1 #LyX 2.3 created this file. For more info see http://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/doc/
9 % DO NOT ALTER THIS PREAMBLE!!!
11 % This preamble is designed to ensure that the file prints
12 % out as advertised. If you mess with this preamble,
13 % parts of this document may not print out as expected. If you
14 % have problems LaTeXing this file, please contact
15 % the documentation team
16 % email: lyx-docs@lists.lyx.org
18 % solves the following problem:
19 % If the dection number consits of too many numerals the section heading
20 % will be printed in the TOC without a space between it and the section number.
21 % As solution more space between the number and the heading is inserted:
22 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
23 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
25 % increase link area for cross-references and autoname them,
26 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
27 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
28 \@ifpackageloaded{babel}{
29 \addto\extrasenglish{%
30 \renewcommand*{\equationautorefname}[1]{}%
31 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
32 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
33 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
37 % don't load packages twice
38 % see first footnote in sec. 9.3
39 \@ifundefined{textcolor}{\usepackage{color}}{}
41 % the pages of the TOC are numbered roman
42 % and a PDF-bookmark for the TOC is added
44 \let\myTOC\tableofcontents
45 \renewcommand{\tableofcontents}{%
47 \pdfbookmark[1]{\contentsname}{}
50 \pagenumbering{arabic}}
52 % add 0.5 mm vertical space for table rows
53 \@ifundefined{extrarowheight} {\usepackage{array}}{}
54 \setlength{\extrarowheight}{0.5mm}
56 % insert additional vertical space of 1.5 mm between footnotes,
58 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
60 % makes caption labels bold
61 \setkomafont{captionlabel}{\bfseries}
63 % enables calculation of values
66 % for multiple columns used in sec. 24.7
72 % for the Fourier transformation symbol
75 % define a color, used in sec.9.3
76 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
78 % declare operators (see sec. 10.4 and sec. 15.2)
79 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
80 \DeclareMathOperator{\sgn}{sgn}
82 % example definitions for sec. 20.1
83 \newcommand{\gr}{\Longrightarrow}
84 \newcommand{\us}[1]{\underline{#1}}
85 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
86 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
87 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
89 % example macro from sec. 19.4
90 %\def\tagform@#1{\maketag@@@{|#1|}}
93 % ------------------------------------
94 % used to check for needed LaTeX packages
97 % check for package undertilde
98 % used for the command \utilde
99 \newboolean{undertilde}
100 \IfFileExists{undertilde.sty}
101 {\usepackage{undertilde}
102 \setboolean{undertilde}{true}}
103 {\setboolean{undertilde}{false}}
105 % check for package eurosym
106 % used for the Euro symbol
108 \IfFileExists{eurosym.sty}
109 {\usepackage[gennarrow]{eurosym}
110 \setboolean{eurosym}{true}}
111 {\setboolean{eurosym}{false}}
113 % check for package braket
114 % used for physical vectors
116 \IfFileExists{braket.sty}
118 \setboolean{braket}{true}}
119 {\setboolean{braket}{false}}
121 % check for package cancel
123 \IfFileExists{cancel.sty}
125 \setboolean{cancel}{true}}
126 {\setboolean{cancel}{false}}
128 % check for package upgreek
130 \IfFileExists{upgreek.sty}
131 {\usepackage{upgreek}
132 \setboolean{upgreek}{true}}
133 {\setboolean{upgreek}{false}}
135 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
136 \use_default_options false
140 \maintain_unincluded_children false
142 \language_package default
145 \font_roman "lmodern" "default"
146 \font_sans "lmss" "default"
147 \font_typewriter "lmtt" "default"
148 \font_math "auto" "auto"
149 \font_default_family default
150 \use_non_tex_fonts false
153 \font_sf_scale 100 100
154 \font_tt_scale 100 100
156 \use_dash_ligatures false
158 \default_output_format pdf2
160 \bibtex_command default
161 \index_command default
165 \pdf_title "LyX's Math Manual"
166 \pdf_author "LyX Team, Uwe Stöhr"
167 \pdf_subject "LyX-documentation about math"
168 \pdf_keywords "LyX, Mathed"
170 \pdf_bookmarksnumbered true
171 \pdf_bookmarksopen true
172 \pdf_bookmarksopenlevel 1
173 \pdf_breaklinks false
177 \pdf_pdfusetitle false
178 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
181 \use_package amsmath 2
182 \use_package amssymb 2
183 \use_package cancel 1
185 \use_package mathdots 1
186 \use_package mathtools 2
187 \use_package mhchem 1
188 \use_package stackrel 1
189 \use_package stmaryrd 1
190 \use_package undertilde 0
192 \cite_engine_type default
196 \paperorientation portrait
201 \notefontcolor #0000ff
208 \paragraph_separation skip
211 \math_numbering_side default
212 \quotes_style english
216 \paperpagestyle plain
220 \tracking_changes false
221 \output_changes false
224 \html_be_strict false
231 's detailed Math manual
235 by the \SpecialChar LyX
240 \begin_layout Plain Layout
242 If you have comments or error corrections, please send them to the \SpecialChar LyX
247 \begin_inset CommandInset href
249 name "lyx-docs@lists.lyx.org"
250 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
262 \begin_inset Note Note
265 \begin_layout Plain Layout
272 \begin_inset Newline newline
276 \begin_inset Newline newline
284 \begin_layout Standard
285 \begin_inset CommandInset toc
286 LatexCommand tableofcontents
293 \begin_layout Standard
294 \begin_inset Note Note
297 \begin_layout Plain Layout
298 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
301 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
308 If they are not installed the document can be exported anyway but the sections
309 where the packages are required will not appear in the output.
314 ; if it is not installed, this file cannot be exported.
317 \begin_layout Plain Layout
318 The latest PDF-version of this document can be found here:
319 \begin_inset Newline newline
324 http://wiki.lyx.org/LyX/Manuals#Math
332 \begin_layout Standard
333 \begin_inset Newpage newpage
339 \begin_layout Section
343 \begin_layout Standard
344 This document explains \SpecialChar LyX
345 's math features and is furthermore a collection
346 of \SpecialChar LaTeX
347 -commands used for mathematical characters and constructs.
348 The explanations are designed for the usage of commands.
349 It is therefore required that you have read the section
360 \begin_layout Standard
361 Most of the characters and many constructs explained in this manual are
362 also accessible via the menu
366 \SpecialChar menuseparator
382 But everybody who has to write lots of formulas will notice that it is
383 much faster to use commands instead of the math toolbar.
384 Therefore this manual is focused on commands but also mentions the correspondin
385 g toolbar buttons when available.
388 \begin_layout Standard
389 If not specially mentioned the commands are only available within formulas.
390 To be able to use all commands explained in this document, the option
394 must be checked in the document settings (menu
396 Document\SpecialChar menuseparator
397 Settings\SpecialChar menuseparator
408 \begin_layout Plain Layout
411 Use AMS math package automatically
417 \begin_layout Plain Layout
426 -math when math constructs are found that are supported by \SpecialChar LyX
435 \begin_layout Standard
436 This document doesn't list all
440 \begin_layout Plain Layout
453 \begin_layout Plain Layout
458 \begin_layout Plain Layout
467 -math commands is in the file
470 \begin_inset CommandInset href
473 target "http://mirrors.ctan.org/macros/amstex/doc/amsguide.pdf"
480 , which is part of every \SpecialChar LaTeX
481 standard installation.
486 for lucidity reasons.
489 \begin_layout Section
493 \begin_layout Standard
494 To create an inline formula
495 \begin_inset Index idx
498 \begin_layout Plain Layout
504 that is embedded into a text line, use one of the shortcuts
510 or the toolbar button
517 \begin_inset Newline newline
520 To create a display style formula
521 \begin_inset Index idx
524 \begin_layout Plain Layout
525 Formula ! display style
530 which will appear bigger, has a different format, and will be in a separate
531 paragraph, use one of these shortcuts:
540 \begin_layout Standard
541 To change a display style formula to an inline formula, set the cursor into
542 the formula and use one of the shortcuts
550 Edit\SpecialChar menuseparator
551 Math\SpecialChar menuseparator
555 The same way is used to change an inline formula to a display style formula.
558 \begin_layout Standard
559 To display parts of an inline formula in the size of a display style formula,
567 \begin_inset Index idx
570 \begin_layout Plain Layout
579 Then a new blue box appears in which the desired formula part is inserted.
582 \begin_layout Standard
583 Only inline formulas are allowed inside tables.
586 \begin_layout Standard
591 can be turned on in the menu
593 View\SpecialChar menuseparator
597 When you click there on
598 \begin_inset Quotes eld
602 \begin_inset Quotes erd
605 the toolbar will be shown permanently at the bottom; this state is visualized
610 menu with a checkmark.
611 When you click in this state again on
612 \begin_inset Quotes eld
616 \begin_inset Quotes erd
627 is only shown when the cursor is within a formula; this state is visualized
628 by the renaming of the menu entry from
629 \begin_inset Quotes eld
633 \begin_inset Quotes erd
637 \begin_inset Quotes eld
645 \begin_inset Quotes erd
651 \begin_layout Standard
654 \begin_inset Index idx
657 \begin_layout Plain Layout
664 is invoked by pressing the toolbar button
672 Insert\SpecialChar menuseparator
684 \begin_layout Standard
685 To change the \SpecialChar LaTeX
687 \begin_inset Index idx
690 \begin_layout Plain Layout
699 Document\SpecialChar menuseparator
700 Settings\SpecialChar menuseparator
710 \begin_layout Standard
711 To edit matrices, case differentiations and multiline formulas subsequently,
714 Edit\SpecialChar menuseparator
719 Edit\SpecialChar menuseparator
721 \begin_inset space \thinspace{}
725 \begin_inset space \thinspace{}
735 When lines and columns are swapped via the menu, the column or line where
736 the cursor is in is exchanged with the column to the right or the line
738 Is the cursor in the last column or row, the exchange is done with the
739 column to the left or the line above.
742 \begin_layout Standard
743 To write text in formulas
747 \begin_layout Plain Layout
748 For multiline formulas the command
755 \begin_inset CommandInset ref
757 reference "subsec:Text-in-multiline"
771 \begin_inset Index idx
774 \begin_layout Plain Layout
781 \begin_inset Index idx
784 \begin_layout Plain Layout
791 This mode is invoked with the shortcut
797 or by the insertion of the command
804 \begin_inset Index idx
807 \begin_layout Plain Layout
816 The text appears black in \SpecialChar LyX
817 and can therefore be distinguished from the
818 other formula parts which appear blue.
819 In the output mathematical text is set upright, in contrary to other formula
823 \begin_layout Subsection*
827 \begin_layout Standard
828 Most of the \SpecialChar LaTeX
829 -commands for math constructs have the following scheme:
832 \begin_layout Standard
848 \begin_layout Standard
849 A command always starts with a backslash
850 \begin_inset Quotes gld
860 \begin_inset Quotes grd
864 To omit optional arguments, also omit the associated brackets.
865 The braces around the required arguments are named in this document as
868 \begin_inset Index idx
871 \begin_layout Plain Layout
879 If you add in a formula a left brace to a command name, \SpecialChar LyX
881 creates a \SpecialChar TeX
883 In all other cases \SpecialChar TeX
884 braces are created in formulas with the command
892 braces appear red in \SpecialChar LyX
893 , in contrary to normal braces which appear blue.
895 mode no command is needed to get \SpecialChar TeX
898 braces don't appear in the output.
901 \begin_layout Standard
902 When commands without arguments, like commands for symbols are entered in
904 mode, a space character must
908 be behind the command to end it.
909 This space doesn't appear in the output.
910 When the space should appear in the output, the space must be followed
911 by a protected space in normal text.
914 \begin_layout Standard
915 A protected space is inserted with
918 arg "command-alternatives space-insert protected ; math-space"
924 \begin_layout Subsection*
925 \begin_inset Newpage newpage
931 \begin_layout Itemize
933 \begin_inset space \textvisiblespace{}
936 denotes a space character to be input.
939 \begin_layout Itemize
941 \begin_inset Formula $\to$
944 denotes the usage of the corresponding arrow key on the keyboard.
949 key can often be used instead of
950 \begin_inset Formula $\to$
954 \begin_inset Formula $\downarrow$
962 \begin_inset Formula $\leftarrow$
966 \begin_inset Formula $\uparrow$
972 \begin_layout Subsection*
976 \begin_layout Standard
978 \begin_inset Float table
984 \begin_layout Plain Layout
986 \begin_inset Caption Standard
988 \begin_layout Plain Layout
989 \begin_inset CommandInset label
991 name "tab:Available-units"
1003 \begin_layout Plain Layout
1005 \begin_inset Tabular
1006 <lyxtabular version="3" rows="13" columns="2">
1007 <features booktabs="true" tabularvalignment="middle">
1008 <column alignment="center" valignment="top">
1009 <column alignment="center" valignment="top" width="0pt">
1011 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1014 \begin_layout Plain Layout
1020 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1023 \begin_layout Plain Layout
1031 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1034 \begin_layout Plain Layout
1040 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1043 \begin_layout Plain Layout
1051 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1054 \begin_layout Plain Layout
1060 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1063 \begin_layout Plain Layout
1071 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1074 \begin_layout Plain Layout
1080 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1083 \begin_layout Plain Layout
1085 \begin_inset space \thinspace{}
1089 \begin_inset space \thinspace{}
1099 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1102 \begin_layout Plain Layout
1108 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1111 \begin_layout Plain Layout
1113 \begin_inset space \thinspace{}
1117 \begin_inset space \thinspace{}
1127 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1130 \begin_layout Plain Layout
1136 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1139 \begin_layout Plain Layout
1141 \begin_inset space \thinspace{}
1145 \begin_inset space \thinspace{}
1155 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1158 \begin_layout Plain Layout
1164 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1167 \begin_layout Plain Layout
1169 \begin_inset space \thinspace{}
1173 \begin_inset space \thinspace{}
1183 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1186 \begin_layout Plain Layout
1192 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1195 \begin_layout Plain Layout
1197 \begin_inset space \thinspace{}
1201 \begin_inset space \thinspace{}
1211 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1214 \begin_layout Plain Layout
1220 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1223 \begin_layout Plain Layout
1225 \begin_inset space \thinspace{}
1229 \begin_inset Formula $\approx$
1233 \begin_inset space \thinspace{}
1243 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1246 \begin_layout Plain Layout
1252 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1255 \begin_layout Plain Layout
1257 \begin_inset space \thinspace{}
1261 \begin_inset space \thinspace{}
1271 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1274 \begin_layout Plain Layout
1280 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1283 \begin_layout Plain Layout
1287 \begin_inset Quotes eld
1293 \begin_inset Quotes erd
1303 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1306 \begin_layout Plain Layout
1312 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1315 \begin_layout Plain Layout
1317 \begin_inset Quotes eld
1325 \begin_inset Quotes erd
1335 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1338 \begin_layout Plain Layout
1344 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1347 \begin_layout Plain Layout
1349 \begin_inset space \thinspace{}
1353 \begin_inset Formula $\nicefrac{1}{18}$
1357 \begin_inset space \thinspace{}
1378 \begin_layout Standard
1379 \begin_inset Newpage newpage
1385 \begin_layout Section
1389 \begin_layout Subsection
1391 \begin_inset Index idx
1394 \begin_layout Plain Layout
1401 \begin_inset Index idx
1404 \begin_layout Plain Layout
1411 \begin_inset Index idx
1414 \begin_layout Plain Layout
1419 \begin_layout Plain Layout
1430 \begin_layout Plain Layout
1443 \begin_inset Index idx
1446 \begin_layout Plain Layout
1451 \begin_layout Plain Layout
1462 \begin_layout Plain Layout
1477 \begin_layout Standard
1478 Indices are created with an underscore
1479 \begin_inset Quotes eld
1483 \begin_inset Quotes erd
1486 or via the math toolbar button
1489 arg "math-subscript"
1492 , exponents with a caret
1493 \begin_inset Quotes eld
1497 \begin_inset Quotes erd
1500 or via the math toolbar button
1503 arg "math-superscript"
1509 \begin_layout Standard
1511 \begin_inset Tabular
1512 <lyxtabular version="3" rows="4" columns="2">
1513 <features booktabs="true" tabularvalignment="middle">
1514 <column alignment="center" valignment="top" width="0pt">
1515 <column alignment="center" valignment="top" width="0pt">
1517 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1520 \begin_layout Plain Layout
1526 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1529 \begin_layout Plain Layout
1537 <cell alignment="center" valignment="top" usebox="none">
1540 \begin_layout Plain Layout
1546 <cell alignment="center" valignment="top" usebox="none">
1549 \begin_layout Plain Layout
1550 \begin_inset Formula $B_{V}$
1559 <row topspace="1.5mm">
1560 <cell alignment="center" valignment="top" usebox="none">
1563 \begin_layout Plain Layout
1569 <cell alignment="center" valignment="top" usebox="none">
1572 \begin_layout Plain Layout
1573 \begin_inset Formula $B^{V}$
1582 <row topspace="1.5mm">
1583 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1586 \begin_layout Plain Layout
1588 \begin_inset space \textvisiblespace{}
1596 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1599 \begin_layout Plain Layout
1600 \begin_inset Formula $B^{A}$
1616 \begin_layout Standard
1617 As the caret is in some languages an accent, vowels will be accentuated
1618 in this case and not set as exponents
1622 \begin_layout Plain Layout
1623 Depending on the used keyboard settings this can also happen for characters
1630 To get exponents in this case, press
1634 after the caret as in the last example.
1637 \begin_layout Subsection
1639 \begin_inset CommandInset label
1641 name "subsec:Fractions"
1646 \begin_inset Index idx
1649 \begin_layout Plain Layout
1658 \begin_layout Standard
1659 Fractions are generated with the command
1666 \begin_inset Index idx
1669 \begin_layout Plain Layout
1677 or via the math toolbar button
1680 arg "math-insert \\frac"
1684 The font size is adjusted automatically, depending on whether the fraction
1685 is in an inline or display style formula.
1686 With the math toolbar button
1689 arg "math-insert \\frac-square"
1692 you can select different fraction types.
1695 \begin_layout Standard
1703 \begin_inset Index idx
1706 \begin_layout Plain Layout
1714 a fraction can be created that always has the size of a display style formula.
1722 \begin_inset Index idx
1725 \begin_layout Plain Layout
1733 the fraction appears always with the size of an inline formula.
1737 \begin_layout Standard
1738 A line with the fraction
1739 \begin_inset Formula $\frac{1}{2}$
1742 that was created with the command
1751 \begin_layout Standard
1752 A line with the fraction
1753 \begin_inset Formula $\dfrac{1}{2}$
1756 that was created with the command
1765 \begin_layout Standard
1767 \begin_inset Tabular
1768 <lyxtabular version="3" rows="4" columns="2">
1769 <features booktabs="true" tabularvalignment="middle">
1770 <column alignment="center" valignment="top" width="0pt">
1771 <column alignment="center" valignment="top" width="0pt">
1773 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1776 \begin_layout Plain Layout
1782 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1785 \begin_layout Plain Layout
1792 <row topspace="1.5mm">
1793 <cell alignment="center" valignment="top" usebox="none">
1796 \begin_layout Plain Layout
1800 \begin_inset space \textvisiblespace{}
1804 \begin_inset Formula $\downarrow$
1812 <cell alignment="center" valignment="top" usebox="none">
1815 \begin_layout Plain Layout
1816 \begin_inset Formula $\frac{A}{B}$
1825 <row topspace="2mm">
1826 <cell alignment="center" valignment="top" usebox="none">
1829 \begin_layout Plain Layout
1833 \begin_inset space \textvisiblespace{}
1837 \begin_inset Formula $\downarrow$
1845 <cell alignment="center" valignment="top" usebox="none">
1848 \begin_layout Plain Layout
1849 \begin_inset Formula $\dfrac{A}{B}$
1858 <row topspace="2mm" bottomspace="1mm">
1859 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1862 \begin_layout Plain Layout
1866 \begin_inset space \textvisiblespace{}
1872 \begin_inset space \textvisiblespace{}
1876 \begin_inset Formula $\downarrow$
1880 \begin_inset Formula $\downarrow\downarrow$
1888 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1891 \begin_layout Plain Layout
1892 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1908 \begin_layout Standard
1909 \begin_inset VSpace bigskip
1913 \begin_inset Newpage newpage
1916 For nested fractions the command
1923 \begin_inset Index idx
1926 \begin_layout Plain Layout
1936 \begin_inset VSpace -3mm
1942 \begin_layout Standard
1943 \begin_inset Formula
1945 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1946 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1954 \begin_layout Standard
1955 The command for the example above is:
1958 \begin_layout Standard
1964 \begin_inset space \textvisiblespace{}
1968 \begin_inset Formula $\downarrow$
1974 \begin_inset space \textvisiblespace{}
1980 \begin_inset space \textvisiblespace{}
1984 \begin_inset Formula $\downarrow$
1988 \begin_inset Formula $\downarrow$
1994 \begin_layout Standard
1995 \begin_inset VSpace medskip
2001 \begin_layout Standard
2008 sets the fraction always in the size of a displayed formula, also when
2009 it is part of another fraction.
