1 #LyX 2.2 created this file. For more info see http://www.lyx.org/
8 % DO NOT ALTER THIS PREAMBLE!!!
10 % This preamble is designed to ensure that the file prints
11 % out as advertised. If you mess with this preamble,
12 % parts of this document may not print out as expected. If you
13 % have problems LaTeXing this file, please contact
14 % the documentation team
15 % email: lyx-docs@lists.lyx.org
17 % solves the following problem:
18 % If the dection number consits of too many numerals the section heading
19 % will be printed in the TOC without a space between it and the section number.
20 % As solution more space between the number and the heading is inserted:
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22 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
24 % increase link area for cross-references and autoname them,
25 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
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31 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
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36 % don't load packages twice
37 % see first footnote in sec. 9.3
38 \@ifundefined{textcolor}{\usepackage{color}}{}
40 % the pages of the TOC are numbered roman
41 % and a PDF-bookmark for the TOC is added
43 \let\myTOC\tableofcontents
44 \renewcommand{\tableofcontents}{%
46 \pdfbookmark[1]{\contentsname}{}
49 \pagenumbering{arabic}}
51 % add 0.5 mm vertical space for table rows
52 \@ifundefined{extrarowheight} {\usepackage{array}}{}
53 \setlength{\extrarowheight}{0.5mm}
55 % insert additional vertical space of 1.5 mm between footnotes,
57 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
59 % makes caption labels bold
60 \setkomafont{captionlabel}{\bfseries}
62 % enables calculation of values
65 % for multiple columns used in sec. 24.7
71 % for the Fourier transformation symbol
74 % define a color, used in sec.9.3
75 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
77 % declare operators (see sec. 10.4 and sec. 15.2)
78 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
79 \DeclareMathOperator{\sgn}{sgn}
81 % example definitions for sec. 20.1
82 \newcommand{\gr}{\Longrightarrow}
83 \newcommand{\us}[1]{\underline{#1}}
84 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
85 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
86 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
88 % example macro from sec. 19.4
89 %\def\tagform@#1{\maketag@@@{|#1|}}
92 % ------------------------------------
93 % used to check for needed LaTeX packages
96 % check for package undertilde
97 % used for the command \utilde
98 \newboolean{undertilde}
99 \IfFileExists{undertilde.sty}
100 {\usepackage{undertilde}
101 \setboolean{undertilde}{true}}
102 {\setboolean{undertilde}{false}}
104 % check for package eurosym
105 % used for the Euro symbol
107 \IfFileExists{eurosym.sty}
108 {\usepackage[gennarrow]{eurosym}
109 \setboolean{eurosym}{true}}
110 {\setboolean{eurosym}{false}}
112 % check for package braket
113 % used for physical vectors
115 \IfFileExists{braket.sty}
117 \setboolean{braket}{true}}
118 {\setboolean{braket}{false}}
120 % check for package cancel
122 \IfFileExists{cancel.sty}
124 \setboolean{cancel}{true}}
125 {\setboolean{cancel}{false}}
127 % check for package upgreek
129 \IfFileExists{upgreek.sty}
130 {\usepackage{upgreek}
131 \setboolean{upgreek}{true}}
132 {\setboolean{upgreek}{false}}
134 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
135 \use_default_options false
136 \maintain_unincluded_children false
138 \language_package default
141 \font_roman "lmodern" "default"
142 \font_sans "lmss" "default"
143 \font_typewriter "lmtt" "default"
144 \font_math "auto" "auto"
145 \font_default_family default
146 \use_non_tex_fonts false
149 \font_sf_scale 100 100
150 \font_tt_scale 100 100
152 \default_output_format pdf2
154 \bibtex_command default
155 \index_command default
159 \pdf_title "LyX's Math Manual"
160 \pdf_author "LyX Team, Uwe Stöhr"
161 \pdf_subject "LyX-documentation about math"
162 \pdf_keywords "LyX, Mathed"
164 \pdf_bookmarksnumbered true
165 \pdf_bookmarksopen true
166 \pdf_bookmarksopenlevel 1
167 \pdf_breaklinks false
171 \pdf_pdfusetitle false
172 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
175 \use_package amsmath 2
176 \use_package amssymb 2
177 \use_package cancel 0
179 \use_package mathdots 1
180 \use_package mathtools 2
181 \use_package mhchem 1
182 \use_package stackrel 0
183 \use_package stmaryrd 0
184 \use_package undertilde 0
186 \cite_engine_type default
190 \paperorientation portrait
194 \notefontcolor #0000ff
201 \paragraph_separation skip
203 \quotes_language english
206 \paperpagestyle plain
210 \tracking_changes false
211 \output_changes false
214 \html_be_strict false
221 's detailed Math manual
225 by the \SpecialChar LyX
230 \begin_layout Plain Layout
232 If you have comments or error corrections, please send them to the \SpecialChar LyX
237 \begin_inset CommandInset href
239 name "lyx-docs@lists.lyx.org"
240 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
251 \begin_inset Note Note
254 \begin_layout Plain Layout
261 \begin_inset Newline newline
265 \begin_inset Newline newline
273 \begin_layout Standard
274 \begin_inset CommandInset toc
275 LatexCommand tableofcontents
282 \begin_layout Standard
283 \begin_inset Note Note
286 \begin_layout Plain Layout
287 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
290 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
297 If they are not installed the document can be exported anyway but the sections
298 where the packages are required will not appear in the output.
303 ; if it is not installed, this file cannot be exported.
306 \begin_layout Plain Layout
307 The latest PDF-version of this document can be found here:
308 \begin_inset Newline newline
313 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
321 \begin_layout Standard
322 \begin_inset Newpage newpage
328 \begin_layout Section
332 \begin_layout Standard
333 This document explains \SpecialChar LyX
334 's math features and is furthermore a collection
335 of \SpecialChar LaTeX
336 -commands used for mathematical characters and constructs.
337 The explanations are designed for the usage of commands.
338 It is therefore required that you have read the section
349 \begin_layout Standard
350 Most of the characters and many constructs explained in this manual are
351 also accessible via the menu
355 \SpecialChar menuseparator
371 But everybody who has to write lots of formulas will notice that it is
372 much faster to use commands instead of the math toolbar.
373 Therefore this manual is focused on commands but also mentions the correspondin
374 g toolbar buttons when available.
377 \begin_layout Standard
378 If not specially mentioned the commands are only available within formulas.
379 To be able to use all commands explained in this document, the option
383 must be checked in the document settings (menu
385 Document\SpecialChar menuseparator
386 Settings\SpecialChar menuseparator
397 \begin_layout Plain Layout
400 Use AMS math package automatically
406 \begin_layout Plain Layout
415 -math when math constructs are found that are supported by \SpecialChar LyX
424 \begin_layout Standard
425 This document doesn't list all
429 \begin_layout Plain Layout
442 \begin_layout Plain Layout
447 \begin_layout Plain Layout
456 -math commands is in the file
459 \begin_inset CommandInset href
462 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
468 , which is part of every \SpecialChar LaTeX
469 standard installation.
474 for lucidity reasons.
477 \begin_layout Section
481 \begin_layout Standard
482 To create an inline formula
483 \begin_inset Index idx
486 \begin_layout Plain Layout
492 that is embedded into a text line, use one of the shortcuts
498 or the toolbar button
505 \begin_inset Newline newline
508 To create a display style formula
509 \begin_inset Index idx
512 \begin_layout Plain Layout
513 Formula ! display style
518 which will appear bigger, has a different format, and will be in a separate
519 paragraph, use one of these shortcuts:
528 \begin_layout Standard
529 To change a display style formula to an inline formula, set the cursor into
530 the formula and use one of the shortcuts
538 Edit\SpecialChar menuseparator
539 Math\SpecialChar menuseparator
543 The same way is used to change an inline formula to a display style formula.
546 \begin_layout Standard
547 To display parts of an inline formula in the size of a display style formula,
555 \begin_inset Index idx
558 \begin_layout Plain Layout
567 Then a new blue box appears in which the desired formula part is inserted.
570 \begin_layout Standard
571 Only inline formulas are allowed inside tables.
574 \begin_layout Standard
579 can be turned on in the menu
581 View\SpecialChar menuseparator
585 When you click there on
586 \begin_inset Quotes eld
590 \begin_inset Quotes erd
593 the toolbar will be shown permanently at the bottom; this state is visualized
598 menu with a checkmark.
599 When you click in this state again on
600 \begin_inset Quotes eld
604 \begin_inset Quotes erd
615 is only shown when the cursor is within a formula; this state is visualized
616 by the renaming of the menu entry from
617 \begin_inset Quotes eld
621 \begin_inset Quotes erd
625 \begin_inset Quotes eld
633 \begin_inset Quotes erd
639 \begin_layout Standard
642 \begin_inset Index idx
645 \begin_layout Plain Layout
652 is invoked by pressing the toolbar button
660 Insert\SpecialChar menuseparator
672 \begin_layout Standard
673 To change the \SpecialChar LaTeX
675 \begin_inset Index idx
678 \begin_layout Plain Layout
687 Document\SpecialChar menuseparator
688 Settings\SpecialChar menuseparator
698 \begin_layout Standard
699 To edit matrices, case differentiations and multiline formulas subsequently,
702 Edit\SpecialChar menuseparator
707 Edit\SpecialChar menuseparator
709 \begin_inset space \thinspace{}
713 \begin_inset space \thinspace{}
723 When lines and columns are swapped via the menu, the column or line where
724 the cursor is in is exchanged with the column to the right or the line
726 Is the cursor in the last column or row, the exchange is done with the
727 column to the left or the line above.
730 \begin_layout Standard
731 To write text in formulas
735 \begin_layout Plain Layout
736 For multiline formulas the command
743 \begin_inset CommandInset ref
745 reference "subsec:Text-in-multiline"
759 \begin_inset Index idx
762 \begin_layout Plain Layout
769 \begin_inset Index idx
772 \begin_layout Plain Layout
779 This mode is invoked with the shortcut
785 or by the insertion of the command
792 \begin_inset Index idx
795 \begin_layout Plain Layout
804 The text appears black in \SpecialChar LyX
805 and can therefore be distinguished from the
806 other formula parts which appear blue.
807 In the output mathematical text is set upright, in contrary to other formula
811 \begin_layout Subsection*
815 \begin_layout Standard
816 Most of the \SpecialChar LaTeX
817 -commands for math constructs have the following scheme:
820 \begin_layout Standard
836 \begin_layout Standard
837 A command always starts with a backslash
838 \begin_inset Quotes gld
848 \begin_inset Quotes grd
852 To omit optional arguments, also omit the associated brackets.
853 The braces around the required arguments are named in this document as
856 \begin_inset Index idx
859 \begin_layout Plain Layout
867 If you add in a formula a left brace to a command name, \SpecialChar LyX
869 creates a \SpecialChar TeX
871 In all other cases \SpecialChar TeX
872 braces are created in formulas with the command
880 braces appear red in \SpecialChar LyX
881 , in contrary to normal braces which appear blue.
883 mode no command is needed to get \SpecialChar TeX
886 braces don't appear in the output.
889 \begin_layout Standard
890 When commands without arguments, like commands for symbols are entered in
892 mode, a space character must
896 be behind the command to end it.
897 This space doesn't appear in the output.
898 When the space should appear in the output, the space must be followed
899 by a protected space in normal text.
902 \begin_layout Standard
903 A protected space is inserted with
906 arg "command-alternatives space-insert protected ; math-space"
912 \begin_layout Subsection*
913 \begin_inset Newpage newpage
919 \begin_layout Itemize
921 \begin_inset space \textvisiblespace{}
924 denotes a space character to be input.
927 \begin_layout Itemize
929 \begin_inset Formula $\to$
932 denotes the usage of the corresponding arrow key on the keyboard.
937 key can often be used instead of
938 \begin_inset Formula $\to$
942 \begin_inset Formula $\downarrow$
950 \begin_inset Formula $\leftarrow$
954 \begin_inset Formula $\uparrow$
960 \begin_layout Subsection*
964 \begin_layout Standard
966 \begin_inset Float table
972 \begin_layout Plain Layout
974 \begin_inset Caption Standard
976 \begin_layout Plain Layout
977 \begin_inset CommandInset label
979 name "tab:Available-units"
991 \begin_layout Plain Layout
994 <lyxtabular version="3" rows="13" columns="2">
995 <features booktabs="true" tabularvalignment="middle">
996 <column alignment="center" valignment="top">
997 <column alignment="center" valignment="top" width="0pt">
999 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1002 \begin_layout Plain Layout
1008 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1011 \begin_layout Plain Layout
1019 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1022 \begin_layout Plain Layout
1028 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1031 \begin_layout Plain Layout
1039 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1042 \begin_layout Plain Layout
1048 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1051 \begin_layout Plain Layout
1059 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1062 \begin_layout Plain Layout
1068 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1071 \begin_layout Plain Layout
1073 \begin_inset space \thinspace{}
1077 \begin_inset space \thinspace{}
1087 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1090 \begin_layout Plain Layout
1096 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1099 \begin_layout Plain Layout
1101 \begin_inset space \thinspace{}
1105 \begin_inset space \thinspace{}
1115 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1118 \begin_layout Plain Layout
1124 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1127 \begin_layout Plain Layout
1129 \begin_inset space \thinspace{}
1133 \begin_inset space \thinspace{}
1143 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1146 \begin_layout Plain Layout
1152 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1155 \begin_layout Plain Layout
1157 \begin_inset space \thinspace{}
1161 \begin_inset space \thinspace{}
1171 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1174 \begin_layout Plain Layout
1180 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1183 \begin_layout Plain Layout
1185 \begin_inset space \thinspace{}
1189 \begin_inset space \thinspace{}
1199 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1202 \begin_layout Plain Layout
1208 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1211 \begin_layout Plain Layout
1213 \begin_inset space \thinspace{}
1217 \begin_inset Formula $\approx$
1221 \begin_inset space \thinspace{}
1231 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1234 \begin_layout Plain Layout
1240 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1243 \begin_layout Plain Layout
1245 \begin_inset space \thinspace{}
1249 \begin_inset space \thinspace{}
1259 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1262 \begin_layout Plain Layout
1268 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1271 \begin_layout Plain Layout
1275 \begin_inset Quotes eld
1281 \begin_inset Quotes erd
1291 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1294 \begin_layout Plain Layout
1300 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1303 \begin_layout Plain Layout
1305 \begin_inset Quotes eld
1313 \begin_inset Quotes erd
1323 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1326 \begin_layout Plain Layout
1332 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1335 \begin_layout Plain Layout
1337 \begin_inset space \thinspace{}
1341 \begin_inset Formula $\nicefrac{1}{18}$
1345 \begin_inset space \thinspace{}
1366 \begin_layout Standard
1367 \begin_inset Newpage newpage
1373 \begin_layout Section
1377 \begin_layout Subsection
1379 \begin_inset Index idx
1382 \begin_layout Plain Layout
1389 \begin_inset Index idx
1392 \begin_layout Plain Layout
1399 \begin_inset Index idx
1402 \begin_layout Plain Layout
1407 \begin_layout Plain Layout
1418 \begin_layout Plain Layout
1431 \begin_inset Index idx
1434 \begin_layout Plain Layout
1439 \begin_layout Plain Layout
1450 \begin_layout Plain Layout
1465 \begin_layout Standard
1466 Indices are created with an underscore
1467 \begin_inset Quotes eld
1471 \begin_inset Quotes erd
1474 or via the math toolbar button
1477 arg "math-subscript"
1480 , exponents with a caret
1481 \begin_inset Quotes eld
1485 \begin_inset Quotes erd
1488 or via the math toolbar button
1491 arg "math-superscript"
1495 \begin_inset Separator parbreak
1501 \begin_layout Standard
1503 \begin_inset Tabular
1504 <lyxtabular version="3" rows="4" columns="2">
1505 <features booktabs="true" tabularvalignment="middle">
1506 <column alignment="center" valignment="top" width="0pt">
1507 <column alignment="center" valignment="top" width="0pt">
1509 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1512 \begin_layout Plain Layout
1518 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1521 \begin_layout Plain Layout
1529 <cell alignment="center" valignment="top" usebox="none">
1532 \begin_layout Plain Layout
1538 <cell alignment="center" valignment="top" usebox="none">
1541 \begin_layout Plain Layout
1542 \begin_inset Formula $B_{V}$
1551 <row topspace="1.5mm">
1552 <cell alignment="center" valignment="top" usebox="none">
1555 \begin_layout Plain Layout
1561 <cell alignment="center" valignment="top" usebox="none">
1564 \begin_layout Plain Layout
1565 \begin_inset Formula $B^{V}$
1574 <row topspace="1.5mm">
1575 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1578 \begin_layout Plain Layout
1580 \begin_inset space \textvisiblespace{}
1588 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1591 \begin_layout Plain Layout
1592 \begin_inset Formula $B^{A}$
1608 \begin_layout Standard
1609 As the caret is in some languages an accent, vowels will be accentuated
1610 in this case and not set as exponents
1614 \begin_layout Plain Layout
1615 Depending on the used keyboard settings this can also happen for characters
1622 To get exponents in this case, press
1626 after the caret as in the last example.
1629 \begin_layout Subsection
1631 \begin_inset CommandInset label
1633 name "subsec:Fractions"
1638 \begin_inset Index idx
1641 \begin_layout Plain Layout
1650 \begin_layout Standard
1651 Fractions are generated with the command
1658 \begin_inset Index idx
1661 \begin_layout Plain Layout
1669 or via the math toolbar button
1672 arg "math-insert \\frac"
1676 The font size is adjusted automatically, depending on whether the fraction
1677 is in an inline or display style formula.
1678 With the math toolbar button
1681 arg "math-insert \\frac-square"
1684 you can select different fraction types.
1687 \begin_layout Standard
1695 \begin_inset Index idx
1698 \begin_layout Plain Layout
1706 a fraction can be created that always has the size of a display style formula.
1714 \begin_inset Index idx
1717 \begin_layout Plain Layout
1725 the fraction appears always with the size of an inline formula.
1729 \begin_layout Standard
1730 A line with the fraction
1731 \begin_inset Formula $\frac{1}{2}$
1734 that was created with the command
1743 \begin_layout Standard
1744 A line with the fraction
1745 \begin_inset Formula $\dfrac{1}{2}$
1748 that was created with the command
1755 \begin_inset Separator parbreak
1761 \begin_layout Standard
1763 \begin_inset Tabular
1764 <lyxtabular version="3" rows="4" columns="2">
1765 <features booktabs="true" tabularvalignment="middle">
1766 <column alignment="center" valignment="top" width="0pt">
1767 <column alignment="center" valignment="top" width="0pt">
1769 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1772 \begin_layout Plain Layout
1778 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1781 \begin_layout Plain Layout
1788 <row topspace="1.5mm">
1789 <cell alignment="center" valignment="top" usebox="none">
1792 \begin_layout Plain Layout
1796 \begin_inset space \textvisiblespace{}
1800 \begin_inset Formula $\downarrow$
1808 <cell alignment="center" valignment="top" usebox="none">
1811 \begin_layout Plain Layout
1812 \begin_inset Formula $\frac{A}{B}$
1821 <row topspace="2mm">
1822 <cell alignment="center" valignment="top" usebox="none">
1825 \begin_layout Plain Layout
1829 \begin_inset space \textvisiblespace{}
1833 \begin_inset Formula $\downarrow$
1841 <cell alignment="center" valignment="top" usebox="none">
1844 \begin_layout Plain Layout
1845 \begin_inset Formula $\dfrac{A}{B}$
1854 <row topspace="2mm" bottomspace="1mm">
1855 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1858 \begin_layout Plain Layout
1862 \begin_inset space \textvisiblespace{}
1868 \begin_inset space \textvisiblespace{}
1872 \begin_inset Formula $\downarrow$
1876 \begin_inset Formula $\downarrow\downarrow$
1884 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1887 \begin_layout Plain Layout
1888 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1904 \begin_layout Standard
1905 \begin_inset VSpace bigskip
1909 \begin_inset Newpage newpage
1912 For nested fractions the command
1919 \begin_inset Index idx
1922 \begin_layout Plain Layout
1932 \begin_inset VSpace -3mm
1938 \begin_layout Standard
1939 \begin_inset Formula
1941 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1942 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1950 \begin_layout Standard
1951 The command for the example above is:
1954 \begin_layout Standard
1960 \begin_inset space \textvisiblespace{}
1964 \begin_inset Formula $\downarrow$
1970 \begin_inset space \textvisiblespace{}
1976 \begin_inset space \textvisiblespace{}
1980 \begin_inset Formula $\downarrow$
1984 \begin_inset Formula $\downarrow$
1990 \begin_layout Standard
1991 \begin_inset VSpace medskip
1997 \begin_layout Standard
2004 sets the fraction always in the size of a displayed formula, also when
2005 it is part of another fraction.
2008 \begin_layout Standard
2009 It is possible to specify the alignment of the numerator.
2016 is used to left align it, the command
2029 centers the numerator.
2030 These fractions demonstrate the different alignments:
2033 \begin_layout Standard
2036 \begin_inset Formula
2038 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2046 \begin_layout Standard
2047 \begin_inset Note Greyedout
2050 \begin_layout Plain Layout
2067 are no real \SpecialChar LaTeX
2068 commands but represent the command
2072 cfrac[alignment]{numerator}{denominator}
2075 Therefore you cannot use them in \SpecialChar TeX
2084 \begin_layout Standard
2085 \begin_inset VSpace medskip
2088 It is often advantageous to combine
2101 \begin_inset Formula
2103 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2111 \begin_layout Standard
2112 For inline fractions with a sloped fraction stroke you can use the command
2120 \begin_inset Index idx
2123 \begin_layout Plain Layout
2132 \begin_inset Formula $\nicefrac{5}{31}$
2142 \begin_inset Index idx
2145 \begin_layout Plain Layout
2154 \begin_inset Formula $\unitfrac{5}{31}$
2157 There is furthermore the command
2163 that offers to write a fraction in combination with a number:
2164 \begin_inset Formula $\unitfrac[2]{1}{3}$
2170 \begin_layout Standard
2171 \begin_inset Note Greyedout
2174 \begin_layout Plain Layout
2185 is not a real \SpecialChar LaTeX
2186 command but the command
2187 \begin_inset Newline newline
2194 unitfrac[number]{numerator}{denominator}
2197 Therefore you cannot use it in \SpecialChar TeX
2206 \begin_layout Standard
2207 How to define own fractions where the fraction stroke can be changed, is
2209 \begin_inset CommandInset ref
2211 reference "subsec:Self-defined-Fractions"
2218 \begin_layout Standard
2219 Multiline fractions are explained in
2220 \begin_inset CommandInset ref
2222 reference "subsec:Multiline-Fractions"
2229 \begin_layout Subsection
2231 \begin_inset Index idx
2234 \begin_layout Plain Layout
2243 \begin_layout Standard
2244 Square roots are created with
2251 \begin_inset Index idx
2254 \begin_layout Plain Layout
2262 or the math toolbar button
2265 arg "math-insert \\sqrt"
2268 , all other roots with the command
2275 \begin_inset Index idx
2278 \begin_layout Plain Layout
2286 or with the math toolbar button
2289 arg "math-insert \\root"
2293 \begin_inset Separator parbreak
2299 \begin_layout Standard
2301 \begin_inset Tabular
2302 <lyxtabular version="3" rows="3" columns="2">
2303 <features booktabs="true" tabularvalignment="middle">
2304 <column alignment="center" valignment="top" width="0pt">
2305 <column alignment="center" valignment="top" width="0pt">
2307 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2310 \begin_layout Plain Layout
2316 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2319 \begin_layout Plain Layout
2326 <row topspace="1mm">
2327 <cell alignment="center" valignment="top" usebox="none">
2330 \begin_layout Plain Layout
2334 \begin_inset space \textvisiblespace{}
2342 <cell alignment="center" valignment="top" usebox="none">
2345 \begin_layout Plain Layout
2346 \begin_inset Formula $\sqrt{A-B}$
2355 <row topspace="1mm">
2356 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2359 \begin_layout Plain Layout
2363 \begin_inset space \textvisiblespace{}
2367 \begin_inset Formula $\downarrow$
2375 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2378 \begin_layout Plain Layout
2379 \begin_inset Formula $\sqrt[3]{A-B}$
2395 \begin_layout Standard
2396 A square root can also be created with
2402 when the root index field is left empty.
2405 \begin_layout Standard
2406 With certain indices the distance to the root is too small, like in this
2408 \begin_inset Formula $\sqrt[\beta]{B}$
2412 \begin_inset Newline newline
2416 \begin_inset Formula $\beta$
2420 To avoid this, the commands
2427 \begin_inset Index idx
2430 \begin_layout Plain Layout
2445 \begin_inset Index idx
2448 \begin_layout Plain Layout
2456 are used with the following scheme:
2459 \begin_layout Standard
2473 \begin_layout Standard
2474 Distance is the number of Big Points (unit bp;
2475 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2478 ), that the index should be moved to the left or top, resp..
2479 The commands are written to the index.
2480 This way the command
2481 \begin_inset Newline newline
2491 \begin_inset Formula $\to$
2497 \begin_inset Formula $\to$
2503 \begin_inset space \textvisiblespace{}
2507 \begin_inset Formula $\to$
2511 \begin_inset Newline newline
2516 produces a correct typeset formula:
2517 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2523 \begin_layout Subsection
2524 Binomial Coefficients
2525 \begin_inset Index idx
2528 \begin_layout Plain Layout
2529 Binomial coefficients
2537 \begin_layout Standard
2538 Binomial coefficients are inserted with the command
2545 \begin_inset Index idx
2548 \begin_layout Plain Layout
2556 or with the submenu of the math toolbar button
2559 arg "math-insert \\frac-square"
2575 there are the commands
2582 \begin_inset Index idx
2585 \begin_layout Plain Layout
2600 \begin_inset Index idx
2603 \begin_layout Plain Layout
2612 For other brackets around binomial coeficients there are the commands
2619 \begin_inset Index idx
2622 \begin_layout Plain Layout
2637 \begin_inset Index idx
2640 \begin_layout Plain Layout
2649 \begin_inset Separator parbreak
2655 \begin_layout Standard
2657 \begin_inset Tabular
2658 <lyxtabular version="3" rows="6" columns="2">
2659 <features booktabs="true" tabularvalignment="middle">
2660 <column alignment="center" valignment="top" width="0pt">
2661 <column alignment="center" valignment="top" width="0pt">
2663 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2666 \begin_layout Plain Layout
2672 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2675 \begin_layout Plain Layout
2682 <row topspace="1mm">
2683 <cell alignment="center" valignment="top" usebox="none">
2686 \begin_layout Plain Layout
2690 \begin_inset space \textvisiblespace{}
2694 \begin_inset Formula $\downarrow$
2702 <cell alignment="center" valignment="top" usebox="none">
2705 \begin_layout Plain Layout
2706 \begin_inset Formula $\binom{A}{B}$
2715 <row topspace="2mm">
2716 <cell alignment="center" valignment="top" usebox="none">
2719 \begin_layout Plain Layout
2723 \begin_inset space \textvisiblespace{}
2727 \begin_inset Formula $\downarrow$
2735 <cell alignment="center" valignment="top" usebox="none">
2738 \begin_layout Plain Layout
2739 \begin_inset Formula $\dbinom{A}{B}$
2748 <row topspace="2mm" bottomspace="0.5mm">
2749 <cell alignment="center" valignment="top" usebox="none">
2752 \begin_layout Plain Layout
2756 \begin_inset space \textvisiblespace{}
2760 \begin_inset Formula $\downarrow$
2768 <cell alignment="center" valignment="top" usebox="none">
2771 \begin_layout Plain Layout
2772 \begin_inset Formula $\tbinom{A}{B}$
2781 <row topspace="1mm">
2782 <cell alignment="center" valignment="top" topline="true" usebox="none">
2785 \begin_layout Plain Layout
2789 \begin_inset space \textvisiblespace{}
2793 \begin_inset Formula $\downarrow$
2801 <cell alignment="center" valignment="top" topline="true" usebox="none">
2804 \begin_layout Plain Layout
2805 \begin_inset Formula ${A \brack B}$
2814 <row topspace="2mm" bottomspace="0.5mm">
2815 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2818 \begin_layout Plain Layout
2822 \begin_inset space \textvisiblespace{}
2826 \begin_inset Formula $\downarrow$
2834 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2837 \begin_layout Plain Layout
2838 \begin_inset Formula ${A \brace B}$
2854 \begin_layout Subsection
2855 Case Differentiations
2856 \begin_inset Index idx
2859 \begin_layout Plain Layout
2860 Case differentiations
2868 \begin_layout Standard
2870 \begin_inset Tabular
2871 <lyxtabular version="3" rows="3" columns="2">
2872 <features booktabs="true" tabularvalignment="middle">
2873 <column alignment="center" valignment="top" width="0pt">
2874 <column alignment="center" valignment="top" width="0pt">
2876 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2879 \begin_layout Plain Layout
2885 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2888 \begin_layout Plain Layout
2896 <cell alignment="center" valignment="top" usebox="none">
2899 \begin_layout Plain Layout
2903 \begin_inset space \textvisiblespace{}
2907 \begin_inset Formula $\to$
2911 \begin_inset Index idx
2914 \begin_layout Plain Layout
2927 <cell alignment="center" valignment="top" usebox="none">
2930 \begin_layout Plain Layout
2931 \begin_inset Formula $\begin{cases}
2941 <row topspace="1.5mm">
2942 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2945 \begin_layout Plain Layout
2949 \begin_inset space \textvisiblespace{}
2955 arg "newline-insert newline"
2963 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2966 \begin_layout Plain Layout
2967 \begin_inset Formula $\begin{cases}
2968 A & \textrm{for }x>0\\
2969 B & \textrm{for }x=0
2986 \begin_layout Standard
2993 or pressing the math toolbar button
2996 arg "math-insert \\cases"
2999 you can create new lines with the shortcut
3002 arg "newline-insert newline"
3005 or the table toolbar button
3008 arg "inset-modify tabular append-row"
3014 \begin_layout Standard
3021 is also available via the menu
3023 Insert\SpecialChar menuseparator
3024 Math\SpecialChar menuseparator
3030 \begin_layout Subsection
3032 \begin_inset Index idx
3035 \begin_layout Plain Layout
3044 \begin_layout Standard
3052 \begin_inset Index idx
3055 \begin_layout Plain Layout
3063 every character can be displayed canceled.
3064 The characters are quasi accentuated by a slash.
3065 \begin_inset Separator parbreak
3071 \begin_layout Standard
3073 \begin_inset Tabular
3074 <lyxtabular version="3" rows="4" columns="2">
3075 <features booktabs="true" tabularvalignment="middle">
3076 <column alignment="center" valignment="top" width="0pt">
3077 <column alignment="center" valignment="top" width="0pt">
3079 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3082 \begin_layout Plain Layout
3088 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3091 \begin_layout Plain Layout
3099 <cell alignment="center" valignment="top" usebox="none">
3102 \begin_layout Plain Layout
3110 <cell alignment="center" valignment="top" usebox="none">
3113 \begin_layout Plain Layout
3114 \begin_inset Formula $\not=$
3124 <cell alignment="center" valignment="top" usebox="none">
3127 \begin_layout Plain Layout
3137 <cell alignment="center" valignment="top" usebox="none">
3140 \begin_layout Plain Layout
3141 \begin_inset Formula $\not\le$
3151 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3154 \begin_layout Plain Layout
3164 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3167 \begin_layout Plain Layout
3168 \begin_inset Formula $\not\parallel$
3184 \begin_layout Standard
3185 The last example shows that not all negations look good.
3186 Therefore there are special commands for some negations (see
3187 \begin_inset CommandInset ref
3189 reference "subsec:Mathematical-Symbols"
3194 \begin_inset CommandInset ref
3196 reference "sec:Relations"
3203 \begin_layout Subsection
3205 \begin_inset CommandInset label
3207 name "subsec:Placeholders"
3212 \begin_inset Index idx
3215 \begin_layout Plain Layout
3222 \begin_inset Index idx
3225 \begin_layout Plain Layout
3226 Chemical characters ! Isotopes
3232 \begin_inset Index idx
3235 \begin_layout Plain Layout
3240 \begin_layout Plain Layout
3251 \begin_layout Plain Layout
3266 \begin_layout Standard
3268 \begin_inset space \thinspace{}
3272 \begin_inset space \space{}
3279 \begin_layout Plain Layout
3280 Typesetting isotopes and chemical symbols is described in
3281 \begin_inset CommandInset ref
3283 reference "subsec:Chemical-Symbols-and"
3292 the following problem occurs:
3293 \begin_inset Separator parbreak
3299 \begin_layout Standard
3301 \begin_inset Tabular
3302 <lyxtabular version="3" rows="2" columns="2">
3303 <features booktabs="true" tabularvalignment="middle">
3304 <column alignment="center" valignment="top" width="0pt">
3305 <column alignment="center" valignment="top" width="0pt">
3307 <cell alignment="center" valignment="top" usebox="none">
3310 \begin_layout Plain Layout
3311 Indices created with sub- and superscripts:
3316 <cell alignment="center" valignment="top" usebox="none">
3319 \begin_layout Plain Layout
3320 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3329 <row topspace="1.5mm">
3330 <cell alignment="center" valignment="top" usebox="none">
3333 \begin_layout Plain Layout
3339 <cell alignment="center" valignment="top" usebox="none">
3342 \begin_layout Plain Layout
3343 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3359 \begin_layout Standard
3360 The shorter index is by default placed below or above the first character
3361 of the longer index.
3362 To avoid this there is the command
3369 \begin_inset Index idx
3372 \begin_layout Plain Layout
3380 or the math toolbar button
3381 \begin_inset space \thinspace{}
3388 \begin_layout Plain Layout
3389 can be found in the submenu of the toolbar button
3392 arg "math-insert \\space"
3401 \begin_inset Graphics
3402 filename ../images/math/phantom.svgz
3408 that creates one or more phantom characters.
3415 a small blue box appears that is superposed with two red arrows.
3416 The arrows indicate that the complete width and height of the box content
3417 will be created as placeholder.
3418 Phantom characters are accordingly placeholders with the size of the characters.
3419 \begin_inset Separator parbreak
3425 \begin_layout Standard
3427 \begin_inset Tabular
3428 <lyxtabular version="3" rows="4" columns="2">
3429 <features booktabs="true" tabularvalignment="middle">
3430 <column alignment="center" valignment="top" width="0pt">
3431 <column alignment="center" valignment="top" width="0pt">
3433 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3436 \begin_layout Plain Layout
3442 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3445 \begin_layout Plain Layout
3452 <row topspace="1.5mm">
3453 <cell alignment="center" valignment="top" usebox="none">
3456 \begin_layout Plain Layout
3458 \begin_inset space \textvisiblespace{}
3464 \begin_inset space \textvisiblespace{}
3468 \begin_inset Formula $\to$
3472 \begin_inset space \textvisiblespace{}
3480 <cell alignment="center" valignment="top" usebox="none">
3483 \begin_layout Plain Layout
3484 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3493 <row topspace="1.5mm" bottomspace="0.5mm">
3494 <cell alignment="center" valignment="top" usebox="none">
3497 \begin_layout Plain Layout
3499 \begin_inset space \textvisiblespace{}
3505 \begin_inset space \textvisiblespace{}
3509 \begin_inset Formula $\to$
3513 \begin_inset space \textvisiblespace{}
3521 <cell alignment="center" valignment="top" usebox="none">
3524 \begin_layout Plain Layout
3525 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3534 <row topspace="1.5mm" bottomspace="0.5mm">
3535 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3538 \begin_layout Plain Layout
3542 \begin_inset space \textvisiblespace{}
3548 \begin_inset space \textvisiblespace{}
3552 \begin_inset Formula $\to$
3556 \begin_inset space \textvisiblespace{}
3564 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3567 \begin_layout Plain Layout
3568 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3584 \begin_layout Standard
3585 Furthermore there are the commands
3592 \begin_inset Index idx
3595 \begin_layout Plain Layout
3604 \begin_inset Graphics
3605 filename ../images/math/vphantom.svgz
3618 \begin_inset Index idx
3621 \begin_layout Plain Layout
3630 \begin_inset Graphics
3631 filename ../images/math/hphantom.svgz
3644 creates only space for the maximal height of the characters in the box
3645 but not for its width.
3652 creates only space for the width of the box content.
3653 Therefore the boxes of both commands have only one red arrow.
3656 \begin_layout Standard
3657 For example the command
3662 \begin_inset space \textvisiblespace{}
3669 creates space for the height of the integral sign,
3673 \begin_layout Plain Layout
3680 creates an integral sign, see
3681 \begin_inset CommandInset ref
3683 reference "subsec:Big-Operators"
3692 because this is the larger character.
3693 An example application is in
3694 \begin_inset CommandInset ref
3696 reference "subsec:Multiline-Brackets"
3703 \begin_layout Standard
3704 Placeholders can also be used for text when they are inserted via the menu
3707 Insert\SpecialChar menuseparator
3708 Formatting\SpecialChar menuseparator
3714 \begin_layout Standard
3716 \begin_inset Newline newline
3720 \begin_inset Phantom Phantom
3723 \begin_layout Plain Layout
3732 \begin_layout Subsection
3734 \begin_inset Index idx
3737 \begin_layout Plain Layout
3744 \begin_inset Index idx
3747 \begin_layout Plain Layout
3748 Formula ! underlined
3756 \begin_layout Standard
3758 \begin_inset Tabular
3759 <lyxtabular version="3" rows="4" columns="2">
3760 <features booktabs="true" tabularvalignment="middle">
3761 <column alignment="center" valignment="top" width="0pt">
3762 <column alignment="center" valignment="top" width="0pt">
3764 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3767 \begin_layout Plain Layout
3773 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3776 \begin_layout Plain Layout
3783 <row topspace="2mm">
3784 <cell alignment="center" valignment="top" usebox="none">
3787 \begin_layout Plain Layout
3791 \begin_inset space \textvisiblespace{}
3795 \begin_inset Index idx
3798 \begin_layout Plain Layout
3811 <cell alignment="center" valignment="top" usebox="none">
3814 \begin_layout Plain Layout
3815 \begin_inset Formula $\overline{A+B}$
3824 <row bottomspace="1mm">
3825 <cell alignment="center" valignment="top" usebox="none">
3828 \begin_layout Plain Layout
3832 \begin_inset space \textvisiblespace{}
3836 \begin_inset Index idx
3839 \begin_layout Plain Layout
3852 <cell alignment="center" valignment="top" usebox="none">
3855 \begin_layout Plain Layout
3856 \begin_inset Formula $\underline{A+B}$
3865 <row topspace="2mm" bottomspace="1mm">
3866 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3869 \begin_layout Plain Layout
3873 \begin_inset space \textvisiblespace{}
3879 \begin_inset space \textvisiblespace{}
3887 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3890 \begin_layout Plain Layout
3891 \begin_inset Formula $\overline{\underline{A+B}}$
3907 \begin_layout Standard
3908 In the last example it doesn't matter if first
3923 \begin_layout Standard
3924 To double underline use
3933 \begin_layout Standard
3934 It is possible to place up to 6 lines above or below characters.
3937 \begin_layout Standard
3938 \begin_inset VSpace bigskip
3941 Custom lines can be created using the command
3948 \begin_inset Index idx
3951 \begin_layout Plain Layout
3959 which has the following scheme:
3962 \begin_layout Standard
3967 rule[vertical offset]{length}{thickness}
3970 \begin_layout Standard
3971 The optional vertical offset shifts the line upwards (or downwards, when
3972 the value is negative).
3974 \begin_inset CommandInset ref
3976 reference "tab:Available-units"
3980 can be used for the values.
3981 Here are two example lines created with the commands
3982 \begin_inset Newline newline
3989 rule[-2ex]{3cm}{2pt}
4000 \begin_layout Standard
4002 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4008 \begin_layout Standard
4015 can also be used for text when a line is inserted via the menu
4017 Insert\SpecialChar menuseparator
4018 Formatting\SpecialChar menuseparator
4020 \begin_inset space ~
4028 \begin_layout Standard
4030 \begin_inset CommandInset line
4041 \begin_layout Subsection
4043 \begin_inset CommandInset label
4045 name "subsec:Ellipses"
4050 \begin_inset Index idx
4053 \begin_layout Plain Layout
4062 \begin_layout Standard
4063 There are different types of ellipses available.
4067 \begin_layout Plain Layout
4068 In the math toolbar in the submenu of the button
4071 arg "math-insert \\ldots"
4079 For listings dots at the baseline are used (
4086 \begin_inset Index idx
4089 \begin_layout Plain Layout
4097 ), while for operations dots are needed that are on the same height as the
4105 \begin_inset Index idx
4108 \begin_layout Plain Layout
4117 When using the command
4124 \begin_inset Index idx
4127 \begin_layout Plain Layout
4135 , \SpecialChar LaTeX
4136 decides on the basis of the next character what type is used.
