisiblespace{}
4981 \begin_inset space \thinspace{}
4989 <cell alignment="center" valignment="top" usebox="none">
4992 \begin_layout Plain Layout
4993 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
4994 0 & \textrm{-}\mathrm{i}\\
4996 \end{array}\end{Bmatrix}$
5006 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5009 \begin_layout Plain Layout
5013 \begin_inset space \textvisiblespace{}
5021 \begin_inset space \thinspace{}
5029 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5032 \begin_layout Plain Layout
5033 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5034 0 & \textrm{-}\mathrm{i}\\
5036 \end{array}\end{pmatrix}$
5050 \begin_inset space \hfill{}
5054 \begin_inset Tabular
5055 <lyxtabular version="3" rows="4" columns="2">
5056 <features booktabs="true" tabularvalignment="middle">
5057 <column alignment="center" valignment="top" width="0pt">
5058 <column alignment="center" valignment="top">
5060 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5063 \begin_layout Plain Layout
5069 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5072 \begin_layout Plain Layout
5079 <row topspace="1.5mm">
5080 <cell alignment="center" valignment="top" usebox="none">
5083 \begin_layout Plain Layout
5087 \begin_inset space \textvisiblespace{}
5095 \begin_inset space \thinspace{}
5103 <cell alignment="center" valignment="top" usebox="none">
5106 \begin_layout Plain Layout
5107 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5108 0 & \textrm{-}\mathrm{i}\\
5110 \end{array}\end{vmatrix}$
5119 <row topspace="1.5mm" bottomspace="0.5mm">
5120 <cell alignment="center" valignment="top" usebox="none">
5123 \begin_layout Plain Layout
5127 \begin_inset space \textvisiblespace{}
5135 \begin_inset space \thinspace{}
5143 <cell alignment="center" valignment="top" usebox="none">
5146 \begin_layout Plain Layout
5147 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5148 0 & \textrm{-}\mathrm{i}\\
5150 \end{array}\end{Vmatrix}$
5160 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5163 \begin_layout Plain Layout
5167 \begin_inset space \textvisiblespace{}
5175 \begin_inset space \thinspace{}
5183 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5186 \begin_layout Plain Layout
5187 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5188 0 & \textrm{-}\mathrm{i}\\
5190 \end{array}\end{matrix}$
5204 \begin_inset space \hfill{}
5210 \begin_layout Standard
5211 \begin_inset VSpace medskip
5215 \begin_inset space \thinspace{}
5219 \begin_inset space \space{}
5228 is inserted, a blue box appears between two vertical lines where the matrix
5230 \begin_inset Newline newline
5233 Note that decorated matrices ignore the vertical alignment.
5236 \begin_layout Standard
5237 \begin_inset VSpace bigskip
5240 As all multiline formulas are matrices, the length
5247 \begin_inset Index idx
5250 \begin_layout Plain Layout
5258 that is described in
5259 \begin_inset CommandInset ref
5261 reference "subsec:Column-Separation"
5265 can also be used to change the column separation of matrices.
5268 \begin_layout Standard
5269 To change the row separation, the command
5276 \begin_inset Index idx
5279 \begin_layout Plain Layout
5288 It is used as follows:
5291 \begin_layout Standard
5298 arraystretch}{stretch factor}
5299 \begin_inset Index idx
5302 \begin_layout Plain Layout
5313 \begin_layout Standard
5320 assigns the stretch factor to the predefined command
5328 \begin_inset space \thinspace{}
5332 \begin_inset space \space{}
5335 the row separation, use the factor 2.
5336 This is then used for all following matrices.
5337 To go back to the original separation, assign the factor 1 to
5346 \begin_layout Standard
5347 To set matrices into a text line, the command
5354 \begin_inset Index idx
5357 \begin_layout Plain Layout
5366 When it is inserted a blue box with two dashed lines appears.
5367 In this box the matrix is inserted.
5370 \begin_layout Standard
5372 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5374 \end{smallmatrix}\right)$
5380 \begin_layout Section
5381 Brackets and Delimiters
5382 \begin_inset Index idx
5385 \begin_layout Plain Layout
5392 \begin_inset Index idx
5395 \begin_layout Plain Layout
5404 \begin_layout Subsection
5405 Vertical Brackets and Delimiters
5406 \begin_inset Index idx
5409 \begin_layout Plain Layout
5418 \begin_layout Standard
5419 \begin_inset space \hfill{}
5423 \begin_inset Tabular
5424 <lyxtabular version="3" rows="9" columns="2">
5425 <features booktabs="true" tabularvalignment="middle">
5426 <column alignment="center" valignment="top" width="0pt">
5427 <column alignment="center" valignment="top" width="0pt">
5429 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5432 \begin_layout Plain Layout
5438 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5441 \begin_layout Plain Layout
5449 <cell alignment="center" valignment="top" usebox="none">
5452 \begin_layout Plain Layout
5458 <cell alignment="center" valignment="top" usebox="none">
5461 \begin_layout Plain Layout
5462 \begin_inset Formula $($
5472 <cell alignment="center" valignment="top" usebox="none">
5475 \begin_layout Plain Layout
5481 <cell alignment="center" valignment="top" usebox="none">
5484 \begin_layout Plain Layout
5485 \begin_inset Formula $\{$
5495 <cell alignment="center" valignment="top" usebox="none">
5498 \begin_layout Plain Layout
5504 <cell alignment="center" valignment="top" usebox="none">
5507 \begin_layout Plain Layout
5508 \begin_inset Formula $[$
5518 <cell alignment="center" valignment="top" usebox="none">
5521 \begin_layout Plain Layout
5529 <cell alignment="center" valignment="top" usebox="none">
5532 \begin_layout Plain Layout
5533 \begin_inset Formula $\langle$
5543 <cell alignment="center" valignment="top" usebox="none">
5546 \begin_layout Plain Layout
5554 <cell alignment="center" valignment="top" usebox="none">
5557 \begin_layout Plain Layout
5558 \begin_inset Formula $\lceil$
5568 <cell alignment="center" valignment="top" usebox="none">
5571 \begin_layout Plain Layout
5579 <cell alignment="center" valignment="top" usebox="none">
5582 \begin_layout Plain Layout
5583 \begin_inset Formula $\lfloor$
5593 <cell alignment="center" valignment="top" usebox="none">
5596 \begin_layout Plain Layout
5602 <cell alignment="center" valignment="top" usebox="none">
5605 \begin_layout Plain Layout
5606 \begin_inset Formula $/$
5616 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5619 \begin_layout Plain Layout
5625 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5628 \begin_layout Plain Layout
5629 \begin_inset Formula $|$
5643 \begin_inset space \hfill{}
5647 \begin_inset Tabular
5648 <lyxtabular version="3" rows="9" columns="2">
5649 <features booktabs="true" tabularvalignment="middle">
5650 <column alignment="center" valignment="top" width="0pt">
5651 <column alignment="center" valignment="top" width="0pt">
5653 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5656 \begin_layout Plain Layout
5662 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5665 \begin_layout Plain Layout
5673 <cell alignment="center" valignment="top" usebox="none">
5676 \begin_layout Plain Layout
5682 <cell alignment="center" valignment="top" usebox="none">
5685 \begin_layout Plain Layout
5686 \begin_inset Formula $)$
5696 <cell alignment="center" valignment="top" usebox="none">
5699 \begin_layout Plain Layout
5705 <cell alignment="center" valignment="top" usebox="none">
5708 \begin_layout Plain Layout
5709 \begin_inset Formula $\}$
5719 <cell alignment="center" valignment="top" usebox="none">
5722 \begin_layout Plain Layout
5728 <cell alignment="center" valignment="top" usebox="none">
5731 \begin_layout Plain Layout
5732 \begin_inset Formula $]$
5742 <cell alignment="center" valignment="top" usebox="none">
5745 \begin_layout Plain Layout
5753 <cell alignment="center" valignment="top" usebox="none">
5756 \begin_layout Plain Layout
5757 \begin_inset Formula $\rangle$
5767 <cell alignment="center" valignment="top" usebox="none">
5770 \begin_layout Plain Layout
5778 <cell alignment="center" valignment="top" usebox="none">
5781 \begin_layout Plain Layout
5782 \begin_inset Formula $\rceil$
5792 <cell alignment="center" valignment="top" usebox="none">
5795 \begin_layout Plain Layout
5803 <cell alignment="center" valignment="top" usebox="none">
5806 \begin_layout Plain Layout
5807 \begin_inset Formula $\rfloor$
5817 <cell alignment="center" valignment="top" usebox="none">
5820 \begin_layout Plain Layout
5830 <cell alignment="center" valignment="top" usebox="none">
5833 \begin_layout Plain Layout
5834 \begin_inset Formula $\backslash$
5844 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5847 \begin_layout Plain Layout
5855 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5858 \begin_layout Plain Layout
5859 \begin_inset Formula $\|$
5873 \begin_inset space \hfill{}
5879 \begin_layout Standard
5882 \begin_inset Note Greyedout
5885 \begin_layout Plain Layout
5898 \begin_inset Index idx
5901 \begin_layout Plain Layout
5909 must be used for the backslash, because the command
5917 produces a line break there.
5925 \begin_layout Standard
5926 For all characters listed above the size can be adjusted with the commands
5927 described in the following two subsections.
5928 When using these commands, the characters < and > can directly be used
5929 instead of the commands
5944 \begin_layout Subsubsection
5946 \begin_inset CommandInset label
5948 name "subsec:Manual-Bracket-Size"
5953 \begin_inset Index idx
5956 \begin_layout Plain Layout
5957 Bracket size ! manual
5965 \begin_layout Standard
5966 The bracket size can be specified manually by the \SpecialChar LaTeX
5974 \begin_inset Index idx
5977 \begin_layout Plain Layout
6010 denotes the smallest and
6016 the largest bracket size.
6019 \begin_layout Standard
6020 These commands are used to emphasize levels of brackets:
6021 \begin_inset Separator parbreak
6027 \begin_layout Standard
6029 \begin_inset Tabular
6030 <lyxtabular version="3" rows="2" columns="2">
6031 <features booktabs="true" tabularvalignment="middle">
6032 <column alignment="center" valignment="top" width="0pt">
6033 <column alignment="center" valignment="top" width="0pt">
6035 <cell alignment="center" valignment="top" usebox="none">
6038 \begin_layout Plain Layout
6039 all brackets in the same size:
6044 <cell alignment="center" valignment="top" usebox="none">
6047 \begin_layout Plain Layout
6048 \begin_inset Formula $((A+B)(A-B))^{C}$
6057 <row topspace="2mm">
6058 <cell alignment="center" valignment="top" usebox="none">
6061 \begin_layout Plain Layout
6067 <cell alignment="center" valignment="top" usebox="none">
6070 \begin_layout Plain Layout
6071 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6087 \begin_layout Standard
6088 For the second formula the command
6095 \begin_inset space \textvisiblespace{}
6103 \begin_layout Standard
6104 Here is an overview about all bracket sizes:
6105 \begin_inset Separator parbreak
6111 \begin_layout Standard
6128 \begin_inset space \textvisiblespace{}
6136 \begin_inset space \textvisiblespace{}
6140 \begin_inset space \textvisiblespace{}
6150 \begin_layout Standard
6152 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6158 \begin_layout Standard
6165 -commands there is the variant
6172 \begin_inset Index idx
6175 \begin_layout Plain Layout
6183 that adds a bit more space between the bracket and its content, and the
6197 \begin_inset Index idx
6200 \begin_layout Plain Layout
6210 , that don't add additional space.
6215 at the end of the command
6221 is for a left bracket; for a right bracket this will be replaced by an
6227 A left or right bracket can each be an opening or closing bracket.
6230 \begin_layout Standard
6231 In the following table is a comparison of the variants:
6232 \begin_inset Separator parbreak
6238 \begin_layout Standard
6240 \begin_inset Tabular
6241 <lyxtabular version="3" rows="5" columns="2">
6242 <features booktabs="true" tabularvalignment="middle">
6243 <column alignment="center" valignment="top" width="0pt">
6244 <column alignment="center" valignment="middle">
6246 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6249 \begin_layout Plain Layout
6255 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6258 \begin_layout Plain Layout
6265 <row topspace="2mm">
6266 <cell alignment="center" valignment="top" usebox="none">
6269 \begin_layout Plain Layout
6279 \begin_inset space \textvisiblespace{}
6289 <cell alignment="center" valignment="top" usebox="none">
6292 \begin_layout Plain Layout
6293 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6302 <row topspace="2mm">
6303 <cell alignment="center" valignment="top" usebox="none">
6306 \begin_layout Plain Layout
6316 \begin_inset space \textvisiblespace{}
6326 <cell alignment="center" valignment="top" usebox="none">
6329 \begin_layout Plain Layout
6330 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6339 <row topspace="2mm" bottomspace="0.5mm">
6340 <cell alignment="center" valignment="top" usebox="none">
6343 \begin_layout Plain Layout
6353 \begin_inset space \textvisiblespace{}
6363 <cell alignment="center" valignment="top" usebox="none">
6366 \begin_layout Plain Layout
6367 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6376 <row topspace="1.5mm" bottomspace="0.5mm">
6377 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6380 \begin_layout Plain Layout
6392 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6395 \begin_layout Plain Layout
6396 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6412 \begin_layout Subsubsection
6413 Automatic Bracket Size
6414 \begin_inset CommandInset label
6416 name "subsec:Automatic-Bracket-Size"
6421 \begin_inset Index idx
6424 \begin_layout Plain Layout
6425 Bracket size ! automatic
6433 \begin_layout Standard
6434 Brackets with variable size can be inserted with the commands
6441 \begin_inset Index idx
6444 \begin_layout Plain Layout
6459 \begin_inset Index idx
6462 \begin_layout Plain Layout
6470 or via the math toolbar button
6473 arg "dialog-show mathdelimiter"
6489 the wanted bracket must be inserted.
6490 The bracket size will then automatically be calculated for the output.
6491 \begin_inset Separator parbreak
6497 \begin_layout Standard
6499 normal bracket: The command
6506 \begin_inset space \textvisiblespace{}
6510 \begin_inset Formula $\downarrow$
6514 \begin_inset space \textvisiblespace{}
6520 \begin_inset Formula
6530 \begin_layout Standard
6532 multiline bracket: The command
6541 \begin_inset space \textvisiblespace{}
6545 \begin_inset Formula $\downarrow$
6549 \begin_inset space \textvisiblespace{}
6557 \begin_inset Formula
6559 \ln\left(\frac{A}{C}\right)
6567 \begin_layout Standard
6583 \begin_inset space ~
6589 This has the advantage that you can see in \SpecialChar LyX
6590 immediately the real bracket
6591 size and that the matching right bracket will be created too.
6592 \begin_inset Newline newline
6595 The command for the last example would then be:
6606 \begin_inset space \textvisiblespace{}
6610 \begin_inset Formula $\downarrow$
6616 \begin_layout Standard
6617 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6618 For example the command
6625 \begin_inset space \textvisiblespace{}
6629 \begin_inset Formula $\downarrow$
6633 \begin_inset space \textvisiblespace{}
6643 \begin_inset Formula
6645 \left.\frac{A}{B}\right\}
6664 will be converted by \SpecialChar LyX
6665 to brackets in the right size when the document is
6666 reloaded and an omitted bracket will appear as dashed line.
6669 \begin_layout Standard
6670 \begin_inset VSpace bigskip
6673 Because all popular \SpecialChar LaTeX
6674 distributions use e\SpecialChar TeX
6675 , an extension to \SpecialChar LaTeX
6684 \begin_inset Index idx
6687 \begin_layout Plain Layout
6695 is additionally available for all brackets and limits.
6696 With this command the height of the following character is adapted to the
6697 one of the surrounding brackets, what is e.
6698 \begin_inset space \thinspace{}
6702 \begin_inset space \space{}
6705 needed for physical vectors:
6706 \begin_inset Formula
6708 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6713 For physical vectors there is a special \SpecialChar LaTeX
6714 -package, described in
6715 \begin_inset CommandInset ref
6717 reference "subsec:Physical-Vectors"
6724 \begin_layout Subsection
6726 \begin_inset Index idx
6729 \begin_layout Plain Layout
6730 Brackets ! horizontal
6738 \begin_layout Standard
6740 \begin_inset Tabular
6741 <lyxtabular version="3" rows="4" columns="2">
6742 <features booktabs="true" tabularvalignment="middle">
6743 <column alignment="center" valignment="top" width="0pt">
6744 <column alignment="center" valignment="top" width="0pt">
6746 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6749 \begin_layout Plain Layout
6755 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6758 \begin_layout Plain Layout
6766 <cell alignment="center" valignment="top" usebox="none">
6769 \begin_layout Plain Layout
6773 \begin_inset space \textvisiblespace{}
6777 \begin_inset space \textvisiblespace{}
6781 \begin_inset Index idx
6784 \begin_layout Plain Layout
6797 <cell alignment="center" valignment="top" usebox="none">
6800 \begin_layout Plain Layout
6801 \begin_inset Formula $\overbrace{A+B}^{3}$
6810 <row topspace="2mm">
6811 <cell alignment="center" valignment="top" usebox="none">
6814 \begin_layout Plain Layout
6818 \begin_inset space \textvisiblespace{}
6822 \begin_inset space \textvisiblespace{}
6826 \begin_inset Index idx
6829 \begin_layout Plain Layout
6842 <cell alignment="center" valignment="top" usebox="none">
6845 \begin_layout Plain Layout
6846 \begin_inset Formula $\underbrace{A+B}_{5}$
6856 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6859 \begin_layout Plain Layout
6863 \begin_inset space \textvisiblespace{}
6869 \begin_inset space \textvisiblespace{}
6873 \begin_inset space \textvisiblespace{}
6877 \begin_inset space \textvisiblespace{}
6881 \begin_inset space \textvisiblespace{}
6885 \begin_inset space \textvisiblespace{}
6889 \begin_inset space \textvisiblespace{}
6897 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6900 \begin_layout Plain Layout
6901 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6917 \begin_layout Standard
6918 In the last example it doesn't matter if
6930 is inserted at first.
6933 \begin_layout Standard
6934 \begin_inset VSpace medskip
6940 \begin_layout Standard
6941 If you set in the document settings under
6944 \begin_inset space ~
6954 \begin_inset Index idx
6957 \begin_layout Plain Layout
6958 Packages ! mathtools
6966 \begin_inset space ~
6971 , you have access to square backets:
6972 \begin_inset Separator parbreak
6978 \begin_layout Standard
6980 \begin_inset Tabular
6981 <lyxtabular version="3" rows="4" columns="2">
6982 <features booktabs="true" tabularvalignment="middle">
6983 <column alignment="center" valignment="top" width="0pt">
6984 <column alignment="center" valignment="top" width="0pt">
6986 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6989 \begin_layout Plain Layout
6995 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6998 \begin_layout Plain Layout
7006 <cell alignment="center" valignment="top" usebox="none">
7009 \begin_layout Plain Layout
7037 \begin_inset space \textvisiblespace{}
7041 \begin_inset Index idx
7044 \begin_layout Plain Layout
7057 <cell alignment="center" valignment="top" usebox="none">
7060 \begin_layout Plain Layout
7061 \begin_inset Formula $\overbracket{A+B}^{3}$
7070 <row topspace="2mm">
7071 <cell alignment="center" valignment="top" usebox="none">
7074 \begin_layout Plain Layout
7102 \begin_inset space \textvisiblespace{}
7106 \begin_inset Index idx
7109 \begin_layout Plain Layout
7134 <cell alignment="center" valignment="top" usebox="none">
7137 \begin_layout Plain Layout
7138 \begin_inset Formula $\underbracket{A+B}_{5}$
7148 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7151 \begin_layout Plain Layout
7157 \begin_inset space \textvisiblespace{}
7161 \begin_inset space \textvisiblespace{}
7165 \begin_inset space \textvisiblespace{}
7169 \begin_inset space \textvisiblespace{}
7173 \begin_inset space \textvisiblespace{}
7181 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7184 \begin_layout Plain Layout
7185 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7201 \begin_layout Standard
7214 you can change the thickness of the bracket's stroke by specifying the
7215 desired thickness in square brackets behind the command:
7216 \begin_inset Separator parbreak
7222 \begin_layout Standard
7224 \begin_inset Tabular
7225 <lyxtabular version="3" rows="3" columns="2">
7226 <features booktabs="true" tabularvalignment="middle">
7227 <column alignment="center" valignment="top" width="0pt">
7228 <column alignment="center" valignment="top" width="0pt">
7230 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7233 \begin_layout Plain Layout
7239 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7242 \begin_layout Plain Layout
7250 <cell alignment="center" valignment="top" usebox="none">
7253 \begin_layout Plain Layout
7283 \begin_inset space \textvisiblespace{}
7291 <cell alignment="center" valignment="top" usebox="none">
7294 \begin_layout Plain Layout
7295 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7304 <row topspace="2mm">
7305 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7308 \begin_layout Plain Layout
7338 \begin_inset space \textvisiblespace{}
7346 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7349 \begin_layout Plain Layout
7350 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7366 \begin_layout Standard
7367 \begin_inset VSpace bigskip
7370 When brackets should overlap each other, multiline formulas, as described
7372 \begin_inset CommandInset ref
7374 reference "sec:Multiline-Formulas"
7379 \begin_inset Formula
7381 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7382 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7387 In the first row the formula is inserted together with the first brace.
7388 It is hereby important that the space command
7392 \begin_layout Plain Layout
7393 Space commands are explained in
7394 \begin_inset CommandInset ref
7396 reference "subsec:Predefined-Space"
7411 is inserted before the first
7412 \begin_inset Formula $d$
7415 , because the brace that ends behind the
7416 \begin_inset Formula $q$
7419 prevents that the following
7420 \begin_inset Quotes eld
7424 \begin_inset Quotes erd
7427 is surrounded by space.
7431 \begin_layout Plain Layout
7432 because a bracket is not handled as a character, see
7433 \begin_inset CommandInset ref
7435 reference "subsec:Binary-Operators"
7444 In the second row the second brace is inserted.
7445 As it should begin before the
7446 \begin_inset Formula $b$
7461 \begin_layout Plain Layout
7469 \begin_inset CommandInset ref
7471 reference "subsec:Placeholders"
7480 This space is needed because the
7481 \begin_inset Quotes eld
7485 \begin_inset Quotes erd
7488 is also surrounded by space in the formula.
7489 The brace is placed under the command
7498 \begin_layout Standard
7499 It gets more complicated when brackets overlap each other above and under
7500 the formula, like in the following example:
7504 \begin_layout Plain Layout
7516 \begin_inset Formula
7518 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7519 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7528 \begin_layout Plain Layout
7539 The first formula row is the same as the second row of the previous example,
7540 with the difference that the brace is above.
7541 The second row contains the formula together with the second brace.
7542 To avoid that there is space between the upper brace in the first row and
7543 the formula, the row spacing needs to be reduced.
7544 This is not easily possible due to a bug in \SpecialChar LyX
7549 \begin_layout Plain Layout
7550 \begin_inset CommandInset href
7552 name "LyX-bug #1505"
7553 target "http://www.lyx.org/trac/ticket/1505"
7562 As a solution for the problem, the global formula row separation
7569 \begin_inset Index idx
7572 \begin_layout Plain Layout
7580 must be changed to -6
7581 \begin_inset space \thinspace{}
7584 pt before the formula with the command
7600 is set back after the formula to the standard value of 3
7601 \begin_inset space \thinspace{}
7604 pt using the same command.
7605 More about the row separation in formulas is explained in
7606 \begin_inset CommandInset ref
7608 reference "subsec:Line-Separation"
7615 \begin_layout Section
7617 \begin_inset Index idx
7620 \begin_layout Plain Layout
7629 \begin_layout Standard
7630 Arrows can be inserted via the math toolbar button
7633 arg "math-insert \\leftarrow"
7636 or the commands listed in the following subsections.
7639 \begin_layout Subsection
7641 \begin_inset Index idx
7644 \begin_layout Plain Layout
7653 \begin_layout Standard
7654 \begin_inset space \hfill{}
7658 \begin_inset Tabular
7659 <lyxtabular version="3" rows="8" columns="2">
7660 <features booktabs="true" tabularvalignment="middle">
7661 <column alignment="center" valignment="top" width="0pt">
7662 <column alignment="center" valignment="top" width="0pt">
7664 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7667 \begin_layout Plain Layout
7673 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7676 \begin_layout Plain Layout
7684 <cell alignment="center" valignment="top" usebox="none">
7687 \begin_layout Plain Layout
7695 <cell alignment="center" valignment="top" usebox="none">
7698 \begin_layout Plain Layout
7699 \begin_inset Formula $\gets$
7709 <cell alignment="center" valignment="top" usebox="none">
7712 \begin_layout Plain Layout
7720 <cell alignment="center" valignment="top" usebox="none">
7723 \begin_layout Plain Layout
7724 \begin_inset Formula $\Leftarrow$
7734 <cell alignment="center" valignment="top" usebox="none">
7737 \begin_layout Plain Layout
7745 <cell alignment="center" valignment="top" usebox="none">
7748 \begin_layout Plain Layout
7749 \begin_inset Formula $\longleftarrow$
7759 <cell alignment="center" valignment="top" usebox="none">
7762 \begin_layout Plain Layout
7770 <cell alignment="center" valignment="top" usebox="none">
7773 \begin_layout Plain Layout
7774 \begin_inset Formula $\Longleftarrow$
7784 <cell alignment="center" valignment="top" usebox="none">
7787 \begin_layout Plain Layout
7795 <cell alignment="center" valignment="top" usebox="none">
7798 \begin_layout Plain Layout
7799 \begin_inset Formula $\leftharpoonup$
7809 <cell alignment="center" valignment="top" usebox="none">
7812 \begin_layout Plain Layout
7820 <cell alignment="center" valignment="top" usebox="none">
7823 \begin_layout Plain Layout
7824 \begin_inset Formula $\leftharpoondown$
7834 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7837 \begin_layout Plain Layout
7845 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7848 \begin_layout Plain Layout
7849 \begin_inset Formula $\hookleftarrow$
7863 \begin_inset space \hfill{}
7867 \begin_inset Tabular
7868 <lyxtabular version="3" rows="8" columns="2">
7869 <features booktabs="true" tabularvalignment="middle">
7870 <column alignment="center" valignment="top" width="0pt">
7871 <column alignment="center" valignment="top" width="0pt">
7873 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7876 \begin_layout Plain Layout
7882 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7885 \begin_layout Plain Layout
7893 <cell alignment="center" valignment="top" usebox="none">
7896 \begin_layout Plain Layout
7904 <cell alignment="center" valignment="top" usebox="none">
7907 \begin_layout Plain Layout
7908 \begin_inset Formula $\to$
7918 <cell alignment="center" valignment="top" usebox="none">
7921 \begin_layout Plain Layout
7929 <cell alignment="center" valignment="top" usebox="none">
7932 \begin_layout Plain Layout
7933 \begin_inset Formula $\Rightarrow$
7943 <cell alignment="center" valignment="top" usebox="none">
7946 \begin_layout Plain Layout
7954 <cell alignment="center" valignment="top" usebox="none">
7957 \begin_layout Plain Layout
7958 \begin_inset Formula $\longrightarrow$
7968 <cell alignment="center" valignment="top" usebox="none">
7971 \begin_layout Plain Layout
7979 <cell alignment="center" valignment="top" usebox="none">
7982 \begin_layout Plain Layout
7983 \begin_inset Formula $\Longrightarrow$
7993 <cell alignment="center" valignment="top" usebox="none">
7996 \begin_layout Plain Layout
8004 <cell alignment="center" valignment="top" usebox="none">
8007 \begin_layout Plain Layout
8008 \begin_inset Formula $\rightharpoonup$
8018 <cell alignment="center" valignment="top" usebox="none">
8021 \begin_layout Plain Layout
8029 <cell alignment="center" valignment="top" usebox="none">
8032 \begin_layout Plain Layout
8033 \begin_inset Formula $\rightharpoondown$
8043 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8046 \begin_layout Plain Layout
8054 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8057 \begin_layout Plain Layout
8058 \begin_inset Formula $\hookrightarrow$
8072 \begin_inset space \hfill{}
8078 \begin_layout Standard
8079 \begin_inset space \hfill{}
8083 \begin_inset Tabular
8084 <lyxtabular version="3" rows="6" columns="2">
8085 <features booktabs="true" tabularvalignment="middle">
8086 <column alignment="center" valignment="top" width="0pt">
8087 <column alignment="center" valignment="top" width="0pt">
8089 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8092 \begin_layout Plain Layout
8098 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8101 \begin_layout Plain Layout
8109 <cell alignment="center" valignment="top" usebox="none">
8112 \begin_layout Plain Layout
8120 <cell alignment="center" valignment="top" usebox="none">
8123 \begin_layout Plain Layout
8124 \begin_inset Formula $\leftrightarrow$
8134 <cell alignment="center" valignment="top" usebox="none">
8137 \begin_layout Plain Layout
8145 <cell alignment="center" valignment="top" usebox="none">
8148 \begin_layout Plain Layout
8149 \begin_inset Formula $\Leftrightarrow$
8159 <cell alignment="center" valignment="top" usebox="none">
8162 \begin_layout Plain Layout
8170 <cell alignment="center" valignment="top" usebox="none">
8173 \begin_layout Plain Layout
8174 \begin_inset Formula $\longleftrightarrow$
8184 <cell alignment="center" valignment="top" usebox="none">
8187 \begin_layout Plain Layout
8195 <cell alignment="center" valignment="top" usebox="none">
8198 \begin_layout Plain Layout
8199 \begin_inset Formula $\Longleftrightarrow$
8209 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8212 \begin_layout Plain Layout
8220 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8223 \begin_layout Plain Layout
8224 \begin_inset Formula $\rightleftharpoons$
8238 \begin_inset space \hspace{}
8243 \begin_inset space \hfill{}
8247 \begin_inset Tabular
8248 <lyxtabular version="3" rows="5" columns="2">
8249 <features booktabs="true" tabularvalignment="middle">
8250 <column alignment="center" valignment="top" width="0pt">
8251 <column alignment="center" valignment="top" width="0pt">
8253 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8256 \begin_layout Plain Layout
8262 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8265 \begin_layout Plain Layout
8273 <cell alignment="center" valignment="top" usebox="none">
8276 \begin_layout Plain Layout
8284 <cell alignment="center" valignment="top" usebox="none">
8287 \begin_layout Plain Layout
8288 \begin_inset Formula $\mapsto$
8298 <cell alignment="center" valignment="top" usebox="none">
8301 \begin_layout Plain Layout
8309 <cell alignment="center" valignment="top" usebox="none">
8312 \begin_layout Plain Layout
8313 \begin_inset Formula $\longmapsto$
8323 <cell alignment="center" valignment="top" usebox="none">
8326 \begin_layout Plain Layout
8334 <cell alignment="center" valignment="top" usebox="none">
8337 \begin_layout Plain Layout
8338 \begin_inset Formula $\leadsto$
8348 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8351 \begin_layout Plain Layout
8359 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8362 \begin_layout Plain Layout
8363 \begin_inset Formula $\dasharrow$
8377 \begin_inset space \hfill{}
8383 \begin_layout Standard
8384 \begin_inset VSpace medskip
8387 Arrows used as accents like e.
8388 \begin_inset space \thinspace{}
8392 \begin_inset space \space{}
8395 vector arrows are listed in
8396 \begin_inset CommandInset ref
8398 reference "sec:Accents"
8405 \begin_layout Standard
8406 \begin_inset VSpace bigskip
8409 Furthermore there are the labeled arrows
8410 \begin_inset Index idx
8413 \begin_layout Plain Layout
8426 \begin_inset Index idx
8429 \begin_layout Plain Layout
8444 \begin_inset Index idx
8447 \begin_layout Plain Layout
8454 \begin_layout Plain Layout
8469 When inserting one of these commands in a formula, an arrow with two blue
8470 boxes appear where the label can be inserted.