2012 \begin_layout Standard
2013 It is possible to specify the alignment of the numerator.
2020 is used to left align it, the command
2033 centers the numerator.
2034 These fractions demonstrate the different alignments:
2037 \begin_layout Standard
2040 \begin_inset Formula
2042 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2050 \begin_layout Standard
2051 \begin_inset Note Greyedout
2054 \begin_layout Plain Layout
2071 are no real \SpecialChar LaTeX
2072 commands but represent the command
2076 cfrac[alignment]{numerator}{denominator}
2079 Therefore you cannot use them in \SpecialChar TeX
2088 \begin_layout Standard
2089 \begin_inset VSpace medskip
2092 It is often advantageous to combine
2105 \begin_inset Formula
2107 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2115 \begin_layout Standard
2116 For inline fractions with a sloped fraction stroke you can use the command
2124 \begin_inset Index idx
2127 \begin_layout Plain Layout
2136 \begin_inset Formula $\nicefrac{5}{31}$
2146 \begin_inset Index idx
2149 \begin_layout Plain Layout
2158 \begin_inset Formula $\unitfrac{5}{31}$
2161 There is furthermore the command
2167 that offers to write a fraction in combination with a number:
2168 \begin_inset Formula $\unitfrac[2]{1}{3}$
2174 \begin_layout Standard
2175 \begin_inset Note Greyedout
2178 \begin_layout Plain Layout
2189 is not a real \SpecialChar LaTeX
2190 command but the command
2191 \begin_inset Newline newline
2198 unitfrac[number]{numerator}{denominator}
2201 Therefore you cannot use it in \SpecialChar TeX
2210 \begin_layout Standard
2211 How to define own fractions where the fraction stroke can be changed, is
2213 \begin_inset CommandInset ref
2215 reference "subsec:Self-defined-Fractions"
2222 \begin_layout Standard
2223 Multiline fractions are explained in
2224 \begin_inset CommandInset ref
2226 reference "subsec:Multiline-Fractions"
2233 \begin_layout Subsection
2235 \begin_inset Index idx
2238 \begin_layout Plain Layout
2247 \begin_layout Standard
2248 Square roots are created with
2255 \begin_inset Index idx
2258 \begin_layout Plain Layout
2266 or the math toolbar button
2269 arg "math-insert \\sqrt"
2272 , all other roots with the command
2279 \begin_inset Index idx
2282 \begin_layout Plain Layout
2290 or with the math toolbar button
2293 arg "math-insert \\root"
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
2651 \begin_layout Standard
2653 \begin_inset Tabular
2654 <lyxtabular version="3" rows="6" columns="2">
2655 <features booktabs="true" tabularvalignment="middle">
2656 <column alignment="center" valignment="top" width="0pt">
2657 <column alignment="center" valignment="top" width="0pt">
2659 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2662 \begin_layout Plain Layout
2668 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2671 \begin_layout Plain Layout
2678 <row topspace="1mm">
2679 <cell alignment="center" valignment="top" usebox="none">
2682 \begin_layout Plain Layout
2686 \begin_inset space \textvisiblespace{}
2690 \begin_inset Formula $\downarrow$
2698 <cell alignment="center" valignment="top" usebox="none">
2701 \begin_layout Plain Layout
2702 \begin_inset Formula $\binom{A}{B}$
2711 <row topspace="2mm">
2712 <cell alignment="center" valignment="top" usebox="none">
2715 \begin_layout Plain Layout
2719 \begin_inset space \textvisiblespace{}
2723 \begin_inset Formula $\downarrow$
2731 <cell alignment="center" valignment="top" usebox="none">
2734 \begin_layout Plain Layout
2735 \begin_inset Formula $\dbinom{A}{B}$
2744 <row topspace="2mm" bottomspace="0.5mm">
2745 <cell alignment="center" valignment="top" usebox="none">
2748 \begin_layout Plain Layout
2752 \begin_inset space \textvisiblespace{}
2756 \begin_inset Formula $\downarrow$
2764 <cell alignment="center" valignment="top" usebox="none">
2767 \begin_layout Plain Layout
2768 \begin_inset Formula $\tbinom{A}{B}$
2777 <row topspace="1mm">
2778 <cell alignment="center" valignment="top" topline="true" usebox="none">
2781 \begin_layout Plain Layout
2785 \begin_inset space \textvisiblespace{}
2789 \begin_inset Formula $\downarrow$
2797 <cell alignment="center" valignment="top" topline="true" usebox="none">
2800 \begin_layout Plain Layout
2801 \begin_inset Formula ${A \brack B}$
2810 <row topspace="2mm" bottomspace="0.5mm">
2811 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2814 \begin_layout Plain Layout
2818 \begin_inset space \textvisiblespace{}
2822 \begin_inset Formula $\downarrow$
2830 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2833 \begin_layout Plain Layout
2834 \begin_inset Formula ${A \brace B}$
2850 \begin_layout Subsection
2851 Case Differentiations
2852 \begin_inset Index idx
2855 \begin_layout Plain Layout
2856 Case differentiations
2864 \begin_layout Standard
2866 \begin_inset Tabular
2867 <lyxtabular version="3" rows="3" columns="2">
2868 <features booktabs="true" tabularvalignment="middle">
2869 <column alignment="center" valignment="top" width="0pt">
2870 <column alignment="center" valignment="top" width="0pt">
2872 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2875 \begin_layout Plain Layout
2881 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2884 \begin_layout Plain Layout
2892 <cell alignment="center" valignment="top" usebox="none">
2895 \begin_layout Plain Layout
2899 \begin_inset space \textvisiblespace{}
2903 \begin_inset Formula $\to$
2907 \begin_inset Index idx
2910 \begin_layout Plain Layout
2923 <cell alignment="center" valignment="top" usebox="none">
2926 \begin_layout Plain Layout
2927 \begin_inset Formula $\begin{cases}
2937 <row topspace="1.5mm">
2938 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2941 \begin_layout Plain Layout
2945 \begin_inset space \textvisiblespace{}
2951 arg "newline-insert newline"
2959 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2962 \begin_layout Plain Layout
2963 \begin_inset Formula $\begin{cases}
2964 A & \textrm{for }x>0\\
2965 B & \textrm{for }x=0
2982 \begin_layout Standard
2989 or pressing the math toolbar button
2992 arg "math-insert \\cases"
2995 you can create new lines with the shortcut
2998 arg "newline-insert newline"
3001 or the table toolbar button
3004 arg "tabular-feature append-row"
3010 \begin_layout Standard
3017 is also available via the menu
3019 Insert\SpecialChar menuseparator
3020 Math\SpecialChar menuseparator
3026 \begin_layout Subsection
3028 \begin_inset Index idx
3031 \begin_layout Plain Layout
3040 \begin_layout Standard
3048 \begin_inset Index idx
3051 \begin_layout Plain Layout
3059 every character can be displayed canceled.
3060 The characters are quasi accentuated by a slash.
3063 \begin_layout Standard
3065 \begin_inset Tabular
3066 <lyxtabular version="3" rows="4" columns="2">
3067 <features booktabs="true" tabularvalignment="middle">
3068 <column alignment="center" valignment="top" width="0pt">
3069 <column alignment="center" valignment="top" width="0pt">
3071 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3074 \begin_layout Plain Layout
3080 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3083 \begin_layout Plain Layout
3091 <cell alignment="center" valignment="top" usebox="none">
3094 \begin_layout Plain Layout
3102 <cell alignment="center" valignment="top" usebox="none">
3105 \begin_layout Plain Layout
3106 \begin_inset Formula $\not=$
3116 <cell alignment="center" valignment="top" usebox="none">
3119 \begin_layout Plain Layout
3129 <cell alignment="center" valignment="top" usebox="none">
3132 \begin_layout Plain Layout
3133 \begin_inset Formula $\not\le$
3143 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3146 \begin_layout Plain Layout
3156 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3159 \begin_layout Plain Layout
3160 \begin_inset Formula $\not\parallel$
3176 \begin_layout Standard
3177 The last example shows that not all negations look good.
3178 Therefore there are special commands for some negations (see
3179 \begin_inset CommandInset ref
3181 reference "subsec:Mathematical-Symbols"
3186 \begin_inset CommandInset ref
3188 reference "sec:Relations"
3195 \begin_layout Subsection
3197 \begin_inset CommandInset label
3199 name "subsec:Placeholders"
3204 \begin_inset Index idx
3207 \begin_layout Plain Layout
3214 \begin_inset Index idx
3217 \begin_layout Plain Layout
3218 Chemical characters ! Isotopes
3224 \begin_inset Index idx
3227 \begin_layout Plain Layout
3232 \begin_layout Plain Layout
3243 \begin_layout Plain Layout
3258 \begin_layout Standard
3260 \begin_inset space \thinspace{}
3264 \begin_inset space \space{}
3271 \begin_layout Plain Layout
3272 Typesetting isotopes and chemical symbols is described in
3273 \begin_inset CommandInset ref
3275 reference "subsec:Chemical-Symbols-and"
3284 the following problem occurs:
3287 \begin_layout Standard
3289 \begin_inset Tabular
3290 <lyxtabular version="3" rows="2" columns="2">
3291 <features booktabs="true" tabularvalignment="middle">
3292 <column alignment="center" valignment="top" width="0pt">
3293 <column alignment="center" valignment="top" width="0pt">
3295 <cell alignment="center" valignment="top" usebox="none">
3298 \begin_layout Plain Layout
3299 Indices created with sub- and superscripts:
3304 <cell alignment="center" valignment="top" usebox="none">
3307 \begin_layout Plain Layout
3308 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3317 <row topspace="1.5mm">
3318 <cell alignment="center" valignment="top" usebox="none">
3321 \begin_layout Plain Layout
3327 <cell alignment="center" valignment="top" usebox="none">
3330 \begin_layout Plain Layout
3331 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3347 \begin_layout Standard
3348 The shorter index is by default placed below or above the first character
3349 of the longer index.
3350 To avoid this there is the command
3357 \begin_inset Index idx
3360 \begin_layout Plain Layout
3368 or the math toolbar button
3369 \begin_inset space \thinspace{}
3376 \begin_layout Plain Layout
3377 can be found in the submenu of the toolbar button
3380 arg "math-insert \\space"
3394 that creates one or more phantom characters.
3401 a small blue box appears that is superposed with two red arrows.
3402 The arrows indicate that the complete width and height of the box content
3403 will be created as placeholder.
3404 Phantom characters are accordingly placeholders with the size of the characters.
3407 \begin_layout Standard
3409 \begin_inset Tabular
3410 <lyxtabular version="3" rows="4" columns="2">
3411 <features booktabs="true" tabularvalignment="middle">
3412 <column alignment="center" valignment="top" width="0pt">
3413 <column alignment="center" valignment="top" width="0pt">
3415 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3418 \begin_layout Plain Layout
3424 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3427 \begin_layout Plain Layout
3434 <row topspace="1.5mm">
3435 <cell alignment="center" valignment="top" usebox="none">
3438 \begin_layout Plain Layout
3440 \begin_inset space \textvisiblespace{}
3446 \begin_inset space \textvisiblespace{}
3450 \begin_inset Formula $\to$
3454 \begin_inset space \textvisiblespace{}
3462 <cell alignment="center" valignment="top" usebox="none">
3465 \begin_layout Plain Layout
3466 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3475 <row topspace="1.5mm" bottomspace="0.5mm">
3476 <cell alignment="center" valignment="top" usebox="none">
3479 \begin_layout Plain Layout
3481 \begin_inset space \textvisiblespace{}
3487 \begin_inset space \textvisiblespace{}
3491 \begin_inset Formula $\to$
3495 \begin_inset space \textvisiblespace{}
3503 <cell alignment="center" valignment="top" usebox="none">
3506 \begin_layout Plain Layout
3507 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3516 <row topspace="1.5mm" bottomspace="0.5mm">
3517 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3520 \begin_layout Plain Layout
3524 \begin_inset space \textvisiblespace{}
3530 \begin_inset space \textvisiblespace{}
3534 \begin_inset Formula $\to$
3538 \begin_inset space \textvisiblespace{}
3546 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3549 \begin_layout Plain Layout
3550 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3566 \begin_layout Standard
3567 Furthermore there are the commands
3574 \begin_inset Index idx
3577 \begin_layout Plain Layout
3598 \begin_inset Index idx
3601 \begin_layout Plain Layout
3622 creates only space for the maximal height of the characters in the box
3623 but not for its width.
3630 creates only space for the width of the box content.
3631 Therefore the boxes of both commands have only one red arrow.
3634 \begin_layout Standard
3635 For example the command
3640 \begin_inset space \textvisiblespace{}
3647 creates space for the height of the integral sign,
3651 \begin_layout Plain Layout
3658 creates an integral sign, see
3659 \begin_inset CommandInset ref
3661 reference "subsec:Big-Operators"
3670 because this is the larger character.
3671 An example application is in
3672 \begin_inset CommandInset ref
3674 reference "subsec:Multiline-Brackets"
3681 \begin_layout Standard
3682 Placeholders can also be used for text when they are inserted via the menu
3685 Insert\SpecialChar menuseparator
3686 Formatting\SpecialChar menuseparator
3692 \begin_layout Standard
3694 \begin_inset Newline newline
3698 \begin_inset Phantom Phantom
3701 \begin_layout Plain Layout
3710 \begin_layout Subsection
3712 \begin_inset Index idx
3715 \begin_layout Plain Layout
3722 \begin_inset Index idx
3725 \begin_layout Plain Layout
3726 Formula ! underlined
3734 \begin_layout Standard
3736 \begin_inset Tabular
3737 <lyxtabular version="3" rows="4" columns="2">
3738 <features booktabs="true" tabularvalignment="middle">
3739 <column alignment="center" valignment="top" width="0pt">
3740 <column alignment="center" valignment="top" width="0pt">
3742 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3745 \begin_layout Plain Layout
3751 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3754 \begin_layout Plain Layout
3761 <row topspace="2mm">
3762 <cell alignment="center" valignment="top" usebox="none">
3765 \begin_layout Plain Layout
3769 \begin_inset space \textvisiblespace{}
3773 \begin_inset Index idx
3776 \begin_layout Plain Layout
3789 <cell alignment="center" valignment="top" usebox="none">
3792 \begin_layout Plain Layout
3793 \begin_inset Formula $\overline{A+B}$
3802 <row bottomspace="1mm">
3803 <cell alignment="center" valignment="top" usebox="none">
3806 \begin_layout Plain Layout
3810 \begin_inset space \textvisiblespace{}
3814 \begin_inset Index idx
3817 \begin_layout Plain Layout
3830 <cell alignment="center" valignment="top" usebox="none">
3833 \begin_layout Plain Layout
3834 \begin_inset Formula $\underline{A+B}$
3843 <row topspace="2mm" bottomspace="1mm">
3844 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3847 \begin_layout Plain Layout
3851 \begin_inset space \textvisiblespace{}
3857 \begin_inset space \textvisiblespace{}
3865 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3868 \begin_layout Plain Layout
3869 \begin_inset Formula $\overline{\underline{A+B}}$
3885 \begin_layout Standard
3886 In the last example it doesn't matter if first
3901 \begin_layout Standard
3902 To double underline use
3911 \begin_layout Standard
3912 It is possible to place up to 6 lines above or below characters.
3915 \begin_layout Standard
3916 \begin_inset VSpace bigskip
3919 Custom lines can be created using the command
3926 \begin_inset Index idx
3929 \begin_layout Plain Layout
3937 which has the following scheme:
3940 \begin_layout Standard
3945 rule[vertical offset]{length}{thickness}
3948 \begin_layout Standard
3949 The optional vertical offset shifts the line upwards (or downwards, when
3950 the value is negative).
3952 \begin_inset CommandInset ref
3954 reference "tab:Available-units"
3958 can be used for the values.
3959 Here are two example lines created with the commands
3960 \begin_inset Newline newline
3967 rule[-2ex]{3cm}{2pt}
3978 \begin_layout Standard
3980 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
3986 \begin_layout Standard
3993 can also be used for text when a line is inserted via the menu
3995 Insert\SpecialChar menuseparator
3996 Formatting\SpecialChar menuseparator
3998 \begin_inset space ~
4006 \begin_layout Standard
4008 \begin_inset CommandInset line
4019 \begin_layout Subsection
4021 \begin_inset CommandInset label
4023 name "subsec:Ellipses"
4028 \begin_inset Index idx
4031 \begin_layout Plain Layout
4040 \begin_layout Standard
4041 There are different types of ellipses available.
4045 \begin_layout Plain Layout
4046 In the math toolbar in the submenu of the button
4049 arg "math-insert \\ldots"
4057 For listings dots at the baseline are used (
4064 \begin_inset Index idx
4067 \begin_layout Plain Layout
4075 ), while for operations dots are needed that are on the same height as the
4083 \begin_inset Index idx
4086 \begin_layout Plain Layout
4095 When using the command
4102 \begin_inset Index idx
4105 \begin_layout Plain Layout
4113 , \SpecialChar LaTeX
4114 decides on the basis of the next character what type is used.
4117 \begin_layout Standard
4119 \begin_inset Tabular
4120 <lyxtabular version="3" rows="9" columns="2">
4121 <features booktabs="true" tabularvalignment="middle">
4122 <column alignment="center" valignment="top" width="0pt">
4123 <column alignment="center" valignment="top" width="0pt">
4125 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4128 \begin_layout Plain Layout
4134 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4137 \begin_layout Plain Layout
4145 <cell alignment="center" valignment="top" usebox="none">
4148 \begin_layout Plain Layout
4150 \begin_inset space \textvisiblespace{}
4156 \begin_inset space \textvisiblespace{}
4164 <cell alignment="center" valignment="top" usebox="none">
4167 \begin_layout Plain Layout
4168 \begin_inset Formula $A_{1},\dots,A_{n}$
4178 <cell alignment="center" valignment="top" usebox="none">
4181 \begin_layout Plain Layout
4183 \begin_inset space \textvisiblespace{}
4189 \begin_inset space \textvisiblespace{}
4197 <cell alignment="center" valignment="top" usebox="none">
4200 \begin_layout Plain Layout
4201 \begin_inset Formula $A_{1}+\dots+A_{n}$
4211 <cell alignment="center" valignment="top" usebox="none">
4214 \begin_layout Plain Layout
4216 \begin_inset space \textvisiblespace{}
4222 \begin_inset space \textvisiblespace{}
4230 <cell alignment="center" valignment="top" usebox="none">
4233 \begin_layout Plain Layout
4234 \begin_inset Formula $A_{1},\ldots,A_{n}$
4244 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4247 \begin_layout Plain Layout
4249 \begin_inset space \textvisiblespace{}
4255 \begin_inset space \textvisiblespace{}
4263 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4266 \begin_layout Plain Layout
4267 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4277 <cell alignment="center" valignment="top" usebox="none">
4280 \begin_layout Plain Layout
4288 <cell alignment="center" valignment="top" usebox="none">
4291 \begin_layout Plain Layout
4292 \begin_inset Formula $\vdots$
4302 <cell alignment="center" valignment="top" usebox="none">
4305 \begin_layout Plain Layout
4313 <cell alignment="center" valignment="top" usebox="none">
4316 \begin_layout Plain Layout
4317 \begin_inset Formula $\ddots$
4327 <cell alignment="center" valignment="top" usebox="none">
4330 \begin_layout Plain Layout
4338 <cell alignment="center" valignment="top" usebox="none">
4341 \begin_layout Plain Layout
4342 \begin_inset Formula $\iddots$
4352 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4355 \begin_layout Plain Layout
4357 \begin_inset space \thinspace{}
4360 matrix with the different dots
4365 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4368 \begin_layout Plain Layout
4369 \begin_inset Formula $\begin{array}{ccc}
4370 A_{11} & \cdots & A_{1m}\\
4371 \vdots & \ddots & \vdots\\
4372 A_{n1} & \cdots & A_{nm}
4389 \begin_layout Standard
4390 The ellipses available in menu
4392 Insert\SpecialChar menuseparator
4394 \begin_inset space ~
4408 \begin_layout Standard
4409 \begin_inset VSpace medskip
4418 , one of the options
4420 Use mathdots package (automatically)
4422 must be set in the document settings under
4425 \begin_inset space ~
4431 \begin_inset Newline newline
4436 Use mathdots package
4438 will improve the appearance of all dots in the documents if their font
4439 style or size is not the default.