4137 \begin_inset Separator parbreak
4143 \begin_layout Standard
4145 \begin_inset Tabular
4146 <lyxtabular version="3" rows="9" columns="2">
4147 <features booktabs="true" tabularvalignment="middle">
4148 <column alignment="center" valignment="top" width="0pt">
4149 <column alignment="center" valignment="top" width="0pt">
4151 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4154 \begin_layout Plain Layout
4160 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4163 \begin_layout Plain Layout
4171 <cell alignment="center" valignment="top" usebox="none">
4174 \begin_layout Plain Layout
4176 \begin_inset space \textvisiblespace{}
4182 \begin_inset space \textvisiblespace{}
4190 <cell alignment="center" valignment="top" usebox="none">
4193 \begin_layout Plain Layout
4194 \begin_inset Formula $A_{1},\dots,A_{n}$
4204 <cell alignment="center" valignment="top" usebox="none">
4207 \begin_layout Plain Layout
4209 \begin_inset space \textvisiblespace{}
4215 \begin_inset space \textvisiblespace{}
4223 <cell alignment="center" valignment="top" usebox="none">
4226 \begin_layout Plain Layout
4227 \begin_inset Formula $A_{1}+\dots+A_{n}$
4237 <cell alignment="center" valignment="top" usebox="none">
4240 \begin_layout Plain Layout
4242 \begin_inset space \textvisiblespace{}
4248 \begin_inset space \textvisiblespace{}
4256 <cell alignment="center" valignment="top" usebox="none">
4259 \begin_layout Plain Layout
4260 \begin_inset Formula $A_{1},\ldots,A_{n}$
4270 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4273 \begin_layout Plain Layout
4275 \begin_inset space \textvisiblespace{}
4281 \begin_inset space \textvisiblespace{}
4289 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4292 \begin_layout Plain Layout
4293 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4303 <cell alignment="center" valignment="top" usebox="none">
4306 \begin_layout Plain Layout
4314 <cell alignment="center" valignment="top" usebox="none">
4317 \begin_layout Plain Layout
4318 \begin_inset Formula $\vdots$
4328 <cell alignment="center" valignment="top" usebox="none">
4331 \begin_layout Plain Layout
4339 <cell alignment="center" valignment="top" usebox="none">
4342 \begin_layout Plain Layout
4343 \begin_inset Formula $\ddots$
4353 <cell alignment="center" valignment="top" usebox="none">
4356 \begin_layout Plain Layout
4364 <cell alignment="center" valignment="top" usebox="none">
4367 \begin_layout Plain Layout
4368 \begin_inset Formula $\iddots$
4378 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4381 \begin_layout Plain Layout
4383 \begin_inset space \thinspace{}
4386 matrix with the different dots
4391 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4394 \begin_layout Plain Layout
4395 \begin_inset Formula $\begin{array}{ccc}
4396 A_{11} & \cdots & A_{1m}\\
4397 \vdots & \ddots & \vdots\\
4398 A_{n1} & \cdots & A_{nm}
4415 \begin_layout Standard
4416 The ellipses available in menu
4418 Insert\SpecialChar menuseparator
4420 \begin_inset space ~
4434 \begin_layout Standard
4435 \begin_inset VSpace medskip
4444 , one of the options
4446 Use mathdots package (automatically)
4448 must be set in the document settings under
4451 \begin_inset space ~
4457 \begin_inset Newline newline
4462 Use mathdots package
4464 will improve the appearance of all dots in the documents if their font
4465 style or size is not the default.
4468 \begin_layout Standard
4469 \begin_inset VSpace medskip
4472 Specially for matrices there are ellipses that span over several columns.
4473 They are created with the command
4480 \begin_inset Index idx
4483 \begin_layout Plain Layout
4491 , that has the following scheme:
4494 \begin_layout Standard
4499 hdotsfor[distance]{number of columns}
4502 \begin_layout Standard
4503 The number of columns specifies how many columns should be spanned.
4504 Distance is a factor for the distance between the dots.
4507 \begin_layout Standard
4508 In the following matrix the command
4514 was inserted in the first box of the second line, to get an ellipsis with
4515 a dot distance twice as long as with the command
4522 \begin_inset Formula
4524 \left(\begin{array}{cccc}
4533 Note that the matrix fields that should be spanned must be empty, otherwise
4534 you get \SpecialChar LaTeX
4538 \begin_layout Standard
4539 \begin_inset VSpace bigskip
4542 Furthermore you can fill with the command
4549 \begin_inset Index idx
4552 \begin_layout Plain Layout
4560 the rest of a line with dots.
4561 The effect of these commands is the same as with
4568 \begin_inset CommandInset ref
4570 reference "subsec:Variable-Space"
4577 \begin_layout Standard
4578 For example the command
4583 \begin_inset space \textvisiblespace{}
4591 \begin_layout Standard
4592 \begin_inset Formula $A\dotfill B$
4598 \begin_layout Standard
4605 there is for a line the command
4612 \begin_inset Index idx
4615 \begin_layout Plain Layout
4626 \begin_layout Standard
4627 \begin_inset Formula $A\hrulefill B$
4633 \begin_layout Standard
4634 To use the commands for text, they have to be inserted in \SpecialChar TeX
4638 \begin_layout Section
4640 \begin_inset CommandInset label
4647 \begin_inset Index idx
4650 \begin_layout Plain Layout
4659 \begin_layout Standard
4660 Matrices can be inserted via the math toolbar button
4663 arg "dialog-show mathmatrix"
4668 Insert\SpecialChar menuseparator
4669 Math\SpecialChar menuseparator
4673 In the matrix dialog you can specify the number of columns and rows, the
4674 alignment and the decoration.
4675 The vertical alignment is only of importance for matrices in inline formulas:
4678 \begin_layout Standard
4679 The first matrix is top
4680 \begin_inset Formula $\begin{array}[t]{cccc}
4688 \begin_inset Formula $\begin{array}{cccc}
4695 and the third bottom
4696 \begin_inset Formula $\begin{array}[b]{cccc}
4706 \begin_layout Standard
4707 The horizontal alignment specifies how the column entries should be aligned.
4708 It is set by entering a letter for every column.
4713 denotes left aligned,
4722 To create for example a 4
4727 \begin_inset space ~
4730 matrix where the first column is left aligned, the second and third are
4731 centered and the last one is right aligned, one enters for the horizontal
4737 Normally in a matrix all columns are centered, therefore the default for
4745 \begin_layout Standard
4746 Horizontal alignment:
4749 \begin_layout Standard
4755 \begin_inset Formula $\begin{array}{lll}
4767 \begin_inset Formula $\begin{array}{ccc}
4779 \begin_inset Formula $\begin{array}{rrr}
4789 \begin_layout Standard
4790 To add or delete rows and columns subsequently, the math toolbar buttons
4794 arg "inset-modify tabular append-row"
4800 arg "inset-modify tabular delete-row"
4804 \begin_inset space \thinspace{}
4809 Edit\SpecialChar menuseparator
4813 New rows can also be created with
4816 arg "newline-insert newline"
4822 \begin_layout Standard
4823 \begin_inset VSpace bigskip
4830 adds parentheses in the selected style around the matrix.
4831 Alternatively, parentheses can can either be created with the commands
4839 \begin_inset Index idx
4842 \begin_layout Plain Layout
4857 \begin_inset Index idx
4860 \begin_layout Plain Layout
4871 \begin_inset space ~
4877 \begin_inset CommandInset ref
4879 reference "subsec:Automatic-Bracket-Size"
4883 , or by using the following commands:
4884 \begin_inset VSpace medskip
4890 \begin_layout Standard
4891 \begin_inset space \hfill{}
4895 \begin_inset Tabular
4896 <lyxtabular version="3" rows="4" columns="2">
4897 <features booktabs="true" tabularvalignment="middle">
4898 <column alignment="center" valignment="top" width="0pt">
4899 <column alignment="center" valignment="top">
4901 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4904 \begin_layout Plain Layout
4910 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4913 \begin_layout Plain Layout
4920 <row topspace="1.5mm">
4921 <cell alignment="center" valignment="top" usebox="none">
4924 \begin_layout Plain Layout
4928 \begin_inset space \textvisiblespace{}
4936 \begin_inset space \thinspace{}
4944 <cell alignment="center" valignment="top" usebox="none">
4947 \begin_layout Plain Layout
4948 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4949 0 & \textrm{-}\mathrm{i}\\
4951 \end{array}\end{bmatrix}$
4960 <row topspace="1.5mm" bottomspace="0.5mm">
4961 <cell alignment="center" valignment="top" usebox="none">
4964 \begin_layout Plain Layout
4968 \begin_inset space \textvisiblespace{}
4976 \begin_inset space \thinspace{}
4984 <cell alignment="center" valignment="top" usebox="none">
4987 \begin_layout Plain Layout
4988 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
4989 0 & \textrm{-}\mathrm{i}\\
4991 \end{array}\end{Bmatrix}$
5001 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5004 \begin_layout Plain Layout
5008 \begin_inset space \textvisiblespace{}
5016 \begin_inset space \thinspace{}
5024 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5027 \begin_layout Plain Layout
5028 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5029 0 & \textrm{-}\mathrm{i}\\
5031 \end{array}\end{pmatrix}$
5045 \begin_inset space \hfill{}
5049 \begin_inset Tabular
5050 <lyxtabular version="3" rows="4" columns="2">
5051 <features booktabs="true" tabularvalignment="middle">
5052 <column alignment="center" valignment="top" width="0pt">
5053 <column alignment="center" valignment="top">
5055 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5058 \begin_layout Plain Layout
5064 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5067 \begin_layout Plain Layout
5074 <row topspace="1.5mm">
5075 <cell alignment="center" valignment="top" usebox="none">
5078 \begin_layout Plain Layout
5082 \begin_inset space \textvisiblespace{}
5090 \begin_inset space \thinspace{}
5098 <cell alignment="center" valignment="top" usebox="none">
5101 \begin_layout Plain Layout
5102 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5103 0 & \textrm{-}\mathrm{i}\\
5105 \end{array}\end{vmatrix}$
5114 <row topspace="1.5mm" bottomspace="0.5mm">
5115 <cell alignment="center" valignment="top" usebox="none">
5118 \begin_layout Plain Layout
5122 \begin_inset space \textvisiblespace{}
5130 \begin_inset space \thinspace{}
5138 <cell alignment="center" valignment="top" usebox="none">
5141 \begin_layout Plain Layout
5142 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5143 0 & \textrm{-}\mathrm{i}\\
5145 \end{array}\end{Vmatrix}$
5155 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5158 \begin_layout Plain Layout
5162 \begin_inset space \textvisiblespace{}
5170 \begin_inset space \thinspace{}
5178 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5181 \begin_layout Plain Layout
5182 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5183 0 & \textrm{-}\mathrm{i}\\
5185 \end{array}\end{matrix}$
5199 \begin_inset space \hfill{}
5205 \begin_layout Standard
5206 \begin_inset VSpace medskip
5210 \begin_inset space \thinspace{}
5214 \begin_inset space \space{}
5223 is inserted, a blue box appears between two vertical lines where the matrix
5225 \begin_inset Newline newline
5228 Note that decorated matrices ignore the vertical alignment.
5231 \begin_layout Standard
5232 \begin_inset VSpace bigskip
5235 As all multiline formulas are matrices, the length
5242 \begin_inset Index idx
5245 \begin_layout Plain Layout
5253 that is described in
5254 \begin_inset CommandInset ref
5256 reference "subsec:Column-Separation"
5260 can also be used to change the column separation of matrices.
5263 \begin_layout Standard
5264 To change the row separation, the command
5271 \begin_inset Index idx
5274 \begin_layout Plain Layout
5283 It is used as follows:
5286 \begin_layout Standard
5293 arraystretch}{stretch factor}
5294 \begin_inset Index idx
5297 \begin_layout Plain Layout
5308 \begin_layout Standard
5315 assigns the stretch factor to the predefined command
5323 \begin_inset space \thinspace{}
5327 \begin_inset space \space{}
5330 the row separation, use the factor 2.
5331 This is then used for all following matrices.
5332 To go back to the original separation, assign the factor 1 to
5341 \begin_layout Standard
5342 To set matrices into a text line, the command
5349 \begin_inset Index idx
5352 \begin_layout Plain Layout
5361 When it is inserted a blue box with two dashed lines appears.
5362 In this box the matrix is inserted.
5365 \begin_layout Standard
5367 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5369 \end{smallmatrix}\right)$
5375 \begin_layout Section
5376 Brackets and Delimiters
5377 \begin_inset Index idx
5380 \begin_layout Plain Layout
5387 \begin_inset Index idx
5390 \begin_layout Plain Layout
5399 \begin_layout Subsection
5400 Vertical Brackets and Delimiters
5401 \begin_inset Index idx
5404 \begin_layout Plain Layout
5413 \begin_layout Standard
5414 \begin_inset space \hfill{}
5418 \begin_inset Tabular
5419 <lyxtabular version="3" rows="9" columns="2">
5420 <features booktabs="true" tabularvalignment="middle">
5421 <column alignment="center" valignment="top" width="0pt">
5422 <column alignment="center" valignment="top" width="0pt">
5424 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5427 \begin_layout Plain Layout
5433 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5436 \begin_layout Plain Layout
5444 <cell alignment="center" valignment="top" usebox="none">
5447 \begin_layout Plain Layout
5453 <cell alignment="center" valignment="top" usebox="none">
5456 \begin_layout Plain Layout
5457 \begin_inset Formula $($
5467 <cell alignment="center" valignment="top" usebox="none">
5470 \begin_layout Plain Layout
5476 <cell alignment="center" valignment="top" usebox="none">
5479 \begin_layout Plain Layout
5480 \begin_inset Formula $\{$
5490 <cell alignment="center" valignment="top" usebox="none">
5493 \begin_layout Plain Layout
5499 <cell alignment="center" valignment="top" usebox="none">
5502 \begin_layout Plain Layout
5503 \begin_inset Formula $[$
5513 <cell alignment="center" valignment="top" usebox="none">
5516 \begin_layout Plain Layout
5524 <cell alignment="center" valignment="top" usebox="none">
5527 \begin_layout Plain Layout
5528 \begin_inset Formula $\langle$
5538 <cell alignment="center" valignment="top" usebox="none">
5541 \begin_layout Plain Layout
5549 <cell alignment="center" valignment="top" usebox="none">
5552 \begin_layout Plain Layout
5553 \begin_inset Formula $\lceil$
5563 <cell alignment="center" valignment="top" usebox="none">
5566 \begin_layout Plain Layout
5574 <cell alignment="center" valignment="top" usebox="none">
5577 \begin_layout Plain Layout
5578 \begin_inset Formula $\lfloor$
5588 <cell alignment="center" valignment="top" usebox="none">
5591 \begin_layout Plain Layout
5597 <cell alignment="center" valignment="top" usebox="none">
5600 \begin_layout Plain Layout
5601 \begin_inset Formula $/$
5611 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5614 \begin_layout Plain Layout
5620 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5623 \begin_layout Plain Layout
5624 \begin_inset Formula $|$
5638 \begin_inset space \hfill{}
5642 \begin_inset Tabular
5643 <lyxtabular version="3" rows="9" columns="2">
5644 <features booktabs="true" tabularvalignment="middle">
5645 <column alignment="center" valignment="top" width="0pt">
5646 <column alignment="center" valignment="top" width="0pt">
5648 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5651 \begin_layout Plain Layout
5657 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5660 \begin_layout Plain Layout
5668 <cell alignment="center" valignment="top" usebox="none">
5671 \begin_layout Plain Layout
5677 <cell alignment="center" valignment="top" usebox="none">
5680 \begin_layout Plain Layout
5681 \begin_inset Formula $)$
5691 <cell alignment="center" valignment="top" usebox="none">
5694 \begin_layout Plain Layout
5700 <cell alignment="center" valignment="top" usebox="none">
5703 \begin_layout Plain Layout
5704 \begin_inset Formula $\}$
5714 <cell alignment="center" valignment="top" usebox="none">
5717 \begin_layout Plain Layout
5723 <cell alignment="center" valignment="top" usebox="none">
5726 \begin_layout Plain Layout
5727 \begin_inset Formula $]$
5737 <cell alignment="center" valignment="top" usebox="none">
5740 \begin_layout Plain Layout
5748 <cell alignment="center" valignment="top" usebox="none">
5751 \begin_layout Plain Layout
5752 \begin_inset Formula $\rangle$
5762 <cell alignment="center" valignment="top" usebox="none">
5765 \begin_layout Plain Layout
5773 <cell alignment="center" valignment="top" usebox="none">
5776 \begin_layout Plain Layout
5777 \begin_inset Formula $\rceil$
5787 <cell alignment="center" valignment="top" usebox="none">
5790 \begin_layout Plain Layout
5798 <cell alignment="center" valignment="top" usebox="none">
5801 \begin_layout Plain Layout
5802 \begin_inset Formula $\rfloor$
5812 <cell alignment="center" valignment="top" usebox="none">
5815 \begin_layout Plain Layout
5825 <cell alignment="center" valignment="top" usebox="none">
5828 \begin_layout Plain Layout
5829 \begin_inset Formula $\backslash$
5839 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5842 \begin_layout Plain Layout
5850 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5853 \begin_layout Plain Layout
5854 \begin_inset Formula $\|$
5868 \begin_inset space \hfill{}
5874 \begin_layout Standard
5877 \begin_inset Note Greyedout
5880 \begin_layout Plain Layout
5893 \begin_inset Index idx
5896 \begin_layout Plain Layout
5904 must be used for the backslash, because the command
5912 produces a line break there.
5920 \begin_layout Standard
5921 For all characters listed above the size can be adjusted with the commands
5922 described in the following two subsections.
5923 When using these commands, the characters < and > can directly be used
5924 instead of the commands
5939 \begin_layout Subsubsection
5941 \begin_inset CommandInset label
5943 name "subsec:Manual-Bracket-Size"
5948 \begin_inset Index idx
5951 \begin_layout Plain Layout
5952 Bracket size ! manual
5960 \begin_layout Standard
5961 The bracket size can be specified manually by the \SpecialChar LaTeX
5969 \begin_inset Index idx
5972 \begin_layout Plain Layout
6005 denotes the smallest and
6011 the largest bracket size.
6014 \begin_layout Standard
6015 These commands are used to emphasize levels of brackets:
6016 \begin_inset Separator parbreak
6022 \begin_layout Standard
6024 \begin_inset Tabular
6025 <lyxtabular version="3" rows="2" columns="2">
6026 <features booktabs="true" tabularvalignment="middle">
6027 <column alignment="center" valignment="top" width="0pt">
6028 <column alignment="center" valignment="top" width="0pt">
6030 <cell alignment="center" valignment="top" usebox="none">
6033 \begin_layout Plain Layout
6034 all brackets in the same size:
6039 <cell alignment="center" valignment="top" usebox="none">
6042 \begin_layout Plain Layout
6043 \begin_inset Formula $((A+B)(A-B))^{C}$
6052 <row topspace="2mm">
6053 <cell alignment="center" valignment="top" usebox="none">
6056 \begin_layout Plain Layout
6062 <cell alignment="center" valignment="top" usebox="none">
6065 \begin_layout Plain Layout
6066 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6082 \begin_layout Standard
6083 For the second formula the command
6090 \begin_inset space \textvisiblespace{}
6098 \begin_layout Standard
6099 Here is an overview about all bracket sizes:
6100 \begin_inset Separator parbreak
6106 \begin_layout Standard
6123 \begin_inset space \textvisiblespace{}
6131 \begin_inset space \textvisiblespace{}
6135 \begin_inset space \textvisiblespace{}
6145 \begin_layout Standard
6147 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6153 \begin_layout Standard
6160 -commands there is the variant
6167 \begin_inset Index idx
6170 \begin_layout Plain Layout
6178 that adds a bit more space between the bracket and its content, and the
6192 \begin_inset Index idx
6195 \begin_layout Plain Layout
6205 , that don't add additional space.
6210 at the end of the command
6216 is for a left bracket; for a right bracket this will be replaced by an
6222 A left or right bracket can each be an opening or closing bracket.
6225 \begin_layout Standard
6226 In the following table is a comparison of the variants:
6227 \begin_inset Separator parbreak
6233 \begin_layout Standard
6235 \begin_inset Tabular
6236 <lyxtabular version="3" rows="5" columns="2">
6237 <features booktabs="true" tabularvalignment="middle">
6238 <column alignment="center" valignment="top" width="0pt">
6239 <column alignment="center" valignment="middle">
6241 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6244 \begin_layout Plain Layout
6250 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6253 \begin_layout Plain Layout
6260 <row topspace="2mm">
6261 <cell alignment="center" valignment="top" usebox="none">
6264 \begin_layout Plain Layout
6274 \begin_inset space \textvisiblespace{}
6284 <cell alignment="center" valignment="top" usebox="none">
6287 \begin_layout Plain Layout
6288 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6297 <row topspace="2mm">
6298 <cell alignment="center" valignment="top" usebox="none">
6301 \begin_layout Plain Layout
6311 \begin_inset space \textvisiblespace{}
6321 <cell alignment="center" valignment="top" usebox="none">
6324 \begin_layout Plain Layout
6325 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6334 <row topspace="2mm" bottomspace="0.5mm">
6335 <cell alignment="center" valignment="top" usebox="none">
6338 \begin_layout Plain Layout
6348 \begin_inset space \textvisiblespace{}
6358 <cell alignment="center" valignment="top" usebox="none">
6361 \begin_layout Plain Layout
6362 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6371 <row topspace="1.5mm" bottomspace="0.5mm">
6372 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6375 \begin_layout Plain Layout
6387 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6390 \begin_layout Plain Layout
6391 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6407 \begin_layout Subsubsection
6408 Automatic Bracket Size
6409 \begin_inset CommandInset label
6411 name "subsec:Automatic-Bracket-Size"
6416 \begin_inset Index idx
6419 \begin_layout Plain Layout
6420 Bracket size ! automatic
6428 \begin_layout Standard
6429 Brackets with variable size can be inserted with the commands
6436 \begin_inset Index idx
6439 \begin_layout Plain Layout
6454 \begin_inset Index idx
6457 \begin_layout Plain Layout
6465 or via the math toolbar button
6468 arg "dialog-show mathdelimiter"
6484 the wanted bracket must be inserted.
6485 The bracket size will then automatically be calculated for the output.
6486 \begin_inset Separator parbreak
6492 \begin_layout Standard
6494 normal bracket: The command
6501 \begin_inset space \textvisiblespace{}
6505 \begin_inset Formula $\downarrow$
6509 \begin_inset space \textvisiblespace{}
6515 \begin_inset Formula
6525 \begin_layout Standard
6527 multiline bracket: The command
6536 \begin_inset space \textvisiblespace{}
6540 \begin_inset Formula $\downarrow$
6544 \begin_inset space \textvisiblespace{}
6552 \begin_inset Formula
6554 \ln\left(\frac{A}{C}\right)
6562 \begin_layout Standard
6578 \begin_inset space ~
6584 This has the advantage that you can see in \SpecialChar LyX
6585 immediately the real bracket
6586 size and that the matching right bracket will be created too.
6587 \begin_inset Newline newline
6590 The command for the last example would then be:
6601 \begin_inset space \textvisiblespace{}
6605 \begin_inset Formula $\downarrow$
6611 \begin_layout Standard
6612 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6613 For example the command
6620 \begin_inset space \textvisiblespace{}
6624 \begin_inset Formula $\downarrow$
6628 \begin_inset space \textvisiblespace{}
6638 \begin_inset Formula
6640 \left.\frac{A}{B}\right\}
6659 will be converted by \SpecialChar LyX
6660 to brackets in the right size when the document is
6661 reloaded and an omitted bracket will appear as dashed line.
6664 \begin_layout Standard
6665 \begin_inset VSpace bigskip
6668 Because all popular \SpecialChar LaTeX
6669 distributions use e\SpecialChar TeX
6670 , an extension to \SpecialChar LaTeX
6679 \begin_inset Index idx
6682 \begin_layout Plain Layout
6690 is additionally available for all brackets and limits.
6691 With this command the height of the following character is adapted to the
6692 one of the surrounding brackets, what is e.
6693 \begin_inset space \thinspace{}
6697 \begin_inset space \space{}
6700 needed for physical vectors:
6701 \begin_inset Formula
6703 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6708 For physical vectors there is a special \SpecialChar LaTeX
6709 -package, described in
6710 \begin_inset CommandInset ref
6712 reference "subsec:Physical-Vectors"
6719 \begin_layout Subsection
6721 \begin_inset Index idx
6724 \begin_layout Plain Layout
6725 Brackets ! horizontal
6733 \begin_layout Standard
6735 \begin_inset Tabular
6736 <lyxtabular version="3" rows="4" columns="2">
6737 <features booktabs="true" tabularvalignment="middle">
6738 <column alignment="center" valignment="top" width="0pt">
6739 <column alignment="center" valignment="top" width="0pt">
6741 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6744 \begin_layout Plain Layout
6750 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6753 \begin_layout Plain Layout
6761 <cell alignment="center" valignment="top" usebox="none">
6764 \begin_layout Plain Layout
6768 \begin_inset space \textvisiblespace{}
6772 \begin_inset space \textvisiblespace{}
6776 \begin_inset Index idx
6779 \begin_layout Plain Layout
6792 <cell alignment="center" valignment="top" usebox="none">
6795 \begin_layout Plain Layout
6796 \begin_inset Formula $\overbrace{A+B}^{3}$
6805 <row topspace="2mm">
6806 <cell alignment="center" valignment="top" usebox="none">
6809 \begin_layout Plain Layout
6813 \begin_inset space \textvisiblespace{}
6817 \begin_inset space \textvisiblespace{}
6821 \begin_inset Index idx
6824 \begin_layout Plain Layout
6837 <cell alignment="center" valignment="top" usebox="none">
6840 \begin_layout Plain Layout
6841 \begin_inset Formula $\underbrace{A+B}_{5}$
6851 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6854 \begin_layout Plain Layout
6858 \begin_inset space \textvisiblespace{}
6864 \begin_inset space \textvisiblespace{}
6868 \begin_inset space \textvisiblespace{}
6872 \begin_inset space \textvisiblespace{}
6876 \begin_inset space \textvisiblespace{}
6880 \begin_inset space \textvisiblespace{}
6884 \begin_inset space \textvisiblespace{}
6892 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6895 \begin_layout Plain Layout
6896 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6912 \begin_layout Standard
6913 In the last example it doesn't matter if
6925 is inserted at first.
6928 \begin_layout Standard
6929 \begin_inset VSpace medskip
6935 \begin_layout Standard
6936 If you set in the document settings under
6939 \begin_inset space ~
6949 \begin_inset Index idx
6952 \begin_layout Plain Layout
6953 Packages ! mathtools
6961 \begin_inset space ~
6966 , you have access to square backets:
6967 \begin_inset Separator parbreak
6973 \begin_layout Standard
6975 \begin_inset Tabular
6976 <lyxtabular version="3" rows="4" columns="2">
6977 <features booktabs="true" tabularvalignment="middle">
6978 <column alignment="center" valignment="top" width="0pt">
6979 <column alignment="center" valignment="top" width="0pt">
6981 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6984 \begin_layout Plain Layout
6990 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6993 \begin_layout Plain Layout
7001 <cell alignment="center" valignment="top" usebox="none">
7004 \begin_layout Plain Layout
7032 \begin_inset space \textvisiblespace{}
7036 \begin_inset Index idx
7039 \begin_layout Plain Layout
7052 <cell alignment="center" valignment="top" usebox="none">
7055 \begin_layout Plain Layout
7056 \begin_inset Formula $\overbracket{A+B}^{3}$
7065 <row topspace="2mm">
7066 <cell alignment="center" valignment="top" usebox="none">
7069 \begin_layout Plain Layout
7097 \begin_inset space \textvisiblespace{}
7101 \begin_inset Index idx
7104 \begin_layout Plain Layout
7129 <cell alignment="center" valignment="top" usebox="none">
7132 \begin_layout Plain Layout
7133 \begin_inset Formula $\underbracket{A+B}_{5}$
7143 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7146 \begin_layout Plain Layout
7152 \begin_inset space \textvisiblespace{}
7156 \begin_inset space \textvisiblespace{}
7160 \begin_inset space \textvisiblespace{}
7164 \begin_inset space \textvisiblespace{}
7168 \begin_inset space \textvisiblespace{}
7176 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7179 \begin_layout Plain Layout
7180 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7196 \begin_layout Standard
7209 you can change the thickness of the bracket's stroke by specifying the
7210 desired thickness in square brackets behind the command:
7211 \begin_inset Separator parbreak
7217 \begin_layout Standard
7219 \begin_inset Tabular
7220 <lyxtabular version="3" rows="3" columns="2">
7221 <features booktabs="true" tabularvalignment="middle">
7222 <column alignment="center" valignment="top" width="0pt">
7223 <column alignment="center" valignment="top" width="0pt">
7225 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7228 \begin_layout Plain Layout
7234 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7237 \begin_layout Plain Layout
7245 <cell alignment="center" valignment="top" usebox="none">
7248 \begin_layout Plain Layout
7278 \begin_inset space \textvisiblespace{}
7286 <cell alignment="center" valignment="top" usebox="none">
7289 \begin_layout Plain Layout
7290 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7299 <row topspace="2mm">
7300 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7303 \begin_layout Plain Layout
7333 \begin_inset space \textvisiblespace{}
7341 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7344 \begin_layout Plain Layout
7345 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7361 \begin_layout Standard
7362 \begin_inset VSpace bigskip
7365 When brackets should overlap each other, multiline formulas, as described
7367 \begin_inset CommandInset ref
7369 reference "sec:Multiline-Formulas"
7374 \begin_inset Formula
7376 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7377 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7382 In the first row the formula is inserted together with the first brace.
7383 It is hereby important that the space command
7387 \begin_layout Plain Layout
7388 Space commands are explained in
7389 \begin_inset CommandInset ref
7391 reference "subsec:Predefined-Space"
7406 is inserted before the first
7407 \begin_inset Formula $d$
7410 , because the brace that ends behind the
7411 \begin_inset Formula $q$
7414 prevents that the following
7415 \begin_inset Quotes eld
7419 \begin_inset Quotes erd
7422 is surrounded by space.
7426 \begin_layout Plain Layout
7427 because a bracket is not handled as a character, see
7428 \begin_inset CommandInset ref
7430 reference "subsec:Binary-Operators"
7439 In the second row the second brace is inserted.
7440 As it should begin before the
7441 \begin_inset Formula $b$
7456 \begin_layout Plain Layout
7464 \begin_inset CommandInset ref
7466 reference "subsec:Placeholders"
7475 This space is needed because the
7476 \begin_inset Quotes eld
7480 \begin_inset Quotes erd
7483 is also surrounded by space in the formula.
7484 The brace is placed under the command
7493 \begin_layout Standard
7494 It gets more complicated when brackets overlap each other above and under
7495 the formula, like in the following example:
7499 \begin_layout Plain Layout
7511 \begin_inset Formula
7513 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7514 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7523 \begin_layout Plain Layout
7534 The first formula row is the same as the second row of the previous example,
7535 with the difference that the brace is above.
7536 The second row contains the formula together with the second brace.
7537 To avoid that there is space between the upper brace in the first row and
7538 the formula, the row spacing needs to be reduced.
7539 This is not easily possible due to a bug in \SpecialChar LyX
7544 \begin_layout Plain Layout
7545 \begin_inset CommandInset href
7547 name "LyX-bug #1505"
7548 target "http://www.lyx.org/trac/ticket/1505"
7557 As a solution for the problem, the global formula row separation
7564 \begin_inset Index idx
7567 \begin_layout Plain Layout
7575 must be changed to -6
7576 \begin_inset space \thinspace{}
7579 pt before the formula with the command
7595 is set back after the formula to the standard value of 3
7596 \begin_inset space \thinspace{}
7599 pt using the same command.
7600 More about the row separation in formulas is explained in
7601 \begin_inset CommandInset ref
7603 reference "subsec:Line-Separation"
7610 \begin_layout Section
7612 \begin_inset Index idx
7615 \begin_layout Plain Layout
7624 \begin_layout Standard
7625 Arrows can be inserted via the math toolbar button
7628 arg "math-insert \\leftarrow"
7631 or the commands listed in the following subsections.
7634 \begin_layout Subsection
7636 \begin_inset Index idx
7639 \begin_layout Plain Layout
7648 \begin_layout Standard
7649 \begin_inset space \hfill{}
7653 \begin_inset Tabular
7654 <lyxtabular version="3" rows="8" columns="2">
7655 <features booktabs="true" tabularvalignment="middle">
7656 <column alignment="center" valignment="top" width="0pt">
7657 <column alignment="center" valignment="top" width="0pt">
7659 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7662 \begin_layout Plain Layout
7668 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7671 \begin_layout Plain Layout
7679 <cell alignment="center" valignment="top" usebox="none">
7682 \begin_layout Plain Layout
7690 <cell alignment="center" valignment="top" usebox="none">
7693 \begin_layout Plain Layout
7694 \begin_inset Formula $\gets$
7704 <cell alignment="center" valignment="top" usebox="none">
7707 \begin_layout Plain Layout
7715 <cell alignment="center" valignment="top" usebox="none">
7718 \begin_layout Plain Layout
7719 \begin_inset Formula $\Leftarrow$
7729 <cell alignment="center" valignment="top" usebox="none">
7732 \begin_layout Plain Layout
7740 <cell alignment="center" valignment="top" usebox="none">
7743 \begin_layout Plain Layout
7744 \begin_inset Formula $\longleftarrow$
7754 <cell alignment="center" valignment="top" usebox="none">
7757 \begin_layout Plain Layout
7765 <cell alignment="center" valignment="top" usebox="none">
7768 \begin_layout Plain Layout
7769 \begin_inset Formula $\Longleftarrow$
7779 <cell alignment="center" valignment="top" usebox="none">
7782 \begin_layout Plain Layout
7790 <cell alignment="center" valignment="top" usebox="none">
7793 \begin_layout Plain Layout
7794 \begin_inset Formula $\leftharpoonup$
7804 <cell alignment="center" valignment="top" usebox="none">
7807 \begin_layout Plain Layout
7815 <cell alignment="center" valignment="top" usebox="none">
7818 \begin_layout Plain Layout
7819 \begin_inset Formula $\leftharpoondown$
7829 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7832 \begin_layout Plain Layout
7840 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7843 \begin_layout Plain Layout
7844 \begin_inset Formula $\hookleftarrow$
7858 \begin_inset space \hfill{}
7862 \begin_inset Tabular
7863 <lyxtabular version="3" rows="8" columns="2">
7864 <features booktabs="true" tabularvalignment="middle">
7865 <column alignment="center" valignment="top" width="0pt">
7866 <column alignment="center" valignment="top" width="0pt">
7868 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7871 \begin_layout Plain Layout
7877 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7880 \begin_layout Plain Layout
7888 <cell alignment="center" valignment="top" usebox="none">
7891 \begin_layout Plain Layout
7899 <cell alignment="center" valignment="top" usebox="none">
7902 \begin_layout Plain Layout
7903 \begin_inset Formula $\to$
7913 <cell alignment="center" valignment="top" usebox="none">
7916 \begin_layout Plain Layout
7924 <cell alignment="center" valignment="top" usebox="none">
7927 \begin_layout Plain Layout
7928 \begin_inset Formula $\Rightarrow$
7938 <cell alignment="center" valignment="top" usebox="none">
7941 \begin_layout Plain Layout
7949 <cell alignment="center" valignment="top" usebox="none">
7952 \begin_layout Plain Layout
7953 \begin_inset Formula $\longrightarrow$
7963 <cell alignment="center" valignment="top" usebox="none">
7966 \begin_layout Plain Layout
7974 <cell alignment="center" valignment="top" usebox="none">
7977 \begin_layout Plain Layout
7978 \begin_inset Formula $\Longrightarrow$
7988 <cell alignment="center" valignment="top" usebox="none">
7991 \begin_layout Plain Layout
7999 <cell alignment="center" valignment="top" usebox="none">
8002 \begin_layout Plain Layout
8003 \begin_inset Formula $\rightharpoonup$
8013 <cell alignment="center" valignment="top" usebox="none">
8016 \begin_layout Plain Layout
8024 <cell alignment="center" valignment="top" usebox="none">
8027 \begin_layout Plain Layout
8028 \begin_inset Formula $\rightharpoondown$
8038 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8041 \begin_layout Plain Layout
8049 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8052 \begin_layout Plain Layout
8053 \begin_inset Formula $\hookrightarrow$
8067 \begin_inset space \hfill{}
8073 \begin_layout Standard
8074 \begin_inset space \hfill{}
8078 \begin_inset Tabular
8079 <lyxtabular version="3" rows="6" columns="2">
8080 <features booktabs="true" tabularvalignment="middle">
8081 <column alignment="center" valignment="top" width="0pt">
8082 <column alignment="center" valignment="top" width="0pt">
8084 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8087 \begin_layout Plain Layout
8093 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8096 \begin_layout Plain Layout
8104 <cell alignment="center" valignment="top" usebox="none">
8107 \begin_layout Plain Layout
8115 <cell alignment="center" valignment="top" usebox="none">
8118 \begin_layout Plain Layout
8119 \begin_inset Formula $\leftrightarrow$
8129 <cell alignment="center" valignment="top" usebox="none">
8132 \begin_layout Plain Layout
8140 <cell alignment="center" valignment="top" usebox="none">
8143 \begin_layout Plain Layout
8144 \begin_inset Formula $\Leftrightarrow$
8154 <cell alignment="center" valignment="top" usebox="none">
8157 \begin_layout Plain Layout
8165 <cell alignment="center" valignment="top" usebox="none">
8168 \begin_layout Plain Layout
8169 \begin_inset Formula $\longleftrightarrow$
8179 <cell alignment="center" valignment="top" usebox="none">
8182 \begin_layout Plain Layout
8190 <cell alignment="center" valignment="top" usebox="none">
8193 \begin_layout Plain Layout
8194 \begin_inset Formula $\Longleftrightarrow$
8204 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8207 \begin_layout Plain Layout
8215 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8218 \begin_layout Plain Layout
8219 \begin_inset Formula $\rightleftharpoons$
8233 \begin_inset space \hspace{}
8238 \begin_inset space \hfill{}
8242 \begin_inset Tabular
8243 <lyxtabular version="3" rows="5" columns="2">
8244 <features booktabs="true" tabularvalignment="middle">
8245 <column alignment="center" valignment="top" width="0pt">
8246 <column alignment="center" valignment="top" width="0pt">
8248 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8251 \begin_layout Plain Layout
8257 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8260 \begin_layout Plain Layout
8268 <cell alignment="center" valignment="top" usebox="none">
8271 \begin_layout Plain Layout
8279 <cell alignment="center" valignment="top" usebox="none">
8282 \begin_layout Plain Layout
8283 \begin_inset Formula $\mapsto$
8293 <cell alignment="center" valignment="top" usebox="none">
8296 \begin_layout Plain Layout
8304 <cell alignment="center" valignment="top" usebox="none">
8307 \begin_layout Plain Layout
8308 \begin_inset Formula $\longmapsto$
8318 <cell alignment="center" valignment="top" usebox="none">
8321 \begin_layout Plain Layout
8329 <cell alignment="center" valignment="top" usebox="none">
8332 \begin_layout Plain Layout
8333 \begin_inset Formula $\leadsto$
8343 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8346 \begin_layout Plain Layout
8354 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8357 \begin_layout Plain Layout
8358 \begin_inset Formula $\dasharrow$
8372 \begin_inset space \hfill{}
8378 \begin_layout Standard
8379 \begin_inset VSpace medskip
8382 Arrows used as accents like e.
8383 \begin_inset space \thinspace{}
8387 \begin_inset space \space{}
8390 vector arrows are listed in
8391 \begin_inset CommandInset ref
8393 reference "sec:Accents"
8400 \begin_layout Standard
8401 \begin_inset VSpace bigskip
8404 Furthermore there are the labeled arrows
8405 \begin_inset Index idx
8408 \begin_layout Plain Layout
8421 \begin_inset Index idx
8424 \begin_layout Plain Layout
8439 \begin_inset Index idx
8442 \begin_layout Plain Layout
8449 \begin_layout Plain Layout
8464 When inserting one of these commands in a formula, an arrow with two blue
8465 boxes appear where the label can be inserted.