8471 The length of the arrow adapts to the label width.
8474 \begin_layout Standard
8476 \begin_inset Tabular
8477 <lyxtabular version="3" rows="3" columns="2">
8478 <features booktabs="true" tabularvalignment="middle">
8479 <column alignment="center" valignment="top" width="0pt">
8480 <column alignment="center" valignment="top" width="0pt">
8482 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8485 \begin_layout Plain Layout
8491 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8494 \begin_layout Plain Layout
8502 <cell alignment="center" valignment="top" usebox="none">
8505 \begin_layout Plain Layout
8509 \begin_inset space \textvisiblespace{}
8513 \begin_inset Formula $\downarrow$
8517 \begin_inset Formula $\to$
8525 <cell alignment="center" valignment="top" usebox="none">
8528 \begin_layout Plain Layout
8529 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8538 <row topspace="2mm">
8539 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8542 \begin_layout Plain Layout
8546 \begin_inset space \textvisiblespace{}
8550 \begin_inset Formula $\downarrow$
8554 \begin_inset Formula $\to$
8562 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8565 \begin_layout Plain Layout
8566 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8582 \begin_layout Standard
8583 \begin_inset VSpace medskip
8589 \begin_layout Standard
8590 If you set in the document settings under
8593 \begin_inset space ~
8603 \begin_inset Index idx
8606 \begin_layout Plain Layout
8607 Packages ! mathtools
8615 \begin_inset space ~
8620 , you have access to the following labeled arrows:
8623 \begin_layout Standard
8624 \begin_inset Newpage newpage
8628 \begin_inset Separator parbreak
8634 \begin_layout Standard
8636 \begin_inset space \hspace*{\fill}
8640 \begin_inset Tabular
8641 <lyxtabular version="3" rows="7" columns="2">
8642 <features booktabs="true" tabularvalignment="middle">
8643 <column alignment="center" valignment="top" width="0pt">
8644 <column alignment="center" valignment="top" width="0pt">
8646 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8649 \begin_layout Plain Layout
8655 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8658 \begin_layout Plain Layout
8666 <cell alignment="center" valignment="top" usebox="none">
8669 \begin_layout Plain Layout
8689 <cell alignment="center" valignment="top" usebox="none">
8692 \begin_layout Plain Layout
8693 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8702 <row topspace="2mm">
8703 <cell alignment="center" valignment="top" usebox="none">
8706 \begin_layout Plain Layout
8726 <cell alignment="center" valignment="top" usebox="none">
8729 \begin_layout Plain Layout
8730 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8739 <row topspace="2mm">
8740 <cell alignment="center" valignment="top" usebox="none">
8743 \begin_layout Plain Layout
8763 <cell alignment="center" valignment="top" usebox="none">
8766 \begin_layout Plain Layout
8767 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8776 <row topspace="2mm">
8777 <cell alignment="center" valignment="top" usebox="none">
8780 \begin_layout Plain Layout
8800 <cell alignment="center" valignment="top" usebox="none">
8803 \begin_layout Plain Layout
8804 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8813 <row topspace="2mm">
8814 <cell alignment="center" valignment="top" usebox="none">
8817 \begin_layout Plain Layout
8837 <cell alignment="center" valignment="top" usebox="none">
8840 \begin_layout Plain Layout
8841 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8850 <row topspace="2mm">
8851 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8854 \begin_layout Plain Layout
8874 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8877 \begin_layout Plain Layout
8878 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8892 \begin_inset space \hspace*{\fill}
8896 \begin_inset Tabular
8897 <lyxtabular version="3" rows="7" columns="2">
8898 <features booktabs="true" tabularvalignment="middle">
8899 <column alignment="center" valignment="top" width="0pt">
8900 <column alignment="center" valignment="top" width="0pt">
8902 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8905 \begin_layout Plain Layout
8911 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8914 \begin_layout Plain Layout
8922 <cell alignment="center" valignment="top" usebox="none">
8925 \begin_layout Plain Layout
8945 <cell alignment="center" valignment="top" usebox="none">
8948 \begin_layout Plain Layout
8949 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8958 <row topspace="2mm">
8959 <cell alignment="center" valignment="top" usebox="none">
8962 \begin_layout Plain Layout
8982 <cell alignment="center" valignment="top" usebox="none">
8985 \begin_layout Plain Layout
8986 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8995 <row topspace="2mm">
8996 <cell alignment="center" valignment="top" usebox="none">
8999 \begin_layout Plain Layout
9019 <cell alignment="center" valignment="top" usebox="none">
9022 \begin_layout Plain Layout
9023 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
9032 <row topspace="2mm">
9033 <cell alignment="center" valignment="top" usebox="none">
9036 \begin_layout Plain Layout
9056 <cell alignment="center" valignment="top" usebox="none">
9059 \begin_layout Plain Layout
9060 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9069 <row topspace="2mm">
9070 <cell alignment="center" valignment="top" usebox="none">
9073 \begin_layout Plain Layout
9093 <cell alignment="center" valignment="top" usebox="none">
9096 \begin_layout Plain Layout
9097 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9106 <row topspace="2mm">
9107 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9110 \begin_layout Plain Layout
9130 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9133 \begin_layout Plain Layout
9134 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9148 \begin_inset space \hspace*{\fill}
9154 \begin_layout Standard
9155 The command scheme is for all these arrows:
9156 \begin_inset Separator parbreak
9162 \begin_layout Standard
9164 \begin_inset Tabular
9165 <lyxtabular version="3" rows="2" columns="2">
9166 <features booktabs="true" tabularvalignment="middle">
9167 <column alignment="center" valignment="top" width="0pt">
9168 <column alignment="center" valignment="top" width="0pt">
9170 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9173 \begin_layout Plain Layout
9179 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9182 \begin_layout Plain Layout
9189 <row bottomspace="0.5mm">
9190 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9193 \begin_layout Plain Layout
9196 xleftrightarrow[x=a]
9199 \begin_inset Formula $\to$
9207 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9210 \begin_layout Plain Layout
9211 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9227 \begin_layout Subsection
9228 Vertical and diagonal Arrows
9229 \begin_inset Index idx
9232 \begin_layout Plain Layout
9239 \begin_inset Index idx
9242 \begin_layout Plain Layout
9251 \begin_layout Standard
9252 \begin_inset space \hfill{}
9256 \begin_inset Tabular
9257 <lyxtabular version="3" rows="7" columns="2">
9258 <features booktabs="true" tabularvalignment="middle">
9259 <column alignment="center" valignment="top" width="0pt">
9260 <column alignment="center" valignment="top" width="0pt">
9262 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9265 \begin_layout Plain Layout
9271 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9274 \begin_layout Plain Layout
9282 <cell alignment="center" valignment="top" usebox="none">
9285 \begin_layout Plain Layout
9293 <cell alignment="center" valignment="top" usebox="none">
9296 \begin_layout Plain Layout
9297 \begin_inset Formula $\uparrow$
9307 <cell alignment="center" valignment="top" usebox="none">
9310 \begin_layout Plain Layout
9318 <cell alignment="center" valignment="top" usebox="none">
9321 \begin_layout Plain Layout
9322 \begin_inset Formula $\Uparrow$
9332 <cell alignment="center" valignment="top" usebox="none">
9335 \begin_layout Plain Layout
9343 <cell alignment="center" valignment="top" usebox="none">
9346 \begin_layout Plain Layout
9347 \begin_inset Formula $\updownarrow$
9357 <cell alignment="center" valignment="top" usebox="none">
9360 \begin_layout Plain Layout
9368 <cell alignment="center" valignment="top" usebox="none">
9371 \begin_layout Plain Layout
9372 \begin_inset Formula $\Updownarrow$
9382 <cell alignment="center" valignment="top" usebox="none">
9385 \begin_layout Plain Layout
9393 <cell alignment="center" valignment="top" usebox="none">
9396 \begin_layout Plain Layout
9397 \begin_inset Formula $\Downarrow$
9407 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9410 \begin_layout Plain Layout
9418 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9421 \begin_layout Plain Layout
9422 \begin_inset Formula $\downarrow$
9436 \begin_inset space \hfill{}
9440 \begin_inset Tabular
9441 <lyxtabular version="3" rows="5" columns="2">
9442 <features booktabs="true" tabularvalignment="middle">
9443 <column alignment="center" valignment="top" width="0pt">
9444 <column alignment="center" valignment="top" width="0pt">
9446 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9449 \begin_layout Plain Layout
9455 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9458 \begin_layout Plain Layout
9466 <cell alignment="center" valignment="top" usebox="none">
9469 \begin_layout Plain Layout
9477 <cell alignment="center" valignment="top" usebox="none">
9480 \begin_layout Plain Layout
9481 \begin_inset Formula $\nearrow$
9491 <cell alignment="center" valignment="top" usebox="none">
9494 \begin_layout Plain Layout
9502 <cell alignment="center" valignment="top" usebox="none">
9505 \begin_layout Plain Layout
9506 \begin_inset Formula $\searrow$
9516 <cell alignment="center" valignment="top" usebox="none">
9519 \begin_layout Plain Layout
9527 <cell alignment="center" valignment="top" usebox="none">
9530 \begin_layout Plain Layout
9531 \begin_inset Formula $\swarrow$
9541 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9544 \begin_layout Plain Layout
9552 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9555 \begin_layout Plain Layout
9556 \begin_inset Formula $\nwarrow$
9570 \begin_inset space \hfill{}
9576 \begin_layout Standard
9577 \begin_inset VSpace medskip
9580 Vertical arrows can be used also as delimiters together with the commands
9582 \begin_inset CommandInset ref
9584 reference "subsec:Manual-Bracket-Size"
9589 \begin_inset CommandInset ref
9591 reference "subsec:Automatic-Bracket-Size"
9598 \begin_layout Section
9600 \begin_inset CommandInset label
9607 \begin_inset Index idx
9610 \begin_layout Plain Layout
9619 \begin_layout Standard
9620 Accents can be inserted via the math toolbar button
9623 arg "math-insert \\hat"
9626 or the commands listed in the following subsections.
9629 \begin_layout Subsection
9630 Accents for one Character
9634 \begin_layout Plain Layout
9647 \begin_layout Plain Layout
9649 \begin_inset CommandInset ref
9651 reference "subsec:Accents-in-Text"
9664 \begin_layout Plain Layout
9672 \begin_inset Note Note
9675 \begin_layout Plain Layout
9682 is used to avoid that the footnote appears in the PDF-bookmark.
9685 \begin_layout Plain Layout
9693 \begin_inset CommandInset ref
9695 reference "subsec:Formulas-in-Section"
9705 \begin_inset CommandInset label
9707 name "subsec:Accents-for-one"
9712 \begin_inset Index idx
9715 \begin_layout Plain Layout
9716 Accents ! for one character
9724 \begin_layout Standard
9725 \begin_inset space \hfill{}
9729 \begin_inset Tabular
9730 <lyxtabular version="3" rows="8" columns="2">
9731 <features booktabs="true" tabularvalignment="middle">
9732 <column alignment="center" valignment="top" width="0pt">
9733 <column alignment="center" valignment="top" width="0pt">
9735 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9738 \begin_layout Plain Layout
9744 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9747 \begin_layout Plain Layout
9754 <row topspace="1.5mm">
9755 <cell alignment="center" valignment="top" usebox="none">
9758 \begin_layout Plain Layout
9762 \begin_inset space \textvisiblespace{}
9770 <cell alignment="center" valignment="top" usebox="none">
9773 \begin_layout Plain Layout
9774 \begin_inset Formula $\dot{A}$
9783 <row topspace="1.5mm">
9784 <cell alignment="center" valignment="top" usebox="none">
9787 \begin_layout Plain Layout
9791 \begin_inset space \textvisiblespace{}
9799 <cell alignment="center" valignment="top" usebox="none">
9802 \begin_layout Plain Layout
9803 \begin_inset Formula $\ddot{A}$
9812 <row topspace="1.5mm">
9813 <cell alignment="center" valignment="top" usebox="none">
9816 \begin_layout Plain Layout
9820 \begin_inset space \textvisiblespace{}
9828 <cell alignment="center" valignment="top" usebox="none">
9831 \begin_layout Plain Layout
9832 \begin_inset Formula $\dddot{A}$
9841 <row topspace="1.5mm">
9842 <cell alignment="center" valignment="top" usebox="none">
9845 \begin_layout Plain Layout
9849 \begin_inset space \textvisiblespace{}
9857 <cell alignment="center" valignment="top" usebox="none">
9860 \begin_layout Plain Layout
9861 \begin_inset Formula $\ddddot{A}$
9870 <row topspace="1.5mm">
9871 <cell alignment="center" valignment="top" usebox="none">
9874 \begin_layout Plain Layout
9878 \begin_inset space \textvisiblespace{}
9882 \begin_inset Index idx
9885 \begin_layout Plain Layout
9896 <cell alignment="center" valignment="top" usebox="none">
9899 \begin_layout Plain Layout
9900 \begin_inset Formula $\vec{A}$
9909 <row topspace="1.5mm">
9910 <cell alignment="center" valignment="top" usebox="none">
9913 \begin_layout Plain Layout
9917 \begin_inset space \textvisiblespace{}
9925 <cell alignment="center" valignment="top" usebox="none">
9928 \begin_layout Plain Layout
9929 \begin_inset Formula $\bar{A}$
9938 <row topspace="1.5mm">
9939 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9942 \begin_layout Plain Layout
9946 \begin_inset space \textvisiblespace{}
9954 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9957 \begin_layout Plain Layout
9958 \begin_inset Formula $\mathring{A}$
9972 \begin_inset space \hfill{}
9976 \begin_inset Tabular
9977 <lyxtabular version="3" rows="7" columns="2">
9978 <features booktabs="true" tabularvalignment="middle">
9979 <column alignment="center" valignment="top" width="0pt">
9980 <column alignment="center" valignment="top" width="0pt">
9982 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9985 \begin_layout Plain Layout
9991 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9994 \begin_layout Plain Layout
10001 <row topspace="1.5mm">
10002 <cell alignment="center" valignment="top" usebox="none">
10005 \begin_layout Plain Layout
10009 \begin_inset space \textvisiblespace{}
10017 <cell alignment="center" valignment="top" usebox="none">
10020 \begin_layout Plain Layout
10021 \begin_inset Formula $\tilde{A}$
10030 <row topspace="1.5mm">
10031 <cell alignment="center" valignment="top" usebox="none">
10034 \begin_layout Plain Layout
10038 \begin_inset space \textvisiblespace{}
10046 <cell alignment="center" valignment="top" usebox="none">
10049 \begin_layout Plain Layout
10050 \begin_inset Formula $\hat{A}$
10059 <row topspace="1.5mm">
10060 <cell alignment="center" valignment="top" usebox="none">
10063 \begin_layout Plain Layout
10067 \begin_inset space \textvisiblespace{}
10075 <cell alignment="center" valignment="top" usebox="none">
10078 \begin_layout Plain Layout
10079 \begin_inset Formula $\check{A}$
10088 <row topspace="1.5mm">
10089 <cell alignment="center" valignment="top" usebox="none">
10092 \begin_layout Plain Layout
10096 \begin_inset space \textvisiblespace{}
10104 <cell alignment="center" valignment="top" usebox="none">
10107 \begin_layout Plain Layout
10108 \begin_inset Formula $\acute{A}$
10117 <row topspace="1.5mm">
10118 <cell alignment="center" valignment="top" usebox="none">
10121 \begin_layout Plain Layout
10125 \begin_inset space \textvisiblespace{}
10133 <cell alignment="center" valignment="top" usebox="none">
10136 \begin_layout Plain Layout
10137 \begin_inset Formula $\grave{A}$
10146 <row topspace="1.5mm">
10147 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10150 \begin_layout Plain Layout
10154 \begin_inset space \textvisiblespace{}
10162 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10165 \begin_layout Plain Layout
10166 \begin_inset Formula $\breve{A}$
10180 \begin_inset space \hfill{}
10186 \begin_layout Standard
10187 \begin_inset VSpace bigskip
10193 \begin_layout Standard
10194 You can directly insert accents like é to formulas.
10196 will transform them to the corresponding accent command.
10198 \begin_inset Index idx
10201 \begin_layout Plain Layout
10207 it is better to insert a quotation mark before the vowel.
10208 These two characters are then treated by \SpecialChar LaTeX
10213 character when the formula part with the umlaut is marked as German.
10221 \begin_inset Quotes eld
10225 \begin_inset Quotes erd
10228 umlauts are created as demonstrated in the following example:
10231 \begin_layout Standard
10232 \begin_inset VSpace -2mm
10238 \begin_layout Standard
10240 \begin_inset Tabular
10241 <lyxtabular version="3" rows="3" columns="2">
10242 <features booktabs="true" tabularvalignment="middle">
10243 <column alignment="center" valignment="top" width="0pt">
10244 <column alignment="center" valignment="top">
10246 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10249 \begin_layout Plain Layout
10255 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10258 \begin_layout Plain Layout
10266 <cell alignment="center" valignment="top" usebox="none">
10269 \begin_layout Plain Layout
10270 \begin_inset Quotes grd
10278 <cell alignment="center" valignment="top" usebox="none">
10281 \begin_layout Plain Layout
10282 \begin_inset space \hspace{}
10289 \begin_inset Formula $"i$
10298 <row topspace="1.5mm">
10299 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10302 \begin_layout Plain Layout
10306 \begin_inset space \textvisiblespace{}
10314 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10317 \begin_layout Plain Layout
10318 \begin_inset Formula $\ddot{i}$
10334 \begin_layout Standard
10335 Another advantage to
10341 is that umlauts can directly be converted to mathematical text because
10342 the accent commands above are
10348 in mathematical text
10351 To convert an accented character to mathematical text, only the character
10352 under the accent may be converted.
10353 This applies also for all other conversions, e.
10354 \begin_inset space \thinspace{}
10358 \begin_inset space \space{}
10364 \begin_layout Standard
10365 In mathematical text, umlauts and other accented characters can directly
10369 \begin_layout Standard
10370 \begin_inset VSpace bigskip
10376 \begin_layout Standard
10378 also supports a tilde under the character if the \SpecialChar LaTeX
10384 \begin_inset Index idx
10387 \begin_layout Plain Layout
10388 Packages ! undertilde
10393 is installed on your system:
10396 \begin_layout Standard
10400 \begin_layout Plain Layout
10410 \begin_inset Note Note
10413 \begin_layout Plain Layout
10414 The following table will only be displayed when the \SpecialChar LaTeX
10425 \begin_inset Separator parbreak
10431 \begin_layout Standard
10434 \begin_inset Tabular
10435 <lyxtabular version="3" rows="2" columns="2">
10436 <features booktabs="true" tabularvalignment="middle">
10437 <column alignment="center" valignment="top" width="0pt">
10438 <column alignment="center" valignment="top" width="0pt">
10440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10443 \begin_layout Plain Layout
10449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10452 \begin_layout Plain Layout
10460 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10463 \begin_layout Plain Layout
10467 \begin_inset space \textvisiblespace{}
10475 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10478 \begin_layout Plain Layout
10479 \begin_inset Formula $\utilde{A}$
10495 \begin_layout Standard
10499 \begin_layout Plain Layout
10509 \begin_inset Note Note
10512 \begin_layout Plain Layout
10513 The following will be displayed when the \SpecialChar LaTeX
10526 \begin_layout Standard
10527 You need to install the \SpecialChar LaTeX
10532 to see the rest of this subsection in the output.
10535 \begin_layout Standard
10539 \begin_layout Plain Layout
10551 \begin_layout Standard
10552 \begin_inset Newpage newpage
10558 \begin_layout Subsection
10559 Accents for several Characters
10560 \begin_inset Index idx
10563 \begin_layout Plain Layout
10564 Accents ! for several characters
10572 \begin_layout Standard
10573 \begin_inset space \hfill{}
10577 \begin_inset Tabular
10578 <lyxtabular version="3" rows="5" columns="2">
10579 <features booktabs="true" tabularvalignment="middle">
10580 <column alignment="center" valignment="top" width="0pt">
10581 <column alignment="center" valignment="top" width="0pt">
10583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10586 \begin_layout Plain Layout
10592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10595 \begin_layout Plain Layout
10602 <row topspace="1.5mm">
10603 <cell alignment="center" valignment="top" usebox="none">
10606 \begin_layout Plain Layout
10610 \begin_inset space \textvisiblespace{}
10618 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10621 \begin_layout Plain Layout
10622 \begin_inset Formula $\overleftarrow{A=B}$
10631 <row topspace="1.5mm">
10632 <cell alignment="center" valignment="top" usebox="none">
10635 \begin_layout Plain Layout
10639 \begin_inset space \textvisiblespace{}
10647 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10650 \begin_layout Plain Layout
10651 \begin_inset Formula $\underleftarrow{A=B}$
10660 <row topspace="1.5mm">
10661 <cell alignment="center" valignment="top" usebox="none">
10664 \begin_layout Plain Layout
10668 \begin_inset space \textvisiblespace{}
10676 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10679 \begin_layout Plain Layout
10680 \begin_inset Formula $\overleftrightarrow{A=B}$
10689 <row topspace="1.5mm" bottomspace="1mm">
10690 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10693 \begin_layout Plain Layout
10696 underleftrightarrow
10697 \begin_inset space \textvisiblespace{}
10705 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10708 \begin_layout Plain Layout
10709 \begin_inset Formula $\underleftrightarrow{A=B}$
10723 \begin_inset space \hfill{}
10727 \begin_inset Tabular
10728 <lyxtabular version="3" rows="5" columns="2">
10729 <features booktabs="true" tabularvalignment="middle">
10730 <column alignment="center" valignment="top" width="0pt">
10731 <column alignment="center" valignment="top" width="0pt">
10733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10736 \begin_layout Plain Layout
10742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10745 \begin_layout Plain Layout
10752 <row topspace="1.5mm">
10753 <cell alignment="center" valignment="top" usebox="none">
10756 \begin_layout Plain Layout
10760 \begin_inset space \textvisiblespace{}
10768 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10771 \begin_layout Plain Layout
10772 \begin_inset Formula $\overrightarrow{A=B}$
10781 <row topspace="1.5mm">
10782 <cell alignment="center" valignment="top" usebox="none">
10785 \begin_layout Plain Layout
10789 \begin_inset space \textvisiblespace{}
10797 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10800 \begin_layout Plain Layout
10801 \begin_inset Formula $\underrightarrow{A=B}$
10810 <row topspace="1.5mm">
10811 <cell alignment="center" valignment="top" usebox="none">
10814 \begin_layout Plain Layout
10818 \begin_inset space \textvisiblespace{}
10826 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10829 \begin_layout Plain Layout
10830 \begin_inset Formula $\widetilde{A=B}$
10839 <row topspace="1.5mm" bottomspace="1mm">
10840 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10843 \begin_layout Plain Layout
10847 \begin_inset space \textvisiblespace{}
10855 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10858 \begin_layout Plain Layout
10859 \begin_inset Formula $\widehat{A=B}$
10873 \begin_inset space \hfill{}
10879 \begin_layout Standard
10880 \begin_inset VSpace medskip
10883 With these commands as many characters as you like can be accented.
10896 will only be set in the output with a length of three characters, as shown
10897 in the following example:
10898 \begin_inset Formula
10900 \widetilde{A+B=C-D}
10908 \begin_layout Standard
10916 \begin_inset Index idx
10919 \begin_layout Plain Layout
10934 \begin_inset Index idx
10937 \begin_layout Plain Layout
10945 described in the previous subsection it is also possible to accent several
10952 \begin_inset space \textvisiblespace{}
10956 \begin_inset Formula $\downarrow$
10962 \begin_inset Formula
10964 \underset{***}{A=B}
10972 \begin_layout Section
10974 \begin_inset CommandInset label
10976 name "subsec:Space"
10981 \begin_inset Index idx
10984 \begin_layout Plain Layout
10993 \begin_layout Subsection
10995 \begin_inset CommandInset label
10997 name "subsec:Predefined-Space"
11002 \begin_inset Index idx
11005 \begin_layout Plain Layout
11006 Space ! horizontal ! predefined
11014 \begin_layout Standard
11015 Sometimes it is necessary to insert horizontal space into a formula.
11016 This is done by inserting a protected space (shortcut
11019 arg "command-alternatives space-insert protected ; math-space"
11024 \begin_inset Quotes eld
11030 \begin_inset space \textvisiblespace{}
11036 \begin_inset Quotes erd
11039 appears and by pressing
11043 several times one can select one of eight different space sizes.
11044 The spaces can also be inserted using the math toolbar button
11047 arg "math-insert \\space"
11050 or special commands.
11051 Independent from the inserted command, one can select the size again by
11057 \begin_inset Separator parbreak
11063 \begin_layout Standard
11066 \begin_inset Tabular
11067 <lyxtabular version="3" rows="6" columns="3">
11068 <features booktabs="true" tabularvalignment="middle">
11069 <column alignment="center" valignment="top">
11070 <column alignment="center" valignment="top" width="15col%">
11071 <column alignment="center" valignment="top">
11073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11076 \begin_layout Plain Layout
11082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11085 \begin_layout Plain Layout
11095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11098 \begin_layout Plain Layout
11106 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11109 \begin_layout Plain Layout
11117 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11120 \begin_layout Plain Layout
11126 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11129 \begin_layout Plain Layout
11130 \begin_inset Formula $A\,B$
11140 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11143 \begin_layout Plain Layout
11151 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11154 \begin_layout Plain Layout
11160 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11163 \begin_layout Plain Layout
11164 \begin_inset Formula $A\:B$
11174 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11177 \begin_layout Plain Layout
11185 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11188 \begin_layout Plain Layout
11194 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11197 \begin_layout Plain Layout
11198 \begin_inset Formula $A\;B$
11208 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11211 \begin_layout Plain Layout
11219 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11222 \begin_layout Plain Layout
11228 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11231 \begin_layout Plain Layout
11232 \begin_inset Formula $A\quad B$
11242 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11245 \begin_layout Plain Layout
11253 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11256 \begin_layout Plain Layout
11262 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11265 \begin_layout Plain Layout
11266 \begin_inset Formula $A\qquad B$
11280 \begin_inset space \hfill{}
11284 \begin_inset Tabular
11285 <lyxtabular version="3" rows="6" columns="3">
11286 <features booktabs="true" tabularvalignment="middle">
11287 <column alignment="center" valignment="top">
11288 <column alignment="center" valignment="top" width="15col%">
11289 <column alignment="center" valignment="top">
11291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11294 \begin_layout Plain Layout
11300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11303 \begin_layout Plain Layout
11313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11316 \begin_layout Plain Layout
11324 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11327 \begin_layout Plain Layout
11335 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11338 \begin_layout Plain Layout
11344 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11347 \begin_layout Plain Layout
11348 \begin_inset Formula $A\hfill B$
11358 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11361 \begin_layout Plain Layout
11369 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11372 \begin_layout Plain Layout
11378 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11381 \begin_layout Plain Layout
11382 \begin_inset Formula $A\hspace*{1em}B$
11392 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11395 \begin_layout Plain Layout
11403 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11406 \begin_layout Plain Layout
11412 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11415 \begin_layout Plain Layout
11416 \begin_inset Formula $A\hspace{1em}B$
11426 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11429 \begin_layout Plain Layout
11433 \begin_inset space \textvisiblespace{}
11441 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11444 \begin_layout Plain Layout
11450 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11453 \begin_layout Plain Layout
11454 \begin_inset Formula $A\ B$
11464 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11467 \begin_layout Plain Layout
11475 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11478 \begin_layout Plain Layout
11484 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11487 \begin_layout Plain Layout
11488 \begin_inset Formula $A\!B$
11504 \begin_layout Standard
11506 \begin_inset space ~
11510 \begin_inset space \thinspace{}
11514 \begin_inset space \thinspace{}
11517 7 are variable spaces which are explained in
11518 \begin_inset CommandInset ref
11520 reference "subsec:Variable-Space"
11526 \begin_inset space ~
11529 9 seems to produce no space.
11530 It is displayed red in \SpecialChar LyX
11531 contrary to the other sizes, because it is a negative
11533 There are two more negative spaces:
11534 \begin_inset Separator parbreak
11540 \begin_layout Standard
11542 \begin_inset Tabular
11543 <lyxtabular version="3" rows="3" columns="3">
11544 <features booktabs="true" tabularvalignment="middle">
11545 <column alignment="center" valignment="middle" width="6.8cm">
11546 <column alignment="center" valignment="top" width="0pt">
11547 <column alignment="center" valignment="top" width="0pt">
11549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11552 \begin_layout Plain Layout
11558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11561 \begin_layout Plain Layout
11569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11572 \begin_layout Plain Layout
11582 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11585 \begin_layout Plain Layout
11590 keystrokes after inserting the protected space
11595 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11598 \begin_layout Plain Layout
11604 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11607 \begin_layout Plain Layout
11615 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11618 \begin_layout Plain Layout
11624 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11627 \begin_layout Plain Layout
11628 \begin_inset Formula $A\negmedspace B$
11636 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11639 \begin_layout Plain Layout
11640 \begin_inset Formula $A\negthickspace B$
11656 \begin_layout Standard
11657 Negative spaces can lead to characters overlapping each other.
11658 Thus they can be used to enforce ligatures, which are e.
11659 \begin_inset space \thinspace{}
11663 \begin_inset space \space{}
11666 useful for summation operators:
11667 \begin_inset Separator parbreak
11673 \begin_layout Standard
11675 \begin_inset Tabular
11676 <lyxtabular version="3" rows="3" columns="2">
11677 <features booktabs="true" tabularvalignment="middle">
11678 <column alignment="center" valignment="top" width="0pt">
11679 <column alignment="center" valignment="top">
11681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11684 \begin_layout Plain Layout
11690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11693 \begin_layout Plain Layout
11701 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11704 \begin_layout Plain Layout
11710 \begin_inset space \textvisiblespace{}
11718 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11721 \begin_layout Plain Layout
11722 \begin_inset Formula $\sum\sum f_{kl}$
11732 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11735 \begin_layout Plain Layout
11743 \begin_inset space \textvisiblespace{}
11751 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11754 \begin_layout Plain Layout
11755 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11771 \begin_layout Standard
11773 \begin_inset VSpace medskip
11779 \begin_layout Standard
11781 Relations like for example equal signs, are always surrounded by space.
11782 To suppress this, the equal sign is placed into a \SpecialChar TeX
11784 The following example demonstrates this:
11785 \begin_inset Separator parbreak
11791 \begin_layout Standard
11793 \begin_inset Tabular
11794 <lyxtabular version="3" rows="2" columns="2">
11795 <features tabularvalignment="middle">
11796 <column alignment="center" valignment="top" width="0pt">
11797 <column alignment="center" valignment="top" width="0pt">
11799 <cell alignment="center" valignment="top" usebox="none">
11802 \begin_layout Plain Layout
11808 <cell alignment="center" valignment="top" usebox="none">
11811 \begin_layout Plain Layout
11812 \begin_inset Formula $A=B$
11822 <cell alignment="center" valignment="top" usebox="none">
11825 \begin_layout Plain Layout
11826 equation without space
11831 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11834 \begin_layout Plain Layout
11835 \begin_inset Formula $A{=}B$
11851 \begin_layout Standard
11853 The command for the last formula is:
11858 \begin_inset Formula $\to$
11864 \begin_layout Standard
11865 \begin_inset VSpace bigskip
11871 \begin_layout Standard
11872 Spaces are needed for physical units, because the space between the value
11873 and the unit is the smallest one and not a normal space.
11874 For units in text, the smallest space is inserted via the menu
11876 Insert\SpecialChar menuseparator
11877 Formatting\SpecialChar menuseparator
11879 \begin_inset space ~
11887 arg "space-insert thin"
11893 \begin_layout Standard
11894 An example to visualize the difference:
11897 \begin_layout Standard
11898 \begin_inset Tabular
11899 <lyxtabular version="3" rows="2" columns="2">
11900 <features tabularvalignment="middle">
11901 <column alignment="left" valignment="top">
11902 <column alignment="left" valignment="top">
11904 <cell alignment="center" valignment="top" usebox="none">
11907 \begin_layout Plain Layout
11909 \begin_inset Formula $\cdot$
11917 <cell alignment="center" valignment="top" usebox="none">
11920 \begin_layout Plain Layout
11921 space between value and unit
11928 <cell alignment="center" valignment="top" usebox="none">
11931 \begin_layout Plain Layout
11933 \begin_inset space \thinspace{}
11937 \begin_inset Formula $\cdot$
11945 <cell alignment="center" valignment="top" usebox="none">
11948 \begin_layout Plain Layout
11949 smallest space between value and unit
11962 \begin_layout Subsection
11967 \begin_layout Plain Layout
11980 \begin_layout Plain Layout
11981 for vertical space in formulas see
11982 \begin_inset CommandInset ref
11984 reference "subsec:Line-Separation"
11997 \begin_layout Plain Layout
12005 \begin_inset Note Note
12008 \begin_layout Plain Layout
12011 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12014 \begin_layout Plain Layout
12017 texorpdfstring is in section
12018 \begin_inset CommandInset ref
12020 reference "subsec:Formulas-in-Section"
12030 \begin_inset CommandInset label
12032 name "subsec:Variable-Space"
12037 \begin_inset Index idx
12040 \begin_layout Plain Layout
12041 Space ! horizontal ! variable
12049 \begin_layout Standard
12050 Space with a defined length can be inserted with the command
12057 \begin_inset Index idx
12060 \begin_layout Plain Layout
12070 \begin_inset Quotes eld
12076 \begin_inset space \textvisiblespace{}
12082 \begin_inset Quotes erd
12086 The length can be specified by left-clicking on the
12087 \begin_inset Quotes eld
12093 \begin_inset space \textvisiblespace{}
12099 \begin_inset Quotes erd
12103 The length may also be negative.
12104 When a space would be the first character in a line it would be omitted.
12105 To force its output use the command
12117 or left-click on the
12118 \begin_inset Quotes eld
12124 \begin_inset space \textvisiblespace{}
12130 \begin_inset Quotes erd
12133 and check the option
12138 \begin_inset Newline newline
12141 To insert as much space as is available, the command
12148 \begin_inset Index idx
12151 \begin_layout Plain Layout
12162 \begin_layout Standard
12164 \begin_inset Tabular
12165 <lyxtabular version="3" rows="4" columns="2">
12166 <features booktabs="true" tabularvalignment="middle">
12167 <column alignment="center" valignment="top" width="0pt">
12168 <column alignment="center" valignment="top">
12170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12173 \begin_layout Plain Layout
12181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12184 \begin_layout Plain Layout
12192 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12195 \begin_layout Plain Layout
12199 \begin_inset space \textvisiblespace{}
12205 \begin_inset space \thinspace{}
12213 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12216 \begin_layout Plain Layout
12217 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12227 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12230 \begin_layout Plain Layout
12234 \begin_inset space \textvisiblespace{}
12240 \begin_inset space \thinspace{}
12248 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12251 \begin_layout Plain Layout
12252 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12265 \begin_layout Plain Layout
12269 \begin_inset space \textvisiblespace{}
12277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12280 \begin_layout Plain Layout
12281 \begin_inset Formula $A=A\hfill B=B$
12297 \begin_layout Standard
12298 In the last example the available space is given by the longest column entry
12300 In an inline formula the space depends on the length of the line in which
12308 Thus, when the line uses the full width, no space will be created.
12315 only has an effect on displayed formulas when the formula style
12320 (Formula styles are explained in
12321 \begin_inset CommandInset ref
12323 reference "sec:Formula-Styles"
12330 \begin_layout Standard
12337 , there are the commands
12349 that fill the space with a pattern, see
12350 \begin_inset CommandInset ref
12352 reference "subsec:Ellipses"
12359 \begin_layout Standard
12360 For text, variable space can be inserted via the menu
12362 Insert\SpecialChar menuseparator
12363 Formatting\SpecialChar menuseparator
12365 \begin_inset space ~
12373 \begin_layout Standard
12374 This is a line with
12375 \begin_inset space \hspace{}
12380 \begin_inset space \thinspace{}
12386 \begin_layout Standard
12387 This is a line with
12388 \begin_inset space \hfill{}
12394 \begin_layout Subsection
12395 Space besides inline Formulas
12396 \begin_inset Index idx
12399 \begin_layout Plain Layout
12400 Space ! besides inline formulas
12408 \begin_layout Standard
12409 The space that surrounds inline formulas can be adjusted with the length
12417 \begin_inset Index idx
12420 \begin_layout Plain Layout
12429 The value of a length is set with the command
12436 \begin_inset Index idx
12439 \begin_layout Plain Layout
12447 which has the following scheme:
12450 \begin_layout Standard
12455 setlength{length name}{value}
12458 \begin_layout Standard
12466 \begin_inset space \thinspace{}
12472 \begin_layout Standard
12482 \begin_layout Standard
12483 is inserted in \SpecialChar TeX
12486 \begin_inset space \thinspace{}
12489 mm space will now be set around all inline formulas:
12493 \begin_layout Plain Layout
12507 \begin_layout Standard
12508 This is a line with an inline formula
12509 \begin_inset Formula $A=B$
12513 \begin_inset space \thinspace{}
12516 mm surrounding space.