4442 \begin_layout Standard
4443 \begin_inset VSpace medskip
4446 Specially for matrices there are ellipses that span over several columns.
4447 They are created with the command
4454 \begin_inset Index idx
4457 \begin_layout Plain Layout
4465 , that has the following scheme:
4468 \begin_layout Standard
4473 hdotsfor[distance]{number of columns}
4476 \begin_layout Standard
4477 The number of columns specifies how many columns should be spanned.
4478 Distance is a factor for the distance between the dots.
4481 \begin_layout Standard
4482 In the following matrix the command
4488 was inserted in the first box of the second line, to get an ellipsis with
4489 a dot distance twice as long as with the command
4496 \begin_inset Formula
4498 \left(\begin{array}{cccc}
4507 Note that the matrix fields that should be spanned must be empty, otherwise
4508 you get \SpecialChar LaTeX
4512 \begin_layout Standard
4513 \begin_inset VSpace bigskip
4516 Furthermore you can fill with the command
4523 \begin_inset Index idx
4526 \begin_layout Plain Layout
4534 the rest of a line with dots.
4535 The effect of these commands is the same as with
4542 \begin_inset CommandInset ref
4544 reference "subsec:Variable-Space"
4551 \begin_layout Standard
4552 For example the command
4557 \begin_inset space \textvisiblespace{}
4565 \begin_layout Standard
4566 \begin_inset Formula $A\dotfill B$
4572 \begin_layout Standard
4579 there is for a line the command
4586 \begin_inset Index idx
4589 \begin_layout Plain Layout
4600 \begin_layout Standard
4601 \begin_inset Formula $A\hrulefill B$
4607 \begin_layout Standard
4608 To use the commands for text, they have to be inserted in \SpecialChar TeX
4612 \begin_layout Section
4614 \begin_inset CommandInset label
4621 \begin_inset Index idx
4624 \begin_layout Plain Layout
4633 \begin_layout Standard
4634 Matrices can be inserted via the math toolbar button
4637 arg "dialog-show mathmatrix"
4642 Insert\SpecialChar menuseparator
4643 Math\SpecialChar menuseparator
4647 In the matrix dialog you can specify the number of columns and rows, the
4648 alignment and the decoration.
4649 The vertical alignment is only of importance for matrices in inline formulas:
4652 \begin_layout Standard
4653 The first matrix is top
4654 \begin_inset Formula $\begin{array}[t]{cccc}
4662 \begin_inset Formula $\begin{array}{cccc}
4669 and the third bottom
4670 \begin_inset Formula $\begin{array}[b]{cccc}
4680 \begin_layout Standard
4681 The horizontal alignment specifies how the column entries should be aligned.
4682 It is set by entering a letter for every column.
4687 denotes left aligned,
4696 To create for example a 4
4701 \begin_inset space ~
4704 matrix where the first column is left aligned, the second and third are
4705 centered and the last one is right aligned, one enters for the horizontal
4711 Normally in a matrix all columns are centered, therefore the default for
4719 \begin_layout Standard
4720 Horizontal alignment:
4723 \begin_layout Standard
4729 \begin_inset Formula $\begin{array}{lll}
4741 \begin_inset Formula $\begin{array}{ccc}
4753 \begin_inset Formula $\begin{array}{rrr}
4763 \begin_layout Standard
4764 To add or delete rows and columns subsequently, the math toolbar buttons
4768 arg "tabular-feature append-row"
4774 arg "tabular-feature delete-row"
4778 \begin_inset space \thinspace{}
4783 Edit\SpecialChar menuseparator
4787 New rows can also be created with
4790 arg "newline-insert newline"
4796 \begin_layout Standard
4797 \begin_inset VSpace bigskip
4804 adds parentheses in the selected style around the matrix.
4805 Alternatively, parentheses can can either be created with the commands
4813 \begin_inset Index idx
4816 \begin_layout Plain Layout
4831 \begin_inset Index idx
4834 \begin_layout Plain Layout
4845 \begin_inset space ~
4851 \begin_inset CommandInset ref
4853 reference "subsec:Automatic-Bracket-Size"
4857 , or by using the following commands:
4858 \begin_inset VSpace medskip
4864 \begin_layout Standard
4865 \begin_inset space \hfill{}
4869 \begin_inset Tabular
4870 <lyxtabular version="3" rows="4" columns="2">
4871 <features booktabs="true" tabularvalignment="middle">
4872 <column alignment="center" valignment="top" width="0pt">
4873 <column alignment="center" valignment="top">
4875 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4878 \begin_layout Plain Layout
4884 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4887 \begin_layout Plain Layout
4894 <row topspace="1.5mm">
4895 <cell alignment="center" valignment="top" usebox="none">
4898 \begin_layout Plain Layout
4902 \begin_inset space \textvisiblespace{}
4910 \begin_inset space \thinspace{}
4918 <cell alignment="center" valignment="top" usebox="none">
4921 \begin_layout Plain Layout
4922 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4923 0 & \textrm{-}\mathrm{i}\\
4925 \end{array}\end{bmatrix}$
4934 <row topspace="1.5mm" bottomspace="0.5mm">
4935 <cell alignment="center" valignment="top" usebox="none">
4938 \begin_layout Plain Layout
4942 \begin_inset space \textvisiblespace{}
4950 \begin_inset space \thinspace{}
4958 <cell alignment="center" valignment="top" usebox="none">
4961 \begin_layout Plain Layout
4962 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
4963 0 & \textrm{-}\mathrm{i}\\
4965 \end{array}\end{Bmatrix}$
4975 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4978 \begin_layout Plain Layout
4982 \begin_inset space \textvisiblespace{}
4990 \begin_inset space \thinspace{}
4998 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5001 \begin_layout Plain Layout
5002 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5003 0 & \textrm{-}\mathrm{i}\\
5005 \end{array}\end{pmatrix}$
5019 \begin_inset space \hfill{}
5023 \begin_inset Tabular
5024 <lyxtabular version="3" rows="4" columns="2">
5025 <features booktabs="true" tabularvalignment="middle">
5026 <column alignment="center" valignment="top" width="0pt">
5027 <column alignment="center" valignment="top">
5029 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5032 \begin_layout Plain Layout
5038 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5041 \begin_layout Plain Layout
5048 <row topspace="1.5mm">
5049 <cell alignment="center" valignment="top" usebox="none">
5052 \begin_layout Plain Layout
5056 \begin_inset space \textvisiblespace{}
5064 \begin_inset space \thinspace{}
5072 <cell alignment="center" valignment="top" usebox="none">
5075 \begin_layout Plain Layout
5076 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5077 0 & \textrm{-}\mathrm{i}\\
5079 \end{array}\end{vmatrix}$
5088 <row topspace="1.5mm" bottomspace="0.5mm">
5089 <cell alignment="center" valignment="top" usebox="none">
5092 \begin_layout Plain Layout
5096 \begin_inset space \textvisiblespace{}
5104 \begin_inset space \thinspace{}
5112 <cell alignment="center" valignment="top" usebox="none">
5115 \begin_layout Plain Layout
5116 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5117 0 & \textrm{-}\mathrm{i}\\
5119 \end{array}\end{Vmatrix}$
5129 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5132 \begin_layout Plain Layout
5136 \begin_inset space \textvisiblespace{}
5144 \begin_inset space \thinspace{}
5152 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5155 \begin_layout Plain Layout
5156 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5157 0 & \textrm{-}\mathrm{i}\\
5159 \end{array}\end{matrix}$
5173 \begin_inset space \hfill{}
5179 \begin_layout Standard
5180 \begin_inset VSpace medskip
5184 \begin_inset space \thinspace{}
5188 \begin_inset space \space{}
5197 is inserted, a blue box appears between two vertical lines where the matrix
5199 \begin_inset Newline newline
5202 Note that decorated matrices ignore the vertical alignment.
5205 \begin_layout Standard
5206 \begin_inset VSpace bigskip
5209 As all multiline formulas are matrices, the length
5216 \begin_inset Index idx
5219 \begin_layout Plain Layout
5227 that is described in
5228 \begin_inset CommandInset ref
5230 reference "subsec:Column-Separation"
5234 can also be used to change the column separation of matrices.
5237 \begin_layout Standard
5238 To change the row separation, the command
5245 \begin_inset Index idx
5248 \begin_layout Plain Layout
5257 It is used as follows:
5260 \begin_layout Standard
5267 arraystretch}{stretch factor}
5268 \begin_inset Index idx
5271 \begin_layout Plain Layout
5282 \begin_layout Standard
5289 assigns the stretch factor to the predefined command
5297 \begin_inset space \thinspace{}
5301 \begin_inset space \space{}
5304 the row separation, use the factor 2.
5305 This is then used for all following matrices.
5306 To go back to the original separation, assign the factor 1 to
5315 \begin_layout Standard
5316 To set matrices into a text line, the command
5323 \begin_inset Index idx
5326 \begin_layout Plain Layout
5335 When it is inserted a blue box with two dashed lines appears.
5336 In this box the matrix is inserted.
5339 \begin_layout Standard
5341 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5343 \end{smallmatrix}\right)$
5349 \begin_layout Section
5350 Brackets and Delimiters
5351 \begin_inset Index idx
5354 \begin_layout Plain Layout
5361 \begin_inset Index idx
5364 \begin_layout Plain Layout
5373 \begin_layout Subsection
5374 Vertical Brackets and Delimiters
5375 \begin_inset Index idx
5378 \begin_layout Plain Layout
5387 \begin_layout Standard
5388 \begin_inset space \hfill{}
5392 \begin_inset Tabular
5393 <lyxtabular version="3" rows="9" columns="2">
5394 <features booktabs="true" tabularvalignment="middle">
5395 <column alignment="center" valignment="top" width="0pt">
5396 <column alignment="center" valignment="top" width="0pt">
5398 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5401 \begin_layout Plain Layout
5407 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5410 \begin_layout Plain Layout
5418 <cell alignment="center" valignment="top" usebox="none">
5421 \begin_layout Plain Layout
5427 <cell alignment="center" valignment="top" usebox="none">
5430 \begin_layout Plain Layout
5431 \begin_inset Formula $($
5441 <cell alignment="center" valignment="top" usebox="none">
5444 \begin_layout Plain Layout
5450 <cell alignment="center" valignment="top" usebox="none">
5453 \begin_layout Plain Layout
5454 \begin_inset Formula $\{$
5464 <cell alignment="center" valignment="top" usebox="none">
5467 \begin_layout Plain Layout
5473 <cell alignment="center" valignment="top" usebox="none">
5476 \begin_layout Plain Layout
5477 \begin_inset Formula $[$
5487 <cell alignment="center" valignment="top" usebox="none">
5490 \begin_layout Plain Layout
5498 <cell alignment="center" valignment="top" usebox="none">
5501 \begin_layout Plain Layout
5502 \begin_inset Formula $\langle$
5512 <cell alignment="center" valignment="top" usebox="none">
5515 \begin_layout Plain Layout
5523 <cell alignment="center" valignment="top" usebox="none">
5526 \begin_layout Plain Layout
5527 \begin_inset Formula $\lceil$
5537 <cell alignment="center" valignment="top" usebox="none">
5540 \begin_layout Plain Layout
5548 <cell alignment="center" valignment="top" usebox="none">
5551 \begin_layout Plain Layout
5552 \begin_inset Formula $\lfloor$
5562 <cell alignment="center" valignment="top" usebox="none">
5565 \begin_layout Plain Layout
5571 <cell alignment="center" valignment="top" usebox="none">
5574 \begin_layout Plain Layout
5575 \begin_inset Formula $/$
5585 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5588 \begin_layout Plain Layout
5594 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5597 \begin_layout Plain Layout
5598 \begin_inset Formula $|$
5612 \begin_inset space \hfill{}
5616 \begin_inset Tabular
5617 <lyxtabular version="3" rows="9" columns="2">
5618 <features booktabs="true" tabularvalignment="middle">
5619 <column alignment="center" valignment="top" width="0pt">
5620 <column alignment="center" valignment="top" width="0pt">
5622 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5625 \begin_layout Plain Layout
5631 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5634 \begin_layout Plain Layout
5642 <cell alignment="center" valignment="top" usebox="none">
5645 \begin_layout Plain Layout
5651 <cell alignment="center" valignment="top" usebox="none">
5654 \begin_layout Plain Layout
5655 \begin_inset Formula $)$
5665 <cell alignment="center" valignment="top" usebox="none">
5668 \begin_layout Plain Layout
5674 <cell alignment="center" valignment="top" usebox="none">
5677 \begin_layout Plain Layout
5678 \begin_inset Formula $\}$
5688 <cell alignment="center" valignment="top" usebox="none">
5691 \begin_layout Plain Layout
5697 <cell alignment="center" valignment="top" usebox="none">
5700 \begin_layout Plain Layout
5701 \begin_inset Formula $]$
5711 <cell alignment="center" valignment="top" usebox="none">
5714 \begin_layout Plain Layout
5722 <cell alignment="center" valignment="top" usebox="none">
5725 \begin_layout Plain Layout
5726 \begin_inset Formula $\rangle$
5736 <cell alignment="center" valignment="top" usebox="none">
5739 \begin_layout Plain Layout
5747 <cell alignment="center" valignment="top" usebox="none">
5750 \begin_layout Plain Layout
5751 \begin_inset Formula $\rceil$
5761 <cell alignment="center" valignment="top" usebox="none">
5764 \begin_layout Plain Layout
5772 <cell alignment="center" valignment="top" usebox="none">
5775 \begin_layout Plain Layout
5776 \begin_inset Formula $\rfloor$
5786 <cell alignment="center" valignment="top" usebox="none">
5789 \begin_layout Plain Layout
5799 <cell alignment="center" valignment="top" usebox="none">
5802 \begin_layout Plain Layout
5803 \begin_inset Formula $\backslash$
5813 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5816 \begin_layout Plain Layout
5824 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5827 \begin_layout Plain Layout
5828 \begin_inset Formula $\|$
5842 \begin_inset space \hfill{}
5848 \begin_layout Standard
5851 \begin_inset Note Greyedout
5854 \begin_layout Plain Layout
5867 \begin_inset Index idx
5870 \begin_layout Plain Layout
5878 must be used for the backslash, because the command
5886 produces a line break there.
5894 \begin_layout Standard
5895 For all characters listed above the size can be adjusted with the commands
5896 described in the following two subsections.
5897 When using these commands, the characters < and > can directly be used
5898 instead of the commands
5913 \begin_layout Subsubsection
5915 \begin_inset CommandInset label
5917 name "subsec:Manual-Bracket-Size"
5922 \begin_inset Index idx
5925 \begin_layout Plain Layout
5926 Bracket size ! manual
5934 \begin_layout Standard
5935 The bracket size can be specified manually by the \SpecialChar LaTeX
5943 \begin_inset Index idx
5946 \begin_layout Plain Layout
5979 denotes the smallest and
5985 the largest bracket size.
5988 \begin_layout Standard
5989 These commands are used to emphasize levels of brackets:
5992 \begin_layout Standard
5994 \begin_inset Tabular
5995 <lyxtabular version="3" rows="2" columns="2">
5996 <features booktabs="true" tabularvalignment="middle">
5997 <column alignment="center" valignment="top" width="0pt">
5998 <column alignment="center" valignment="top" width="0pt">
6000 <cell alignment="center" valignment="top" usebox="none">
6003 \begin_layout Plain Layout
6004 all brackets in the same size:
6009 <cell alignment="center" valignment="top" usebox="none">
6012 \begin_layout Plain Layout
6013 \begin_inset Formula $((A+B)(A-B))^{C}$
6022 <row topspace="2mm">
6023 <cell alignment="center" valignment="top" usebox="none">
6026 \begin_layout Plain Layout
6032 <cell alignment="center" valignment="top" usebox="none">
6035 \begin_layout Plain Layout
6036 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6052 \begin_layout Standard
6053 For the second formula the command
6060 \begin_inset space \textvisiblespace{}
6068 \begin_layout Standard
6069 Here is an overview about all bracket sizes:
6072 \begin_layout Standard
6089 \begin_inset space \textvisiblespace{}
6097 \begin_inset space \textvisiblespace{}
6101 \begin_inset space \textvisiblespace{}
6111 \begin_layout Standard
6113 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6119 \begin_layout Standard
6126 -commands there is the variant
6133 \begin_inset Index idx
6136 \begin_layout Plain Layout
6144 that adds a bit more space between the bracket and its content, and the
6158 \begin_inset Index idx
6161 \begin_layout Plain Layout
6171 , that don't add additional space.
6176 at the end of the command
6182 is for a left bracket; for a right bracket this will be replaced by an
6188 A left or right bracket can each be an opening or closing bracket.
6191 \begin_layout Standard
6192 In the following table is a comparison of the variants:
6195 \begin_layout Standard
6197 \begin_inset Tabular
6198 <lyxtabular version="3" rows="5" columns="2">
6199 <features booktabs="true" tabularvalignment="middle">
6200 <column alignment="center" valignment="top" width="0pt">
6201 <column alignment="center" valignment="middle">
6203 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6206 \begin_layout Plain Layout
6212 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6215 \begin_layout Plain Layout
6222 <row topspace="2mm">
6223 <cell alignment="center" valignment="top" usebox="none">
6226 \begin_layout Plain Layout
6236 \begin_inset space \textvisiblespace{}
6246 <cell alignment="center" valignment="top" usebox="none">
6249 \begin_layout Plain Layout
6250 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6259 <row topspace="2mm">
6260 <cell alignment="center" valignment="top" usebox="none">
6263 \begin_layout Plain Layout
6273 \begin_inset space \textvisiblespace{}
6283 <cell alignment="center" valignment="top" usebox="none">
6286 \begin_layout Plain Layout
6287 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6296 <row topspace="2mm" bottomspace="0.5mm">
6297 <cell alignment="center" valignment="top" usebox="none">
6300 \begin_layout Plain Layout
6310 \begin_inset space \textvisiblespace{}
6320 <cell alignment="center" valignment="top" usebox="none">
6323 \begin_layout Plain Layout
6324 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6333 <row topspace="1.5mm" bottomspace="0.5mm">
6334 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6337 \begin_layout Plain Layout
6349 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6352 \begin_layout Plain Layout
6353 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6369 \begin_layout Subsubsection
6370 Automatic Bracket Size
6371 \begin_inset CommandInset label
6373 name "subsec:Automatic-Bracket-Size"
6378 \begin_inset Index idx
6381 \begin_layout Plain Layout
6382 Bracket size ! automatic
6390 \begin_layout Standard
6391 Brackets with variable size can be inserted with the commands
6398 \begin_inset Index idx
6401 \begin_layout Plain Layout
6416 \begin_inset Index idx
6419 \begin_layout Plain Layout
6427 or via the math toolbar button
6430 arg "dialog-show mathdelimiter"
6446 the wanted bracket must be inserted.
6447 The bracket size will then automatically be calculated for the output.
6450 \begin_layout Standard
6452 normal bracket: The command
6459 \begin_inset space \textvisiblespace{}
6463 \begin_inset Formula $\downarrow$
6467 \begin_inset space \textvisiblespace{}
6473 \begin_inset Formula
6483 \begin_layout Standard
6485 multiline bracket: The command
6494 \begin_inset space \textvisiblespace{}
6498 \begin_inset Formula $\downarrow$
6502 \begin_inset space \textvisiblespace{}
6510 \begin_inset Formula
6512 \ln\left(\frac{A}{C}\right)
6520 \begin_layout Standard
6536 \begin_inset space ~
6542 This has the advantage that you can see in \SpecialChar LyX
6543 immediately the real bracket
6544 size and that the matching right bracket will be created too.
6545 \begin_inset Newline newline
6548 The command for the last example would then be:
6559 \begin_inset space \textvisiblespace{}
6563 \begin_inset Formula $\downarrow$
6569 \begin_layout Standard
6570 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6571 For example the command
6578 \begin_inset space \textvisiblespace{}
6582 \begin_inset Formula $\downarrow$
6586 \begin_inset space \textvisiblespace{}
6596 \begin_inset Formula
6598 \left.\frac{A}{B}\right\}
6617 will be converted by \SpecialChar LyX
6618 to brackets in the right size when the document is
6619 reloaded and an omitted bracket will appear as dashed line.
6622 \begin_layout Standard
6623 \begin_inset VSpace bigskip
6626 Because all popular \SpecialChar LaTeX
6627 distributions use e\SpecialChar TeX
6628 , an extension to \SpecialChar LaTeX
6637 \begin_inset Index idx
6640 \begin_layout Plain Layout
6648 is additionally available for all brackets and limits.
6649 With this command the height of the following character is adapted to the
6650 one of the surrounding brackets, what is e.