8466 The length of the arrow adapts to the label width.
8469 \begin_layout Standard
8471 \begin_inset Tabular
8472 <lyxtabular version="3" rows="3" columns="2">
8473 <features booktabs="true" tabularvalignment="middle">
8474 <column alignment="center" valignment="top" width="0pt">
8475 <column alignment="center" valignment="top" width="0pt">
8477 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8480 \begin_layout Plain Layout
8486 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8489 \begin_layout Plain Layout
8497 <cell alignment="center" valignment="top" usebox="none">
8500 \begin_layout Plain Layout
8504 \begin_inset space \textvisiblespace{}
8508 \begin_inset Formula $\downarrow$
8512 \begin_inset Formula $\to$
8520 <cell alignment="center" valignment="top" usebox="none">
8523 \begin_layout Plain Layout
8524 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8533 <row topspace="2mm">
8534 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8537 \begin_layout Plain Layout
8541 \begin_inset space \textvisiblespace{}
8545 \begin_inset Formula $\downarrow$
8549 \begin_inset Formula $\to$
8557 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8560 \begin_layout Plain Layout
8561 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8577 \begin_layout Standard
8578 \begin_inset VSpace medskip
8584 \begin_layout Standard
8585 If you set in the document settings under
8588 \begin_inset space ~
8598 \begin_inset Index idx
8601 \begin_layout Plain Layout
8602 Packages ! mathtools
8610 \begin_inset space ~
8615 , you have access to the following labeled arrows:
8618 \begin_layout Standard
8619 \begin_inset Newpage newpage
8623 \begin_inset Separator parbreak
8629 \begin_layout Standard
8631 \begin_inset space \hspace*{\fill}
8635 \begin_inset Tabular
8636 <lyxtabular version="3" rows="7" columns="2">
8637 <features booktabs="true" tabularvalignment="middle">
8638 <column alignment="center" valignment="top" width="0pt">
8639 <column alignment="center" valignment="top" width="0pt">
8641 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8644 \begin_layout Plain Layout
8650 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8653 \begin_layout Plain Layout
8661 <cell alignment="center" valignment="top" usebox="none">
8664 \begin_layout Plain Layout
8684 <cell alignment="center" valignment="top" usebox="none">
8687 \begin_layout Plain Layout
8688 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8697 <row topspace="2mm">
8698 <cell alignment="center" valignment="top" usebox="none">
8701 \begin_layout Plain Layout
8721 <cell alignment="center" valignment="top" usebox="none">
8724 \begin_layout Plain Layout
8725 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8734 <row topspace="2mm">
8735 <cell alignment="center" valignment="top" usebox="none">
8738 \begin_layout Plain Layout
8758 <cell alignment="center" valignment="top" usebox="none">
8761 \begin_layout Plain Layout
8762 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8771 <row topspace="2mm">
8772 <cell alignment="center" valignment="top" usebox="none">
8775 \begin_layout Plain Layout
8795 <cell alignment="center" valignment="top" usebox="none">
8798 \begin_layout Plain Layout
8799 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8808 <row topspace="2mm">
8809 <cell alignment="center" valignment="top" usebox="none">
8812 \begin_layout Plain Layout
8832 <cell alignment="center" valignment="top" usebox="none">
8835 \begin_layout Plain Layout
8836 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8845 <row topspace="2mm">
8846 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8849 \begin_layout Plain Layout
8869 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8872 \begin_layout Plain Layout
8873 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8887 \begin_inset space \hspace*{\fill}
8891 \begin_inset Tabular
8892 <lyxtabular version="3" rows="7" columns="2">
8893 <features booktabs="true" tabularvalignment="middle">
8894 <column alignment="center" valignment="top" width="0pt">
8895 <column alignment="center" valignment="top" width="0pt">
8897 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8900 \begin_layout Plain Layout
8906 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8909 \begin_layout Plain Layout
8917 <cell alignment="center" valignment="top" usebox="none">
8920 \begin_layout Plain Layout
8940 <cell alignment="center" valignment="top" usebox="none">
8943 \begin_layout Plain Layout
8944 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8953 <row topspace="2mm">
8954 <cell alignment="center" valignment="top" usebox="none">
8957 \begin_layout Plain Layout
8977 <cell alignment="center" valignment="top" usebox="none">
8980 \begin_layout Plain Layout
8981 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8990 <row topspace="2mm">
8991 <cell alignment="center" valignment="top" usebox="none">
8994 \begin_layout Plain Layout
9014 <cell alignment="center" valignment="top" usebox="none">
9017 \begin_layout Plain Layout
9018 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
9027 <row topspace="2mm">
9028 <cell alignment="center" valignment="top" usebox="none">
9031 \begin_layout Plain Layout
9051 <cell alignment="center" valignment="top" usebox="none">
9054 \begin_layout Plain Layout
9055 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9064 <row topspace="2mm">
9065 <cell alignment="center" valignment="top" usebox="none">
9068 \begin_layout Plain Layout
9088 <cell alignment="center" valignment="top" usebox="none">
9091 \begin_layout Plain Layout
9092 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9101 <row topspace="2mm">
9102 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9105 \begin_layout Plain Layout
9125 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9128 \begin_layout Plain Layout
9129 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9143 \begin_inset space \hspace*{\fill}
9149 \begin_layout Standard
9150 The command scheme is for all these arrows:
9151 \begin_inset Separator parbreak
9157 \begin_layout Standard
9159 \begin_inset Tabular
9160 <lyxtabular version="3" rows="2" columns="2">
9161 <features booktabs="true" tabularvalignment="middle">
9162 <column alignment="center" valignment="top" width="0pt">
9163 <column alignment="center" valignment="top" width="0pt">
9165 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9168 \begin_layout Plain Layout
9174 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9177 \begin_layout Plain Layout
9184 <row bottomspace="0.5mm">
9185 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9188 \begin_layout Plain Layout
9191 xleftrightarrow[x=a]
9194 \begin_inset Formula $\to$
9202 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9205 \begin_layout Plain Layout
9206 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9222 \begin_layout Subsection
9223 Vertical and diagonal Arrows
9224 \begin_inset Index idx
9227 \begin_layout Plain Layout
9234 \begin_inset Index idx
9237 \begin_layout Plain Layout
9246 \begin_layout Standard
9247 \begin_inset space \hfill{}
9251 \begin_inset Tabular
9252 <lyxtabular version="3" rows="7" columns="2">
9253 <features booktabs="true" tabularvalignment="middle">
9254 <column alignment="center" valignment="top" width="0pt">
9255 <column alignment="center" valignment="top" width="0pt">
9257 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9260 \begin_layout Plain Layout
9266 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9269 \begin_layout Plain Layout
9277 <cell alignment="center" valignment="top" usebox="none">
9280 \begin_layout Plain Layout
9288 <cell alignment="center" valignment="top" usebox="none">
9291 \begin_layout Plain Layout
9292 \begin_inset Formula $\uparrow$
9302 <cell alignment="center" valignment="top" usebox="none">
9305 \begin_layout Plain Layout
9313 <cell alignment="center" valignment="top" usebox="none">
9316 \begin_layout Plain Layout
9317 \begin_inset Formula $\Uparrow$
9327 <cell alignment="center" valignment="top" usebox="none">
9330 \begin_layout Plain Layout
9338 <cell alignment="center" valignment="top" usebox="none">
9341 \begin_layout Plain Layout
9342 \begin_inset Formula $\updownarrow$
9352 <cell alignment="center" valignment="top" usebox="none">
9355 \begin_layout Plain Layout
9363 <cell alignment="center" valignment="top" usebox="none">
9366 \begin_layout Plain Layout
9367 \begin_inset Formula $\Updownarrow$
9377 <cell alignment="center" valignment="top" usebox="none">
9380 \begin_layout Plain Layout
9388 <cell alignment="center" valignment="top" usebox="none">
9391 \begin_layout Plain Layout
9392 \begin_inset Formula $\Downarrow$
9402 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9405 \begin_layout Plain Layout
9413 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9416 \begin_layout Plain Layout
9417 \begin_inset Formula $\downarrow$
9431 \begin_inset space \hfill{}
9435 \begin_inset Tabular
9436 <lyxtabular version="3" rows="5" columns="2">
9437 <features booktabs="true" tabularvalignment="middle">
9438 <column alignment="center" valignment="top" width="0pt">
9439 <column alignment="center" valignment="top" width="0pt">
9441 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9444 \begin_layout Plain Layout
9450 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9453 \begin_layout Plain Layout
9461 <cell alignment="center" valignment="top" usebox="none">
9464 \begin_layout Plain Layout
9472 <cell alignment="center" valignment="top" usebox="none">
9475 \begin_layout Plain Layout
9476 \begin_inset Formula $\nearrow$
9486 <cell alignment="center" valignment="top" usebox="none">
9489 \begin_layout Plain Layout
9497 <cell alignment="center" valignment="top" usebox="none">
9500 \begin_layout Plain Layout
9501 \begin_inset Formula $\searrow$
9511 <cell alignment="center" valignment="top" usebox="none">
9514 \begin_layout Plain Layout
9522 <cell alignment="center" valignment="top" usebox="none">
9525 \begin_layout Plain Layout
9526 \begin_inset Formula $\swarrow$
9536 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9539 \begin_layout Plain Layout
9547 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9550 \begin_layout Plain Layout
9551 \begin_inset Formula $\nwarrow$
9565 \begin_inset space \hfill{}
9571 \begin_layout Standard
9572 \begin_inset VSpace medskip
9575 Vertical arrows can be used also as delimiters together with the commands
9577 \begin_inset CommandInset ref
9579 reference "subsec:Manual-Bracket-Size"
9584 \begin_inset CommandInset ref
9586 reference "subsec:Automatic-Bracket-Size"
9593 \begin_layout Section
9595 \begin_inset CommandInset label
9602 \begin_inset Index idx
9605 \begin_layout Plain Layout
9614 \begin_layout Standard
9615 Accents can be inserted via the math toolbar button
9618 arg "math-insert \\hat"
9621 or the commands listed in the following subsections.
9624 \begin_layout Subsection
9625 Accents for one Character
9629 \begin_layout Plain Layout
9642 \begin_layout Plain Layout
9644 \begin_inset CommandInset ref
9646 reference "subsec:Accents-in-Text"
9659 \begin_layout Plain Layout
9667 \begin_inset Note Note
9670 \begin_layout Plain Layout
9677 is used to avoid that the footnote appears in the PDF-bookmark.
9680 \begin_layout Plain Layout
9688 \begin_inset CommandInset ref
9690 reference "subsec:Formulas-in-Section"
9700 \begin_inset CommandInset label
9702 name "subsec:Accents-for-one"
9707 \begin_inset Index idx
9710 \begin_layout Plain Layout
9711 Accents ! for one character
9719 \begin_layout Standard
9720 \begin_inset space \hfill{}
9724 \begin_inset Tabular
9725 <lyxtabular version="3" rows="8" columns="2">
9726 <features booktabs="true" tabularvalignment="middle">
9727 <column alignment="center" valignment="top" width="0pt">
9728 <column alignment="center" valignment="top" width="0pt">
9730 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9733 \begin_layout Plain Layout
9739 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9742 \begin_layout Plain Layout
9749 <row topspace="1.5mm">
9750 <cell alignment="center" valignment="top" usebox="none">
9753 \begin_layout Plain Layout
9757 \begin_inset space \textvisiblespace{}
9765 <cell alignment="center" valignment="top" usebox="none">
9768 \begin_layout Plain Layout
9769 \begin_inset Formula $\dot{A}$
9778 <row topspace="1.5mm">
9779 <cell alignment="center" valignment="top" usebox="none">
9782 \begin_layout Plain Layout
9786 \begin_inset space \textvisiblespace{}
9794 <cell alignment="center" valignment="top" usebox="none">
9797 \begin_layout Plain Layout
9798 \begin_inset Formula $\ddot{A}$
9807 <row topspace="1.5mm">
9808 <cell alignment="center" valignment="top" usebox="none">
9811 \begin_layout Plain Layout
9815 \begin_inset space \textvisiblespace{}
9823 <cell alignment="center" valignment="top" usebox="none">
9826 \begin_layout Plain Layout
9827 \begin_inset Formula $\dddot{A}$
9836 <row topspace="1.5mm">
9837 <cell alignment="center" valignment="top" usebox="none">
9840 \begin_layout Plain Layout
9844 \begin_inset space \textvisiblespace{}
9852 <cell alignment="center" valignment="top" usebox="none">
9855 \begin_layout Plain Layout
9856 \begin_inset Formula $\ddddot{A}$
9865 <row topspace="1.5mm">
9866 <cell alignment="center" valignment="top" usebox="none">
9869 \begin_layout Plain Layout
9873 \begin_inset space \textvisiblespace{}
9877 \begin_inset Index idx
9880 \begin_layout Plain Layout
9891 <cell alignment="center" valignment="top" usebox="none">
9894 \begin_layout Plain Layout
9895 \begin_inset Formula $\vec{A}$
9904 <row topspace="1.5mm">
9905 <cell alignment="center" valignment="top" usebox="none">
9908 \begin_layout Plain Layout
9912 \begin_inset space \textvisiblespace{}
9920 <cell alignment="center" valignment="top" usebox="none">
9923 \begin_layout Plain Layout
9924 \begin_inset Formula $\bar{A}$
9933 <row topspace="1.5mm">
9934 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9937 \begin_layout Plain Layout
9941 \begin_inset space \textvisiblespace{}
9949 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9952 \begin_layout Plain Layout
9953 \begin_inset Formula $\mathring{A}$
9967 \begin_inset space \hfill{}
9971 \begin_inset Tabular
9972 <lyxtabular version="3" rows="7" columns="2">
9973 <features booktabs="true" tabularvalignment="middle">
9974 <column alignment="center" valignment="top" width="0pt">
9975 <column alignment="center" valignment="top" width="0pt">
9977 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9980 \begin_layout Plain Layout
9986 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9989 \begin_layout Plain Layout
9996 <row topspace="1.5mm">
9997 <cell alignment="center" valignment="top" usebox="none">
10000 \begin_layout Plain Layout
10004 \begin_inset space \textvisiblespace{}
10012 <cell alignment="center" valignment="top" usebox="none">
10015 \begin_layout Plain Layout
10016 \begin_inset Formula $\tilde{A}$
10025 <row topspace="1.5mm">
10026 <cell alignment="center" valignment="top" usebox="none">
10029 \begin_layout Plain Layout
10033 \begin_inset space \textvisiblespace{}
10041 <cell alignment="center" valignment="top" usebox="none">
10044 \begin_layout Plain Layout
10045 \begin_inset Formula $\hat{A}$
10054 <row topspace="1.5mm">
10055 <cell alignment="center" valignment="top" usebox="none">
10058 \begin_layout Plain Layout
10062 \begin_inset space \textvisiblespace{}
10070 <cell alignment="center" valignment="top" usebox="none">
10073 \begin_layout Plain Layout
10074 \begin_inset Formula $\check{A}$
10083 <row topspace="1.5mm">
10084 <cell alignment="center" valignment="top" usebox="none">
10087 \begin_layout Plain Layout
10091 \begin_inset space \textvisiblespace{}
10099 <cell alignment="center" valignment="top" usebox="none">
10102 \begin_layout Plain Layout
10103 \begin_inset Formula $\acute{A}$
10112 <row topspace="1.5mm">
10113 <cell alignment="center" valignment="top" usebox="none">
10116 \begin_layout Plain Layout
10120 \begin_inset space \textvisiblespace{}
10128 <cell alignment="center" valignment="top" usebox="none">
10131 \begin_layout Plain Layout
10132 \begin_inset Formula $\grave{A}$
10141 <row topspace="1.5mm">
10142 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10145 \begin_layout Plain Layout
10149 \begin_inset space \textvisiblespace{}
10157 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10160 \begin_layout Plain Layout
10161 \begin_inset Formula $\breve{A}$
10175 \begin_inset space \hfill{}
10181 \begin_layout Standard
10182 \begin_inset VSpace bigskip
10188 \begin_layout Standard
10189 You can directly insert accents like é to formulas.
10191 will transform them to the corresponding accent command.
10193 \begin_inset Index idx
10196 \begin_layout Plain Layout
10202 it is better to insert a quotation mark before the vowel.
10203 These two characters are then treated by \SpecialChar LaTeX
10208 character when the formula part with the umlaut is marked as German.
10216 \begin_inset Quotes eld
10220 \begin_inset Quotes erd
10223 umlauts are created as demonstrated in the following example:
10226 \begin_layout Standard
10227 \begin_inset VSpace -2mm
10233 \begin_layout Standard
10235 \begin_inset Tabular
10236 <lyxtabular version="3" rows="3" columns="2">
10237 <features booktabs="true" tabularvalignment="middle">
10238 <column alignment="center" valignment="top" width="0pt">
10239 <column alignment="center" valignment="top">
10241 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10244 \begin_layout Plain Layout
10250 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10253 \begin_layout Plain Layout
10261 <cell alignment="center" valignment="top" usebox="none">
10264 \begin_layout Plain Layout
10265 \begin_inset Quotes grd
10273 <cell alignment="center" valignment="top" usebox="none">
10276 \begin_layout Plain Layout
10277 \begin_inset space \hspace{}
10284 \begin_inset Formula $"i$
10293 <row topspace="1.5mm">
10294 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10297 \begin_layout Plain Layout
10301 \begin_inset space \textvisiblespace{}
10309 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10312 \begin_layout Plain Layout
10313 \begin_inset Formula $\ddot{i}$
10329 \begin_layout Standard
10330 Another advantage to
10336 is that umlauts can directly be converted to mathematical text because
10337 the accent commands above are
10343 in mathematical text
10346 To convert an accented character to mathematical text, only the character
10347 under the accent may be converted.
10348 This applies also for all other conversions, e.
10349 \begin_inset space \thinspace{}
10353 \begin_inset space \space{}
10359 \begin_layout Standard
10360 In mathematical text, umlauts and other accented characters can directly
10364 \begin_layout Standard
10365 \begin_inset VSpace bigskip
10371 \begin_layout Standard
10373 also supports a tilde under the character if the \SpecialChar LaTeX
10379 \begin_inset Index idx
10382 \begin_layout Plain Layout
10383 Packages ! undertilde
10388 is installed on your system:
10391 \begin_layout Standard
10395 \begin_layout Plain Layout
10405 \begin_inset Note Note
10408 \begin_layout Plain Layout
10409 The following table will only be displayed when the \SpecialChar LaTeX
10420 \begin_inset Separator parbreak
10426 \begin_layout Standard
10429 \begin_inset Tabular
10430 <lyxtabular version="3" rows="2" columns="2">
10431 <features booktabs="true" tabularvalignment="middle">
10432 <column alignment="center" valignment="top" width="0pt">
10433 <column alignment="center" valignment="top" width="0pt">
10435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10438 \begin_layout Plain Layout
10444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10447 \begin_layout Plain Layout
10455 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10458 \begin_layout Plain Layout
10462 \begin_inset space \textvisiblespace{}
10470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10473 \begin_layout Plain Layout
10474 \begin_inset Formula $\utilde{A}$
10490 \begin_layout Standard
10494 \begin_layout Plain Layout
10504 \begin_inset Note Note
10507 \begin_layout Plain Layout
10508 The following will be displayed when the \SpecialChar LaTeX
10521 \begin_layout Standard
10522 You need to install the \SpecialChar LaTeX
10527 to see the rest of this subsection in the output.
10530 \begin_layout Standard
10534 \begin_layout Plain Layout
10546 \begin_layout Standard
10547 \begin_inset Newpage newpage
10553 \begin_layout Subsection
10554 Accents for several Characters
10555 \begin_inset Index idx
10558 \begin_layout Plain Layout
10559 Accents ! for several characters
10567 \begin_layout Standard
10568 \begin_inset space \hfill{}
10572 \begin_inset Tabular
10573 <lyxtabular version="3" rows="5" columns="2">
10574 <features booktabs="true" tabularvalignment="middle">
10575 <column alignment="center" valignment="top" width="0pt">
10576 <column alignment="center" valignment="top" width="0pt">
10578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10581 \begin_layout Plain Layout
10587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10590 \begin_layout Plain Layout
10597 <row topspace="1.5mm">
10598 <cell alignment="center" valignment="top" usebox="none">
10601 \begin_layout Plain Layout
10605 \begin_inset space \textvisiblespace{}
10613 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10616 \begin_layout Plain Layout
10617 \begin_inset Formula $\overleftarrow{A=B}$
10626 <row topspace="1.5mm">
10627 <cell alignment="center" valignment="top" usebox="none">
10630 \begin_layout Plain Layout
10634 \begin_inset space \textvisiblespace{}
10642 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10645 \begin_layout Plain Layout
10646 \begin_inset Formula $\underleftarrow{A=B}$
10655 <row topspace="1.5mm">
10656 <cell alignment="center" valignment="top" usebox="none">
10659 \begin_layout Plain Layout
10663 \begin_inset space \textvisiblespace{}
10671 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10674 \begin_layout Plain Layout
10675 \begin_inset Formula $\overleftrightarrow{A=B}$
10684 <row topspace="1.5mm" bottomspace="1mm">
10685 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10688 \begin_layout Plain Layout
10691 underleftrightarrow
10692 \begin_inset space \textvisiblespace{}
10700 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10703 \begin_layout Plain Layout
10704 \begin_inset Formula $\underleftrightarrow{A=B}$
10718 \begin_inset space \hfill{}
10722 \begin_inset Tabular
10723 <lyxtabular version="3" rows="5" columns="2">
10724 <features booktabs="true" tabularvalignment="middle">
10725 <column alignment="center" valignment="top" width="0pt">
10726 <column alignment="center" valignment="top" width="0pt">
10728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10731 \begin_layout Plain Layout
10737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10740 \begin_layout Plain Layout
10747 <row topspace="1.5mm">
10748 <cell alignment="center" valignment="top" usebox="none">
10751 \begin_layout Plain Layout
10755 \begin_inset space \textvisiblespace{}
10763 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10766 \begin_layout Plain Layout
10767 \begin_inset Formula $\overrightarrow{A=B}$
10776 <row topspace="1.5mm">
10777 <cell alignment="center" valignment="top" usebox="none">
10780 \begin_layout Plain Layout
10784 \begin_inset space \textvisiblespace{}
10792 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10795 \begin_layout Plain Layout
10796 \begin_inset Formula $\underrightarrow{A=B}$
10805 <row topspace="1.5mm">
10806 <cell alignment="center" valignment="top" usebox="none">
10809 \begin_layout Plain Layout
10813 \begin_inset space \textvisiblespace{}
10821 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10824 \begin_layout Plain Layout
10825 \begin_inset Formula $\widetilde{A=B}$
10834 <row topspace="1.5mm" bottomspace="1mm">
10835 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10838 \begin_layout Plain Layout
10842 \begin_inset space \textvisiblespace{}
10850 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10853 \begin_layout Plain Layout
10854 \begin_inset Formula $\widehat{A=B}$
10868 \begin_inset space \hfill{}
10874 \begin_layout Standard
10875 \begin_inset VSpace medskip
10878 With these commands as many characters as you like can be accented.
10891 will only be set in the output with a length of three characters, as shown
10892 in the following example:
10893 \begin_inset Formula
10895 \widetilde{A+B=C-D}
10903 \begin_layout Standard
10911 \begin_inset Index idx
10914 \begin_layout Plain Layout
10929 \begin_inset Index idx
10932 \begin_layout Plain Layout
10940 described in the previous subsection it is also possible to accent several
10947 \begin_inset space \textvisiblespace{}
10951 \begin_inset Formula $\downarrow$
10957 \begin_inset Formula
10959 \underset{***}{A=B}
10967 \begin_layout Section
10969 \begin_inset CommandInset label
10971 name "subsec:Space"
10976 \begin_inset Index idx
10979 \begin_layout Plain Layout
10988 \begin_layout Subsection
10990 \begin_inset CommandInset label
10992 name "subsec:Predefined-Space"
10997 \begin_inset Index idx
11000 \begin_layout Plain Layout
11001 Space ! horizontal ! predefined
11009 \begin_layout Standard
11010 Sometimes it is necessary to insert horizontal space into a formula.
11011 This is done by inserting a protected space (shortcut
11014 arg "command-alternatives space-insert protected ; math-space"
11019 \begin_inset Quotes eld
11025 \begin_inset space \textvisiblespace{}
11031 \begin_inset Quotes erd
11034 appears and by pressing
11038 several times one can select one of eight different space sizes.
11039 The spaces can also be inserted using the math toolbar button
11042 arg "math-insert \\space"
11045 or special commands.
11046 Independent from the inserted command, one can select the size again by
11052 \begin_inset Separator parbreak
11058 \begin_layout Standard
11061 \begin_inset Tabular
11062 <lyxtabular version="3" rows="6" columns="3">
11063 <features booktabs="true" tabularvalignment="middle">
11064 <column alignment="center" valignment="top">
11065 <column alignment="center" valignment="top" width="15col%">
11066 <column alignment="center" valignment="top">
11068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11071 \begin_layout Plain Layout
11077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11080 \begin_layout Plain Layout
11090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11093 \begin_layout Plain Layout
11101 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11104 \begin_layout Plain Layout
11112 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11115 \begin_layout Plain Layout
11121 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11124 \begin_layout Plain Layout
11125 \begin_inset Formula $A\,B$
11135 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11138 \begin_layout Plain Layout
11146 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11149 \begin_layout Plain Layout
11155 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11158 \begin_layout Plain Layout
11159 \begin_inset Formula $A\:B$
11169 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11172 \begin_layout Plain Layout
11180 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11183 \begin_layout Plain Layout
11189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11192 \begin_layout Plain Layout
11193 \begin_inset Formula $A\;B$
11203 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11206 \begin_layout Plain Layout
11214 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11217 \begin_layout Plain Layout
11223 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11226 \begin_layout Plain Layout
11227 \begin_inset Formula $A\quad B$
11237 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11240 \begin_layout Plain Layout
11248 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11251 \begin_layout Plain Layout
11257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11260 \begin_layout Plain Layout
11261 \begin_inset Formula $A\qquad B$
11275 \begin_inset space \hfill{}
11279 \begin_inset Tabular
11280 <lyxtabular version="3" rows="6" columns="3">
11281 <features booktabs="true" tabularvalignment="middle">
11282 <column alignment="center" valignment="top">
11283 <column alignment="center" valignment="top" width="15col%">
11284 <column alignment="center" valignment="top">
11286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11289 \begin_layout Plain Layout
11295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11298 \begin_layout Plain Layout
11308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11311 \begin_layout Plain Layout
11319 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11322 \begin_layout Plain Layout
11330 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11333 \begin_layout Plain Layout
11339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11342 \begin_layout Plain Layout
11343 \begin_inset Formula $A\hfill B$
11353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11356 \begin_layout Plain Layout
11364 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11367 \begin_layout Plain Layout
11373 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11376 \begin_layout Plain Layout
11377 \begin_inset Formula $A\hspace*{1em}B$
11387 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11390 \begin_layout Plain Layout
11398 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11401 \begin_layout Plain Layout
11407 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11410 \begin_layout Plain Layout
11411 \begin_inset Formula $A\hspace{1em}B$
11421 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11424 \begin_layout Plain Layout
11428 \begin_inset space \textvisiblespace{}
11436 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11439 \begin_layout Plain Layout
11445 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11448 \begin_layout Plain Layout
11449 \begin_inset Formula $A\ B$
11459 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11462 \begin_layout Plain Layout
11470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11473 \begin_layout Plain Layout
11479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11482 \begin_layout Plain Layout
11483 \begin_inset Formula $A\!B$
11499 \begin_layout Standard
11501 \begin_inset space ~
11505 \begin_inset space \thinspace{}
11509 \begin_inset space \thinspace{}
11512 7 are variable spaces which are explained in
11513 \begin_inset CommandInset ref
11515 reference "subsec:Variable-Space"
11521 \begin_inset space ~
11524 9 seems to produce no space.
11525 It is displayed red in \SpecialChar LyX
11526 contrary to the other sizes, because it is a negative
11528 There are two more negative spaces:
11529 \begin_inset Separator parbreak
11535 \begin_layout Standard
11537 \begin_inset Tabular
11538 <lyxtabular version="3" rows="3" columns="3">
11539 <features booktabs="true" tabularvalignment="middle">
11540 <column alignment="center" valignment="middle" width="6.8cm">
11541 <column alignment="center" valignment="top" width="0pt">
11542 <column alignment="center" valignment="top" width="0pt">
11544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11547 \begin_layout Plain Layout
11553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11556 \begin_layout Plain Layout
11564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11567 \begin_layout Plain Layout
11577 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11580 \begin_layout Plain Layout
11585 keystrokes after inserting the protected space
11590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11593 \begin_layout Plain Layout
11599 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11602 \begin_layout Plain Layout
11610 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11613 \begin_layout Plain Layout
11619 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11622 \begin_layout Plain Layout
11623 \begin_inset Formula $A\negmedspace B$
11631 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11634 \begin_layout Plain Layout
11635 \begin_inset Formula $A\negthickspace B$
11651 \begin_layout Standard
11652 Negative spaces can lead to characters overlapping each other.
11653 Thus they can be used to enforce ligatures, which are e.
11654 \begin_inset space \thinspace{}
11658 \begin_inset space \space{}
11661 useful for summation operators:
11662 \begin_inset Separator parbreak
11668 \begin_layout Standard
11670 \begin_inset Tabular
11671 <lyxtabular version="3" rows="3" columns="2">
11672 <features booktabs="true" tabularvalignment="middle">
11673 <column alignment="center" valignment="top" width="0pt">
11674 <column alignment="center" valignment="top">
11676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11679 \begin_layout Plain Layout
11685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11688 \begin_layout Plain Layout
11696 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11699 \begin_layout Plain Layout
11705 \begin_inset space \textvisiblespace{}
11713 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11716 \begin_layout Plain Layout
11717 \begin_inset Formula $\sum\sum f_{kl}$
11727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11730 \begin_layout Plain Layout
11738 \begin_inset space \textvisiblespace{}
11746 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11749 \begin_layout Plain Layout
11750 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11766 \begin_layout Standard
11768 \begin_inset VSpace medskip
11774 \begin_layout Standard
11776 Relations like for example equal signs, are always surrounded by space.
11777 To suppress this, the equal sign is placed into a \SpecialChar TeX
11779 The following example demonstrates this:
11780 \begin_inset Separator parbreak
11786 \begin_layout Standard
11788 \begin_inset Tabular
11789 <lyxtabular version="3" rows="2" columns="2">
11790 <features tabularvalignment="middle">
11791 <column alignment="center" valignment="top" width="0pt">
11792 <column alignment="center" valignment="top" width="0pt">
11794 <cell alignment="center" valignment="top" usebox="none">
11797 \begin_layout Plain Layout
11803 <cell alignment="center" valignment="top" usebox="none">
11806 \begin_layout Plain Layout
11807 \begin_inset Formula $A=B$
11817 <cell alignment="center" valignment="top" usebox="none">
11820 \begin_layout Plain Layout
11821 equation without space
11826 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11829 \begin_layout Plain Layout
11830 \begin_inset Formula $A{=}B$
11846 \begin_layout Standard
11848 The command for the last formula is:
11853 \begin_inset Formula $\to$
11859 \begin_layout Standard
11860 \begin_inset VSpace bigskip
11866 \begin_layout Standard
11867 Spaces are needed for physical units, because the space between the value
11868 and the unit is the smallest one and not a normal space.
11869 For units in text, the smallest space is inserted via the menu
11871 Insert\SpecialChar menuseparator
11872 Formatting\SpecialChar menuseparator
11874 \begin_inset space ~
11882 arg "space-insert thin"
11888 \begin_layout Standard
11889 An example to visualize the difference:
11892 \begin_layout Standard
11893 \begin_inset Tabular
11894 <lyxtabular version="3" rows="2" columns="2">
11895 <features tabularvalignment="middle">
11896 <column alignment="left" valignment="top">
11897 <column alignment="left" valignment="top">
11899 <cell alignment="center" valignment="top" usebox="none">
11902 \begin_layout Plain Layout
11904 \begin_inset Formula $\cdot$
11912 <cell alignment="center" valignment="top" usebox="none">
11915 \begin_layout Plain Layout
11916 space between value and unit
11923 <cell alignment="center" valignment="top" usebox="none">
11926 \begin_layout Plain Layout
11928 \begin_inset space \thinspace{}
11932 \begin_inset Formula $\cdot$
11940 <cell alignment="center" valignment="top" usebox="none">
11943 \begin_layout Plain Layout
11944 smallest space between value and unit
11957 \begin_layout Subsection
11962 \begin_layout Plain Layout
11975 \begin_layout Plain Layout
11976 for vertical space in formulas see
11977 \begin_inset CommandInset ref
11979 reference "subsec:Line-Separation"
11992 \begin_layout Plain Layout
12000 \begin_inset Note Note
12003 \begin_layout Plain Layout
12006 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12009 \begin_layout Plain Layout
12012 texorpdfstring is in section
12013 \begin_inset CommandInset ref
12015 reference "subsec:Formulas-in-Section"
12025 \begin_inset CommandInset label
12027 name "subsec:Variable-Space"
12032 \begin_inset Index idx
12035 \begin_layout Plain Layout
12036 Space ! horizontal ! variable
12044 \begin_layout Standard
12045 Space with a defined length can be inserted with the command
12052 \begin_inset Index idx
12055 \begin_layout Plain Layout
12065 \begin_inset Quotes eld
12071 \begin_inset space \textvisiblespace{}
12077 \begin_inset Quotes erd
12081 The length can be specified by left-clicking on the
12082 \begin_inset Quotes eld
12088 \begin_inset space \textvisiblespace{}
12094 \begin_inset Quotes erd
12098 The length may also be negative.
12099 When a space would be the first character in a line it would be omitted.
12100 To force its output use the command
12112 or left-click on the
12113 \begin_inset Quotes eld
12119 \begin_inset space \textvisiblespace{}
12125 \begin_inset Quotes erd
12128 and check the option
12133 \begin_inset Newline newline
12136 To insert as much space as is available, the command
12143 \begin_inset Index idx
12146 \begin_layout Plain Layout
12157 \begin_layout Standard
12159 \begin_inset Tabular
12160 <lyxtabular version="3" rows="4" columns="2">
12161 <features booktabs="true" tabularvalignment="middle">
12162 <column alignment="center" valignment="top" width="0pt">
12163 <column alignment="center" valignment="top">
12165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12168 \begin_layout Plain Layout
12176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12179 \begin_layout Plain Layout
12187 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12190 \begin_layout Plain Layout
12194 \begin_inset space \textvisiblespace{}
12200 \begin_inset space \thinspace{}
12208 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12211 \begin_layout Plain Layout
12212 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12222 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12225 \begin_layout Plain Layout
12229 \begin_inset space \textvisiblespace{}
12235 \begin_inset space \thinspace{}
12243 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12246 \begin_layout Plain Layout
12247 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12260 \begin_layout Plain Layout
12264 \begin_inset space \textvisiblespace{}
12272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12275 \begin_layout Plain Layout
12276 \begin_inset Formula $A=A\hfill B=B$
12292 \begin_layout Standard
12293 In the last example the available space is given by the longest column entry
12295 In an inline formula the space depends on the length of the line in which
12303 Thus, when the line uses the full width, no space will be created.
12310 only has an effect on displayed formulas when the formula style
12315 (Formula styles are explained in
12316 \begin_inset CommandInset ref
12318 reference "sec:Formula-Styles"
12325 \begin_layout Standard
12332 , there are the commands
12344 that fill the space with a pattern, see
12345 \begin_inset CommandInset ref
12347 reference "subsec:Ellipses"
12354 \begin_layout Standard
12355 For text, variable space can be inserted via the menu
12357 Insert\SpecialChar menuseparator
12358 Formatting\SpecialChar menuseparator
12360 \begin_inset space ~
12368 \begin_layout Standard
12369 This is a line with
12370 \begin_inset space \hspace{}
12375 \begin_inset space \thinspace{}
12381 \begin_layout Standard
12382 This is a line with
12383 \begin_inset space \hfill{}
12389 \begin_layout Subsection
12390 Space besides inline Formulas
12391 \begin_inset Index idx
12394 \begin_layout Plain Layout
12395 Space ! besides inline formulas
12403 \begin_layout Standard
12404 The space that surrounds inline formulas can be adjusted with the length
12412 \begin_inset Index idx
12415 \begin_layout Plain Layout
12424 The value of a length is set with the command
12431 \begin_inset Index idx
12434 \begin_layout Plain Layout
12442 which has the following scheme:
12445 \begin_layout Standard
12450 setlength{length name}{value}
12453 \begin_layout Standard
12461 \begin_inset space \thinspace{}
12467 \begin_layout Standard
12477 \begin_layout Standard
12478 is inserted in \SpecialChar TeX
12481 \begin_inset space \thinspace{}
12484 mm space will now be set around all inline formulas:
12488 \begin_layout Plain Layout
12502 \begin_layout Standard
12503 This is a line with an inline formula
12504 \begin_inset Formula $A=B$
12508 \begin_inset space \thinspace{}
12511 mm surrounding space.
12515 \begin_layout Plain Layout
12529 \begin_layout Standard
12530 To return to the predefined value,
12536 is set to the value 0
12537 \begin_inset space \thinspace{}
12543 \begin_layout Standard
12544 \begin_inset Newpage newpage
12550 \begin_layout Section
12552 \begin_inset Index idx
12555 \begin_layout Plain Layout
12562 \begin_inset Index idx
12565 \begin_layout Plain Layout
12570 \begin_layout Plain Layout
12581 \begin_layout Plain Layout
12596 \begin_layout Standard
12597 Boxes for text are described in chapter
12604 \begin_inset space ~
12612 \begin_layout Subsection
12614 \begin_inset CommandInset label
12616 name "subsec:Boxes-with-Frame"
12621 \begin_inset Index idx
12624 \begin_layout Plain Layout
12633 \begin_layout Standard
12634 It is possible to frame a formula or part of one with the commands
12641 \begin_inset Index idx
12644 \begin_layout Plain Layout
12659 \begin_inset Index idx
12662 \begin_layout Plain Layout
12673 \begin_layout Standard
12674 When one of these commands is inserted in a formula, a blue box appears
12675 within a frame to enter formula parts.
12682 an additional formula has to be created by
12686 within this box, because the box content will otherwise be treated as mathemati
12694 is used, a new formula is automatically created inside the frame.
12697 \begin_layout Standard
12704 is not suitable to frame displayed formulas because the formula will always
12705 be set in the size of the text.
12712 is in contrary not suitable to frame inline formulas, because the formula
12713 will always be set in the size of a displayed formula.
12716 \begin_layout Standard
12730 \begin_inset Index idx
12733 \begin_layout Plain Layout
12741 where additionally the frame width and the alignment can be specified.
12748 is used in the following scheme:
12751 \begin_layout Standard
12756 framebox[frame width][position]{box content}
12759 \begin_layout Standard
12760 The position can either be
12777 right aligns the formula in the box.
12778 When no position is given, the formula will be centered.
12779 \begin_inset Newline newline
12782 If no width is given, also no position can be given.
12783 In this case the frame width is adjusted to the box content like for
12792 \begin_layout Standard
12799 is inserted, a box appears containing three blue boxes.
12800 The first two boxes are surrounded by brackets and denote the two optional
12802 The third box is for formula parts like for
12809 \begin_inset Separator parbreak
12815 \begin_layout Standard
12817 \begin_inset Tabular
12818 <lyxtabular version="3" rows="5" columns="2">
12819 <features booktabs="true" tabularvalignment="middle">
12820 <column alignment="center" valignment="top" width="0pt">
12821 <column alignment="center" valignment="top">
12823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12826 \begin_layout Plain Layout
12832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12835 \begin_layout Plain Layout
12842 <row topspace="1.5mm">
12843 <cell alignment="center" valignment="top" usebox="none">
12846 \begin_layout Plain Layout
12850 \begin_inset space \textvisiblespace{}
12860 \begin_inset space \textvisiblespace{}
12868 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12871 \begin_layout Plain Layout
12872 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12881 <row topspace="1.5mm">
12882 <cell alignment="center" valignment="top" usebox="none">
12885 \begin_layout Plain Layout
12889 \begin_inset space \textvisiblespace{}
12895 \begin_inset space \textvisiblespace{}
12903 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12906 \begin_layout Plain Layout
12907 \begin_inset Formula $\boxed{\int A=B}$
12916 <row topspace="1.5mm">
12917 <cell alignment="center" valignment="top" usebox="none">
12920 \begin_layout Plain Layout
12924 \begin_inset space \textvisiblespace{}
12932 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12935 \begin_layout Plain Layout
12936 \begin_inset Formula $A+\fbox{B}$
12945 <row topspace="1.5mm" bottomspace="1mm">
12946 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12949 \begin_layout Plain Layout
12953 \begin_inset space \textvisiblespace{}
12957 \begin_inset Formula $\to$
12961 \begin_inset Formula $\to$
12971 \begin_inset space \textvisiblespace{}
12975 \begin_inset Formula $\downarrow$
12983 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12986 \begin_layout Plain Layout
12987 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13003 \begin_layout Standard
13004 The frame thickness can also be adjusted.
13005 To do this the following commands have to be inserted in \SpecialChar TeX
13010 \begin_layout Standard
13020 \begin_inset Quotes eld
13024 \begin_inset Quotes erd
13038 \begin_inset Quotes eld
13042 \begin_inset Quotes erd
13048 \begin_layout Standard
13049 \begin_inset Quotes eld
13053 \begin_inset Quotes erd
13056 specifies the minimal distance between the frame and the first character
13058 An example for this is the following framed formula:
13062 \begin_layout Plain Layout
13074 \begin_inset Formula
13081 Before this formula the commands
13084 \begin_layout Standard
13106 \begin_layout Standard
13107 were inserted in \SpecialChar TeX
13109 The given values are used for all following boxes.
13112 \begin_layout Standard
13113 To return to the standard frame size, the command
13116 \begin_layout Standard
13141 \begin_layout Plain Layout
13155 \begin_layout Standard
13156 is inserted in \SpecialChar TeX
13157 mode before the next formula.