12520 \begin_layout Plain Layout
12534 \begin_layout Standard
12535 To return to the predefined value,
12541 is set to the value 0
12542 \begin_inset space \thinspace{}
12548 \begin_layout Standard
12549 \begin_inset Newpage newpage
12555 \begin_layout Section
12557 \begin_inset Index idx
12560 \begin_layout Plain Layout
12567 \begin_inset Index idx
12570 \begin_layout Plain Layout
12575 \begin_layout Plain Layout
12586 \begin_layout Plain Layout
12601 \begin_layout Standard
12602 Boxes for text are described in chapter
12609 \begin_inset space ~
12617 \begin_layout Subsection
12619 \begin_inset CommandInset label
12621 name "subsec:Boxes-with-Frame"
12626 \begin_inset Index idx
12629 \begin_layout Plain Layout
12638 \begin_layout Standard
12639 It is possible to frame a formula or part of one with the commands
12646 \begin_inset Index idx
12649 \begin_layout Plain Layout
12664 \begin_inset Index idx
12667 \begin_layout Plain Layout
12678 \begin_layout Standard
12679 When one of these commands is inserted in a formula, a blue box appears
12680 within a frame to enter formula parts.
12687 an additional formula has to be created by
12691 within this box, because the box content will otherwise be treated as mathemati
12699 is used, a new formula is automatically created inside the frame.
12702 \begin_layout Standard
12709 is not suitable to frame displayed formulas because the formula will always
12710 be set in the size of the text.
12717 is in contrary not suitable to frame inline formulas, because the formula
12718 will always be set in the size of a displayed formula.
12721 \begin_layout Standard
12735 \begin_inset Index idx
12738 \begin_layout Plain Layout
12746 where additionally the frame width and the alignment can be specified.
12753 is used in the following scheme:
12756 \begin_layout Standard
12761 framebox[frame width][position]{box content}
12764 \begin_layout Standard
12765 The position can either be
12782 right aligns the formula in the box.
12783 When no position is given, the formula will be centered.
12784 \begin_inset Newline newline
12787 If no width is given, also no position can be given.
12788 In this case the frame width is adjusted to the box content like for
12797 \begin_layout Standard
12804 is inserted, a box appears containing three blue boxes.
12805 The first two boxes are surrounded by brackets and denote the two optional
12807 The third box is for formula parts like for
12814 \begin_inset Separator parbreak
12820 \begin_layout Standard
12822 \begin_inset Tabular
12823 <lyxtabular version="3" rows="5" columns="2">
12824 <features booktabs="true" tabularvalignment="middle">
12825 <column alignment="center" valignment="top" width="0pt">
12826 <column alignment="center" valignment="top">
12828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12831 \begin_layout Plain Layout
12837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12840 \begin_layout Plain Layout
12847 <row topspace="1.5mm">
12848 <cell alignment="center" valignment="top" usebox="none">
12851 \begin_layout Plain Layout
12855 \begin_inset space \textvisiblespace{}
12865 \begin_inset space \textvisiblespace{}
12873 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12876 \begin_layout Plain Layout
12877 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12886 <row topspace="1.5mm">
12887 <cell alignment="center" valignment="top" usebox="none">
12890 \begin_layout Plain Layout
12894 \begin_inset space \textvisiblespace{}
12900 \begin_inset space \textvisiblespace{}
12908 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12911 \begin_layout Plain Layout
12912 \begin_inset Formula $\boxed{\int A=B}$
12921 <row topspace="1.5mm">
12922 <cell alignment="center" valignment="top" usebox="none">
12925 \begin_layout Plain Layout
12929 \begin_inset space \textvisiblespace{}
12937 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12940 \begin_layout Plain Layout
12941 \begin_inset Formula $A+\fbox{B}$
12950 <row topspace="1.5mm" bottomspace="1mm">
12951 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12954 \begin_layout Plain Layout
12958 \begin_inset space \textvisiblespace{}
12962 \begin_inset Formula $\to$
12966 \begin_inset Formula $\to$
12976 \begin_inset space \textvisiblespace{}
12980 \begin_inset Formula $\downarrow$
12988 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12991 \begin_layout Plain Layout
12992 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13008 \begin_layout Standard
13009 The frame thickness can also be adjusted.
13010 To do this the following commands have to be inserted in \SpecialChar TeX
13015 \begin_layout Standard
13025 \begin_inset Quotes eld
13029 \begin_inset Quotes erd
13043 \begin_inset Quotes eld
13047 \begin_inset Quotes erd
13053 \begin_layout Standard
13054 \begin_inset Quotes eld
13058 \begin_inset Quotes erd
13061 specifies the minimal distance between the frame and the first character
13063 An example for this is the following framed formula:
13067 \begin_layout Plain Layout
13079 \begin_inset Formula
13086 Before this formula the commands
13089 \begin_layout Standard
13111 \begin_layout Standard
13112 were inserted in \SpecialChar TeX
13114 The given values are used for all following boxes.
13117 \begin_layout Standard
13118 To return to the standard frame size, the command
13121 \begin_layout Standard
13146 \begin_layout Plain Layout
13160 \begin_layout Standard
13161 is inserted in \SpecialChar TeX
13162 mode before the next formula.
13165 \begin_layout Subsection
13166 Boxes without Frame
13167 \begin_inset CommandInset label
13169 name "subsec:Boxes-without-Frame"
13174 \begin_inset Index idx
13177 \begin_layout Plain Layout
13178 Boxes ! without frame
13186 \begin_layout Standard
13187 For boxes without a frame there are the following box commands:
13194 \begin_inset Index idx
13197 \begin_layout Plain Layout
13212 \begin_inset Index idx
13215 \begin_layout Plain Layout
13230 \begin_inset Index idx
13233 \begin_layout Plain Layout
13244 \begin_layout Standard
13251 a box can be super- or subscripted.
13252 But in contrary to normal super- and subscripting, the characters in the
13253 box keep their font size.
13260 is used in the following scheme:
13263 \begin_layout Standard
13268 raisebox{height}{box content}
13271 \begin_layout Standard
13272 When the box should contain a formula, an extra formula is needed like for
13283 \begin_inset Note Greyedout
13286 \begin_layout Plain Layout
13297 this extra formula is created by pressing
13301 twice instead of once because \SpecialChar LyX
13302 doesn't yet support
13316 \begin_inset Separator parbreak
13322 \begin_layout Standard
13324 \begin_inset Tabular
13325 <lyxtabular version="3" rows="4" columns="2">
13326 <features booktabs="true" tabularvalignment="middle">
13327 <column alignment="center" valignment="top" width="0pt">
13328 <column alignment="center" valignment="top">
13330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13333 \begin_layout Plain Layout
13339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13342 \begin_layout Plain Layout
13350 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13353 \begin_layout Plain Layout
13357 \begin_inset Formula $\to$
13363 \begin_inset Formula $\to$
13371 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13374 \begin_layout Plain Layout
13375 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13385 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13388 \begin_layout Plain Layout
13392 \begin_inset Formula $\to$
13398 \begin_inset Formula $\to$
13406 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13409 \begin_layout Plain Layout
13410 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13423 \begin_layout Plain Layout
13427 \begin_inset Formula $\to$
13443 \begin_inset space \textvisiblespace{}
13451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13454 \begin_layout Plain Layout
13455 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13471 \begin_layout Standard
13496 , with the difference that there is no frame.
13499 \begin_layout Subsection
13501 \begin_inset CommandInset label
13503 name "subsec:Colored-Boxes"
13508 \begin_inset Index idx
13511 \begin_layout Plain Layout
13520 \begin_layout Standard
13521 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13530 \begin_layout Plain Layout
13531 The \SpecialChar LaTeX
13536 is part of every \SpecialChar LaTeX
13537 standard installation.
13543 \begin_inset Index idx
13546 \begin_layout Plain Layout
13552 has to be loaded in the \SpecialChar LaTeX
13553 -preamble with the line
13557 \begin_layout Plain Layout
13558 When text is colored somewhere in the document with a predefined color,
13560 loads the \SpecialChar LaTeX
13566 Thus it is possible that the package is loaded twice, but this does not
13573 \begin_inset Note Note
13576 \begin_layout Plain Layout
13577 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13586 \begin_layout Standard
13594 \begin_layout Standard
13595 \begin_inset VSpace medskip
13598 To color boxes, the command
13605 \begin_inset Index idx
13608 \begin_layout Plain Layout
13616 is used in the following scheme:
13619 \begin_layout Standard
13624 colorbox{color}{box content}
13627 \begin_layout Standard
13628 The box content can also be a box and a
13634 can also be part of another box (see the 2nd and 3rd example).
13635 When the box should contain a formula, an extra formula has to be created,
13636 the same way as for
13646 \begin_layout Plain Layout
13647 This also applies for the command
13661 \begin_layout Standard
13662 One of the following predefined colors can be chosen:
13665 \begin_layout Standard
13699 \begin_inset Separator parbreak
13705 \begin_layout Standard
13707 \begin_inset Tabular
13708 <lyxtabular version="3" rows="4" columns="2">
13709 <features booktabs="true" tabularvalignment="middle">
13710 <column alignment="center" valignment="top" width="0pt">
13711 <column alignment="center" valignment="top">
13713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13716 \begin_layout Plain Layout
13722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13725 \begin_layout Plain Layout
13733 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13736 \begin_layout Plain Layout
13740 \begin_inset Formula $\to$
13750 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13753 \begin_layout Plain Layout
13754 \begin_inset Formula $\colorbox{yellow}{A=B}$
13763 <row topspace="1.5mm">
13764 <cell alignment="center" valignment="top" usebox="none">
13767 \begin_layout Plain Layout
13771 \begin_inset Formula $\to$
13779 \begin_inset space \textvisiblespace{}
13787 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13790 \begin_layout Plain Layout
13791 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13800 <row topspace="1.5mm" bottomspace="1mm">
13801 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13804 \begin_layout Plain Layout
13808 \begin_inset space \textvisiblespace{}
13814 \begin_inset Formula $\to$
13830 \begin_inset space \textvisiblespace{}
13838 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13841 \begin_layout Plain Layout
13842 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13858 \begin_layout Standard
13865 only colors the box but not the characters in the box.
13866 To color all characters, the whole formula is highlighted and the desired
13867 color is chosen in the
13870 \begin_inset space ~
13876 The dialog can be called with the toolbar button
13879 arg "dialog-show character"
13884 Edit\SpecialChar menuseparator
13886 \begin_inset space ~
13889 Style\SpecialChar menuseparator
13893 The formula number then has the same color as the formula.
13894 When the formula number should get another color than the formula characters,
13895 the color must be changed within the formula.
13898 \begin_layout Standard
13902 \begin_layout Standard
13905 \begin_inset Formula
13907 \int A=B\label{eq:red}
13915 \begin_inset Formula
13917 \textcolor{red}{\int A=B}\label{eq:redgreen}
13925 \begin_layout Standard
13927 \begin_inset CommandInset ref
13933 is completely colored red.
13934 \begin_inset Newline newline
13938 \begin_inset CommandInset ref
13940 reference "eq:redgreen"
13944 was first completely colored green to set the color for the formula number.
13945 Subsequently the formula characters were colored red.
13948 \begin_layout Standard
13949 \begin_inset VSpace bigskip
13952 To color the frame different than the rest of the box, the command
13959 \begin_inset Index idx
13962 \begin_layout Plain Layout
13970 is used in the following scheme:
13973 \begin_layout Standard
13978 fcolorbox{frame color}{color}{box content}
13981 \begin_layout Standard
13988 is an extension of the command
13995 The frame width is set, like for
14018 \begin_layout Plain Layout
14030 \begin_inset Formula
14032 \fcolorbox{cyan}{magenta}{A=B}
14041 \begin_layout Plain Layout
14055 \begin_layout Standard
14056 This formula was created with the command
14057 \begin_inset Newline newline
14065 \begin_inset Formula $\to$
14071 \begin_inset Formula $\to$
14081 \begin_layout Standard
14082 \begin_inset VSpace bigskip
14085 To use other colors than the predefined ones, they have to be defined first.
14088 \begin_layout Standard
14089 One can for example define the color
14090 \begin_inset Quotes eld
14098 \begin_inset Quotes erd
14101 with the \SpecialChar LaTeX
14105 \begin_layout Standard
14110 definecolor{darkgreen}{cmyk}{0.5,
14125 \begin_inset Index idx
14128 \begin_layout Plain Layout
14139 \begin_layout Standard
14144 is the color space that denotes the colors
14161 The four comma separated numbers are the portion factor for the corresponding
14162 colors of the color space.
14163 The factors can be in the range of 0
14164 \begin_inset space \thinspace{}
14168 \begin_inset space \thinspace{}
14176 also the color space
14180 can be used for definitions.
14197 , so that there are in this case three portion factors for the corresponding
14199 Furthermore there is the color space
14203 with one portion factor for the gray value.
14206 \begin_layout Standard
14207 As example a framed box with the new defined color
14211 where the characters have been colored
14216 \begin_inset Formula
14218 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14226 \begin_layout Standard
14227 Self-defined colors can also be used for text with the help of the command
14235 \begin_inset Index idx
14238 \begin_layout Plain Layout
14247 \begin_layout Standard
14251 \begin_layout Plain Layout
14255 textcolor{darkgreen}{
14261 \begin_inset Quotes eld
14265 \begin_inset Quotes erd
14272 \begin_layout Plain Layout
14282 \begin_layout Standard
14290 \begin_inset Index idx
14293 \begin_layout Plain Layout
14301 is used in the scheme
14305 textcolor{color}{characters to color}
14310 \begin_layout Subsection
14312 \begin_inset CommandInset label
14314 name "subsec:Paragraph-Boxes"
14319 \begin_inset Index idx
14322 \begin_layout Plain Layout
14323 Boxes ! as paragraph
14331 \begin_layout Standard
14332 A box that can contain several lines and paragraphs, a so-called paragraph
14333 box (parbox), can be created with the menu
14335 Insert\SpecialChar menuseparator
14338 or the toolbar button
14347 \begin_layout Standard
14348 The following example shows a framed parbox in a line:
14351 \begin_layout Standard
14352 \begin_inset VSpace medskip
14356 \begin_inset Box Boxed
14366 height_special "totalheight"
14371 backgroundcolor "none"
14374 \begin_layout Plain Layout
14375 This is a paragraph box.
14377 \begin_inset space \thinspace{}
14380 cm long and can also contain formulas:
14381 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14392 \begin_layout Standard
14393 \begin_inset VSpace medskip
14399 \begin_layout Standard
14400 Such a box is created by right-clicking on the gray box inset.
14401 A dialog pops up showing the box properties.
14415 \begin_inset space \thinspace{}
14420 Vertical Box Alignment
14425 \begin_layout Standard
14426 \begin_inset VSpace medskip
14429 In \SpecialChar LaTeX
14430 a parbox is created with the command
14437 \begin_inset Index idx
14440 \begin_layout Plain Layout
14448 which has the following scheme:
14451 \begin_layout Standard
14456 parbox[position]{width}{box content}
14459 \begin_layout Standard
14474 \begin_inset Quotes eld
14478 \begin_inset Quotes erd
14481 means that the box is aligned within the surrounding text with its last
14488 \begin_inset Quotes eld
14492 \begin_inset Quotes erd
14495 this is done with the first line.
14496 When no position is given, the box will be vertically centered, see section
14504 \begin_inset space ~
14509 manual for examples.
14512 \begin_layout Standard
14513 \begin_inset VSpace bigskip
14516 To frame formulas completely, including the formula number, the formula
14517 must be set into a parbox.
14518 To do this, the command
14532 is inserted in \SpecialChar TeX
14533 mode before the formula.
14541 \begin_inset Index idx
14544 \begin_layout Plain Layout
14552 is hereby the line width set for the document.
14553 Because the frame is outside the parbox, 2
14554 \begin_inset space \thinspace{}
14557 times the frame separation and the frame thickness must be subtracted from
14559 As this is not automatically done by \SpecialChar LyX
14564 \begin_layout Plain Layout
14565 \begin_inset CommandInset href
14567 name "LyX-bug #4483"
14568 target "http://www.lyx.org/trac/ticket/4483"
14578 mode has to be used.
14579 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14588 \begin_layout Plain Layout
14593 is part of every \SpecialChar LaTeX
14594 standard installation.
14600 \begin_inset Index idx
14603 \begin_layout Plain Layout
14609 must be loaded in the \SpecialChar LaTeX
14610 -preamble with the line
14613 \begin_layout Standard
14621 \begin_layout Standard
14622 Behind the formula both boxes are closed by entering
14626 in \SpecialChar TeX
14628 Here is an example:
14632 \begin_layout Plain Layout
14646 \begin_layout Standard
14650 \begin_layout Plain Layout
14668 \begin_inset Formula
14670 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14679 \begin_layout Plain Layout
14690 \begin_layout Plain Layout
14704 \begin_layout Standard
14705 \begin_inset VSpace medskip
14708 As a parbox is used as the argument of
14714 , there is in this case no difference between
14729 \begin_layout Standard
14730 \begin_inset VSpace bigskip
14733 Paragraph boxes are very useful to comment formulas directly.
14740 is used in combination with the command
14754 \begin_inset CommandInset ref
14756 reference "subsec:User-defined-Numbering"
14763 \begin_layout Standard
14764 An example of a formula commented with
14773 \begin_layout Standard
14777 \begin_layout Plain Layout
14790 This is a description.
14791 It is distinctly separated from the formula and multiline.
14795 \begin_layout Plain Layout
14807 \begin_layout Standard
14808 Such a formula must be inserted completely in \SpecialChar TeX
14809 mode because \SpecialChar LyX
14811 support the command
14818 The formula is created with the following command sequence:
14821 \begin_layout Standard
14834 is inserted in \SpecialChar TeX
14839 \begin_layout Plain Layout
14840 When the formula style
14852 can also be replaced by
14859 (formula styles see
14860 \begin_inset CommandInset ref
14862 reference "sec:Formula-Styles"
14871 Then the description follows as normal text and finally
14877 is inserted in \SpecialChar TeX
14891 hereby create a displayed formula.
14894 \begin_layout Standard
14901 can be seen in this example that was
14902 \begin_inset Quotes eld
14906 \begin_inset Quotes erd
14909 using the mathematical textmode:
14910 \begin_inset Formula
14912 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14920 \begin_layout Section
14922 \begin_inset Index idx
14925 \begin_layout Plain Layout
14934 \begin_layout Subsection
14936 \begin_inset CommandInset label
14938 name "subsec:Big-Operators"
14943 \begin_inset Index idx
14946 \begin_layout Plain Layout
14953 \begin_inset Index idx
14956 \begin_layout Plain Layout
14963 \begin_inset Index idx
14966 \begin_layout Plain Layout
14975 \begin_layout Standard
14976 To be able to use all integral operators listed here, the option
14978 Use esint package automatically
14980 must be set in the document settings under
14983 \begin_inset space ~
14991 \begin_layout Standard
14992 \begin_inset space \hfill{}
14996 \begin_inset Tabular
14997 <lyxtabular version="3" rows="11" columns="2">
14998 <features booktabs="true" tabularvalignment="middle">
14999 <column alignment="center" valignment="top" width="0pt">
15000 <column alignment="center" valignment="top" width="0pt">
15002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15005 \begin_layout Plain Layout
15011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15014 \begin_layout Plain Layout
15022 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15025 \begin_layout Plain Layout
15029 \begin_inset Index idx
15032 \begin_layout Plain Layout
15045 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15048 \begin_layout Plain Layout
15049 \begin_inset Formula $\int$
15059 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15062 \begin_layout Plain Layout
15070 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15073 \begin_layout Plain Layout
15074 \begin_inset Formula $\oint$
15084 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15087 \begin_layout Plain Layout
15095 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15098 \begin_layout Plain Layout
15099 \begin_inset Formula $\ointctrclockwise$
15109 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15112 \begin_layout Plain Layout
15120 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15123 \begin_layout Plain Layout
15124 \begin_inset Formula $\ointclockwise$
15134 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15137 \begin_layout Plain Layout
15145 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15148 \begin_layout Plain Layout
15149 \begin_inset Formula $\sqint$
15159 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15162 \begin_layout Plain Layout
15170 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15173 \begin_layout Plain Layout
15175 \begin_inset Formula $\fint$
15185 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15188 \begin_layout Plain Layout
15196 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15199 \begin_layout Plain Layout
15201 \begin_inset Formula $\landupint$
15211 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15214 \begin_layout Plain Layout
15222 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15225 \begin_layout Plain Layout
15227 \begin_inset Formula $\landdownint$
15237 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15240 \begin_layout Plain Layout
15248 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15251 \begin_layout Plain Layout
15252 \begin_inset Formula $\bigcap$
15262 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15265 \begin_layout Plain Layout
15273 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15276 \begin_layout Plain Layout
15277 \begin_inset Formula $\bigcup$
15291 \begin_inset space \hfill{}
15295 \begin_inset Tabular
15296 <lyxtabular version="3" rows="11" columns="2">
15297 <features booktabs="true" tabularvalignment="middle">
15298 <column alignment="center" valignment="top" width="0pt">
15299 <column alignment="center" valignment="top" width="0pt">
15301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15304 \begin_layout Plain Layout
15310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15313 \begin_layout Plain Layout
15321 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15324 \begin_layout Plain Layout
15328 \begin_inset Index idx
15331 \begin_layout Plain Layout
15344 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15347 \begin_layout Plain Layout
15348 \begin_inset Formula $\sum$
15358 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15361 \begin_layout Plain Layout
15365 \begin_inset Index idx
15368 \begin_layout Plain Layout
15375 \begin_layout Plain Layout
15394 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15397 \begin_layout Plain Layout
15398 \begin_inset Formula $\prod$
15408 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15411 \begin_layout Plain Layout
15419 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15422 \begin_layout Plain Layout
15423 \begin_inset Formula $\coprod$
15433 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15436 \begin_layout Plain Layout
15444 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15447 \begin_layout Plain Layout
15448 \begin_inset Formula $\bigodot$
15458 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15461 \begin_layout Plain Layout
15469 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15472 \begin_layout Plain Layout
15473 \begin_inset Formula $\bigotimes$
15483 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15486 \begin_layout Plain Layout
15494 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15497 \begin_layout Plain Layout
15498 \begin_inset Formula $\bigoplus$
15508 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15511 \begin_layout Plain Layout
15519 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15522 \begin_layout Plain Layout
15523 \begin_inset Formula $\bigwedge$
15533 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15536 \begin_layout Plain Layout
15544 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15547 \begin_layout Plain Layout
15548 \begin_inset Formula $\bigvee$
15558 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15561 \begin_layout Plain Layout
15569 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15572 \begin_layout Plain Layout
15573 \begin_inset Formula $\bigsqcup$
15583 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15586 \begin_layout Plain Layout
15594 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15597 \begin_layout Plain Layout
15598 \begin_inset Formula $\biguplus$
15612 \begin_inset space \hfill{}
15618 \begin_layout Standard
15619 All big operators can also be inserted via the math toolbar button
15622 arg "math-insert \\intop"
15628 \begin_layout Standard
15629 The operators are called big because they are bigger than the sometimes
15630 equal looking binary operators.
15631 All big operators can have limits as described in the next subsection.
15634 \begin_layout Standard
15635 For all integral operators there is a second version available, ending in
15653 These operators are different from
15660 \begin_inset space \space{}
15663 in the style the operator limits are displayed, see
15664 \begin_inset CommandInset ref
15666 reference "subsec:Operator-Limits"
15674 \begin_layout Subsubsection*
15675 Advice for Integrals
15678 \begin_layout Standard
15683 in an integral is an operator, that therefore has to be set upright.
15684 This is done by highlighting the
15688 and using the keyboard shortcut
15698 \begin_layout Plain Layout
15704 \begin_inset CommandInset ref
15706 reference "subsec:Font-Styles"
15716 Finally the smallest space is inserted before the
15720 , as this is usual for operators.
15724 \begin_layout Standard
15726 \begin_inset Formula $\int A(x)dx$
15730 \begin_inset Newline newline
15734 \begin_inset Phantom HPhantom
15737 \begin_layout Plain Layout
15744 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15750 \begin_layout Standard
15751 For multiple integrals there are the following commands:
15752 \begin_inset VSpace medskip
15758 \begin_layout Standard
15759 \begin_inset space \hfill{}
15763 \begin_inset Tabular
15764 <lyxtabular version="3" rows="4" columns="2">
15765 <features booktabs="true" tabularvalignment="middle">
15766 <column alignment="center" valignment="top" width="0pt">
15767 <column alignment="center" valignment="top" width="0pt">
15769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15772 \begin_layout Plain Layout
15778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15781 \begin_layout Plain Layout
15788 <row bottomspace="1mm">
15789 <cell alignment="center" valignment="top" usebox="none">
15792 \begin_layout Plain Layout
15800 <cell alignment="center" valignment="top" usebox="none">
15803 \begin_layout Plain Layout
15804 \begin_inset Formula $\iint$
15813 <row bottomspace="1mm">
15814 <cell alignment="center" valignment="top" usebox="none">
15817 \begin_layout Plain Layout
15825 <cell alignment="center" valignment="top" usebox="none">
15828 \begin_layout Plain Layout
15829 \begin_inset Formula $\oiint$
15838 <row bottomspace="1mm">
15839 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15842 \begin_layout Plain Layout
15850 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15853 \begin_layout Plain Layout
15854 \begin_inset Formula $\sqiint$
15868 \begin_inset space \hfill{}
15872 \begin_inset Tabular
15873 <lyxtabular version="3" rows="4" columns="2">
15874 <features booktabs="true" tabularvalignment="middle">
15875 <column alignment="center" valignment="top" width="0pt">
15876 <column alignment="center" valignment="top" width="0pt">
15878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15881 \begin_layout Plain Layout
15887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15890 \begin_layout Plain Layout
15897 <row bottomspace="1mm">
15898 <cell alignment="center" valignment="top" usebox="none">
15901 \begin_layout Plain Layout
15909 <cell alignment="center" valignment="top" usebox="none">
15912 \begin_layout Plain Layout
15913 \begin_inset Formula $\iiint$
15922 <row bottomspace="1mm">
15923 <cell alignment="center" valignment="top" usebox="none">
15926 \begin_layout Plain Layout
15934 <cell alignment="center" valignment="top" usebox="none">
15937 \begin_layout Plain Layout
15938 \begin_inset Formula $\iiiint$
15947 <row bottomspace="1mm">
15948 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15951 \begin_layout Plain Layout
15959 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15962 \begin_layout Plain Layout
15963 \begin_inset Formula $\dotsint$
15977 \begin_inset space \hfill{}
15983 \begin_layout Subsection
15985 \begin_inset CommandInset label
15987 name "subsec:Operator-Limits"
15992 \begin_inset Index idx
15995 \begin_layout Plain Layout
16004 \begin_layout Standard
16005 Limits are created by super- and subscripts:
16006 \begin_inset Separator parbreak
16012 \begin_layout Standard
16014 \begin_inset Tabular
16015 <lyxtabular version="3" rows="2" columns="2">
16016 <features booktabs="true" tabularvalignment="middle">
16017 <column alignment="center" valignment="top" width="0pt">
16018 <column alignment="center" valignment="top" width="0pt">
16020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16023 \begin_layout Plain Layout
16029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16032 \begin_layout Plain Layout
16040 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16043 \begin_layout Plain Layout
16049 \begin_inset space \textvisiblespace{}
16053 \begin_inset Formula $\to$
16057 \begin_inset Formula $\to$
16065 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16068 \begin_layout Plain Layout
16069 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
16085 \begin_layout Standard
16086 Limits of inline formulas are set right beside the operator.
16087 Limits in displayed formulas are set above or below the operator, except
16088 for integral limits.
16091 \begin_layout Standard
16092 To force that the limits are set beside the operator, the cursor is set
16093 directly behind the operator and the limits type is changed with the menu
16096 Edit\SpecialChar menuseparator
16097 Math\SpecialChar menuseparator
16116 \begin_layout Standard
16117 The default limits type is this:
16118 \begin_inset Formula
16120 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16125 This is how it looks when the limits type was changed to
16132 \begin_inset Formula
16134 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16139 For integrals, except those ending with
16155 etc., the limits are by default set beside the operator.
16156 But for multiple integrals the limits are often set below the operator.
16157 In the following example the limits type was therefore set to
16161 and so set below the integrals:
16162 \begin_inset Formula
16164 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16172 \begin_layout Standard
16173 \begin_inset VSpace medskip
16176 To specify conditions for limits, the commands
16183 \begin_inset Index idx
16186 \begin_layout Plain Layout
16201 \begin_inset Index idx
16204 \begin_layout Plain Layout
16213 To create for example this expression
16214 \begin_inset Formula
16216 \sum_{\begin{subarray}{c}
16220 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16228 \begin_layout Standard
16229 the following has to be done:
16230 \begin_inset Newline newline
16242 \begin_inset space \textvisiblespace{}
16248 One is now in a blue box under the summation operator and insert there
16254 \begin_inset space \textvisiblespace{}
16260 The blue box is now within a purple box and now several lines can be written
16262 A new line is created by inserting a line break (
16265 arg "newline-insert newline"
16270 \begin_inset Newline newline
16275 0<k<1000 Ctrl+Return
16276 \begin_inset Newline newline
16281 is typed in, a new box appears below for the new line.
16284 \begin_layout Standard
16285 The alignment of the lines can be changed to left aligned with the
16295 Edit\SpecialChar menuseparator
16299 To get right alignment,
16304 \begin_inset space \textvisiblespace{}
16309 is inserted at the beginning of the line.
16312 \begin_layout Standard
16325 with the difference that the lines are always centered.
16328 \begin_layout Standard
16329 \begin_inset VSpace bigskip
16333 \begin_inset CommandInset ref
16335 reference "eq:substack"
16339 there can be too much space beside an operator, because the characters
16340 following the operator are set beside the limits.
16341 To avoid this the command
16348 \begin_inset Index idx
16351 \begin_layout Plain Layout
16360 To activate it, set in the document settings under
16363 \begin_inset space ~
16373 \begin_inset Index idx
16376 \begin_layout Plain Layout
16377 Packages ! mathtools
16385 \begin_inset space ~
16397 sets the space besides the operator to 0
16398 \begin_inset space \thinspace{}
16402 \begin_inset Newline newline
16406 \begin_inset CommandInset ref
16408 reference "eq:substack"
16412 , one uses the command
16415 \begin_layout Standard
16423 \begin_layout Standard
16424 and inserts the operator with its limits into the braces.
16425 Behind the brace one continues the formula:
16426 \begin_inset Formula
16428 \smashoperator{\sum_{\begin{subarray}{c}
16432 \end{subarray}}^{n}}k^{-2}
16440 \begin_layout Standard
16441 It is possible to set the space of only one side of the operator to 0
16442 \begin_inset space \thinspace{}
16446 To do this write either
16465 stands for the left and
16469 for the right side of the operator.
16470 Here is an example of the possible
16479 \begin_layout Standard
16480 \begin_inset Formula
16482 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}
16490 \begin_layout Standard
16491 \begin_inset VSpace bigskip
16497 \begin_layout Standard
16498 When several consecutive operators have limits the typesetting of the limits
16499 looks often imperfect in the output, see this example:
16500 \begin_inset Formula
16502 \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}
16507 To improve the typesetting set in the document settings under
16510 \begin_inset space ~
16520 \begin_inset Index idx
16523 \begin_layout Plain Layout
16524 Packages ! mathtools
16532 \begin_inset space ~
16538 Then insert into your formula the command
16545 \begin_inset Index idx
16548 \begin_layout Plain Layout
16556 directly before the first operator.
16557 The example will then look like this:
16558 \begin_inset Formula
16560 \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}
16568 \begin_layout Standard
16569 \begin_inset VSpace bigskip
16572 How to use one limit for several operators is described in
16573 \begin_inset CommandInset ref
16575 reference "subsec:Self-defined-Operators"
16582 \begin_layout Subsection
16583 Decoration for Operators
16584 \begin_inset Index idx
16587 \begin_layout Plain Layout
16588 Operators ! Decoration
16596 \begin_layout Standard
16604 \begin_inset Index idx
16607 \begin_layout Plain Layout
16622 \begin_inset Index idx
16625 \begin_layout Plain Layout
16633 characters can be placed above or below an operator, respectively.
16641 \begin_inset Index idx
16644 \begin_layout Plain Layout
16652 characters can be set before and behind a big operator.
16655 \begin_layout Standard
16657 \begin_inset space ~
16669 \begin_layout Itemize
16676 is used to set characters at the corners of the operator
16679 \begin_layout Itemize
16686 is used to set characters before and/or behind the operator (this variant
16687 represents \SpecialChar LaTeX
16697 \begin_layout Itemize
16704 is used to set characters at the left corners and/or behind the operator
16707 \begin_layout Itemize
16714 is used to set characters at the right corners and/or before the operator
16717 \begin_layout Standard
16718 For example the command
16723 \begin_inset space \textvisiblespace{}
16729 \begin_inset space \textvisiblespace{}
16733 \begin_inset Formula $\to$
16737 \begin_inset Formula $\to$
16741 \begin_inset space \textvisiblespace{}
16751 \begin_inset Formula
16753 \sideset{}{'}\sum_{k=1}^{n}
16761 \begin_layout Standard
16762 \begin_inset Note Greyedout
16765 \begin_layout Plain Layout
16772 can only be used to decorate big operators, binary operators are not allowed.
16780 \begin_layout Standard
16793 can also be used to decorate symbols and characters.
16794 For example, the command
16799 \begin_inset space \textvisiblespace{}
16805 \begin_inset space \textvisiblespace{}
16811 \begin_inset Formula $\uparrow$
16819 \begin_inset Formula
16821 \overset{a}{\maltese}
16829 \begin_layout Subsection
16831 \begin_inset CommandInset label
16833 name "subsec:Binary-Operators"
16838 \begin_inset Index idx
16841 \begin_layout Plain Layout
16850 \begin_layout Standard
16851 Binary operators are surrounded by space when there is a character before
16853 \begin_inset VSpace medskip
16859 \begin_layout Standard
16860 \begin_inset Tabular
16861 <lyxtabular version="3" rows="13" columns="2">
16862 <features booktabs="true" tabularvalignment="middle">
16863 <column alignment="center" valignment="top" width="0pt">
16864 <column alignment="center" valignment="top" width="0pt">
16866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16869 \begin_layout Plain Layout
16871 \begin_inset Note Note
16874 \begin_layout Plain Layout
16881 is only used as spacer.