6651 \begin_inset space \thinspace{}
6655 \begin_inset space \space{}
6658 needed for physical vectors:
6659 \begin_inset Formula
6661 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6666 For physical vectors there is a special \SpecialChar LaTeX
6667 -package, described in
6668 \begin_inset CommandInset ref
6670 reference "subsec:Physical-Vectors"
6677 \begin_layout Subsection
6679 \begin_inset Index idx
6682 \begin_layout Plain Layout
6683 Brackets ! horizontal
6691 \begin_layout Standard
6693 \begin_inset Tabular
6694 <lyxtabular version="3" rows="4" columns="2">
6695 <features booktabs="true" tabularvalignment="middle">
6696 <column alignment="center" valignment="top" width="0pt">
6697 <column alignment="center" valignment="top" width="0pt">
6699 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6702 \begin_layout Plain Layout
6708 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6711 \begin_layout Plain Layout
6719 <cell alignment="center" valignment="top" usebox="none">
6722 \begin_layout Plain Layout
6726 \begin_inset space \textvisiblespace{}
6730 \begin_inset space \textvisiblespace{}
6734 \begin_inset Index idx
6737 \begin_layout Plain Layout
6750 <cell alignment="center" valignment="top" usebox="none">
6753 \begin_layout Plain Layout
6754 \begin_inset Formula $\overbrace{A+B}^{3}$
6763 <row topspace="2mm">
6764 <cell alignment="center" valignment="top" usebox="none">
6767 \begin_layout Plain Layout
6771 \begin_inset space \textvisiblespace{}
6775 \begin_inset space \textvisiblespace{}
6779 \begin_inset Index idx
6782 \begin_layout Plain Layout
6795 <cell alignment="center" valignment="top" usebox="none">
6798 \begin_layout Plain Layout
6799 \begin_inset Formula $\underbrace{A+B}_{5}$
6809 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6812 \begin_layout Plain Layout
6816 \begin_inset space \textvisiblespace{}
6822 \begin_inset space \textvisiblespace{}
6826 \begin_inset space \textvisiblespace{}
6830 \begin_inset space \textvisiblespace{}
6834 \begin_inset space \textvisiblespace{}
6838 \begin_inset space \textvisiblespace{}
6842 \begin_inset space \textvisiblespace{}
6850 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6853 \begin_layout Plain Layout
6854 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6870 \begin_layout Standard
6871 In the last example it doesn't matter if
6883 is inserted at first.
6886 \begin_layout Standard
6887 \begin_inset VSpace medskip
6893 \begin_layout Standard
6894 If you set in the document settings under
6897 \begin_inset space ~
6907 \begin_inset Index idx
6910 \begin_layout Plain Layout
6911 Packages ! mathtools
6919 \begin_inset space ~
6924 , you have access to square backets:
6927 \begin_layout Standard
6929 \begin_inset Tabular
6930 <lyxtabular version="3" rows="4" columns="2">
6931 <features booktabs="true" tabularvalignment="middle">
6932 <column alignment="center" valignment="top" width="0pt">
6933 <column alignment="center" valignment="top" width="0pt">
6935 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6938 \begin_layout Plain Layout
6944 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6947 \begin_layout Plain Layout
6955 <cell alignment="center" valignment="top" usebox="none">
6958 \begin_layout Plain Layout
6986 \begin_inset space \textvisiblespace{}
6990 \begin_inset Index idx
6993 \begin_layout Plain Layout
7006 <cell alignment="center" valignment="top" usebox="none">
7009 \begin_layout Plain Layout
7010 \begin_inset Formula $\overbracket{A+B}^{3}$
7019 <row topspace="2mm">
7020 <cell alignment="center" valignment="top" usebox="none">
7023 \begin_layout Plain Layout
7051 \begin_inset space \textvisiblespace{}
7055 \begin_inset Index idx
7058 \begin_layout Plain Layout
7083 <cell alignment="center" valignment="top" usebox="none">
7086 \begin_layout Plain Layout
7087 \begin_inset Formula $\underbracket{A+B}_{5}$
7097 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7100 \begin_layout Plain Layout
7106 \begin_inset space \textvisiblespace{}
7110 \begin_inset space \textvisiblespace{}
7114 \begin_inset space \textvisiblespace{}
7118 \begin_inset space \textvisiblespace{}
7122 \begin_inset space \textvisiblespace{}
7130 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7133 \begin_layout Plain Layout
7134 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7150 \begin_layout Standard
7163 you can change the thickness of the bracket's stroke by specifying the
7164 desired thickness in square brackets behind the command:
7167 \begin_layout Standard
7169 \begin_inset Tabular
7170 <lyxtabular version="3" rows="3" columns="2">
7171 <features booktabs="true" tabularvalignment="middle">
7172 <column alignment="center" valignment="top" width="0pt">
7173 <column alignment="center" valignment="top" width="0pt">
7175 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7178 \begin_layout Plain Layout
7184 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7187 \begin_layout Plain Layout
7195 <cell alignment="center" valignment="top" usebox="none">
7198 \begin_layout Plain Layout
7228 \begin_inset space \textvisiblespace{}
7236 <cell alignment="center" valignment="top" usebox="none">
7239 \begin_layout Plain Layout
7240 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7249 <row topspace="2mm">
7250 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7253 \begin_layout Plain Layout
7283 \begin_inset space \textvisiblespace{}
7291 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7294 \begin_layout Plain Layout
7295 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7311 \begin_layout Standard
7312 \begin_inset VSpace bigskip
7315 When brackets should overlap each other, multiline formulas, as described
7317 \begin_inset CommandInset ref
7319 reference "sec:Multiline-Formulas"
7324 \begin_inset Formula
7326 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7327 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7332 In the first row the formula is inserted together with the first brace.
7333 It is hereby important that the space command
7337 \begin_layout Plain Layout
7338 Space commands are explained in
7339 \begin_inset CommandInset ref
7341 reference "subsec:Predefined-Space"
7356 is inserted before the first
7357 \begin_inset Formula $d$
7360 , because the brace that ends behind the
7361 \begin_inset Formula $q$
7364 prevents that the following
7365 \begin_inset Quotes eld
7369 \begin_inset Quotes erd
7372 is surrounded by space.
7376 \begin_layout Plain Layout
7377 because a bracket is not handled as a character, see
7378 \begin_inset CommandInset ref
7380 reference "subsec:Binary-Operators"
7389 In the second row the second brace is inserted.
7390 As it should begin before the
7391 \begin_inset Formula $b$
7406 \begin_layout Plain Layout
7414 \begin_inset CommandInset ref
7416 reference "subsec:Placeholders"
7425 This space is needed because the
7426 \begin_inset Quotes eld
7430 \begin_inset Quotes erd
7433 is also surrounded by space in the formula.
7434 The brace is placed under the command
7443 \begin_layout Standard
7444 It gets more complicated when brackets overlap each other above and under
7445 the formula, like in the following example:
7449 \begin_layout Plain Layout
7461 \begin_inset Formula
7463 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7464 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7473 \begin_layout Plain Layout
7484 The first formula row is the same as the second row of the previous example,
7485 with the difference that the brace is above.
7486 The second row contains the formula together with the second brace.
7487 To avoid that there is space between the upper brace in the first row and
7488 the formula, the row spacing needs to be reduced.
7489 This is not easily possible due to a bug in \SpecialChar LyX
7494 \begin_layout Plain Layout
7495 \begin_inset CommandInset href
7497 name "LyX-bug #1505"
7498 target "http://www.lyx.org/trac/ticket/1505"
7508 As a solution for the problem, the global formula row separation
7515 \begin_inset Index idx
7518 \begin_layout Plain Layout
7526 must be changed to -6
7527 \begin_inset space \thinspace{}
7530 pt before the formula with the command
7546 is set back after the formula to the standard value of 3
7547 \begin_inset space \thinspace{}
7550 pt using the same command.
7551 More about the row separation in formulas is explained in
7552 \begin_inset CommandInset ref
7554 reference "subsec:Line-Separation"
7561 \begin_layout Section
7563 \begin_inset Index idx
7566 \begin_layout Plain Layout
7575 \begin_layout Standard
7576 Arrows can be inserted via the math toolbar button
7579 arg "math-insert \\leftarrow"
7582 or the commands listed in the following subsections.
7585 \begin_layout Subsection
7587 \begin_inset Index idx
7590 \begin_layout Plain Layout
7599 \begin_layout Standard
7600 \begin_inset space \hfill{}
7604 \begin_inset Tabular
7605 <lyxtabular version="3" rows="8" columns="2">
7606 <features booktabs="true" tabularvalignment="middle">
7607 <column alignment="center" valignment="top" width="0pt">
7608 <column alignment="center" valignment="top" width="0pt">
7610 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7613 \begin_layout Plain Layout
7619 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7622 \begin_layout Plain Layout
7630 <cell alignment="center" valignment="top" usebox="none">
7633 \begin_layout Plain Layout
7641 <cell alignment="center" valignment="top" usebox="none">
7644 \begin_layout Plain Layout
7645 \begin_inset Formula $\gets$
7655 <cell alignment="center" valignment="top" usebox="none">
7658 \begin_layout Plain Layout
7666 <cell alignment="center" valignment="top" usebox="none">
7669 \begin_layout Plain Layout
7670 \begin_inset Formula $\Leftarrow$
7680 <cell alignment="center" valignment="top" usebox="none">
7683 \begin_layout Plain Layout
7691 <cell alignment="center" valignment="top" usebox="none">
7694 \begin_layout Plain Layout
7695 \begin_inset Formula $\longleftarrow$
7705 <cell alignment="center" valignment="top" usebox="none">
7708 \begin_layout Plain Layout
7716 <cell alignment="center" valignment="top" usebox="none">
7719 \begin_layout Plain Layout
7720 \begin_inset Formula $\Longleftarrow$
7730 <cell alignment="center" valignment="top" usebox="none">
7733 \begin_layout Plain Layout
7741 <cell alignment="center" valignment="top" usebox="none">
7744 \begin_layout Plain Layout
7745 \begin_inset Formula $\leftharpoonup$
7755 <cell alignment="center" valignment="top" usebox="none">
7758 \begin_layout Plain Layout
7766 <cell alignment="center" valignment="top" usebox="none">
7769 \begin_layout Plain Layout
7770 \begin_inset Formula $\leftharpoondown$
7780 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7783 \begin_layout Plain Layout
7791 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7794 \begin_layout Plain Layout
7795 \begin_inset Formula $\hookleftarrow$
7809 \begin_inset space \hfill{}
7813 \begin_inset Tabular
7814 <lyxtabular version="3" rows="8" columns="2">
7815 <features booktabs="true" tabularvalignment="middle">
7816 <column alignment="center" valignment="top" width="0pt">
7817 <column alignment="center" valignment="top" width="0pt">
7819 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7822 \begin_layout Plain Layout
7828 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7831 \begin_layout Plain Layout
7839 <cell alignment="center" valignment="top" usebox="none">
7842 \begin_layout Plain Layout
7850 <cell alignment="center" valignment="top" usebox="none">
7853 \begin_layout Plain Layout
7854 \begin_inset Formula $\to$
7864 <cell alignment="center" valignment="top" usebox="none">
7867 \begin_layout Plain Layout
7875 <cell alignment="center" valignment="top" usebox="none">
7878 \begin_layout Plain Layout
7879 \begin_inset Formula $\Rightarrow$
7889 <cell alignment="center" valignment="top" usebox="none">
7892 \begin_layout Plain Layout
7900 <cell alignment="center" valignment="top" usebox="none">
7903 \begin_layout Plain Layout
7904 \begin_inset Formula $\longrightarrow$
7914 <cell alignment="center" valignment="top" usebox="none">
7917 \begin_layout Plain Layout
7925 <cell alignment="center" valignment="top" usebox="none">
7928 \begin_layout Plain Layout
7929 \begin_inset Formula $\Longrightarrow$
7939 <cell alignment="center" valignment="top" usebox="none">
7942 \begin_layout Plain Layout
7950 <cell alignment="center" valignment="top" usebox="none">
7953 \begin_layout Plain Layout
7954 \begin_inset Formula $\rightharpoonup$
7964 <cell alignment="center" valignment="top" usebox="none">
7967 \begin_layout Plain Layout
7975 <cell alignment="center" valignment="top" usebox="none">
7978 \begin_layout Plain Layout
7979 \begin_inset Formula $\rightharpoondown$
7989 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7992 \begin_layout Plain Layout
8000 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8003 \begin_layout Plain Layout
8004 \begin_inset Formula $\hookrightarrow$
8018 \begin_inset space \hfill{}
8024 \begin_layout Standard
8025 \begin_inset space \hfill{}
8029 \begin_inset Tabular
8030 <lyxtabular version="3" rows="6" columns="2">
8031 <features booktabs="true" tabularvalignment="middle">
8032 <column alignment="center" valignment="top" width="0pt">
8033 <column alignment="center" valignment="top" width="0pt">
8035 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8038 \begin_layout Plain Layout
8044 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8047 \begin_layout Plain Layout
8055 <cell alignment="center" valignment="top" usebox="none">
8058 \begin_layout Plain Layout
8066 <cell alignment="center" valignment="top" usebox="none">
8069 \begin_layout Plain Layout
8070 \begin_inset Formula $\leftrightarrow$
8080 <cell alignment="center" valignment="top" usebox="none">
8083 \begin_layout Plain Layout
8091 <cell alignment="center" valignment="top" usebox="none">
8094 \begin_layout Plain Layout
8095 \begin_inset Formula $\Leftrightarrow$
8105 <cell alignment="center" valignment="top" usebox="none">
8108 \begin_layout Plain Layout
8116 <cell alignment="center" valignment="top" usebox="none">
8119 \begin_layout Plain Layout
8120 \begin_inset Formula $\longleftrightarrow$
8130 <cell alignment="center" valignment="top" usebox="none">
8133 \begin_layout Plain Layout
8141 <cell alignment="center" valignment="top" usebox="none">
8144 \begin_layout Plain Layout
8145 \begin_inset Formula $\Longleftrightarrow$
8155 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8158 \begin_layout Plain Layout
8166 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8169 \begin_layout Plain Layout
8170 \begin_inset Formula $\rightleftharpoons$
8184 \begin_inset space \hspace{}
8189 \begin_inset space \hfill{}
8193 \begin_inset Tabular
8194 <lyxtabular version="3" rows="5" columns="2">
8195 <features booktabs="true" tabularvalignment="middle">
8196 <column alignment="center" valignment="top" width="0pt">
8197 <column alignment="center" valignment="top" width="0pt">
8199 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8202 \begin_layout Plain Layout
8208 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8211 \begin_layout Plain Layout
8219 <cell alignment="center" valignment="top" usebox="none">
8222 \begin_layout Plain Layout
8230 <cell alignment="center" valignment="top" usebox="none">
8233 \begin_layout Plain Layout
8234 \begin_inset Formula $\mapsto$
8244 <cell alignment="center" valignment="top" usebox="none">
8247 \begin_layout Plain Layout
8255 <cell alignment="center" valignment="top" usebox="none">
8258 \begin_layout Plain Layout
8259 \begin_inset Formula $\longmapsto$
8269 <cell alignment="center" valignment="top" usebox="none">
8272 \begin_layout Plain Layout
8280 <cell alignment="center" valignment="top" usebox="none">
8283 \begin_layout Plain Layout
8284 \begin_inset Formula $\leadsto$
8294 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8297 \begin_layout Plain Layout
8305 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8308 \begin_layout Plain Layout
8309 \begin_inset Formula $\dasharrow$
8323 \begin_inset space \hfill{}
8329 \begin_layout Standard
8330 \begin_inset VSpace medskip
8333 Arrows used as accents like e.
8334 \begin_inset space \thinspace{}
8338 \begin_inset space \space{}
8341 vector arrows are listed in
8342 \begin_inset CommandInset ref
8344 reference "sec:Accents"
8351 \begin_layout Standard
8352 \begin_inset VSpace bigskip
8355 Furthermore there are the labeled arrows
8356 \begin_inset Index idx
8359 \begin_layout Plain Layout
8372 \begin_inset Index idx
8375 \begin_layout Plain Layout
8390 \begin_inset Index idx
8393 \begin_layout Plain Layout
8400 \begin_layout Plain Layout
8415 When inserting one of these commands in a formula, an arrow with two blue
8416 boxes appear where the label can be inserted.
8417 The length of the arrow adapts to the label width.
8420 \begin_layout Standard
8422 \begin_inset Tabular
8423 <lyxtabular version="3" rows="3" columns="2">
8424 <features booktabs="true" tabularvalignment="middle">
8425 <column alignment="center" valignment="top" width="0pt">
8426 <column alignment="center" valignment="top" width="0pt">
8428 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8431 \begin_layout Plain Layout
8437 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8440 \begin_layout Plain Layout
8448 <cell alignment="center" valignment="top" usebox="none">
8451 \begin_layout Plain Layout
8455 \begin_inset space \textvisiblespace{}
8459 \begin_inset Formula $\downarrow$
8463 \begin_inset Formula $\to$
8471 <cell alignment="center" valignment="top" usebox="none">
8474 \begin_layout Plain Layout
8475 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8484 <row topspace="2mm">
8485 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8488 \begin_layout Plain Layout
8492 \begin_inset space \textvisiblespace{}
8496 \begin_inset Formula $\downarrow$
8500 \begin_inset Formula $\to$
8508 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8511 \begin_layout Plain Layout
8512 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8528 \begin_layout Standard
8529 \begin_inset VSpace medskip
8535 \begin_layout Standard
8536 If you set in the document settings under
8539 \begin_inset space ~
8549 \begin_inset Index idx
8552 \begin_layout Plain Layout
8553 Packages ! mathtools
8561 \begin_inset space ~
8566 , you have access to the following labeled arrows:
8569 \begin_layout Standard
8570 \begin_inset Newpage newpage
8576 \begin_layout Standard
8578 \begin_inset space \hspace*{\fill}
8582 \begin_inset Tabular
8583 <lyxtabular version="3" rows="7" columns="2">
8584 <features booktabs="true" tabularvalignment="middle">
8585 <column alignment="center" valignment="top" width="0pt">
8586 <column alignment="center" valignment="top" width="0pt">
8588 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8591 \begin_layout Plain Layout
8597 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8600 \begin_layout Plain Layout
8608 <cell alignment="center" valignment="top" usebox="none">
8611 \begin_layout Plain Layout
8631 <cell alignment="center" valignment="top" usebox="none">
8634 \begin_layout Plain Layout
8635 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8644 <row topspace="2mm">
8645 <cell alignment="center" valignment="top" usebox="none">
8648 \begin_layout Plain Layout
8668 <cell alignment="center" valignment="top" usebox="none">
8671 \begin_layout Plain Layout
8672 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8681 <row topspace="2mm">
8682 <cell alignment="center" valignment="top" usebox="none">
8685 \begin_layout Plain Layout
8705 <cell alignment="center" valignment="top" usebox="none">
8708 \begin_layout Plain Layout
8709 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8718 <row topspace="2mm">
8719 <cell alignment="center" valignment="top" usebox="none">
8722 \begin_layout Plain Layout
8742 <cell alignment="center" valignment="top" usebox="none">
8745 \begin_layout Plain Layout
8746 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8755 <row topspace="2mm">
8756 <cell alignment="center" valignment="top" usebox="none">
8759 \begin_layout Plain Layout
8779 <cell alignment="center" valignment="top" usebox="none">
8782 \begin_layout Plain Layout
8783 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8792 <row topspace="2mm">
8793 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8796 \begin_layout Plain Layout
8816 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8819 \begin_layout Plain Layout
8820 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8834 \begin_inset space \hspace*{\fill}
8838 \begin_inset Tabular
8839 <lyxtabular version="3" rows="7" columns="2">
8840 <features booktabs="true" tabularvalignment="middle">
8841 <column alignment="center" valignment="top" width="0pt">
8842 <column alignment="center" valignment="top" width="0pt">
8844 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8847 \begin_layout Plain Layout
8853 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8856 \begin_layout Plain Layout
8864 <cell alignment="center" valignment="top" usebox="none">
8867 \begin_layout Plain Layout
8887 <cell alignment="center" valignment="top" usebox="none">
8890 \begin_layout Plain Layout
8891 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8900 <row topspace="2mm">
8901 <cell alignment="center" valignment="top" usebox="none">
8904 \begin_layout Plain Layout
8924 <cell alignment="center" valignment="top" usebox="none">
8927 \begin_layout Plain Layout
8928 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8937 <row topspace="2mm">
8938 <cell alignment="center" valignment="top" usebox="none">
8941 \begin_layout Plain Layout
8961 <cell alignment="center" valignment="top" usebox="none">
8964 \begin_layout Plain Layout
8965 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
8974 <row topspace="2mm">
8975 <cell alignment="center" valignment="top" usebox="none">
8978 \begin_layout Plain Layout
8998 <cell alignment="center" valignment="top" usebox="none">
9001 \begin_layout Plain Layout
9002 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9011 <row topspace="2mm">
9012 <cell alignment="center" valignment="top" usebox="none">
9015 \begin_layout Plain Layout
9035 <cell alignment="center" valignment="top" usebox="none">
9038 \begin_layout Plain Layout
9039 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9048 <row topspace="2mm">
9049 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9052 \begin_layout Plain Layout
9072 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9075 \begin_layout Plain Layout
9076 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9090 \begin_inset space \hspace*{\fill}
9096 \begin_layout Standard
9097 The command scheme is for all these arrows:
9100 \begin_layout Standard
9102 \begin_inset Tabular
9103 <lyxtabular version="3" rows="2" columns="2">
9104 <features booktabs="true" tabularvalignment="middle">
9105 <column alignment="center" valignment="top" width="0pt">
9106 <column alignment="center" valignment="top" width="0pt">
9108 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9111 \begin_layout Plain Layout
9117 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9120 \begin_layout Plain Layout
9127 <row bottomspace="0.5mm">
9128 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9131 \begin_layout Plain Layout
9134 xleftrightarrow[x=a]
9137 \begin_inset Formula $\to$
9145 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9148 \begin_layout Plain Layout
9149 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9165 \begin_layout Subsection
9166 Vertical and diagonal Arrows
9167 \begin_inset Index idx
9170 \begin_layout Plain Layout
9177 \begin_inset Index idx
9180 \begin_layout Plain Layout
9189 \begin_layout Standard
9190 \begin_inset space \hfill{}
9194 \begin_inset Tabular
9195 <lyxtabular version="3" rows="7" columns="2">
9196 <features booktabs="true" tabularvalignment="middle">
9197 <column alignment="center" valignment="top" width="0pt">
9198 <column alignment="center" valignment="top" width="0pt">
9200 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9203 \begin_layout Plain Layout
9209 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9212 \begin_layout Plain Layout
9220 <cell alignment="center" valignment="top" usebox="none">
9223 \begin_layout Plain Layout
9231 <cell alignment="center" valignment="top" usebox="none">
9234 \begin_layout Plain Layout
9235 \begin_inset Formula $\uparrow$
9245 <cell alignment="center" valignment="top" usebox="none">
9248 \begin_layout Plain Layout
9256 <cell alignment="center" valignment="top" usebox="none">
9259 \begin_layout Plain Layout
9260 \begin_inset Formula $\Uparrow$
9270 <cell alignment="center" valignment="top" usebox="none">
9273 \begin_layout Plain Layout
9281 <cell alignment="center" valignment="top" usebox="none">
9284 \begin_layout Plain Layout
9285 \begin_inset Formula $\updownarrow$
9295 <cell alignment="center" valignment="top" usebox="none">
9298 \begin_layout Plain Layout
9306 <cell alignment="center" valignment="top" usebox="none">
9309 \begin_layout Plain Layout
9310 \begin_inset Formula $\Updownarrow$
9320 <cell alignment="center" valignment="top" usebox="none">
9323 \begin_layout Plain Layout
9331 <cell alignment="center" valignment="top" usebox="none">
9334 \begin_layout Plain Layout
9335 \begin_inset Formula $\Downarrow$
9345 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9348 \begin_layout Plain Layout
9356 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9359 \begin_layout Plain Layout
9360 \begin_inset Formula $\downarrow$
9374 \begin_inset space \hfill{}
9378 \begin_inset Tabular
9379 <lyxtabular version="3" rows="5" columns="2">
9380 <features booktabs="true" tabularvalignment="middle">
9381 <column alignment="center" valignment="top" width="0pt">
9382 <column alignment="center" valignment="top" width="0pt">
9384 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9387 \begin_layout Plain Layout
9393 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9396 \begin_layout Plain Layout
9404 <cell alignment="center" valignment="top" usebox="none">
9407 \begin_layout Plain Layout
9415 <cell alignment="center" valignment="top" usebox="none">
9418 \begin_layout Plain Layout
9419 \begin_inset Formula $\nearrow$
9429 <cell alignment="center" valignment="top" usebox="none">
9432 \begin_layout Plain Layout
9440 <cell alignment="center" valignment="top" usebox="none">
9443 \begin_layout Plain Layout
9444 \begin_inset Formula $\searrow$
9454 <cell alignment="center" valignment="top" usebox="none">
9457 \begin_layout Plain Layout
9465 <cell alignment="center" valignment="top" usebox="none">
9468 \begin_layout Plain Layout
9469 \begin_inset Formula $\swarrow$
9479 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9482 \begin_layout Plain Layout
9490 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9493 \begin_layout Plain Layout
9494 \begin_inset Formula $\nwarrow$
9508 \begin_inset space \hfill{}
9514 \begin_layout Standard
9515 \begin_inset VSpace medskip
9518 Vertical arrows can be used also as delimiters together with the commands
9520 \begin_inset CommandInset ref
9522 reference "subsec:Manual-Bracket-Size"
9527 \begin_inset CommandInset ref
9529 reference "subsec:Automatic-Bracket-Size"
9536 \begin_layout Section
9538 \begin_inset CommandInset label
9545 \begin_inset Index idx
9548 \begin_layout Plain Layout
9557 \begin_layout Standard
9558 Accents can be inserted via the math toolbar button
9561 arg "math-insert \\hat"
9564 or the commands listed in the following subsections.