13160 \begin_layout Subsection
13161 Boxes without Frame
13162 \begin_inset CommandInset label
13164 name "subsec:Boxes-without-Frame"
13169 \begin_inset Index idx
13172 \begin_layout Plain Layout
13173 Boxes ! without frame
13181 \begin_layout Standard
13182 For boxes without a frame there are the following box commands:
13189 \begin_inset Index idx
13192 \begin_layout Plain Layout
13207 \begin_inset Index idx
13210 \begin_layout Plain Layout
13225 \begin_inset Index idx
13228 \begin_layout Plain Layout
13239 \begin_layout Standard
13246 a box can be super- or subscripted.
13247 But in contrary to normal super- and subscripting, the characters in the
13248 box keep their font size.
13255 is used in the following scheme:
13258 \begin_layout Standard
13263 raisebox{height}{box content}
13266 \begin_layout Standard
13267 When the box should contain a formula, an extra formula is needed like for
13278 \begin_inset Note Greyedout
13281 \begin_layout Plain Layout
13292 this extra formula is created by pressing
13296 twice instead of once because \SpecialChar LyX
13297 doesn't yet support
13311 \begin_inset Separator parbreak
13317 \begin_layout Standard
13319 \begin_inset Tabular
13320 <lyxtabular version="3" rows="4" columns="2">
13321 <features booktabs="true" tabularvalignment="middle">
13322 <column alignment="center" valignment="top" width="0pt">
13323 <column alignment="center" valignment="top">
13325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13328 \begin_layout Plain Layout
13334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13337 \begin_layout Plain Layout
13345 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13348 \begin_layout Plain Layout
13352 \begin_inset Formula $\to$
13358 \begin_inset Formula $\to$
13366 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13369 \begin_layout Plain Layout
13370 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13380 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13383 \begin_layout Plain Layout
13387 \begin_inset Formula $\to$
13393 \begin_inset Formula $\to$
13401 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13404 \begin_layout Plain Layout
13405 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13418 \begin_layout Plain Layout
13422 \begin_inset Formula $\to$
13438 \begin_inset space \textvisiblespace{}
13446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13449 \begin_layout Plain Layout
13450 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13466 \begin_layout Standard
13491 , with the difference that there is no frame.
13494 \begin_layout Subsection
13496 \begin_inset CommandInset label
13498 name "subsec:Colored-Boxes"
13503 \begin_inset Index idx
13506 \begin_layout Plain Layout
13515 \begin_layout Standard
13516 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13525 \begin_layout Plain Layout
13526 The \SpecialChar LaTeX
13531 is part of every \SpecialChar LaTeX
13532 standard installation.
13538 \begin_inset Index idx
13541 \begin_layout Plain Layout
13547 has to be loaded in the \SpecialChar LaTeX
13548 -preamble with the line
13552 \begin_layout Plain Layout
13553 When text is colored somewhere in the document with a predefined color,
13555 loads the \SpecialChar LaTeX
13561 Thus it is possible that the package is loaded twice, but this does not
13568 \begin_inset Note Note
13571 \begin_layout Plain Layout
13572 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13581 \begin_layout Standard
13589 \begin_layout Standard
13590 \begin_inset VSpace medskip
13593 To color boxes, the command
13600 \begin_inset Index idx
13603 \begin_layout Plain Layout
13611 is used in the following scheme:
13614 \begin_layout Standard
13619 colorbox{color}{box content}
13622 \begin_layout Standard
13623 The box content can also be a box and a
13629 can also be part of another box (see the 2nd and 3rd example).
13630 When the box should contain a formula, an extra formula has to be created,
13631 the same way as for
13641 \begin_layout Plain Layout
13642 This also applies for the command
13656 \begin_layout Standard
13657 One of the following predefined colors can be chosen:
13660 \begin_layout Standard
13694 \begin_inset Separator parbreak
13700 \begin_layout Standard
13702 \begin_inset Tabular
13703 <lyxtabular version="3" rows="4" columns="2">
13704 <features booktabs="true" tabularvalignment="middle">
13705 <column alignment="center" valignment="top" width="0pt">
13706 <column alignment="center" valignment="top">
13708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13711 \begin_layout Plain Layout
13717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13720 \begin_layout Plain Layout
13728 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13731 \begin_layout Plain Layout
13735 \begin_inset Formula $\to$
13745 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13748 \begin_layout Plain Layout
13749 \begin_inset Formula $\colorbox{yellow}{A=B}$
13758 <row topspace="1.5mm">
13759 <cell alignment="center" valignment="top" usebox="none">
13762 \begin_layout Plain Layout
13766 \begin_inset Formula $\to$
13774 \begin_inset space \textvisiblespace{}
13782 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13785 \begin_layout Plain Layout
13786 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13795 <row topspace="1.5mm" bottomspace="1mm">
13796 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13799 \begin_layout Plain Layout
13803 \begin_inset space \textvisiblespace{}
13809 \begin_inset Formula $\to$
13825 \begin_inset space \textvisiblespace{}
13833 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13836 \begin_layout Plain Layout
13837 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13853 \begin_layout Standard
13860 only colors the box but not the characters in the box.
13861 To color all characters, the whole formula is highlighted and the desired
13862 color is chosen in the
13865 \begin_inset space ~
13871 The dialog can be called with the toolbar button
13874 arg "dialog-show character"
13879 Edit\SpecialChar menuseparator
13881 \begin_inset space ~
13884 Style\SpecialChar menuseparator
13888 The formula number then has the same color as the formula.
13889 When the formula number should get another color than the formula characters,
13890 the color must be changed within the formula.
13893 \begin_layout Standard
13897 \begin_layout Standard
13900 \begin_inset Formula
13902 \int A=B\label{eq:red}
13910 \begin_inset Formula
13912 \textcolor{red}{\int A=B}\label{eq:redgreen}
13920 \begin_layout Standard
13922 \begin_inset CommandInset ref
13928 is completely colored red.
13929 \begin_inset Newline newline
13933 \begin_inset CommandInset ref
13935 reference "eq:redgreen"
13939 was first completely colored green to set the color for the formula number.
13940 Subsequently the formula characters were colored red.
13943 \begin_layout Standard
13944 \begin_inset VSpace bigskip
13947 To color the frame different than the rest of the box, the command
13954 \begin_inset Index idx
13957 \begin_layout Plain Layout
13965 is used in the following scheme:
13968 \begin_layout Standard
13973 fcolorbox{frame color}{color}{box content}
13976 \begin_layout Standard
13983 is an extension of the command
13990 The frame width is set, like for
14013 \begin_layout Plain Layout
14025 \begin_inset Formula
14027 \fcolorbox{cyan}{magenta}{A=B}
14036 \begin_layout Plain Layout
14050 \begin_layout Standard
14051 This formula was created with the command
14052 \begin_inset Newline newline
14060 \begin_inset Formula $\to$
14066 \begin_inset Formula $\to$
14076 \begin_layout Standard
14077 \begin_inset VSpace bigskip
14080 To use other colors than the predefined ones, they have to be defined first.
14083 \begin_layout Standard
14084 One can for example define the color
14085 \begin_inset Quotes eld
14093 \begin_inset Quotes erd
14096 with the \SpecialChar LaTeX
14100 \begin_layout Standard
14105 definecolor{darkgreen}{cmyk}{0.5,
14120 \begin_inset Index idx
14123 \begin_layout Plain Layout
14134 \begin_layout Standard
14139 is the color space that denotes the colors
14156 The four comma separated numbers are the portion factor for the corresponding
14157 colors of the color space.
14158 The factors can be in the range of 0
14159 \begin_inset space \thinspace{}
14163 \begin_inset space \thinspace{}
14171 also the color space
14175 can be used for definitions.
14192 , so that there are in this case three portion factors for the corresponding
14194 Furthermore there is the color space
14198 with one portion factor for the gray value.
14201 \begin_layout Standard
14202 As example a framed box with the new defined color
14206 where the characters have been colored
14211 \begin_inset Formula
14213 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14221 \begin_layout Standard
14222 Self-defined colors can also be used for text with the help of the command
14230 \begin_inset Index idx
14233 \begin_layout Plain Layout
14242 \begin_layout Standard
14246 \begin_layout Plain Layout
14250 textcolor{darkgreen}{
14256 \begin_inset Quotes eld
14260 \begin_inset Quotes erd
14267 \begin_layout Plain Layout
14277 \begin_layout Standard
14285 \begin_inset Index idx
14288 \begin_layout Plain Layout
14296 is used in the scheme
14300 textcolor{color}{characters to color}
14305 \begin_layout Subsection
14307 \begin_inset CommandInset label
14309 name "subsec:Paragraph-Boxes"
14314 \begin_inset Index idx
14317 \begin_layout Plain Layout
14318 Boxes ! as paragraph
14326 \begin_layout Standard
14327 A box that can contain several lines and paragraphs, a so-called paragraph
14328 box (parbox), can be created with the menu
14330 Insert\SpecialChar menuseparator
14333 or the toolbar button
14342 \begin_layout Standard
14343 The following example shows a framed parbox in a line:
14346 \begin_layout Standard
14347 \begin_inset VSpace medskip
14351 \begin_inset Box Boxed
14361 height_special "totalheight"
14366 backgroundcolor "none"
14369 \begin_layout Plain Layout
14370 This is a paragraph box.
14372 \begin_inset space \thinspace{}
14375 cm long and can also contain formulas:
14376 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14387 \begin_layout Standard
14388 \begin_inset VSpace medskip
14394 \begin_layout Standard
14395 Such a box is created by right-clicking on the gray box inset.
14396 A dialog pops up showing the box properties.
14410 \begin_inset space \thinspace{}
14415 Vertical Box Alignment
14420 \begin_layout Standard
14421 \begin_inset VSpace medskip
14424 In \SpecialChar LaTeX
14425 a parbox is created with the command
14432 \begin_inset Index idx
14435 \begin_layout Plain Layout
14443 which has the following scheme:
14446 \begin_layout Standard
14451 parbox[position]{width}{box content}
14454 \begin_layout Standard
14469 \begin_inset Quotes eld
14473 \begin_inset Quotes erd
14476 means that the box is aligned within the surrounding text with its last
14483 \begin_inset Quotes eld
14487 \begin_inset Quotes erd
14490 this is done with the first line.
14491 When no position is given, the box will be vertically centered, see section
14499 \begin_inset space ~
14504 manual for examples.
14507 \begin_layout Standard
14508 \begin_inset VSpace bigskip
14511 To frame formulas completely, including the formula number, the formula
14512 must be set into a parbox.
14513 To do this, the command
14527 is inserted in \SpecialChar TeX
14528 mode before the formula.
14536 \begin_inset Index idx
14539 \begin_layout Plain Layout
14547 is hereby the line width set for the document.
14548 Because the frame is outside the parbox, 2
14549 \begin_inset space \thinspace{}
14552 times the frame separation and the frame thickness must be subtracted from
14554 As this is not automatically done by \SpecialChar LyX
14559 \begin_layout Plain Layout
14560 \begin_inset CommandInset href
14562 name "LyX-bug #4483"
14563 target "http://www.lyx.org/trac/ticket/4483"
14573 mode has to be used.
14574 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14583 \begin_layout Plain Layout
14588 is part of every \SpecialChar LaTeX
14589 standard installation.
14595 \begin_inset Index idx
14598 \begin_layout Plain Layout
14604 must be loaded in the \SpecialChar LaTeX
14605 -preamble with the line
14608 \begin_layout Standard
14616 \begin_layout Standard
14617 Behind the formula both boxes are closed by entering
14621 in \SpecialChar TeX
14623 Here is an example:
14627 \begin_layout Plain Layout
14641 \begin_layout Standard
14645 \begin_layout Plain Layout
14663 \begin_inset Formula
14665 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14674 \begin_layout Plain Layout
14685 \begin_layout Plain Layout
14699 \begin_layout Standard
14700 \begin_inset VSpace medskip
14703 As a parbox is used as the argument of
14709 , there is in this case no difference between
14724 \begin_layout Standard
14725 \begin_inset VSpace bigskip
14728 Paragraph boxes are very useful to comment formulas directly.
14735 is used in combination with the command
14749 \begin_inset CommandInset ref
14751 reference "subsec:User-defined-Numbering"
14758 \begin_layout Standard
14759 An example of a formula commented with
14768 \begin_layout Standard
14772 \begin_layout Plain Layout
14785 This is a description.
14786 It is distinctly separated from the formula and multiline.
14790 \begin_layout Plain Layout
14802 \begin_layout Standard
14803 Such a formula must be inserted completely in \SpecialChar TeX
14804 mode because \SpecialChar LyX
14806 support the command
14813 The formula is created with the following command sequence:
14816 \begin_layout Standard
14829 is inserted in \SpecialChar TeX
14834 \begin_layout Plain Layout
14835 When the formula style
14847 can also be replaced by
14854 (formula styles see
14855 \begin_inset CommandInset ref
14857 reference "sec:Formula-Styles"
14866 Then the description follows as normal text and finally
14872 is inserted in \SpecialChar TeX
14886 hereby create a displayed formula.
14889 \begin_layout Standard
14896 can be seen in this example that was
14897 \begin_inset Quotes eld
14901 \begin_inset Quotes erd
14904 using the mathematical textmode:
14905 \begin_inset Formula
14907 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14915 \begin_layout Section
14917 \begin_inset Index idx
14920 \begin_layout Plain Layout
14929 \begin_layout Subsection
14931 \begin_inset CommandInset label
14933 name "subsec:Big-Operators"
14938 \begin_inset Index idx
14941 \begin_layout Plain Layout
14948 \begin_inset Index idx
14951 \begin_layout Plain Layout
14958 \begin_inset Index idx
14961 \begin_layout Plain Layout
14970 \begin_layout Standard
14971 To be able to use all integral operators listed here, the option
14973 Use esint package automatically
14975 must be set in the document settings under
14978 \begin_inset space ~
14986 \begin_layout Standard
14987 \begin_inset space \hfill{}
14991 \begin_inset Tabular
14992 <lyxtabular version="3" rows="11" columns="2">
14993 <features booktabs="true" tabularvalignment="middle">
14994 <column alignment="center" valignment="top" width="0pt">
14995 <column alignment="center" valignment="top" width="0pt">
14997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15000 \begin_layout Plain Layout
15006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15009 \begin_layout Plain Layout
15017 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15020 \begin_layout Plain Layout
15024 \begin_inset Index idx
15027 \begin_layout Plain Layout
15040 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15043 \begin_layout Plain Layout
15044 \begin_inset Formula $\int$
15054 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15057 \begin_layout Plain Layout
15065 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15068 \begin_layout Plain Layout
15069 \begin_inset Formula $\oint$
15079 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15082 \begin_layout Plain Layout
15090 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15093 \begin_layout Plain Layout
15094 \begin_inset Formula $\ointctrclockwise$
15104 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15107 \begin_layout Plain Layout
15115 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15118 \begin_layout Plain Layout
15119 \begin_inset Formula $\ointclockwise$
15129 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15132 \begin_layout Plain Layout
15140 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15143 \begin_layout Plain Layout
15144 \begin_inset Formula $\sqint$
15154 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15157 \begin_layout Plain Layout
15165 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15168 \begin_layout Plain Layout
15170 \begin_inset Formula $\fint$
15180 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15183 \begin_layout Plain Layout
15191 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15194 \begin_layout Plain Layout
15196 \begin_inset Formula $\landupint$
15206 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15209 \begin_layout Plain Layout
15217 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15220 \begin_layout Plain Layout
15222 \begin_inset Formula $\landdownint$
15232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15235 \begin_layout Plain Layout
15243 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15246 \begin_layout Plain Layout
15247 \begin_inset Formula $\bigcap$
15257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15260 \begin_layout Plain Layout
15268 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15271 \begin_layout Plain Layout
15272 \begin_inset Formula $\bigcup$
15286 \begin_inset space \hfill{}
15290 \begin_inset Tabular
15291 <lyxtabular version="3" rows="11" columns="2">
15292 <features booktabs="true" tabularvalignment="middle">
15293 <column alignment="center" valignment="top" width="0pt">
15294 <column alignment="center" valignment="top" width="0pt">
15296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15299 \begin_layout Plain Layout
15305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15308 \begin_layout Plain Layout
15316 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15319 \begin_layout Plain Layout
15323 \begin_inset Index idx
15326 \begin_layout Plain Layout
15339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15342 \begin_layout Plain Layout
15343 \begin_inset Formula $\sum$
15353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15356 \begin_layout Plain Layout
15360 \begin_inset Index idx
15363 \begin_layout Plain Layout
15370 \begin_layout Plain Layout
15389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15392 \begin_layout Plain Layout
15393 \begin_inset Formula $\prod$
15403 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15406 \begin_layout Plain Layout
15414 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15417 \begin_layout Plain Layout
15418 \begin_inset Formula $\coprod$
15428 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15431 \begin_layout Plain Layout
15439 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15442 \begin_layout Plain Layout
15443 \begin_inset Formula $\bigodot$
15453 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15456 \begin_layout Plain Layout
15464 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15467 \begin_layout Plain Layout
15468 \begin_inset Formula $\bigotimes$
15478 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15481 \begin_layout Plain Layout
15489 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15492 \begin_layout Plain Layout
15493 \begin_inset Formula $\bigoplus$
15503 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15506 \begin_layout Plain Layout
15514 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15517 \begin_layout Plain Layout
15518 \begin_inset Formula $\bigwedge$
15528 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15531 \begin_layout Plain Layout
15539 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15542 \begin_layout Plain Layout
15543 \begin_inset Formula $\bigvee$
15553 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15556 \begin_layout Plain Layout
15564 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15567 \begin_layout Plain Layout
15568 \begin_inset Formula $\bigsqcup$
15578 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15581 \begin_layout Plain Layout
15589 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15592 \begin_layout Plain Layout
15593 \begin_inset Formula $\biguplus$
15607 \begin_inset space \hfill{}
15613 \begin_layout Standard
15614 All big operators can also be inserted via the math toolbar button
15617 arg "math-insert \\intop"
15623 \begin_layout Standard
15624 The operators are called big because they are bigger than the sometimes
15625 equal looking binary operators.
15626 All big operators can have limits as described in the next subsection.
15629 \begin_layout Standard
15630 For all integral operators there is a second version available, ending in
15648 These operators are different from
15655 \begin_inset space \space{}
15658 in the style the operator limits are displayed, see
15659 \begin_inset CommandInset ref
15661 reference "subsec:Operator-Limits"
15669 \begin_layout Subsubsection*
15670 Advice for Integrals
15673 \begin_layout Standard
15678 in an integral is an operator, that therefore has to be set upright.
15679 This is done by highlighting the
15683 and using the keyboard shortcut
15693 \begin_layout Plain Layout
15699 \begin_inset CommandInset ref
15701 reference "subsec:Font-Styles"
15711 Finally the smallest space is inserted before the
15715 , as this is usual for operators.
15719 \begin_layout Standard
15721 \begin_inset Formula $\int A(x)dx$
15725 \begin_inset Newline newline
15729 \begin_inset Phantom HPhantom
15732 \begin_layout Plain Layout
15739 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15745 \begin_layout Standard
15746 For multiple integrals there are the following commands:
15747 \begin_inset VSpace medskip
15753 \begin_layout Standard
15754 \begin_inset space \hfill{}
15758 \begin_inset Tabular
15759 <lyxtabular version="3" rows="4" columns="2">
15760 <features booktabs="true" tabularvalignment="middle">
15761 <column alignment="center" valignment="top" width="0pt">
15762 <column alignment="center" valignment="top" width="0pt">
15764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15767 \begin_layout Plain Layout
15773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15776 \begin_layout Plain Layout
15783 <row bottomspace="1mm">
15784 <cell alignment="center" valignment="top" usebox="none">
15787 \begin_layout Plain Layout
15795 <cell alignment="center" valignment="top" usebox="none">
15798 \begin_layout Plain Layout
15799 \begin_inset Formula $\iint$
15808 <row bottomspace="1mm">
15809 <cell alignment="center" valignment="top" usebox="none">
15812 \begin_layout Plain Layout
15820 <cell alignment="center" valignment="top" usebox="none">
15823 \begin_layout Plain Layout
15824 \begin_inset Formula $\oiint$
15833 <row bottomspace="1mm">
15834 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15837 \begin_layout Plain Layout
15845 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15848 \begin_layout Plain Layout
15849 \begin_inset Formula $\sqiint$
15863 \begin_inset space \hfill{}
15867 \begin_inset Tabular
15868 <lyxtabular version="3" rows="4" columns="2">
15869 <features booktabs="true" tabularvalignment="middle">
15870 <column alignment="center" valignment="top" width="0pt">
15871 <column alignment="center" valignment="top" width="0pt">
15873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15876 \begin_layout Plain Layout
15882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15885 \begin_layout Plain Layout
15892 <row bottomspace="1mm">
15893 <cell alignment="center" valignment="top" usebox="none">
15896 \begin_layout Plain Layout
15904 <cell alignment="center" valignment="top" usebox="none">
15907 \begin_layout Plain Layout
15908 \begin_inset Formula $\iiint$
15917 <row bottomspace="1mm">
15918 <cell alignment="center" valignment="top" usebox="none">
15921 \begin_layout Plain Layout
15929 <cell alignment="center" valignment="top" usebox="none">
15932 \begin_layout Plain Layout
15933 \begin_inset Formula $\iiiint$
15942 <row bottomspace="1mm">
15943 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15946 \begin_layout Plain Layout
15954 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15957 \begin_layout Plain Layout
15958 \begin_inset Formula $\dotsint$
15972 \begin_inset space \hfill{}
15978 \begin_layout Subsection
15980 \begin_inset CommandInset label
15982 name "subsec:Operator-Limits"
15987 \begin_inset Index idx
15990 \begin_layout Plain Layout
15999 \begin_layout Standard
16000 Limits are created by super- and subscripts:
16001 \begin_inset Separator parbreak
16007 \begin_layout Standard
16009 \begin_inset Tabular
16010 <lyxtabular version="3" rows="2" columns="2">
16011 <features booktabs="true" tabularvalignment="middle">
16012 <column alignment="center" valignment="top" width="0pt">
16013 <column alignment="center" valignment="top" width="0pt">
16015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16018 \begin_layout Plain Layout
16024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16027 \begin_layout Plain Layout
16035 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16038 \begin_layout Plain Layout
16044 \begin_inset space \textvisiblespace{}
16048 \begin_inset Formula $\to$
16052 \begin_inset Formula $\to$
16060 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16063 \begin_layout Plain Layout
16064 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
16080 \begin_layout Standard
16081 Limits of inline formulas are set right beside the operator.
16082 Limits in displayed formulas are set above or below the operator, except
16083 for integral limits.
16086 \begin_layout Standard
16087 To force that the limits are set beside the operator, the cursor is set
16088 directly behind the operator and the limits type is changed with the menu
16091 Edit\SpecialChar menuseparator
16092 Math\SpecialChar menuseparator
16111 \begin_layout Standard
16112 The default limits type is this:
16113 \begin_inset Formula
16115 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16120 This is how it looks when the limits type was changed to
16127 \begin_inset Formula
16129 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16134 For integrals, except those ending with
16150 etc., the limits are by default set beside the operator.
16151 But for multiple integrals the limits are often set below the operator.
16152 In the following example the limits type was therefore set to
16156 and so set below the integrals:
16157 \begin_inset Formula
16159 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16167 \begin_layout Standard
16168 \begin_inset VSpace medskip
16171 To specify conditions for limits, the commands
16178 \begin_inset Index idx
16181 \begin_layout Plain Layout
16196 \begin_inset Index idx
16199 \begin_layout Plain Layout
16208 To create for example this expression
16209 \begin_inset Formula
16211 \sum_{\begin{subarray}{c}
16215 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16223 \begin_layout Standard
16224 the following has to be done:
16225 \begin_inset Newline newline
16237 \begin_inset space \textvisiblespace{}
16243 One is now in a blue box under the summation operator and insert there
16249 \begin_inset space \textvisiblespace{}
16255 The blue box is now within a purple box and now several lines can be written
16257 A new line is created by inserting a line break (
16260 arg "newline-insert newline"
16265 \begin_inset Newline newline
16270 0<k<1000 Ctrl+Return
16271 \begin_inset Newline newline
16276 is typed in, a new box appears below for the new line.
16279 \begin_layout Standard
16280 The alignment of the lines can be changed to left aligned with the
16290 Edit\SpecialChar menuseparator
16294 To get right alignment,
16299 \begin_inset space \textvisiblespace{}
16304 is inserted at the beginning of the line.
16307 \begin_layout Standard
16320 with the difference that the lines are always centered.
16323 \begin_layout Standard
16324 \begin_inset VSpace bigskip
16328 \begin_inset CommandInset ref
16330 reference "eq:substack"
16334 there can be too much space beside an operator, because the characters
16335 following the operator are set beside the limits.
16336 To avoid this the command
16343 \begin_inset Index idx
16346 \begin_layout Plain Layout
16355 To activate it, set in the document settings under
16358 \begin_inset space ~
16368 \begin_inset Index idx
16371 \begin_layout Plain Layout
16372 Packages ! mathtools
16380 \begin_inset space ~
16392 sets the space besides the operator to 0
16393 \begin_inset space \thinspace{}
16397 \begin_inset Newline newline
16401 \begin_inset CommandInset ref
16403 reference "eq:substack"
16407 , one uses the command
16410 \begin_layout Standard
16418 \begin_layout Standard
16419 and inserts the operator with its limits into the braces.
16420 Behind the brace one continues the formula:
16421 \begin_inset Formula
16423 \smashoperator{\sum_{\begin{subarray}{c}
16427 \end{subarray}}^{n}}k^{-2}
16435 \begin_layout Standard
16436 It is possible to set the space of only one side of the operator to 0
16437 \begin_inset space \thinspace{}
16441 To do this write either
16460 stands for the left and
16464 for the right side of the operator.
16465 Here is an example of the possible
16474 \begin_layout Standard
16475 \begin_inset Formula
16477 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}
16485 \begin_layout Standard
16486 \begin_inset VSpace bigskip
16492 \begin_layout Standard
16493 When several consecutive operators have limits the typesetting of the limits
16494 looks often imperfect in the output, see this example:
16495 \begin_inset Formula
16497 \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}
16502 To improve the typesetting set in the document settings under
16505 \begin_inset space ~
16515 \begin_inset Index idx
16518 \begin_layout Plain Layout
16519 Packages ! mathtools
16527 \begin_inset space ~
16533 Then insert into your formula the command
16540 \begin_inset Index idx
16543 \begin_layout Plain Layout
16551 directly before the first operator.
16552 The example will then look like this:
16553 \begin_inset Formula
16555 \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}
16563 \begin_layout Standard
16564 \begin_inset VSpace bigskip
16567 How to use one limit for several operators is described in
16568 \begin_inset CommandInset ref
16570 reference "subsec:Self-defined-Operators"
16577 \begin_layout Subsection
16578 Decoration for Operators
16579 \begin_inset Index idx
16582 \begin_layout Plain Layout
16583 Operators ! Decoration
16591 \begin_layout Standard
16599 \begin_inset Index idx
16602 \begin_layout Plain Layout
16617 \begin_inset Index idx
16620 \begin_layout Plain Layout
16628 characters can be placed above or below an operator, respectively.
16636 \begin_inset Index idx
16639 \begin_layout Plain Layout
16647 characters can be set before and behind a big operator.
16650 \begin_layout Standard
16652 \begin_inset space ~
16664 \begin_layout Itemize
16671 is used to set characters at the corners of the operator
16674 \begin_layout Itemize
16681 is used to set characters before and/or behind the operator (this variant
16682 represents \SpecialChar LaTeX
16692 \begin_layout Itemize
16699 is used to set characters at the left corners and/or behind the operator
16702 \begin_layout Itemize
16709 is used to set characters at the right corners and/or before the operator
16712 \begin_layout Standard
16713 For example the command
16718 \begin_inset space \textvisiblespace{}
16724 \begin_inset space \textvisiblespace{}
16728 \begin_inset Formula $\to$
16732 \begin_inset Formula $\to$
16736 \begin_inset space \textvisiblespace{}
16746 \begin_inset Formula
16748 \sideset{}{'}\sum_{k=1}^{n}
16756 \begin_layout Standard
16757 \begin_inset Note Greyedout
16760 \begin_layout Plain Layout
16767 can only be used to decorate big operators, binary operators are not allowed.
16775 \begin_layout Standard
16788 can also be used to decorate symbols and characters.
16789 For example, the command
16794 \begin_inset space \textvisiblespace{}
16800 \begin_inset space \textvisiblespace{}
16806 \begin_inset Formula $\uparrow$
16814 \begin_inset Formula
16816 \overset{a}{\maltese}
16824 \begin_layout Subsection
16826 \begin_inset CommandInset label
16828 name "subsec:Binary-Operators"
16833 \begin_inset Index idx
16836 \begin_layout Plain Layout
16845 \begin_layout Standard
16846 Binary operators are surrounded by space when there is a character before
16848 \begin_inset VSpace medskip
16854 \begin_layout Standard
16855 \begin_inset Tabular
16856 <lyxtabular version="3" rows="13" columns="2">
16857 <features booktabs="true" tabularvalignment="middle">
16858 <column alignment="center" valignment="top" width="0pt">
16859 <column alignment="center" valignment="top" width="0pt">
16861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16864 \begin_layout Plain Layout
16866 \begin_inset Note Note
16869 \begin_layout Plain Layout
16876 is only used as spacer.
16886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16889 \begin_layout Plain Layout
16897 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16900 \begin_layout Plain Layout
16906 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16909 \begin_layout Plain Layout
16910 \begin_inset Formula $+$
16920 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16923 \begin_layout Plain Layout
16929 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16932 \begin_layout Plain Layout
16933 \begin_inset Formula $-$
16943 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16946 \begin_layout Plain Layout
16954 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16957 \begin_layout Plain Layout
16958 \begin_inset Formula $\pm$
16968 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16971 \begin_layout Plain Layout
16979 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16982 \begin_layout Plain Layout
16983 \begin_inset Formula $\mp$
16993 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16996 \begin_layout Plain Layout
17004 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17007 \begin_layout Plain Layout
17008 \begin_inset Formula $\cdot$
17018 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17021 \begin_layout Plain Layout
17029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17032 \begin_layout Plain Layout
17033 \begin_inset Formula $\times$
17043 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17046 \begin_layout Plain Layout
17054 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17057 \begin_layout Plain Layout
17058 \begin_inset Formula $\div$
17068 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17071 \begin_layout Plain Layout
17075 \begin_layout Plain Layout
17088 \begin_layout Plain Layout
17100 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17103 \begin_layout Plain Layout
17104 \begin_inset Formula $*$
17114 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17117 \begin_layout Plain Layout
17125 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17128 \begin_layout Plain Layout
17129 \begin_inset Formula $\star$
17139 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17142 \begin_layout Plain Layout
17150 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17153 \begin_layout Plain Layout
17154 \begin_inset Formula $\circ$
17164 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17167 \begin_layout Plain Layout
17175 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17178 \begin_layout Plain Layout
17179 \begin_inset Formula $\diamond$
17189 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17192 \begin_layout Plain Layout
17200 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17203 \begin_layout Plain Layout
17204 \begin_inset Formula $\bullet$
17218 \begin_inset space \hfill{}
17222 \begin_inset Tabular
17223 <lyxtabular version="3" rows="13" columns="2">
17224 <features booktabs="true" tabularvalignment="middle">
17225 <column alignment="center" valignment="top" width="0pt">
17226 <column alignment="center" valignment="top" width="0pt">
17228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17231 \begin_layout Plain Layout
17237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17240 \begin_layout Plain Layout
17248 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17251 \begin_layout Plain Layout
17259 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17262 \begin_layout Plain Layout
17263 \begin_inset Formula $\nabla$
17273 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17276 \begin_layout Plain Layout
17284 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17287 \begin_layout Plain Layout
17288 \begin_inset Formula $\bigtriangledown$
17298 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17301 \begin_layout Plain Layout
17309 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17312 \begin_layout Plain Layout
17313 \begin_inset Formula $\bigtriangleup$
17323 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17326 \begin_layout Plain Layout
17334 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17337 \begin_layout Plain Layout
17338 \begin_inset Formula $\Box$
17348 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17351 \begin_layout Plain Layout
17359 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17362 \begin_layout Plain Layout
17363 \begin_inset Formula $\cap$
17373 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17376 \begin_layout Plain Layout
17384 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17387 \begin_layout Plain Layout
17388 \begin_inset Formula $\cup$
17398 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17401 \begin_layout Plain Layout
17409 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17412 \begin_layout Plain Layout
17413 \begin_inset Formula $\dagger$
17423 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17426 \begin_layout Plain Layout
17434 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17437 \begin_layout Plain Layout
17438 \begin_inset Formula $\ddagger$
17448 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17451 \begin_layout Plain Layout
17459 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17462 \begin_layout Plain Layout
17463 \begin_inset Formula $\wr$
17473 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17476 \begin_layout Plain Layout
17484 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17487 \begin_layout Plain Layout
17488 \begin_inset Formula $\bigcirc$
17498 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17501 \begin_layout Plain Layout
17509 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17512 \begin_layout Plain Layout
17513 \begin_inset Formula $\wedge$
17523 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17526 \begin_layout Plain Layout
17534 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17537 \begin_layout Plain Layout
17538 \begin_inset Formula $\vee$
17552 \begin_inset space \hfill{}
17556 \begin_inset Tabular
17557 <lyxtabular version="3" rows="13" columns="2">
17558 <features booktabs="true" tabularvalignment="middle">
17559 <column alignment="center" valignment="top" width="0pt">
17560 <column alignment="center" valignment="top" width="0pt">
17562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17565 \begin_layout Plain Layout
17571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17574 \begin_layout Plain Layout
17582 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17585 \begin_layout Plain Layout
17593 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17596 \begin_layout Plain Layout
17597 \begin_inset Formula $\oplus$
17607 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17610 \begin_layout Plain Layout
17618 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17621 \begin_layout Plain Layout
17622 \begin_inset Formula $\ominus$
17632 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17635 \begin_layout Plain Layout
17643 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17646 \begin_layout Plain Layout
17647 \begin_inset Formula $\otimes$
17657 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17660 \begin_layout Plain Layout
17668 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17671 \begin_layout Plain Layout
17672 \begin_inset Formula $\oslash$
17682 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17685 \begin_layout Plain Layout
17693 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17696 \begin_layout Plain Layout
17697 \begin_inset Formula $\odot$
17707 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17710 \begin_layout Plain Layout
17718 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17721 \begin_layout Plain Layout
17722 \begin_inset Formula $\amalg$
17732 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17735 \begin_layout Plain Layout
17743 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17746 \begin_layout Plain Layout
17747 \begin_inset Formula $\uplus$
17757 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17760 \begin_layout Plain Layout
17768 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17771 \begin_layout Plain Layout
17772 \begin_inset Formula $\setminus$
17782 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17785 \begin_layout Plain Layout
17793 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17796 \begin_layout Plain Layout
17797 \begin_inset Formula $\sqcap$
17807 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17810 \begin_layout Plain Layout
17818 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17821 \begin_layout Plain Layout
17822 \begin_inset Formula $\sqcup$
17832 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17835 \begin_layout Plain Layout
17843 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17846 \begin_layout Plain Layout
17847 \begin_inset Formula $\triangleleft$
17857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17860 \begin_layout Plain Layout
17868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17871 \begin_layout Plain Layout
17872 \begin_inset Formula $\triangleright$
17888 \begin_layout Standard
17889 All binary operators can also be inserted via the math toolbar button
17892 arg "math-insert \\pm"
17898 \begin_layout Standard
17899 To typeset the Laplace operator also
17916 \begin_inset Formula $\nabla^{2}$
17919 ) can be used instead of
17928 \begin_layout Standard
17935 Insert\SpecialChar menuseparator
17947 \begin_layout Subsection
17948 Self-defined Operators
17949 \begin_inset CommandInset label
17951 name "subsec:Self-defined-Operators"
17956 \begin_inset Index idx
17959 \begin_layout Plain Layout
17960 Operators ! self-defined
17968 \begin_layout Standard
17969 With the help of the command
17973 DeclareMathOperator
17976 \begin_inset Index idx
17979 \begin_layout Plain Layout
17984 DeclareMathOperator
17989 custom operators can be defined in the \SpecialChar LaTeX
17991 Its command scheme is:
17994 \begin_layout Standard
17999 DeclareMathOperator{new command}{display}
18002 \begin_layout Standard
18003 Display can be characters or symbols that define how the operator looks
18005 To define a big operator a * is set behind the command.
18006 All self-defined big operators can have limits as described in
18007 \begin_inset CommandInset ref
18009 reference "subsec:Operator-Limits"
18016 \begin_layout Standard
18017 For example the \SpecialChar LaTeX
18021 \begin_layout Standard
18026 DeclareMathOperator*{
18033 \begin_layout Standard
18034 defines the command
18040 , that inserts a big operator consisting of the lozenge symbol from
18041 \begin_inset CommandInset ref
18043 reference "subsec:Miscellaneous-Symbols"
18048 \begin_inset Formula
18050 \Lozenge_{n=1}^{\infty}
18055 The command for this formula is:
18066 \begin_inset Formula $\to$
18072 \begin_layout Standard
18073 \begin_inset VSpace bigskip
18076 When self-defined operators are not used several times in the document,
18077 they can also be defined with the commands
18084 \begin_inset Index idx
18087 \begin_layout Plain Layout
18102 \begin_inset Index idx
18105 \begin_layout Plain Layout
18113 , which have the following scheme:
18116 \begin_layout Standard
18130 \begin_layout Standard
18137 defines big operators,
18146 \begin_layout Standard
18154 \begin_inset space \thinspace{}
18158 \begin_inset space \space{}
18161 be used to use one limit for several operators:
18164 \begin_layout Standard
18165 \begin_inset Formula
18167 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18175 \begin_layout Standard
18176 The command for the formula above is:
18177 \begin_inset Newline newline
18193 \begin_inset space \textvisiblespace{}
18199 \begin_inset Formula $\to$
18205 \begin_inset space \textvisiblespace{}
18213 \begin_layout Section
18215 \begin_inset Index idx
18218 \begin_layout Plain Layout
18227 \begin_layout Subsection
18229 \begin_inset CommandInset label
18231 name "subsec:Font-Styles"
18236 \begin_inset Index idx
18239 \begin_layout Plain Layout
18248 \begin_layout Standard
18249 Latin letters in formulas can be set in one of the following font styles:
18252 \begin_layout Standard
18254 \begin_inset space \hfill{}
18258 \begin_inset Tabular
18259 <lyxtabular version="3" rows="6" columns="2">
18260 <features booktabs="true" tabularvalignment="middle">
18261 <column alignment="center" valignment="top" width="0pt">
18262 <column alignment="center" valignment="top">
18264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18267 \begin_layout Plain Layout
18273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18276 \begin_layout Plain Layout
18284 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18287 \begin_layout Plain Layout
18293 \begin_inset space \textvisiblespace{}
18303 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18306 \begin_layout Plain Layout
18307 \begin_inset Formula $\mathbb{ABC}$
18317 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18320 \begin_layout Plain Layout
18326 \begin_inset space \textvisiblespace{}
18336 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18339 \begin_layout Plain Layout
18340 \begin_inset Formula $\mathbf{AbC}$
18350 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18353 \begin_layout Plain Layout
18359 \begin_inset space \textvisiblespace{}
18369 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18372 \begin_layout Plain Layout
18373 \begin_inset Formula $\boldsymbol{AbC}$
18383 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18386 \begin_layout Plain Layout
18392 \begin_inset space \textvisiblespace{}
18402 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18405 \begin_layout Plain Layout
18406 \begin_inset Formula $\mathcal{ABC}$
18416 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18419 \begin_layout Plain Layout
18425 \begin_inset space \textvisiblespace{}
18435 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18438 \begin_layout Plain Layout
18439 \begin_inset Formula $\mathfrak{AbC}$
18453 \begin_inset space \hfill{}
18457 \begin_inset Tabular
18458 <lyxtabular version="3" rows="6" columns="2">
18459 <features booktabs="true" tabularvalignment="middle">
18460 <column alignment="center" valignment="top" width="0pt">
18461 <column alignment="center" valignment="top">
18463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18466 \begin_layout Plain Layout
18472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18475 \begin_layout Plain Layout
18483 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18486 \begin_layout Plain Layout
18492 \begin_inset space \textvisiblespace{}
18502 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18505 \begin_layout Plain Layout
18506 \begin_inset Formula $\mathit{AbC}$
18516 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18519 \begin_layout Plain Layout
18525 \begin_inset space \textvisiblespace{}
18535 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18538 \begin_layout Plain Layout
18539 \begin_inset Formula $\mathrm{AbC}$
18549 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18552 \begin_layout Plain Layout
18558 \begin_inset space \textvisiblespace{}
18568 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18571 \begin_layout Plain Layout
18572 \begin_inset Formula $\mathsf{AbC}$
18582 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18585 \begin_layout Plain Layout
18591 \begin_inset space \textvisiblespace{}
18601 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18604 \begin_layout Plain Layout
18605 \begin_inset Formula $\mathtt{AbC}$
18615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18618 \begin_layout Plain Layout
18624 \begin_inset space \textvisiblespace{}
18634 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18637 \begin_layout Plain Layout
18638 \begin_inset Formula $\mathscr{ABC}$
18652 \begin_inset space \hfill{}
18658 \begin_layout Standard
18659 \begin_inset Note Greyedout
18662 \begin_layout Plain Layout
18685 can only be used for big letters.