16891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16894 \begin_layout Plain Layout
16902 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16905 \begin_layout Plain Layout
16911 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16914 \begin_layout Plain Layout
16915 \begin_inset Formula $+$
16925 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16928 \begin_layout Plain Layout
16934 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16937 \begin_layout Plain Layout
16938 \begin_inset Formula $-$
16948 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16951 \begin_layout Plain Layout
16959 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16962 \begin_layout Plain Layout
16963 \begin_inset Formula $\pm$
16973 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16976 \begin_layout Plain Layout
16984 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16987 \begin_layout Plain Layout
16988 \begin_inset Formula $\mp$
16998 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17001 \begin_layout Plain Layout
17009 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17012 \begin_layout Plain Layout
17013 \begin_inset Formula $\cdot$
17023 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17026 \begin_layout Plain Layout
17034 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17037 \begin_layout Plain Layout
17038 \begin_inset Formula $\times$
17048 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17051 \begin_layout Plain Layout
17059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17062 \begin_layout Plain Layout
17063 \begin_inset Formula $\div$
17073 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17076 \begin_layout Plain Layout
17080 \begin_layout Plain Layout
17093 \begin_layout Plain Layout
17105 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17108 \begin_layout Plain Layout
17109 \begin_inset Formula $*$
17119 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17122 \begin_layout Plain Layout
17130 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17133 \begin_layout Plain Layout
17134 \begin_inset Formula $\star$
17144 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17147 \begin_layout Plain Layout
17155 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17158 \begin_layout Plain Layout
17159 \begin_inset Formula $\circ$
17169 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17172 \begin_layout Plain Layout
17180 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17183 \begin_layout Plain Layout
17184 \begin_inset Formula $\diamond$
17194 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17197 \begin_layout Plain Layout
17205 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17208 \begin_layout Plain Layout
17209 \begin_inset Formula $\bullet$
17223 \begin_inset space \hfill{}
17227 \begin_inset Tabular
17228 <lyxtabular version="3" rows="13" columns="2">
17229 <features booktabs="true" tabularvalignment="middle">
17230 <column alignment="center" valignment="top" width="0pt">
17231 <column alignment="center" valignment="top" width="0pt">
17233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17236 \begin_layout Plain Layout
17242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17245 \begin_layout Plain Layout
17253 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17256 \begin_layout Plain Layout
17264 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17267 \begin_layout Plain Layout
17268 \begin_inset Formula $\nabla$
17278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17281 \begin_layout Plain Layout
17289 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17292 \begin_layout Plain Layout
17293 \begin_inset Formula $\bigtriangledown$
17303 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17306 \begin_layout Plain Layout
17314 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17317 \begin_layout Plain Layout
17318 \begin_inset Formula $\bigtriangleup$
17328 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17331 \begin_layout Plain Layout
17339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17342 \begin_layout Plain Layout
17343 \begin_inset Formula $\Box$
17353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17356 \begin_layout Plain Layout
17364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17367 \begin_layout Plain Layout
17368 \begin_inset Formula $\cap$
17378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17381 \begin_layout Plain Layout
17389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17392 \begin_layout Plain Layout
17393 \begin_inset Formula $\cup$
17403 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17406 \begin_layout Plain Layout
17414 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17417 \begin_layout Plain Layout
17418 \begin_inset Formula $\dagger$
17428 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17431 \begin_layout Plain Layout
17439 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17442 \begin_layout Plain Layout
17443 \begin_inset Formula $\ddagger$
17453 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17456 \begin_layout Plain Layout
17464 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17467 \begin_layout Plain Layout
17468 \begin_inset Formula $\wr$
17478 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17481 \begin_layout Plain Layout
17489 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17492 \begin_layout Plain Layout
17493 \begin_inset Formula $\bigcirc$
17503 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17506 \begin_layout Plain Layout
17514 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17517 \begin_layout Plain Layout
17518 \begin_inset Formula $\wedge$
17528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17531 \begin_layout Plain Layout
17539 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17542 \begin_layout Plain Layout
17543 \begin_inset Formula $\vee$
17557 \begin_inset space \hfill{}
17561 \begin_inset Tabular
17562 <lyxtabular version="3" rows="13" columns="2">
17563 <features booktabs="true" tabularvalignment="middle">
17564 <column alignment="center" valignment="top" width="0pt">
17565 <column alignment="center" valignment="top" width="0pt">
17567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17570 \begin_layout Plain Layout
17576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17579 \begin_layout Plain Layout
17587 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17590 \begin_layout Plain Layout
17598 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17601 \begin_layout Plain Layout
17602 \begin_inset Formula $\oplus$
17612 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17615 \begin_layout Plain Layout
17623 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17626 \begin_layout Plain Layout
17627 \begin_inset Formula $\ominus$
17637 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17640 \begin_layout Plain Layout
17648 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17651 \begin_layout Plain Layout
17652 \begin_inset Formula $\otimes$
17662 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17665 \begin_layout Plain Layout
17673 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17676 \begin_layout Plain Layout
17677 \begin_inset Formula $\oslash$
17687 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17690 \begin_layout Plain Layout
17698 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17701 \begin_layout Plain Layout
17702 \begin_inset Formula $\odot$
17712 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17715 \begin_layout Plain Layout
17723 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17726 \begin_layout Plain Layout
17727 \begin_inset Formula $\amalg$
17737 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17740 \begin_layout Plain Layout
17748 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17751 \begin_layout Plain Layout
17752 \begin_inset Formula $\uplus$
17762 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17765 \begin_layout Plain Layout
17773 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17776 \begin_layout Plain Layout
17777 \begin_inset Formula $\setminus$
17787 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17790 \begin_layout Plain Layout
17798 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17801 \begin_layout Plain Layout
17802 \begin_inset Formula $\sqcap$
17812 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17815 \begin_layout Plain Layout
17823 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17826 \begin_layout Plain Layout
17827 \begin_inset Formula $\sqcup$
17837 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17840 \begin_layout Plain Layout
17848 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17851 \begin_layout Plain Layout
17852 \begin_inset Formula $\triangleleft$
17862 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17865 \begin_layout Plain Layout
17873 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17876 \begin_layout Plain Layout
17877 \begin_inset Formula $\triangleright$
17893 \begin_layout Standard
17894 All binary operators can also be inserted via the math toolbar button
17897 arg "math-insert \\pm"
17903 \begin_layout Standard
17904 To typeset the Laplace operator also
17921 \begin_inset Formula $\nabla^{2}$
17924 ) can be used instead of
17933 \begin_layout Standard
17940 Insert\SpecialChar menuseparator
17952 \begin_layout Subsection
17953 Self-defined Operators
17954 \begin_inset CommandInset label
17956 name "subsec:Self-defined-Operators"
17961 \begin_inset Index idx
17964 \begin_layout Plain Layout
17965 Operators ! self-defined
17973 \begin_layout Standard
17974 With the help of the command
17978 DeclareMathOperator
17981 \begin_inset Index idx
17984 \begin_layout Plain Layout
17989 DeclareMathOperator
17994 custom operators can be defined in the \SpecialChar LaTeX
17996 Its command scheme is:
17999 \begin_layout Standard
18004 DeclareMathOperator{new command}{display}
18007 \begin_layout Standard
18008 Display can be characters or symbols that define how the operator looks
18010 To define a big operator a * is set behind the command.
18011 All self-defined big operators can have limits as described in
18012 \begin_inset CommandInset ref
18014 reference "subsec:Operator-Limits"
18021 \begin_layout Standard
18022 For example the \SpecialChar LaTeX
18026 \begin_layout Standard
18031 DeclareMathOperator*{
18038 \begin_layout Standard
18039 defines the command
18045 , that inserts a big operator consisting of the lozenge symbol from
18046 \begin_inset CommandInset ref
18048 reference "subsec:Miscellaneous-Symbols"
18053 \begin_inset Formula
18055 \Lozenge_{n=1}^{\infty}
18060 The command for this formula is:
18071 \begin_inset Formula $\to$
18077 \begin_layout Standard
18078 \begin_inset VSpace bigskip
18081 When self-defined operators are not used several times in the document,
18082 they can also be defined with the commands
18089 \begin_inset Index idx
18092 \begin_layout Plain Layout
18107 \begin_inset Index idx
18110 \begin_layout Plain Layout
18118 , which have the following scheme:
18121 \begin_layout Standard
18135 \begin_layout Standard
18142 defines big operators,
18151 \begin_layout Standard
18159 \begin_inset space \thinspace{}
18163 \begin_inset space \space{}
18166 be used to use one limit for several operators:
18169 \begin_layout Standard
18170 \begin_inset Formula
18172 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18180 \begin_layout Standard
18181 The command for the formula above is:
18182 \begin_inset Newline newline
18198 \begin_inset space \textvisiblespace{}
18204 \begin_inset Formula $\to$
18210 \begin_inset space \textvisiblespace{}
18218 \begin_layout Section
18220 \begin_inset Index idx
18223 \begin_layout Plain Layout
18232 \begin_layout Subsection
18234 \begin_inset CommandInset label
18236 name "subsec:Font-Styles"
18241 \begin_inset Index idx
18244 \begin_layout Plain Layout
18253 \begin_layout Standard
18254 Latin letters in formulas can be set in one of the following font styles:
18257 \begin_layout Standard
18259 \begin_inset space \hfill{}
18263 \begin_inset Tabular
18264 <lyxtabular version="3" rows="6" columns="2">
18265 <features booktabs="true" tabularvalignment="middle">
18266 <column alignment="center" valignment="top" width="0pt">
18267 <column alignment="center" valignment="top">
18269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18272 \begin_layout Plain Layout
18278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18281 \begin_layout Plain Layout
18289 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18292 \begin_layout Plain Layout
18298 \begin_inset space \textvisiblespace{}
18308 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18311 \begin_layout Plain Layout
18312 \begin_inset Formula $\mathbb{ABC}$
18322 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18325 \begin_layout Plain Layout
18331 \begin_inset space \textvisiblespace{}
18341 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18344 \begin_layout Plain Layout
18345 \begin_inset Formula $\mathbf{AbC}$
18355 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18358 \begin_layout Plain Layout
18364 \begin_inset space \textvisiblespace{}
18374 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18377 \begin_layout Plain Layout
18378 \begin_inset Formula $\boldsymbol{AbC}$
18388 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18391 \begin_layout Plain Layout
18397 \begin_inset space \textvisiblespace{}
18407 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18410 \begin_layout Plain Layout
18411 \begin_inset Formula $\mathcal{ABC}$
18421 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18424 \begin_layout Plain Layout
18430 \begin_inset space \textvisiblespace{}
18440 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18443 \begin_layout Plain Layout
18444 \begin_inset Formula $\mathfrak{AbC}$
18458 \begin_inset space \hfill{}
18462 \begin_inset Tabular
18463 <lyxtabular version="3" rows="6" columns="2">
18464 <features booktabs="true" tabularvalignment="middle">
18465 <column alignment="center" valignment="top" width="0pt">
18466 <column alignment="center" valignment="top">
18468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18471 \begin_layout Plain Layout
18477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18480 \begin_layout Plain Layout
18488 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18491 \begin_layout Plain Layout
18497 \begin_inset space \textvisiblespace{}
18507 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18510 \begin_layout Plain Layout
18511 \begin_inset Formula $\mathit{AbC}$
18521 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18524 \begin_layout Plain Layout
18530 \begin_inset space \textvisiblespace{}
18540 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18543 \begin_layout Plain Layout
18544 \begin_inset Formula $\mathrm{AbC}$
18554 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18557 \begin_layout Plain Layout
18563 \begin_inset space \textvisiblespace{}
18573 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18576 \begin_layout Plain Layout
18577 \begin_inset Formula $\mathsf{AbC}$
18587 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18590 \begin_layout Plain Layout
18596 \begin_inset space \textvisiblespace{}
18606 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18609 \begin_layout Plain Layout
18610 \begin_inset Formula $\mathtt{AbC}$
18620 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18623 \begin_layout Plain Layout
18629 \begin_inset space \textvisiblespace{}
18639 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18642 \begin_layout Plain Layout
18643 \begin_inset Formula $\mathscr{ABC}$
18657 \begin_inset space \hfill{}
18663 \begin_layout Standard
18664 \begin_inset Note Greyedout
18667 \begin_layout Plain Layout
18690 can only be used for big letters.
18698 \begin_layout Standard
18699 Predefined is the style
18708 \begin_layout Standard
18709 The style commands work also for letters in mathematical constructs:
18710 \begin_inset Formula
18712 \mathfrak{A=\frac{b}{C}}
18720 \begin_layout Standard
18721 Characters in mathematical text don't appear in a math font style but in
18722 the text font style
18729 That their style can't be set correctly via the text style dialog is a
18730 bug in \SpecialChar LyX
18735 \begin_layout Plain Layout
18736 \begin_inset CommandInset href
18738 name "LyX-bug #4629"
18739 target "http://www.lyx.org/trac/ticket/4629"
18751 \begin_layout Standard
18752 Instead of the style commands the dialog
18754 Edit\SpecialChar menuseparator
18755 Math\SpecialChar menuseparator
18758 or the toolbar button
18761 arg "math-insert \\font"
18767 \begin_layout Subsection
18769 \begin_inset CommandInset label
18771 name "subsec:Bold-Formulas"
18776 \begin_inset Index idx
18779 \begin_layout Plain Layout
18788 \begin_layout Standard
18789 To make a complete formula bold, the command
18795 from the previous subsection cannot be used, because it doesn't work for
18796 small Greek letters.
18797 Furthermore it prints Latin letters always upright, like in the following
18801 \begin_layout Standard
18802 \begin_inset Formula
18804 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18812 \begin_layout Standard
18813 To display the formula correctly, the command
18820 \begin_inset Formula
18822 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18827 It is also possible to set the formula in a
18829 boldmath environment
18832 This environment is created by inserting the command
18839 \begin_inset Index idx
18842 \begin_layout Plain Layout
18850 in \SpecialChar TeX
18852 To end the environment, the command
18859 \begin_inset Index idx
18862 \begin_layout Plain Layout
18870 is inserted in \SpecialChar TeX
18875 \begin_layout Plain Layout
18885 \begin_inset Formula
18887 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18896 \begin_layout Plain Layout
18908 \begin_layout Subsection
18910 \begin_inset Index idx
18913 \begin_layout Plain Layout
18922 \begin_layout Standard
18923 Formulas can be colored like normal text: Highlight a formula or a formula
18929 Here is a formula in magenta:
18930 \begin_inset Formula
18932 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18940 \begin_layout Standard
18941 You can also define your own colors as described in
18942 \begin_inset CommandInset ref
18944 reference "subsec:Colored-Boxes"
18949 They can be used with the \SpecialChar TeX
18957 \begin_inset Index idx
18960 \begin_layout Plain Layout
18971 \begin_layout Standard
18976 textcolor{color}{characters or formula}
18979 \begin_layout Standard
18980 The following example was colored completely dark green and partly red:
18983 \begin_layout Standard
18987 \begin_layout Plain Layout
18991 textcolor{darkgreen}{
18997 \begin_inset Formula
18999 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19008 \begin_layout Plain Layout
19018 \begin_layout Standard
19019 Due to a bug in \SpecialChar LyX
19020 only complete formulas can be colored with self-defined
19025 \begin_layout Plain Layout
19026 \begin_inset CommandInset href
19028 name "LyX-bug #5269"
19029 target "http://www.lyx.org/trac/ticket/5269"
19041 \begin_layout Subsection
19043 \begin_inset CommandInset label
19045 name "subsec:Font-Sizes"
19050 \begin_inset Index idx
19053 \begin_layout Plain Layout
19062 \begin_layout Standard
19063 For characters in formulas there are, analog to characters in text, the
19064 following size commands:
19067 \begin_layout Standard
19111 \begin_inset Newline newline
19133 \begin_layout Standard
19134 The size produced by the commands depends on the document font size, which
19135 corresponds to the command
19142 The other commands produce smaller or larger sizes than
19149 The font size can however not exceed a certain value.
19150 Is for example the document font size 12
19151 \begin_inset space \thinspace{}
19160 switches to the same size as
19170 \begin_layout Standard
19171 A size command is inserted in \SpecialChar TeX
19172 mode before the formula and sets the size
19173 for all following formula and text characters.
19174 To switch back to the initial size, the command
19180 is inserted behind the formula in \SpecialChar TeX
19184 \begin_layout Standard
19185 Within a formula the size can be changed using the following size commands
19186 or the toolbar button
19189 arg "math-insert \\style"
19193 \begin_inset Separator parbreak
19199 \begin_layout Standard
19202 \begin_inset Tabular
19203 <lyxtabular version="3" rows="5" columns="2">
19204 <features booktabs="true" tabularvalignment="middle">
19205 <column alignment="center" valignment="top" width="0pt">
19206 <column alignment="center" valignment="top">
19208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19211 \begin_layout Plain Layout
19217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19220 \begin_layout Plain Layout
19228 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19231 \begin_layout Plain Layout
19235 \begin_inset Index idx
19238 \begin_layout Plain Layout
19251 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19254 \begin_layout Plain Layout
19255 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19264 <row topspace="1mm">
19265 <cell alignment="center" valignment="top" usebox="none">
19268 \begin_layout Plain Layout
19276 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19279 \begin_layout Plain Layout
19280 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19290 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19293 \begin_layout Plain Layout
19301 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19304 \begin_layout Plain Layout
19305 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19318 \begin_layout Plain Layout
19326 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19329 \begin_layout Plain Layout
19330 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19346 \begin_layout Standard
19347 After entering these commands, a blue box appears in which the formula parts
19351 \begin_layout Standard
19352 There is a further method to change the font size, that though only works
19353 for symbols or letters in mathematical text.
19354 To use it, one of the above text size commands is inserted in mathematical
19356 All following characters until the end of the mathematical text or until
19357 another size command will have the selected size.
19359 \begin_inset VSpace -2mm
19365 \begin_layout Standard
19369 \begin_layout Plain Layout
19379 \begin_inset Formula
19381 A=\frac{B}{c}\cdot\maltese
19387 \begin_inset Formula
19389 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19398 \begin_layout Plain Layout
19410 \begin_layout Standard
19411 \begin_inset VSpace medskip
19414 Before both formulas the command
19421 The command for the second formula is:
19422 \begin_inset Newline newline
19430 \begin_inset space \textvisiblespace{}
19436 \begin_inset space \textvisiblespace{}
19442 \begin_inset space \textvisiblespace{}
19448 \begin_inset space \textvisiblespace{}
19452 \begin_inset Formula $\to$
19456 \begin_inset Formula $\to$
19460 \begin_inset Newline newline
19464 \begin_inset space \hspace*{}
19475 \begin_inset space \textvisiblespace{}
19481 \begin_inset space \textvisiblespace{}
19487 \begin_inset space \textvisiblespace{}
19493 \begin_layout Standard
19494 If a symbol cannot be displayed in different sizes, it will always be displayed
19495 in the default size.
19498 \begin_layout Section
19500 \begin_inset Index idx
19503 \begin_layout Plain Layout
19512 \begin_layout Standard
19513 Greek letters can also be inserted via the toolbar button
19516 arg "math-insert \\alpha"
19520 All international typesetting norms purport that Greek letters in math
19521 have to be typeset italic/slanted.
19522 In some languages, like French or Russian, they are nevertheless sometimes
19526 \begin_layout Subsection
19528 \begin_inset Index idx
19531 \begin_layout Plain Layout
19532 Greek letters ! small
19540 \begin_layout Standard
19541 \begin_inset space \hfill{}
19545 \begin_inset Tabular
19546 <lyxtabular version="3" rows="11" columns="2">
19547 <features booktabs="true" tabularvalignment="middle">
19548 <column alignment="center" valignment="top" width="0pt">
19549 <column alignment="center" valignment="top" width="0pt">
19551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19554 \begin_layout Plain Layout
19560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19563 \begin_layout Plain Layout
19571 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19574 \begin_layout Plain Layout
19582 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19585 \begin_layout Plain Layout
19586 \begin_inset Formula $\alpha$
19596 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19599 \begin_layout Plain Layout
19607 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19610 \begin_layout Plain Layout
19611 \begin_inset Formula $\beta$
19621 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19624 \begin_layout Plain Layout
19632 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19635 \begin_layout Plain Layout
19636 \begin_inset Formula $\gamma$
19646 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19649 \begin_layout Plain Layout
19657 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19660 \begin_layout Plain Layout
19661 \begin_inset Formula $\delta$
19671 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19674 \begin_layout Plain Layout
19682 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19685 \begin_layout Plain Layout
19686 \begin_inset Formula $\epsilon$
19696 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19699 \begin_layout Plain Layout
19707 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19710 \begin_layout Plain Layout
19711 \begin_inset Formula $\varepsilon$
19721 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19724 \begin_layout Plain Layout
19732 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19735 \begin_layout Plain Layout
19736 \begin_inset Formula $\zeta$
19746 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19749 \begin_layout Plain Layout
19757 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19760 \begin_layout Plain Layout
19761 \begin_inset Formula $\eta$
19771 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19774 \begin_layout Plain Layout
19782 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19785 \begin_layout Plain Layout
19786 \begin_inset Formula $\theta$
19796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19799 \begin_layout Plain Layout
19807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19810 \begin_layout Plain Layout
19811 \begin_inset Formula $\vartheta$
19825 \begin_inset space \hfill{}
19829 \begin_inset Tabular
19830 <lyxtabular version="3" rows="12" columns="2">
19831 <features booktabs="true" tabularvalignment="middle">
19832 <column alignment="center" valignment="top" width="0pt">
19833 <column alignment="center" valignment="top" width="0pt">
19835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19838 \begin_layout Plain Layout
19844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19847 \begin_layout Plain Layout
19855 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19858 \begin_layout Plain Layout
19866 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19869 \begin_layout Plain Layout
19870 \begin_inset Formula $\iota$
19880 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19883 \begin_layout Plain Layout
19891 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19894 \begin_layout Plain Layout
19895 \begin_inset Formula $\kappa$
19905 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19908 \begin_layout Plain Layout
19916 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19919 \begin_layout Plain Layout
19920 \begin_inset Formula $\varkappa$
19930 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19933 \begin_layout Plain Layout
19941 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19944 \begin_layout Plain Layout
19945 \begin_inset Formula $\lambda$
19955 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19958 \begin_layout Plain Layout
19966 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19969 \begin_layout Plain Layout
19970 \begin_inset Formula $\mu$
19980 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19983 \begin_layout Plain Layout
19991 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19994 \begin_layout Plain Layout
19995 \begin_inset Formula $\nu$
20005 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20008 \begin_layout Plain Layout
20016 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20019 \begin_layout Plain Layout
20020 \begin_inset Formula $\xi$
20030 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20033 \begin_layout Plain Layout
20039 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20042 \begin_layout Plain Layout
20043 \begin_inset Formula $o$
20053 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20056 \begin_layout Plain Layout
20064 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20067 \begin_layout Plain Layout
20068 \begin_inset Formula $\pi$
20078 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20081 \begin_layout Plain Layout
20089 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20092 \begin_layout Plain Layout
20093 \begin_inset Formula $\varpi$
20103 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20106 \begin_layout Plain Layout
20114 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20117 \begin_layout Plain Layout
20118 \begin_inset Formula $\rho$
20132 \begin_inset space \hfill{}
20136 \begin_inset Tabular
20137 <lyxtabular version="3" rows="11" columns="2">
20138 <features booktabs="true" tabularvalignment="middle">
20139 <column alignment="center" valignment="top" width="0pt">
20140 <column alignment="center" valignment="top" width="0pt">
20142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20145 \begin_layout Plain Layout
20151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20154 \begin_layout Plain Layout
20162 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20165 \begin_layout Plain Layout
20173 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20176 \begin_layout Plain Layout
20177 \begin_inset Formula $\varrho$
20187 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20190 \begin_layout Plain Layout
20198 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20201 \begin_layout Plain Layout
20202 \begin_inset Formula $\sigma$
20212 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20215 \begin_layout Plain Layout
20223 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20226 \begin_layout Plain Layout
20227 \begin_inset Formula $\varsigma$
20237 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20240 \begin_layout Plain Layout
20248 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20251 \begin_layout Plain Layout
20252 \begin_inset Formula $\tau$
20262 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20265 \begin_layout Plain Layout
20273 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20276 \begin_layout Plain Layout
20277 \begin_inset Formula $\upsilon$
20287 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20290 \begin_layout Plain Layout
20298 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20301 \begin_layout Plain Layout
20302 \begin_inset Formula $\phi$
20312 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20315 \begin_layout Plain Layout
20323 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20326 \begin_layout Plain Layout
20327 \begin_inset Formula $\varphi$
20337 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20340 \begin_layout Plain Layout
20348 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20351 \begin_layout Plain Layout
20352 \begin_inset Formula $\chi$
20362 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20365 \begin_layout Plain Layout
20373 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20376 \begin_layout Plain Layout
20377 \begin_inset Formula $\psi$
20387 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20390 \begin_layout Plain Layout
20398 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20401 \begin_layout Plain Layout
20402 \begin_inset Formula $\omega$
20416 \begin_inset space \hfill{}
20422 \begin_layout Standard
20423 \begin_inset VSpace medskip
20429 \begin_layout Standard
20430 How to create special upright Greek letters is explained in
20431 \begin_inset CommandInset ref
20433 reference "subsec:Upright-small-Greek"
20440 \begin_layout Subsection
20442 \begin_inset Index idx
20445 \begin_layout Plain Layout
20446 Greek letters ! big
20454 \begin_layout Standard
20455 \begin_inset space \hfill{}
20459 \begin_inset Tabular
20460 <lyxtabular version="3" rows="7" columns="2">
20461 <features booktabs="true" tabularvalignment="middle">
20462 <column alignment="center" valignment="top" width="0pt">
20463 <column alignment="center" valignment="top" width="0pt">
20465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20468 \begin_layout Plain Layout
20474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20477 \begin_layout Plain Layout
20485 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20488 \begin_layout Plain Layout
20496 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20499 \begin_layout Plain Layout
20500 \begin_inset Formula $\Gamma$
20510 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20513 \begin_layout Plain Layout
20521 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20524 \begin_layout Plain Layout
20525 \begin_inset Formula $\Delta$
20535 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20538 \begin_layout Plain Layout
20546 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20549 \begin_layout Plain Layout
20550 \begin_inset Formula $\Theta$
20560 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20563 \begin_layout Plain Layout
20571 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20574 \begin_layout Plain Layout
20575 \begin_inset Formula $\Lambda$
20585 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20588 \begin_layout Plain Layout
20596 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20599 \begin_layout Plain Layout
20600 \begin_inset Formula $\Xi$
20610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20613 \begin_layout Plain Layout
20621 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20624 \begin_layout Plain Layout
20625 \begin_inset Formula $\Pi$
20639 \begin_inset space \hfill{}
20643 \begin_inset Tabular
20644 <lyxtabular version="3" rows="6" columns="2">
20645 <features booktabs="true" tabularvalignment="middle">
20646 <column alignment="center" valignment="top" width="0pt">
20647 <column alignment="center" valignment="top" width="0pt">
20649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20652 \begin_layout Plain Layout
20658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20661 \begin_layout Plain Layout
20669 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20672 \begin_layout Plain Layout
20680 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20683 \begin_layout Plain Layout
20684 \begin_inset Formula $\Sigma$
20694 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20697 \begin_layout Plain Layout
20705 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20708 \begin_layout Plain Layout
20709 \begin_inset Formula $\Upsilon$
20719 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20722 \begin_layout Plain Layout
20730 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20733 \begin_layout Plain Layout
20734 \begin_inset Formula $\Phi$
20744 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20747 \begin_layout Plain Layout
20755 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20758 \begin_layout Plain Layout
20759 \begin_inset Formula $\Psi$
20769 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20772 \begin_layout Plain Layout
20780 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20783 \begin_layout Plain Layout
20784 \begin_inset Formula $\Omega$
20798 \begin_inset space \hfill{}
20804 \begin_layout Standard
20805 \begin_inset VSpace medskip
20808 That the big Greek letters appear upright is caused by a design bug when
20811 To get correct italic big letters, begin every command with
20816 For example the command
20823 \begin_inset Formula $\varGamma$
20827 Another way is to load the package
20835 \begin_layout Plain Layout
20840 is part of the \SpecialChar LaTeX
20846 \begin_inset Index idx
20849 \begin_layout Plain Layout
20854 \begin_layout Plain Layout
20874 \begin_inset Index idx
20877 \begin_layout Plain Layout
20883 with the \SpecialChar LaTeX
20887 \begin_layout Standard
20892 usepackage{fixmath}
20895 \begin_layout Standard
20896 Then all big Greek letters in a document will automatically be typeset italic.
20899 \begin_layout Subsection
20901 \begin_inset Index idx
20904 \begin_layout Plain Layout
20905 Greek letters ! bold
20913 \begin_layout Standard
20914 Greek letters cannot be set with different font styles like Latin letters.
20915 They can only be made bold with the command
20922 \begin_inset Index idx
20925 \begin_layout Plain Layout
20934 \begin_inset Separator parbreak
20940 \begin_layout Standard
20942 \begin_inset Tabular
20943 <lyxtabular version="3" rows="3" columns="2">
20944 <features booktabs="true" tabularvalignment="middle">
20945 <column alignment="center" valignment="top" width="0pt">
20946 <column alignment="center" valignment="top">
20948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20951 \begin_layout Plain Layout
20957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20960 \begin_layout Plain Layout
20968 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20971 \begin_layout Plain Layout
20983 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20986 \begin_layout Plain Layout
20987 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20997 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21000 \begin_layout Plain Layout
21012 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21015 \begin_layout Plain Layout
21016 \begin_inset Formula $\theta\boldsymbol{\theta}$
21032 \begin_layout Section
21037 \begin_layout Plain Layout
21050 \begin_layout Plain Layout
21051 A list with all symbols of most of the \SpecialChar LaTeX
21052 -packages can be found in
21053 \begin_inset CommandInset citation
21068 \begin_layout Plain Layout
21076 \begin_inset Note Note
21079 \begin_layout Plain Layout
21082 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21085 \begin_layout Plain Layout
21088 texorpdfstring is in section
21089 \begin_inset CommandInset ref
21091 reference "subsec:Formulas-in-Section"
21101 \begin_inset Index idx
21104 \begin_layout Plain Layout
21113 \begin_layout Standard
21114 Many of the symbols listed in this section can also be inserted via the
21118 arg "math-insert \\nabla"
21124 arg "math-insert \\digamma"
21130 \begin_layout Subsection
21131 Mathematical Symbols
21132 \begin_inset CommandInset label
21134 name "subsec:Mathematical-Symbols"
21139 \begin_inset Index idx
21142 \begin_layout Plain Layout
21143 Symbols ! mathematical
21151 \begin_layout Standard
21152 \begin_inset Tabular
21153 <lyxtabular version="3" rows="10" columns="2">
21154 <features booktabs="true" tabularvalignment="middle">
21155 <column alignment="center" valignment="top" width="0pt">
21156 <column alignment="center" valignment="top" width="0pt">
21158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21161 \begin_layout Plain Layout
21167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21170 \begin_layout Plain Layout
21178 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21181 \begin_layout Plain Layout
21189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21192 \begin_layout Plain Layout
21193 \begin_inset Formula $\neg$
21203 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21206 \begin_layout Plain Layout
21214 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21217 \begin_layout Plain Layout
21218 \begin_inset Formula $\Im$
21228 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21231 \begin_layout Plain Layout
21239 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21242 \begin_layout Plain Layout
21243 \begin_inset Formula $\Re$
21253 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21256 \begin_layout Plain Layout
21264 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21267 \begin_layout Plain Layout
21268 \begin_inset Formula $\aleph$
21278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21281 \begin_layout Plain Layout
21289 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21292 \begin_layout Plain Layout
21293 \begin_inset Formula $\partial$
21303 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21306 \begin_layout Plain Layout
21314 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21317 \begin_layout Plain Layout
21318 \begin_inset Formula $\infty$
21328 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21331 \begin_layout Plain Layout
21339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21342 \begin_layout Plain Layout
21343 \begin_inset Formula $\wp$
21353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21356 \begin_layout Plain Layout
21364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21367 \begin_layout Plain Layout
21368 \begin_inset Formula $\imath$
21378 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21381 \begin_layout Plain Layout
21389 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21392 \begin_layout Plain Layout
21393 \begin_inset Formula $\jmath$
21407 \begin_inset space \hfill{}
21411 \begin_inset Tabular
21412 <lyxtabular version="3" rows="10" columns="2">
21413 <features booktabs="true" tabularvalignment="middle">
21414 <column alignment="center" valignment="top" width="0pt">
21415 <column alignment="center" valignment="top" width="0pt">
21417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21420 \begin_layout Plain Layout
21426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21429 \begin_layout Plain Layout
21431 \begin_inset Note Note
21434 \begin_layout Plain Layout
21441 is only used as spacer.