9567 \begin_layout Subsection
9568 Accents for one Character
9572 \begin_layout Plain Layout
9585 \begin_layout Plain Layout
9587 \begin_inset CommandInset ref
9589 reference "subsec:Accents-in-Text"
9602 \begin_layout Plain Layout
9610 \begin_inset Note Note
9613 \begin_layout Plain Layout
9620 is used to avoid that the footnote appears in the PDF-bookmark.
9623 \begin_layout Plain Layout
9631 \begin_inset CommandInset ref
9633 reference "subsec:Formulas-in-Section"
9643 \begin_inset CommandInset label
9645 name "subsec:Accents-for-one"
9650 \begin_inset Index idx
9653 \begin_layout Plain Layout
9654 Accents ! for one character
9662 \begin_layout Standard
9663 \begin_inset space \hfill{}
9667 \begin_inset Tabular
9668 <lyxtabular version="3" rows="8" columns="2">
9669 <features booktabs="true" tabularvalignment="middle">
9670 <column alignment="center" valignment="top" width="0pt">
9671 <column alignment="center" valignment="top" width="0pt">
9673 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9676 \begin_layout Plain Layout
9682 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9685 \begin_layout Plain Layout
9692 <row topspace="1.5mm">
9693 <cell alignment="center" valignment="top" usebox="none">
9696 \begin_layout Plain Layout
9700 \begin_inset space \textvisiblespace{}
9708 <cell alignment="center" valignment="top" usebox="none">
9711 \begin_layout Plain Layout
9712 \begin_inset Formula $\dot{A}$
9721 <row topspace="1.5mm">
9722 <cell alignment="center" valignment="top" usebox="none">
9725 \begin_layout Plain Layout
9729 \begin_inset space \textvisiblespace{}
9737 <cell alignment="center" valignment="top" usebox="none">
9740 \begin_layout Plain Layout
9741 \begin_inset Formula $\ddot{A}$
9750 <row topspace="1.5mm">
9751 <cell alignment="center" valignment="top" usebox="none">
9754 \begin_layout Plain Layout
9758 \begin_inset space \textvisiblespace{}
9766 <cell alignment="center" valignment="top" usebox="none">
9769 \begin_layout Plain Layout
9770 \begin_inset Formula $\dddot{A}$
9779 <row topspace="1.5mm">
9780 <cell alignment="center" valignment="top" usebox="none">
9783 \begin_layout Plain Layout
9787 \begin_inset space \textvisiblespace{}
9795 <cell alignment="center" valignment="top" usebox="none">
9798 \begin_layout Plain Layout
9799 \begin_inset Formula $\ddddot{A}$
9808 <row topspace="1.5mm">
9809 <cell alignment="center" valignment="top" usebox="none">
9812 \begin_layout Plain Layout
9816 \begin_inset space \textvisiblespace{}
9820 \begin_inset Index idx
9823 \begin_layout Plain Layout
9834 <cell alignment="center" valignment="top" usebox="none">
9837 \begin_layout Plain Layout
9838 \begin_inset Formula $\vec{A}$
9847 <row topspace="1.5mm">
9848 <cell alignment="center" valignment="top" usebox="none">
9851 \begin_layout Plain Layout
9855 \begin_inset space \textvisiblespace{}
9863 <cell alignment="center" valignment="top" usebox="none">
9866 \begin_layout Plain Layout
9867 \begin_inset Formula $\bar{A}$
9876 <row topspace="1.5mm">
9877 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9880 \begin_layout Plain Layout
9884 \begin_inset space \textvisiblespace{}
9892 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9895 \begin_layout Plain Layout
9896 \begin_inset Formula $\mathring{A}$
9910 \begin_inset space \hfill{}
9914 \begin_inset Tabular
9915 <lyxtabular version="3" rows="7" columns="2">
9916 <features booktabs="true" tabularvalignment="middle">
9917 <column alignment="center" valignment="top" width="0pt">
9918 <column alignment="center" valignment="top" width="0pt">
9920 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9923 \begin_layout Plain Layout
9929 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9932 \begin_layout Plain Layout
9939 <row topspace="1.5mm">
9940 <cell alignment="center" valignment="top" usebox="none">
9943 \begin_layout Plain Layout
9947 \begin_inset space \textvisiblespace{}
9955 <cell alignment="center" valignment="top" usebox="none">
9958 \begin_layout Plain Layout
9959 \begin_inset Formula $\tilde{A}$
9968 <row topspace="1.5mm">
9969 <cell alignment="center" valignment="top" usebox="none">
9972 \begin_layout Plain Layout
9976 \begin_inset space \textvisiblespace{}
9984 <cell alignment="center" valignment="top" usebox="none">
9987 \begin_layout Plain Layout
9988 \begin_inset Formula $\hat{A}$
9997 <row topspace="1.5mm">
9998 <cell alignment="center" valignment="top" usebox="none">
10001 \begin_layout Plain Layout
10005 \begin_inset space \textvisiblespace{}
10013 <cell alignment="center" valignment="top" usebox="none">
10016 \begin_layout Plain Layout
10017 \begin_inset Formula $\check{A}$
10026 <row topspace="1.5mm">
10027 <cell alignment="center" valignment="top" usebox="none">
10030 \begin_layout Plain Layout
10034 \begin_inset space \textvisiblespace{}
10042 <cell alignment="center" valignment="top" usebox="none">
10045 \begin_layout Plain Layout
10046 \begin_inset Formula $\acute{A}$
10055 <row topspace="1.5mm">
10056 <cell alignment="center" valignment="top" usebox="none">
10059 \begin_layout Plain Layout
10063 \begin_inset space \textvisiblespace{}
10071 <cell alignment="center" valignment="top" usebox="none">
10074 \begin_layout Plain Layout
10075 \begin_inset Formula $\grave{A}$
10084 <row topspace="1.5mm">
10085 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10088 \begin_layout Plain Layout
10092 \begin_inset space \textvisiblespace{}
10100 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10103 \begin_layout Plain Layout
10104 \begin_inset Formula $\breve{A}$
10118 \begin_inset space \hfill{}
10124 \begin_layout Standard
10125 \begin_inset VSpace bigskip
10131 \begin_layout Standard
10132 You can directly insert accents like é to formulas.
10134 will transform them to the corresponding accent command.
10136 \begin_inset Index idx
10139 \begin_layout Plain Layout
10145 it is better to insert a quotation mark before the vowel.
10146 These two characters are then treated by \SpecialChar LaTeX
10151 character when the formula part with the umlaut is marked as German.
10159 \begin_inset Quotes eld
10163 \begin_inset Quotes erd
10166 umlauts are created as demonstrated in the following example:
10169 \begin_layout Standard
10170 \begin_inset VSpace -2mm
10176 \begin_layout Standard
10178 \begin_inset Tabular
10179 <lyxtabular version="3" rows="3" columns="2">
10180 <features booktabs="true" tabularvalignment="middle">
10181 <column alignment="center" valignment="top" width="0pt">
10182 <column alignment="center" valignment="top">
10184 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10187 \begin_layout Plain Layout
10193 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10196 \begin_layout Plain Layout
10204 <cell alignment="center" valignment="top" usebox="none">
10207 \begin_layout Plain Layout
10208 \begin_inset Quotes grd
10216 <cell alignment="center" valignment="top" usebox="none">
10219 \begin_layout Plain Layout
10220 \begin_inset space \hspace{}
10227 \begin_inset Formula $"i$
10236 <row topspace="1.5mm">
10237 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10240 \begin_layout Plain Layout
10244 \begin_inset space \textvisiblespace{}
10252 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10255 \begin_layout Plain Layout
10256 \begin_inset Formula $\ddot{i}$
10272 \begin_layout Standard
10273 Another advantage to
10279 is that umlauts can directly be converted to mathematical text because
10280 the accent commands above are
10286 in mathematical text
10289 To convert an accented character to mathematical text, only the character
10290 under the accent may be converted.
10291 This applies also for all other conversions, e.
10292 \begin_inset space \thinspace{}
10296 \begin_inset space \space{}
10302 \begin_layout Standard
10303 In mathematical text, umlauts and other accented characters can directly
10307 \begin_layout Standard
10308 \begin_inset VSpace bigskip
10314 \begin_layout Standard
10316 also supports a tilde under the character if the \SpecialChar LaTeX
10322 \begin_inset Index idx
10325 \begin_layout Plain Layout
10326 Packages ! undertilde
10331 is installed on your system:
10334 \begin_layout Standard
10338 \begin_layout Plain Layout
10348 \begin_inset Note Note
10351 \begin_layout Plain Layout
10352 The following table will only be displayed when the \SpecialChar LaTeX
10365 \begin_layout Standard
10368 \begin_inset Tabular
10369 <lyxtabular version="3" rows="2" columns="2">
10370 <features booktabs="true" tabularvalignment="middle">
10371 <column alignment="center" valignment="top" width="0pt">
10372 <column alignment="center" valignment="top" width="0pt">
10374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10377 \begin_layout Plain Layout
10383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10386 \begin_layout Plain Layout
10394 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10397 \begin_layout Plain Layout
10401 \begin_inset space \textvisiblespace{}
10409 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10412 \begin_layout Plain Layout
10413 \begin_inset Formula $\utilde{A}$
10429 \begin_layout Standard
10433 \begin_layout Plain Layout
10443 \begin_inset Note Note
10446 \begin_layout Plain Layout
10447 The following will be displayed when the \SpecialChar LaTeX
10460 \begin_layout Standard
10461 You need to install the \SpecialChar LaTeX
10466 to see the rest of this subsection in the output.
10469 \begin_layout Standard
10473 \begin_layout Plain Layout
10485 \begin_layout Standard
10486 \begin_inset Newpage newpage
10492 \begin_layout Subsection
10493 Accents for several Characters
10494 \begin_inset Index idx
10497 \begin_layout Plain Layout
10498 Accents ! for several characters
10506 \begin_layout Standard
10507 \begin_inset space \hfill{}
10511 \begin_inset Tabular
10512 <lyxtabular version="3" rows="5" columns="2">
10513 <features booktabs="true" tabularvalignment="middle">
10514 <column alignment="center" valignment="top" width="0pt">
10515 <column alignment="center" valignment="top" width="0pt">
10517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10520 \begin_layout Plain Layout
10526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10529 \begin_layout Plain Layout
10536 <row topspace="1.5mm">
10537 <cell alignment="center" valignment="top" usebox="none">
10540 \begin_layout Plain Layout
10544 \begin_inset space \textvisiblespace{}
10552 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10555 \begin_layout Plain Layout
10556 \begin_inset Formula $\overleftarrow{A=B}$
10565 <row topspace="1.5mm">
10566 <cell alignment="center" valignment="top" usebox="none">
10569 \begin_layout Plain Layout
10573 \begin_inset space \textvisiblespace{}
10581 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10584 \begin_layout Plain Layout
10585 \begin_inset Formula $\underleftarrow{A=B}$
10594 <row topspace="1.5mm">
10595 <cell alignment="center" valignment="top" usebox="none">
10598 \begin_layout Plain Layout
10602 \begin_inset space \textvisiblespace{}
10610 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10613 \begin_layout Plain Layout
10614 \begin_inset Formula $\overleftrightarrow{A=B}$
10623 <row topspace="1.5mm" bottomspace="1mm">
10624 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10627 \begin_layout Plain Layout
10630 underleftrightarrow
10631 \begin_inset space \textvisiblespace{}
10639 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10642 \begin_layout Plain Layout
10643 \begin_inset Formula $\underleftrightarrow{A=B}$
10657 \begin_inset space \hfill{}
10661 \begin_inset Tabular
10662 <lyxtabular version="3" rows="5" columns="2">
10663 <features booktabs="true" tabularvalignment="middle">
10664 <column alignment="center" valignment="top" width="0pt">
10665 <column alignment="center" valignment="top" width="0pt">
10667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10670 \begin_layout Plain Layout
10676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10679 \begin_layout Plain Layout
10686 <row topspace="1.5mm">
10687 <cell alignment="center" valignment="top" usebox="none">
10690 \begin_layout Plain Layout
10694 \begin_inset space \textvisiblespace{}
10702 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10705 \begin_layout Plain Layout
10706 \begin_inset Formula $\overrightarrow{A=B}$
10715 <row topspace="1.5mm">
10716 <cell alignment="center" valignment="top" usebox="none">
10719 \begin_layout Plain Layout
10723 \begin_inset space \textvisiblespace{}
10731 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10734 \begin_layout Plain Layout
10735 \begin_inset Formula $\underrightarrow{A=B}$
10744 <row topspace="1.5mm">
10745 <cell alignment="center" valignment="top" usebox="none">
10748 \begin_layout Plain Layout
10752 \begin_inset space \textvisiblespace{}
10760 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10763 \begin_layout Plain Layout
10764 \begin_inset Formula $\widetilde{A=B}$
10773 <row topspace="1.5mm" bottomspace="1mm">
10774 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10777 \begin_layout Plain Layout
10781 \begin_inset space \textvisiblespace{}
10789 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10792 \begin_layout Plain Layout
10793 \begin_inset Formula $\widehat{A=B}$
10807 \begin_inset space \hfill{}
10813 \begin_layout Standard
10814 \begin_inset VSpace medskip
10817 With these commands as many characters as you like can be accented.
10830 will only be set in the output with a length of three characters, as shown
10831 in the following example:
10832 \begin_inset Formula
10834 \widetilde{A+B=C-D}
10842 \begin_layout Standard
10850 \begin_inset Index idx
10853 \begin_layout Plain Layout
10868 \begin_inset Index idx
10871 \begin_layout Plain Layout
10879 described in the previous subsection it is also possible to accent several
10886 \begin_inset space \textvisiblespace{}
10890 \begin_inset Formula $\downarrow$
10896 \begin_inset Formula
10898 \underset{***}{A=B}
10906 \begin_layout Section
10908 \begin_inset CommandInset label
10910 name "subsec:Space"
10915 \begin_inset Index idx
10918 \begin_layout Plain Layout
10927 \begin_layout Subsection
10929 \begin_inset CommandInset label
10931 name "subsec:Predefined-Space"
10936 \begin_inset Index idx
10939 \begin_layout Plain Layout
10940 Space ! horizontal ! predefined
10948 \begin_layout Standard
10949 Sometimes it is necessary to insert horizontal space into a formula.
10950 This is done by inserting a protected space (shortcut
10953 arg "command-alternatives space-insert protected ; math-space"
10958 \begin_inset Quotes eld
10964 \begin_inset space \textvisiblespace{}
10970 \begin_inset Quotes erd
10973 appears and by pressing
10977 several times one can select one of eight different space sizes.
10978 The spaces can also be inserted using the math toolbar button
10981 arg "math-insert \\space"
10984 or special commands.