18693 \begin_layout Standard
18694 Predefined is the style
18703 \begin_layout Standard
18704 The style commands work also for letters in mathematical constructs:
18705 \begin_inset Formula
18707 \mathfrak{A=\frac{b}{C}}
18715 \begin_layout Standard
18716 Characters in mathematical text don't appear in a math font style but in
18717 the text font style
18724 That their style can't be set correctly via the text style dialog is a
18725 bug in \SpecialChar LyX
18730 \begin_layout Plain Layout
18731 \begin_inset CommandInset href
18733 name "LyX-bug #4629"
18734 target "http://www.lyx.org/trac/ticket/4629"
18746 \begin_layout Standard
18747 Instead of the style commands the dialog
18749 Edit\SpecialChar menuseparator
18750 Math\SpecialChar menuseparator
18753 or the toolbar button
18756 arg "math-insert \\font"
18762 \begin_layout Subsection
18764 \begin_inset CommandInset label
18766 name "subsec:Bold-Formulas"
18771 \begin_inset Index idx
18774 \begin_layout Plain Layout
18783 \begin_layout Standard
18784 To make a complete formula bold, the command
18790 from the previous subsection cannot be used, because it doesn't work for
18791 small Greek letters.
18792 Furthermore it prints Latin letters always upright, like in the following
18796 \begin_layout Standard
18797 \begin_inset Formula
18799 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18807 \begin_layout Standard
18808 To display the formula correctly, the command
18815 \begin_inset Formula
18817 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18822 It is also possible to set the formula in a
18824 boldmath environment
18827 This environment is created by inserting the command
18834 \begin_inset Index idx
18837 \begin_layout Plain Layout
18845 in \SpecialChar TeX
18847 To end the environment, the command
18854 \begin_inset Index idx
18857 \begin_layout Plain Layout
18865 is inserted in \SpecialChar TeX
18870 \begin_layout Plain Layout
18880 \begin_inset Formula
18882 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18891 \begin_layout Plain Layout
18903 \begin_layout Subsection
18905 \begin_inset Index idx
18908 \begin_layout Plain Layout
18917 \begin_layout Standard
18918 Formulas can be colored like normal text: Highlight a formula or a formula
18924 Here is a formula in magenta:
18925 \begin_inset Formula
18927 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18935 \begin_layout Standard
18936 You can also define your own colors as described in
18937 \begin_inset CommandInset ref
18939 reference "subsec:Colored-Boxes"
18944 They can be used with the \SpecialChar TeX
18952 \begin_inset Index idx
18955 \begin_layout Plain Layout
18966 \begin_layout Standard
18971 textcolor{color}{characters or formula}
18974 \begin_layout Standard
18975 The following example was colored completely dark green and partly red:
18978 \begin_layout Standard
18982 \begin_layout Plain Layout
18986 textcolor{darkgreen}{
18992 \begin_inset Formula
18994 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19003 \begin_layout Plain Layout
19013 \begin_layout Standard
19014 Due to a bug in \SpecialChar LyX
19015 only complete formulas can be colored with self-defined
19020 \begin_layout Plain Layout
19021 \begin_inset CommandInset href
19023 name "LyX-bug #5269"
19024 target "http://www.lyx.org/trac/ticket/5269"
19036 \begin_layout Subsection
19038 \begin_inset CommandInset label
19040 name "subsec:Font-Sizes"
19045 \begin_inset Index idx
19048 \begin_layout Plain Layout
19057 \begin_layout Standard
19058 For characters in formulas there are, analog to characters in text, the
19059 following size commands:
19062 \begin_layout Standard
19106 \begin_inset Newline newline
19128 \begin_layout Standard
19129 The size produced by the commands depends on the document font size, which
19130 corresponds to the command
19137 The other commands produce smaller or larger sizes than
19144 The font size can however not exceed a certain value.
19145 Is for example the document font size 12
19146 \begin_inset space \thinspace{}
19155 switches to the same size as
19165 \begin_layout Standard
19166 A size command is inserted in \SpecialChar TeX
19167 mode before the formula and sets the size
19168 for all following formula and text characters.
19169 To switch back to the initial size, the command
19175 is inserted behind the formula in \SpecialChar TeX
19179 \begin_layout Standard
19180 Within a formula the size can be changed using the following size commands
19181 or the toolbar button
19184 arg "math-insert \\style"
19188 \begin_inset Separator parbreak
19194 \begin_layout Standard
19197 \begin_inset Tabular
19198 <lyxtabular version="3" rows="5" columns="2">
19199 <features booktabs="true" tabularvalignment="middle">
19200 <column alignment="center" valignment="top" width="0pt">
19201 <column alignment="center" valignment="top">
19203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19206 \begin_layout Plain Layout
19212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19215 \begin_layout Plain Layout
19223 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19226 \begin_layout Plain Layout
19230 \begin_inset Index idx
19233 \begin_layout Plain Layout
19246 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19249 \begin_layout Plain Layout
19250 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19259 <row topspace="1mm">
19260 <cell alignment="center" valignment="top" usebox="none">
19263 \begin_layout Plain Layout
19271 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19274 \begin_layout Plain Layout
19275 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19285 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19288 \begin_layout Plain Layout
19296 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19299 \begin_layout Plain Layout
19300 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19310 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19313 \begin_layout Plain Layout
19321 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19324 \begin_layout Plain Layout
19325 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19341 \begin_layout Standard
19342 After entering these commands, a blue box appears in which the formula parts
19346 \begin_layout Standard
19347 There is a further method to change the font size, that though only works
19348 for symbols or letters in mathematical text.
19349 To use it, one of the above text size commands is inserted in mathematical
19351 All following characters until the end of the mathematical text or until
19352 another size command will have the selected size.
19354 \begin_inset VSpace -2mm
19360 \begin_layout Standard
19364 \begin_layout Plain Layout
19374 \begin_inset Formula
19376 A=\frac{B}{c}\cdot\maltese
19382 \begin_inset Formula
19384 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19393 \begin_layout Plain Layout
19405 \begin_layout Standard
19406 \begin_inset VSpace medskip
19409 Before both formulas the command
19416 The command for the second formula is:
19417 \begin_inset Newline newline
19425 \begin_inset space \textvisiblespace{}
19431 \begin_inset space \textvisiblespace{}
19437 \begin_inset space \textvisiblespace{}
19443 \begin_inset space \textvisiblespace{}
19447 \begin_inset Formula $\to$
19451 \begin_inset Formula $\to$
19455 \begin_inset Newline newline
19459 \begin_inset space \hspace*{}
19470 \begin_inset space \textvisiblespace{}
19476 \begin_inset space \textvisiblespace{}
19482 \begin_inset space \textvisiblespace{}
19488 \begin_layout Standard
19489 If a symbol cannot be displayed in different sizes, it will always be displayed
19490 in the default size.
19493 \begin_layout Section
19495 \begin_inset Index idx
19498 \begin_layout Plain Layout
19507 \begin_layout Standard
19508 Greek letters can also be inserted via the toolbar button
19511 arg "math-insert \\alpha"
19515 All international typesetting norms purport that Greek letters in math
19516 have to be typeset italic/slanted.
19517 In some languages, like French or Russian, they are nevertheless sometimes
19521 \begin_layout Subsection
19523 \begin_inset Index idx
19526 \begin_layout Plain Layout
19527 Greek letters ! small
19535 \begin_layout Standard
19536 \begin_inset space \hfill{}
19540 \begin_inset Tabular
19541 <lyxtabular version="3" rows="11" columns="2">
19542 <features booktabs="true" tabularvalignment="middle">
19543 <column alignment="center" valignment="top" width="0pt">
19544 <column alignment="center" valignment="top" width="0pt">
19546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19549 \begin_layout Plain Layout
19555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19558 \begin_layout Plain Layout
19566 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19569 \begin_layout Plain Layout
19577 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19580 \begin_layout Plain Layout
19581 \begin_inset Formula $\alpha$
19591 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19594 \begin_layout Plain Layout
19602 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19605 \begin_layout Plain Layout
19606 \begin_inset Formula $\beta$
19616 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19619 \begin_layout Plain Layout
19627 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19630 \begin_layout Plain Layout
19631 \begin_inset Formula $\gamma$
19641 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19644 \begin_layout Plain Layout
19652 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19655 \begin_layout Plain Layout
19656 \begin_inset Formula $\delta$
19666 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19669 \begin_layout Plain Layout
19677 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19680 \begin_layout Plain Layout
19681 \begin_inset Formula $\epsilon$
19691 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19694 \begin_layout Plain Layout
19702 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19705 \begin_layout Plain Layout
19706 \begin_inset Formula $\varepsilon$
19716 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19719 \begin_layout Plain Layout
19727 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19730 \begin_layout Plain Layout
19731 \begin_inset Formula $\zeta$
19741 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19744 \begin_layout Plain Layout
19752 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19755 \begin_layout Plain Layout
19756 \begin_inset Formula $\eta$
19766 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19769 \begin_layout Plain Layout
19777 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19780 \begin_layout Plain Layout
19781 \begin_inset Formula $\theta$
19791 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19794 \begin_layout Plain Layout
19802 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19805 \begin_layout Plain Layout
19806 \begin_inset Formula $\vartheta$
19820 \begin_inset space \hfill{}
19824 \begin_inset Tabular
19825 <lyxtabular version="3" rows="12" columns="2">
19826 <features booktabs="true" tabularvalignment="middle">
19827 <column alignment="center" valignment="top" width="0pt">
19828 <column alignment="center" valignment="top" width="0pt">
19830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19833 \begin_layout Plain Layout
19839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19842 \begin_layout Plain Layout
19850 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19853 \begin_layout Plain Layout
19861 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19864 \begin_layout Plain Layout
19865 \begin_inset Formula $\iota$
19875 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19878 \begin_layout Plain Layout
19886 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19889 \begin_layout Plain Layout
19890 \begin_inset Formula $\kappa$
19900 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19903 \begin_layout Plain Layout
19911 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19914 \begin_layout Plain Layout
19915 \begin_inset Formula $\varkappa$
19925 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19928 \begin_layout Plain Layout
19936 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19939 \begin_layout Plain Layout
19940 \begin_inset Formula $\lambda$
19950 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19953 \begin_layout Plain Layout
19961 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19964 \begin_layout Plain Layout
19965 \begin_inset Formula $\mu$
19975 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19978 \begin_layout Plain Layout
19986 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19989 \begin_layout Plain Layout
19990 \begin_inset Formula $\nu$
20000 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20003 \begin_layout Plain Layout
20011 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20014 \begin_layout Plain Layout
20015 \begin_inset Formula $\xi$
20025 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20028 \begin_layout Plain Layout
20034 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20037 \begin_layout Plain Layout
20038 \begin_inset Formula $o$
20048 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20051 \begin_layout Plain Layout
20059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20062 \begin_layout Plain Layout
20063 \begin_inset Formula $\pi$
20073 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20076 \begin_layout Plain Layout
20084 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20087 \begin_layout Plain Layout
20088 \begin_inset Formula $\varpi$
20098 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20101 \begin_layout Plain Layout
20109 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20112 \begin_layout Plain Layout
20113 \begin_inset Formula $\rho$
20127 \begin_inset space \hfill{}
20131 \begin_inset Tabular
20132 <lyxtabular version="3" rows="11" columns="2">
20133 <features booktabs="true" tabularvalignment="middle">
20134 <column alignment="center" valignment="top" width="0pt">
20135 <column alignment="center" valignment="top" width="0pt">
20137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20140 \begin_layout Plain Layout
20146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20149 \begin_layout Plain Layout
20157 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20160 \begin_layout Plain Layout
20168 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20171 \begin_layout Plain Layout
20172 \begin_inset Formula $\varrho$
20182 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20185 \begin_layout Plain Layout
20193 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20196 \begin_layout Plain Layout
20197 \begin_inset Formula $\sigma$
20207 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20210 \begin_layout Plain Layout
20218 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20221 \begin_layout Plain Layout
20222 \begin_inset Formula $\varsigma$
20232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20235 \begin_layout Plain Layout
20243 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20246 \begin_layout Plain Layout
20247 \begin_inset Formula $\tau$
20257 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20260 \begin_layout Plain Layout
20268 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20271 \begin_layout Plain Layout
20272 \begin_inset Formula $\upsilon$
20282 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20285 \begin_layout Plain Layout
20293 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20296 \begin_layout Plain Layout
20297 \begin_inset Formula $\phi$
20307 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20310 \begin_layout Plain Layout
20318 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20321 \begin_layout Plain Layout
20322 \begin_inset Formula $\varphi$
20332 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20335 \begin_layout Plain Layout
20343 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20346 \begin_layout Plain Layout
20347 \begin_inset Formula $\chi$
20357 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20360 \begin_layout Plain Layout
20368 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20371 \begin_layout Plain Layout
20372 \begin_inset Formula $\psi$
20382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20385 \begin_layout Plain Layout
20393 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20396 \begin_layout Plain Layout
20397 \begin_inset Formula $\omega$
20411 \begin_inset space \hfill{}
20417 \begin_layout Standard
20418 \begin_inset VSpace medskip
20424 \begin_layout Standard
20425 How to create special upright Greek letters is explained in
20426 \begin_inset CommandInset ref
20428 reference "subsec:Upright-small-Greek"
20435 \begin_layout Subsection
20437 \begin_inset Index idx
20440 \begin_layout Plain Layout
20441 Greek letters ! big
20449 \begin_layout Standard
20450 \begin_inset space \hfill{}
20454 \begin_inset Tabular
20455 <lyxtabular version="3" rows="7" columns="2">
20456 <features booktabs="true" tabularvalignment="middle">
20457 <column alignment="center" valignment="top" width="0pt">
20458 <column alignment="center" valignment="top" width="0pt">
20460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20463 \begin_layout Plain Layout
20469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20472 \begin_layout Plain Layout
20480 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20483 \begin_layout Plain Layout
20491 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20494 \begin_layout Plain Layout
20495 \begin_inset Formula $\Gamma$
20505 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20508 \begin_layout Plain Layout
20516 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20519 \begin_layout Plain Layout
20520 \begin_inset Formula $\Delta$
20530 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20533 \begin_layout Plain Layout
20541 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20544 \begin_layout Plain Layout
20545 \begin_inset Formula $\Theta$
20555 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20558 \begin_layout Plain Layout
20566 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20569 \begin_layout Plain Layout
20570 \begin_inset Formula $\Lambda$
20580 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20583 \begin_layout Plain Layout
20591 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20594 \begin_layout Plain Layout
20595 \begin_inset Formula $\Xi$
20605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20608 \begin_layout Plain Layout
20616 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20619 \begin_layout Plain Layout
20620 \begin_inset Formula $\Pi$
20634 \begin_inset space \hfill{}
20638 \begin_inset Tabular
20639 <lyxtabular version="3" rows="6" columns="2">
20640 <features booktabs="true" tabularvalignment="middle">
20641 <column alignment="center" valignment="top" width="0pt">
20642 <column alignment="center" valignment="top" width="0pt">
20644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20647 \begin_layout Plain Layout
20653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20656 \begin_layout Plain Layout
20664 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20667 \begin_layout Plain Layout
20675 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20678 \begin_layout Plain Layout
20679 \begin_inset Formula $\Sigma$
20689 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20692 \begin_layout Plain Layout
20700 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20703 \begin_layout Plain Layout
20704 \begin_inset Formula $\Upsilon$
20714 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20717 \begin_layout Plain Layout
20725 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20728 \begin_layout Plain Layout
20729 \begin_inset Formula $\Phi$
20739 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20742 \begin_layout Plain Layout
20750 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20753 \begin_layout Plain Layout
20754 \begin_inset Formula $\Psi$
20764 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20767 \begin_layout Plain Layout
20775 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20778 \begin_layout Plain Layout
20779 \begin_inset Formula $\Omega$
20793 \begin_inset space \hfill{}
20799 \begin_layout Standard
20800 \begin_inset VSpace medskip
20803 That the big Greek letters appear upright is caused by a design bug when
20806 To get correct italic big letters, begin every command with
20811 For example the command
20818 \begin_inset Formula $\varGamma$
20822 Another way is to load the package
20830 \begin_layout Plain Layout
20835 is part of the \SpecialChar LaTeX
20841 \begin_inset Index idx
20844 \begin_layout Plain Layout
20849 \begin_layout Plain Layout
20869 \begin_inset Index idx
20872 \begin_layout Plain Layout
20878 with the \SpecialChar LaTeX
20882 \begin_layout Standard
20887 usepackage{fixmath}
20890 \begin_layout Standard
20891 Then all big Greek letters in a document will automatically be typeset italic.
20894 \begin_layout Subsection
20896 \begin_inset Index idx
20899 \begin_layout Plain Layout
20900 Greek letters ! bold
20908 \begin_layout Standard
20909 Greek letters cannot be set with different font styles like Latin letters.
20910 They can only be made bold with the command
20917 \begin_inset Index idx
20920 \begin_layout Plain Layout
20929 \begin_inset Separator parbreak
20935 \begin_layout Standard
20937 \begin_inset Tabular
20938 <lyxtabular version="3" rows="3" columns="2">
20939 <features booktabs="true" tabularvalignment="middle">
20940 <column alignment="center" valignment="top" width="0pt">
20941 <column alignment="center" valignment="top">
20943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20946 \begin_layout Plain Layout
20952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20955 \begin_layout Plain Layout
20963 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20966 \begin_layout Plain Layout
20978 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20981 \begin_layout Plain Layout
20982 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20992 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20995 \begin_layout Plain Layout
21007 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21010 \begin_layout Plain Layout
21011 \begin_inset Formula $\theta\boldsymbol{\theta}$
21027 \begin_layout Section
21032 \begin_layout Plain Layout
21045 \begin_layout Plain Layout
21046 A list with all symbols of most of the \SpecialChar LaTeX
21047 -packages can be found in
21048 \begin_inset CommandInset citation
21063 \begin_layout Plain Layout
21071 \begin_inset Note Note
21074 \begin_layout Plain Layout
21077 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21080 \begin_layout Plain Layout
21083 texorpdfstring is in section
21084 \begin_inset CommandInset ref
21086 reference "subsec:Formulas-in-Section"
21096 \begin_inset Index idx
21099 \begin_layout Plain Layout
21108 \begin_layout Standard
21109 Many of the symbols listed in this section can also be inserted via the
21113 arg "math-insert \\nabla"
21119 arg "math-insert \\digamma"
21125 \begin_layout Subsection
21126 Mathematical Symbols
21127 \begin_inset CommandInset label
21129 name "subsec:Mathematical-Symbols"
21134 \begin_inset Index idx
21137 \begin_layout Plain Layout
21138 Symbols ! mathematical
21146 \begin_layout Standard
21147 \begin_inset Tabular
21148 <lyxtabular version="3" rows="10" columns="2">
21149 <features booktabs="true" tabularvalignment="middle">
21150 <column alignment="center" valignment="top" width="0pt">
21151 <column alignment="center" valignment="top" width="0pt">
21153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21156 \begin_layout Plain Layout
21162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21165 \begin_layout Plain Layout
21173 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21176 \begin_layout Plain Layout
21184 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21187 \begin_layout Plain Layout
21188 \begin_inset Formula $\neg$
21198 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21201 \begin_layout Plain Layout
21209 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21212 \begin_layout Plain Layout
21213 \begin_inset Formula $\Im$
21223 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21226 \begin_layout Plain Layout
21234 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21237 \begin_layout Plain Layout
21238 \begin_inset Formula $\Re$
21248 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21251 \begin_layout Plain Layout
21259 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21262 \begin_layout Plain Layout
21263 \begin_inset Formula $\aleph$
21273 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21276 \begin_layout Plain Layout
21284 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21287 \begin_layout Plain Layout
21288 \begin_inset Formula $\partial$
21298 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21301 \begin_layout Plain Layout
21309 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21312 \begin_layout Plain Layout
21313 \begin_inset Formula $\infty$
21323 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21326 \begin_layout Plain Layout
21334 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21337 \begin_layout Plain Layout
21338 \begin_inset Formula $\wp$
21348 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21351 \begin_layout Plain Layout
21359 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21362 \begin_layout Plain Layout
21363 \begin_inset Formula $\imath$
21373 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21376 \begin_layout Plain Layout
21384 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21387 \begin_layout Plain Layout
21388 \begin_inset Formula $\jmath$
21402 \begin_inset space \hfill{}
21406 \begin_inset Tabular
21407 <lyxtabular version="3" rows="10" columns="2">
21408 <features booktabs="true" tabularvalignment="middle">
21409 <column alignment="center" valignment="top" width="0pt">
21410 <column alignment="center" valignment="top" width="0pt">
21412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21415 \begin_layout Plain Layout
21421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21424 \begin_layout Plain Layout
21426 \begin_inset Note Note
21429 \begin_layout Plain Layout
21436 is only used as spacer.
21448 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21451 \begin_layout Plain Layout
21459 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21462 \begin_layout Plain Layout
21463 \begin_inset Formula $\forall$
21473 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21476 \begin_layout Plain Layout
21484 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21487 \begin_layout Plain Layout
21488 \begin_inset Formula $\exists$
21498 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21501 \begin_layout Plain Layout
21509 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21512 \begin_layout Plain Layout
21513 \begin_inset Formula $\nexists$
21523 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21526 \begin_layout Plain Layout
21534 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21537 \begin_layout Plain Layout
21538 \begin_inset Formula $\emptyset$
21548 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21551 \begin_layout Plain Layout
21559 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21562 \begin_layout Plain Layout
21563 \begin_inset Formula $\varnothing$
21573 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21576 \begin_layout Plain Layout
21584 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21587 \begin_layout Plain Layout
21588 \begin_inset Formula $\dag$
21598 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21601 \begin_layout Plain Layout
21609 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21612 \begin_layout Plain Layout
21613 \begin_inset Formula $\ddag$
21623 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21626 \begin_layout Plain Layout
21634 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21637 \begin_layout Plain Layout
21641 \begin_layout Plain Layout
21651 \begin_inset Formula $\complement$
21658 \begin_layout Plain Layout
21672 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21675 \begin_layout Plain Layout
21683 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21686 \begin_layout Plain Layout
21687 \begin_inset Formula $\Bbbk$
21701 \begin_inset space \hfill{}
21705 \begin_inset Tabular
21706 <lyxtabular version="3" rows="10" columns="2">
21707 <features booktabs="true" tabularvalignment="middle">
21708 <column alignment="center" valignment="top" width="0pt">
21709 <column alignment="center" valignment="top" width="0pt">
21711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21714 \begin_layout Plain Layout
21720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21723 \begin_layout Plain Layout
21731 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21734 \begin_layout Plain Layout
21742 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21745 \begin_layout Plain Layout
21746 \begin_inset Formula $\prime$
21756 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21759 \begin_layout Plain Layout
21767 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21770 \begin_layout Plain Layout
21771 \begin_inset Formula $\backprime$
21781 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21784 \begin_layout Plain Layout
21792 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21795 \begin_layout Plain Layout
21796 \begin_inset Formula $\mho$
21806 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21809 \begin_layout Plain Layout
21817 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21820 \begin_layout Plain Layout
21821 \begin_inset Formula $\triangle$
21831 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21834 \begin_layout Plain Layout
21842 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21845 \begin_layout Plain Layout
21846 \begin_inset Formula $\angle$
21856 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21859 \begin_layout Plain Layout
21867 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21870 \begin_layout Plain Layout
21871 \begin_inset Formula $\measuredangle$
21881 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21884 \begin_layout Plain Layout
21892 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21895 \begin_layout Plain Layout
21896 \begin_inset Formula $\sphericalangle$
21906 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21909 \begin_layout Plain Layout
21917 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21920 \begin_layout Plain Layout
21921 \begin_inset Formula $\top$
21931 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21934 \begin_layout Plain Layout
21942 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21945 \begin_layout Plain Layout
21946 \begin_inset Formula $\bot$
21962 \begin_layout Standard
21963 \begin_inset Newpage newpage
21969 \begin_layout Subsection
21970 Miscellaneous Symbols
21971 \begin_inset CommandInset label
21973 name "subsec:Miscellaneous-Symbols"
21978 \begin_inset Index idx
21981 \begin_layout Plain Layout
21982 Symbols ! miscellaneous
21990 \begin_layout Standard
21993 \begin_inset Tabular
21994 <lyxtabular version="3" rows="10" columns="2">
21995 <features booktabs="true" tabularvalignment="middle">
21996 <column alignment="center" valignment="top" width="0pt">
21997 <column alignment="center" valignment="top" width="0pt">
21999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22002 \begin_layout Plain Layout
22008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22011 \begin_layout Plain Layout
22019 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22022 \begin_layout Plain Layout
22030 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22033 \begin_layout Plain Layout
22034 \begin_inset Formula $\flat$
22044 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22047 \begin_layout Plain Layout
22055 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22058 \begin_layout Plain Layout
22059 \begin_inset Formula $\natural$
22069 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22072 \begin_layout Plain Layout
22080 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22083 \begin_layout Plain Layout
22084 \begin_inset Formula $\sharp$
22094 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22097 \begin_layout Plain Layout
22105 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22108 \begin_layout Plain Layout
22109 \begin_inset Formula $\surd$
22119 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22122 \begin_layout Plain Layout
22130 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22133 \begin_layout Plain Layout
22134 \begin_inset Formula $\checkmark$
22144 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22147 \begin_layout Plain Layout
22155 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22158 \begin_layout Plain Layout
22159 \begin_inset Formula $\yen$
22169 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22172 \begin_layout Plain Layout
22180 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22183 \begin_layout Plain Layout
22184 \begin_inset Formula $\pounds$
22194 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22197 \begin_layout Plain Layout
22203 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22206 \begin_layout Plain Layout
22207 \begin_inset Formula $\$$
22217 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22220 \begin_layout Plain Layout
22226 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22229 \begin_layout Plain Layout
22230 \begin_inset Formula $§$
22244 \begin_inset space \hfill{}
22248 \begin_inset Tabular
22249 <lyxtabular version="3" rows="10" columns="2">
22250 <features booktabs="true" tabularvalignment="middle">
22251 <column alignment="center" valignment="top" width="0pt">
22252 <column alignment="center" valignment="top">
22254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22257 \begin_layout Plain Layout
22263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22266 \begin_layout Plain Layout
22274 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22277 \begin_layout Plain Layout
22285 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22288 \begin_layout Plain Layout
22289 \begin_inset Formula $\hbar$
22299 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22302 \begin_layout Plain Layout
22310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22313 \begin_layout Plain Layout
22314 \begin_inset Formula $\hslash$
22324 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22327 \begin_layout Plain Layout
22335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22338 \begin_layout Plain Layout
22339 \begin_inset Formula $\clubsuit$
22349 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22352 \begin_layout Plain Layout
22360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22363 \begin_layout Plain Layout
22364 \begin_inset Formula $\spadesuit$
22374 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22377 \begin_layout Plain Layout
22385 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22388 \begin_layout Plain Layout
22389 \begin_inset Formula $\bigstar$
22399 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22402 \begin_layout Plain Layout
22410 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22413 \begin_layout Plain Layout
22414 \begin_inset Formula $\blacklozenge$
22424 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22427 \begin_layout Plain Layout
22435 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22438 \begin_layout Plain Layout
22439 \begin_inset Formula $\blacktriangle$
22449 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22452 \begin_layout Plain Layout
22460 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22463 \begin_layout Plain Layout
22464 \begin_inset Formula $\blacktriangledown$
22474 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22477 \begin_layout Plain Layout
22485 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22488 \begin_layout Plain Layout
22489 \begin_inset Formula $\bullet$
22503 \begin_inset space \hfill{}
22507 \begin_inset Tabular
22508 <lyxtabular version="3" rows="10" columns="2">
22509 <features booktabs="true" tabularvalignment="middle">
22510 <column alignment="center" valignment="top" width="0pt">
22511 <column alignment="center" valignment="top" width="0pt">
22513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22516 \begin_layout Plain Layout
22522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22525 \begin_layout Plain Layout
22533 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22536 \begin_layout Plain Layout
22544 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22547 \begin_layout Plain Layout
22548 \begin_inset Formula $\diamondsuit$
22558 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22561 \begin_layout Plain Layout
22569 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22572 \begin_layout Plain Layout
22573 \begin_inset Formula $\Diamond$
22583 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22586 \begin_layout Plain Layout
22594 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22597 \begin_layout Plain Layout
22598 \begin_inset Formula $\heartsuit$
22608 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22611 \begin_layout Plain Layout
22619 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22622 \begin_layout Plain Layout
22623 \begin_inset Formula $\P$
22633 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22636 \begin_layout Plain Layout
22644 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22647 \begin_layout Plain Layout
22648 \begin_inset Formula $\copyright$
22658 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22661 \begin_layout Plain Layout
22669 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22672 \begin_layout Plain Layout
22673 \begin_inset Formula $\circledR$
22683 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22686 \begin_layout Plain Layout
22694 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22697 \begin_layout Plain Layout
22698 \begin_inset Formula $\maltese$
22708 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22711 \begin_layout Plain Layout
22719 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22722 \begin_layout Plain Layout
22723 \begin_inset Formula $\diagup$
22733 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22736 \begin_layout Plain Layout
22744 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22747 \begin_layout Plain Layout
22748 \begin_inset Formula $\diagdown$
22764 \begin_layout Standard
22765 \begin_inset VSpace medskip
22771 \begin_layout Standard
22772 Some symbols can be displayed in different sizes, see
22773 \begin_inset CommandInset ref
22775 reference "subsec:Font-Sizes"
22782 \begin_layout Subsection
22784 \begin_inset Index idx
22787 \begin_layout Plain Layout
22788 Symbols ! Euro-symbol
22794 \begin_inset Index idx
22797 \begin_layout Plain Layout
22804 \begin_layout Plain Layout
22821 \begin_layout Standard
22822 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22828 \begin_inset Index idx
22831 \begin_layout Plain Layout
22837 must be installed and loaded with the \SpecialChar LaTeX
22841 \begin_layout Standard
22846 usepackage[gennarrow]{eurosym}
22849 \begin_layout Standard
22850 The Euro symbol can now be inserted with the command
22857 \begin_inset Index idx
22860 \begin_layout Plain Layout
22871 \begin_layout Standard
22872 The Euro symbol can directly be inserted with the € key in mathematical
22873 text, without having
22888 can also be inserted in \SpecialChar TeX
22890 The official currency symbol can then be inserted with the command
22897 \begin_inset Index idx
22900 \begin_layout Plain Layout
22908 , that is only available in \SpecialChar TeX
22912 \begin_layout Standard
22916 \begin_layout Plain Layout
22926 \begin_inset Note Note
22929 \begin_layout Plain Layout
22930 The following table will only be displayed when the \SpecialChar LaTeX
22943 \begin_layout Standard
22944 An overview about the different Euro symbols:
22945 \begin_inset Separator parbreak
22951 \begin_layout Standard
22953 \begin_inset Tabular
22954 <lyxtabular version="3" rows="4" columns="3">
22955 <features booktabs="true" tabularvalignment="middle">
22956 <column alignment="center" valignment="top" width="0pt">
22957 <column alignment="center" valignment="top" width="0pt">
22958 <column alignment="center" valignment="top" width="0pt">
22960 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22963 \begin_layout Plain Layout
22967 \begin_layout Plain Layout
22971 cmidrule[0.08em]{2-3}
22981 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22984 \begin_layout Plain Layout
22990 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22993 \begin_layout Plain Layout
23001 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23004 \begin_layout Plain Layout
23010 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23013 \begin_layout Plain Layout
23021 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23024 \begin_layout Plain Layout
23025 \begin_inset Formula $\euro$
23035 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23038 \begin_layout Plain Layout
23044 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23047 \begin_layout Plain Layout
23053 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23056 \begin_layout Plain Layout
23057 \begin_inset Formula $\mbox{€}$
23067 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23070 \begin_layout Plain Layout
23077 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23080 \begin_layout Plain Layout
23088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23091 \begin_layout Plain Layout
23095 \begin_layout Plain Layout
23115 \begin_inset Note Note
23118 \begin_layout Plain Layout
23125 is used here only for table borders.
23135 manual for details.
23143 \begin_layout Standard
23147 \begin_layout Plain Layout
23157 \begin_inset Note Note
23160 \begin_layout Plain Layout
23161 The following will be displayed when the \SpecialChar LaTeX
23174 \begin_layout Standard
23175 You need to install the \SpecialChar LaTeX
23180 to see the rest of this subsection in the output.
23183 \begin_layout Standard
23187 \begin_layout Plain Layout
23199 \begin_layout Standard
23200 \begin_inset Newpage newpage
23206 \begin_layout Section
23208 \begin_inset CommandInset label
23210 name "sec:Relations"
23215 \begin_inset Index idx
23218 \begin_layout Plain Layout
23225 \begin_inset Index idx
23228 \begin_layout Plain Layout
23233 \begin_layout Plain Layout
23244 \begin_layout Plain Layout
23259 \begin_layout Standard
23260 All following relations can also be inserted via the toolbar button
23263 arg "math-insert \\leq"
23269 \begin_layout Standard
23270 \begin_inset Tabular
23271 <lyxtabular version="3" rows="17" columns="2">
23272 <features booktabs="true" tabularvalignment="middle">
23273 <column alignment="center" valignment="top" width="0pt">
23274 <column alignment="center" valignment="top" width="0pt">
23276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23279 \begin_layout Plain Layout
23285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23288 \begin_layout Plain Layout
23296 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23299 \begin_layout Plain Layout
23305 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23308 \begin_layout Plain Layout
23309 \begin_inset Formula $<$
23319 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23322 \begin_layout Plain Layout
23330 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23333 \begin_layout Plain Layout
23334 \begin_inset Formula $\le$
23344 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23347 \begin_layout Plain Layout
23355 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23358 \begin_layout Plain Layout
23359 \begin_inset Formula $\ll$
23369 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23372 \begin_layout Plain Layout
23380 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23383 \begin_layout Plain Layout
23384 \begin_inset Formula $\prec$
23394 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23397 \begin_layout Plain Layout
23405 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23408 \begin_layout Plain Layout
23409 \begin_inset Formula $\preceq$
23419 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23422 \begin_layout Plain Layout
23430 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23433 \begin_layout Plain Layout
23434 \begin_inset Formula $\subset$
23444 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23447 \begin_layout Plain Layout
23455 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23458 \begin_layout Plain Layout
23459 \begin_inset Formula $\subseteq$
23469 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23472 \begin_layout Plain Layout
23480 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23483 \begin_layout Plain Layout
23484 \begin_inset Formula $\sqsubseteq$
23494 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23497 \begin_layout Plain Layout
23505 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23508 \begin_layout Plain Layout
23509 \begin_inset Formula $\in$
23519 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23522 \begin_layout Plain Layout
23530 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23533 \begin_layout Plain Layout
23534 \begin_inset Formula $\vdash$
23544 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23547 \begin_layout Plain Layout
23555 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23558 \begin_layout Plain Layout
23559 \begin_inset Formula $\smile$
23569 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23572 \begin_layout Plain Layout
23580 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23583 \begin_layout Plain Layout
23584 \begin_inset Formula $\lhd$
23594 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23597 \begin_layout Plain Layout
23605 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23608 \begin_layout Plain Layout
23609 \begin_inset Formula $\unlhd$
23619 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23622 \begin_layout Plain Layout
23630 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23633 \begin_layout Plain Layout
23634 \begin_inset Formula $\gtrless$
23644 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23647 \begin_layout Plain Layout
23655 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23658 \begin_layout Plain Layout
23659 \begin_inset Formula $\mid$
23669 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23672 \begin_layout Plain Layout
23680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23683 \begin_layout Plain Layout
23684 \begin_inset Formula $\nmid$
23698 \begin_inset space \hfill{}
23702 \begin_inset Tabular
23703 <lyxtabular version="3" rows="17" columns="2">
23704 <features booktabs="true" tabularvalignment="middle">
23705 <column alignment="center" valignment="top" width="0pt">
23706 <column alignment="center" valignment="top" width="0pt">
23708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23711 \begin_layout Plain Layout
23717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23720 \begin_layout Plain Layout
23728 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23731 \begin_layout Plain Layout
23737 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23740 \begin_layout Plain Layout
23741 \begin_inset Formula $=$
23751 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23754 \begin_layout Plain Layout
23762 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23765 \begin_layout Plain Layout
23766 \begin_inset Formula $\not=$
23776 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23779 \begin_layout Plain Layout
23787 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23790 \begin_layout Plain Layout
23791 \begin_inset Formula $\equiv$
23801 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23804 \begin_layout Plain Layout
23812 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23815 \begin_layout Plain Layout
23816 \begin_inset Formula $\sim$
23826 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23829 \begin_layout Plain Layout
23837 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23840 \begin_layout Plain Layout
23841 \begin_inset Formula $\simeq$
23851 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23854 \begin_layout Plain Layout
23862 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23865 \begin_layout Plain Layout
23866 \begin_inset Formula $\approx$
23876 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23879 \begin_layout Plain Layout
23887 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23890 \begin_layout Plain Layout
23891 \begin_inset Formula $\cong$
23901 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23904 \begin_layout Plain Layout
23912 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23915 \begin_layout Plain Layout
23916 \begin_inset Formula $\bowtie$
23926 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23929 \begin_layout Plain Layout
23937 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23940 \begin_layout Plain Layout
23941 \begin_inset Formula $\notin$
23951 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23954 \begin_layout Plain Layout
23962 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23965 \begin_layout Plain Layout
23966 \begin_inset Formula $\perp$
23976 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23979 \begin_layout Plain Layout
23987 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23990 \begin_layout Plain Layout
23991 \begin_inset Formula $\propto$
24001 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24004 \begin_layout Plain Layout
24012 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24015 \begin_layout Plain Layout
24016 \begin_inset Formula $\asymp$
24026 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24029 \begin_layout Plain Layout
24037 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24040 \begin_layout Plain Layout
24041 \begin_inset Formula $\doteq$
24051 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24054 \begin_layout Plain Layout
24062 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24065 \begin_layout Plain Layout
24066 \begin_inset Formula $\circeq$
24076 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24079 \begin_layout Plain Layout
24087 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24090 \begin_layout Plain Layout
24091 \begin_inset Formula $\models$
24101 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24104 \begin_layout Plain Layout
24112 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24115 \begin_layout Plain Layout
24116 \begin_inset Formula $\widehat{=}$
24130 \begin_inset space \hfill{}
24134 \begin_inset Tabular
24135 <lyxtabular version="3" rows="17" columns="2">
24136 <features booktabs="true" tabularvalignment="middle">
24137 <column alignment="center" valignment="top" width="0pt">
24138 <column alignment="center" valignment="top" width="0pt">
24140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24143 \begin_layout Plain Layout
24149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24152 \begin_layout Plain Layout
24160 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24163 \begin_layout Plain Layout
24169 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24172 \begin_layout Plain Layout
24173 \begin_inset Formula $>$
24183 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24186 \begin_layout Plain Layout
24194 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24197 \begin_layout Plain Layout
24198 \begin_inset Formula $\ge$
24208 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24211 \begin_layout Plain Layout
24219 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24222 \begin_layout Plain Layout
24223 \begin_inset Formula $\gg$
24233 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24236 \begin_layout Plain Layout
24244 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24247 \begin_layout Plain Layout
24248 \begin_inset Formula $\succ$
24258 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24261 \begin_layout Plain Layout
24269 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24272 \begin_layout Plain Layout
24273 \begin_inset Formula $\succeq$
24283 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24286 \begin_layout Plain Layout
24294 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24297 \begin_layout Plain Layout
24298 \begin_inset Formula $\supset$
24308 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24311 \begin_layout Plain Layout
24319 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24322 \begin_layout Plain Layout
24323 \begin_inset Formula $\supseteq$
24333 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24336 \begin_layout Plain Layout
24344 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24347 \begin_layout Plain Layout
24348 \begin_inset Formula $\sqsupseteq$
24358 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24361 \begin_layout Plain Layout
24369 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24372 \begin_layout Plain Layout
24373 \begin_inset Formula $\ni$
24383 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24386 \begin_layout Plain Layout
24394 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24397 \begin_layout Plain Layout
24398 \begin_inset Formula $\dashv$
24408 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24411 \begin_layout Plain Layout
24419 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24422 \begin_layout Plain Layout
24423 \begin_inset Formula $\frown$
24433 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24436 \begin_layout Plain Layout
24444 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24447 \begin_layout Plain Layout
24448 \begin_inset Formula $\rhd$
24458 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24461 \begin_layout Plain Layout
24469 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24472 \begin_layout Plain Layout
24473 \begin_inset Formula $\unrhd$
24483 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24486 \begin_layout Plain Layout
24494 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24497 \begin_layout Plain Layout
24498 \begin_inset Formula $\lessgtr$
24508 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24511 \begin_layout Plain Layout
24519 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24522 \begin_layout Plain Layout
24523 \begin_inset Formula $\parallel$
24533 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24536 \begin_layout Plain Layout
24544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24547 \begin_layout Plain Layout
24548 \begin_inset Formula $\nparallel$
24564 \begin_layout Standard
24565 \begin_inset VSpace medskip
24580 are bigger than the equal looking operators
24595 \begin_layout Standard
24597 supports also many special relations.
24598 Use the toolbar button
24601 arg "math-insert \\leqq"
24604 to see a list of these relations.