21453 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21456 \begin_layout Plain Layout
21464 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21467 \begin_layout Plain Layout
21468 \begin_inset Formula $\forall$
21478 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21481 \begin_layout Plain Layout
21489 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21492 \begin_layout Plain Layout
21493 \begin_inset Formula $\exists$
21503 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21506 \begin_layout Plain Layout
21514 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21517 \begin_layout Plain Layout
21518 \begin_inset Formula $\nexists$
21528 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21531 \begin_layout Plain Layout
21539 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21542 \begin_layout Plain Layout
21543 \begin_inset Formula $\emptyset$
21553 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21556 \begin_layout Plain Layout
21564 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21567 \begin_layout Plain Layout
21568 \begin_inset Formula $\varnothing$
21578 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21581 \begin_layout Plain Layout
21589 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21592 \begin_layout Plain Layout
21593 \begin_inset Formula $\dag$
21603 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21606 \begin_layout Plain Layout
21614 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21617 \begin_layout Plain Layout
21618 \begin_inset Formula $\ddag$
21628 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21631 \begin_layout Plain Layout
21639 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21642 \begin_layout Plain Layout
21646 \begin_layout Plain Layout
21656 \begin_inset Formula $\complement$
21663 \begin_layout Plain Layout
21677 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21680 \begin_layout Plain Layout
21688 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21691 \begin_layout Plain Layout
21692 \begin_inset Formula $\Bbbk$
21706 \begin_inset space \hfill{}
21710 \begin_inset Tabular
21711 <lyxtabular version="3" rows="10" columns="2">
21712 <features booktabs="true" tabularvalignment="middle">
21713 <column alignment="center" valignment="top" width="0pt">
21714 <column alignment="center" valignment="top" width="0pt">
21716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21719 \begin_layout Plain Layout
21725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21728 \begin_layout Plain Layout
21736 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21739 \begin_layout Plain Layout
21747 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21750 \begin_layout Plain Layout
21751 \begin_inset Formula $\prime$
21761 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21764 \begin_layout Plain Layout
21772 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21775 \begin_layout Plain Layout
21776 \begin_inset Formula $\backprime$
21786 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21789 \begin_layout Plain Layout
21797 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21800 \begin_layout Plain Layout
21801 \begin_inset Formula $\mho$
21811 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21814 \begin_layout Plain Layout
21822 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21825 \begin_layout Plain Layout
21826 \begin_inset Formula $\triangle$
21836 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21839 \begin_layout Plain Layout
21847 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21850 \begin_layout Plain Layout
21851 \begin_inset Formula $\angle$
21861 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21864 \begin_layout Plain Layout
21872 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21875 \begin_layout Plain Layout
21876 \begin_inset Formula $\measuredangle$
21886 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21889 \begin_layout Plain Layout
21897 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21900 \begin_layout Plain Layout
21901 \begin_inset Formula $\sphericalangle$
21911 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21914 \begin_layout Plain Layout
21922 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21925 \begin_layout Plain Layout
21926 \begin_inset Formula $\top$
21936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21939 \begin_layout Plain Layout
21947 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21950 \begin_layout Plain Layout
21951 \begin_inset Formula $\bot$
21967 \begin_layout Standard
21968 \begin_inset Newpage newpage
21974 \begin_layout Subsection
21975 Miscellaneous Symbols
21976 \begin_inset CommandInset label
21978 name "subsec:Miscellaneous-Symbols"
21983 \begin_inset Index idx
21986 \begin_layout Plain Layout
21987 Symbols ! miscellaneous
21995 \begin_layout Standard
21998 \begin_inset Tabular
21999 <lyxtabular version="3" rows="10" columns="2">
22000 <features booktabs="true" tabularvalignment="middle">
22001 <column alignment="center" valignment="top" width="0pt">
22002 <column alignment="center" valignment="top" width="0pt">
22004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22007 \begin_layout Plain Layout
22013 <cell alignment="center" valignment="top" topline="true" bottomline="true" 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
22035 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22038 \begin_layout Plain Layout
22039 \begin_inset Formula $\flat$
22049 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22052 \begin_layout Plain Layout
22060 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22063 \begin_layout Plain Layout
22064 \begin_inset Formula $\natural$
22074 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22077 \begin_layout Plain Layout
22085 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22088 \begin_layout Plain Layout
22089 \begin_inset Formula $\sharp$
22099 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22102 \begin_layout Plain Layout
22110 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22113 \begin_layout Plain Layout
22114 \begin_inset Formula $\surd$
22124 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22127 \begin_layout Plain Layout
22135 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22138 \begin_layout Plain Layout
22139 \begin_inset Formula $\checkmark$
22149 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22152 \begin_layout Plain Layout
22160 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22163 \begin_layout Plain Layout
22164 \begin_inset Formula $\yen$
22174 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22177 \begin_layout Plain Layout
22185 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22188 \begin_layout Plain Layout
22189 \begin_inset Formula $\pounds$
22199 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22202 \begin_layout Plain Layout
22208 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22211 \begin_layout Plain Layout
22212 \begin_inset Formula $\$$
22222 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22225 \begin_layout Plain Layout
22231 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22234 \begin_layout Plain Layout
22235 \begin_inset Formula $§$
22249 \begin_inset space \hfill{}
22253 \begin_inset Tabular
22254 <lyxtabular version="3" rows="10" columns="2">
22255 <features booktabs="true" tabularvalignment="middle">
22256 <column alignment="center" valignment="top" width="0pt">
22257 <column alignment="center" valignment="top">
22259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22262 \begin_layout Plain Layout
22268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22271 \begin_layout Plain Layout
22279 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22282 \begin_layout Plain Layout
22290 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22293 \begin_layout Plain Layout
22294 \begin_inset Formula $\hbar$
22304 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22307 \begin_layout Plain Layout
22315 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22318 \begin_layout Plain Layout
22319 \begin_inset Formula $\hslash$
22329 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22332 \begin_layout Plain Layout
22340 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22343 \begin_layout Plain Layout
22344 \begin_inset Formula $\clubsuit$
22354 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22357 \begin_layout Plain Layout
22365 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22368 \begin_layout Plain Layout
22369 \begin_inset Formula $\spadesuit$
22379 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22382 \begin_layout Plain Layout
22390 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22393 \begin_layout Plain Layout
22394 \begin_inset Formula $\bigstar$
22404 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22407 \begin_layout Plain Layout
22415 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22418 \begin_layout Plain Layout
22419 \begin_inset Formula $\blacklozenge$
22429 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22432 \begin_layout Plain Layout
22440 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22443 \begin_layout Plain Layout
22444 \begin_inset Formula $\blacktriangle$
22454 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22457 \begin_layout Plain Layout
22465 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22468 \begin_layout Plain Layout
22469 \begin_inset Formula $\blacktriangledown$
22479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22482 \begin_layout Plain Layout
22490 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22493 \begin_layout Plain Layout
22494 \begin_inset Formula $\bullet$
22508 \begin_inset space \hfill{}
22512 \begin_inset Tabular
22513 <lyxtabular version="3" rows="10" columns="2">
22514 <features booktabs="true" tabularvalignment="middle">
22515 <column alignment="center" valignment="top" width="0pt">
22516 <column alignment="center" valignment="top" width="0pt">
22518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22521 \begin_layout Plain Layout
22527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22530 \begin_layout Plain Layout
22538 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22541 \begin_layout Plain Layout
22549 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22552 \begin_layout Plain Layout
22553 \begin_inset Formula $\diamondsuit$
22563 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22566 \begin_layout Plain Layout
22574 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22577 \begin_layout Plain Layout
22578 \begin_inset Formula $\Diamond$
22588 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22591 \begin_layout Plain Layout
22599 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22602 \begin_layout Plain Layout
22603 \begin_inset Formula $\heartsuit$
22613 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22616 \begin_layout Plain Layout
22624 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22627 \begin_layout Plain Layout
22628 \begin_inset Formula $\P$
22638 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22641 \begin_layout Plain Layout
22649 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22652 \begin_layout Plain Layout
22653 \begin_inset Formula $\copyright$
22663 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22666 \begin_layout Plain Layout
22674 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22677 \begin_layout Plain Layout
22678 \begin_inset Formula $\circledR$
22688 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22691 \begin_layout Plain Layout
22699 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22702 \begin_layout Plain Layout
22703 \begin_inset Formula $\maltese$
22713 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22716 \begin_layout Plain Layout
22724 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22727 \begin_layout Plain Layout
22728 \begin_inset Formula $\diagup$
22738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22741 \begin_layout Plain Layout
22749 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22752 \begin_layout Plain Layout
22753 \begin_inset Formula $\diagdown$
22769 \begin_layout Standard
22770 \begin_inset VSpace medskip
22776 \begin_layout Standard
22777 Some symbols can be displayed in different sizes, see
22778 \begin_inset CommandInset ref
22780 reference "subsec:Font-Sizes"
22787 \begin_layout Subsection
22789 \begin_inset Index idx
22792 \begin_layout Plain Layout
22793 Symbols ! Euro-symbol
22799 \begin_inset Index idx
22802 \begin_layout Plain Layout
22809 \begin_layout Plain Layout
22826 \begin_layout Standard
22827 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22833 \begin_inset Index idx
22836 \begin_layout Plain Layout
22842 must be installed and loaded with the \SpecialChar LaTeX
22846 \begin_layout Standard
22851 usepackage[gennarrow]{eurosym}
22854 \begin_layout Standard
22855 The Euro symbol can now be inserted with the command
22862 \begin_inset Index idx
22865 \begin_layout Plain Layout
22876 \begin_layout Standard
22877 The Euro symbol can directly be inserted with the € key in mathematical
22878 text, without having
22893 can also be inserted in \SpecialChar TeX
22895 The official currency symbol can then be inserted with the command
22902 \begin_inset Index idx
22905 \begin_layout Plain Layout
22913 , that is only available in \SpecialChar TeX
22917 \begin_layout Standard
22921 \begin_layout Plain Layout
22931 \begin_inset Note Note
22934 \begin_layout Plain Layout
22935 The following table will only be displayed when the \SpecialChar LaTeX
22948 \begin_layout Standard
22949 An overview about the different Euro symbols:
22950 \begin_inset Separator parbreak
22956 \begin_layout Standard
22958 \begin_inset Tabular
22959 <lyxtabular version="3" rows="4" columns="3">
22960 <features booktabs="true" tabularvalignment="middle">
22961 <column alignment="center" valignment="top" width="0pt">
22962 <column alignment="center" valignment="top" width="0pt">
22963 <column alignment="center" valignment="top" width="0pt">
22965 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22968 \begin_layout Plain Layout
22972 \begin_layout Plain Layout
22976 cmidrule[0.08em]{2-3}
22986 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22989 \begin_layout Plain Layout
22995 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22998 \begin_layout Plain Layout
23006 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23009 \begin_layout Plain Layout
23015 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23018 \begin_layout Plain Layout
23026 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23029 \begin_layout Plain Layout
23030 \begin_inset Formula $\euro$
23040 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23043 \begin_layout Plain Layout
23049 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23052 \begin_layout Plain Layout
23058 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23061 \begin_layout Plain Layout
23062 \begin_inset Formula $\mbox{€}$
23072 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23075 \begin_layout Plain Layout
23082 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23085 \begin_layout Plain Layout
23093 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23096 \begin_layout Plain Layout
23100 \begin_layout Plain Layout
23120 \begin_inset Note Note
23123 \begin_layout Plain Layout
23130 is used here only for table borders.
23140 manual for details.
23148 \begin_layout Standard
23152 \begin_layout Plain Layout
23162 \begin_inset Note Note
23165 \begin_layout Plain Layout
23166 The following will be displayed when the \SpecialChar LaTeX
23179 \begin_layout Standard
23180 You need to install the \SpecialChar LaTeX
23185 to see the rest of this subsection in the output.
23188 \begin_layout Standard
23192 \begin_layout Plain Layout
23204 \begin_layout Standard
23205 \begin_inset Newpage newpage
23211 \begin_layout Section
23213 \begin_inset CommandInset label
23215 name "sec:Relations"
23220 \begin_inset Index idx
23223 \begin_layout Plain Layout
23230 \begin_inset Index idx
23233 \begin_layout Plain Layout
23238 \begin_layout Plain Layout
23249 \begin_layout Plain Layout
23264 \begin_layout Standard
23265 All following relations can also be inserted via the toolbar button
23268 arg "math-insert \\leq"
23274 \begin_layout Standard
23275 \begin_inset Tabular
23276 <lyxtabular version="3" rows="17" columns="2">
23277 <features booktabs="true" tabularvalignment="middle">
23278 <column alignment="center" valignment="top" width="0pt">
23279 <column alignment="center" valignment="top" width="0pt">
23281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23284 \begin_layout Plain Layout
23290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23293 \begin_layout Plain Layout
23301 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23304 \begin_layout Plain Layout
23310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23313 \begin_layout Plain Layout
23314 \begin_inset Formula $<$
23324 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23327 \begin_layout Plain Layout
23335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23338 \begin_layout Plain Layout
23339 \begin_inset Formula $\le$
23349 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23352 \begin_layout Plain Layout
23360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23363 \begin_layout Plain Layout
23364 \begin_inset Formula $\ll$
23374 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23377 \begin_layout Plain Layout
23385 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23388 \begin_layout Plain Layout
23389 \begin_inset Formula $\prec$
23399 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23402 \begin_layout Plain Layout
23410 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23413 \begin_layout Plain Layout
23414 \begin_inset Formula $\preceq$
23424 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23427 \begin_layout Plain Layout
23435 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23438 \begin_layout Plain Layout
23439 \begin_inset Formula $\subset$
23449 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23452 \begin_layout Plain Layout
23460 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23463 \begin_layout Plain Layout
23464 \begin_inset Formula $\subseteq$
23474 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23477 \begin_layout Plain Layout
23485 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23488 \begin_layout Plain Layout
23489 \begin_inset Formula $\sqsubseteq$
23499 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23502 \begin_layout Plain Layout
23510 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23513 \begin_layout Plain Layout
23514 \begin_inset Formula $\in$
23524 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23527 \begin_layout Plain Layout
23535 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23538 \begin_layout Plain Layout
23539 \begin_inset Formula $\vdash$
23549 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23552 \begin_layout Plain Layout
23560 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23563 \begin_layout Plain Layout
23564 \begin_inset Formula $\smile$
23574 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23577 \begin_layout Plain Layout
23585 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23588 \begin_layout Plain Layout
23589 \begin_inset Formula $\lhd$
23599 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23602 \begin_layout Plain Layout
23610 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23613 \begin_layout Plain Layout
23614 \begin_inset Formula $\unlhd$
23624 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23627 \begin_layout Plain Layout
23635 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23638 \begin_layout Plain Layout
23639 \begin_inset Formula $\gtrless$
23649 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23652 \begin_layout Plain Layout
23660 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23663 \begin_layout Plain Layout
23664 \begin_inset Formula $\mid$
23674 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23677 \begin_layout Plain Layout
23685 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23688 \begin_layout Plain Layout
23689 \begin_inset Formula $\nmid$
23703 \begin_inset space \hfill{}
23707 \begin_inset Tabular
23708 <lyxtabular version="3" rows="17" columns="2">
23709 <features booktabs="true" tabularvalignment="middle">
23710 <column alignment="center" valignment="top" width="0pt">
23711 <column alignment="center" valignment="top" width="0pt">
23713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23716 \begin_layout Plain Layout
23722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23725 \begin_layout Plain Layout
23733 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23736 \begin_layout Plain Layout
23742 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23745 \begin_layout Plain Layout
23746 \begin_inset Formula $=$
23756 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23759 \begin_layout Plain Layout
23767 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23770 \begin_layout Plain Layout
23771 \begin_inset Formula $\not=$
23781 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23784 \begin_layout Plain Layout
23792 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23795 \begin_layout Plain Layout
23796 \begin_inset Formula $\equiv$
23806 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23809 \begin_layout Plain Layout
23817 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23820 \begin_layout Plain Layout
23821 \begin_inset Formula $\sim$
23831 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23834 \begin_layout Plain Layout
23842 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23845 \begin_layout Plain Layout
23846 \begin_inset Formula $\simeq$
23856 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23859 \begin_layout Plain Layout
23867 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23870 \begin_layout Plain Layout
23871 \begin_inset Formula $\approx$
23881 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23884 \begin_layout Plain Layout
23892 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23895 \begin_layout Plain Layout
23896 \begin_inset Formula $\cong$
23906 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23909 \begin_layout Plain Layout
23917 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23920 \begin_layout Plain Layout
23921 \begin_inset Formula $\bowtie$
23931 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23934 \begin_layout Plain Layout
23942 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23945 \begin_layout Plain Layout
23946 \begin_inset Formula $\notin$
23956 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23959 \begin_layout Plain Layout
23967 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23970 \begin_layout Plain Layout
23971 \begin_inset Formula $\perp$
23981 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23984 \begin_layout Plain Layout
23992 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23995 \begin_layout Plain Layout
23996 \begin_inset Formula $\propto$
24006 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24009 \begin_layout Plain Layout
24017 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24020 \begin_layout Plain Layout
24021 \begin_inset Formula $\asymp$
24031 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24034 \begin_layout Plain Layout
24042 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24045 \begin_layout Plain Layout
24046 \begin_inset Formula $\doteq$
24056 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24059 \begin_layout Plain Layout
24067 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24070 \begin_layout Plain Layout
24071 \begin_inset Formula $\circeq$
24081 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24084 \begin_layout Plain Layout
24092 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24095 \begin_layout Plain Layout
24096 \begin_inset Formula $\models$
24106 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24109 \begin_layout Plain Layout
24117 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24120 \begin_layout Plain Layout
24121 \begin_inset Formula $\widehat{=}$
24135 \begin_inset space \hfill{}
24139 \begin_inset Tabular
24140 <lyxtabular version="3" rows="17" columns="2">
24141 <features booktabs="true" tabularvalignment="middle">
24142 <column alignment="center" valignment="top" width="0pt">
24143 <column alignment="center" valignment="top" width="0pt">
24145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24148 \begin_layout Plain Layout
24154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24157 \begin_layout Plain Layout
24165 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24168 \begin_layout Plain Layout
24174 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24177 \begin_layout Plain Layout
24178 \begin_inset Formula $>$
24188 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24191 \begin_layout Plain Layout
24199 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24202 \begin_layout Plain Layout
24203 \begin_inset Formula $\ge$
24213 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24216 \begin_layout Plain Layout
24224 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24227 \begin_layout Plain Layout
24228 \begin_inset Formula $\gg$
24238 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24241 \begin_layout Plain Layout
24249 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24252 \begin_layout Plain Layout
24253 \begin_inset Formula $\succ$
24263 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24266 \begin_layout Plain Layout
24274 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24277 \begin_layout Plain Layout
24278 \begin_inset Formula $\succeq$
24288 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24291 \begin_layout Plain Layout
24299 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24302 \begin_layout Plain Layout
24303 \begin_inset Formula $\supset$
24313 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24316 \begin_layout Plain Layout
24324 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24327 \begin_layout Plain Layout
24328 \begin_inset Formula $\supseteq$
24338 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24341 \begin_layout Plain Layout
24349 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24352 \begin_layout Plain Layout
24353 \begin_inset Formula $\sqsupseteq$
24363 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24366 \begin_layout Plain Layout
24374 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24377 \begin_layout Plain Layout
24378 \begin_inset Formula $\ni$
24388 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24391 \begin_layout Plain Layout
24399 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24402 \begin_layout Plain Layout
24403 \begin_inset Formula $\dashv$
24413 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24416 \begin_layout Plain Layout
24424 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24427 \begin_layout Plain Layout
24428 \begin_inset Formula $\frown$
24438 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24441 \begin_layout Plain Layout
24449 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24452 \begin_layout Plain Layout
24453 \begin_inset Formula $\rhd$
24463 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24466 \begin_layout Plain Layout
24474 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24477 \begin_layout Plain Layout
24478 \begin_inset Formula $\unrhd$
24488 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24491 \begin_layout Plain Layout
24499 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24502 \begin_layout Plain Layout
24503 \begin_inset Formula $\lessgtr$
24513 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24516 \begin_layout Plain Layout
24524 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24527 \begin_layout Plain Layout
24528 \begin_inset Formula $\parallel$
24538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24541 \begin_layout Plain Layout
24549 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24552 \begin_layout Plain Layout
24553 \begin_inset Formula $\nparallel$
24569 \begin_layout Standard
24570 \begin_inset VSpace medskip
24585 are bigger than the equal looking operators
24600 \begin_layout Standard
24602 supports also many special relations.
24603 Use the toolbar button
24606 arg "math-insert \\leqq"
24609 to see a list of these relations.
24612 \begin_layout Standard
24613 Relations are, in contrary to symbols, always surrounded by space.
24616 \begin_layout Standard
24617 Relations with labels can be created with the command
24624 \begin_inset Index idx
24627 \begin_layout Plain Layout
24636 \begin_inset Separator parbreak
24642 \begin_layout Standard
24644 \begin_inset Tabular
24645 <lyxtabular version="3" rows="2" columns="2">
24646 <features booktabs="true" tabularvalignment="middle">
24647 <column alignment="center" valignment="top" width="0pt">
24648 <column alignment="center" valignment="top">
24650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24653 \begin_layout Plain Layout
24659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24662 \begin_layout Plain Layout
24669 <row topspace="1.5mm">
24670 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24673 \begin_layout Plain Layout
24677 \begin_inset space \textvisiblespace{}
24685 \begin_inset space \textvisiblespace{}
24689 \begin_inset Formula $\downarrow$
24695 \begin_inset space \textvisiblespace{}
24699 \begin_inset space \textvisiblespace{}
24707 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24710 \begin_layout Plain Layout
24711 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24727 \begin_layout Section
24731 \begin_layout Subsection
24732 Predefined Functions
24733 \begin_inset CommandInset label
24735 name "subsec:Predefined-Functions"
24740 \begin_inset Index idx
24743 \begin_layout Plain Layout
24744 Functions ! predefined
24752 \begin_layout Standard
24753 In general, variables are set
24757 in mathematical expressions, but not function names, because
24758 \begin_inset Formula $sin$
24761 could be misunderstood as
24762 \begin_inset Formula $s\cdot i\cdot n$
24766 Therefore there are predefined functionswhich are additionally a bit separated
24768 They are inserted as commands starting with a backslash before their name.
24769 \begin_inset Separator parbreak
24775 \begin_layout Standard
24777 \begin_inset Tabular
24778 <lyxtabular version="3" rows="2" columns="2">
24779 <features booktabs="true" tabularvalignment="middle">
24780 <column alignment="center" valignment="top" width="0pt">
24781 <column alignment="center" valignment="top" width="0pt">
24783 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24786 \begin_layout Plain Layout
24792 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24795 \begin_layout Plain Layout
24803 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24806 \begin_layout Plain Layout
24812 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24815 \begin_layout Plain Layout
24816 \begin_inset Formula $Asin(x)+B$
24830 \begin_inset space \quad{}
24834 \begin_inset Tabular
24835 <lyxtabular version="3" rows="2" columns="2">
24836 <features booktabs="true" tabularvalignment="middle">
24837 <column alignment="center" valignment="top" width="0pt">
24838 <column alignment="center" valignment="top" width="0pt">
24840 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24843 \begin_layout Plain Layout
24849 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24852 \begin_layout Plain Layout
24860 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24863 \begin_layout Plain Layout
24871 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24874 \begin_layout Plain Layout
24875 \begin_inset Formula $A\sin(x)+B$
24891 \begin_layout Standard
24892 The following functions are predefined:
24895 \begin_layout Standard
24896 \begin_inset VSpace -2mm
24902 \begin_layout Standard
24904 \begin_inset Tabular
24905 <lyxtabular version="3" rows="9" columns="4">
24906 <features booktabs="true" tabularvalignment="middle">
24907 <column alignment="center" valignment="top" width="0pt">
24908 <column alignment="center" valignment="top" width="0pt">
24909 <column alignment="center" valignment="top" width="0pt">
24910 <column alignment="center" valignment="top" width="0pt">
24912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24915 \begin_layout Plain Layout
24921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24924 \begin_layout Plain Layout
24930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24933 \begin_layout Plain Layout
24939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="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" usebox="none">
24975 \begin_layout Plain Layout
24983 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24986 \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" usebox="none">
25021 \begin_layout Plain Layout
25029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25032 \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" usebox="none">
25067 \begin_layout Plain Layout
25075 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25078 \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" usebox="none">
25113 \begin_layout Plain Layout
25121 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25124 \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" usebox="none">
25159 \begin_layout Plain Layout
25167 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25170 \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" usebox="none">
25205 \begin_layout Plain Layout
25213 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25216 \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" usebox="none">
25251 \begin_layout Plain Layout
25259 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25262 \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" usebox="none">
25297 \begin_layout Plain Layout
25305 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25308 \begin_layout Plain Layout
25324 \begin_layout Standard
25325 They can also be inserted with the math toolbar button
25328 arg "math-insert \\functions"
25334 \begin_layout Subsection
25335 Self-defined Functions
25336 \begin_inset Index idx
25339 \begin_layout Plain Layout
25340 Functions ! self-defined
25348 \begin_layout Standard
25349 To use a function that is not predefined, like for example the sign function
25350 sgn(x), there are two possibilities:
25353 \begin_layout Itemize
25354 Define the function by inserting the following line to the \SpecialChar LaTeX
25359 \begin_layout Plain Layout
25364 DeclareMathOperator
25367 \begin_inset CommandInset ref
25369 reference "subsec:Self-defined-Operators"
25379 \begin_inset Newline newline
25383 \begin_inset VSpace -3mm
25387 \begin_inset Newline newline
25394 DeclareMathOperator{
25399 \begin_inset Index idx
25402 \begin_layout Plain Layout
25407 DeclareMathOperator
25413 \begin_inset Newline newline
25417 \begin_inset VSpace -2mm
25421 \begin_inset Newline newline
25424 Now the new defined function can be called with the command
25433 \begin_layout Itemize
25434 Write the formula as usual, mark the formula name, in our example the letters
25439 , and change it to mathematical text.
25440 Finally, a space is inserted between prefactor and function.
25443 \begin_layout Standard
25444 The result is the same with both methods as with a predefined function
25448 \begin_layout Plain Layout
25449 In \SpecialChar LyX
25450 self-defined functions are displayed red, predefined ones black.
25456 \begin_inset Separator parbreak
25462 \begin_layout Standard
25464 \begin_inset Tabular
25465 <lyxtabular version="3" rows="3" columns="2">
25466 <features booktabs="true" tabularvalignment="middle">
25467 <column alignment="center" valignment="top" width="0pt">
25468 <column alignment="center" valignment="top" width="0pt">
25470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25473 \begin_layout Plain Layout
25479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25482 \begin_layout Plain Layout
25490 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25493 \begin_layout Plain Layout
25501 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25504 \begin_layout Plain Layout
25505 \begin_inset Formula $A\sgn(x)+B$
25515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25518 \begin_layout Plain Layout
25522 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25533 \begin_layout Plain Layout
25534 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25550 \begin_layout Standard
25551 The first method is more suitable when the self-defined function should
25552 be used several times.
25555 \begin_layout Subsection
25557 \begin_inset Index idx
25560 \begin_layout Plain Layout
25569 \begin_layout Standard
25570 For limits, in addition to the commands
25577 \begin_inset Index idx
25580 \begin_layout Plain Layout
25600 the following functions are defined:
25601 \begin_inset Separator parbreak
25607 \begin_layout Standard
25609 \begin_inset Tabular
25610 <lyxtabular version="3" rows="5" columns="2">
25611 <features booktabs="true" tabularvalignment="middle">
25612 <column alignment="center" valignment="top" width="0pt">
25613 <column alignment="center" valignment="top" width="0pt">
25615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25618 \begin_layout Plain Layout
25624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25627 \begin_layout Plain Layout
25635 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25638 \begin_layout Plain Layout
25646 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25649 \begin_layout Plain Layout
25650 \begin_inset Formula $\varliminf$
25659 <row topspace="1.5mm">
25660 <cell alignment="center" valignment="top" usebox="none">
25663 \begin_layout Plain Layout
25671 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25674 \begin_layout Plain Layout
25675 \begin_inset Formula $\varlimsup$
25684 <row topspace="1.5mm">
25685 <cell alignment="center" valignment="top" usebox="none">
25688 \begin_layout Plain Layout
25696 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25699 \begin_layout Plain Layout
25700 \begin_inset Formula $\varprojlim$
25709 <row topspace="1.5mm" bottomspace="1mm">
25710 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25713 \begin_layout Plain Layout
25721 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25724 \begin_layout Plain Layout
25725 \begin_inset Formula $\varinjlim$
25741 \begin_layout Standard
25742 \begin_inset VSpace medskip
25745 The limit is created by inserting a subscript.
25746 It is set right beside the function in an inline formula:
25749 \begin_layout Standard
25751 \begin_inset Tabular
25752 <lyxtabular version="3" rows="2" columns="2">
25753 <features booktabs="true" tabularvalignment="middle">
25754 <column alignment="center" valignment="top" width="0pt">
25755 <column alignment="center" valignment="top" width="0pt">
25757 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25760 \begin_layout Plain Layout
25766 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25769 \begin_layout Plain Layout
25777 <cell alignment="center" valignment="top" usebox="none">
25780 \begin_layout Plain Layout
25786 \begin_inset space \textvisiblespace{}
25790 \begin_inset space \textvisiblespace{}
25798 <cell alignment="center" valignment="top" usebox="none">
25801 \begin_layout Plain Layout
25802 \begin_inset Formula $\lim_{x\to A}x=B$
25818 \begin_layout Standard
25819 In a displayed formula the limit is set below the formula, as usual:
25820 \begin_inset Formula
25830 \begin_layout Standard
25831 \begin_inset VSpace medskip
25837 \begin_layout Standard
25838 How to adjust the typesetting of the limits see
25839 \begin_inset CommandInset ref
25841 reference "subsec:Operator-Limits"
25848 \begin_layout Subsection
25850 \begin_inset Index idx
25853 \begin_layout Plain Layout
25854 Functions ! modulo-
25862 \begin_layout Standard
25863 The modulo-function is special, because it exists in four variants.
25864 The variants in a displayed formula are:
25865 \begin_inset Formula
25867 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25868 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25869 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25870 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25871 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25879 \begin_layout Standard
25880 In an inline formula less space is set before the function names for all
25882 By default the modulo-functions take only the first following character
25884 To use more than one character, one has to put them into \SpecialChar TeX
25886 \begin_inset Formula
25888 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25889 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25890 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25898 \begin_layout Section
25900 \begin_inset Index idx
25903 \begin_layout Plain Layout
25912 \begin_layout Standard
25913 The characters ^ and _ would normally create a superscript and subscript,
25915 To get these characters you have to insert them with a leading
25918 \begin_inset Separator parbreak
25924 \begin_layout Standard
25927 \begin_inset Tabular
25928 <lyxtabular version="3" rows="3" columns="2">
25929 <features booktabs="true" tabularvalignment="middle">
25930 <column alignment="left" valignment="top" width="0pt">
25931 <column alignment="block" valignment="top">
25933 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25936 \begin_layout Plain Layout
25942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25945 \begin_layout Plain Layout
25953 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25956 \begin_layout Plain Layout
25960 \begin_inset space \textvisiblespace{}
25968 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25971 \begin_layout Plain Layout
25972 \begin_inset Formula $\mathcircumflex$
25982 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25985 \begin_layout Plain Layout
25993 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25996 \begin_layout Plain Layout
25997 \begin_inset Formula $\_$
26013 \begin_layout Subsection
26014 Special Characters in Mathematical Text
26017 \begin_layout Standard
26018 The following commands can only be used in mathematical text or in \SpecialChar TeX
26022 \begin_layout Standard
26023 \begin_inset space \hfill{}
26027 \begin_inset Tabular
26028 <lyxtabular version="3" rows="8" columns="2">
26029 <features booktabs="true" tabularvalignment="middle">
26030 <column alignment="left" valignment="top" width="0pt">
26031 <column alignment="block" valignment="top">
26033 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26036 \begin_layout Plain Layout
26042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26045 \begin_layout Plain Layout
26053 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26056 \begin_layout Plain Layout
26064 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26067 \begin_layout Plain Layout
26068 \begin_inset Formula $\textrm{œ}$
26078 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26081 \begin_layout Plain Layout
26089 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26092 \begin_layout Plain Layout
26093 \begin_inset Formula $\textrm{Œ}$
26103 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26106 \begin_layout Plain Layout
26114 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26117 \begin_layout Plain Layout
26118 \begin_inset Formula $\textrm{æ}$
26128 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26131 \begin_layout Plain Layout
26139 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26142 \begin_layout Plain Layout
26143 \begin_inset Formula $\textrm{Æ}$
26153 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26156 \begin_layout Plain Layout
26164 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26167 \begin_layout Plain Layout
26168 \begin_inset Formula $\textrm{\aa}$
26178 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26181 \begin_layout Plain Layout
26185 \begin_inset Index idx
26188 \begin_layout Plain Layout
26195 \begin_layout Plain Layout
26216 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26219 \begin_layout Plain Layout
26220 \begin_inset Formula $\textrm{Å}$
26230 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26233 \begin_layout Plain Layout
26241 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26244 \begin_layout Plain Layout
26245 \begin_inset Formula $\textrm{ı}$
26259 \begin_inset space \hfill{}
26263 \begin_inset Tabular
26264 <lyxtabular version="3" rows="8" columns="2">
26265 <features booktabs="true" tabularvalignment="middle">
26266 <column alignment="left" valignment="top" width="0pt">
26267 <column alignment="center" valignment="top">
26269 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26272 \begin_layout Plain Layout
26274 \begin_inset Note Note
26277 \begin_layout Plain Layout
26279 \begin_inset space \thinspace{}
26282 mm is used for separation, because otherwise the output will be ¡ and ¿
26293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26296 \begin_layout Plain Layout
26304 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26307 \begin_layout Plain Layout
26315 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26318 \begin_layout Plain Layout
26319 \begin_inset Formula $\textrm{ø}$
26329 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26332 \begin_layout Plain Layout
26340 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26343 \begin_layout Plain Layout
26344 \begin_inset Formula $\textrm{Ø}$
26354 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26357 \begin_layout Plain Layout
26365 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26368 \begin_layout Plain Layout
26369 \begin_inset Formula $\textrm{ł}$
26379 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26382 \begin_layout Plain Layout
26390 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26393 \begin_layout Plain Layout
26394 \begin_inset Formula $\textrm{Ł}$
26404 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26407 \begin_layout Plain Layout
26409 \begin_inset space \hspace{}
26414 \begin_inset space \textvisiblespace{}
26422 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26425 \begin_layout Plain Layout
26426 \begin_inset Formula $\textrm{!`}$
26436 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26439 \begin_layout Plain Layout
26441 \begin_inset space \hspace{}
26446 \begin_inset space \textvisiblespace{}
26454 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26457 \begin_layout Plain Layout
26458 \begin_inset Formula $\textrm{?`}$
26468 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26471 \begin_layout Plain Layout
26479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26482 \begin_layout Plain Layout
26483 \begin_inset Formula $\textrm{ȷ}$
26497 \begin_inset space \hfill{}
26503 \begin_layout Standard
26505 \begin_inset Formula $\textrm{\textrm{Å}}$
26509 \begin_inset Formula $\textrm{\textrm{Ø}}$
26512 can also be inserted via the math toolbar button
26515 arg "math-insert \\digamma"
26521 \begin_layout Standard
26522 An exception are the commands
26525 \begin_inset space \hspace{}
26534 \begin_inset space \hspace{}
26540 , because they can be inserted in \SpecialChar LyX
26544 \begin_layout Subsection
26546 \begin_inset CommandInset label
26548 name "subsec:Accents-in-Text"
26553 \begin_inset Index idx
26556 \begin_layout Plain Layout
26565 \begin_layout Standard
26566 With the following commands all letters can be accented.
26567 The commands must be inserted in \SpecialChar TeX
26571 \begin_layout Standard
26572 \begin_inset space \hfill{}
26576 \begin_inset Tabular
26577 <lyxtabular version="3" rows="8" columns="2">
26578 <features booktabs="true" tabularvalignment="middle">
26579 <column alignment="left" valignment="top" width="0pt">
26580 <column alignment="block" valignment="top">
26582 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26585 \begin_layout Plain Layout
26591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26594 \begin_layout Plain Layout
26602 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26605 \begin_layout Plain Layout
26609 \begin_inset Quotes grd
26617 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26620 \begin_layout Plain Layout
26624 \begin_layout Plain Layout
26640 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26643 \begin_layout Plain Layout
26651 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26654 \begin_layout Plain Layout
26658 \begin_layout Plain Layout
26674 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26677 \begin_layout Plain Layout
26681 \begin_inset space \textvisiblespace{}
26689 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26692 \begin_layout Plain Layout
26696 \begin_layout Plain Layout
26712 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26715 \begin_layout Plain Layout
26723 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26726 \begin_layout Plain Layout
26730 \begin_layout Plain Layout
26746 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26749 \begin_layout Plain Layout
26753 \begin_inset space \textvisiblespace{}
26761 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26764 \begin_layout Plain Layout
26768 \begin_layout Plain Layout
26784 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26787 \begin_layout Plain Layout
26791 \begin_inset space \textvisiblespace{}
26799 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26802 \begin_layout Plain Layout
26806 \begin_layout Plain Layout
26822 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26825 \begin_layout Plain Layout
26829 \begin_inset space \textvisiblespace{}
26837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26840 \begin_layout Plain Layout
26844 \begin_layout Plain Layout
26864 \begin_inset space \hfill{}
26868 \begin_inset Tabular
26869 <lyxtabular version="3" rows="8" columns="2">
26870 <features booktabs="true" tabularvalignment="middle">
26871 <column alignment="left" valignment="top" width="0pt">
26872 <column alignment="center" valignment="top">
26874 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26877 \begin_layout Plain Layout
26883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26886 \begin_layout Plain Layout
26894 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26897 \begin_layout Plain Layout
26901 \begin_inset space \textvisiblespace{}
26909 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26912 \begin_layout Plain Layout
26916 \begin_layout Plain Layout
26932 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26935 \begin_layout Plain Layout
26943 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26946 \begin_layout Plain Layout
26950 \begin_layout Plain Layout
26966 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26969 \begin_layout Plain Layout
26973 \begin_inset Index idx
26976 \begin_layout Plain Layout
26987 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26990 \begin_layout Plain Layout
26994 \begin_layout Plain Layout
27010 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27013 \begin_layout Plain Layout
27021 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27024 \begin_layout Plain Layout
27028 \begin_layout Plain Layout
27044 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27047 \begin_layout Plain Layout
27051 \begin_inset space \textvisiblespace{}
27059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27062 \begin_layout Plain Layout
27066 \begin_layout Plain Layout
27082 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27085 \begin_layout Plain Layout
27089 \begin_inset space \textvisiblespace{}
27097 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27100 \begin_layout Plain Layout
27104 \begin_layout Plain Layout
27120 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27123 \begin_layout Plain Layout
27127 \begin_inset space \textvisiblespace{}
27135 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27138 \begin_layout Plain Layout
27142 \begin_layout Plain Layout
27162 \begin_inset space \hfill{}
27168 \begin_layout Standard
27169 \begin_inset VSpace medskip
27178 also two different characters can be accented.