10985 Independent from the inserted command, one can select the size again by
10993 \begin_layout Standard
10996 \begin_inset Tabular
10997 <lyxtabular version="3" rows="6" columns="3">
10998 <features booktabs="true" tabularvalignment="middle">
10999 <column alignment="center" valignment="top">
11000 <column alignment="center" valignment="top" width="15col%">
11001 <column alignment="center" valignment="top">
11003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11006 \begin_layout Plain Layout
11012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11015 \begin_layout Plain Layout
11025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11028 \begin_layout Plain Layout
11036 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11039 \begin_layout Plain Layout
11047 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11050 \begin_layout Plain Layout
11056 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11059 \begin_layout Plain Layout
11060 \begin_inset Formula $A\,B$
11070 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11073 \begin_layout Plain Layout
11081 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11084 \begin_layout Plain Layout
11090 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11093 \begin_layout Plain Layout
11094 \begin_inset Formula $A\:B$
11104 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11107 \begin_layout Plain Layout
11115 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11118 \begin_layout Plain Layout
11124 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11127 \begin_layout Plain Layout
11128 \begin_inset Formula $A\;B$
11138 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11141 \begin_layout Plain Layout
11149 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11152 \begin_layout Plain Layout
11158 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11161 \begin_layout Plain Layout
11162 \begin_inset Formula $A\quad B$
11172 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11175 \begin_layout Plain Layout
11183 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11186 \begin_layout Plain Layout
11192 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11195 \begin_layout Plain Layout
11196 \begin_inset Formula $A\qquad B$
11210 \begin_inset space \hfill{}
11214 \begin_inset Tabular
11215 <lyxtabular version="3" rows="6" columns="3">
11216 <features booktabs="true" tabularvalignment="middle">
11217 <column alignment="center" valignment="top">
11218 <column alignment="center" valignment="top" width="15col%">
11219 <column alignment="center" valignment="top">
11221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11224 \begin_layout Plain Layout
11230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11233 \begin_layout Plain Layout
11243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11246 \begin_layout Plain Layout
11254 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11257 \begin_layout Plain Layout
11265 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11268 \begin_layout Plain Layout
11274 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11277 \begin_layout Plain Layout
11278 \begin_inset Formula $A\hfill B$
11288 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11291 \begin_layout Plain Layout
11299 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11302 \begin_layout Plain Layout
11308 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11311 \begin_layout Plain Layout
11312 \begin_inset Formula $A\hspace*{1em}B$
11322 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11325 \begin_layout Plain Layout
11333 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11336 \begin_layout Plain Layout
11342 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11345 \begin_layout Plain Layout
11346 \begin_inset Formula $A\hspace{1em}B$
11356 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11359 \begin_layout Plain Layout
11363 \begin_inset space \textvisiblespace{}
11371 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11374 \begin_layout Plain Layout
11380 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11383 \begin_layout Plain Layout
11384 \begin_inset Formula $A\ B$
11394 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11397 \begin_layout Plain Layout
11405 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11408 \begin_layout Plain Layout
11414 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11417 \begin_layout Plain Layout
11418 \begin_inset Formula $A\!B$
11434 \begin_layout Standard
11436 \begin_inset space ~
11440 \begin_inset space \thinspace{}
11444 \begin_inset space \thinspace{}
11447 7 are variable spaces which are explained in
11448 \begin_inset CommandInset ref
11450 reference "subsec:Variable-Space"
11456 \begin_inset space ~
11459 9 seems to produce no space.
11460 It is displayed red in \SpecialChar LyX
11461 contrary to the other sizes, because it is a negative
11463 There are two more negative spaces:
11466 \begin_layout Standard
11468 \begin_inset Tabular
11469 <lyxtabular version="3" rows="3" columns="3">
11470 <features booktabs="true" tabularvalignment="middle">
11471 <column alignment="center" valignment="middle" width="6.8cm">
11472 <column alignment="center" valignment="top" width="0pt">
11473 <column alignment="center" valignment="top" width="0pt">
11475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11478 \begin_layout Plain Layout
11484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11487 \begin_layout Plain Layout
11495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11498 \begin_layout Plain Layout
11508 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11511 \begin_layout Plain Layout
11516 keystrokes after inserting the protected space
11521 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11524 \begin_layout Plain Layout
11530 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11533 \begin_layout Plain Layout
11541 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11544 \begin_layout Plain Layout
11550 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11553 \begin_layout Plain Layout
11554 \begin_inset Formula $A\negmedspace B$
11562 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11565 \begin_layout Plain Layout
11566 \begin_inset Formula $A\negthickspace B$
11582 \begin_layout Standard
11583 Negative spaces can lead to characters overlapping each other.
11584 Thus they can be used to enforce ligatures, which are e.
11585 \begin_inset space \thinspace{}
11589 \begin_inset space \space{}
11592 useful for summation operators:
11595 \begin_layout Standard
11597 \begin_inset Tabular
11598 <lyxtabular version="3" rows="3" columns="2">
11599 <features booktabs="true" tabularvalignment="middle">
11600 <column alignment="center" valignment="top" width="0pt">
11601 <column alignment="center" valignment="top">
11603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11606 \begin_layout Plain Layout
11612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11615 \begin_layout Plain Layout
11623 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11626 \begin_layout Plain Layout
11632 \begin_inset space \textvisiblespace{}
11640 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11643 \begin_layout Plain Layout
11644 \begin_inset Formula $\sum\sum f_{kl}$
11654 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11657 \begin_layout Plain Layout
11665 \begin_inset space \textvisiblespace{}
11673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11676 \begin_layout Plain Layout
11677 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11693 \begin_layout Standard
11695 \begin_inset VSpace medskip
11701 \begin_layout Standard
11703 Relations like for example equal signs, are always surrounded by space.
11704 To suppress this, the equal sign is placed into a \SpecialChar TeX
11706 The following example demonstrates this:
11709 \begin_layout Standard
11711 \begin_inset Tabular
11712 <lyxtabular version="3" rows="2" columns="2">
11713 <features tabularvalignment="middle">
11714 <column alignment="center" valignment="top" width="0pt">
11715 <column alignment="center" valignment="top" width="0pt">
11717 <cell alignment="center" valignment="top" usebox="none">
11720 \begin_layout Plain Layout
11726 <cell alignment="center" valignment="top" usebox="none">
11729 \begin_layout Plain Layout
11730 \begin_inset Formula $A=B$
11740 <cell alignment="center" valignment="top" usebox="none">
11743 \begin_layout Plain Layout
11744 equation without space
11749 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11752 \begin_layout Plain Layout
11753 \begin_inset Formula $A{=}B$
11769 \begin_layout Standard
11771 The command for the last formula is:
11776 \begin_inset Formula $\to$
11782 \begin_layout Standard
11783 \begin_inset VSpace bigskip
11789 \begin_layout Standard
11790 Spaces are needed for physical units, because the space between the value
11791 and the unit is the smallest one and not a normal space.
11792 For units in text, the smallest space is inserted via the menu
11794 Insert\SpecialChar menuseparator
11795 Formatting\SpecialChar menuseparator
11797 \begin_inset space ~
11805 arg "space-insert thin"
11811 \begin_layout Standard
11812 An example to visualize the difference:
11815 \begin_layout Standard
11816 \begin_inset Tabular
11817 <lyxtabular version="3" rows="2" columns="2">
11818 <features tabularvalignment="middle">
11819 <column alignment="left" valignment="top">
11820 <column alignment="left" valignment="top">
11822 <cell alignment="center" valignment="top" usebox="none">
11825 \begin_layout Plain Layout
11827 \begin_inset Formula $\cdot$
11835 <cell alignment="center" valignment="top" usebox="none">
11838 \begin_layout Plain Layout
11839 space between value and unit
11846 <cell alignment="center" valignment="top" usebox="none">
11849 \begin_layout Plain Layout
11851 \begin_inset space \thinspace{}
11855 \begin_inset Formula $\cdot$
11863 <cell alignment="center" valignment="top" usebox="none">
11866 \begin_layout Plain Layout
11867 smallest space between value and unit
11880 \begin_layout Subsection
11885 \begin_layout Plain Layout
11898 \begin_layout Plain Layout
11899 for vertical space in formulas see
11900 \begin_inset CommandInset ref
11902 reference "subsec:Line-Separation"
11915 \begin_layout Plain Layout
11923 \begin_inset Note Note
11926 \begin_layout Plain Layout
11929 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11932 \begin_layout Plain Layout
11935 texorpdfstring is in section
11936 \begin_inset CommandInset ref
11938 reference "subsec:Formulas-in-Section"
11948 \begin_inset CommandInset label
11950 name "subsec:Variable-Space"
11955 \begin_inset Index idx
11958 \begin_layout Plain Layout
11959 Space ! horizontal ! variable
11967 \begin_layout Standard
11968 Space with a defined length can be inserted with the command
11975 \begin_inset Index idx
11978 \begin_layout Plain Layout
11988 \begin_inset Quotes eld
11994 \begin_inset space \textvisiblespace{}
12000 \begin_inset Quotes erd
12004 The length can be specified by left-clicking on the
12005 \begin_inset Quotes eld
12011 \begin_inset space \textvisiblespace{}
12017 \begin_inset Quotes erd
12021 The length may also be negative.
12022 When a space would be the first character in a line it would be omitted.
12023 To force its output use the command
12035 or left-click on the
12036 \begin_inset Quotes eld
12042 \begin_inset space \textvisiblespace{}
12048 \begin_inset Quotes erd
12051 and check the option
12056 \begin_inset Newline newline
12059 To insert as much space as is available, the command
12066 \begin_inset Index idx
12069 \begin_layout Plain Layout
12080 \begin_layout Standard
12082 \begin_inset Tabular
12083 <lyxtabular version="3" rows="4" columns="2">
12084 <features booktabs="true" tabularvalignment="middle">
12085 <column alignment="center" valignment="top" width="0pt">
12086 <column alignment="center" valignment="top">
12088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12091 \begin_layout Plain Layout
12099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12102 \begin_layout Plain Layout
12110 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12113 \begin_layout Plain Layout
12117 \begin_inset space \textvisiblespace{}
12123 \begin_inset space \thinspace{}
12131 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12134 \begin_layout Plain Layout
12135 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12145 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12148 \begin_layout Plain Layout
12152 \begin_inset space \textvisiblespace{}
12158 \begin_inset space \thinspace{}
12166 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12169 \begin_layout Plain Layout
12170 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12183 \begin_layout Plain Layout
12187 \begin_inset space \textvisiblespace{}
12195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12198 \begin_layout Plain Layout
12199 \begin_inset Formula $A=A\hfill B=B$
12215 \begin_layout Standard
12216 In the last example the available space is given by the longest column entry
12218 In an inline formula the space depends on the length of the line in which
12226 Thus, when the line uses the full width, no space will be created.
12233 only has an effect on displayed formulas when the formula style
12238 (Formula styles are explained in
12239 \begin_inset CommandInset ref
12241 reference "sec:Formula-Styles"
12248 \begin_layout Standard
12255 , there are the commands
12267 that fill the space with a pattern, see
12268 \begin_inset CommandInset ref
12270 reference "subsec:Ellipses"
12277 \begin_layout Standard
12278 For text, variable space can be inserted via the menu
12280 Insert\SpecialChar menuseparator
12281 Formatting\SpecialChar menuseparator
12283 \begin_inset space ~
12291 \begin_layout Standard
12292 This is a line with
12293 \begin_inset space \hspace{}
12298 \begin_inset space \thinspace{}
12304 \begin_layout Standard
12305 This is a line with
12306 \begin_inset space \hfill{}
12312 \begin_layout Subsection
12313 Space besides inline Formulas
12314 \begin_inset Index idx
12317 \begin_layout Plain Layout
12318 Space ! besides inline formulas
12326 \begin_layout Standard
12327 The space that surrounds inline formulas can be adjusted with the length
12335 \begin_inset Index idx
12338 \begin_layout Plain Layout
12347 The value of a length is set with the command
12354 \begin_inset Index idx
12357 \begin_layout Plain Layout
12365 which has the following scheme:
12368 \begin_layout Standard
12373 setlength{length name}{value}
12376 \begin_layout Standard
12384 \begin_inset space \thinspace{}
12390 \begin_layout Standard
12400 \begin_layout Standard
12401 is inserted in \SpecialChar TeX
12404 \begin_inset space \thinspace{}
12407 mm space will now be set around all inline formulas:
12411 \begin_layout Plain Layout
12425 \begin_layout Standard
12426 This is a line with an inline formula
12427 \begin_inset Formula $A=B$
12431 \begin_inset space \thinspace{}
12434 mm surrounding space.
12438 \begin_layout Plain Layout
12452 \begin_layout Standard
12453 To return to the predefined value,
12459 is set to the value 0
12460 \begin_inset space \thinspace{}
12466 \begin_layout Standard
12467 \begin_inset Newpage newpage
12473 \begin_layout Section
12475 \begin_inset Index idx
12478 \begin_layout Plain Layout
12485 \begin_inset Index idx
12488 \begin_layout Plain Layout
12493 \begin_layout Plain Layout
12504 \begin_layout Plain Layout
12519 \begin_layout Standard
12520 Boxes for text are described in chapter
12527 \begin_inset space ~
12535 \begin_layout Subsection
12537 \begin_inset CommandInset label
12539 name "subsec:Boxes-with-Frame"
12544 \begin_inset Index idx
12547 \begin_layout Plain Layout
12556 \begin_layout Standard
12557 It is possible to frame a formula or part of one with the commands
12564 \begin_inset Index idx
12567 \begin_layout Plain Layout
12582 \begin_inset Index idx
12585 \begin_layout Plain Layout
12596 \begin_layout Standard
12597 When one of these commands is inserted in a formula, a blue box appears
12598 within a frame to enter formula parts.
12605 an additional formula has to be created by
12609 within this box, because the box content will otherwise be treated as mathemati
12617 is used, a new formula is automatically created inside the frame.
12620 \begin_layout Standard
12627 is not suitable to frame displayed formulas because the formula will always
12628 be set in the size of the text.
12635 is in contrary not suitable to frame inline formulas, because the formula
12636 will always be set in the size of a displayed formula.
12639 \begin_layout Standard
12653 \begin_inset Index idx
12656 \begin_layout Plain Layout
12664 where additionally the frame width and the alignment can be specified.
12671 is used in the following scheme:
12674 \begin_layout Standard
12679 framebox[frame width][position]{box content}
12682 \begin_layout Standard
12683 The position can either be
12700 right aligns the formula in the box.
12701 When no position is given, the formula will be centered.
12702 \begin_inset Newline newline
12705 If no width is given, also no position can be given.
12706 In this case the frame width is adjusted to the box content like for
12715 \begin_layout Standard
12722 is inserted, a box appears containing three blue boxes.
12723 The first two boxes are surrounded by brackets and denote the two optional
12725 The third box is for formula parts like for
12734 \begin_layout Standard
12736 \begin_inset Tabular
12737 <lyxtabular version="3" rows="5" columns="2">
12738 <features booktabs="true" tabularvalignment="middle">
12739 <column alignment="center" valignment="top" width="0pt">
12740 <column alignment="center" valignment="top">
12742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12745 \begin_layout Plain Layout
12751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12754 \begin_layout Plain Layout
12761 <row topspace="1.5mm">
12762 <cell alignment="center" valignment="top" usebox="none">
12765 \begin_layout Plain Layout
12769 \begin_inset space \textvisiblespace{}
12779 \begin_inset space \textvisiblespace{}
12787 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12790 \begin_layout Plain Layout
12791 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12800 <row topspace="1.5mm">
12801 <cell alignment="center" valignment="top" usebox="none">
12804 \begin_layout Plain Layout
12808 \begin_inset space \textvisiblespace{}
12814 \begin_inset space \textvisiblespace{}
12822 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12825 \begin_layout Plain Layout
12826 \begin_inset Formula $\boxed{\int A=B}$
12835 <row topspace="1.5mm">
12836 <cell alignment="center" valignment="top" usebox="none">
12839 \begin_layout Plain Layout
12843 \begin_inset space \textvisiblespace{}
12851 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12854 \begin_layout Plain Layout
12855 \begin_inset Formula $A+\fbox{B}$
12864 <row topspace="1.5mm" bottomspace="1mm">
12865 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12868 \begin_layout Plain Layout
12872 \begin_inset space \textvisiblespace{}
12876 \begin_inset Formula $\to$
12880 \begin_inset Formula $\to$
12890 \begin_inset space \textvisiblespace{}
12894 \begin_inset Formula $\downarrow$
12902 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12905 \begin_layout Plain Layout
12906 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12922 \begin_layout Standard
12923 The frame thickness can also be adjusted.
12924 To do this the following commands have to be inserted in \SpecialChar TeX
12929 \begin_layout Standard
12939 \begin_inset Quotes eld
12943 \begin_inset Quotes erd
12957 \begin_inset Quotes eld
12961 \begin_inset Quotes erd
12967 \begin_layout Standard
12968 \begin_inset Quotes eld
12972 \begin_inset Quotes erd
12975 specifies the minimal distance between the frame and the first character
12977 An example for this is the following framed formula:
12981 \begin_layout Plain Layout
12993 \begin_inset Formula
13000 Before this formula the commands
13003 \begin_layout Standard
13025 \begin_layout Standard
13026 were inserted in \SpecialChar TeX
13028 The given values are used for all following boxes.
13031 \begin_layout Standard
13032 To return to the standard frame size, the command
13035 \begin_layout Standard
13060 \begin_layout Plain Layout
13074 \begin_layout Standard
13075 is inserted in \SpecialChar TeX
13076 mode before the next formula.
13079 \begin_layout Subsection
13080 Boxes without Frame
13081 \begin_inset CommandInset label
13083 name "subsec:Boxes-without-Frame"
13088 \begin_inset Index idx
13091 \begin_layout Plain Layout
13092 Boxes ! without frame
13100 \begin_layout Standard
13101 For boxes without a frame there are the following box commands:
13108 \begin_inset Index idx
13111 \begin_layout Plain Layout
13126 \begin_inset Index idx
13129 \begin_layout Plain Layout
13144 \begin_inset Index idx
13147 \begin_layout Plain Layout
13158 \begin_layout Standard
13165 a box can be super- or subscripted.
13166 But in contrary to normal super- and subscripting, the characters in the
13167 box keep their font size.
13174 is used in the following scheme:
13177 \begin_layout Standard
13182 raisebox{height}{box content}
13185 \begin_layout Standard
13186 When the box should contain a formula, an extra formula is needed like for
13197 \begin_inset Note Greyedout
13200 \begin_layout Plain Layout
13211 this extra formula is created by pressing
13215 twice instead of once because \SpecialChar LyX
13216 doesn't yet support
13230 \begin_layout Standard
13232 \begin_inset Tabular
13233 <lyxtabular version="3" rows="4" columns="2">
13234 <features booktabs="true" tabularvalignment="middle">
13235 <column alignment="center" valignment="top" width="0pt">
13236 <column alignment="center" valignment="top">
13238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13241 \begin_layout Plain Layout
13247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13250 \begin_layout Plain Layout
13258 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13261 \begin_layout Plain Layout
13265 \begin_inset Formula $\to$
13271 \begin_inset Formula $\to$
13279 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13282 \begin_layout Plain Layout
13283 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13293 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13296 \begin_layout Plain Layout
13300 \begin_inset Formula $\to$
13306 \begin_inset Formula $\to$
13314 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13317 \begin_layout Plain Layout
13318 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13331 \begin_layout Plain Layout
13335 \begin_inset Formula $\to$
13351 \begin_inset space \textvisiblespace{}
13359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13362 \begin_layout Plain Layout
13363 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13379 \begin_layout Standard
13404 , with the difference that there is no frame.
13407 \begin_layout Subsection
13409 \begin_inset CommandInset label
13411 name "subsec:Colored-Boxes"
13416 \begin_inset Index idx
13419 \begin_layout Plain Layout
13428 \begin_layout Standard
13429 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13438 \begin_layout Plain Layout
13439 The \SpecialChar LaTeX
13444 is part of every \SpecialChar LaTeX
13445 standard installation.
13451 \begin_inset Index idx
13454 \begin_layout Plain Layout
13460 has to be loaded in the \SpecialChar LaTeX
13461 -preamble with the line
13465 \begin_layout Plain Layout
13466 When text is colored somewhere in the document with a predefined color,
13468 loads the \SpecialChar LaTeX
13474 Thus it is possible that the package is loaded twice, but this does not
13481 \begin_inset Note Note
13484 \begin_layout Plain Layout
13485 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13494 \begin_layout Standard
13502 \begin_layout Standard
13503 \begin_inset VSpace medskip
13506 To color boxes, the command
13513 \begin_inset Index idx
13516 \begin_layout Plain Layout
13524 is used in the following scheme:
13527 \begin_layout Standard
13532 colorbox{color}{box content}
13535 \begin_layout Standard
13536 The box content can also be a box and a
13542 can also be part of another box (see the 2nd and 3rd example).
13543 When the box should contain a formula, an extra formula has to be created,
13544 the same way as for
13554 \begin_layout Plain Layout
13555 This also applies for the command
13569 \begin_layout Standard
13570 One of the following predefined colors can be chosen:
13573 \begin_layout Standard
13607 \begin_layout Standard
13609 \begin_inset Tabular
13610 <lyxtabular version="3" rows="4" columns="2">
13611 <features booktabs="true" tabularvalignment="middle">
13612 <column alignment="center" valignment="top" width="0pt">
13613 <column alignment="center" valignment="top">
13615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13618 \begin_layout Plain Layout
13624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13627 \begin_layout Plain Layout
13635 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13638 \begin_layout Plain Layout
13642 \begin_inset Formula $\to$
13652 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13655 \begin_layout Plain Layout
13656 \begin_inset Formula $\colorbox{yellow}{A=B}$
13665 <row topspace="1.5mm">
13666 <cell alignment="center" valignment="top" usebox="none">
13669 \begin_layout Plain Layout
13673 \begin_inset Formula $\to$
13681 \begin_inset space \textvisiblespace{}
13689 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13692 \begin_layout Plain Layout
13693 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13702 <row topspace="1.5mm" bottomspace="1mm">
13703 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13706 \begin_layout Plain Layout
13710 \begin_inset space \textvisiblespace{}
13716 \begin_inset Formula $\to$
13732 \begin_inset space \textvisiblespace{}
13740 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13743 \begin_layout Plain Layout
13744 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13760 \begin_layout Standard
13767 only colors the box but not the characters in the box.