24607 \begin_layout Standard
24608 Relations are, in contrary to symbols, always surrounded by space.
24611 \begin_layout Standard
24612 Relations with labels can be created with the command
24619 \begin_inset Index idx
24622 \begin_layout Plain Layout
24631 \begin_inset Separator parbreak
24637 \begin_layout Standard
24639 \begin_inset Tabular
24640 <lyxtabular version="3" rows="2" columns="2">
24641 <features booktabs="true" tabularvalignment="middle">
24642 <column alignment="center" valignment="top" width="0pt">
24643 <column alignment="center" valignment="top">
24645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24648 \begin_layout Plain Layout
24654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24657 \begin_layout Plain Layout
24664 <row topspace="1.5mm">
24665 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24668 \begin_layout Plain Layout
24672 \begin_inset space \textvisiblespace{}
24680 \begin_inset space \textvisiblespace{}
24684 \begin_inset Formula $\downarrow$
24690 \begin_inset space \textvisiblespace{}
24694 \begin_inset space \textvisiblespace{}
24702 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24705 \begin_layout Plain Layout
24706 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24722 \begin_layout Section
24726 \begin_layout Subsection
24727 Predefined Functions
24728 \begin_inset CommandInset label
24730 name "subsec:Predefined-Functions"
24735 \begin_inset Index idx
24738 \begin_layout Plain Layout
24739 Functions ! predefined
24747 \begin_layout Standard
24748 In general, variables are set
24752 in mathematical expressions, but not function names, because
24753 \begin_inset Formula $sin$
24756 could be misunderstood as
24757 \begin_inset Formula $s\cdot i\cdot n$
24761 Therefore there are predefined functionswhich are additionally a bit separated
24763 They are inserted as commands starting with a backslash before their name.
24764 \begin_inset Separator parbreak
24770 \begin_layout Standard
24772 \begin_inset Tabular
24773 <lyxtabular version="3" rows="2" columns="2">
24774 <features booktabs="true" tabularvalignment="middle">
24775 <column alignment="center" valignment="top" width="0pt">
24776 <column alignment="center" valignment="top" width="0pt">
24778 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24781 \begin_layout Plain Layout
24787 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24790 \begin_layout Plain Layout
24798 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24801 \begin_layout Plain Layout
24807 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24810 \begin_layout Plain Layout
24811 \begin_inset Formula $Asin(x)+B$
24825 \begin_inset space \quad{}
24829 \begin_inset Tabular
24830 <lyxtabular version="3" rows="2" columns="2">
24831 <features booktabs="true" tabularvalignment="middle">
24832 <column alignment="center" valignment="top" width="0pt">
24833 <column alignment="center" valignment="top" width="0pt">
24835 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24838 \begin_layout Plain Layout
24844 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24847 \begin_layout Plain Layout
24855 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24858 \begin_layout Plain Layout
24866 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24869 \begin_layout Plain Layout
24870 \begin_inset Formula $A\sin(x)+B$
24886 \begin_layout Standard
24887 The following functions are predefined:
24890 \begin_layout Standard
24891 \begin_inset VSpace -2mm
24897 \begin_layout Standard
24899 \begin_inset Tabular
24900 <lyxtabular version="3" rows="9" columns="4">
24901 <features booktabs="true" tabularvalignment="middle">
24902 <column alignment="center" valignment="top" width="0pt">
24903 <column alignment="center" valignment="top" width="0pt">
24904 <column alignment="center" valignment="top" width="0pt">
24905 <column alignment="center" valignment="top" width="0pt">
24907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24910 \begin_layout Plain Layout
24916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24919 \begin_layout Plain Layout
24925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24928 \begin_layout Plain Layout
24934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24937 \begin_layout Plain Layout
24945 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24948 \begin_layout Plain Layout
24956 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24959 \begin_layout Plain Layout
24967 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24970 \begin_layout Plain Layout
24978 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24981 \begin_layout Plain Layout
24991 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24994 \begin_layout Plain Layout
25002 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25005 \begin_layout Plain Layout
25013 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25016 \begin_layout Plain Layout
25024 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25027 \begin_layout Plain Layout
25037 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25040 \begin_layout Plain Layout
25048 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25051 \begin_layout Plain Layout
25059 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25062 \begin_layout Plain Layout
25070 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25073 \begin_layout Plain Layout
25083 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25086 \begin_layout Plain Layout
25094 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25097 \begin_layout Plain Layout
25105 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25108 \begin_layout Plain Layout
25116 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25119 \begin_layout Plain Layout
25129 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25132 \begin_layout Plain Layout
25140 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25143 \begin_layout Plain Layout
25151 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25154 \begin_layout Plain Layout
25162 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25165 \begin_layout Plain Layout
25175 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25178 \begin_layout Plain Layout
25186 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25189 \begin_layout Plain Layout
25197 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25200 \begin_layout Plain Layout
25208 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25211 \begin_layout Plain Layout
25221 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25224 \begin_layout Plain Layout
25232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25235 \begin_layout Plain Layout
25243 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25246 \begin_layout Plain Layout
25254 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25257 \begin_layout Plain Layout
25267 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25270 \begin_layout Plain Layout
25278 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25281 \begin_layout Plain Layout
25289 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25292 \begin_layout Plain Layout
25300 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25303 \begin_layout Plain Layout
25319 \begin_layout Standard
25320 They can also be inserted with the math toolbar button
25323 arg "math-insert \\functions"
25329 \begin_layout Subsection
25330 Self-defined Functions
25331 \begin_inset Index idx
25334 \begin_layout Plain Layout
25335 Functions ! self-defined
25343 \begin_layout Standard
25344 To use a function that is not predefined, like for example the sign function
25345 sgn(x), there are two possibilities:
25348 \begin_layout Itemize
25349 Define the function by inserting the following line to the \SpecialChar LaTeX
25354 \begin_layout Plain Layout
25359 DeclareMathOperator
25362 \begin_inset CommandInset ref
25364 reference "subsec:Self-defined-Operators"
25374 \begin_inset Newline newline
25378 \begin_inset VSpace -3mm
25382 \begin_inset Newline newline
25389 DeclareMathOperator{
25394 \begin_inset Index idx
25397 \begin_layout Plain Layout
25402 DeclareMathOperator
25408 \begin_inset Newline newline
25412 \begin_inset VSpace -2mm
25416 \begin_inset Newline newline
25419 Now the new defined function can be called with the command
25428 \begin_layout Itemize
25429 Write the formula as usual, mark the formula name, in our example the letters
25434 , and change it to mathematical text.
25435 Finally, a space is inserted between prefactor and function.
25438 \begin_layout Standard
25439 The result is the same with both methods as with a predefined function
25443 \begin_layout Plain Layout
25444 In \SpecialChar LyX
25445 self-defined functions are displayed red, predefined ones black.
25451 \begin_inset Separator parbreak
25457 \begin_layout Standard
25459 \begin_inset Tabular
25460 <lyxtabular version="3" rows="3" columns="2">
25461 <features booktabs="true" tabularvalignment="middle">
25462 <column alignment="center" valignment="top" width="0pt">
25463 <column alignment="center" valignment="top" width="0pt">
25465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25468 \begin_layout Plain Layout
25474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25477 \begin_layout Plain Layout
25485 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25488 \begin_layout Plain Layout
25496 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25499 \begin_layout Plain Layout
25500 \begin_inset Formula $A\sgn(x)+B$
25510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25513 \begin_layout Plain Layout
25517 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25528 \begin_layout Plain Layout
25529 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25545 \begin_layout Standard
25546 The first method is more suitable when the self-defined function should
25547 be used several times.
25550 \begin_layout Subsection
25552 \begin_inset Index idx
25555 \begin_layout Plain Layout
25564 \begin_layout Standard
25565 For limits, in addition to the commands
25572 \begin_inset Index idx
25575 \begin_layout Plain Layout
25595 the following functions are defined:
25596 \begin_inset Separator parbreak
25602 \begin_layout Standard
25604 \begin_inset Tabular
25605 <lyxtabular version="3" rows="5" columns="2">
25606 <features booktabs="true" tabularvalignment="middle">
25607 <column alignment="center" valignment="top" width="0pt">
25608 <column alignment="center" valignment="top" width="0pt">
25610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25613 \begin_layout Plain Layout
25619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25622 \begin_layout Plain Layout
25630 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25633 \begin_layout Plain Layout
25641 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25644 \begin_layout Plain Layout
25645 \begin_inset Formula $\varliminf$
25654 <row topspace="1.5mm">
25655 <cell alignment="center" valignment="top" usebox="none">
25658 \begin_layout Plain Layout
25666 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25669 \begin_layout Plain Layout
25670 \begin_inset Formula $\varlimsup$
25679 <row topspace="1.5mm">
25680 <cell alignment="center" valignment="top" usebox="none">
25683 \begin_layout Plain Layout
25691 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25694 \begin_layout Plain Layout
25695 \begin_inset Formula $\varprojlim$
25704 <row topspace="1.5mm" bottomspace="1mm">
25705 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25708 \begin_layout Plain Layout
25716 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25719 \begin_layout Plain Layout
25720 \begin_inset Formula $\varinjlim$
25736 \begin_layout Standard
25737 \begin_inset VSpace medskip
25740 The limit is created by inserting a subscript.
25741 It is set right beside the function in an inline formula:
25744 \begin_layout Standard
25746 \begin_inset Tabular
25747 <lyxtabular version="3" rows="2" columns="2">
25748 <features booktabs="true" tabularvalignment="middle">
25749 <column alignment="center" valignment="top" width="0pt">
25750 <column alignment="center" valignment="top" width="0pt">
25752 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25755 \begin_layout Plain Layout
25761 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25764 \begin_layout Plain Layout
25772 <cell alignment="center" valignment="top" usebox="none">
25775 \begin_layout Plain Layout
25781 \begin_inset space \textvisiblespace{}
25785 \begin_inset space \textvisiblespace{}
25793 <cell alignment="center" valignment="top" usebox="none">
25796 \begin_layout Plain Layout
25797 \begin_inset Formula $\lim_{x\to A}x=B$
25813 \begin_layout Standard
25814 In a displayed formula the limit is set below the formula, as usual:
25815 \begin_inset Formula
25825 \begin_layout Standard
25826 \begin_inset VSpace medskip
25832 \begin_layout Standard
25833 How to adjust the typesetting of the limits see
25834 \begin_inset CommandInset ref
25836 reference "subsec:Operator-Limits"
25843 \begin_layout Subsection
25845 \begin_inset Index idx
25848 \begin_layout Plain Layout
25849 Functions ! modulo-
25857 \begin_layout Standard
25858 The modulo-function is special, because it exists in four variants.
25859 The variants in a displayed formula are:
25860 \begin_inset Formula
25862 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25863 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25864 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25865 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25866 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25874 \begin_layout Standard
25875 In an inline formula less space is set before the function names for all
25877 By default the modulo-functions take only the first following character
25879 To use more than one character, one has to put them into \SpecialChar TeX
25881 \begin_inset Formula
25883 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25884 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25885 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25893 \begin_layout Section
25895 \begin_inset Index idx
25898 \begin_layout Plain Layout
25907 \begin_layout Standard
25908 The characters ^ and _ would normally create a superscript and subscript,
25910 To get these characters you have to insert them with a leading
25913 \begin_inset Separator parbreak
25919 \begin_layout Standard
25922 \begin_inset Tabular
25923 <lyxtabular version="3" rows="3" columns="2">
25924 <features booktabs="true" tabularvalignment="middle">
25925 <column alignment="left" valignment="top" width="0pt">
25926 <column alignment="block" valignment="top">
25928 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25931 \begin_layout Plain Layout
25937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25940 \begin_layout Plain Layout
25948 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25951 \begin_layout Plain Layout
25955 \begin_inset space \textvisiblespace{}
25963 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25966 \begin_layout Plain Layout
25967 \begin_inset Formula $\mathcircumflex$
25977 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25980 \begin_layout Plain Layout
25988 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25991 \begin_layout Plain Layout
25992 \begin_inset Formula $\_$
26008 \begin_layout Subsection
26009 Special Characters in Mathematical Text
26012 \begin_layout Standard
26013 The following commands can only be used in mathematical text or in \SpecialChar TeX
26017 \begin_layout Standard
26018 \begin_inset space \hfill{}
26022 \begin_inset Tabular
26023 <lyxtabular version="3" rows="8" columns="2">
26024 <features booktabs="true" tabularvalignment="middle">
26025 <column alignment="left" valignment="top" width="0pt">
26026 <column alignment="block" valignment="top">
26028 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26031 \begin_layout Plain Layout
26037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26040 \begin_layout Plain Layout
26048 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26051 \begin_layout Plain Layout
26059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26062 \begin_layout Plain Layout
26063 \begin_inset Formula $\textrm{œ}$
26073 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26076 \begin_layout Plain Layout
26084 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26087 \begin_layout Plain Layout
26088 \begin_inset Formula $\textrm{Œ}$
26098 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26101 \begin_layout Plain Layout
26109 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26112 \begin_layout Plain Layout
26113 \begin_inset Formula $\textrm{æ}$
26123 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26126 \begin_layout Plain Layout
26134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26137 \begin_layout Plain Layout
26138 \begin_inset Formula $\textrm{Æ}$
26148 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26151 \begin_layout Plain Layout
26159 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26162 \begin_layout Plain Layout
26163 \begin_inset Formula $\textrm{\aa}$
26173 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26176 \begin_layout Plain Layout
26180 \begin_inset Index idx
26183 \begin_layout Plain Layout
26190 \begin_layout Plain Layout
26211 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26214 \begin_layout Plain Layout
26215 \begin_inset Formula $\textrm{Å}$
26225 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26228 \begin_layout Plain Layout
26236 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26239 \begin_layout Plain Layout
26240 \begin_inset Formula $\textrm{ı}$
26254 \begin_inset space \hfill{}
26258 \begin_inset Tabular
26259 <lyxtabular version="3" rows="8" columns="2">
26260 <features booktabs="true" tabularvalignment="middle">
26261 <column alignment="left" valignment="top" width="0pt">
26262 <column alignment="center" valignment="top">
26264 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26267 \begin_layout Plain Layout
26269 \begin_inset Note Note
26272 \begin_layout Plain Layout
26274 \begin_inset space \thinspace{}
26277 mm is used for separation, because otherwise the output will be ¡ and ¿
26288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26291 \begin_layout Plain Layout
26299 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26302 \begin_layout Plain Layout
26310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26313 \begin_layout Plain Layout
26314 \begin_inset Formula $\textrm{ø}$
26324 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26327 \begin_layout Plain Layout
26335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26338 \begin_layout Plain Layout
26339 \begin_inset Formula $\textrm{Ø}$
26349 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26352 \begin_layout Plain Layout
26360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26363 \begin_layout Plain Layout
26364 \begin_inset Formula $\textrm{ł}$
26374 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26377 \begin_layout Plain Layout
26385 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26388 \begin_layout Plain Layout
26389 \begin_inset Formula $\textrm{Ł}$
26399 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26402 \begin_layout Plain Layout
26404 \begin_inset space \hspace{}
26409 \begin_inset space \textvisiblespace{}
26417 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26420 \begin_layout Plain Layout
26421 \begin_inset Formula $\textrm{!`}$
26431 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26434 \begin_layout Plain Layout
26436 \begin_inset space \hspace{}
26441 \begin_inset space \textvisiblespace{}
26449 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26452 \begin_layout Plain Layout
26453 \begin_inset Formula $\textrm{?`}$
26463 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26466 \begin_layout Plain Layout
26474 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26477 \begin_layout Plain Layout
26478 \begin_inset Formula $\textrm{ȷ}$
26492 \begin_inset space \hfill{}
26498 \begin_layout Standard
26500 \begin_inset Formula $\textrm{\textrm{Å}}$
26504 \begin_inset Formula $\textrm{\textrm{Ø}}$
26507 can also be inserted via the math toolbar button
26510 arg "math-insert \\digamma"
26516 \begin_layout Standard
26517 An exception are the commands
26520 \begin_inset space \hspace{}
26529 \begin_inset space \hspace{}
26535 , because they can be inserted in \SpecialChar LyX
26539 \begin_layout Subsection
26541 \begin_inset CommandInset label
26543 name "subsec:Accents-in-Text"
26548 \begin_inset Index idx
26551 \begin_layout Plain Layout
26560 \begin_layout Standard
26561 With the following commands all letters can be accented.
26562 The commands must be inserted in \SpecialChar TeX
26566 \begin_layout Standard
26567 \begin_inset space \hfill{}
26571 \begin_inset Tabular
26572 <lyxtabular version="3" rows="8" columns="2">
26573 <features booktabs="true" tabularvalignment="middle">
26574 <column alignment="left" valignment="top" width="0pt">
26575 <column alignment="block" valignment="top">
26577 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26580 \begin_layout Plain Layout
26586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26589 \begin_layout Plain Layout
26597 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26600 \begin_layout Plain Layout
26604 \begin_inset Quotes grd
26612 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26615 \begin_layout Plain Layout
26619 \begin_layout Plain Layout
26635 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26638 \begin_layout Plain Layout
26646 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26649 \begin_layout Plain Layout
26653 \begin_layout Plain Layout
26669 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26672 \begin_layout Plain Layout
26676 \begin_inset space \textvisiblespace{}
26684 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26687 \begin_layout Plain Layout
26691 \begin_layout Plain Layout
26707 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26710 \begin_layout Plain Layout
26718 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26721 \begin_layout Plain Layout
26725 \begin_layout Plain Layout
26741 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26744 \begin_layout Plain Layout
26748 \begin_inset space \textvisiblespace{}
26756 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26759 \begin_layout Plain Layout
26763 \begin_layout Plain Layout
26779 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26782 \begin_layout Plain Layout
26786 \begin_inset space \textvisiblespace{}
26794 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26797 \begin_layout Plain Layout
26801 \begin_layout Plain Layout
26817 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26820 \begin_layout Plain Layout
26824 \begin_inset space \textvisiblespace{}
26832 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26835 \begin_layout Plain Layout
26839 \begin_layout Plain Layout
26859 \begin_inset space \hfill{}
26863 \begin_inset Tabular
26864 <lyxtabular version="3" rows="8" columns="2">
26865 <features booktabs="true" tabularvalignment="middle">
26866 <column alignment="left" valignment="top" width="0pt">
26867 <column alignment="center" valignment="top">
26869 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26872 \begin_layout Plain Layout
26878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26881 \begin_layout Plain Layout
26889 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26892 \begin_layout Plain Layout
26896 \begin_inset space \textvisiblespace{}
26904 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26907 \begin_layout Plain Layout
26911 \begin_layout Plain Layout
26927 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26930 \begin_layout Plain Layout
26938 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26941 \begin_layout Plain Layout
26945 \begin_layout Plain Layout
26961 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26964 \begin_layout Plain Layout
26968 \begin_inset Index idx
26971 \begin_layout Plain Layout
26982 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26985 \begin_layout Plain Layout
26989 \begin_layout Plain Layout
27005 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27008 \begin_layout Plain Layout
27016 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27019 \begin_layout Plain Layout
27023 \begin_layout Plain Layout
27039 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27042 \begin_layout Plain Layout
27046 \begin_inset space \textvisiblespace{}
27054 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27057 \begin_layout Plain Layout
27061 \begin_layout Plain Layout
27077 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27080 \begin_layout Plain Layout
27084 \begin_inset space \textvisiblespace{}
27092 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27095 \begin_layout Plain Layout
27099 \begin_layout Plain Layout
27115 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27118 \begin_layout Plain Layout
27122 \begin_inset space \textvisiblespace{}
27130 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27133 \begin_layout Plain Layout
27137 \begin_layout Plain Layout
27157 \begin_inset space \hfill{}
27163 \begin_layout Standard
27164 \begin_inset VSpace medskip
27173 also two different characters can be accented.
27179 \begin_inset space \textvisiblespace{}
27188 \begin_layout Plain Layout
27200 \begin_layout Standard
27213 can in combination with vowels directly be inserted with the keyboard without
27214 using \SpecialChar TeX
27216 The same applies for the tilde
27220 \begin_layout Plain Layout
27221 This only applies for keyboards where the tilde is defined as accent.
27230 in combination with
27245 \begin_layout Standard
27288 and accents that are inserted directly with the keyboard are also available
27289 in mathematical text.
27290 For the other accents there are special math commands to be used in formulas,
27292 \begin_inset CommandInset ref
27294 reference "subsec:Accents-for-one"
27301 \begin_layout Standard
27302 \begin_inset VSpace bigskip
27305 Furthermore, with the command
27312 \begin_inset Index idx
27315 \begin_layout Plain Layout
27323 all numbers and letters can be set into a circle, quasi accented with a
27324 circle, similar to the copyright symbol.
27327 \begin_layout Standard
27329 \begin_inset Tabular
27330 <lyxtabular version="3" rows="3" columns="2">
27331 <features booktabs="true" tabularvalignment="middle">
27332 <column alignment="center" valignment="top" width="0pt">
27333 <column alignment="center" valignment="top">
27335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27338 \begin_layout Plain Layout
27344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27347 \begin_layout Plain Layout
27355 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27358 \begin_layout Plain Layout
27366 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27369 \begin_layout Plain Layout
27373 \begin_layout Plain Layout
27388 <row topspace="1mm">
27389 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27392 \begin_layout Plain Layout
27403 raisebox{-1.5pt}{W}}
27408 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27411 \begin_layout Plain Layout
27415 \begin_layout Plain Layout
27445 \begin_layout Standard
27446 One has to take care that the character fits in the circle.
27457 \begin_layout Plain Layout
27459 \begin_inset CommandInset ref
27461 reference "subsec:Font-Sizes"
27470 specifies thereby the size of the circle.
27481 \begin_layout Plain Layout
27483 \begin_inset CommandInset ref
27485 reference "subsec:Boxes-without-Frame"
27494 the character can be centered.
27497 \begin_layout Subsection
27499 \begin_inset Index idx
27502 \begin_layout Plain Layout
27511 \begin_layout Standard
27512 Old-style figures (also known as old-style numerals) are created with the
27520 \begin_inset Index idx
27523 \begin_layout Plain Layout
27532 The command can be used in formulas and in \SpecialChar TeX
27534 The command scheme is:
27537 \begin_layout Standard
27542 oldstylenums{number}
27545 \begin_layout Standard
27550 oldstylenums{0123456789
27553 \begin_inset Formula $\oldstylenums{0123456789}$
27559 \begin_layout Section
27561 \begin_inset CommandInset label
27563 name "sec:Formula-Styles"
27568 \begin_inset Index idx
27571 \begin_layout Plain Layout
27580 \begin_layout Itemize
27581 There are two different alignment styles:
27582 \begin_inset Separator parbreak
27589 \begin_layout Description
27590 Centered is the predefined standard
27593 \begin_layout Description
27594 Indented for this the option
27598 must be inserted in the menu
27600 Document\SpecialChar menuseparator
27606 \begin_inset space ~
27612 \begin_layout Standard
27617 is used, the indentation can be adjusted with the length
27624 \begin_inset Index idx
27627 \begin_layout Plain Layout
27636 Should the distance be 15
27637 \begin_inset space \thinspace{}
27640 mm, the following command line is inserted in the \SpecialChar LaTeX
27644 \begin_layout Standard
27654 \begin_layout Standard
27655 When no length is specified, the predefined value of 30
27656 \begin_inset space \thinspace{}
27663 \begin_layout Itemize
27664 And two different numbering styles:
27665 \begin_inset Separator parbreak
27672 \begin_layout Description
27673 Right is the predefined standard
27676 \begin_layout Description
27677 Left for this the option
27681 must be inserted in the menu
27683 Document\SpecialChar menuseparator
27689 \begin_inset space ~
27696 \begin_layout Standard
27705 can also be used together.
27706 In this case both options are inserted, separated by a comma.
27709 \begin_layout Standard
27710 The chosen styles are used for all displayed formulas of the document.
27711 When both, centered and indented formulas should be created in a document,
27717 The indented formulas are then set in a flalign environment, see
27718 \begin_inset CommandInset ref
27720 reference "subsec:Flalign-Environment"
27727 \begin_layout Section
27729 \begin_inset CommandInset label
27731 name "sec:Multiline-Formulas"
27736 \begin_inset Index idx
27739 \begin_layout Plain Layout
27740 Formula ! multiline
27748 \begin_layout Subsection
27752 \begin_layout Standard
27753 In \SpecialChar LyX
27754 multiline formulas are created by pressing
27757 arg "newline-insert newline"
27761 This creates either an
27763 eqnarray environment
27765 that is described in
27766 \begin_inset CommandInset ref
27768 reference "subsec:Eqnarray-Environment"
27772 or, when the option
27774 Use AMS math package
27776 in the document settings is selected, an
27780 that is described in
27781 \begin_inset CommandInset ref
27783 reference "subsec:Standard-align-Environment"
27788 The align environment is recommended because it provides in any case a
27789 typographically correct output.
27792 \begin_layout Standard
27793 There are other multiline formula environments that can be created via the
27796 Insert\SpecialChar menuseparator
27800 These environments are described in the following sections.
27803 \begin_layout Standard
27804 In all multiline formula environments a new line is created by pressing
27808 arg "newline-insert newline"
27812 To add or delete lines, the math toolbar buttons
27815 arg "inset-modify tabular append-row"
27821 arg "inset-modify tabular delete-row"
27824 , respectively, or the menu
27826 Edit\SpecialChar menuseparator
27832 \begin_layout Subsubsection
27834 \begin_inset CommandInset label
27836 name "subsec:Line-Separation"
27841 \begin_inset Index idx
27844 \begin_layout Plain Layout
27845 Formula ! multiline ! Line separation
27853 \begin_layout Standard
27854 There is sometimes not enough space in multiline formulas between the lines:
27855 \begin_inset Formula
27857 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}\\
27858 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
27866 \begin_layout Standard
27867 In \SpecialChar LaTeX
27868 additional line space is specified as optional argument of the new line
27870 This is not yet possible in \SpecialChar LyX
27875 \begin_layout Plain Layout
27877 \begin_inset CommandInset href
27879 name "LyX-bug #1505"
27880 target "http://www.lyx.org/trac/ticket/1505"
27889 , therefore the whole formula must be inserted in \SpecialChar TeX
27891 To add in our example space, the command
27899 is inserted at the end of the first line.
27904 \begin_layout Plain Layout
27911 \begin_layout Plain Layout
27913 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27916 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27923 \begin_layout Plain Layout
27927 left(B^{2}+x_{0}^{2}
27935 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27940 \begin_layout Plain Layout
27952 \begin_layout Standard
27953 \begin_inset VSpace bigskip
27956 To set the line separation for all lines in a formula, the length
27963 \begin_inset Index idx
27966 \begin_layout Plain Layout
27976 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27987 \begin_inset space \thinspace{}
27992 \begin_inset space \thinspace{}
27995 mm additional line separation as in the previous example, the command
27998 \begin_layout Standard
28008 \begin_layout Standard
28009 is inserted in \SpecialChar TeX
28010 mode before the formula.
28011 This requires that the \SpecialChar LaTeX
28020 \begin_layout Plain Layout
28025 is part of every \SpecialChar LaTeX
28026 standard installation.
28032 \begin_inset Index idx
28035 \begin_layout Plain Layout
28041 was loaded in \SpecialChar LaTeX
28042 -preamble with the line
28045 \begin_layout Standard
28053 \begin_layout Standard
28058 \begin_layout Plain Layout
28070 \begin_inset Formula
28072 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}\\
28073 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
28081 \begin_layout Standard
28085 \begin_layout Plain Layout
28096 To get back to the predefined distance,
28102 is set to the value 3
28103 \begin_inset space \thinspace{}
28109 \begin_layout Subsubsection
28111 \begin_inset CommandInset label
28113 name "subsec:Column-Separation"
28118 \begin_inset Index idx
28121 \begin_layout Plain Layout
28122 Formula ! multiline ! Column separation
28130 \begin_layout Standard
28131 Multiline formulas form a matrix.
28132 A formula in the eqnarray environment is for example a matrix with three
28134 By changing the column separation in this environment, the space beside
28135 the relation sign can be changed.
28138 \begin_layout Standard
28139 The column separation is specified with the length
28146 \begin_inset Index idx
28149 \begin_layout Plain Layout
28158 \begin_inset Newline newline
28161 column separation = 2
28162 \begin_inset space \thinspace{}
28172 \begin_inset Newline newline
28178 \begin_layout Standard
28188 \begin_layout Standard
28189 inserted in \SpecialChar TeX
28190 mode, sets for all following formulas a column separation of
28192 \begin_inset space \thinspace{}
28196 To get back to the predefined distance,
28203 \begin_inset space \thinspace{}
28209 \begin_layout Standard
28211 \begin_inset space \thinspace{}
28214 cm column separation:
28218 \begin_layout Plain Layout
28230 \begin_inset Formula
28238 A formula with the predefined column separation for matrices of 10
28239 \begin_inset space \thinspace{}
28246 \begin_layout Plain Layout
28258 \begin_inset Formula
28269 \begin_layout Subsubsection
28271 \begin_inset Index idx
28274 \begin_layout Plain Layout
28283 \begin_layout Standard
28284 Long formulas can be typeset using these methods:
28287 \begin_layout Itemize
28288 When one side of the equation is much shorter than the line width, this
28289 one is chosen for the left side and the right side is typeset over two
28291 \begin_inset Formula
28293 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 \\
28294 & & -\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}
28299 The minus sign at the beginning of the second line does normally not appear
28300 as an operator because it is the first character of the line.
28301 Thus it would not be surrounded by space and could not be distinguished
28302 from the fraction bar.
28304 \begin_inset space \thinspace{}
28307 pt space was inserted behind the minus sign with the command
28317 \begin_layout Plain Layout
28325 \begin_inset CommandInset ref
28327 reference "subsec:Variable-Space"
28337 \begin_inset Index idx
28340 \begin_layout Plain Layout
28351 \begin_layout Itemize
28352 When both sides of the equation are too long, the command
28359 \begin_inset Index idx
28362 \begin_layout Plain Layout
28371 It is inserted in the first column of the first line and causes all further
28372 insertions to overwrite the following columns:
28373 \begin_inset Formula
28375 \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 \\
28376 & & -\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 \\
28377 & & =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}
28382 After the insertion of
28388 , the cursor is in a purple box that is a bit shifted to the left from the
28390 In this the formula is inserted.
28391 \begin_inset Newline newline
28394 The content of the further lines is inserted to the second or another formula
28396 The greater the column number where it was inserted, the larger the indentation.
28397 \begin_inset VSpace medskip
28401 \begin_inset Newline newline
28405 \begin_inset Note Greyedout
28408 \begin_layout Plain Layout
28409 Note the following when using
28418 \begin_layout Itemize
28419 The formula doesn't use the full page width.
28421 \begin_inset space \thinspace{}
28425 \begin_inset space \space{}
28429 \begin_inset Formula $-B^{2}$
28432 is added to the first line in the above example, it would have been outside
28434 To better use the width, negative space can be inserted at the beginning
28438 \begin_layout Itemize
28439 Due to a bug in \SpecialChar LyX
28440 the cursor cannot be set with the mouse into the first
28445 \begin_layout Plain Layout
28446 \begin_inset CommandInset href
28448 name "LyX-bug #1429"
28449 target "http://www.lyx.org/trac/ticket/1429"
28458 One can only set the cursor at the beginning of the line and move it with
28467 \begin_layout Itemize
28468 Other methods to set long formulas are offered by the environments described
28470 \begin_inset CommandInset ref
28472 reference "subsec:Multline-Environment"
28477 \begin_inset CommandInset ref
28479 reference "subsec:Multiline-Formula-Parts"
28486 \begin_layout Subsubsection
28487 Multiline Fractions
28488 \begin_inset CommandInset label
28490 name "subsec:Multiline-Fractions"
28495 \begin_inset Index idx
28498 \begin_layout Plain Layout
28499 Fractions ! multiline
28507 \begin_layout Standard
28508 There are cases where the denominator and/or the numerator of a fraction
28509 is so long that the fraction does not fit into one line.
28510 It is then necessary to add a line break within the fraction.
28511 This can be done using the command
28518 \begin_inset Index idx
28521 \begin_layout Plain Layout
28530 To activate it, set in the document settings under
28533 \begin_inset space ~
28543 \begin_inset Index idx
28546 \begin_layout Plain Layout
28547 Packages ! mathtools
28555 \begin_inset space ~
28570 \begin_layout Standard
28575 splitfrac{first line}{second line}
28578 \begin_layout Standard
28579 and is used as denominator and/or numerator:
28582 \begin_layout Standard
28583 \begin_inset Formula
28585 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}
28590 The command for the first numerator above is:
28593 \begin_layout Standard
28598 splitfrac{xy+xy+xy+xy+xy
28599 \begin_inset space \textvisiblespace{}
28607 \begin_layout Subsubsection
28609 \begin_inset CommandInset label
28611 name "subsec:Multiline-Brackets"
28616 \begin_inset Index idx
28619 \begin_layout Plain Layout
28620 Brackets ! for multiline expressions
28628 \begin_layout Standard
28629 For brackets spanning multiple lines the following problem occurs:
28630 \begin_inset Formula
28632 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28633 & & \left.\cdots+B-D\right]
28641 \begin_layout Standard
28642 The closing bracket is smaller than the opening bracket because brackets
28643 with variable size may not span multiple lines.
28646 \begin_layout Standard
28647 To set the bracket size for the second line correctly, the first line is
28655 \begin_inset Index idx
28658 \begin_layout Plain Layout
28666 and the second line with
28674 \begin_layout Plain Layout
28688 \begin_inset CommandInset ref
28690 reference "subsec:Automatic-Bracket-Size"
28702 \begin_inset Index idx
28705 \begin_layout Plain Layout
28728 \begin_inset space \textvisiblespace{}
28738 \begin_inset space \textvisiblespace{}
28748 \begin_inset space \textvisiblespace{}
28754 \begin_inset Formula $\downarrow$
28760 \begin_inset Index idx
28763 \begin_layout Plain Layout
28771 is inserted, because the multiplication operator with its limits is the
28772 largest symbol in the first line and this should be the size for the bracket
28773 in the second line.
28776 \begin_layout Standard
28777 The result is this:
28778 \begin_inset Formula
28780 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28781 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28789 \begin_layout Subsection
28793 \begin_layout Standard
28794 Align environments can be used for every kind of multiline formulas.
28795 They are especially useful to set several formulas side by side.
28798 \begin_layout Standard
28799 Align environments consist of columns.
28800 The odd columns are right aligned, the even ones left aligned.
28801 Every line in an Align environment can be numbered.
28804 \begin_layout Standard
28805 Align environments are created via the menu
28807 Insert\SpecialChar menuseparator
28813 Edit\SpecialChar menuseparator
28814 Math\SpecialChar menuseparator
28815 Change Formula Type
28817 already existing formulas can be converted to Align environments.
28820 \begin_layout Standard
28821 To add or delete columns, the math toolbar buttons
28824 arg "inset-modify tabular append-column"
28830 arg "inset-modify tabular delete-column"
28833 , respectively, or the menu
28835 Edit\SpecialChar menuseparator
28841 \begin_layout Subsubsection
28842 Standard align Environment
28843 \begin_inset CommandInset label
28845 name "subsec:Standard-align-Environment"
28850 \begin_inset Index idx
28853 \begin_layout Plain Layout
28854 Formula ! multiline ! align environment
28862 \begin_layout Standard
28863 This Align environment is created by pressing
28866 arg "newline-insert newline"
28869 in a formula or by the menu
28871 Insert\SpecialChar menuseparator
28872 Math\SpecialChar menuseparator
28873 AMS align Environment
28878 \begin_layout Standard
28879 An example for two formulas set side by side, that are created with a four
28880 column align environment:
28881 \begin_inset Formula
28883 A & =\sin(B) & C & =D\\
28884 C & \ne A & B & \ne D
28889 As it can be seen, the formulas in this environment are placed so as if
28898 \begin_layout Plain Layout
28906 \begin_inset CommandInset ref
28908 reference "subsec:Variable-Space"
28919 before the first and after every even column.
28920 When the formula style
28926 \begin_layout Plain Layout
28928 \begin_inset CommandInset ref
28930 reference "sec:Formula-Styles"
28941 is used, the formula is set without the
28947 before the first column.
28950 \begin_layout Subsubsection
28951 Alignat Environment
28952 \begin_inset Index idx
28955 \begin_layout Plain Layout
28956 Formula ! multiline ! alignat environment
28964 \begin_layout Standard
28965 The alignat environment has no predefined column separation.
28966 It can be inserted manually with the spaces that are described
28967 \begin_inset CommandInset ref
28969 reference "subsec:Space"
28976 \begin_layout Standard
28977 The above example in the alignat environment where 1
28978 \begin_inset space \thinspace{}
28981 cm space was inserted at the beginning of the second formula:
28982 \begin_inset Formula
28983 \begin{alignat*}{2}
28984 A & =\sin(B) & \hspace{1cm}C & =D\\
28985 C & \ne A & B & \ne D
28990 Because the column separation can be set separately for every column, this
28991 environment is especially suitable to set three and more formulas side
28995 \begin_layout Subsubsection
28996 Flalign Environment
28997 \begin_inset CommandInset label
28999 name "subsec:Flalign-Environment"
29004 \begin_inset Index idx
29007 \begin_layout Plain Layout
29008 Formula ! multiline ! flalign environment
29016 \begin_layout Standard
29017 In this environment the first two columns are always set as much as possible
29018 to the left and the last two ones to the right.
29020 \begin_inset Formula
29022 A & =1 & B & =2 & C & =3\\
29023 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29031 \begin_layout Standard
29032 By creating a flalign environment with an odd number of columns where an
29033 empty \SpecialChar TeX
29034 brace is inserted to the last column, several formulas in a document
29035 can be set to the left, although the formula style
29040 As example the indented formula
29041 \begin_inset CommandInset ref
29043 reference "eq:VolInt"
29048 \begin_inset Formula
29050 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29055 The first two columns contain the formula.
29056 To indent it as with the formula style
29061 \begin_inset space \thinspace{}
29064 pt space was inserted at the beginning of the first column.
29067 \begin_layout Subsection
29068 Eqnarray Environment
29069 \begin_inset CommandInset label
29071 name "subsec:Eqnarray-Environment"
29076 \begin_inset Index idx
29079 \begin_layout Plain Layout
29080 Formula ! multiline ! eqnarray environment
29088 \begin_layout Standard
29089 When this environment has been created, three blue boxes appear.
29090 The content of the first box is right aligned, the content of the last
29092 The content of the middle box appears centered and a bit smaller, because
29093 it is designed to insert there only relation characters.
29094 \begin_inset Formula
29096 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29106 \begin_layout Subsection
29108 \begin_inset Index idx
29111 \begin_layout Plain Layout
29112 Formula ! multiline ! gather environment
29120 \begin_layout Standard
29121 This environment consists of only one centered column.
29122 Every line can be numbered.
29123 \begin_inset Formula
29134 \begin_layout Subsection
29135 Multline Environment
29136 \begin_inset CommandInset label
29138 name "subsec:Multline-Environment"
29143 \begin_inset Index idx
29146 \begin_layout Plain Layout
29147 Formula ! multiline ! multline environment
29155 \begin_layout Standard
29156 The multline environment consists, like the gather environment, of only
29158 But the first line is left aligned, the last one right aligned.
29159 All other lines are centered.
29160 Therefore this environment is suitable for long formulas.
29162 \begin_inset CommandInset ref
29164 reference "eq:lefteqn"
29168 in the multline environment:
29169 \begin_inset Formula
29171 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}\\
29172 -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}\\
29173 =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}}
29181 \begin_layout Standard
29182 In the output only the last (first) line of a multline environment appears
29183 numbered when the document numbering is right (left).
29187 \begin_layout Plain Layout
29188 numbering styles see
29189 \begin_inset CommandInset ref
29191 reference "sec:Formula-Styles"
29203 \begin_layout Standard
29211 \begin_inset Index idx
29214 \begin_layout Plain Layout
29229 \begin_inset Index idx
29232 \begin_layout Plain Layout
29240 a centered line can be right or left aligned, respectively.
29241 The commands are used as follows:
29244 \begin_layout Standard
29249 shoveright{line content}
29255 shoveleft{line content}
29258 \begin_layout Standard
29259 \begin_inset VSpace medskip
29269 \begin_inset Index idx
29272 \begin_layout Plain Layout
29280 specifies the distance of the first line from the left page margin.
29281 Predefined is the length 0
29282 \begin_inset space \thinspace{}
29288 \begin_layout Standard
29289 As example the above formula where the command
29292 \begin_layout Standard
29302 \begin_layout Standard
29303 was inserted in \SpecialChar TeX
29308 \begin_layout Plain Layout
29320 \begin_inset Formula
29322 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}\\
29323 \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}}\\
29324 =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}}
29333 \begin_layout Plain Layout
29344 The second line was left aligned using
29353 \begin_layout Subsection
29354 Multiline Formula Parts
29355 \begin_inset CommandInset label
29357 name "subsec:Multiline-Formula-Parts"
29362 \begin_inset Index idx
29365 \begin_layout Plain Layout
29366 Formula ! multiline ! formula parts
29374 \begin_layout Standard
29375 To display only parts of a formula with multiple lines, one of the following
29376 environments is used:
29393 They can be inserted via the menu
29395 Insert\SpecialChar menuseparator
29398 or by using the commands described in this section.