27184 \begin_inset space \textvisiblespace{}
27193 \begin_layout Plain Layout
27205 \begin_layout Standard
27218 can in combination with vowels directly be inserted with the keyboard without
27219 using \SpecialChar TeX
27221 The same applies for the tilde
27225 \begin_layout Plain Layout
27226 This only applies for keyboards where the tilde is defined as accent.
27235 in combination with
27250 \begin_layout Standard
27293 and accents that are inserted directly with the keyboard are also available
27294 in mathematical text.
27295 For the other accents there are special math commands to be used in formulas,
27297 \begin_inset CommandInset ref
27299 reference "subsec:Accents-for-one"
27306 \begin_layout Standard
27307 \begin_inset VSpace bigskip
27310 Furthermore, with the command
27317 \begin_inset Index idx
27320 \begin_layout Plain Layout
27328 all numbers and letters can be set into a circle, quasi accented with a
27329 circle, similar to the copyright symbol.
27332 \begin_layout Standard
27334 \begin_inset Tabular
27335 <lyxtabular version="3" rows="3" columns="2">
27336 <features booktabs="true" tabularvalignment="middle">
27337 <column alignment="center" valignment="top" width="0pt">
27338 <column alignment="center" valignment="top">
27340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27343 \begin_layout Plain Layout
27349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27352 \begin_layout Plain Layout
27360 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27363 \begin_layout Plain Layout
27371 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27374 \begin_layout Plain Layout
27378 \begin_layout Plain Layout
27393 <row topspace="1mm">
27394 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27397 \begin_layout Plain Layout
27408 raisebox{-1.5pt}{W}}
27413 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27416 \begin_layout Plain Layout
27420 \begin_layout Plain Layout
27450 \begin_layout Standard
27451 One has to take care that the character fits in the circle.
27462 \begin_layout Plain Layout
27464 \begin_inset CommandInset ref
27466 reference "subsec:Font-Sizes"
27475 specifies thereby the size of the circle.
27486 \begin_layout Plain Layout
27488 \begin_inset CommandInset ref
27490 reference "subsec:Boxes-without-Frame"
27499 the character can be centered.
27502 \begin_layout Subsection
27504 \begin_inset Index idx
27507 \begin_layout Plain Layout
27516 \begin_layout Standard
27517 Old-style figures (also known as old-style numerals) are created with the
27525 \begin_inset Index idx
27528 \begin_layout Plain Layout
27537 The command can be used in formulas and in \SpecialChar TeX
27539 The command scheme is:
27542 \begin_layout Standard
27547 oldstylenums{number}
27550 \begin_layout Standard
27555 oldstylenums{0123456789
27558 \begin_inset Formula $\oldstylenums{0123456789}$
27564 \begin_layout Section
27566 \begin_inset CommandInset label
27568 name "sec:Formula-Styles"
27573 \begin_inset Index idx
27576 \begin_layout Plain Layout
27585 \begin_layout Itemize
27586 There are two different alignment styles:
27587 \begin_inset Separator parbreak
27594 \begin_layout Description
27595 Centered is the predefined standard
27598 \begin_layout Description
27599 Indented for this the option
27603 must be inserted in the menu
27605 Document\SpecialChar menuseparator
27611 \begin_inset space ~
27617 \begin_layout Standard
27622 is used, the indentation can be adjusted with the length
27629 \begin_inset Index idx
27632 \begin_layout Plain Layout
27641 Should the distance be 15
27642 \begin_inset space \thinspace{}
27645 mm, the following command line is inserted in the \SpecialChar LaTeX
27649 \begin_layout Standard
27659 \begin_layout Standard
27660 When no length is specified, the predefined value of 30
27661 \begin_inset space \thinspace{}
27668 \begin_layout Itemize
27669 And two different numbering styles:
27670 \begin_inset Separator parbreak
27677 \begin_layout Description
27678 Right is the predefined standard
27681 \begin_layout Description
27682 Left for this the option
27686 must be inserted in the menu
27688 Document\SpecialChar menuseparator
27694 \begin_inset space ~
27701 \begin_layout Standard
27710 can also be used together.
27711 In this case both options are inserted, separated by a comma.
27714 \begin_layout Standard
27715 The chosen styles are used for all displayed formulas of the document.
27716 When both, centered and indented formulas should be created in a document,
27722 The indented formulas are then set in a flalign environment, see
27723 \begin_inset CommandInset ref
27725 reference "subsec:Flalign-Environment"
27732 \begin_layout Section
27734 \begin_inset CommandInset label
27736 name "sec:Multiline-Formulas"
27741 \begin_inset Index idx
27744 \begin_layout Plain Layout
27745 Formula ! multiline
27753 \begin_layout Subsection
27757 \begin_layout Standard
27758 In \SpecialChar LyX
27759 multiline formulas are created by pressing
27762 arg "newline-insert newline"
27766 This creates either an
27768 eqnarray environment
27770 that is described in
27771 \begin_inset CommandInset ref
27773 reference "subsec:Eqnarray-Environment"
27777 or, when the option
27779 Use AMS math package
27781 in the document settings is selected, an
27785 that is described in
27786 \begin_inset CommandInset ref
27788 reference "subsec:Standard-align-Environment"
27793 The align environment is recommended because it provides in any case a
27794 typographically correct output.
27797 \begin_layout Standard
27798 There are other multiline formula environments that can be created via the
27801 Insert\SpecialChar menuseparator
27805 These environments are described in the following sections.
27808 \begin_layout Standard
27809 In all multiline formula environments a new line is created by pressing
27813 arg "newline-insert newline"
27817 To add or delete lines, the math toolbar buttons
27820 arg "inset-modify tabular append-row"
27826 arg "inset-modify tabular delete-row"
27829 , respectively, or the menu
27831 Edit\SpecialChar menuseparator
27837 \begin_layout Subsubsection
27839 \begin_inset CommandInset label
27841 name "subsec:Line-Separation"
27846 \begin_inset Index idx
27849 \begin_layout Plain Layout
27850 Formula ! multiline ! Line separation
27858 \begin_layout Standard
27859 There is sometimes not enough space in multiline formulas between the lines:
27860 \begin_inset Formula
27862 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}\\
27863 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
27871 \begin_layout Standard
27872 In \SpecialChar LaTeX
27873 additional line space is specified as optional argument of the new line
27875 This is not yet possible in \SpecialChar LyX
27880 \begin_layout Plain Layout
27882 \begin_inset CommandInset href
27884 name "LyX-bug #1505"
27885 target "http://www.lyx.org/trac/ticket/1505"
27894 , therefore the whole formula must be inserted in \SpecialChar TeX
27896 To add in our example space, the command
27904 is inserted at the end of the first line.
27909 \begin_layout Plain Layout
27916 \begin_layout Plain Layout
27918 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27921 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27928 \begin_layout Plain Layout
27932 left(B^{2}+x_{0}^{2}
27940 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27945 \begin_layout Plain Layout
27957 \begin_layout Standard
27958 \begin_inset VSpace bigskip
27961 To set the line separation for all lines in a formula, the length
27968 \begin_inset Index idx
27971 \begin_layout Plain Layout
27981 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27992 \begin_inset space \thinspace{}
27997 \begin_inset space \thinspace{}
28000 mm additional line separation as in the previous example, the command
28003 \begin_layout Standard
28013 \begin_layout Standard
28014 is inserted in \SpecialChar TeX
28015 mode before the formula.
28016 This requires that the \SpecialChar LaTeX
28025 \begin_layout Plain Layout
28030 is part of every \SpecialChar LaTeX
28031 standard installation.
28037 \begin_inset Index idx
28040 \begin_layout Plain Layout
28046 was loaded in \SpecialChar LaTeX
28047 -preamble with the line
28050 \begin_layout Standard
28058 \begin_layout Standard
28063 \begin_layout Plain Layout
28075 \begin_inset Formula
28077 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}\\
28078 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
28086 \begin_layout Standard
28090 \begin_layout Plain Layout
28101 To get back to the predefined distance,
28107 is set to the value 3
28108 \begin_inset space \thinspace{}
28114 \begin_layout Subsubsection
28116 \begin_inset CommandInset label
28118 name "subsec:Column-Separation"
28123 \begin_inset Index idx
28126 \begin_layout Plain Layout
28127 Formula ! multiline ! Column separation
28135 \begin_layout Standard
28136 Multiline formulas form a matrix.
28137 A formula in the eqnarray environment is for example a matrix with three
28139 By changing the column separation in this environment, the space beside
28140 the relation sign can be changed.
28143 \begin_layout Standard
28144 The column separation is specified with the length
28151 \begin_inset Index idx
28154 \begin_layout Plain Layout
28163 \begin_inset Newline newline
28166 column separation = 2
28167 \begin_inset space \thinspace{}
28177 \begin_inset Newline newline
28183 \begin_layout Standard
28193 \begin_layout Standard
28194 inserted in \SpecialChar TeX
28195 mode, sets for all following formulas a column separation of
28197 \begin_inset space \thinspace{}
28201 To get back to the predefined distance,
28208 \begin_inset space \thinspace{}
28214 \begin_layout Standard
28216 \begin_inset space \thinspace{}
28219 cm column separation:
28223 \begin_layout Plain Layout
28235 \begin_inset Formula
28243 A formula with the predefined column separation for matrices of 10
28244 \begin_inset space \thinspace{}
28251 \begin_layout Plain Layout
28263 \begin_inset Formula
28274 \begin_layout Subsubsection
28276 \begin_inset Index idx
28279 \begin_layout Plain Layout
28288 \begin_layout Standard
28289 Long formulas can be typeset using these methods:
28292 \begin_layout Itemize
28293 When one side of the equation is much shorter than the line width, this
28294 one is chosen for the left side and the right side is typeset over two
28296 \begin_inset Formula
28298 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 \\
28299 & & -\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}
28304 The minus sign at the beginning of the second line does normally not appear
28305 as an operator because it is the first character of the line.
28306 Thus it would not be surrounded by space and could not be distinguished
28307 from the fraction bar.
28309 \begin_inset space \thinspace{}
28312 pt space was inserted behind the minus sign with the command
28322 \begin_layout Plain Layout
28330 \begin_inset CommandInset ref
28332 reference "subsec:Variable-Space"
28342 \begin_inset Index idx
28345 \begin_layout Plain Layout
28356 \begin_layout Itemize
28357 When both sides of the equation are too long, the command
28364 \begin_inset Index idx
28367 \begin_layout Plain Layout
28376 It is inserted in the first column of the first line and causes all further
28377 insertions to overwrite the following columns:
28378 \begin_inset Formula
28380 \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 \\
28381 & & -\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 \\
28382 & & =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}
28387 After the insertion of
28393 , the cursor is in a purple box that is a bit shifted to the left from the
28395 In this the formula is inserted.
28396 \begin_inset Newline newline
28399 The content of the further lines is inserted to the second or another formula
28401 The greater the column number where it was inserted, the larger the indentation.
28402 \begin_inset VSpace medskip
28406 \begin_inset Newline newline
28410 \begin_inset Note Greyedout
28413 \begin_layout Plain Layout
28414 Note the following when using
28423 \begin_layout Itemize
28424 The formula doesn't use the full page width.
28426 \begin_inset space \thinspace{}
28430 \begin_inset space \space{}
28434 \begin_inset Formula $-B^{2}$
28437 is added to the first line in the above example, it would have been outside
28439 To better use the width, negative space can be inserted at the beginning
28443 \begin_layout Itemize
28444 Due to a bug in \SpecialChar LyX
28445 the cursor cannot be set with the mouse into the first
28450 \begin_layout Plain Layout
28451 \begin_inset CommandInset href
28453 name "LyX-bug #1429"
28454 target "http://www.lyx.org/trac/ticket/1429"
28463 One can only set the cursor at the beginning of the line and move it with
28472 \begin_layout Itemize
28473 Other methods to set long formulas are offered by the environments described
28475 \begin_inset CommandInset ref
28477 reference "subsec:Multline-Environment"
28482 \begin_inset CommandInset ref
28484 reference "subsec:Multiline-Formula-Parts"
28491 \begin_layout Subsubsection
28492 Multiline Fractions
28493 \begin_inset CommandInset label
28495 name "subsec:Multiline-Fractions"
28500 \begin_inset Index idx
28503 \begin_layout Plain Layout
28504 Fractions ! multiline
28512 \begin_layout Standard
28513 There are cases where the denominator and/or the numerator of a fraction
28514 is so long that the fraction does not fit into one line.
28515 It is then necessary to add a line break within the fraction.
28516 This can be done using the command
28523 \begin_inset Index idx
28526 \begin_layout Plain Layout
28535 To activate it, set in the document settings under
28538 \begin_inset space ~
28548 \begin_inset Index idx
28551 \begin_layout Plain Layout
28552 Packages ! mathtools
28560 \begin_inset space ~
28575 \begin_layout Standard
28580 splitfrac{first line}{second line}
28583 \begin_layout Standard
28584 and is used as denominator and/or numerator:
28587 \begin_layout Standard
28588 \begin_inset Formula
28590 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}
28595 The command for the first numerator above is:
28598 \begin_layout Standard
28603 splitfrac{xy+xy+xy+xy+xy
28604 \begin_inset space \textvisiblespace{}
28612 \begin_layout Subsubsection
28614 \begin_inset CommandInset label
28616 name "subsec:Multiline-Brackets"
28621 \begin_inset Index idx
28624 \begin_layout Plain Layout
28625 Brackets ! for multiline expressions
28633 \begin_layout Standard
28634 For brackets spanning multiple lines the following problem occurs:
28635 \begin_inset Formula
28637 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28638 & & \left.\cdots+B-D\right]
28646 \begin_layout Standard
28647 The closing bracket is smaller than the opening bracket because brackets
28648 with variable size may not span multiple lines.
28651 \begin_layout Standard
28652 To set the bracket size for the second line correctly, the first line is
28660 \begin_inset Index idx
28663 \begin_layout Plain Layout
28671 and the second line with
28679 \begin_layout Plain Layout
28693 \begin_inset CommandInset ref
28695 reference "subsec:Automatic-Bracket-Size"
28707 \begin_inset Index idx
28710 \begin_layout Plain Layout
28733 \begin_inset space \textvisiblespace{}
28743 \begin_inset space \textvisiblespace{}
28753 \begin_inset space \textvisiblespace{}
28759 \begin_inset Formula $\downarrow$
28765 \begin_inset Index idx
28768 \begin_layout Plain Layout
28776 is inserted, because the multiplication operator with its limits is the
28777 largest symbol in the first line and this should be the size for the bracket
28778 in the second line.
28781 \begin_layout Standard
28782 The result is this:
28783 \begin_inset Formula
28785 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28786 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28794 \begin_layout Subsection
28798 \begin_layout Standard
28799 Align environments can be used for every kind of multiline formulas.
28800 They are especially useful to set several formulas side by side.
28803 \begin_layout Standard
28804 Align environments consist of columns.
28805 The odd columns are right aligned, the even ones left aligned.
28806 Every line in an Align environment can be numbered.
28809 \begin_layout Standard
28810 Align environments are created via the menu
28812 Insert\SpecialChar menuseparator
28818 Edit\SpecialChar menuseparator
28819 Math\SpecialChar menuseparator
28820 Change Formula Type
28822 already existing formulas can be converted to Align environments.
28825 \begin_layout Standard
28826 To add or delete columns, the math toolbar buttons
28829 arg "inset-modify tabular append-column"
28835 arg "inset-modify tabular delete-column"
28838 , respectively, or the menu
28840 Edit\SpecialChar menuseparator
28846 \begin_layout Subsubsection
28847 Standard align Environment
28848 \begin_inset CommandInset label
28850 name "subsec:Standard-align-Environment"
28855 \begin_inset Index idx
28858 \begin_layout Plain Layout
28859 Formula ! multiline ! align environment
28867 \begin_layout Standard
28868 This Align environment is created by pressing
28871 arg "newline-insert newline"
28874 in a formula or by the menu
28876 Insert\SpecialChar menuseparator
28877 Math\SpecialChar menuseparator
28878 AMS align Environment
28883 \begin_layout Standard
28884 An example for two formulas set side by side, that are created with a four
28885 column align environment:
28886 \begin_inset Formula
28888 A & =\sin(B) & C & =D\\
28889 C & \ne A & B & \ne D
28894 As it can be seen, the formulas in this environment are placed so as if
28903 \begin_layout Plain Layout
28911 \begin_inset CommandInset ref
28913 reference "subsec:Variable-Space"
28924 before the first and after every even column.
28925 When the formula style
28931 \begin_layout Plain Layout
28933 \begin_inset CommandInset ref
28935 reference "sec:Formula-Styles"
28946 is used, the formula is set without the
28952 before the first column.
28955 \begin_layout Subsubsection
28956 Alignat Environment
28957 \begin_inset Index idx
28960 \begin_layout Plain Layout
28961 Formula ! multiline ! alignat environment
28969 \begin_layout Standard
28970 The alignat environment has no predefined column separation.
28971 It can be inserted manually with the spaces that are described
28972 \begin_inset CommandInset ref
28974 reference "subsec:Space"
28981 \begin_layout Standard
28982 The above example in the alignat environment where 1
28983 \begin_inset space \thinspace{}
28986 cm space was inserted at the beginning of the second formula:
28987 \begin_inset Formula
28988 \begin{alignat*}{2}
28989 A & =\sin(B) & \hspace{1cm}C & =D\\
28990 C & \ne A & B & \ne D
28995 Because the column separation can be set separately for every column, this
28996 environment is especially suitable to set three and more formulas side
29000 \begin_layout Subsubsection
29001 Flalign Environment
29002 \begin_inset CommandInset label
29004 name "subsec:Flalign-Environment"
29009 \begin_inset Index idx
29012 \begin_layout Plain Layout
29013 Formula ! multiline ! flalign environment
29021 \begin_layout Standard
29022 In this environment the first two columns are always set as much as possible
29023 to the left and the last two ones to the right.
29025 \begin_inset Formula
29027 A & =1 & B & =2 & C & =3\\
29028 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29036 \begin_layout Standard
29037 By creating a flalign environment with an odd number of columns where an
29038 empty \SpecialChar TeX
29039 brace is inserted to the last column, several formulas in a document
29040 can be set to the left, although the formula style
29045 As example the indented formula
29046 \begin_inset CommandInset ref
29048 reference "eq:VolInt"
29053 \begin_inset Formula
29055 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29060 The first two columns contain the formula.
29061 To indent it as with the formula style
29066 \begin_inset space \thinspace{}
29069 pt space was inserted at the beginning of the first column.
29072 \begin_layout Subsection
29073 Eqnarray Environment
29074 \begin_inset CommandInset label
29076 name "subsec:Eqnarray-Environment"
29081 \begin_inset Index idx
29084 \begin_layout Plain Layout
29085 Formula ! multiline ! eqnarray environment
29093 \begin_layout Standard
29094 When this environment has been created, three blue boxes appear.
29095 The content of the first box is right aligned, the content of the last
29097 The content of the middle box appears centered and a bit smaller, because
29098 it is designed to insert there only relation characters.
29099 \begin_inset Formula
29101 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29111 \begin_layout Subsection
29113 \begin_inset Index idx
29116 \begin_layout Plain Layout
29117 Formula ! multiline ! gather environment
29125 \begin_layout Standard
29126 This environment consists of only one centered column.
29127 Every line can be numbered.
29128 \begin_inset Formula
29139 \begin_layout Subsection
29140 Multline Environment
29141 \begin_inset CommandInset label
29143 name "subsec:Multline-Environment"
29148 \begin_inset Index idx
29151 \begin_layout Plain Layout
29152 Formula ! multiline ! multline environment
29160 \begin_layout Standard
29161 The multline environment consists, like the gather environment, of only
29163 But the first line is left aligned, the last one right aligned.
29164 All other lines are centered.
29165 Therefore this environment is suitable for long formulas.
29167 \begin_inset CommandInset ref
29169 reference "eq:lefteqn"
29173 in the multline environment:
29174 \begin_inset Formula
29176 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}\\
29177 -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}\\
29178 =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}}
29186 \begin_layout Standard
29187 In the output only the last (first) line of a multline environment appears
29188 numbered when the document numbering is right (left).
29192 \begin_layout Plain Layout
29193 numbering styles see
29194 \begin_inset CommandInset ref
29196 reference "sec:Formula-Styles"
29208 \begin_layout Standard
29216 \begin_inset Index idx
29219 \begin_layout Plain Layout
29234 \begin_inset Index idx
29237 \begin_layout Plain Layout
29245 a centered line can be right or left aligned, respectively.
29246 The commands are used as follows:
29249 \begin_layout Standard
29254 shoveright{line content}
29260 shoveleft{line content}
29263 \begin_layout Standard
29264 \begin_inset VSpace medskip
29274 \begin_inset Index idx
29277 \begin_layout Plain Layout
29285 specifies the distance of the first line from the left page margin.
29286 Predefined is the length 0
29287 \begin_inset space \thinspace{}
29293 \begin_layout Standard
29294 As example the above formula where the command
29297 \begin_layout Standard
29307 \begin_layout Standard
29308 was inserted in \SpecialChar TeX
29313 \begin_layout Plain Layout
29325 \begin_inset Formula
29327 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}\\
29328 \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}}\\
29329 =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}}
29338 \begin_layout Plain Layout
29349 The second line was left aligned using
29358 \begin_layout Subsection
29359 Multiline Formula Parts
29360 \begin_inset CommandInset label
29362 name "subsec:Multiline-Formula-Parts"
29367 \begin_inset Index idx
29370 \begin_layout Plain Layout
29371 Formula ! multiline ! formula parts
29379 \begin_layout Standard
29380 To display only parts of a formula with multiple lines, one of the following
29381 environments is used:
29398 They can be inserted via the menu
29400 Insert\SpecialChar menuseparator
29403 or by using the commands described in this section.
29406 \begin_layout Standard
29407 The first three have the same properties as the corresponding multiline
29408 formula environments, but it is possible to set further formula parts beside
29411 \begin_inset Formula
29413 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29414 \Delta E\Delta t & \ge\frac{\hbar}{2}
29416 \right\} \textrm{Uncertainty relations}
29424 \begin_layout Standard
29425 To get this formula, a displayed formula is created where the command
29432 \begin_inset Index idx
29435 \begin_layout Plain Layout
29444 A purple box appears around the blue formula box where now columns and
29445 lines can be added.
29446 Outside the multiline environment other formula parts can be set, like
29450 \begin_layout Standard
29451 The aligned environment is also suitable for long formulas whose lines are
29452 horizontally aligned.
29453 Using aligned in a displayed formula has the advantage that the formula
29454 number is vertically centered behind the lines.
29456 \begin_inset CommandInset ref
29458 reference "eq:shortlong"
29462 in the aligned environment:
29463 \begin_inset Formula
29465 \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}|}\\
29466 & -\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}|}
29475 \begin_layout Standard
29476 To use the environments
29495 \begin_inset Index idx
29498 \begin_layout Plain Layout
29513 \begin_inset Index idx
29516 \begin_layout Plain Layout
29531 \begin_inset Index idx
29534 \begin_layout Plain Layout
29542 are inserted, respectively.
29543 The split environment has the same properties as the aligned environment
29544 but it can only have two columns.
29547 \begin_layout Subsection
29548 Text in multiline Formulas
29549 \begin_inset CommandInset label
29551 name "subsec:Text-in-multiline"
29556 \begin_inset Index idx
29559 \begin_layout Plain Layout
29566 \begin_inset Index idx
29569 \begin_layout Plain Layout
29570 Formula ! multiline ! text
29578 \begin_layout Standard
29579 In the Align environments, and the multline and gather environment, text
29580 can be inserted that will appear in a separate line and doesn't affect
29581 the column alignment.
29582 To do this, the command
29589 \begin_inset Index idx
29592 \begin_layout Plain Layout
29600 is used in the following scheme:
29603 \begin_layout Standard
29611 \begin_layout Standard
29612 The text should not be longer than a line because it cannot be hyphenated.
29613 As \SpecialChar LyX
29614 doesn't yet support
29620 directly, the text is written as mathematical text.
29627 must hereby be at the beginning of a line and appears in the output above
29629 An example where the text was inserted at the beginning of the second line:
29630 \begin_inset Formula
29632 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29633 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29641 \begin_layout Standard
29648 always creates some vertical space between the text and the formula lines.
29649 To avoid this space, set in the document settings under
29652 \begin_inset space ~
29662 \begin_inset Index idx
29665 \begin_layout Plain Layout
29666 Packages ! mathtools
29674 \begin_inset space ~
29680 Then you can use the command
29687 \begin_inset Index idx
29690 \begin_layout Plain Layout
29707 \begin_layout Standard
29708 \begin_inset Formula
29710 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29711 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29719 \begin_layout Section
29721 \begin_inset Index idx
29724 \begin_layout Plain Layout
29731 \begin_inset Index idx
29734 \begin_layout Plain Layout
29735 Formula ! numbering|see
29739 \begin_layout Plain Layout
29750 \begin_layout Plain Layout
29765 \begin_layout Subsection
29769 \begin_layout Standard
29770 Numbered formulas can be created with the menu
29772 Insert\SpecialChar menuseparator
29773 Math\SpecialChar menuseparator
29775 \begin_inset space ~
29783 \begin_inset space ~
29789 Existing formulas can be numbered with the menu
29791 Edit\SpecialChar menuseparator
29792 Math\SpecialChar menuseparator
29794 \begin_inset space ~
29802 arg "math-number-toggle"
29806 The formula number is displayed in \SpecialChar LyX
29807 behind the formula as a number sign
29809 The number sign is replaced in the output by the formula number.
29812 \begin_layout Standard
29813 When numbering is turned on in multiline formulas, all lines will be numbered.
29814 But the numbering can be controlled with the menu
29816 Edit\SpecialChar menuseparator
29817 Math\SpecialChar menuseparator
29819 \begin_inset space ~
29823 \begin_inset space ~
29827 \begin_inset space ~
29835 arg "math-number-line-toggle"
29841 \begin_layout Standard
29842 Except for inline formulas, all formulas can be numbered with two different
29844 \begin_inset CommandInset ref
29846 reference "sec:Formula-Styles"
29853 \begin_layout Subsection
29855 \begin_inset Index idx
29858 \begin_layout Plain Layout
29859 Cross-references ! to formulas
29867 \begin_layout Standard
29868 All labeled formulas can be cross-referenced.
29869 A label is added by the menu
29871 Insert\SpecialChar menuseparator
29874 or the toolbar button
29881 The cursor must hereby be inside a displayed formula.
29882 Alternatively you can right-click on the formula and choose
29887 A dialog pops up displaying the prefix
29892 The label is inserted there behind the prefix.
29893 The predefined prefix means
29894 \begin_inset Quotes eld
29898 \begin_inset Quotes erd
29901 and makes it easier to find labels in large documents because it marks
29902 it as formula label to divide it from e.
29903 \begin_inset space \thinspace{}
29907 \begin_inset space \space{}
29911 To change a label, the menu
29913 Insert\SpecialChar menuseparator
29916 is used again or you right-click on a formula and then on
29923 \begin_layout Standard
29924 The name of the label is displayed in \SpecialChar LyX
29925 within two parentheses behind formula.
29926 A formula with a label is always numbered.
29929 \begin_layout Standard
29930 Cross-references are inserted via the menu
29932 Insert\SpecialChar menuseparator
29935 or with the toolbar button
29938 arg "dialog-show-new-inset ref"
29942 A formula cross-reference appears in the output as formula number.
29943 When in the cross-reference dialog window the format
29947 is chosen, the cross-reference appears in the output as formula number
29949 \begin_inset Newline newline
29952 By right-clicking on a cross-reference in \SpecialChar LyX
29953 , one jumps to the formula that
29957 \begin_layout Standard
29958 Here are as examples cross-references to formulas of the following subsections:
29959 \begin_inset Note Note
29962 \begin_layout Plain Layout
29963 Note the different cross-reference types.
29971 \begin_layout Standard
29973 \begin_inset CommandInset ref
29980 \begin_inset CommandInset ref
29988 \begin_inset CommandInset ref
29994 ) big Latin letters are used for the numbering in contrary to (
29995 \begin_inset CommandInset ref
30004 \begin_layout Standard
30005 \begin_inset VSpace medskip
30008 When the argument of
30016 \begin_layout Plain Layout
30024 \begin_inset CommandInset ref
30026 reference "subsec:User-defined-Numbering"
30037 contains a box like in
30038 \begin_inset CommandInset ref
30040 reference "subsec:Paragraph-Boxes"
30044 , the formula cannot be referenced.
30047 \begin_layout Subsection
30049 \begin_inset Index idx
30052 \begin_layout Plain Layout
30053 Formula numbering ! subnumbering
30061 \begin_layout Standard
30062 With the help of the commands
30066 begin{subequations}
30074 formulas can be subnumbered.
30075 Both commands are inserted in \SpecialChar TeX
30079 \begin_layout Standard
30081 \begin_inset Formula
30092 \begin_layout Plain Layout
30096 addtocounter{equation}{-1}
30105 \begin_layout Plain Layout
30109 begin{subequations}
30115 \begin_inset VSpace -5mm
30119 \begin_inset Formula
30127 \begin_inset Formula
30137 \begin_layout Standard
30141 \begin_layout Plain Layout
30153 \begin_layout Standard
30154 To create the example, the following is done:
30157 \begin_layout Enumerate
30158 first formula is inserted
30161 \begin_layout Enumerate
30166 addtocounter{equation}{-1}
30168 begin{subequations}
30169 \begin_inset Index idx
30172 \begin_layout Plain Layout
30181 \begin_inset Newline newline
30186 is inserted after the first formula
30189 \begin_layout Enumerate
30190 second formula is inserted
30193 \begin_layout Enumerate
30194 third formula is inserted
30197 \begin_layout Enumerate
30204 is inserted after the third formula
30207 \begin_layout Standard
30208 Every formula between the commands
30220 is subnumbered as a, b,
30221 \begin_inset Newline linebreak
30224 c, \SpecialChar ldots
30225 For multiline formulas every line will be subnumbered.
30226 All subnumbered formulas are treated as
30231 But as every numbered formula increases the counter
30235 by one, the command
30241 is needed to decrease it.
30242 Otherwise the formulas
30243 \begin_inset CommandInset ref
30250 \begin_inset CommandInset ref
30257 \begin_inset CommandInset ref
30263 would be numbered as
30264 \begin_inset CommandInset ref
30271 \begin_inset CommandInset ref
30278 \begin_inset CommandInset ref
30287 \begin_layout Standard
30288 By inserting the commands in \SpecialChar TeX
30289 mode, a space is created between the first
30292 \begin_inset space \thinspace{}
30295 mm vertical space is inserted after the command
30299 begin{subequations}
30302 When the formula style
30308 \begin_layout Plain Layout
30310 \begin_inset CommandInset ref
30312 reference "sec:Formula-Styles"
30324 \begin_inset space \thinspace{}
30327 mm space is inserted instead.
30330 \begin_layout Standard
30331 Here is an example for a multiline formula where the numbering was turned
30332 off for the second line:
30336 \begin_layout Plain Layout
30340 begin{subequations}
30346 \begin_inset Formula
30348 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30349 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30350 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30359 \begin_layout Plain Layout
30371 \begin_layout Subsection
30372 User-defined Numbering
30373 \begin_inset CommandInset label
30375 name "subsec:User-defined-Numbering"
30380 \begin_inset Index idx
30383 \begin_layout Plain Layout
30384 Formula numbering ! user-defined
30392 \begin_layout Standard
30393 \begin_inset Index idx
30396 \begin_layout Plain Layout
30397 Formula numbering ! self-defined delimiters
30402 With the standard numbering parentheses are set around the formula number.
30403 To replace the parentheses for example by vertical bars, the following
30404 line is added to the \SpecialChar LaTeX
30408 \begin_layout Standard
30420 \begin_inset Note Note
30423 \begin_layout Plain Layout
30424 This macro is already declared in the \SpecialChar LaTeX
30425 -preamble for testing.
30426 To activate it, remove the percent sign at the beginning.
30434 \begin_layout Standard
30435 To use other characters, the vertical bars besides the
30439 are replaced by one ore more characters.
30440 To get only the formula number the vertical bars are omitted.
30443 \begin_layout Standard
30444 \begin_inset VSpace bigskip
30447 When there should be an expression of your choice instead of the consecutive
30448 formula number in parentheses behind the formula, the command
30455 \begin_inset Index idx
30458 \begin_layout Plain Layout
30467 \begin_inset Formula
30469 A+B=C\tag{something}\label{eq:tag}
30474 In this example the command
30479 \begin_inset space \textvisiblespace{}
30484 was inserted in the formula.