13768 To color all characters, the whole formula is highlighted and the desired
13769 color is chosen in the
13772 \begin_inset space ~
13778 The dialog can be called with the toolbar button
13781 arg "dialog-show character"
13786 Edit\SpecialChar menuseparator
13788 \begin_inset space ~
13791 Style\SpecialChar menuseparator
13795 The formula number then has the same color as the formula.
13796 When the formula number should get another color than the formula characters,
13797 the color must be changed within the formula.
13800 \begin_layout Standard
13804 \begin_layout Standard
13807 \begin_inset Formula
13809 \int A=B\label{eq:red}
13817 \begin_inset Formula
13819 \textcolor{red}{\int A=B}\label{eq:redgreen}
13827 \begin_layout Standard
13829 \begin_inset CommandInset ref
13835 is completely colored red.
13836 \begin_inset Newline newline
13840 \begin_inset CommandInset ref
13842 reference "eq:redgreen"
13846 was first completely colored green to set the color for the formula number.
13847 Subsequently the formula characters were colored red.
13850 \begin_layout Standard
13851 \begin_inset VSpace bigskip
13854 To color the frame different than the rest of the box, the command
13861 \begin_inset Index idx
13864 \begin_layout Plain Layout
13872 is used in the following scheme:
13875 \begin_layout Standard
13880 fcolorbox{frame color}{color}{box content}
13883 \begin_layout Standard
13890 is an extension of the command
13897 The frame width is set, like for
13920 \begin_layout Plain Layout
13932 \begin_inset Formula
13934 \fcolorbox{cyan}{magenta}{A=B}
13943 \begin_layout Plain Layout
13957 \begin_layout Standard
13958 This formula was created with the command
13959 \begin_inset Newline newline
13967 \begin_inset Formula $\to$
13973 \begin_inset Formula $\to$
13983 \begin_layout Standard
13984 \begin_inset VSpace bigskip
13987 To use other colors than the predefined ones, they have to be defined first.
13990 \begin_layout Standard
13991 One can for example define the color
13992 \begin_inset Quotes eld
14000 \begin_inset Quotes erd
14003 with the \SpecialChar LaTeX
14007 \begin_layout Standard
14012 definecolor{darkgreen}{cmyk}{0.5,
14027 \begin_inset Index idx
14030 \begin_layout Plain Layout
14041 \begin_layout Standard
14046 is the color space that denotes the colors
14063 The four comma separated numbers are the portion factor for the corresponding
14064 colors of the color space.
14065 The factors can be in the range of 0
14066 \begin_inset space \thinspace{}
14070 \begin_inset space \thinspace{}
14078 also the color space
14082 can be used for definitions.
14099 , so that there are in this case three portion factors for the corresponding
14101 Furthermore there is the color space
14105 with one portion factor for the gray value.
14108 \begin_layout Standard
14109 As example a framed box with the new defined color
14113 where the characters have been colored
14118 \begin_inset Formula
14120 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14128 \begin_layout Standard
14129 Self-defined colors can also be used for text with the help of the command
14137 \begin_inset Index idx
14140 \begin_layout Plain Layout
14149 \begin_layout Standard
14153 \begin_layout Plain Layout
14157 textcolor{darkgreen}{
14163 \begin_inset Quotes eld
14167 \begin_inset Quotes erd
14174 \begin_layout Plain Layout
14184 \begin_layout Standard
14192 \begin_inset Index idx
14195 \begin_layout Plain Layout
14203 is used in the scheme
14207 textcolor{color}{characters to color}
14212 \begin_layout Subsection
14214 \begin_inset CommandInset label
14216 name "subsec:Paragraph-Boxes"
14221 \begin_inset Index idx
14224 \begin_layout Plain Layout
14225 Boxes ! as paragraph
14233 \begin_layout Standard
14234 A box that can contain several lines and paragraphs, a so-called paragraph
14235 box (parbox), can be created with the menu
14237 Insert\SpecialChar menuseparator
14240 or the toolbar button
14249 \begin_layout Standard
14250 The following example shows a framed parbox in a line:
14253 \begin_layout Standard
14254 \begin_inset VSpace medskip
14258 \begin_inset Box Boxed
14268 height_special "totalheight"
14273 backgroundcolor "none"
14276 \begin_layout Plain Layout
14277 This is a paragraph box.
14279 \begin_inset space \thinspace{}
14282 cm long and can also contain formulas:
14283 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14294 \begin_layout Standard
14295 \begin_inset VSpace medskip
14301 \begin_layout Standard
14302 Such a box is created by right-clicking on the gray box inset.
14303 A dialog pops up showing the box properties.
14317 \begin_inset space \thinspace{}
14322 Vertical Box Alignment
14327 \begin_layout Standard
14328 \begin_inset VSpace medskip
14331 In \SpecialChar LaTeX
14332 a parbox is created with the command
14339 \begin_inset Index idx
14342 \begin_layout Plain Layout
14350 which has the following scheme:
14353 \begin_layout Standard
14358 parbox[position]{width}{box content}
14361 \begin_layout Standard
14376 \begin_inset Quotes eld
14380 \begin_inset Quotes erd
14383 means that the box is aligned within the surrounding text with its last
14390 \begin_inset Quotes eld
14394 \begin_inset Quotes erd
14397 this is done with the first line.
14398 When no position is given, the box will be vertically centered, see section
14406 \begin_inset space ~
14411 manual for examples.
14414 \begin_layout Standard
14415 \begin_inset VSpace bigskip
14418 To frame formulas completely, including the formula number, the formula
14419 must be set into a parbox.
14420 To do this, the command
14434 is inserted in \SpecialChar TeX
14435 mode before the formula.
14443 \begin_inset Index idx
14446 \begin_layout Plain Layout
14454 is hereby the line width set for the document.
14455 Because the frame is outside the parbox, 2
14456 \begin_inset space \thinspace{}
14459 times the frame separation and the frame thickness must be subtracted from
14461 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14470 \begin_layout Plain Layout
14475 is part of every \SpecialChar LaTeX
14476 standard installation.
14482 \begin_inset Index idx
14485 \begin_layout Plain Layout
14491 must be loaded in the \SpecialChar LaTeX
14492 -preamble with the line
14495 \begin_layout Standard
14503 \begin_layout Standard
14504 Behind the formula both boxes are closed by entering
14508 in \SpecialChar TeX
14510 Here is an example:
14514 \begin_layout Plain Layout
14528 \begin_layout Standard
14532 \begin_layout Plain Layout
14550 \begin_inset Formula
14552 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14561 \begin_layout Plain Layout
14572 \begin_layout Plain Layout
14586 \begin_layout Standard
14587 \begin_inset VSpace medskip
14590 As a parbox is used as the argument of
14596 , there is in this case no difference between
14611 \begin_layout Standard
14612 \begin_inset VSpace bigskip
14615 Paragraph boxes are very useful to comment formulas directly.
14622 is used in combination with the command
14636 \begin_inset CommandInset ref
14638 reference "subsec:User-defined-Numbering"
14645 \begin_layout Standard
14646 An example of a formula commented with
14655 \begin_layout Standard
14659 \begin_layout Plain Layout
14672 This is a description.
14673 It is distinctly separated from the formula and multiline.
14677 \begin_layout Plain Layout
14689 \begin_layout Standard
14690 Such a formula must be inserted completely in \SpecialChar TeX
14691 mode because \SpecialChar LyX
14693 support the command
14700 The formula is created with the following command sequence:
14703 \begin_layout Standard
14716 is inserted in \SpecialChar TeX
14721 \begin_layout Plain Layout
14722 When the formula style
14734 can also be replaced by
14741 (formula styles see
14742 \begin_inset CommandInset ref
14744 reference "sec:Formula-Styles"
14753 Then the description follows as normal text and finally
14759 is inserted in \SpecialChar TeX
14773 hereby create a displayed formula.
14776 \begin_layout Standard
14783 can be seen in this example that was
14784 \begin_inset Quotes eld
14788 \begin_inset Quotes erd
14791 using the mathematical textmode:
14792 \begin_inset Formula
14794 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14802 \begin_layout Section
14804 \begin_inset Index idx
14807 \begin_layout Plain Layout
14816 \begin_layout Subsection
14818 \begin_inset CommandInset label
14820 name "subsec:Big-Operators"
14825 \begin_inset Index idx
14828 \begin_layout Plain Layout
14835 \begin_inset Index idx
14838 \begin_layout Plain Layout
14845 \begin_inset Index idx
14848 \begin_layout Plain Layout
14857 \begin_layout Standard
14858 To be able to use all integral operators listed here, the option
14860 Use esint package automatically
14862 must be set in the document settings under
14865 \begin_inset space ~
14873 \begin_layout Standard
14874 \begin_inset space \hfill{}
14878 \begin_inset Tabular
14879 <lyxtabular version="3" rows="11" columns="2">
14880 <features booktabs="true" tabularvalignment="middle">
14881 <column alignment="center" valignment="top" width="0pt">
14882 <column alignment="center" valignment="top" width="0pt">
14884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14887 \begin_layout Plain Layout
14893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14896 \begin_layout Plain Layout
14904 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14907 \begin_layout Plain Layout
14911 \begin_inset Index idx
14914 \begin_layout Plain Layout
14927 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14930 \begin_layout Plain Layout
14931 \begin_inset Formula $\int$
14941 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14944 \begin_layout Plain Layout
14952 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14955 \begin_layout Plain Layout
14956 \begin_inset Formula $\oint$
14966 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14969 \begin_layout Plain Layout
14977 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14980 \begin_layout Plain Layout
14981 \begin_inset Formula $\ointctrclockwise$
14991 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14994 \begin_layout Plain Layout
15002 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15005 \begin_layout Plain Layout
15006 \begin_inset Formula $\ointclockwise$
15016 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15019 \begin_layout Plain Layout
15027 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15030 \begin_layout Plain Layout
15031 \begin_inset Formula $\sqint$
15041 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15044 \begin_layout Plain Layout
15052 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15055 \begin_layout Plain Layout
15057 \begin_inset Formula $\fint$
15067 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15070 \begin_layout Plain Layout
15078 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15081 \begin_layout Plain Layout
15083 \begin_inset Formula $\landupint$
15093 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15096 \begin_layout Plain Layout
15104 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15107 \begin_layout Plain Layout
15109 \begin_inset Formula $\landdownint$
15119 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15122 \begin_layout Plain Layout
15130 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15133 \begin_layout Plain Layout
15134 \begin_inset Formula $\bigcap$
15144 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15147 \begin_layout Plain Layout
15155 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15158 \begin_layout Plain Layout
15159 \begin_inset Formula $\bigcup$
15173 \begin_inset space \hfill{}
15177 \begin_inset Tabular
15178 <lyxtabular version="3" rows="11" columns="2">
15179 <features booktabs="true" tabularvalignment="middle">
15180 <column alignment="center" valignment="top" width="0pt">
15181 <column alignment="center" valignment="top" width="0pt">
15183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15186 \begin_layout Plain Layout
15192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15195 \begin_layout Plain Layout
15203 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15206 \begin_layout Plain Layout
15210 \begin_inset Index idx
15213 \begin_layout Plain Layout
15226 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15229 \begin_layout Plain Layout
15230 \begin_inset Formula $\sum$
15240 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15243 \begin_layout Plain Layout
15247 \begin_inset Index idx
15250 \begin_layout Plain Layout
15257 \begin_layout Plain Layout
15276 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15279 \begin_layout Plain Layout
15280 \begin_inset Formula $\prod$
15290 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15293 \begin_layout Plain Layout
15301 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15304 \begin_layout Plain Layout
15305 \begin_inset Formula $\coprod$
15315 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15318 \begin_layout Plain Layout
15326 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15329 \begin_layout Plain Layout
15330 \begin_inset Formula $\bigodot$
15340 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15343 \begin_layout Plain Layout
15351 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15354 \begin_layout Plain Layout
15355 \begin_inset Formula $\bigotimes$
15365 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15368 \begin_layout Plain Layout
15376 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15379 \begin_layout Plain Layout
15380 \begin_inset Formula $\bigoplus$
15390 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15393 \begin_layout Plain Layout
15401 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15404 \begin_layout Plain Layout
15405 \begin_inset Formula $\bigwedge$
15415 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15418 \begin_layout Plain Layout
15426 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15429 \begin_layout Plain Layout
15430 \begin_inset Formula $\bigvee$
15440 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15443 \begin_layout Plain Layout
15451 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15454 \begin_layout Plain Layout
15455 \begin_inset Formula $\bigsqcup$
15465 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15468 \begin_layout Plain Layout
15476 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15479 \begin_layout Plain Layout
15480 \begin_inset Formula $\biguplus$
15494 \begin_inset space \hfill{}
15500 \begin_layout Standard
15501 All big operators can also be inserted via the math toolbar button
15504 arg "math-insert \\intop"
15510 \begin_layout Standard
15511 The operators are called big because they are bigger than the sometimes
15512 equal looking binary operators.
15513 All big operators can have limits as described in the next subsection.
15516 \begin_layout Standard
15517 For all integral operators there is a second version available, ending in
15535 These operators are different from
15542 \begin_inset space \space{}
15545 in the style the operator limits are displayed, see
15546 \begin_inset CommandInset ref
15548 reference "subsec:Operator-Limits"
15556 \begin_layout Subsubsection*
15557 Advice for Integrals
15560 \begin_layout Standard
15565 in an integral is an operator, that therefore has to be set upright.
15566 This is done by highlighting the
15570 and using the keyboard shortcut
15580 \begin_layout Plain Layout
15586 \begin_inset CommandInset ref
15588 reference "subsec:Font-Styles"
15598 Finally the smallest space is inserted before the
15602 , as this is usual for operators.
15606 \begin_layout Standard
15608 \begin_inset Formula $\int A(x)dx$
15612 \begin_inset Newline newline
15616 \begin_inset Phantom HPhantom
15619 \begin_layout Plain Layout
15626 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15632 \begin_layout Standard
15633 For multiple integrals there are the following commands:
15634 \begin_inset VSpace medskip
15640 \begin_layout Standard
15641 \begin_inset space \hfill{}
15645 \begin_inset Tabular
15646 <lyxtabular version="3" rows="4" columns="2">
15647 <features booktabs="true" tabularvalignment="middle">
15648 <column alignment="center" valignment="top" width="0pt">
15649 <column alignment="center" valignment="top" width="0pt">
15651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15654 \begin_layout Plain Layout
15660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15663 \begin_layout Plain Layout
15670 <row bottomspace="1mm">
15671 <cell alignment="center" valignment="top" usebox="none">
15674 \begin_layout Plain Layout
15682 <cell alignment="center" valignment="top" usebox="none">
15685 \begin_layout Plain Layout
15686 \begin_inset Formula $\iint$
15695 <row bottomspace="1mm">
15696 <cell alignment="center" valignment="top" usebox="none">
15699 \begin_layout Plain Layout
15707 <cell alignment="center" valignment="top" usebox="none">
15710 \begin_layout Plain Layout
15711 \begin_inset Formula $\oiint$
15720 <row bottomspace="1mm">
15721 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15724 \begin_layout Plain Layout
15732 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15735 \begin_layout Plain Layout
15736 \begin_inset Formula $\sqiint$
15750 \begin_inset space \hfill{}
15754 \begin_inset Tabular
15755 <lyxtabular version="3" rows="4" columns="2">
15756 <features booktabs="true" tabularvalignment="middle">
15757 <column alignment="center" valignment="top" width="0pt">
15758 <column alignment="center" valignment="top" width="0pt">
15760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15763 \begin_layout Plain Layout
15769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15772 \begin_layout Plain Layout
15779 <row bottomspace="1mm">
15780 <cell alignment="center" valignment="top" usebox="none">
15783 \begin_layout Plain Layout
15791 <cell alignment="center" valignment="top" usebox="none">
15794 \begin_layout Plain Layout
15795 \begin_inset Formula $\iiint$
15804 <row bottomspace="1mm">
15805 <cell alignment="center" valignment="top" usebox="none">
15808 \begin_layout Plain Layout
15816 <cell alignment="center" valignment="top" usebox="none">
15819 \begin_layout Plain Layout
15820 \begin_inset Formula $\iiiint$
15829 <row bottomspace="1mm">
15830 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15833 \begin_layout Plain Layout
15841 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15844 \begin_layout Plain Layout
15845 \begin_inset Formula $\dotsint$
15859 \begin_inset space \hfill{}
15865 \begin_layout Subsection
15867 \begin_inset CommandInset label
15869 name "subsec:Operator-Limits"
15874 \begin_inset Index idx
15877 \begin_layout Plain Layout
15886 \begin_layout Standard
15887 Limits are created by super- and subscripts:
15890 \begin_layout Standard
15892 \begin_inset Tabular
15893 <lyxtabular version="3" rows="2" columns="2">
15894 <features booktabs="true" tabularvalignment="middle">
15895 <column alignment="center" valignment="top" width="0pt">
15896 <column alignment="center" valignment="top" width="0pt">
15898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15901 \begin_layout Plain Layout
15907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15910 \begin_layout Plain Layout
15918 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15921 \begin_layout Plain Layout
15927 \begin_inset space \textvisiblespace{}
15931 \begin_inset Formula $\to$
15935 \begin_inset Formula $\to$
15943 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15946 \begin_layout Plain Layout
15947 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
15963 \begin_layout Standard
15964 Limits of inline formulas are set right beside the operator.
15965 Limits in displayed formulas are set above or below the operator, except
15966 for integral limits.
15969 \begin_layout Standard
15970 To force that the limits are set beside the operator, the cursor is set
15971 directly behind the operator and the limits type is changed with the menu
15974 Edit\SpecialChar menuseparator
15975 Math\SpecialChar menuseparator
15994 \begin_layout Standard
15995 The default limits type is this:
15996 \begin_inset Formula
15998 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16003 This is how it looks when the limits type was changed to
16010 \begin_inset Formula
16012 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16017 For integrals, except those ending with
16033 etc., the limits are by default set beside the operator.
16034 But for multiple integrals the limits are often set below the operator.
16035 In the following example the limits type was therefore set to
16039 and so set below the integrals:
16040 \begin_inset Formula
16042 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16050 \begin_layout Standard
16051 \begin_inset VSpace medskip
16054 To specify conditions for limits, the commands
16061 \begin_inset Index idx
16064 \begin_layout Plain Layout
16079 \begin_inset Index idx
16082 \begin_layout Plain Layout
16091 To create for example this expression
16092 \begin_inset Formula
16094 \sum_{\begin{subarray}{c}
16098 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16106 \begin_layout Standard
16107 the following has to be done:
16108 \begin_inset Newline newline
16120 \begin_inset space \textvisiblespace{}
16126 One is now in a blue box under the summation operator and insert there
16132 \begin_inset space \textvisiblespace{}
16138 The blue box is now within a purple box and now several lines can be written
16140 A new line is created by inserting a line break (
16143 arg "newline-insert newline"
16148 \begin_inset Newline newline
16153 0<k<1000 Ctrl+Return
16154 \begin_inset Newline newline
16159 is typed in, a new box appears below for the new line.
16162 \begin_layout Standard
16163 The alignment of the lines can be changed to left aligned with the
16173 Edit\SpecialChar menuseparator
16177 To get right alignment,
16182 \begin_inset space \textvisiblespace{}
16187 is inserted at the beginning of the line.
16190 \begin_layout Standard
16203 with the difference that the lines are always centered.
16206 \begin_layout Standard
16207 \begin_inset VSpace bigskip
16211 \begin_inset CommandInset ref
16213 reference "eq:substack"
16217 there can be too much space beside an operator, because the characters
16218 following the operator are set beside the limits.
16219 To avoid this the command
16226 \begin_inset Index idx
16229 \begin_layout Plain Layout
16238 To activate it, set in the document settings under
16241 \begin_inset space ~
16251 \begin_inset Index idx
16254 \begin_layout Plain Layout
16255 Packages ! mathtools
16263 \begin_inset space ~
16275 sets the space besides the operator to 0
16276 \begin_inset space \thinspace{}
16280 \begin_inset Newline newline
16284 \begin_inset CommandInset ref
16286 reference "eq:substack"
16290 , one uses the command
16293 \begin_layout Standard
16301 \begin_layout Standard
16302 and inserts the operator with its limits into the braces.
16303 Behind the brace one continues the formula:
16304 \begin_inset Formula
16306 \smashoperator{\sum_{\begin{subarray}{c}
16310 \end{subarray}}^{n}}k^{-2}
16318 \begin_layout Standard
16319 It is possible to set the space of only one side of the operator to 0
16320 \begin_inset space \thinspace{}
16324 To do this write either
16343 stands for the left and
16347 for the right side of the operator.