29401 \begin_layout Standard
29402 The first three have the same properties as the corresponding multiline
29403 formula environments, but it is possible to set further formula parts beside
29406 \begin_inset Formula
29408 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29409 \Delta E\Delta t & \ge\frac{\hbar}{2}
29411 \right\} \textrm{Uncertainty relations}
29419 \begin_layout Standard
29420 To get this formula, a displayed formula is created where the command
29427 \begin_inset Index idx
29430 \begin_layout Plain Layout
29439 A purple box appears around the blue formula box where now columns and
29440 lines can be added.
29441 Outside the multiline environment other formula parts can be set, like
29445 \begin_layout Standard
29446 The aligned environment is also suitable for long formulas whose lines are
29447 horizontally aligned.
29448 Using aligned in a displayed formula has the advantage that the formula
29449 number is vertically centered behind the lines.
29451 \begin_inset CommandInset ref
29453 reference "eq:shortlong"
29457 in the aligned environment:
29458 \begin_inset Formula
29460 \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}|}\\
29461 & -\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}|}
29470 \begin_layout Standard
29471 To use the environments
29490 \begin_inset Index idx
29493 \begin_layout Plain Layout
29508 \begin_inset Index idx
29511 \begin_layout Plain Layout
29526 \begin_inset Index idx
29529 \begin_layout Plain Layout
29537 are inserted, respectively.
29538 The split environment has the same properties as the aligned environment
29539 but it can only have two columns.
29542 \begin_layout Subsection
29543 Text in multiline Formulas
29544 \begin_inset CommandInset label
29546 name "subsec:Text-in-multiline"
29551 \begin_inset Index idx
29554 \begin_layout Plain Layout
29561 \begin_inset Index idx
29564 \begin_layout Plain Layout
29565 Formula ! multiline ! text
29573 \begin_layout Standard
29574 In the Align environments, and the multline and gather environment, text
29575 can be inserted that will appear in a separate line and doesn't affect
29576 the column alignment.
29577 To do this, the command
29584 \begin_inset Index idx
29587 \begin_layout Plain Layout
29595 is used in the following scheme:
29598 \begin_layout Standard
29606 \begin_layout Standard
29607 The text should not be longer than a line because it cannot be hyphenated.
29608 As \SpecialChar LyX
29609 doesn't yet support
29615 directly, the text is written as mathematical text.
29622 must hereby be at the beginning of a line and appears in the output above
29624 An example where the text was inserted at the beginning of the second line:
29625 \begin_inset Formula
29627 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29628 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29636 \begin_layout Standard
29643 always creates some vertical space between the text and the formula lines.
29644 To avoid this space, set in the document settings under
29647 \begin_inset space ~
29657 \begin_inset Index idx
29660 \begin_layout Plain Layout
29661 Packages ! mathtools
29669 \begin_inset space ~
29675 Then you can use the command
29682 \begin_inset Index idx
29685 \begin_layout Plain Layout
29702 \begin_layout Standard
29703 \begin_inset Formula
29705 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29706 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29714 \begin_layout Section
29716 \begin_inset Index idx
29719 \begin_layout Plain Layout
29726 \begin_inset Index idx
29729 \begin_layout Plain Layout
29730 Formula ! numbering|see
29734 \begin_layout Plain Layout
29745 \begin_layout Plain Layout
29760 \begin_layout Subsection
29764 \begin_layout Standard
29765 Numbered formulas can be created with the menu
29767 Insert\SpecialChar menuseparator
29768 Math\SpecialChar menuseparator
29770 \begin_inset space ~
29778 \begin_inset space ~
29784 Existing formulas can be numbered with the menu
29786 Edit\SpecialChar menuseparator
29787 Math\SpecialChar menuseparator
29789 \begin_inset space ~
29797 arg "math-number-toggle"
29801 The formula number is displayed in \SpecialChar LyX
29802 behind the formula as a number sign
29804 The number sign is replaced in the output by the formula number.
29807 \begin_layout Standard
29808 When numbering is turned on in multiline formulas, all lines will be numbered.
29809 But the numbering can be controlled with the menu
29811 Edit\SpecialChar menuseparator
29812 Math\SpecialChar menuseparator
29814 \begin_inset space ~
29818 \begin_inset space ~
29822 \begin_inset space ~
29830 arg "math-number-line-toggle"
29836 \begin_layout Standard
29837 Except for inline formulas, all formulas can be numbered with two different
29839 \begin_inset CommandInset ref
29841 reference "sec:Formula-Styles"
29848 \begin_layout Subsection
29850 \begin_inset Index idx
29853 \begin_layout Plain Layout
29854 Cross-references ! to formulas
29862 \begin_layout Standard
29863 All labeled formulas can be cross-referenced.
29864 A label is added by the menu
29866 Insert\SpecialChar menuseparator
29869 or the toolbar button
29876 The cursor must hereby be inside a displayed formula.
29877 Alternatively you can right-click on the formula and choose
29882 A dialog pops up displaying the prefix
29887 The label is inserted there behind the prefix.
29888 The predefined prefix means
29889 \begin_inset Quotes eld
29893 \begin_inset Quotes erd
29896 and makes it easier to find labels in large documents because it marks
29897 it as formula label to divide it from e.
29898 \begin_inset space \thinspace{}
29902 \begin_inset space \space{}
29906 To change a label, the menu
29908 Insert\SpecialChar menuseparator
29911 is used again or you right-click on a formula and then on
29918 \begin_layout Standard
29919 The name of the label is displayed in \SpecialChar LyX
29920 within two parentheses behind formula.
29921 A formula with a label is always numbered.
29924 \begin_layout Standard
29925 Cross-references are inserted via the menu
29927 Insert\SpecialChar menuseparator
29930 or with the toolbar button
29933 arg "dialog-show-new-inset ref"
29937 A formula cross-reference appears in the output as formula number.
29938 When in the cross-reference dialog window the format
29942 is chosen, the cross-reference appears in the output as formula number
29944 \begin_inset Newline newline
29947 By right-clicking on a cross-reference in \SpecialChar LyX
29948 , one jumps to the formula that
29952 \begin_layout Standard
29953 Here are as examples cross-references to formulas of the following subsections:
29954 \begin_inset Note Note
29957 \begin_layout Plain Layout
29958 Note the different cross-reference types.
29966 \begin_layout Standard
29968 \begin_inset CommandInset ref
29975 \begin_inset CommandInset ref
29983 \begin_inset CommandInset ref
29989 ) big Latin letters are used for the numbering in contrary to (
29990 \begin_inset CommandInset ref
29999 \begin_layout Standard
30000 \begin_inset VSpace medskip
30003 When the argument of
30011 \begin_layout Plain Layout
30019 \begin_inset CommandInset ref
30021 reference "subsec:User-defined-Numbering"
30032 contains a box like in
30033 \begin_inset CommandInset ref
30035 reference "subsec:Paragraph-Boxes"
30039 , the formula cannot be referenced.
30042 \begin_layout Subsection
30044 \begin_inset Index idx
30047 \begin_layout Plain Layout
30048 Formula numbering ! subnumbering
30056 \begin_layout Standard
30057 With the help of the commands
30061 begin{subequations}
30069 formulas can be subnumbered.
30070 Both commands are inserted in \SpecialChar TeX
30074 \begin_layout Standard
30076 \begin_inset Formula
30087 \begin_layout Plain Layout
30091 addtocounter{equation}{-1}
30100 \begin_layout Plain Layout
30104 begin{subequations}
30110 \begin_inset VSpace -5mm
30114 \begin_inset Formula
30122 \begin_inset Formula
30132 \begin_layout Standard
30136 \begin_layout Plain Layout
30148 \begin_layout Standard
30149 To create the example, the following is done:
30152 \begin_layout Enumerate
30153 first formula is inserted
30156 \begin_layout Enumerate
30161 addtocounter{equation}{-1}
30163 begin{subequations}
30164 \begin_inset Index idx
30167 \begin_layout Plain Layout
30176 \begin_inset Newline newline
30181 is inserted after the first formula
30184 \begin_layout Enumerate
30185 second formula is inserted
30188 \begin_layout Enumerate
30189 third formula is inserted
30192 \begin_layout Enumerate
30199 is inserted after the third formula
30202 \begin_layout Standard
30203 Every formula between the commands
30215 is subnumbered as a, b,
30216 \begin_inset Newline linebreak
30219 c, \SpecialChar ldots
30220 For multiline formulas every line will be subnumbered.
30221 All subnumbered formulas are treated as
30226 But as every numbered formula increases the counter
30230 by one, the command
30236 is needed to decrease it.
30237 Otherwise the formulas
30238 \begin_inset CommandInset ref
30245 \begin_inset CommandInset ref
30252 \begin_inset CommandInset ref
30258 would be numbered as
30259 \begin_inset CommandInset ref
30266 \begin_inset CommandInset ref
30273 \begin_inset CommandInset ref
30282 \begin_layout Standard
30283 By inserting the commands in \SpecialChar TeX
30284 mode, a space is created between the first
30287 \begin_inset space \thinspace{}
30290 mm vertical space is inserted after the command
30294 begin{subequations}
30297 When the formula style
30303 \begin_layout Plain Layout
30305 \begin_inset CommandInset ref
30307 reference "sec:Formula-Styles"
30319 \begin_inset space \thinspace{}
30322 mm space is inserted instead.
30325 \begin_layout Standard
30326 Here is an example for a multiline formula where the numbering was turned
30327 off for the second line:
30331 \begin_layout Plain Layout
30335 begin{subequations}
30341 \begin_inset Formula
30343 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30344 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30345 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30354 \begin_layout Plain Layout
30366 \begin_layout Subsection
30367 User-defined Numbering
30368 \begin_inset CommandInset label
30370 name "subsec:User-defined-Numbering"
30375 \begin_inset Index idx
30378 \begin_layout Plain Layout
30379 Formula numbering ! user-defined
30387 \begin_layout Standard
30388 \begin_inset Index idx
30391 \begin_layout Plain Layout
30392 Formula numbering ! self-defined delimiters
30397 With the standard numbering parentheses are set around the formula number.
30398 To replace the parentheses for example by vertical bars, the following
30399 line is added to the \SpecialChar LaTeX
30403 \begin_layout Standard
30415 \begin_inset Note Note
30418 \begin_layout Plain Layout
30419 This macro is already declared in the \SpecialChar LaTeX
30420 -preamble for testing.
30421 To activate it, remove the percent sign at the beginning.
30429 \begin_layout Standard
30430 To use other characters, the vertical bars besides the
30434 are replaced by one ore more characters.
30435 To get only the formula number the vertical bars are omitted.
30438 \begin_layout Standard
30439 \begin_inset VSpace bigskip
30442 When there should be an expression of your choice instead of the consecutive
30443 formula number in parentheses behind the formula, the command
30450 \begin_inset Index idx
30453 \begin_layout Plain Layout
30462 \begin_inset Formula
30464 A+B=C\tag{something}\label{eq:tag}
30469 In this example the command
30474 \begin_inset space \textvisiblespace{}
30479 was inserted in the formula.
30482 \begin_layout Standard
30488 \begin_inset space \textvisiblespace{}
30493 is inserted instead, the star prevents the parentheses around the expression:
30494 \begin_inset Formula
30496 A+B=C\tag*{something}
30504 \begin_layout Standard
30505 \begin_inset VSpace bigskip
30508 To restart the formula numbering with new document parts or sections, the
30509 following command is used:
30512 \begin_layout Standard
30517 @addtoreset{equation}{part}
30520 \begin_inset Index idx
30523 \begin_layout Plain Layout
30528 \begin_layout Plain Layout
30539 \begin_layout Plain Layout
30552 \begin_layout Plain Layout
30563 \begin_layout Plain Layout
30576 \begin_inset Newline newline
30580 \begin_inset Newline newline
30587 @addtoreset{equation}{section}
30590 \begin_layout Standard
30591 To be able to use these commands in \SpecialChar TeX
30593 \begin_inset Quotes eld
30597 \begin_inset Quotes erd
30600 character has to be made
30601 \begin_inset Quotes eld
30605 \begin_inset Quotes erd
30608 for \SpecialChar LaTeX
30623 So the command sequence in \SpecialChar TeX
30627 \begin_layout Standard
30633 \begin_inset Newline newline
30638 @addtoreset{equation}{section}
30639 \begin_inset Newline newline
30647 \begin_layout Standard
30648 In the \SpecialChar LaTeX
30661 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30665 \begin_layout Standard
30680 \begin_layout Plain Layout
30685 is part of the \SpecialChar LaTeX
30691 \begin_inset Index idx
30694 \begin_layout Plain Layout
30695 Packages ! carlisle
30700 that is part of every \SpecialChar LaTeX
30701 standard installation.
30707 \begin_inset Index idx
30710 \begin_layout Plain Layout
30711 Packages ! remreset
30716 has to be loaded in the \SpecialChar LaTeX
30717 -preamble with the line
30720 \begin_layout Standard
30725 usepackage{remreset}
30728 \begin_layout Standard
30736 \begin_inset Index idx
30739 \begin_layout Plain Layout
30744 \begin_layout Plain Layout
30755 \begin_layout Plain Layout
30768 \begin_layout Plain Layout
30779 \begin_layout Plain Layout
30791 can be used with the same scheme as
30800 \begin_layout Standard
30801 \begin_inset VSpace bigskip
30804 Sometimes formulas should be numbered in the following form:
30807 \begin_layout Standard
30810 (section number.formula number)
30813 \begin_layout Standard
30814 The formula number should start with every section with
30815 \begin_inset Quotes eld
30819 \begin_inset Quotes erd
30825 \begin_layout Standard
30826 For this case there is the command
30833 \begin_inset Index idx
30836 \begin_layout Plain Layout
30844 , which is used with the following scheme:
30847 \begin_layout Standard
30852 numberwithin{counter}{sectioning}
30855 \begin_layout Standard
30856 Counter denotes what kind of numbering is affected, sectioning denotes what
30857 number is before the dot.
30860 \begin_layout Standard
30861 Thus in our case the following \SpecialChar LaTeX
30862 preamble or \SpecialChar TeX
30866 \begin_layout Standard
30871 numberwithin{equation}{section}
30874 \begin_layout Standard
30875 This is the result:
30879 \begin_layout Plain Layout
30883 numberwithin{equation}{section}
30889 \begin_inset Formula
30899 \begin_layout Standard
30901 \begin_inset space \thinspace{}
30905 \begin_inset space \space{}
30908 tables so that the number of the part is the sectioning,
30909 \begin_inset Newline newline
30916 numberwithin{table}{part}
30921 \begin_layout Standard
30922 To go back to the standard numbering or to prevent this kind of numbering
30923 when it is defined by the document class, the following command is inserted
30924 as \SpecialChar TeX
30925 code or to the \SpecialChar LaTeX
30929 \begin_layout Standard
30939 \begin_inset Index idx
30942 \begin_layout Plain Layout
30956 \begin_layout Plain Layout
30972 \begin_inset Newline newline
30980 \begin_inset Newline newline
30992 \begin_layout Standard
30999 uses internally the command
31005 , described above, that also needs to be reverted.
31009 \begin_layout Plain Layout
31016 \begin_layout Plain Layout
31020 @removefromreset{equation}{section}
31023 \begin_layout Plain Layout
31035 \begin_layout Subsection
31036 Numbering with Roman Numbers and Letters
31037 \begin_inset Index idx
31040 \begin_layout Plain Layout
31041 Formula numbering ! with letters
31047 \begin_inset Index idx
31050 \begin_layout Plain Layout
31051 Formula numbering ! with Roman numbers
31059 \begin_layout Standard
31060 Formulas can also be numbered with Roman numbers and Latin letters.
31061 To number for example with small Roman numbers, the command
31064 \begin_layout Standard
31076 \begin_layout Standard
31077 is inserted before the formula in \SpecialChar TeX
31086 \begin_inset Index idx
31089 \begin_layout Plain Layout
31097 redefines the predefined command
31113 \begin_layout Plain Layout
31120 has the same scheme like the command
31126 that is described in
31127 \begin_inset CommandInset ref
31129 reference "subsec:The-Command-newcommand"
31142 is the formula counter.
31149 is used as prefix for a counter, the value of the counter is output as
31151 When a formula is numbered, \SpecialChar LaTeX
31152 sets internally the command
31158 behind the formula.
31164 \begin_inset Index idx
31167 \begin_layout Plain Layout
31177 outputs the counter as small Roman number.
31180 \begin_layout Standard
31181 All formulas behind the command
31191 are now numbered Roman.
31192 To switch to numbering with big Roman numbers, the command is inserted
31206 \begin_inset Index idx
31209 \begin_layout Plain Layout
31221 \begin_inset Quotes eld
31225 \begin_inset Quotes erd
31228 with small Latin letters there is the command
31235 \begin_inset Index idx
31238 \begin_layout Plain Layout
31246 , for big ones there is the command
31253 \begin_inset Index idx
31256 \begin_layout Plain Layout
31269 \begin_layout Standard
31270 \begin_inset Note Greyedout
31273 \begin_layout Plain Layout
31280 \begin_inset space ~
31283 formulas can be numbered with Latin letters in one document.
31291 \begin_layout Standard
31295 \begin_layout Plain Layout
31311 \begin_layout Standard
31312 \begin_inset Formula
31314 A=\textrm{small roman}
31323 \begin_layout Plain Layout
31337 \begin_inset Formula
31339 B=\textrm{big Roman}\label{eq:Rom}
31348 \begin_layout Plain Layout
31362 \begin_inset Formula
31364 C=\textrm{small Latin}
31373 \begin_layout Plain Layout
31387 \begin_inset Formula
31389 D=\textrm{big Latin}\label{eq:Lat}
31397 \begin_layout Standard
31398 To switch back to the default numbering, insert the command:
31401 \begin_layout Standard
31411 \begin_inset Index idx
31414 \begin_layout Plain Layout
31425 \begin_layout Standard
31429 \begin_layout Plain Layout
31443 \begin_inset Formula
31453 \begin_layout Standard
31454 \begin_inset VSpace medskip
31457 As you see, formulas are numbered serially independent from the numbering
31459 When then numbering should start with
31460 \begin_inset Quotes eld
31464 \begin_inset Quotes erd
31467 when the style is changed, new equation counters have to be defined.
31468 A description about this can be found in the file
31469 \begin_inset CommandInset href
31471 name "Formula-numbering.lyx"
31472 target "run:Formula-numbering.lyx"
31479 \begin_layout Section
31480 Chemical Symbols and Equations
31481 \begin_inset CommandInset label
31483 name "subsec:Chemical-Symbols-and"
31488 \begin_inset Index idx
31491 \begin_layout Plain Layout
31492 Chemical characters ! Symbols
31498 \begin_inset Index idx
31501 \begin_layout Plain Layout
31508 \begin_inset Index idx
31511 \begin_layout Plain Layout
31520 \begin_layout Standard
31521 An example text from chemistry:
31524 \begin_layout Quote
31526 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31529 -ion reacts with two
31530 \begin_inset Formula $\mathrm{Na^{+}}$
31533 -ions to sodium sulfate
31534 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31538 The chemical equation for this is:
31539 \begin_inset Formula
31541 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31549 \begin_layout Standard
31550 This chemical equation can directly be created as formula.
31551 To avoid that the symbols appear italic, everything is highlighted and
31552 changed by the shortcut
31558 to the upright font style.
31562 \begin_layout Plain Layout
31568 \begin_inset CommandInset ref
31570 reference "subsec:Font-Styles"
31582 \begin_layout Standard
31583 A more convenient way to typeset chemical formulas is to use the command
31591 \begin_inset Index idx
31594 \begin_layout Plain Layout
31602 that is available when the \SpecialChar LaTeX
31608 \begin_inset Index idx
31611 \begin_layout Plain Layout
31624 to a formula a new blue box appears where chemical formulas can be inserted
31625 in an intuitive way.
31626 \begin_inset Separator parbreak
31632 \begin_layout Standard
31634 \begin_inset Tabular
31635 <lyxtabular version="3" rows="10" columns="2">
31636 <features booktabs="true" tabularvalignment="middle">
31637 <column alignment="center" valignment="top" width="0pt">
31638 <column alignment="center" valignment="top">
31640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31643 \begin_layout Plain Layout
31649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31652 \begin_layout Plain Layout
31660 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31663 \begin_layout Plain Layout
31667 \begin_inset space \textvisiblespace{}
31675 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31678 \begin_layout Plain Layout
31679 \begin_inset Formula $\ce{H2CO3}$
31688 <row topspace="1.5mm">
31689 <cell alignment="center" valignment="top" usebox="none">
31692 \begin_layout Plain Layout
31696 \begin_inset space \textvisiblespace{}
31704 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31707 \begin_layout Plain Layout
31708 \begin_inset Formula $\ce{SO4^{2-}}$
31717 <row topspace="1.5mm">
31718 <cell alignment="center" valignment="top" usebox="none">
31721 \begin_layout Plain Layout
31725 \begin_inset space \textvisiblespace{}
31733 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31736 \begin_layout Plain Layout
31737 \begin_inset Formula $\ce{(NH4)2S}$
31746 <row topspace="1.5mm">
31747 <cell alignment="center" valignment="top" usebox="none">
31750 \begin_layout Plain Layout
31754 \begin_inset space \textvisiblespace{}
31762 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31765 \begin_layout Plain Layout
31766 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31775 <row topspace="1.5mm">
31776 <cell alignment="center" valignment="top" usebox="none">
31779 \begin_layout Plain Layout
31783 \begin_inset space \textvisiblespace{}
31789 \begin_inset space \textvisiblespace{}
31795 \begin_inset space \textvisiblespace{}
31803 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31806 \begin_layout Plain Layout
31807 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31816 <row topspace="1.5mm">
31817 <cell alignment="center" valignment="top" usebox="none">
31820 \begin_layout Plain Layout
31824 \begin_inset space \textvisiblespace{}
31828 \begin_inset Formula $\downarrow$
31832 \begin_inset Formula $\to$
31840 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31843 \begin_layout Plain Layout
31844 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31854 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31857 \begin_layout Plain Layout
31861 \begin_inset space \textvisiblespace{}
31867 \begin_inset space \textvisiblespace{}
31873 \begin_inset space \textvisiblespace{}
31881 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31884 \begin_layout Plain Layout
31885 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31898 \begin_layout Plain Layout
31902 \begin_inset space \textvisiblespace{}
31906 \begin_inset space \textvisiblespace{}
31910 \begin_inset space \textvisiblespace{}
31914 \begin_inset space \textvisiblespace{}
31918 \begin_inset space \textvisiblespace{}
31926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31929 \begin_layout Plain Layout
31930 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31939 <row topspace="1.5mm">
31940 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31943 \begin_layout Plain Layout
31947 \begin_inset space \textvisiblespace{}
31951 \begin_inset space \textvisiblespace{}
31955 \begin_inset space \textvisiblespace{}
31959 \begin_inset space \textvisiblespace{}
31967 \begin_inset space \textvisiblespace{}
31975 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31978 \begin_layout Plain Layout
31979 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
31995 \begin_layout Standard
31996 \begin_inset Note Greyedout
31999 \begin_layout Plain Layout
32005 It is not possible in \SpecialChar LyX
32006 to use the character ^ to get an up-arrow as described
32012 One instead uses a negative thin space followed by the command
32019 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32030 \begin_layout Standard
32037 the command for equation
32038 \begin_inset space ~
32042 \begin_inset CommandInset ref
32044 reference "eq:chem-reaction"
32049 \begin_inset Newline newline
32057 \begin_inset space \textvisiblespace{}
32061 \begin_inset space \textvisiblespace{}
32065 \begin_inset space \textvisiblespace{}
32069 \begin_inset space \textvisiblespace{}
32073 \begin_inset space \textvisiblespace{}
32077 \begin_inset space \textvisiblespace{}
32083 \begin_layout Standard
32084 To create multiline chemical equations first a multiline formula is created
32086 \begin_inset CommandInset ref
32088 reference "sec:Multiline-Formulas"
32093 Afterwards the command
32099 is used in every small blue box of the formula.
32101 \begin_inset CommandInset ref
32103 reference "eq:TEOS-reaction-1"
32108 \begin_inset CommandInset ref
32110 reference "eq:TEOS-reaction-2"
32114 are an example of a multi-stage chemical reaction where every equation
32115 has its own number.
32116 \begin_inset Formula
32118 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32119 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32127 \begin_layout Standard
32138 package provides the command
32145 \begin_inset Index idx
32148 \begin_layout Plain Layout
32156 that has to be used for special cases.
32157 For more information about
32163 and more examples have a look at the documentation of
32168 \begin_inset CommandInset citation
32177 \begin_layout Section
32181 \begin_layout Standard
32183 supports two types of commutative diagrams:
32191 that are explained in the following.
32194 \begin_layout Subsection
32196 \begin_inset Index idx
32199 \begin_layout Plain Layout
32208 \begin_layout Standard
32209 Diagrams of this type visualize relations by vertical and horizontal lines
32211 \begin_inset Formula
32213 \begin{CD}A@>>>B@>>>C\\
32224 \begin_layout Standard
32225 To get them, the command
32230 \begin_inset Index idx
32233 \begin_layout Plain Layout
32243 is inserted to a formula.
32244 A blue box appears with two dashed lines where further commands can be
32249 arg "newline-insert newline"
32252 a new line is created.
32253 Horizontal relations are inserted in odd, vertical in even formula lines.
32256 \begin_layout Standard
32257 To create the relations there are the following commands:
32260 \begin_layout Itemize
32265 creates a left arrow,
32276 \begin_layout Itemize
32281 creates an up arrow,
32289 a vertical equal sign
32292 \begin_layout Itemize
32298 is a placeholder for non-existent relations
32301 \begin_layout Standard
32302 All arrows can be labeled as follows:
32305 \begin_layout Itemize
32306 If text inserted between the first and second < or >, resp., it is placed
32308 When it is inserted between the second and third one, it appears under
32312 \begin_layout Itemize
32313 When text for vertical arrows is inserted between the first and second A
32314 or V, resp., it is placed left beside the arrow.
32315 When it is inserted between the second and third one, it appears right
32317 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32321 \begin_layout Standard
32322 As example a diagram with all possible relations:
32325 \begin_layout Standard
32326 \begin_inset Formula
32328 \begin{CD}A@>j>>B@>>k>C@=F\\
32339 \begin_layout Standard
32340 The command for this is:
32341 \begin_inset Newline newline
32349 \begin_inset space \textvisiblespace{}
32352 A@>j>>B@>>k>C@=F Ctrl+Return
32353 \begin_inset Newline newline
32357 \begin_inset Phantom HPhantom
32360 \begin_layout Plain Layout
32366 \begin_inset space \textvisiblespace{}
32379 \begin_inset Formula $\to$
32385 \begin_inset Newline newline
32389 \begin_inset Phantom HPhantom
32392 \begin_layout Plain Layout
32398 \begin_inset space \textvisiblespace{}
32409 \begin_layout Subsection
32411 \begin_inset Index idx
32414 \begin_layout Plain Layout
32415 Diagrams ! xymatrix
32423 \begin_layout Standard
32424 To be able to use xymatrices, the \SpecialChar LaTeX
32430 A xymatrix is created by inserting the command
32437 Then you are able to add new matrix columns and rows like for normal matrices,
32439 \begin_inset CommandInset ref
32441 reference "sec:Matrices"
32448 \begin_layout Standard
32449 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32451 All possibilities to create commutative diagrams and decorations are explained
32456 that you find in the menu
32458 Help\SpecialChar menuseparator
32460 \begin_inset space ~
32468 \begin_layout Subsection
32474 \begin_inset Index idx
32477 \begin_layout Plain Layout
32486 \begin_layout Standard
32491 -diagrams, the \SpecialChar LaTeX
32501 -diagram is created by inserting the command
32508 Then you are able to add new matrix columns and rows like for normal matrices,
32510 \begin_inset CommandInset ref
32512 reference "sec:Matrices"
32519 \begin_layout Standard
32520 Examples how to create
32524 diagrams in \SpecialChar LyX
32527 Feynman-diagram manual
32529 that you find in the menu
32531 Help\SpecialChar menuseparator
32533 \begin_inset space ~
32541 \begin_layout Standard
32542 \begin_inset Newpage newpage
32548 \begin_layout Section
32549 User-defined Commands
32550 \begin_inset Index idx
32553 \begin_layout Plain Layout
32554 User-defined commands
32562 \begin_layout Standard
32563 \begin_inset Note Greyedout
32566 \begin_layout Plain Layout
32571 The names of user-defined commands and macros may only consist of Latin
32580 \begin_layout Subsection
32584 \begin_inset CommandInset label
32586 name "subsec:The-Command-newcommand"
32591 \begin_inset Index idx
32594 \begin_layout Plain Layout
32595 User-defined commands !
32603 \begin_inset Index idx
32606 \begin_layout Plain Layout
32617 \begin_layout Standard
32618 Many \SpecialChar LaTeX
32619 -commands are too long to be used frequently.
32620 But it is possible to define with the command
32626 new shorter commands.
32629 \begin_layout Standard
32630 The command scheme of
32639 \begin_layout Standard
32644 newcommand{new command name}[number of arguments][optional
32649 \begin_inset Newline newline
32653 \begin_inset Phantom HPhantom
32656 \begin_layout Plain Layout
32666 {command definition}
32669 \begin_layout Standard
32670 \begin_inset Note Greyedout
32673 \begin_layout Plain Layout
32678 Assure that the name of the new command is not already used in your document
32679 or by \SpecialChar LaTeX
32680 -packages that you use.
32681 When you for example define the command
32693 , you get an error message because
32699 is already defined as command for
32700 \begin_inset Quotes eld
32704 \begin_inset Formula $\le$
32708 \begin_inset Quotes erd
32719 \begin_layout Standard
32720 The number of arguments is an integer in the range 0
32721 \begin_inset space \thinspace{}
32725 \begin_inset space \thinspace{}
32728 9 and specifies how many arguments the new command should have.
32729 With the optional value a value for an optional argument can be predefined.
32730 When this is done, the
32738 rgument of the new command is automatically an optional one.
32741 \begin_layout Standard
32742 Here are some examples:
32745 \begin_layout Itemize
32746 To define the command
32758 , the \SpecialChar LaTeX
32760 \begin_inset VSpace medskip
32764 \begin_inset Newline newline
32778 \begin_layout Itemize
32779 To define the command
32791 , the argument (that should be underlined) must be taken into account.
32792 For this the preamble line is:
32793 \begin_inset VSpace medskip
32797 \begin_inset Newline newline
32811 \begin_inset VSpace medskip
32815 \begin_inset Newline newline
32822 acts as argument placeholder, the
32826 behind it denotes that it is the placeholder for the first argument.
32829 \begin_layout Itemize
32837 \begin_inset space \thinspace{}
32841 \begin_inset space \space{}
32851 \begin_inset VSpace medskip
32855 \begin_inset Newline newline
32866 framebox#1#2{$#3$}}
32869 \begin_inset VSpace medskip
32873 \begin_inset Newline newline
32876 The two Dollar signs creates the extra formula needed for
32883 \begin_inset CommandInset ref
32885 reference "subsec:Boxes-with-Frame"
32892 \begin_layout Itemize
32893 To create a new command for
32899 where the color for the box need not be specified, the argument for the
32900 color is defined optional:
32901 \begin_inset VSpace medskip
32905 \begin_inset Newline newline
32916 fcolorbox{#2}{#1}{$#3$}}
32919 \begin_inset VSpace medskip
32923 \begin_inset Newline newline
32926 When the color is not specified when using
32932 , the predefined color
32939 \begin_layout Standard
32940 A test of the new defined commands:
32941 \begin_inset Separator parbreak
32947 \begin_layout Standard
32949 \begin_inset Tabular
32950 <lyxtabular version="3" rows="6" columns="2">
32951 <features booktabs="true" tabularvalignment="middle">
32952 <column alignment="center" valignment="top" width="0pt">
32953 <column alignment="center" valignment="top">
32955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32958 \begin_layout Plain Layout
32964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32967 \begin_layout Plain Layout
32975 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32978 \begin_layout Plain Layout
32982 \begin_inset space \textvisiblespace{}
32990 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32993 \begin_layout Plain Layout
32994 \begin_inset Formula $A\gr B$
33004 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33007 \begin_layout Plain Layout
33015 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33018 \begin_layout Plain Layout
33019 \begin_inset Formula $\us{ABcd}$
33028 <row topspace="1mm">
33029 <cell alignment="center" valignment="top" usebox="none">
33032 \begin_layout Plain Layout
33036 \begin_inset Formula $\to$
33042 \begin_inset Formula $\to$
33050 \begin_inset space \textvisiblespace{}
33058 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33061 \begin_layout Plain Layout
33062 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33071 <row topspace="1.5mm">
33072 <cell alignment="center" valignment="top" usebox="none">
33075 \begin_layout Plain Layout
33079 \begin_inset Formula $\to$
33087 \begin_inset space \textvisiblespace{}
33095 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33098 \begin_layout Plain Layout
33099 \begin_inset Formula $\cb{red}{\int A=B}$
33108 <row topspace="1.5mm" bottomspace="1mm">
33109 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33112 \begin_layout Plain Layout
33118 \begin_inset Formula $\to$
33126 \begin_inset space \textvisiblespace{}
33134 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33137 \begin_layout Plain Layout
33138 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33154 \begin_layout Subsection
33156 \begin_inset Index idx
33159 \begin_layout Plain Layout
33160 User-defined commands! Math macros
33166 \begin_inset Index idx
33169 \begin_layout Plain Layout
33178 \begin_layout Standard
33179 User-defined commands are especially convenient for complex expressions.
33180 When you are for example dealing with a document that has quadratic equations,
33181 the same solution type occurs several times.
33182 The general form of a quadratic equation is
33183 \begin_inset Formula
33185 0=\lambda^{2}+p\lambda+q
33190 The general form of the solution is
33191 \begin_inset Formula
33193 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33201 \begin_layout Standard
33202 To define a command for the solution formula where only the three parameters
33204 \begin_inset Formula $\lambda$
33208 \begin_inset Formula $p$
33212 \begin_inset Formula $q$
33215 need to be specified and the index of
33216 \begin_inset Formula $\lambda$
33219 can be given optionally, the \SpecialChar LaTeX
33221 \begin_inset Newline newline
33237 \begin_inset Newline newline
33241 \begin_inset Phantom HPhantom
33244 \begin_layout Plain Layout
33258 frac{#3^{2}}{4}-#4}}
33261 \begin_layout Standard
33262 To create with this the solution formula, the command
33263 \begin_inset Newline newline
33273 \begin_inset Formula $\to$
33279 \begin_inset Formula $\to$
33286 is inserted to a formula
33291 \begin_layout Standard
33292 The definition of the new command is unintuitive because one has to know
33293 the schemes of all used \SpecialChar LaTeX
33295 \begin_inset space \thinspace{}
33299 \begin_inset space \space{}
33302 that a fraction is inserted in \SpecialChar LaTeX
33307 frac{numerator}{denominator}
33310 Furthermore one can easily forget a brace in the definition and cannot
33311 see in \SpecialChar LyX
33312 what the new command is doing.
33313 To avoid these problems \SpecialChar LyX
33314 offers the possibility to use math macros instead
33324 \begin_layout Standard
33325 A math macro is created by using the menu
33327 Insert\SpecialChar menuseparator
33328 Math\SpecialChar menuseparator
33331 or the toolbar button
33334 arg "math-macro newmacroname_newcommand"
33338 The math macro toolbar appears together with the following box where the
33340 \begin_inset Newline newline
33344 \begin_inset space \hspace*{\fill}
33348 \begin_inset Graphics
33349 filename clipart/macrobox.png
33355 \begin_inset space \hspace*{\fill}
33359 \begin_inset Newline newline
33363 \begin_inset FormulaMacro
33364 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33369 newmacroname is the default name of the macro that should be changed to
33370 something sensible.
33371 The wanted formula is inserted in the first blue box.
33372 An argument placeholder is inserted with the command
33379 \begin_inset space \thinspace{}
33383 \begin_inset space \space{}
33392 or by using the macro toolbar button
33395 arg "math-macro-add-param"
33399 Argument placeholders are displayed red.
33401 \begin_inset space ~
33404 arguments are possible.
33405 Optional arguments are created with the toolbar button
33408 arg "math-macro-add-optional-param"
33412 The first non-optional argument can be transformed to an optional one with
33416 arg "math-macro-make-optional"
33420 In the second blue box the appearance of the macro in \SpecialChar LyX
33422 Normally you want to see it as it is defined, so the box is kept empty.
33423 But when you have created a macro that needs lot of space on the screen,
33424 you can insert in the box for example
33425 \begin_inset Newline newline
33455 \begin_inset Newline newline
33460 For the macro only the arguments with the macro name in front of them will
33461 then be displayed in \SpecialChar LyX
33462 , leading to a better overview.
33463 The formula appears in the output as defined in the first box.
33464 \begin_inset Newline newline
33467 The appearance of macros in formulas can furthermore be changed for single
33468 macros by setting the cursor in the macro and using the menu
33470 View\SpecialChar menuseparator
33472 \begin_inset space ~
33476 \begin_inset space ~
33484 \begin_layout Standard
33485 To use a macro, the macro name is inserted as command to a formula, in our
33493 Our macro looks in \SpecialChar LyX
33495 \begin_inset Newline newline
33499 \begin_inset space \hspace*{\fill}
33503 \begin_inset Graphics
33504 filename clipart/macrouse.png
33510 \begin_inset space \hspace*{\fill}
33514 \begin_inset Newline newline
33517 Here is our macro example with the arguments
33518 \begin_inset Formula $x$
33522 \begin_inset Formula $\ln(x)$
33526 \begin_inset Formula $B$
33532 \begin_layout Standard
33533 \begin_inset Formula
33543 \begin_layout Standard
33547 Tools\SpecialChar menuseparator
33548 Preferences\SpecialChar menuseparator
33549 Editing\SpecialChar menuseparator
33552 different styles to edit macros.
33553 To find the style that suits you the most, choose a style and set the cursor
33554 in a macro formula to see the difference.
33557 \begin_layout Standard
33558 A math macro is transformed internally to a
33564 command when exporting the document.
33571 command is not placed in the \SpecialChar LaTeX
33572 -preamble, therefore macros can only be used
33573 in formulas that are in the document below the macro definition box.
33576 \begin_layout Standard
33577 Math macros can also be directly created from a
33584 When writing for example the command
33587 \begin_inset Newline newline
33596 xleftarrow[#2]{#1}}
33597 \begin_inset Newline newline
33602 in \SpecialChar LyX
33603 as normal text, highlighting it completely and using then the shortcut
33608 , the command will be transformed to a math macro.
33609 Using this method you need to be careful that the
33615 command is typed correctly, otherwise you get a faulty macro leading to
33620 \begin_layout Standard
33621 Math macros currently have the problem that further formulas in macro definition
33622 s are handled wrongly.
33623 Therefore the example
33630 \begin_inset CommandInset ref
33632 reference "subsec:The-Command-newcommand"
33636 cannot be created as macro.