30487 \begin_layout Standard
30493 \begin_inset space \textvisiblespace{}
30498 is inserted instead, the star prevents the parentheses around the expression:
30499 \begin_inset Formula
30501 A+B=C\tag*{something}
30509 \begin_layout Standard
30510 \begin_inset VSpace bigskip
30513 To restart the formula numbering with new document parts or sections, the
30514 following command is used:
30517 \begin_layout Standard
30522 @addtoreset{equation}{part}
30525 \begin_inset Index idx
30528 \begin_layout Plain Layout
30533 \begin_layout Plain Layout
30544 \begin_layout Plain Layout
30557 \begin_layout Plain Layout
30568 \begin_layout Plain Layout
30581 \begin_inset Newline newline
30585 \begin_inset Newline newline
30592 @addtoreset{equation}{section}
30595 \begin_layout Standard
30596 To be able to use these commands in \SpecialChar TeX
30598 \begin_inset Quotes eld
30602 \begin_inset Quotes erd
30605 character has to be made
30606 \begin_inset Quotes eld
30610 \begin_inset Quotes erd
30613 for \SpecialChar LaTeX
30628 So the command sequence in \SpecialChar TeX
30632 \begin_layout Standard
30638 \begin_inset Newline newline
30643 @addtoreset{equation}{section}
30644 \begin_inset Newline newline
30652 \begin_layout Standard
30653 In the \SpecialChar LaTeX
30666 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30670 \begin_layout Standard
30685 \begin_layout Plain Layout
30690 is part of the \SpecialChar LaTeX
30696 \begin_inset Index idx
30699 \begin_layout Plain Layout
30700 Packages ! carlisle
30705 that is part of every \SpecialChar LaTeX
30706 standard installation.
30712 \begin_inset Index idx
30715 \begin_layout Plain Layout
30716 Packages ! remreset
30721 has to be loaded in the \SpecialChar LaTeX
30722 -preamble with the line
30725 \begin_layout Standard
30730 usepackage{remreset}
30733 \begin_layout Standard
30741 \begin_inset Index idx
30744 \begin_layout Plain Layout
30749 \begin_layout Plain Layout
30760 \begin_layout Plain Layout
30773 \begin_layout Plain Layout
30784 \begin_layout Plain Layout
30796 can be used with the same scheme as
30805 \begin_layout Standard
30806 \begin_inset VSpace bigskip
30809 Sometimes formulas should be numbered in the following form:
30812 \begin_layout Standard
30815 (section number.formula number)
30818 \begin_layout Standard
30819 The formula number should start with every section with
30820 \begin_inset Quotes eld
30824 \begin_inset Quotes erd
30830 \begin_layout Standard
30831 For this case there is the command
30838 \begin_inset Index idx
30841 \begin_layout Plain Layout
30849 , which is used with the following scheme:
30852 \begin_layout Standard
30857 numberwithin{counter}{sectioning}
30860 \begin_layout Standard
30861 Counter denotes what kind of numbering is affected, sectioning denotes what
30862 number is before the dot.
30865 \begin_layout Standard
30866 Thus in our case the following \SpecialChar LaTeX
30867 preamble or \SpecialChar TeX
30871 \begin_layout Standard
30876 numberwithin{equation}{section}
30879 \begin_layout Standard
30880 This is the result:
30884 \begin_layout Plain Layout
30888 numberwithin{equation}{section}
30894 \begin_inset Formula
30904 \begin_layout Standard
30906 \begin_inset space \thinspace{}
30910 \begin_inset space \space{}
30913 tables so that the number of the part is the sectioning,
30914 \begin_inset Newline newline
30921 numberwithin{table}{part}
30926 \begin_layout Standard
30927 To go back to the standard numbering or to prevent this kind of numbering
30928 when it is defined by the document class, the following command is inserted
30929 as \SpecialChar TeX
30930 code or to the \SpecialChar LaTeX
30934 \begin_layout Standard
30944 \begin_inset Index idx
30947 \begin_layout Plain Layout
30961 \begin_layout Plain Layout
30977 \begin_inset Newline newline
30985 \begin_inset Newline newline
30997 \begin_layout Standard
31004 uses internally the command
31010 , described above, that also needs to be reverted.
31014 \begin_layout Plain Layout
31021 \begin_layout Plain Layout
31025 @removefromreset{equation}{section}
31028 \begin_layout Plain Layout
31040 \begin_layout Subsection
31041 Numbering with Roman Numbers and Letters
31042 \begin_inset Index idx
31045 \begin_layout Plain Layout
31046 Formula numbering ! with letters
31052 \begin_inset Index idx
31055 \begin_layout Plain Layout
31056 Formula numbering ! with Roman numbers
31064 \begin_layout Standard
31065 Formulas can also be numbered with Roman numbers and Latin letters.
31066 To number for example with small Roman numbers, the command
31069 \begin_layout Standard
31081 \begin_layout Standard
31082 is inserted before the formula in \SpecialChar TeX
31091 \begin_inset Index idx
31094 \begin_layout Plain Layout
31102 redefines the predefined command
31118 \begin_layout Plain Layout
31125 has the same scheme like the command
31131 that is described in
31132 \begin_inset CommandInset ref
31134 reference "subsec:The-Command-newcommand"
31147 is the formula counter.
31154 is used as prefix for a counter, the value of the counter is output as
31156 When a formula is numbered, \SpecialChar LaTeX
31157 sets internally the command
31163 behind the formula.
31169 \begin_inset Index idx
31172 \begin_layout Plain Layout
31182 outputs the counter as small Roman number.
31185 \begin_layout Standard
31186 All formulas behind the command
31196 are now numbered Roman.
31197 To switch to numbering with big Roman numbers, the command is inserted
31211 \begin_inset Index idx
31214 \begin_layout Plain Layout
31226 \begin_inset Quotes eld
31230 \begin_inset Quotes erd
31233 with small Latin letters there is the command
31240 \begin_inset Index idx
31243 \begin_layout Plain Layout
31251 , for big ones there is the command
31258 \begin_inset Index idx
31261 \begin_layout Plain Layout
31274 \begin_layout Standard
31275 \begin_inset Note Greyedout
31278 \begin_layout Plain Layout
31285 \begin_inset space ~
31288 formulas can be numbered with Latin letters in one document.
31296 \begin_layout Standard
31300 \begin_layout Plain Layout
31316 \begin_layout Standard
31317 \begin_inset Formula
31319 A=\textrm{small roman}
31328 \begin_layout Plain Layout
31342 \begin_inset Formula
31344 B=\textrm{big Roman}\label{eq:Rom}
31353 \begin_layout Plain Layout
31367 \begin_inset Formula
31369 C=\textrm{small Latin}
31378 \begin_layout Plain Layout
31392 \begin_inset Formula
31394 D=\textrm{big Latin}\label{eq:Lat}
31402 \begin_layout Standard
31403 To switch back to the default numbering, insert the command:
31406 \begin_layout Standard
31416 \begin_inset Index idx
31419 \begin_layout Plain Layout
31430 \begin_layout Standard
31434 \begin_layout Plain Layout
31448 \begin_inset Formula
31458 \begin_layout Standard
31459 \begin_inset VSpace medskip
31462 As you see, formulas are numbered serially independent from the numbering
31464 When then numbering should start with
31465 \begin_inset Quotes eld
31469 \begin_inset Quotes erd
31472 when the style is changed, new equation counters have to be defined.
31473 A description about this can be found in the file
31474 \begin_inset CommandInset href
31476 name "Formula-numbering.lyx"
31477 target "run:Formula-numbering.lyx"
31484 \begin_layout Section
31485 Chemical Symbols and Equations
31486 \begin_inset CommandInset label
31488 name "subsec:Chemical-Symbols-and"
31493 \begin_inset Index idx
31496 \begin_layout Plain Layout
31497 Chemical characters ! Symbols
31503 \begin_inset Index idx
31506 \begin_layout Plain Layout
31513 \begin_inset Index idx
31516 \begin_layout Plain Layout
31525 \begin_layout Standard
31526 An example text from chemistry:
31529 \begin_layout Quote
31531 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31534 -ion reacts with two
31535 \begin_inset Formula $\mathrm{Na^{+}}$
31538 -ions to sodium sulfate
31539 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31543 The chemical equation for this is:
31544 \begin_inset Formula
31546 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31554 \begin_layout Standard
31555 This chemical equation can directly be created as formula.
31556 To avoid that the symbols appear italic, everything is highlighted and
31557 changed by the shortcut
31563 to the upright font style.
31567 \begin_layout Plain Layout
31573 \begin_inset CommandInset ref
31575 reference "subsec:Font-Styles"
31587 \begin_layout Standard
31588 A more convenient way to typeset chemical formulas is to use the command
31596 \begin_inset Index idx
31599 \begin_layout Plain Layout
31607 that is available when the \SpecialChar LaTeX
31613 \begin_inset Index idx
31616 \begin_layout Plain Layout
31629 to a formula a new blue box appears where chemical formulas can be inserted
31630 in an intuitive way.
31631 \begin_inset Separator parbreak
31637 \begin_layout Standard
31639 \begin_inset Tabular
31640 <lyxtabular version="3" rows="10" columns="2">
31641 <features booktabs="true" tabularvalignment="middle">
31642 <column alignment="center" valignment="top" width="0pt">
31643 <column alignment="center" valignment="top">
31645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31648 \begin_layout Plain Layout
31654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31657 \begin_layout Plain Layout
31665 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31668 \begin_layout Plain Layout
31672 \begin_inset space \textvisiblespace{}
31680 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31683 \begin_layout Plain Layout
31684 \begin_inset Formula $\ce{H2CO3}$
31693 <row topspace="1.5mm">
31694 <cell alignment="center" valignment="top" usebox="none">
31697 \begin_layout Plain Layout
31701 \begin_inset space \textvisiblespace{}
31709 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31712 \begin_layout Plain Layout
31713 \begin_inset Formula $\ce{SO4^{2-}}$
31722 <row topspace="1.5mm">
31723 <cell alignment="center" valignment="top" usebox="none">
31726 \begin_layout Plain Layout
31730 \begin_inset space \textvisiblespace{}
31738 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31741 \begin_layout Plain Layout
31742 \begin_inset Formula $\ce{(NH4)2S}$
31751 <row topspace="1.5mm">
31752 <cell alignment="center" valignment="top" usebox="none">
31755 \begin_layout Plain Layout
31759 \begin_inset space \textvisiblespace{}
31767 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31770 \begin_layout Plain Layout
31771 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31780 <row topspace="1.5mm">
31781 <cell alignment="center" valignment="top" usebox="none">
31784 \begin_layout Plain Layout
31788 \begin_inset space \textvisiblespace{}
31794 \begin_inset space \textvisiblespace{}
31800 \begin_inset space \textvisiblespace{}
31808 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31811 \begin_layout Plain Layout
31812 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31821 <row topspace="1.5mm">
31822 <cell alignment="center" valignment="top" usebox="none">
31825 \begin_layout Plain Layout
31829 \begin_inset space \textvisiblespace{}
31833 \begin_inset Formula $\downarrow$
31837 \begin_inset Formula $\to$
31845 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31848 \begin_layout Plain Layout
31849 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31859 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31862 \begin_layout Plain Layout
31866 \begin_inset space \textvisiblespace{}
31872 \begin_inset space \textvisiblespace{}
31878 \begin_inset space \textvisiblespace{}
31886 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31889 \begin_layout Plain Layout
31890 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31903 \begin_layout Plain Layout
31907 \begin_inset space \textvisiblespace{}
31911 \begin_inset space \textvisiblespace{}
31915 \begin_inset space \textvisiblespace{}
31919 \begin_inset space \textvisiblespace{}
31923 \begin_inset space \textvisiblespace{}
31931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31934 \begin_layout Plain Layout
31935 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31944 <row topspace="1.5mm">
31945 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31948 \begin_layout Plain Layout
31952 \begin_inset space \textvisiblespace{}
31956 \begin_inset space \textvisiblespace{}
31960 \begin_inset space \textvisiblespace{}
31964 \begin_inset space \textvisiblespace{}
31972 \begin_inset space \textvisiblespace{}
31980 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31983 \begin_layout Plain Layout
31984 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
32000 \begin_layout Standard
32001 \begin_inset Note Greyedout
32004 \begin_layout Plain Layout
32010 It is not possible in \SpecialChar LyX
32011 to use the character ^ to get an up-arrow as described
32017 One instead uses a negative thin space followed by the command
32024 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32035 \begin_layout Standard
32042 the command for equation
32043 \begin_inset space ~
32047 \begin_inset CommandInset ref
32049 reference "eq:chem-reaction"
32054 \begin_inset Newline newline
32062 \begin_inset space \textvisiblespace{}
32066 \begin_inset space \textvisiblespace{}
32070 \begin_inset space \textvisiblespace{}
32074 \begin_inset space \textvisiblespace{}
32078 \begin_inset space \textvisiblespace{}
32082 \begin_inset space \textvisiblespace{}
32088 \begin_layout Standard
32089 To create multiline chemical equations first a multiline formula is created
32091 \begin_inset CommandInset ref
32093 reference "sec:Multiline-Formulas"
32098 Afterwards the command
32104 is used in every small blue box of the formula.
32106 \begin_inset CommandInset ref
32108 reference "eq:TEOS-reaction-1"
32113 \begin_inset CommandInset ref
32115 reference "eq:TEOS-reaction-2"
32119 are an example of a multi-stage chemical reaction where every equation
32120 has its own number.
32121 \begin_inset Formula
32123 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32124 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32132 \begin_layout Standard
32143 package provides the command
32150 \begin_inset Index idx
32153 \begin_layout Plain Layout
32161 that has to be used for special cases.
32162 For more information about
32168 and more examples have a look at the documentation of
32173 \begin_inset CommandInset citation
32182 \begin_layout Section
32186 \begin_layout Standard
32188 supports two types of commutative diagrams:
32196 that are explained in the following.
32199 \begin_layout Subsection
32201 \begin_inset Index idx
32204 \begin_layout Plain Layout
32213 \begin_layout Standard
32214 Diagrams of this type visualize relations by vertical and horizontal lines
32216 \begin_inset Formula
32218 \begin{CD}A@>>>B@>>>C\\
32229 \begin_layout Standard
32230 To get them, the command
32235 \begin_inset Index idx
32238 \begin_layout Plain Layout
32248 is inserted to a formula.
32249 A blue box appears with two dashed lines where further commands can be
32254 arg "newline-insert newline"
32257 a new line is created.
32258 Horizontal relations are inserted in odd, vertical in even formula lines.
32261 \begin_layout Standard
32262 To create the relations there are the following commands:
32265 \begin_layout Itemize
32270 creates a left arrow,
32281 \begin_layout Itemize
32286 creates an up arrow,
32294 a vertical equal sign
32297 \begin_layout Itemize
32303 is a placeholder for non-existent relations
32306 \begin_layout Standard
32307 All arrows can be labeled as follows:
32310 \begin_layout Itemize
32311 If text inserted between the first and second < or >, resp., it is placed
32313 When it is inserted between the second and third one, it appears under
32317 \begin_layout Itemize
32318 When text for vertical arrows is inserted between the first and second A
32319 or V, resp., it is placed left beside the arrow.
32320 When it is inserted between the second and third one, it appears right
32322 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32326 \begin_layout Standard
32327 As example a diagram with all possible relations:
32330 \begin_layout Standard
32331 \begin_inset Formula
32333 \begin{CD}A@>j>>B@>>k>C@=F\\
32344 \begin_layout Standard
32345 The command for this is:
32346 \begin_inset Newline newline
32354 \begin_inset space \textvisiblespace{}
32357 A@>j>>B@>>k>C@=F Ctrl+Return
32358 \begin_inset Newline newline
32362 \begin_inset Phantom HPhantom
32365 \begin_layout Plain Layout
32371 \begin_inset space \textvisiblespace{}
32384 \begin_inset Formula $\to$
32390 \begin_inset Newline newline
32394 \begin_inset Phantom HPhantom
32397 \begin_layout Plain Layout
32403 \begin_inset space \textvisiblespace{}
32414 \begin_layout Subsection
32416 \begin_inset Index idx
32419 \begin_layout Plain Layout
32420 Diagrams ! xymatrix
32428 \begin_layout Standard
32429 To be able to use xymatrices, the \SpecialChar LaTeX
32435 A xymatrix is created by inserting the command
32442 Then you are able to add new matrix columns and rows like for normal matrices,
32444 \begin_inset CommandInset ref
32446 reference "sec:Matrices"
32453 \begin_layout Standard
32454 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32456 All possibilities to create commutative diagrams and decorations are explained
32461 that you find in the menu
32463 Help\SpecialChar menuseparator
32465 \begin_inset space ~
32473 \begin_layout Subsection
32479 \begin_inset Index idx
32482 \begin_layout Plain Layout
32491 \begin_layout Standard
32496 -diagrams, the \SpecialChar LaTeX
32506 -diagram is created by inserting the command
32513 Then you are able to add new matrix columns and rows like for normal matrices,
32515 \begin_inset CommandInset ref
32517 reference "sec:Matrices"
32524 \begin_layout Standard
32525 Examples how to create
32529 diagrams in \SpecialChar LyX
32532 Feynman-diagram manual
32534 that you find in the menu
32536 Help\SpecialChar menuseparator
32538 \begin_inset space ~
32546 \begin_layout Standard
32547 \begin_inset Newpage newpage
32553 \begin_layout Section
32554 User-defined Commands
32555 \begin_inset Index idx
32558 \begin_layout Plain Layout
32559 User-defined commands
32567 \begin_layout Standard
32568 \begin_inset Note Greyedout
32571 \begin_layout Plain Layout
32576 The names of user-defined commands and macros may only consist of Latin
32585 \begin_layout Subsection
32589 \begin_inset CommandInset label
32591 name "subsec:The-Command-newcommand"
32596 \begin_inset Index idx
32599 \begin_layout Plain Layout
32600 User-defined commands !
32608 \begin_inset Index idx
32611 \begin_layout Plain Layout
32622 \begin_layout Standard
32623 Many \SpecialChar LaTeX
32624 -commands are too long to be used frequently.
32625 But it is possible to define with the command
32631 new shorter commands.
32634 \begin_layout Standard
32635 The command scheme of
32644 \begin_layout Standard
32649 newcommand{new command name}[number of arguments][optional
32654 \begin_inset Newline newline
32658 \begin_inset Phantom HPhantom
32661 \begin_layout Plain Layout
32671 {command definition}
32674 \begin_layout Standard
32675 \begin_inset Note Greyedout
32678 \begin_layout Plain Layout
32683 Assure that the name of the new command is not already used in your document
32684 or by \SpecialChar LaTeX
32685 -packages that you use.
32686 When you for example define the command
32698 , you get an error message because
32704 is already defined as command for
32705 \begin_inset Quotes eld
32709 \begin_inset Formula $\le$
32713 \begin_inset Quotes erd
32724 \begin_layout Standard
32725 The number of arguments is an integer in the range 0
32726 \begin_inset space \thinspace{}
32730 \begin_inset space \thinspace{}
32733 9 and specifies how many arguments the new command should have.
32734 With the optional value a value for an optional argument can be predefined.
32735 When this is done, the
32743 rgument of the new command is automatically an optional one.
32746 \begin_layout Standard
32747 Here are some examples:
32750 \begin_layout Itemize
32751 To define the command
32763 , the \SpecialChar LaTeX
32765 \begin_inset VSpace medskip
32769 \begin_inset Newline newline
32783 \begin_layout Itemize
32784 To define the command
32796 , the argument (that should be underlined) must be taken into account.
32797 For this the preamble line is:
32798 \begin_inset VSpace medskip
32802 \begin_inset Newline newline
32816 \begin_inset VSpace medskip
32820 \begin_inset Newline newline
32827 acts as argument placeholder, the
32831 behind it denotes that it is the placeholder for the first argument.
32834 \begin_layout Itemize
32842 \begin_inset space \thinspace{}
32846 \begin_inset space \space{}
32856 \begin_inset VSpace medskip
32860 \begin_inset Newline newline
32871 framebox#1#2{$#3$}}
32874 \begin_inset VSpace medskip
32878 \begin_inset Newline newline
32881 The two Dollar signs creates the extra formula needed for
32888 \begin_inset CommandInset ref
32890 reference "subsec:Boxes-with-Frame"
32897 \begin_layout Itemize
32898 To create a new command for
32904 where the color for the box need not be specified, the argument for the
32905 color is defined optional:
32906 \begin_inset VSpace medskip
32910 \begin_inset Newline newline
32921 fcolorbox{#2}{#1}{$#3$}}
32924 \begin_inset VSpace medskip
32928 \begin_inset Newline newline
32931 When the color is not specified when using
32937 , the predefined color
32944 \begin_layout Standard
32945 A test of the new defined commands:
32946 \begin_inset Separator parbreak
32952 \begin_layout Standard
32954 \begin_inset Tabular
32955 <lyxtabular version="3" rows="6" columns="2">
32956 <features booktabs="true" tabularvalignment="middle">
32957 <column alignment="center" valignment="top" width="0pt">
32958 <column alignment="center" valignment="top">
32960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32963 \begin_layout Plain Layout
32969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32972 \begin_layout Plain Layout
32980 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32983 \begin_layout Plain Layout
32987 \begin_inset space \textvisiblespace{}
32995 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32998 \begin_layout Plain Layout
32999 \begin_inset Formula $A\gr B$
33009 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33012 \begin_layout Plain Layout
33020 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33023 \begin_layout Plain Layout
33024 \begin_inset Formula $\us{ABcd}$
33033 <row topspace="1mm">
33034 <cell alignment="center" valignment="top" usebox="none">
33037 \begin_layout Plain Layout
33041 \begin_inset Formula $\to$
33047 \begin_inset Formula $\to$
33055 \begin_inset space \textvisiblespace{}
33063 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33066 \begin_layout Plain Layout
33067 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33076 <row topspace="1.5mm">
33077 <cell alignment="center" valignment="top" usebox="none">
33080 \begin_layout Plain Layout
33084 \begin_inset Formula $\to$
33092 \begin_inset space \textvisiblespace{}
33100 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33103 \begin_layout Plain Layout
33104 \begin_inset Formula $\cb{red}{\int A=B}$
33113 <row topspace="1.5mm" bottomspace="1mm">
33114 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33117 \begin_layout Plain Layout
33123 \begin_inset Formula $\to$
33131 \begin_inset space \textvisiblespace{}
33139 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33142 \begin_layout Plain Layout
33143 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33159 \begin_layout Subsection
33161 \begin_inset Index idx
33164 \begin_layout Plain Layout
33165 User-defined commands! Math macros
33171 \begin_inset Index idx
33174 \begin_layout Plain Layout
33183 \begin_layout Standard
33184 User-defined commands are especially convenient for complex expressions.
33185 When you are for example dealing with a document that has quadratic equations,
33186 the same solution type occurs several times.
33187 The general form of a quadratic equation is
33188 \begin_inset Formula
33190 0=\lambda^{2}+p\lambda+q
33195 The general form of the solution is
33196 \begin_inset Formula
33198 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33206 \begin_layout Standard
33207 To define a command for the solution formula where only the three parameters
33209 \begin_inset Formula $\lambda$
33213 \begin_inset Formula $p$
33217 \begin_inset Formula $q$
33220 need to be specified and the index of
33221 \begin_inset Formula $\lambda$
33224 can be given optionally, the \SpecialChar LaTeX
33226 \begin_inset Newline newline
33242 \begin_inset Newline newline
33246 \begin_inset Phantom HPhantom
33249 \begin_layout Plain Layout
33263 frac{#3^{2}}{4}-#4}}
33266 \begin_layout Standard
33267 To create with this the solution formula, the command
33268 \begin_inset Newline newline
33278 \begin_inset Formula $\to$
33284 \begin_inset Formula $\to$
33291 is inserted to a formula
33296 \begin_layout Standard
33297 The definition of the new command is unintuitive because one has to know
33298 the schemes of all used \SpecialChar LaTeX
33300 \begin_inset space \thinspace{}
33304 \begin_inset space \space{}
33307 that a fraction is inserted in \SpecialChar LaTeX
33312 frac{numerator}{denominator}
33315 Furthermore one can easily forget a brace in the definition and cannot
33316 see in \SpecialChar LyX
33317 what the new command is doing.
33318 To avoid these problems \SpecialChar LyX
33319 offers the possibility to use math macros instead
33329 \begin_layout Standard
33330 A math macro is created by using the menu
33332 Insert\SpecialChar menuseparator
33333 Math\SpecialChar menuseparator
33336 or the toolbar button
33339 arg "math-macro newmacroname_newcommand"
33343 The math macro toolbar appears together with the following box where the
33345 \begin_inset Newline newline
33349 \begin_inset space \hspace*{\fill}
33353 \begin_inset Graphics
33354 filename clipart/macrobox.png
33360 \begin_inset space \hspace*{\fill}
33364 \begin_inset Newline newline
33368 \begin_inset FormulaMacro
33369 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33374 newmacroname is the default name of the macro that should be changed to
33375 something sensible.
33376 The wanted formula is inserted in the first blue box.
33377 An argument placeholder is inserted with the command
33384 \begin_inset space \thinspace{}
33388 \begin_inset space \space{}
33397 or by using the macro toolbar button
33400 arg "math-macro-add-param"
33404 Argument placeholders are displayed red.
33406 \begin_inset space ~
33409 arguments are possible.
33410 Optional arguments are created with the toolbar button
33413 arg "math-macro-add-optional-param"
33417 The first non-optional argument can be transformed to an optional one with
33421 arg "math-macro-make-optional"
33425 In the second blue box the appearance of the macro in \SpecialChar LyX
33427 Normally you want to see it as it is defined, so the box is kept empty.
33428 But when you have created a macro that needs lot of space on the screen,
33429 you can insert in the box for example
33430 \begin_inset Newline newline
33460 \begin_inset Newline newline
33465 For the macro only the arguments with the macro name in front of them will
33466 then be displayed in \SpecialChar LyX
33467 , leading to a better overview.
33468 The formula appears in the output as defined in the first box.
33469 \begin_inset Newline newline
33472 The appearance of macros in formulas can furthermore be changed for single
33473 macros by setting the cursor in the macro and using the menu
33475 View\SpecialChar menuseparator
33477 \begin_inset space ~
33481 \begin_inset space ~
33489 \begin_layout Standard
33490 To use a macro, the macro name is inserted as command to a formula, in our
33498 Our macro looks in \SpecialChar LyX
33500 \begin_inset Newline newline
33504 \begin_inset space \hspace*{\fill}
33508 \begin_inset Graphics
33509 filename clipart/macrouse.png
33515 \begin_inset space \hspace*{\fill}
33519 \begin_inset Newline newline
33522 Here is our macro example with the arguments
33523 \begin_inset Formula $x$
33527 \begin_inset Formula $\ln(x)$
33531 \begin_inset Formula $B$
33537 \begin_layout Standard
33538 \begin_inset Formula
33548 \begin_layout Standard
33552 Tools\SpecialChar menuseparator
33553 Preferences\SpecialChar menuseparator
33554 Editing\SpecialChar menuseparator
33557 different styles to edit macros.
33558 To find the style that suits you the most, choose a style and set the cursor
33559 in a macro formula to see the difference.
33562 \begin_layout Standard
33563 A math macro is transformed internally to a
33569 command when exporting the document.
33576 command is not placed in the \SpecialChar LaTeX
33577 -preamble, therefore macros can only be used
33578 in formulas that are in the document below the macro definition box.
33581 \begin_layout Standard
33582 Math macros can also be directly created from a
33589 When writing for example the command
33592 \begin_inset Newline newline
33601 xleftarrow[#2]{#1}}
33602 \begin_inset Newline newline
33607 in \SpecialChar LyX
33608 as normal text, highlighting it completely and using then the shortcut
33613 , the command will be transformed to a math macro.
33614 Using this method you need to be careful that the
33620 command is typed correctly, otherwise you get a faulty macro leading to
33625 \begin_layout Standard
33626 Math macros currently have the problem that further formulas in macro definition
33627 s are handled wrongly.
33628 Therefore the example
33635 \begin_inset CommandInset ref
33637 reference "subsec:The-Command-newcommand"
33641 cannot be created as macro.
33644 \begin_layout Standard
33645 When the cursor is in a macro definition box, you will see the macro toolbar
33646 in \SpecialChar LyX
33650 \begin_layout Standard
33651 \begin_inset VSpace defskip
33657 \begin_layout Standard
33658 \begin_inset Graphics
33659 filename clipart/MacroToolbar.png
33664 \begin_inset Index idx
33667 \begin_layout Plain Layout
33676 \begin_layout Standard
33677 \begin_inset VSpace defskip
33683 \begin_layout Standard
33684 The macro toolbar contains from left to right the following buttons:
33687 \begin_layout Standard
33688 \begin_inset VSpace defskip
33694 \begin_layout Standard
33695 \begin_inset Tabular
33696 <lyxtabular version="3" rows="9" columns="2">
33697 <features islongtable="true" longtabularalignment="center">
33698 <column alignment="left" valignment="top">
33699 <column alignment="left" valignment="top" width="85col%">
33700 <row interlinespace="2.5mm">
33701 <cell alignment="center" valignment="top" usebox="none">
33704 \begin_layout Plain Layout
33707 arg "math-macro-remove-param"
33715 <cell alignment="center" valignment="top" usebox="none">
33718 \begin_layout Plain Layout
33721 Edit\SpecialChar menuseparator
33722 Math\SpecialChar menuseparator
33724 \begin_inset space ~
33727 Definition\SpecialChar menuseparator
33728 Remove Last Argument
33734 <row interlinespace="2.5mm">
33735 <cell alignment="center" valignment="top" usebox="none">
33738 \begin_layout Plain Layout
33741 arg "math-macro-add-param"
33749 <cell alignment="center" valignment="top" usebox="none">
33752 \begin_layout Plain Layout
33755 Edit\SpecialChar menuseparator
33756 Math\SpecialChar menuseparator
33758 \begin_inset space ~
33761 Definition\SpecialChar menuseparator
33768 <row interlinespace="2.5mm">
33769 <cell alignment="center" valignment="top" usebox="none">
33772 \begin_layout Plain Layout
33775 arg "math-macro-make-optional"
33783 <cell alignment="center" valignment="top" usebox="none">
33786 \begin_layout Plain Layout
33789 Edit\SpecialChar menuseparator
33790 Math\SpecialChar menuseparator
33792 \begin_inset space ~
33795 Definition\SpecialChar menuseparator
33796 Transform First Non-Optional to
33797 \begin_inset Newline newline
33801 \begin_inset Phantom HPhantom
33804 \begin_layout Plain Layout
33807 Edit\SpecialChar menuseparator
33808 Math\SpecialChar menuseparator
33810 \begin_inset space ~
33813 Definition\SpecialChar menuseparator
33825 <row interlinespace="2.5mm">
33826 <cell alignment="center" valignment="top" usebox="none">
33829 \begin_layout Plain Layout
33832 arg "math-macro-make-nonoptional"
33840 <cell alignment="center" valignment="top" usebox="none">
33843 \begin_layout Plain Layout
33846 Edit\SpecialChar menuseparator
33847 Math\SpecialChar menuseparator
33849 \begin_inset space ~
33852 Definition\SpecialChar menuseparator
33853 Transform Last Optional to
33854 \begin_inset Newline newline
33858 \begin_inset Phantom HPhantom
33861 \begin_layout Plain Layout
33864 Edit\SpecialChar menuseparator
33865 Math\SpecialChar menuseparator
33867 \begin_inset space ~
33870 Definition\SpecialChar menuseparator
33876 Non-Optional Argument
33882 <row interlinespace="2.5mm">
33883 <cell alignment="center" valignment="top" usebox="none">
33886 \begin_layout Plain Layout
33889 arg "math-macro-remove-optional-param"
33897 <cell alignment="center" valignment="top" usebox="none">
33900 \begin_layout Plain Layout
33903 Edit\SpecialChar menuseparator
33904 Math\SpecialChar menuseparator
33906 \begin_inset space ~
33909 Definition\SpecialChar menuseparator
33910 Remove Optional Argument
33916 <row interlinespace="2.5mm">
33917 <cell alignment="center" valignment="top" usebox="none">
33920 \begin_layout Plain Layout
33923 arg "math-macro-add-optional-param"
33931 <cell alignment="center" valignment="top" usebox="none">
33934 \begin_layout Plain Layout
33937 Edit\SpecialChar menuseparator
33938 Math\SpecialChar menuseparator
33940 \begin_inset space ~
33943 Definition\SpecialChar menuseparator
33944 Insert Optional Argument
33950 <row interlinespace="2.5mm">
33951 <cell alignment="center" valignment="top" usebox="none">
33954 \begin_layout Plain Layout
33957 arg "math-macro-remove-greedy-param"
33965 <cell alignment="center" valignment="top" usebox="none">
33968 \begin_layout Plain Layout
33971 Edit\SpecialChar menuseparator
33972 Math\SpecialChar menuseparator
33974 \begin_inset space ~
33977 Definition\SpecialChar menuseparator
33978 Remove Last Argument
33979 \begin_inset Newline newline
33983 \begin_inset Phantom HPhantom
33986 \begin_layout Plain Layout
33989 Edit\SpecialChar menuseparator
33990 Math\SpecialChar menuseparator
33992 \begin_inset space ~
33995 Definition\SpecialChar menuseparator
34001 Spitting Out To The Right
34007 <row interlinespace="2.5mm">
34008 <cell alignment="center" valignment="top" usebox="none">
34011 \begin_layout Plain Layout
34014 arg "math-macro-append-greedy-param"
34022 <cell alignment="center" valignment="top" usebox="none">
34025 \begin_layout Plain Layout
34028 Edit\SpecialChar menuseparator
34029 Math\SpecialChar menuseparator
34031 \begin_inset space ~
34034 Definition\SpecialChar menuseparator
34036 \begin_inset Newline newline
34040 \begin_inset Phantom HPhantom
34043 \begin_layout Plain Layout
34046 Edit\SpecialChar menuseparator
34047 Math\SpecialChar menuseparator
34049 \begin_inset space ~
34052 Definition\SpecialChar menuseparator
34058 Eating From The Right
34064 <row interlinespace="2.5mm">
34065 <cell alignment="center" valignment="top" usebox="none">
34068 \begin_layout Plain Layout
34071 arg "math-macro-add-greedy-optional-param"
34079 <cell alignment="center" valignment="top" usebox="none">
34082 \begin_layout Plain Layout
34085 Edit\SpecialChar menuseparator
34086 Math\SpecialChar menuseparator
34088 \begin_inset space ~
34091 Definition\SpecialChar menuseparator
34092 Append Optional Argument
34093 \begin_inset Newline newline
34097 \begin_inset Phantom HPhantom
34100 \begin_layout Plain Layout
34103 Edit\SpecialChar menuseparator
34104 Math\SpecialChar menuseparator
34106 \begin_inset space ~
34109 Definition\SpecialChar menuseparator
34115 Eating From The Right
34128 \begin_layout Section
34129 Computer Algebra Systems
34132 \begin_layout Standard
34134 offers the exchange between mathematical expressions written in \SpecialChar LyX
34136 editor and external applications or user defined scripts.
34137 Currently supported applications are
34154 Note that the set of supported mathematical constructs is limited only
34155 to very simple cases.
34158 \begin_layout Subsection
34162 \begin_layout Standard
34163 Write some expression in a formula, go to the
34165 Edit\SpecialChar menuseparator
34166 Math\SpecialChar menuseparator
34167 Use Computer Algebra System
34169 menu and choose the application you have installed on the computer.
34170 After that the result of computation should show on the right side of the
34171 expression together with the
34172 \begin_inset Quotes eld
34176 \begin_inset Quotes erd
34182 \begin_layout Standard
34183 Here are few simple examples (with results from
34187 ) to show what kind of computations can be performed:
34190 \begin_layout Itemize
34191 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34197 \begin_layout Itemize
34198 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34204 \begin_layout Itemize
34205 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34211 \begin_layout Itemize
34212 \begin_inset Formula $\det\left[\begin{array}{ccc}
34216 \end{array}\right]=-56$
34222 \begin_layout Itemize
34223 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34229 \begin_layout Subsection
34233 \begin_layout Standard
34234 Currently there is no keyboard shortcut for calling the algebra applications.
34235 One can easily bind a shortcut to the
34249 \begin_inset space \thinspace{}
34253 \begin_inset space \space{}
34260 key inside the math editor.
34265 one would use this shortcut definition command:
34268 \begin_layout Standard
34271 command-alternatives paragraph-break;math-extern maxima
34274 \begin_layout Section
34276 \begin_inset Index idx
34279 \begin_layout Plain Layout
34288 \begin_layout Subsection
34290 \begin_inset Index idx
34293 \begin_layout Plain Layout
34302 \begin_layout Standard
34303 Negative numbers often look ugly in formulas because the minus sign before
34304 the number is set with the same length as the minus operator sign.
34305 When writing the negative number in normal text, the minus sign appears
34309 \begin_layout Standard
34310 Thus, the problem disappears when converting the minus sign to mathematical
34314 \begin_layout Standard
34315 An example to visualize the problem:
34316 \begin_inset Separator parbreak
34322 \begin_layout Standard
34324 \begin_inset Tabular
34325 <lyxtabular version="3" rows="3" columns="2">
34326 <features booktabs="true" tabularvalignment="middle">
34327 <column alignment="right" valignment="top" width="0pt">
34328 <column alignment="left" valignment="top">
34330 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34333 \begin_layout Plain Layout
34339 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34342 \begin_layout Plain Layout
34350 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34353 \begin_layout Plain Layout
34359 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34362 \begin_layout Plain Layout
34363 \begin_inset Formula $x=-2$
34373 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34376 \begin_layout Plain Layout
34382 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34385 \begin_layout Plain Layout
34386 \begin_inset Formula $x=\textrm{-}2$
34402 \begin_layout Subsection
34403 Comma as decimal Separator
34404 \begin_inset Index idx
34407 \begin_layout Plain Layout
34416 \begin_layout Standard
34417 In \SpecialChar LaTeX
34418 a comma inside a formula is used, according to the English convention,
34419 as number group separator.
34420 So there will be space added behind all commas in formulas.
34423 \begin_layout Standard
34424 To avoid this, the comma is highlighted and changed to mathematical text
34434 \begin_layout Standard
34435 To use all formula commas in the document as decimal separator, the file
34444 \begin_layout Plain Layout
34449 is part of the \SpecialChar LaTeX
34455 \begin_inset Index idx
34458 \begin_layout Plain Layout
34463 \begin_layout Plain Layout
34483 \begin_inset Index idx
34486 \begin_layout Plain Layout
34492 is loaded with the \SpecialChar LaTeX
34496 \begin_layout Standard
34504 \begin_layout Subsection
34506 \begin_inset CommandInset label
34508 name "subsec:Physical-Vectors"
34513 \begin_inset Index idx
34516 \begin_layout Plain Layout
34525 \begin_layout Standard
34526 Predefined vectors are offered by the \SpecialChar LaTeX
34532 \begin_inset Index idx
34535 \begin_layout Plain Layout
34541 that is loaded with the \SpecialChar LaTeX
34545 \begin_layout Standard
34553 \begin_layout Standard
34557 \begin_layout Plain Layout
34567 \begin_inset Note Note
34570 \begin_layout Plain Layout
34571 The following table will only be displayed when the \SpecialChar LaTeX
34584 \begin_layout Standard
34585 The following commands are defined:
34586 \begin_inset Separator parbreak
34592 \begin_layout Standard
34594 \begin_inset Tabular
34595 <lyxtabular version="3" rows="4" columns="2">
34596 <features booktabs="true" tabularvalignment="middle">
34597 <column alignment="center" valignment="top" width="0pt">
34598 <column alignment="center" valignment="top">
34600 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34603 \begin_layout Plain Layout
34609 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34612 \begin_layout Plain Layout
34620 <cell alignment="center" valignment="top" usebox="none">
34623 \begin_layout Plain Layout
34633 <cell alignment="center" valignment="top" usebox="none">
34636 \begin_layout Plain Layout
34637 \begin_inset Formula $\Bra{\psi}$
34647 <cell alignment="center" valignment="top" usebox="none">
34650 \begin_layout Plain Layout
34660 <cell alignment="center" valignment="top" usebox="none">
34663 \begin_layout Plain Layout
34664 \begin_inset Formula $\Ket{\psi}$
34674 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34677 \begin_layout Plain Layout
34689 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34692 \begin_layout Plain Layout
34693 \begin_inset Formula $\Braket{\psi|\phi}$
34709 \begin_layout Standard
34716 assures that all vertical bars are set in the size of the surrounding brackets:
34717 \begin_inset Formula
34719 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34728 \begin_layout Plain Layout
34738 \begin_inset Note Note
34741 \begin_layout Plain Layout
34742 The following will be displayed when the \SpecialChar LaTeX
34755 \begin_layout Standard
34756 You need to install the \SpecialChar LaTeX
34761 to see the rest of this subsection in the output.
34764 \begin_layout Standard
34768 \begin_layout Plain Layout
34780 \begin_layout Standard
34787 can also be achieved using the command
34793 , that is described in
34794 \begin_inset CommandInset ref
34796 reference "subsec:Automatic-Bracket-Size"
34803 \begin_layout Subsection
34804 Self-defined Fractions
34805 \begin_inset CommandInset label
34807 name "subsec:Self-defined-Fractions"
34812 \begin_inset Index idx
34815 \begin_layout Plain Layout
34816 Fractions ! self-defined
34824 \begin_layout Standard
34825 To define custom commands for fractions, the command
34832 \begin_inset Index idx
34835 \begin_layout Plain Layout
34842 \begin_layout Plain Layout
34856 is used in the following scheme:
34859 \begin_layout Standard
34872 bracket}{fraction bar thickness}{style}
34873 \begin_inset Newline newline
34877 \begin_inset Phantom HPhantom
34880 \begin_layout Plain Layout
34890 {numerator}{denominator}
34893 \begin_layout Standard
34894 The style is a number in the range of 0
34895 \begin_inset space \thinspace{}
34899 \begin_inset space \thinspace{}
34903 \begin_inset Separator parbreak
34909 \begin_layout Standard
34911 \begin_inset Tabular
34912 <lyxtabular version="3" rows="5" columns="2">
34913 <features booktabs="true" tabularvalignment="middle">
34914 <column alignment="center" valignment="top" width="0pt">
34915 <column alignment="center" valignment="top">
34917 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34920 \begin_layout Plain Layout
34926 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34929 \begin_layout Plain Layout
34937 <cell alignment="center" valignment="top" usebox="none">
34940 \begin_layout Plain Layout
34946 <cell alignment="center" valignment="top" usebox="none">
34949 \begin_layout Plain Layout
34950 display style formula
34957 <cell alignment="center" valignment="top" usebox="none">
34960 \begin_layout Plain Layout
34966 <cell alignment="center" valignment="top" usebox="none">
34969 \begin_layout Plain Layout
34977 <cell alignment="center" valignment="top" usebox="none">
34980 \begin_layout Plain Layout
34986 <cell alignment="center" valignment="top" usebox="none">
34989 \begin_layout Plain Layout
34997 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35000 \begin_layout Plain Layout
35006 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35009 \begin_layout Plain Layout
35023 \begin_layout Standard
35024 When no style is given, the size is adjusted to the surrounding environment
35025 like for the command
35034 \begin_layout Standard
35035 When no fraction bar thickness is given, the predefined value of 0.4
35036 \begin_inset space \thinspace{}
35042 \begin_layout Standard
35043 \begin_inset VSpace medskip
35046 For example, the commands
35059 \begin_inset CommandInset ref
35061 reference "subsec:Fractions"
35065 are defined with the commands
35068 \begin_layout Standard
35077 genfrac{}{}{}{0}{#1}{#2}}
35080 \begin_layout Standard
35084 \begin_layout Standard
35093 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35096 \begin_layout Standard
35097 \begin_inset VSpace medskip
35100 To define a fraction where the fraction bar thickness can be given as optional
35101 argument, the following line is inserted to the \SpecialChar LaTeX
35105 \begin_layout Standard
35114 genfrac{}{}{#1}{}{#2}{#3}}
35117 \begin_layout Standard
35119 \begin_inset Formula
35121 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35122 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35127 As one can see, the distance of the numerator and the denominator to the
35128 fraction bar is round about three times the bar thickness.
35131 \begin_layout Subsection
35133 \begin_inset Index idx
35136 \begin_layout Plain Layout
35145 \begin_layout Standard
35146 There are four ways to cancel formulas or parts of formulas:
35149 \begin_layout Standard
35153 \begin_layout Plain Layout
35163 \begin_inset Note Note
35166 \begin_layout Plain Layout
35167 The following table will only be displayed when the \SpecialChar LaTeX
35178 \begin_inset Separator parbreak
35184 \begin_layout Standard
35186 \begin_inset Tabular
35187 <lyxtabular version="3" rows="5" columns="2">
35188 <features booktabs="true" tabularvalignment="middle">
35189 <column alignment="center" valignment="top" width="0pt">
35190 <column alignment="center" valignment="top">
35192 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35195 \begin_layout Plain Layout
35201 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35204 \begin_layout Plain Layout
35212 <cell alignment="center" valignment="top" usebox="none">
35215 \begin_layout Plain Layout
35219 \begin_inset space \textvisiblespace{}
35225 \begin_inset space \textvisiblespace{}
35233 <cell alignment="center" valignment="top" usebox="none">
35236 \begin_layout Plain Layout
35237 \begin_inset Formula $\cancel{\int A=B}$
35246 <row topspace="1.5mm">
35247 <cell alignment="center" valignment="top" usebox="none">
35250 \begin_layout Plain Layout
35254 \begin_inset space \textvisiblespace{}
35260 \begin_inset space \textvisiblespace{}
35268 <cell alignment="center" valignment="top" usebox="none">
35271 \begin_layout Plain Layout
35272 \begin_inset Formula $\bcancel{\int A=B}$
35281 <row topspace="1.5mm">
35282 <cell alignment="center" valignment="top" usebox="none">
35285 \begin_layout Plain Layout
35289 \begin_inset space \textvisiblespace{}
35295 \begin_inset space \textvisiblespace{}
35303 <cell alignment="center" valignment="top" usebox="none">
35306 \begin_layout Plain Layout
35307 \begin_inset Formula $\xcancel{\int A=B}$
35317 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35320 \begin_layout Plain Layout
35324 \begin_inset space \textvisiblespace{}
35330 \begin_inset space \textvisiblespace{}
35334 \begin_inset Formula $\to$
35342 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35345 \begin_layout Plain Layout
35346 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35362 \begin_layout Standard
35369 is especially suitable to visualize the reduction of fractions within formulas:
35370 \begin_inset Formula
35372 \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}}}
35380 \begin_layout Standard
35381 To change the size of
35388 \begin_inset Quotes eld
35392 \begin_inset Quotes erd
35395 value one can add the \SpecialChar LaTeX
35399 \begin_layout Standard
35404 PassOptionsToPackage{option}{cancel}
35407 \begin_layout Standard
35416 which leads to the same size as for the canceled value, or
35420 which makes is it a bit smaller than normal.
35423 \begin_layout Standard
35424 To color the cancellation bar one adds this command as \SpecialChar TeX
35428 \begin_layout Standard
35440 \begin_layout Standard
35445 can be replaced by a color of your choice.
35448 \begin_layout Standard
35452 \begin_layout Plain Layout
35468 \begin_layout Standard
35469 \begin_inset Formula
35471 \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}}}
35479 \begin_layout Standard
35483 \begin_layout Plain Layout
35497 \begin_inset Note Note
35500 \begin_layout Plain Layout
35509 \begin_layout Standard
35510 For further customizations, see the documentation of the package
35515 \begin_inset CommandInset citation
35522 \begin_inset Index idx
35525 \begin_layout Plain Layout
35534 \begin_layout Standard
35538 \begin_layout Plain Layout
35548 \begin_inset Note Note
35551 \begin_layout Plain Layout
35552 The following will be displayed when the \SpecialChar LaTeX
35565 \begin_layout Standard
35566 You need to install the \SpecialChar LaTeX
35571 to see the rest of this subsection in the output.
35574 \begin_layout Standard
35578 \begin_layout Plain Layout
35590 \begin_layout Subsection
35591 Formulas in Section Headings
35592 \begin_inset CommandInset label
35594 name "subsec:Formulas-in-Section"
35599 \begin_inset Index idx
35602 \begin_layout Plain Layout
35603 Formula ! in section headings
35611 \begin_layout Standard
35612 When formulas are used in section headings, the following has to be taken
35616 \begin_layout Standard
35617 \begin_inset Note Greyedout
35620 \begin_layout Plain Layout
35626 \begin_inset Index idx
35629 \begin_layout Plain Layout
35630 Packages ! hyperref
35635 support is enabled in the document settings dialog under
35638 \begin_inset space ~
35643 , PDF-bookmarks are created for every section heading in the table of contents.
35644 If a section heading contains formulas, they are incorrectly displayed
35645 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35654 \begin_layout Standard
35655 Both problems can be solved by inserting at the end of the section heading
35656 a short title with the menu
35658 Insert\SpecialChar menuseparator
35660 \begin_inset space ~
35666 Short titles are used as alternative for multiline section headings to
35667 keep the table of contents clearly arranged.
35668 Only the short title appears in the table of contents and therefore also
35669 in the PDF-bookmark.
35672 \begin_layout Standard
35673 When formulas should be used in the table of contents but
35677 is used, one can use the following command in \SpecialChar TeX
35681 \begin_layout Standard
35686 texorpdfstring{part}{alternative}
35687 \begin_inset Index idx
35690 \begin_layout Plain Layout
35701 \begin_layout Standard
35702 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35703 This can be characters, formulas, footnotes, but also cross-references.
35704 The alternative is used instead of the part for the bookmark.
35707 \begin_layout Standard
35708 Here are two example headings:
35709 \begin_inset VSpace -3mm
35716 \begin_layout Plain Layout
35728 \begin_layout Subsubsection
35729 Heading without formula in table of contents
35730 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35734 \begin_inset Argument 1
35737 \begin_layout Plain Layout
35738 Heading without formula in table of contents
35746 \begin_layout Subsubsection
35747 Heading with formula in table of contents
35751 \begin_layout Plain Layout
35761 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35768 \begin_layout Plain Layout
35778 \begin_layout Standard
35782 \begin_layout Plain Layout
35791 In the first heading a short title was used, in the second one
35800 \begin_layout Standard
35801 To get the same formatting as for the other headings, the complete heading
35810 \begin_layout Plain Layout
35812 \begin_inset CommandInset ref
35814 reference "subsec:Bold-Formulas"
35826 \begin_layout Subsection
35827 Formulas in multi-column Text
35828 \begin_inset Index idx
35831 \begin_layout Plain Layout
35832 Formula ! in multi-column text
35840 \begin_layout Standard
35841 Formulas in multi-column text are often too wide to fit into a column and
35842 thus need to be set over the whole page width.
35843 This is done by using the \SpecialChar LaTeX
35852 \begin_layout Plain Layout
35857 is part of every \SpecialChar LaTeX
35858 standard installation.
35864 \begin_inset Index idx
35867 \begin_layout Plain Layout
35868 Packages ! multicol
35873 , that is loaded with the \SpecialChar LaTeX
35877 \begin_layout Standard
35882 usepackage{multicol}
35885 \begin_layout Standard
35886 \begin_inset Note Greyedout
35889 \begin_layout Plain Layout
35890 Note that in this case the setting
35893 \begin_inset space ~
35900 Document\SpecialChar menuseparator
35906 \begin_inset space ~
35926 \begin_layout Standard
35927 Before the multi-column text the command
35930 \begin_layout Standard
35935 begin{multicols}{column number}
35938 \begin_layout Standard
35939 is written in \SpecialChar TeX
35941 The column number is a number in the range of 2
35942 \begin_inset space \thinspace{}
35946 \begin_inset space \thinspace{}
35950 Before the formula the multi-column text is ended by inserting the command
35953 \begin_layout Standard
35961 \begin_layout Standard
35962 in \SpecialChar TeX
35966 \begin_layout Standard
35967 Due to the command some space is automatically added before the formula.
35969 \begin_inset space \thinspace{}
35972 mm vertical space is inserted before the formula.
35973 When the formula style
35979 \begin_layout Plain Layout
35981 \begin_inset CommandInset ref
35983 reference "sec:Formula-Styles"
35995 \begin_inset space \thinspace{}
35998 mm space is inserted instead.
36001 \begin_layout Standard
36002 As example a multi-column text with a displayed formula:
36005 \begin_layout Standard
36011 \begin_layout Plain Layout
36015 begin{multicols}{2}
36020 Das Spektrum wird fouriertransformiert.
36021 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36022 , Lösungsmittel) zu trennen.
36023 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36024 nun das Aussehen des Ausgangssignals.
36025 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36026 über alle Phasen integrieren muss.
36028 \begin_inset Formula $S$
36031 unser normiertes Ausgangssignal und
36032 \begin_inset Formula $P$
36035 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36039 \begin_layout Plain Layout
36049 \begin_inset VSpace -6mm
36053 \begin_inset Formula
36055 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36064 \begin_layout Plain Layout
36068 begin{multicols}{2}
36074 \begin_inset Formula $S_{0}$
36077 das Signal ohne Gradient ist und die Normierungsbedingung
36078 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36082 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36084 \begin_inset Formula $\nicefrac{\pi}{2}$
36088 \begin_inset space \thinspace{}
36091 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36092 das Signal zusätzlich abschwächt.
36093 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36095 \begin_inset Formula $T_{2}$
36101 \begin_layout Standard
36107 \begin_layout Plain Layout
36119 \begin_layout Subsection
36120 Formulas with Description of Variables
36121 \begin_inset Index idx
36124 \begin_layout Plain Layout
36125 Formula ! with description of variables
36133 \begin_layout Standard
36134 To describe variables within a formula, like in formula
36135 \begin_inset CommandInset ref
36137 reference "eq:within"
36146 \begin_inset Formula $n$
36150 \begin_inset space ~
36153 matrix is used with left aligned columns for the
36154 \begin_inset Formula $n$
36161 \begin_layout Plain Layout
36163 \begin_inset CommandInset ref
36165 reference "sec:Matrices"
36174 To set the description in a smaller size, before the matrix e.
36175 \begin_inset space \thinspace{}
36179 \begin_inset space \space{}
36192 \begin_layout Plain Layout
36194 \begin_inset CommandInset ref
36196 reference "subsec:Font-Sizes"
36208 \begin_layout Standard
36209 When the formula style
36215 \begin_layout Plain Layout
36217 \begin_inset CommandInset ref
36219 reference "sec:Formula-Styles"
36240 \begin_layout Plain Layout
36247 only works in formulas with the style
36252 \begin_inset CommandInset ref
36254 reference "subsec:Variable-Space"
36263 is inserted before and after the matrix to have the same separation of
36264 the matrix from the equation and the side margin.
36267 \begin_layout Standard
36268 When the formula style
36272 is used, the method described in
36273 \begin_inset CommandInset ref
36275 reference "subsec:Flalign-Environment"
36279 is used to indent formulas.
36281 \begin_inset CommandInset ref
36283 reference "eq:within"
36287 consists of five columns where in the first two columns contain the equation,
36288 the third the matrix and the last one an empty \SpecialChar TeX
36290 \begin_inset Formula
36292 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36293 \rho & \textrm{density}\\
36294 V & \textrm{volume}\\
36295 g & \textrm{gravitational acceleration}
36296 \end{array} & & {}\label{eq:within}
36304 \begin_layout Subsection
36305 Upright small Greek Letters
36306 \begin_inset CommandInset label
36308 name "subsec:Upright-small-Greek"
36313 \begin_inset Index idx
36316 \begin_layout Plain Layout
36317 Greek letters ! upright
36325 \begin_layout Standard
36326 Most of the math fonts only provide italic small Greek letters.
36327 But for symbols of elementary particles like pions and neutrinos, upright
36328 Greek letters are needed.
36337 \begin_layout Plain Layout
36342 is part of the \SpecialChar LaTeX
36348 \begin_inset Index idx
36351 \begin_layout Plain Layout
36356 \begin_layout Plain Layout
36376 \begin_inset Index idx
36379 \begin_layout Plain Layout
36385 that is loaded with the \SpecialChar LaTeX
36389 \begin_layout Standard
36394 usepackage{upgreek}
36397 \begin_layout Standard
36403 \begin_layout Plain Layout
36413 \begin_inset Note Note
36416 \begin_layout Plain Layout
36417 The following table will only be displayed when the \SpecialChar LaTeX
36427 They are created when the command for a small Greek letter is started with
36433 For example the command
36440 \begin_inset Formula $\uptau$
36446 \begin_layout Standard
36447 With these commands reactions of elementary particles can be typeset:
36448 \begin_inset Formula
36450 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36458 \begin_layout Standard
36459 The upright letters are more bold and wider than the italic ones.
36460 They should therefore not be used for units like
36461 \begin_inset Quotes eld
36465 \begin_inset Quotes erd
36471 \begin_layout Standard
36475 \begin_layout Plain Layout
36485 \begin_inset Note Note
36488 \begin_layout Plain Layout
36489 The following will be displayed when the \SpecialChar LaTeX
36502 \begin_layout Standard
36503 You need to install the \SpecialChar LaTeX
36508 to see the rest of this subsection in the output.
36511 \begin_layout Standard
36515 \begin_layout Plain Layout
36527 \begin_layout Subsection
36528 Text Characters in Formulas
36529 \begin_inset Index idx
36532 \begin_layout Plain Layout
36541 \begin_layout Standard
36542 In some cases you might want to insert text characters directly into formulas.
36543 When for example the centered dot · is often used in formulas like
36544 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36547 , one would have to insert the command
36557 \begin_layout Plain Layout
36559 \begin_inset CommandInset ref
36561 reference "subsec:Binary-Operators"
36570 all the time, because this character is defined in all encodings as text
36572 But the encoding can be changed by this \SpecialChar LaTeX
36576 \begin_layout Standard
36581 Declare Inputtext{183}{
36591 f\SpecialChar ligaturebreak
36595 \begin_layout Standard
36596 The character encoding (menu
36598 Document\SpecialChar menuseparator
36599 Settings\SpecialChar menuseparator
36602 ) specifies what character appears when a keyboard key is pressed.
36603 When the key for the character '·' is pressed, internally the command
36610 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36612 With the changed encoding the right command is chosen automatically, depending
36613 on if the character was inserted into a formula or not.
36616 \begin_layout Standard
36617 The encoding of several characters is saved in definition files.
36618 For example the encoding
36622 is defined in the file
36626 which is in the installation folder of \SpecialChar LaTeX
36628 Encodings should only be changed via the \SpecialChar LaTeX
36629 -preamble and not in the definition
36631 Otherwise documents could not be edited by other \SpecialChar LyX
36632 users working on other
36636 \begin_layout Standard
36637 \begin_inset VSpace medskip
36640 Besides the centered dot, in this document the degree sign ° is defined
36641 with the following \SpecialChar LaTeX
36642 -preamble line so that it can be directly inserted into
36646 \begin_layout Standard
36651 DeclareInputtext{176}{
36661 f\SpecialChar ligaturebreak
36665 \begin_layout Subsection
36667 -comments in formulas
36668 \begin_inset Index idx
36671 \begin_layout Plain Layout
36681 \begin_layout Standard
36682 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36684 code of your file with the menu
36686 Insert\SpecialChar menuseparator
36687 Note\SpecialChar menuseparator
36691 This is not possible in a formula but you can insert \SpecialChar LaTeX
36696 \begin_layout Standard
36704 \begin_layout Standard
36705 This creates a box in which you can write your comment.
36706 Due to a bug in \SpecialChar LyX
36711 \begin_layout Plain Layout
36712 \begin_inset CommandInset href
36714 name "LyX-bug #9002"
36715 target "http://www.lyx.org/trac/ticket/9002"
36724 you cannot write normal text inside the comment, even when you use mathematical
36725 text, you will see its \SpecialChar LaTeX
36726 -commands in the \SpecialChar LaTeX
36728 \begin_inset Newline newline
36731 This a formula with a \SpecialChar LaTeX
36733 \begin_inset Formula
36735 A=B%\text{This is the comment}
36743 \begin_layout Standard
36744 \begin_inset Newpage newpage
36750 \begin_layout Section
36753 \begin_inset Index idx
36756 \begin_layout Plain Layout
36765 \begin_layout Standard
36766 This section is a summary of the most important typographic rules, listed
36771 \begin_layout Plain Layout
36772 This collection was partly taken from the German semi-official dictionary
36774 \begin_inset Quotes eld
36778 \begin_inset Quotes erd
36782 \begin_inset CommandInset citation
36788 that lists some of the ISO rules.
36789 More rules are listed in
36790 \begin_inset CommandInset citation
36804 \begin_layout Itemize
36813 \begin_layout Plain Layout
36814 done with font styles, see
36815 \begin_inset CommandInset ref
36817 reference "subsec:Font-Styles"
36826 , no matter if they appear in italic text: 30
36827 \begin_inset space \thinspace{}
36831 \begin_inset Newline newline
36834 Between the value and the unit is the smallest space, see
36835 \begin_inset CommandInset ref
36837 reference "subsec:Predefined-Space"
36842 \begin_inset Newline newline
36845 This convention is automatically fulfilled when the command
36852 When it is entered to a formula, two boxes appear.
36853 In the first one the value is inserted, in the second one the unit, and
36855 \begin_inset Formula $\unit[30]{km/h}$
36859 \begin_inset space \thinspace{}
36869 is not a real \SpecialChar LaTeX
36870 command but the command
36876 , therefore you cannot use it in \SpecialChar TeX
36880 \begin_layout Itemize
36881 Percent and perthousand signs are set like physical units:
36882 \begin_inset Newline newline
36886 \begin_inset space \thinspace{}
36892 \begin_layout Itemize
36893 The degree sign follows directly on the value: 15°, but not when it is used
36895 \begin_inset space \thinspace{}
36901 \begin_layout Itemize
36902 In numbers with more than four digits the smallest space is inserted before
36903 every third digit to group them:
36913 \begin_inset space \thinspace{}
36917 \begin_inset space \thinspace{}
36923 \begin_layout Itemize
36924 For dimensions like 120×90×40
36925 \begin_inset space \thinspace{}
36928 cm the multiplication sign
36929 \begin_inset Quotes eld
36933 \begin_inset Quotes erd
36937 It is available either via the command
36945 Insert\SpecialChar menuseparator
36946 Special Character\SpecialChar menuseparator
36952 \begin_layout Itemize
36953 Functions with names consisting of several letters are set upright to avoid
36955 \begin_inset CommandInset ref
36957 reference "subsec:Predefined-Functions"
36964 \begin_layout Itemize
36965 Indices consisting of several letters, are set upright:
36966 \begin_inset Formula $E_{\mathrm{kin}}$
36970 \begin_inset Newline newline
36973 Components of matrices are set italic:
36974 \begin_inset Formula $\hat{H}_{kl}$
36980 \begin_layout Itemize
36981 The differentiation/integration operator 'd', the Euler's number 'e' and
36982 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36986 \begin_layout Itemize
36987 The character that denotes a
36991 transformation is inserted either by the command
36996 \begin_inset space \textvisiblespace{}
37003 Insert\SpecialChar menuseparator
37004 Special Character\SpecialChar menuseparator
37005 Symbols\SpecialChar menuseparator
37007 \begin_inset space ~
37013 \begin_inset Formula $\mathscr{F}$
37019 \begin_layout Standard
37020 \begin_inset Newpage newpage
37026 \begin_layout Section
37028 \begin_inset Index idx
37031 \begin_layout Plain Layout
37040 \begin_layout Standard
37041 Some characters and symbols can be created with several commands.
37042 Here is a list of the synonym commands:
37045 \begin_layout Standard
37046 \begin_inset VSpace bigskip
37050 \begin_inset space \hfill{}
37054 \begin_inset Tabular
37055 <lyxtabular version="3" rows="12" columns="2">
37056 <features booktabs="true" tabularvalignment="middle">
37057 <column alignment="center" valignment="top" width="0pt">
37058 <column alignment="center" valignment="top" width="0pt">
37060 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37063 \begin_layout Plain Layout
37069 <cell alignment="center" valignment="top" topline="true" bottomline="true" 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
37113 <cell alignment="center" valignment="top" usebox="none">
37116 \begin_layout Plain Layout
37126 <cell alignment="center" valignment="top" usebox="none">
37129 \begin_layout Plain Layout
37137 <cell alignment="center" valignment="top" usebox="none">
37140 \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
37205 <cell alignment="center" valignment="top" usebox="none">
37208 \begin_layout Plain Layout
37218 <cell alignment="center" valignment="top" usebox="none">
37221 \begin_layout Plain Layout
37229 <cell alignment="center" valignment="top" usebox="none">
37232 \begin_layout Plain Layout
37242 <cell alignment="center" valignment="top" usebox="none">
37245 \begin_layout Plain Layout
37253 <cell alignment="center" valignment="top" usebox="none">
37256 \begin_layout Plain Layout
37266 <cell alignment="center" valignment="top" usebox="none">
37269 \begin_layout Plain Layout
37277 <cell alignment="center" valignment="top" usebox="none">
37280 \begin_layout Plain Layout
37290 <cell alignment="center" valignment="top" usebox="none">
37293 \begin_layout Plain Layout
37301 <cell alignment="center" valignment="top" usebox="none">
37304 \begin_layout Plain Layout
37312 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37315 \begin_layout Plain Layout
37323 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37326 \begin_layout Plain Layout
37338 \begin_inset space \hfill{}
37342 \begin_inset Tabular
37343 <lyxtabular version="3" rows="12" columns="2">
37344 <features booktabs="true" tabularvalignment="middle">
37345 <column alignment="center" valignment="top" width="0pt">
37346 <column alignment="center" valignment="top" width="0pt">
37348 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37351 \begin_layout Plain Layout
37357 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37360 \begin_layout Plain Layout
37368 <cell alignment="center" valignment="top" usebox="none">
37371 \begin_layout Plain Layout
37379 <cell alignment="center" valignment="top" usebox="none">
37382 \begin_layout Plain Layout
37394 <cell alignment="center" valignment="top" usebox="none">
37397 \begin_layout Plain Layout
37405 <cell alignment="center" valignment="top" usebox="none">
37408 \begin_layout Plain Layout
37418 <cell alignment="center" valignment="top" usebox="none">
37421 \begin_layout Plain Layout
37429 <cell alignment="center" valignment="top" usebox="none">
37432 \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
37497 <cell alignment="center" valignment="top" usebox="none">
37500 \begin_layout Plain Layout
37510 <cell alignment="center" valignment="top" usebox="none">
37513 \begin_layout Plain Layout
37521 <cell alignment="center" valignment="top" usebox="none">
37524 \begin_layout Plain Layout
37534 <cell alignment="center" valignment="top" usebox="none">
37537 \begin_layout Plain Layout
37545 <cell alignment="center" valignment="top" usebox="none">
37548 \begin_layout Plain Layout
37558 <cell alignment="center" valignment="top" usebox="none">
37561 \begin_layout Plain Layout
37569 <cell alignment="center" valignment="top" usebox="none">
37572 \begin_layout Plain Layout
37582 <cell alignment="center" valignment="top" usebox="none">
37585 \begin_layout Plain Layout
37593 <cell alignment="center" valignment="top" usebox="none">
37596 \begin_layout Plain Layout
37606 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37609 \begin_layout Plain Layout
37617 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37620 \begin_layout Plain Layout
37634 \begin_inset space \hfill{}
37640 \begin_layout Standard
37641 \begin_inset Newpage newpage
37647 \begin_layout Bibliography
37648 \begin_inset CommandInset bibitem
37649 LatexCommand bibitem
37661 The \SpecialChar LaTeX
37665 Addison Wesley, 2004
37668 \begin_layout Bibliography
37669 \begin_inset CommandInset bibitem
37670 LatexCommand bibitem
37676 \begin_inset CommandInset href
37679 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37683 of \SpecialChar LaTeX
37687 \begin_layout Bibliography
37688 \begin_inset CommandInset bibitem
37689 LatexCommand bibitem
37695 \begin_inset CommandInset href
37698 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37706 \begin_layout Plain Layout
37715 -\SpecialChar LaTeX
37719 \begin_layout Bibliography
37720 \begin_inset CommandInset bibitem
37721 LatexCommand bibitem
37727 \begin_inset CommandInset href
37730 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37734 of all symbols available with \SpecialChar LaTeX
37738 \begin_layout Bibliography
37739 \begin_inset CommandInset bibitem
37740 LatexCommand bibitem
37746 \begin_inset CommandInset href
37748 name "Documentation"
37749 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37753 of the \SpecialChar LaTeX
37759 \begin_inset Index idx
37762 \begin_layout Plain Layout
37771 \begin_layout Bibliography
37772 \begin_inset CommandInset bibitem
37773 LatexCommand bibitem
37779 \begin_inset CommandInset href
37781 name "Documentation"
37782 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37786 of the \SpecialChar LaTeX
37792 \begin_inset Index idx
37795 \begin_layout Plain Layout
37796 Packages ! hyperref
37804 \begin_layout Bibliography
37805 \begin_inset CommandInset bibitem
37806 LatexCommand bibitem
37812 \begin_inset CommandInset href
37814 name "Documentation"
37815 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37819 of the \SpecialChar LaTeX
37825 \begin_inset Index idx
37828 \begin_layout Plain Layout
37837 \begin_layout Bibliography
37838 \begin_inset CommandInset bibitem
37839 LatexCommand bibitem
37850 Auflage, Duden 2001
37853 \begin_layout Bibliography
37854 \begin_inset CommandInset bibitem
37855 LatexCommand bibitem
37861 \begin_inset CommandInset href
37864 target "http://physics.nist.gov/Document/checklist.pdf"
37868 for reviewing manuscripts
37871 \begin_layout Standard
37872 \begin_inset CommandInset index_print
37873 LatexCommand printindex