33639 \begin_layout Standard
33640 When the cursor is in a macro definition box, you will see the macro toolbar
33641 in \SpecialChar LyX
33645 \begin_layout Standard
33646 \begin_inset VSpace defskip
33652 \begin_layout Standard
33653 \begin_inset Graphics
33654 filename clipart/MacroToolbar.png
33659 \begin_inset Index idx
33662 \begin_layout Plain Layout
33671 \begin_layout Standard
33672 \begin_inset VSpace defskip
33678 \begin_layout Standard
33679 The macro toolbar contains from left to right the following buttons:
33682 \begin_layout Standard
33683 \begin_inset VSpace defskip
33689 \begin_layout Standard
33690 \begin_inset Tabular
33691 <lyxtabular version="3" rows="9" columns="2">
33692 <features islongtable="true" longtabularalignment="center">
33693 <column alignment="left" valignment="top">
33694 <column alignment="left" valignment="top" width="85col%">
33695 <row interlinespace="2.5mm">
33696 <cell alignment="center" valignment="top" usebox="none">
33699 \begin_layout Plain Layout
33702 arg "math-macro-remove-param"
33710 <cell alignment="center" valignment="top" usebox="none">
33713 \begin_layout Plain Layout
33716 Edit\SpecialChar menuseparator
33717 Math\SpecialChar menuseparator
33719 \begin_inset space ~
33722 Definition\SpecialChar menuseparator
33723 Remove Last Argument
33729 <row interlinespace="2.5mm">
33730 <cell alignment="center" valignment="top" usebox="none">
33733 \begin_layout Plain Layout
33736 arg "math-macro-add-param"
33744 <cell alignment="center" valignment="top" usebox="none">
33747 \begin_layout Plain Layout
33750 Edit\SpecialChar menuseparator
33751 Math\SpecialChar menuseparator
33753 \begin_inset space ~
33756 Definition\SpecialChar menuseparator
33763 <row interlinespace="2.5mm">
33764 <cell alignment="center" valignment="top" usebox="none">
33767 \begin_layout Plain Layout
33770 arg "math-macro-make-optional"
33778 <cell alignment="center" valignment="top" usebox="none">
33781 \begin_layout Plain Layout
33784 Edit\SpecialChar menuseparator
33785 Math\SpecialChar menuseparator
33787 \begin_inset space ~
33790 Definition\SpecialChar menuseparator
33791 Transform First Non-Optional to
33792 \begin_inset Newline newline
33796 \begin_inset Phantom HPhantom
33799 \begin_layout Plain Layout
33802 Edit\SpecialChar menuseparator
33803 Math\SpecialChar menuseparator
33805 \begin_inset space ~
33808 Definition\SpecialChar menuseparator
33820 <row interlinespace="2.5mm">
33821 <cell alignment="center" valignment="top" usebox="none">
33824 \begin_layout Plain Layout
33827 arg "math-macro-make-nonoptional"
33835 <cell alignment="center" valignment="top" usebox="none">
33838 \begin_layout Plain Layout
33841 Edit\SpecialChar menuseparator
33842 Math\SpecialChar menuseparator
33844 \begin_inset space ~
33847 Definition\SpecialChar menuseparator
33848 Transform Last Optional to
33849 \begin_inset Newline newline
33853 \begin_inset Phantom HPhantom
33856 \begin_layout Plain Layout
33859 Edit\SpecialChar menuseparator
33860 Math\SpecialChar menuseparator
33862 \begin_inset space ~
33865 Definition\SpecialChar menuseparator
33871 Non-Optional Argument
33877 <row interlinespace="2.5mm">
33878 <cell alignment="center" valignment="top" usebox="none">
33881 \begin_layout Plain Layout
33884 arg "math-macro-remove-optional-param"
33892 <cell alignment="center" valignment="top" usebox="none">
33895 \begin_layout Plain Layout
33898 Edit\SpecialChar menuseparator
33899 Math\SpecialChar menuseparator
33901 \begin_inset space ~
33904 Definition\SpecialChar menuseparator
33905 Remove Optional Argument
33911 <row interlinespace="2.5mm">
33912 <cell alignment="center" valignment="top" usebox="none">
33915 \begin_layout Plain Layout
33918 arg "math-macro-add-optional-param"
33926 <cell alignment="center" valignment="top" usebox="none">
33929 \begin_layout Plain Layout
33932 Edit\SpecialChar menuseparator
33933 Math\SpecialChar menuseparator
33935 \begin_inset space ~
33938 Definition\SpecialChar menuseparator
33939 Insert Optional Argument
33945 <row interlinespace="2.5mm">
33946 <cell alignment="center" valignment="top" usebox="none">
33949 \begin_layout Plain Layout
33952 arg "math-macro-remove-greedy-param"
33960 <cell alignment="center" valignment="top" usebox="none">
33963 \begin_layout Plain Layout
33966 Edit\SpecialChar menuseparator
33967 Math\SpecialChar menuseparator
33969 \begin_inset space ~
33972 Definition\SpecialChar menuseparator
33973 Remove Last Argument
33974 \begin_inset Newline newline
33978 \begin_inset Phantom HPhantom
33981 \begin_layout Plain Layout
33984 Edit\SpecialChar menuseparator
33985 Math\SpecialChar menuseparator
33987 \begin_inset space ~
33990 Definition\SpecialChar menuseparator
33996 Spitting Out To The Right
34002 <row interlinespace="2.5mm">
34003 <cell alignment="center" valignment="top" usebox="none">
34006 \begin_layout Plain Layout
34009 arg "math-macro-append-greedy-param"
34017 <cell alignment="center" valignment="top" usebox="none">
34020 \begin_layout Plain Layout
34023 Edit\SpecialChar menuseparator
34024 Math\SpecialChar menuseparator
34026 \begin_inset space ~
34029 Definition\SpecialChar menuseparator
34031 \begin_inset Newline newline
34035 \begin_inset Phantom HPhantom
34038 \begin_layout Plain Layout
34041 Edit\SpecialChar menuseparator
34042 Math\SpecialChar menuseparator
34044 \begin_inset space ~
34047 Definition\SpecialChar menuseparator
34053 Eating From The Right
34059 <row interlinespace="2.5mm">
34060 <cell alignment="center" valignment="top" usebox="none">
34063 \begin_layout Plain Layout
34066 arg "math-macro-add-greedy-optional-param"
34074 <cell alignment="center" valignment="top" usebox="none">
34077 \begin_layout Plain Layout
34080 Edit\SpecialChar menuseparator
34081 Math\SpecialChar menuseparator
34083 \begin_inset space ~
34086 Definition\SpecialChar menuseparator
34087 Append Optional Argument
34088 \begin_inset Newline newline
34092 \begin_inset Phantom HPhantom
34095 \begin_layout Plain Layout
34098 Edit\SpecialChar menuseparator
34099 Math\SpecialChar menuseparator
34101 \begin_inset space ~
34104 Definition\SpecialChar menuseparator
34110 Eating From The Right
34123 \begin_layout Section
34124 Computer Algebra Systems
34127 \begin_layout Standard
34129 offers the exchange between mathematical expressions written in \SpecialChar LyX
34131 editor and external applications or user defined scripts.
34132 Currently supported applications are
34149 Note that the set of supported mathematical constructs is limited only
34150 to very simple cases.
34153 \begin_layout Subsection
34157 \begin_layout Standard
34158 Write some expression in a formula, go to the
34160 Edit\SpecialChar menuseparator
34161 Math\SpecialChar menuseparator
34162 Use Computer Algebra System
34164 menu and choose the application you have installed on the computer.
34165 After that the result of computation should show on the right side of the
34166 expression together with the
34167 \begin_inset Quotes eld
34171 \begin_inset Quotes erd
34177 \begin_layout Standard
34178 Here are few simple examples (with results from
34182 ) to show what kind of computations can be performed:
34185 \begin_layout Itemize
34186 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34192 \begin_layout Itemize
34193 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34199 \begin_layout Itemize
34200 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34206 \begin_layout Itemize
34207 \begin_inset Formula $\det\left[\begin{array}{ccc}
34211 \end{array}\right]=-56$
34217 \begin_layout Itemize
34218 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34224 \begin_layout Subsection
34228 \begin_layout Standard
34229 Currently there is no keyboard shortcut for calling the algebra applications.
34230 One can easily bind a shortcut to the
34244 \begin_inset space \thinspace{}
34248 \begin_inset space \space{}
34255 key inside the math editor.
34260 one would use this shortcut definition command:
34263 \begin_layout Standard
34266 command-alternatives paragraph-break;math-extern maxima
34269 \begin_layout Section
34271 \begin_inset Index idx
34274 \begin_layout Plain Layout
34283 \begin_layout Subsection
34285 \begin_inset Index idx
34288 \begin_layout Plain Layout
34297 \begin_layout Standard
34298 Negative numbers often look ugly in formulas because the minus sign before
34299 the number is set with the same length as the minus operator sign.
34300 When writing the negative number in normal text, the minus sign appears
34304 \begin_layout Standard
34305 Thus, the problem disappears when converting the minus sign to mathematical
34309 \begin_layout Standard
34310 An example to visualize the problem:
34311 \begin_inset Separator parbreak
34317 \begin_layout Standard
34319 \begin_inset Tabular
34320 <lyxtabular version="3" rows="3" columns="2">
34321 <features booktabs="true" tabularvalignment="middle">
34322 <column alignment="right" valignment="top" width="0pt">
34323 <column alignment="left" valignment="top">
34325 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34328 \begin_layout Plain Layout
34334 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34337 \begin_layout Plain Layout
34345 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34348 \begin_layout Plain Layout
34354 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34357 \begin_layout Plain Layout
34358 \begin_inset Formula $x=-2$
34368 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34371 \begin_layout Plain Layout
34377 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34380 \begin_layout Plain Layout
34381 \begin_inset Formula $x=\textrm{-}2$
34397 \begin_layout Subsection
34398 Comma as decimal Separator
34399 \begin_inset Index idx
34402 \begin_layout Plain Layout
34411 \begin_layout Standard
34412 In \SpecialChar LaTeX
34413 a comma inside a formula is used, according to the English convention,
34414 as number group separator.
34415 So there will be space added behind all commas in formulas.
34418 \begin_layout Standard
34419 To avoid this, the comma is highlighted and changed to mathematical text
34429 \begin_layout Standard
34430 To use all formula commas in the document as decimal separator, the file
34439 \begin_layout Plain Layout
34444 is part of the \SpecialChar LaTeX
34450 \begin_inset Index idx
34453 \begin_layout Plain Layout
34458 \begin_layout Plain Layout
34478 \begin_inset Index idx
34481 \begin_layout Plain Layout
34487 is loaded with the \SpecialChar LaTeX
34491 \begin_layout Standard
34499 \begin_layout Subsection
34501 \begin_inset CommandInset label
34503 name "subsec:Physical-Vectors"
34508 \begin_inset Index idx
34511 \begin_layout Plain Layout
34520 \begin_layout Standard
34521 Predefined vectors are offered by the \SpecialChar LaTeX
34527 \begin_inset Index idx
34530 \begin_layout Plain Layout
34536 that is loaded with the \SpecialChar LaTeX
34540 \begin_layout Standard
34548 \begin_layout Standard
34552 \begin_layout Plain Layout
34562 \begin_inset Note Note
34565 \begin_layout Plain Layout
34566 The following table will only be displayed when the \SpecialChar LaTeX
34579 \begin_layout Standard
34580 The following commands are defined:
34581 \begin_inset Separator parbreak
34587 \begin_layout Standard
34589 \begin_inset Tabular
34590 <lyxtabular version="3" rows="4" columns="2">
34591 <features booktabs="true" tabularvalignment="middle">
34592 <column alignment="center" valignment="top" width="0pt">
34593 <column alignment="center" valignment="top">
34595 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34598 \begin_layout Plain Layout
34604 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34607 \begin_layout Plain Layout
34615 <cell alignment="center" valignment="top" usebox="none">
34618 \begin_layout Plain Layout
34628 <cell alignment="center" valignment="top" usebox="none">
34631 \begin_layout Plain Layout
34632 \begin_inset Formula $\Bra{\psi}$
34642 <cell alignment="center" valignment="top" usebox="none">
34645 \begin_layout Plain Layout
34655 <cell alignment="center" valignment="top" usebox="none">
34658 \begin_layout Plain Layout
34659 \begin_inset Formula $\Ket{\psi}$
34669 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34672 \begin_layout Plain Layout
34684 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34687 \begin_layout Plain Layout
34688 \begin_inset Formula $\Braket{\psi|\phi}$
34704 \begin_layout Standard
34711 assures that all vertical bars are set in the size of the surrounding brackets:
34712 \begin_inset Formula
34714 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34723 \begin_layout Plain Layout
34733 \begin_inset Note Note
34736 \begin_layout Plain Layout
34737 The following will be displayed when the \SpecialChar LaTeX
34750 \begin_layout Standard
34751 You need to install the \SpecialChar LaTeX
34756 to see the rest of this subsection in the output.
34759 \begin_layout Standard
34763 \begin_layout Plain Layout
34775 \begin_layout Standard
34782 can also be achieved using the command
34788 , that is described in
34789 \begin_inset CommandInset ref
34791 reference "subsec:Automatic-Bracket-Size"
34798 \begin_layout Subsection
34799 Self-defined Fractions
34800 \begin_inset CommandInset label
34802 name "subsec:Self-defined-Fractions"
34807 \begin_inset Index idx
34810 \begin_layout Plain Layout
34811 Fractions ! self-defined
34819 \begin_layout Standard
34820 To define custom commands for fractions, the command
34827 \begin_inset Index idx
34830 \begin_layout Plain Layout
34837 \begin_layout Plain Layout
34851 is used in the following scheme:
34854 \begin_layout Standard
34867 bracket}{fraction bar thickness}{style}
34868 \begin_inset Newline newline
34872 \begin_inset Phantom HPhantom
34875 \begin_layout Plain Layout
34885 {numerator}{denominator}
34888 \begin_layout Standard
34889 The style is a number in the range of 0
34890 \begin_inset space \thinspace{}
34894 \begin_inset space \thinspace{}
34898 \begin_inset Separator parbreak
34904 \begin_layout Standard
34906 \begin_inset Tabular
34907 <lyxtabular version="3" rows="5" columns="2">
34908 <features booktabs="true" tabularvalignment="middle">
34909 <column alignment="center" valignment="top" width="0pt">
34910 <column alignment="center" valignment="top">
34912 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34915 \begin_layout Plain Layout
34921 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34924 \begin_layout Plain Layout
34932 <cell alignment="center" valignment="top" usebox="none">
34935 \begin_layout Plain Layout
34941 <cell alignment="center" valignment="top" usebox="none">
34944 \begin_layout Plain Layout
34945 display style formula
34952 <cell alignment="center" valignment="top" usebox="none">
34955 \begin_layout Plain Layout
34961 <cell alignment="center" valignment="top" usebox="none">
34964 \begin_layout Plain Layout
34972 <cell alignment="center" valignment="top" usebox="none">
34975 \begin_layout Plain Layout
34981 <cell alignment="center" valignment="top" usebox="none">
34984 \begin_layout Plain Layout
34992 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34995 \begin_layout Plain Layout
35001 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35004 \begin_layout Plain Layout
35018 \begin_layout Standard
35019 When no style is given, the size is adjusted to the surrounding environment
35020 like for the command
35029 \begin_layout Standard
35030 When no fraction bar thickness is given, the predefined value of 0.4
35031 \begin_inset space \thinspace{}
35037 \begin_layout Standard
35038 \begin_inset VSpace medskip
35041 For example, the commands
35054 \begin_inset CommandInset ref
35056 reference "subsec:Fractions"
35060 are defined with the commands
35063 \begin_layout Standard
35072 genfrac{}{}{}{0}{#1}{#2}}
35075 \begin_layout Standard
35079 \begin_layout Standard
35088 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35091 \begin_layout Standard
35092 \begin_inset VSpace medskip
35095 To define a fraction where the fraction bar thickness can be given as optional
35096 argument, the following line is inserted to the \SpecialChar LaTeX
35100 \begin_layout Standard
35109 genfrac{}{}{#1}{}{#2}{#3}}
35112 \begin_layout Standard
35114 \begin_inset Formula
35116 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35117 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35122 As one can see, the distance of the numerator and the denominator to the
35123 fraction bar is round about three times the bar thickness.
35126 \begin_layout Subsection
35128 \begin_inset Index idx
35131 \begin_layout Plain Layout
35140 \begin_layout Standard
35141 There are four ways to cancel formulas or parts of formulas:
35144 \begin_layout Standard
35148 \begin_layout Plain Layout
35158 \begin_inset Note Note
35161 \begin_layout Plain Layout
35162 The following table will only be displayed when the \SpecialChar LaTeX
35173 \begin_inset Separator parbreak
35179 \begin_layout Standard
35181 \begin_inset Tabular
35182 <lyxtabular version="3" rows="5" columns="2">
35183 <features booktabs="true" tabularvalignment="middle">
35184 <column alignment="center" valignment="top" width="0pt">
35185 <column alignment="center" valignment="top">
35187 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35190 \begin_layout Plain Layout
35196 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35199 \begin_layout Plain Layout
35207 <cell alignment="center" valignment="top" usebox="none">
35210 \begin_layout Plain Layout
35214 \begin_inset space \textvisiblespace{}
35220 \begin_inset space \textvisiblespace{}
35228 <cell alignment="center" valignment="top" usebox="none">
35231 \begin_layout Plain Layout
35232 \begin_inset Formula $\cancel{\int A=B}$
35241 <row topspace="1.5mm">
35242 <cell alignment="center" valignment="top" usebox="none">
35245 \begin_layout Plain Layout
35249 \begin_inset space \textvisiblespace{}
35255 \begin_inset space \textvisiblespace{}
35263 <cell alignment="center" valignment="top" usebox="none">
35266 \begin_layout Plain Layout
35267 \begin_inset Formula $\bcancel{\int A=B}$
35276 <row topspace="1.5mm">
35277 <cell alignment="center" valignment="top" usebox="none">
35280 \begin_layout Plain Layout
35284 \begin_inset space \textvisiblespace{}
35290 \begin_inset space \textvisiblespace{}
35298 <cell alignment="center" valignment="top" usebox="none">
35301 \begin_layout Plain Layout
35302 \begin_inset Formula $\xcancel{\int A=B}$
35312 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35315 \begin_layout Plain Layout
35319 \begin_inset space \textvisiblespace{}
35325 \begin_inset space \textvisiblespace{}
35329 \begin_inset Formula $\to$
35337 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35340 \begin_layout Plain Layout
35341 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35357 \begin_layout Standard
35364 is especially suitable to visualize the reduction of fractions within formulas:
35365 \begin_inset Formula
35367 \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}}}
35375 \begin_layout Standard
35376 To change the size of
35383 \begin_inset Quotes eld
35387 \begin_inset Quotes erd
35390 value one can add the \SpecialChar LaTeX
35394 \begin_layout Standard
35399 PassOptionsToPackage{option}{cancel}
35402 \begin_layout Standard
35411 which leads to the same size as for the canceled value, or
35415 which makes is it a bit smaller than normal.
35418 \begin_layout Standard
35419 To color the cancellation bar one adds this command as \SpecialChar TeX
35423 \begin_layout Standard
35435 \begin_layout Standard
35440 can be replaced by a color of your choice.
35443 \begin_layout Standard
35447 \begin_layout Plain Layout
35463 \begin_layout Standard
35464 \begin_inset Formula
35466 \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}}}
35474 \begin_layout Standard
35478 \begin_layout Plain Layout
35492 \begin_inset Note Note
35495 \begin_layout Plain Layout
35504 \begin_layout Standard
35505 For further customizations, see the documentation of the package
35510 \begin_inset CommandInset citation
35517 \begin_inset Index idx
35520 \begin_layout Plain Layout
35529 \begin_layout Standard
35533 \begin_layout Plain Layout
35543 \begin_inset Note Note
35546 \begin_layout Plain Layout
35547 The following will be displayed when the \SpecialChar LaTeX
35560 \begin_layout Standard
35561 You need to install the \SpecialChar LaTeX
35566 to see the rest of this subsection in the output.
35569 \begin_layout Standard
35573 \begin_layout Plain Layout
35585 \begin_layout Subsection
35586 Formulas in Section Headings
35587 \begin_inset CommandInset label
35589 name "subsec:Formulas-in-Section"
35594 \begin_inset Index idx
35597 \begin_layout Plain Layout
35598 Formula ! in section headings
35606 \begin_layout Standard
35607 When formulas are used in section headings, the following has to be taken
35611 \begin_layout Standard
35612 \begin_inset Note Greyedout
35615 \begin_layout Plain Layout
35621 \begin_inset Index idx
35624 \begin_layout Plain Layout
35625 Packages ! hyperref
35630 support is enabled in the document settings dialog under
35633 \begin_inset space ~
35638 , PDF-bookmarks are created for every section heading in the table of contents.
35639 If a section heading contains formulas, they are incorrectly displayed
35640 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35649 \begin_layout Standard
35650 Both problems can be solved by inserting at the end of the section heading
35651 a short title with the menu
35653 Insert\SpecialChar menuseparator
35655 \begin_inset space ~
35661 Short titles are used as alternative for multiline section headings to
35662 keep the table of contents clearly arranged.
35663 Only the short title appears in the table of contents and therefore also
35664 in the PDF-bookmark.
35667 \begin_layout Standard
35668 When formulas should be used in the table of contents but
35672 is used, one can use the following command in \SpecialChar TeX
35676 \begin_layout Standard
35681 texorpdfstring{part}{alternative}
35682 \begin_inset Index idx
35685 \begin_layout Plain Layout
35696 \begin_layout Standard
35697 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35698 This can be characters, formulas, footnotes, but also cross-references.
35699 The alternative is used instead of the part for the bookmark.
35702 \begin_layout Standard
35703 Here are two example headings:
35704 \begin_inset VSpace -3mm
35711 \begin_layout Plain Layout
35723 \begin_layout Subsubsection
35724 Heading without formula in table of contents
35725 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35729 \begin_inset Argument 1
35732 \begin_layout Plain Layout
35733 Heading without formula in table of contents
35741 \begin_layout Subsubsection
35742 Heading with formula in table of contents
35746 \begin_layout Plain Layout
35756 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35763 \begin_layout Plain Layout
35773 \begin_layout Standard
35777 \begin_layout Plain Layout
35786 In the first heading a short title was used, in the second one
35795 \begin_layout Standard
35796 To get the same formatting as for the other headings, the complete heading
35805 \begin_layout Plain Layout
35807 \begin_inset CommandInset ref
35809 reference "subsec:Bold-Formulas"
35821 \begin_layout Subsection
35822 Formulas in multi-column Text
35823 \begin_inset Index idx
35826 \begin_layout Plain Layout
35827 Formula ! in multi-column text
35835 \begin_layout Standard
35836 Formulas in multi-column text are often too wide to fit into a column and
35837 thus need to be set over the whole page width.
35838 This is done by using the \SpecialChar LaTeX
35847 \begin_layout Plain Layout
35852 is part of every \SpecialChar LaTeX
35853 standard installation.
35859 \begin_inset Index idx
35862 \begin_layout Plain Layout
35863 Packages ! multicol
35868 , that is loaded with the \SpecialChar LaTeX
35872 \begin_layout Standard
35877 usepackage{multicol}
35880 \begin_layout Standard
35881 \begin_inset Note Greyedout
35884 \begin_layout Plain Layout
35885 Note that in this case the setting
35888 \begin_inset space ~
35895 Document\SpecialChar menuseparator
35901 \begin_inset space ~
35921 \begin_layout Standard
35922 Before the multi-column text the command
35925 \begin_layout Standard
35930 begin{multicols}{column number}
35933 \begin_layout Standard
35934 is written in \SpecialChar TeX
35936 The column number is a number in the range of 2
35937 \begin_inset space \thinspace{}
35941 \begin_inset space \thinspace{}
35945 Before the formula the multi-column text is ended by inserting the command
35948 \begin_layout Standard
35956 \begin_layout Standard
35957 in \SpecialChar TeX
35961 \begin_layout Standard
35962 Due to the command some space is automatically added before the formula.
35964 \begin_inset space \thinspace{}
35967 mm vertical space is inserted before the formula.
35968 When the formula style
35974 \begin_layout Plain Layout
35976 \begin_inset CommandInset ref
35978 reference "sec:Formula-Styles"
35990 \begin_inset space \thinspace{}
35993 mm space is inserted instead.
35996 \begin_layout Standard
35997 As example a multi-column text with a displayed formula:
36000 \begin_layout Standard
36006 \begin_layout Plain Layout
36010 begin{multicols}{2}
36015 Das Spektrum wird fouriertransformiert.
36016 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36017 , Lösungsmittel) zu trennen.
36018 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36019 nun das Aussehen des Ausgangssignals.
36020 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36021 über alle Phasen integrieren muss.
36023 \begin_inset Formula $S$
36026 unser normiertes Ausgangssignal und
36027 \begin_inset Formula $P$
36030 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36034 \begin_layout Plain Layout
36044 \begin_inset VSpace -6mm
36048 \begin_inset Formula
36050 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36059 \begin_layout Plain Layout
36063 begin{multicols}{2}
36069 \begin_inset Formula $S_{0}$
36072 das Signal ohne Gradient ist und die Normierungsbedingung
36073 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36077 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36079 \begin_inset Formula $\nicefrac{\pi}{2}$
36083 \begin_inset space \thinspace{}
36086 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36087 das Signal zusätzlich abschwächt.
36088 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36090 \begin_inset Formula $T_{2}$
36096 \begin_layout Standard
36102 \begin_layout Plain Layout
36114 \begin_layout Subsection
36115 Formulas with Description of Variables
36116 \begin_inset Index idx
36119 \begin_layout Plain Layout
36120 Formula ! with description of variables
36128 \begin_layout Standard
36129 To describe variables within a formula, like in formula
36130 \begin_inset CommandInset ref
36132 reference "eq:within"
36141 \begin_inset Formula $n$
36145 \begin_inset space ~
36148 matrix is used with left aligned columns for the
36149 \begin_inset Formula $n$
36156 \begin_layout Plain Layout
36158 \begin_inset CommandInset ref
36160 reference "sec:Matrices"
36169 To set the description in a smaller size, before the matrix e.
36170 \begin_inset space \thinspace{}
36174 \begin_inset space \space{}
36187 \begin_layout Plain Layout
36189 \begin_inset CommandInset ref
36191 reference "subsec:Font-Sizes"
36203 \begin_layout Standard
36204 When the formula style
36210 \begin_layout Plain Layout
36212 \begin_inset CommandInset ref
36214 reference "sec:Formula-Styles"
36235 \begin_layout Plain Layout
36242 only works in formulas with the style
36247 \begin_inset CommandInset ref
36249 reference "subsec:Variable-Space"
36258 is inserted before and after the matrix to have the same separation of
36259 the matrix from the equation and the side margin.
36262 \begin_layout Standard
36263 When the formula style
36267 is used, the method described in
36268 \begin_inset CommandInset ref
36270 reference "subsec:Flalign-Environment"
36274 is used to indent formulas.
36276 \begin_inset CommandInset ref
36278 reference "eq:within"
36282 consists of five columns where in the first two columns contain the equation,
36283 the third the matrix and the last one an empty \SpecialChar TeX
36285 \begin_inset Formula
36287 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36288 \rho & \textrm{density}\\
36289 V & \textrm{volume}\\
36290 g & \textrm{gravitational acceleration}
36291 \end{array} & & {}\label{eq:within}
36299 \begin_layout Subsection
36300 Upright small Greek Letters
36301 \begin_inset CommandInset label
36303 name "subsec:Upright-small-Greek"
36308 \begin_inset Index idx
36311 \begin_layout Plain Layout
36312 Greek letters ! upright
36320 \begin_layout Standard
36321 Most of the math fonts only provide italic small Greek letters.
36322 But for symbols of elementary particles like pions and neutrinos, upright
36323 Greek letters are needed.
36332 \begin_layout Plain Layout
36337 is part of the \SpecialChar LaTeX
36343 \begin_inset Index idx
36346 \begin_layout Plain Layout
36351 \begin_layout Plain Layout
36371 \begin_inset Index idx
36374 \begin_layout Plain Layout
36380 that is loaded with the \SpecialChar LaTeX
36384 \begin_layout Standard
36389 usepackage{upgreek}
36392 \begin_layout Standard
36398 \begin_layout Plain Layout
36408 \begin_inset Note Note
36411 \begin_layout Plain Layout
36412 The following table will only be displayed when the \SpecialChar LaTeX
36422 They are created when the command for a small Greek letter is started with
36428 For example the command
36435 \begin_inset Formula $\uptau$
36441 \begin_layout Standard
36442 With these commands reactions of elementary particles can be typeset:
36443 \begin_inset Formula
36445 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36453 \begin_layout Standard
36454 The upright letters are more bold and wider than the italic ones.
36455 They should therefore not be used for units like
36456 \begin_inset Quotes eld
36460 \begin_inset Quotes erd
36466 \begin_layout Standard
36470 \begin_layout Plain Layout
36480 \begin_inset Note Note
36483 \begin_layout Plain Layout
36484 The following will be displayed when the \SpecialChar LaTeX
36497 \begin_layout Standard
36498 You need to install the \SpecialChar LaTeX
36503 to see the rest of this subsection in the output.
36506 \begin_layout Standard
36510 \begin_layout Plain Layout
36522 \begin_layout Subsection
36523 Text Characters in Formulas
36524 \begin_inset Index idx
36527 \begin_layout Plain Layout
36536 \begin_layout Standard
36537 In some cases you might want to insert text characters directly into formulas.
36538 When for example the centered dot · is often used in formulas like
36539 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36542 , one would have to insert the command
36552 \begin_layout Plain Layout
36554 \begin_inset CommandInset ref
36556 reference "subsec:Binary-Operators"
36565 all the time, because this character is defined in all encodings as text
36567 But the encoding can be changed by this \SpecialChar LaTeX
36571 \begin_layout Standard
36576 Declare Inputtext{183}{
36586 f\SpecialChar ligaturebreak
36590 \begin_layout Standard
36591 The character encoding (menu
36593 Document\SpecialChar menuseparator
36594 Settings\SpecialChar menuseparator
36597 ) specifies what character appears when a keyboard key is pressed.
36598 When the key for the character '·' is pressed, internally the command
36605 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36607 With the changed encoding the right command is chosen automatically, depending
36608 on if the character was inserted into a formula or not.
36611 \begin_layout Standard
36612 The encoding of several characters is saved in definition files.
36613 For example the encoding
36617 is defined in the file
36621 which is in the installation folder of \SpecialChar LaTeX
36623 Encodings should only be changed via the \SpecialChar LaTeX
36624 -preamble and not in the definition
36626 Otherwise documents could not be edited by other \SpecialChar LyX
36627 users working on other
36631 \begin_layout Standard
36632 \begin_inset VSpace medskip
36635 Besides the centered dot, in this document the degree sign ° is defined
36636 with the following \SpecialChar LaTeX
36637 -preamble line so that it can be directly inserted into
36641 \begin_layout Standard
36646 DeclareInputtext{176}{
36656 f\SpecialChar ligaturebreak
36660 \begin_layout Subsection
36662 -comments in formulas
36663 \begin_inset Index idx
36666 \begin_layout Plain Layout
36676 \begin_layout Standard
36677 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36679 code of your file with the menu
36681 Insert\SpecialChar menuseparator
36682 Note\SpecialChar menuseparator
36686 This is not possible in a formula but you can insert \SpecialChar LaTeX
36691 \begin_layout Standard
36699 \begin_layout Standard
36700 This creates a box in which you can write your comment.
36701 Due to a bug in \SpecialChar LyX
36706 \begin_layout Plain Layout
36707 \begin_inset CommandInset href
36709 name "LyX-bug #9002"
36710 target "http://www.lyx.org/trac/ticket/9002"
36719 you cannot write normal text inside the comment, even when you use mathematical
36720 text, you will see its \SpecialChar LaTeX
36721 -commands in the \SpecialChar LaTeX
36723 \begin_inset Newline newline
36726 This a formula with a \SpecialChar LaTeX
36728 \begin_inset Formula
36730 A=B%\text{This is the comment}
36738 \begin_layout Standard
36739 \begin_inset Newpage newpage
36745 \begin_layout Section
36748 \begin_inset Index idx
36751 \begin_layout Plain Layout
36760 \begin_layout Standard
36761 This section is a summary of the most important typographic rules, listed
36766 \begin_layout Plain Layout
36767 This collection was partly taken from the German semi-official dictionary
36769 \begin_inset Quotes eld
36773 \begin_inset Quotes erd
36777 \begin_inset CommandInset citation
36783 that lists some of the ISO rules.
36784 More rules are listed in
36785 \begin_inset CommandInset citation
36799 \begin_layout Itemize
36808 \begin_layout Plain Layout
36809 done with font styles, see
36810 \begin_inset CommandInset ref
36812 reference "subsec:Font-Styles"
36821 , no matter if they appear in italic text: 30
36822 \begin_inset space \thinspace{}
36826 \begin_inset Newline newline
36829 Between the value and the unit is the smallest space, see
36830 \begin_inset CommandInset ref
36832 reference "subsec:Predefined-Space"
36837 \begin_inset Newline newline
36840 This convention is automatically fulfilled when the command
36847 When it is entered to a formula, two boxes appear.
36848 In the first one the value is inserted, in the second one the unit, and
36850 \begin_inset Formula $\unit[30]{km/h}$
36854 \begin_inset space \thinspace{}
36864 is not a real \SpecialChar LaTeX
36865 command but the command
36871 , therefore you cannot use it in \SpecialChar TeX
36875 \begin_layout Itemize
36876 Percent and perthousand signs are set like physical units:
36877 \begin_inset Newline newline
36881 \begin_inset space \thinspace{}
36887 \begin_layout Itemize
36888 The degree sign follows directly on the value: 15°, but not when it is used
36890 \begin_inset space \thinspace{}
36896 \begin_layout Itemize
36897 In numbers with more than four digits the smallest space is inserted before
36898 every third digit to group them:
36908 \begin_inset space \thinspace{}
36912 \begin_inset space \thinspace{}
36918 \begin_layout Itemize
36919 For dimensions like 120×90×40
36920 \begin_inset space \thinspace{}
36923 cm the multiplication sign
36924 \begin_inset Quotes eld
36928 \begin_inset Quotes erd
36932 It is available either via the command
36940 Insert\SpecialChar menuseparator
36941 Special Character\SpecialChar menuseparator
36947 \begin_layout Itemize
36948 Functions with names consisting of several letters are set upright to avoid
36950 \begin_inset CommandInset ref
36952 reference "subsec:Predefined-Functions"
36959 \begin_layout Itemize
36960 Indices consisting of several letters, are set upright:
36961 \begin_inset Formula $E_{\mathrm{kin}}$
36965 \begin_inset Newline newline
36968 Components of matrices are set italic:
36969 \begin_inset Formula $\hat{H}_{kl}$
36975 \begin_layout Itemize
36976 The differentiation/integration operator 'd', the Euler's number 'e' and
36977 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36981 \begin_layout Itemize
36982 The character that denotes a
36986 transformation is inserted either by the command
36991 \begin_inset space \textvisiblespace{}
36998 Insert\SpecialChar menuseparator
36999 Special Character\SpecialChar menuseparator
37000 Symbols\SpecialChar menuseparator
37002 \begin_inset space ~
37008 \begin_inset Formula $\mathscr{F}$
37014 \begin_layout Standard
37015 \begin_inset Newpage newpage
37021 \begin_layout Section
37023 \begin_inset Index idx
37026 \begin_layout Plain Layout
37035 \begin_layout Standard
37036 Some characters and symbols can be created with several commands.
37037 Here is a list of the synonym commands:
37040 \begin_layout Standard
37041 \begin_inset VSpace bigskip
37045 \begin_inset space \hfill{}
37049 \begin_inset Tabular
37050 <lyxtabular version="3" rows="12" columns="2">
37051 <features booktabs="true" tabularvalignment="middle">
37052 <column alignment="center" valignment="top" width="0pt">
37053 <column alignment="center" valignment="top" width="0pt">
37055 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37058 \begin_layout Plain Layout
37064 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37067 \begin_layout Plain Layout
37075 <cell alignment="center" valignment="top" usebox="none">
37078 \begin_layout Plain Layout
37086 <cell alignment="center" valignment="top" usebox="none">
37089 \begin_layout Plain Layout
37097 <cell alignment="center" valignment="top" usebox="none">
37100 \begin_layout Plain Layout
37108 <cell alignment="center" valignment="top" usebox="none">
37111 \begin_layout Plain Layout
37121 <cell alignment="center" valignment="top" usebox="none">
37124 \begin_layout Plain Layout
37132 <cell alignment="center" valignment="top" usebox="none">
37135 \begin_layout Plain Layout
37145 <cell alignment="center" valignment="top" usebox="none">
37148 \begin_layout Plain Layout
37156 <cell alignment="center" valignment="top" usebox="none">
37159 \begin_layout Plain Layout
37167 <cell alignment="center" valignment="top" usebox="none">
37170 \begin_layout Plain Layout
37178 <cell alignment="center" valignment="top" usebox="none">
37181 \begin_layout Plain Layout
37189 <cell alignment="center" valignment="top" usebox="none">
37192 \begin_layout Plain Layout
37200 <cell alignment="center" valignment="top" usebox="none">
37203 \begin_layout Plain Layout
37213 <cell alignment="center" valignment="top" usebox="none">
37216 \begin_layout Plain Layout
37224 <cell alignment="center" valignment="top" usebox="none">
37227 \begin_layout Plain Layout
37237 <cell alignment="center" valignment="top" usebox="none">
37240 \begin_layout Plain Layout
37248 <cell alignment="center" valignment="top" usebox="none">
37251 \begin_layout Plain Layout
37261 <cell alignment="center" valignment="top" usebox="none">
37264 \begin_layout Plain Layout
37272 <cell alignment="center" valignment="top" usebox="none">
37275 \begin_layout Plain Layout
37285 <cell alignment="center" valignment="top" usebox="none">
37288 \begin_layout Plain Layout
37296 <cell alignment="center" valignment="top" usebox="none">
37299 \begin_layout Plain Layout
37307 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37310 \begin_layout Plain Layout
37318 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37321 \begin_layout Plain Layout
37333 \begin_inset space \hfill{}
37337 \begin_inset Tabular
37338 <lyxtabular version="3" rows="12" columns="2">
37339 <features booktabs="true" tabularvalignment="middle">
37340 <column alignment="center" valignment="top" width="0pt">
37341 <column alignment="center" valignment="top" width="0pt">
37343 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37346 \begin_layout Plain Layout
37352 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37355 \begin_layout Plain Layout
37363 <cell alignment="center" valignment="top" usebox="none">
37366 \begin_layout Plain Layout
37374 <cell alignment="center" valignment="top" usebox="none">
37377 \begin_layout Plain Layout
37389 <cell alignment="center" valignment="top" usebox="none">
37392 \begin_layout Plain Layout
37400 <cell alignment="center" valignment="top" usebox="none">
37403 \begin_layout Plain Layout
37413 <cell alignment="center" valignment="top" usebox="none">
37416 \begin_layout Plain Layout
37424 <cell alignment="center" valignment="top" usebox="none">
37427 \begin_layout Plain Layout
37437 <cell alignment="center" valignment="top" usebox="none">
37440 \begin_layout Plain Layout
37448 <cell alignment="center" valignment="top" usebox="none">
37451 \begin_layout Plain Layout
37459 <cell alignment="center" valignment="top" usebox="none">
37462 \begin_layout Plain Layout
37470 <cell alignment="center" valignment="top" usebox="none">
37473 \begin_layout Plain Layout
37481 <cell alignment="center" valignment="top" usebox="none">
37484 \begin_layout Plain Layout
37492 <cell alignment="center" valignment="top" usebox="none">
37495 \begin_layout Plain Layout
37505 <cell alignment="center" valignment="top" usebox="none">
37508 \begin_layout Plain Layout
37516 <cell alignment="center" valignment="top" usebox="none">
37519 \begin_layout Plain Layout
37529 <cell alignment="center" valignment="top" usebox="none">
37532 \begin_layout Plain Layout
37540 <cell alignment="center" valignment="top" usebox="none">
37543 \begin_layout Plain Layout
37553 <cell alignment="center" valignment="top" usebox="none">
37556 \begin_layout Plain Layout
37564 <cell alignment="center" valignment="top" usebox="none">
37567 \begin_layout Plain Layout
37577 <cell alignment="center" valignment="top" usebox="none">
37580 \begin_layout Plain Layout
37588 <cell alignment="center" valignment="top" usebox="none">
37591 \begin_layout Plain Layout
37601 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37604 \begin_layout Plain Layout
37612 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37615 \begin_layout Plain Layout
37629 \begin_inset space \hfill{}
37635 \begin_layout Standard
37636 \begin_inset Newpage newpage
37642 \begin_layout Bibliography
37643 \begin_inset CommandInset bibitem
37644 LatexCommand bibitem
37656 The \SpecialChar LaTeX
37660 Addison Wesley, 2004
37663 \begin_layout Bibliography
37664 \begin_inset CommandInset bibitem
37665 LatexCommand bibitem
37671 \begin_inset CommandInset href
37674 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37678 of \SpecialChar LaTeX
37682 \begin_layout Bibliography
37683 \begin_inset CommandInset bibitem
37684 LatexCommand bibitem
37690 \begin_inset CommandInset href
37693 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37701 \begin_layout Plain Layout
37710 -\SpecialChar LaTeX
37714 \begin_layout Bibliography
37715 \begin_inset CommandInset bibitem
37716 LatexCommand bibitem
37722 \begin_inset CommandInset href
37725 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37729 of all symbols available with \SpecialChar LaTeX
37733 \begin_layout Bibliography
37734 \begin_inset CommandInset bibitem
37735 LatexCommand bibitem
37741 \begin_inset CommandInset href
37743 name "Documentation"
37744 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37748 of the \SpecialChar LaTeX
37754 \begin_inset Index idx
37757 \begin_layout Plain Layout
37766 \begin_layout Bibliography
37767 \begin_inset CommandInset bibitem
37768 LatexCommand bibitem
37774 \begin_inset CommandInset href
37776 name "Documentation"
37777 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37781 of the \SpecialChar LaTeX
37787 \begin_inset Index idx
37790 \begin_layout Plain Layout
37791 Packages ! hyperref
37799 \begin_layout Bibliography
37800 \begin_inset CommandInset bibitem
37801 LatexCommand bibitem
37807 \begin_inset CommandInset href
37809 name "Documentation"
37810 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37814 of the \SpecialChar LaTeX
37820 \begin_inset Index idx
37823 \begin_layout Plain Layout
37832 \begin_layout Bibliography
37833 \begin_inset CommandInset bibitem
37834 LatexCommand bibitem
37845 Auflage, Duden 2001
37848 \begin_layout Bibliography
37849 \begin_inset CommandInset bibitem
37850 LatexCommand bibitem
37856 \begin_inset CommandInset href
37859 target "http://physics.nist.gov/Document/checklist.pdf"
37863 for reviewing manuscripts
37866 \begin_layout Standard
37867 \begin_inset CommandInset index_print
37868 LatexCommand printindex