16348 Here is an example of the possible
16357 \begin_layout Standard
16358 \begin_inset Formula
16360 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}
16368 \begin_layout Standard
16369 \begin_inset VSpace bigskip
16375 \begin_layout Standard
16376 When several consecutive operators have limits the typesetting of the limits
16377 looks often imperfect in the output, see this example:
16378 \begin_inset Formula
16380 \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}
16385 To improve the typesetting set in the document settings under
16388 \begin_inset space ~
16398 \begin_inset Index idx
16401 \begin_layout Plain Layout
16402 Packages ! mathtools
16410 \begin_inset space ~
16416 Then insert into your formula the command
16423 \begin_inset Index idx
16426 \begin_layout Plain Layout
16434 directly before the first operator.
16435 The example will then look like this:
16436 \begin_inset Formula
16438 \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}
16446 \begin_layout Standard
16447 \begin_inset VSpace bigskip
16450 How to use one limit for several operators is described in
16451 \begin_inset CommandInset ref
16453 reference "subsec:Self-defined-Operators"
16460 \begin_layout Subsection
16461 Decoration for Operators
16462 \begin_inset Index idx
16465 \begin_layout Plain Layout
16466 Operators ! Decoration
16474 \begin_layout Standard
16482 \begin_inset Index idx
16485 \begin_layout Plain Layout
16500 \begin_inset Index idx
16503 \begin_layout Plain Layout
16511 characters can be placed above or below an operator, respectively.
16519 \begin_inset Index idx
16522 \begin_layout Plain Layout
16530 characters can be set before and behind a big operator.
16533 \begin_layout Standard
16535 \begin_inset space ~
16547 \begin_layout Itemize
16554 is used to set characters at the corners of the operator
16557 \begin_layout Itemize
16564 is used to set characters before and/or behind the operator (this variant
16565 represents \SpecialChar LaTeX
16575 \begin_layout Itemize
16582 is used to set characters at the left corners and/or behind the operator
16585 \begin_layout Itemize
16592 is used to set characters at the right corners and/or before the operator
16595 \begin_layout Standard
16596 For example the command
16601 \begin_inset space \textvisiblespace{}
16607 \begin_inset space \textvisiblespace{}
16611 \begin_inset Formula $\to$
16615 \begin_inset Formula $\to$
16619 \begin_inset space \textvisiblespace{}
16629 \begin_inset Formula
16631 \sideset{}{'}\sum_{k=1}^{n}
16639 \begin_layout Standard
16640 \begin_inset Note Greyedout
16643 \begin_layout Plain Layout
16650 can only be used to decorate big operators, binary operators are not allowed.
16658 \begin_layout Standard
16671 can also be used to decorate symbols and characters.
16672 For example, the command
16677 \begin_inset space \textvisiblespace{}
16683 \begin_inset space \textvisiblespace{}
16689 \begin_inset Formula $\uparrow$
16697 \begin_inset Formula
16699 \overset{a}{\maltese}
16707 \begin_layout Subsection
16709 \begin_inset CommandInset label
16711 name "subsec:Binary-Operators"
16716 \begin_inset Index idx
16719 \begin_layout Plain Layout
16728 \begin_layout Standard
16729 Binary operators are surrounded by space when there is a character before
16731 \begin_inset VSpace medskip
16737 \begin_layout Standard
16738 \begin_inset Tabular
16739 <lyxtabular version="3" rows="13" columns="2">
16740 <features booktabs="true" tabularvalignment="middle">
16741 <column alignment="center" valignment="top" width="0pt">
16742 <column alignment="center" valignment="top" width="0pt">
16744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16747 \begin_layout Plain Layout
16749 \begin_inset Note Note
16752 \begin_layout Plain Layout
16759 is only used as spacer.
16769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16772 \begin_layout Plain Layout
16780 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16783 \begin_layout Plain Layout
16789 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16792 \begin_layout Plain Layout
16793 \begin_inset Formula $+$
16803 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16806 \begin_layout Plain Layout
16812 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16815 \begin_layout Plain Layout
16816 \begin_inset Formula $-$
16826 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16829 \begin_layout Plain Layout
16837 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16840 \begin_layout Plain Layout
16841 \begin_inset Formula $\pm$
16851 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16854 \begin_layout Plain Layout
16862 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16865 \begin_layout Plain Layout
16866 \begin_inset Formula $\mp$
16876 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16879 \begin_layout Plain Layout
16887 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16890 \begin_layout Plain Layout
16891 \begin_inset Formula $\cdot$
16901 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16904 \begin_layout Plain Layout
16912 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16915 \begin_layout Plain Layout
16916 \begin_inset Formula $\times$
16926 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16929 \begin_layout Plain Layout
16937 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16940 \begin_layout Plain Layout
16941 \begin_inset Formula $\div$
16951 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16954 \begin_layout Plain Layout
16958 \begin_layout Plain Layout
16971 \begin_layout Plain Layout
16983 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16986 \begin_layout Plain Layout
16987 \begin_inset Formula $*$
16997 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17000 \begin_layout Plain Layout
17008 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17011 \begin_layout Plain Layout
17012 \begin_inset Formula $\star$
17022 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17025 \begin_layout Plain Layout
17033 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17036 \begin_layout Plain Layout
17037 \begin_inset Formula $\circ$
17047 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17050 \begin_layout Plain Layout
17058 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17061 \begin_layout Plain Layout
17062 \begin_inset Formula $\diamond$
17072 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17075 \begin_layout Plain Layout
17083 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17086 \begin_layout Plain Layout
17087 \begin_inset Formula $\bullet$
17101 \begin_inset space \hfill{}
17105 \begin_inset Tabular
17106 <lyxtabular version="3" rows="13" columns="2">
17107 <features booktabs="true" tabularvalignment="middle">
17108 <column alignment="center" valignment="top" width="0pt">
17109 <column alignment="center" valignment="top" width="0pt">
17111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17114 \begin_layout Plain Layout
17120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17123 \begin_layout Plain Layout
17131 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17134 \begin_layout Plain Layout
17142 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17145 \begin_layout Plain Layout
17146 \begin_inset Formula $\nabla$
17156 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17159 \begin_layout Plain Layout
17167 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17170 \begin_layout Plain Layout
17171 \begin_inset Formula $\bigtriangledown$
17181 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17184 \begin_layout Plain Layout
17192 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17195 \begin_layout Plain Layout
17196 \begin_inset Formula $\bigtriangleup$
17206 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17209 \begin_layout Plain Layout
17217 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17220 \begin_layout Plain Layout
17221 \begin_inset Formula $\Box$
17231 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17234 \begin_layout Plain Layout
17242 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17245 \begin_layout Plain Layout
17246 \begin_inset Formula $\cap$
17256 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17259 \begin_layout Plain Layout
17267 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17270 \begin_layout Plain Layout
17271 \begin_inset Formula $\cup$
17281 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17284 \begin_layout Plain Layout
17292 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17295 \begin_layout Plain Layout
17296 \begin_inset Formula $\dagger$
17306 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17309 \begin_layout Plain Layout
17317 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17320 \begin_layout Plain Layout
17321 \begin_inset Formula $\ddagger$
17331 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17334 \begin_layout Plain Layout
17342 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17345 \begin_layout Plain Layout
17346 \begin_inset Formula $\wr$
17356 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17359 \begin_layout Plain Layout
17367 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17370 \begin_layout Plain Layout
17371 \begin_inset Formula $\bigcirc$
17381 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17384 \begin_layout Plain Layout
17392 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17395 \begin_layout Plain Layout
17396 \begin_inset Formula $\wedge$
17406 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17409 \begin_layout Plain Layout
17417 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17420 \begin_layout Plain Layout
17421 \begin_inset Formula $\vee$
17435 \begin_inset space \hfill{}
17439 \begin_inset Tabular
17440 <lyxtabular version="3" rows="13" columns="2">
17441 <features booktabs="true" tabularvalignment="middle">
17442 <column alignment="center" valignment="top" width="0pt">
17443 <column alignment="center" valignment="top" width="0pt">
17445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17448 \begin_layout Plain Layout
17454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17457 \begin_layout Plain Layout
17465 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17468 \begin_layout Plain Layout
17476 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17479 \begin_layout Plain Layout
17480 \begin_inset Formula $\oplus$
17490 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17493 \begin_layout Plain Layout
17501 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17504 \begin_layout Plain Layout
17505 \begin_inset Formula $\ominus$
17515 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17518 \begin_layout Plain Layout
17526 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17529 \begin_layout Plain Layout
17530 \begin_inset Formula $\otimes$
17540 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17543 \begin_layout Plain Layout
17551 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17554 \begin_layout Plain Layout
17555 \begin_inset Formula $\oslash$
17565 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17568 \begin_layout Plain Layout
17576 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17579 \begin_layout Plain Layout
17580 \begin_inset Formula $\odot$
17590 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17593 \begin_layout Plain Layout
17601 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17604 \begin_layout Plain Layout
17605 \begin_inset Formula $\amalg$
17615 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17618 \begin_layout Plain Layout
17626 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17629 \begin_layout Plain Layout
17630 \begin_inset Formula $\uplus$
17640 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17643 \begin_layout Plain Layout
17651 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17654 \begin_layout Plain Layout
17655 \begin_inset Formula $\setminus$
17665 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17668 \begin_layout Plain Layout
17676 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17679 \begin_layout Plain Layout
17680 \begin_inset Formula $\sqcap$
17690 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17693 \begin_layout Plain Layout
17701 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17704 \begin_layout Plain Layout
17705 \begin_inset Formula $\sqcup$
17715 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17718 \begin_layout Plain Layout
17726 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17729 \begin_layout Plain Layout
17730 \begin_inset Formula $\triangleleft$
17740 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17743 \begin_layout Plain Layout
17751 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17754 \begin_layout Plain Layout
17755 \begin_inset Formula $\triangleright$
17771 \begin_layout Standard
17772 All binary operators can also be inserted via the math toolbar button
17775 arg "math-insert \\pm"
17781 \begin_layout Standard
17782 To typeset the Laplace operator also
17799 \begin_inset Formula $\nabla^{2}$
17802 ) can be used instead of
17811 \begin_layout Standard
17818 Insert\SpecialChar menuseparator
17830 \begin_layout Subsection
17831 Self-defined Operators
17832 \begin_inset CommandInset label
17834 name "subsec:Self-defined-Operators"
17839 \begin_inset Index idx
17842 \begin_layout Plain Layout
17843 Operators ! self-defined
17851 \begin_layout Standard
17852 With the help of the command
17856 DeclareMathOperator
17859 \begin_inset Index idx
17862 \begin_layout Plain Layout
17867 DeclareMathOperator
17872 custom operators can be defined in the \SpecialChar LaTeX
17874 Its command scheme is:
17877 \begin_layout Standard
17882 DeclareMathOperator{new command}{display}
17885 \begin_layout Standard
17886 Display can be characters or symbols that define how the operator looks
17888 To define a big operator a * is set behind the command.
17889 All self-defined big operators can have limits as described in
17890 \begin_inset CommandInset ref
17892 reference "subsec:Operator-Limits"
17899 \begin_layout Standard
17900 For example the \SpecialChar LaTeX
17904 \begin_layout Standard
17909 DeclareMathOperator*{
17916 \begin_layout Standard
17917 defines the command
17923 , that inserts a big operator consisting of the lozenge symbol from
17924 \begin_inset CommandInset ref
17926 reference "subsec:Miscellaneous-Symbols"
17931 \begin_inset Formula
17933 \Lozenge_{n=1}^{\infty}
17938 The command for this formula is:
17949 \begin_inset Formula $\to$
17955 \begin_layout Standard
17956 \begin_inset VSpace bigskip
17959 When self-defined operators are not used several times in the document,
17960 they can also be defined with the commands
17967 \begin_inset Index idx
17970 \begin_layout Plain Layout
17985 \begin_inset Index idx
17988 \begin_layout Plain Layout
17996 , which have the following scheme:
17999 \begin_layout Standard
18013 \begin_layout Standard
18020 defines big operators,
18029 \begin_layout Standard
18037 \begin_inset space \thinspace{}
18041 \begin_inset space \space{}
18044 be used to use one limit for several operators:
18047 \begin_layout Standard
18048 \begin_inset Formula
18050 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18058 \begin_layout Standard
18059 The command for the formula above is:
18060 \begin_inset Newline newline
18076 \begin_inset space \textvisiblespace{}
18082 \begin_inset Formula $\to$
18088 \begin_inset space \textvisiblespace{}
18096 \begin_layout Section
18098 \begin_inset Index idx
18101 \begin_layout Plain Layout
18110 \begin_layout Subsection
18112 \begin_inset CommandInset label
18114 name "subsec:Font-Styles"
18119 \begin_inset Index idx
18122 \begin_layout Plain Layout
18131 \begin_layout Standard
18132 Latin letters in formulas can be set in one of the following font styles:
18135 \begin_layout Standard
18137 \begin_inset Tabular
18138 <lyxtabular version="3" rows="6" columns="3">
18139 <features booktabs="true" tabularvalignment="middle">
18140 <column alignment="center" valignment="top" width="0pt">
18141 <column alignment="center" valignment="top">
18142 <column alignment="center" valignment="top">
18144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18147 \begin_layout Plain Layout
18153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18156 \begin_layout Plain Layout
18162 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18165 \begin_layout Plain Layout
18173 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18176 \begin_layout Plain Layout
18182 \begin_inset space \textvisiblespace{}
18192 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18195 \begin_layout Plain Layout
18196 \begin_inset Formula $\mathbb{ABC}$
18204 <cell alignment="center" valignment="top" usebox="none">
18207 \begin_layout Plain Layout
18215 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18218 \begin_layout Plain Layout
18224 \begin_inset space \textvisiblespace{}
18234 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18237 \begin_layout Plain Layout
18238 \begin_inset Formula $\mathbf{AbC}$
18246 <cell alignment="center" valignment="top" usebox="none">
18249 \begin_layout Plain Layout
18262 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18265 \begin_layout Plain Layout
18271 \begin_inset space \textvisiblespace{}
18281 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18284 \begin_layout Plain Layout
18285 \begin_inset Formula $\boldsymbol{AbC}$
18293 <cell alignment="center" valignment="top" usebox="none">
18296 \begin_layout Plain Layout
18299 arg "font-boldsymbol"
18309 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18312 \begin_layout Plain Layout
18318 \begin_inset space \textvisiblespace{}
18328 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18331 \begin_layout Plain Layout
18332 \begin_inset Formula $\mathcal{ABC}$
18340 <cell alignment="center" valignment="top" usebox="none">
18343 \begin_layout Plain Layout
18351 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18354 \begin_layout Plain Layout
18360 \begin_inset space \textvisiblespace{}
18370 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18373 \begin_layout Plain Layout
18374 \begin_inset Formula $\mathfrak{AbC}$
18382 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18385 \begin_layout Plain Layout
18399 \begin_layout Standard
18401 \begin_inset Tabular
18402 <lyxtabular version="3" rows="6" columns="3">
18403 <features booktabs="true" tabularvalignment="middle">
18404 <column alignment="center" valignment="top" width="0pt">
18405 <column alignment="center" valignment="top">
18406 <column alignment="center" valignment="top">
18408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18411 \begin_layout Plain Layout
18417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18420 \begin_layout Plain Layout
18426 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18429 \begin_layout Plain Layout
18437 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18440 \begin_layout Plain Layout
18446 \begin_inset space \textvisiblespace{}
18456 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18459 \begin_layout Plain Layout
18460 \begin_inset Formula $\mathit{AbC}$
18468 <cell alignment="center" valignment="top" usebox="none">
18471 \begin_layout Plain Layout
18479 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18482 \begin_layout Plain Layout
18488 \begin_inset space \textvisiblespace{}
18498 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18501 \begin_layout Plain Layout
18502 \begin_inset Formula $\mathrm{AbC}$
18510 <cell alignment="center" valignment="top" usebox="none">
18513 \begin_layout Plain Layout
18526 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18529 \begin_layout Plain Layout
18535 \begin_inset space \textvisiblespace{}
18545 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18548 \begin_layout Plain Layout
18549 \begin_inset Formula $\mathsf{AbC}$
18557 <cell alignment="center" valignment="top" usebox="none">
18560 \begin_layout Plain Layout
18573 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18576 \begin_layout Plain Layout
18582 \begin_inset space \textvisiblespace{}
18592 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18595 \begin_layout Plain Layout
18596 \begin_inset Formula $\mathtt{AbC}$
18604 <cell alignment="center" valignment="top" usebox="none">
18607 \begin_layout Plain Layout
18610 arg "font-typewriter"
18620 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18623 \begin_layout Plain Layout
18629 \begin_inset space \textvisiblespace{}
18639 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18642 \begin_layout Plain Layout
18643 \begin_inset Formula $\mathscr{ABC}$
18651 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18654 \begin_layout Plain Layout
18668 \begin_layout Standard
18669 \begin_inset Note Greyedout
18672 \begin_layout Plain Layout
18695 can only be used for big letters.
18703 \begin_layout Standard
18704 Predefined is the style
18713 \begin_layout Standard
18714 The style commands work also for letters in mathematical constructs:
18715 \begin_inset Formula
18717 \mathfrak{A=\frac{b}{C}}
18725 \begin_layout Standard
18726 Characters in mathematical text don't appear in a math font style but in
18727 the text font style
18734 That their style can't be set correctly via the text style dialog is a
18735 bug in \SpecialChar LyX
18740 \begin_layout Plain Layout
18741 \begin_inset CommandInset href
18743 name "LyX-bug #4629"
18744 target "http://www.lyx.org/trac/ticket/4629"
18757 \begin_layout Standard
18758 Instead of the style commands the dialog
18760 Edit\SpecialChar menuseparator
18761 Math\SpecialChar menuseparator
18764 or the toolbar button
18767 arg "math-insert \\font"
18773 \begin_layout Subsection
18775 \begin_inset CommandInset label
18777 name "subsec:Bold-Formulas"
18782 \begin_inset Index idx
18785 \begin_layout Plain Layout
18794 \begin_layout Standard
18795 To make a complete formula bold, the command
18801 from the previous subsection cannot be used, because it doesn't work for
18802 small Greek letters.
18803 Furthermore it prints Latin letters always upright, like in the following
18807 \begin_layout Standard
18808 \begin_inset Formula
18810 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18818 \begin_layout Standard
18819 To display the formula correctly, the command
18826 \begin_inset Formula
18828 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18833 It is also possible to set the formula in a
18835 boldmath environment
18838 This environment is created by inserting the command
18845 \begin_inset Index idx
18848 \begin_layout Plain Layout
18856 in \SpecialChar TeX
18858 To end the environment, the command
18865 \begin_inset Index idx
18868 \begin_layout Plain Layout
18876 is inserted in \SpecialChar TeX
18881 \begin_layout Plain Layout
18891 \begin_inset Formula
18893 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18902 \begin_layout Plain Layout
18914 \begin_layout Subsection
18916 \begin_inset Index idx
18919 \begin_layout Plain Layout
18928 \begin_layout Standard
18929 Formulas can be colored like normal text: Highlight a formula or a formula
18935 Here is a formula in magenta:
18936 \begin_inset Formula
18938 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18946 \begin_layout Standard
18947 You can also define your own colors as described in
18948 \begin_inset CommandInset ref
18950 reference "subsec:Colored-Boxes"
18955 They can be used with the \SpecialChar TeX
18963 \begin_inset Index idx
18966 \begin_layout Plain Layout
18977 \begin_layout Standard
18982 textcolor{color}{characters or formula}
18985 \begin_layout Standard
18986 The following example was colored completely dark green and partly red:
18989 \begin_layout Standard
18993 \begin_layout Plain Layout
18997 textcolor{darkgreen}{
19003 \begin_inset Formula
19005 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19014 \begin_layout Plain Layout
19024 \begin_layout Standard
19025 Due to a bug in \SpecialChar LyX
19026 only complete formulas can be colored with self-defined
19031 \begin_layout Plain Layout
19032 \begin_inset CommandInset href
19034 name "LyX-bug #5269"
19035 target "http://www.lyx.org/trac/ticket/5269"
19048 \begin_layout Subsection
19050 \begin_inset CommandInset label
19052 name "subsec:Font-Sizes"
19057 \begin_inset Index idx
19060 \begin_layout Plain Layout
19069 \begin_layout Standard
19070 For characters in formulas there are, analog to characters in text, the
19071 following size commands:
19074 \begin_layout Standard
19118 \begin_inset Newline newline
19140 \begin_layout Standard
19141 The size produced by the commands depends on the document font size, which
19142 corresponds to the command
19149 The other commands produce smaller or larger sizes than
19156 The font size can however not exceed a certain value.
19157 Is for example the document font size 12
19158 \begin_inset space \thinspace{}
19167 switches to the same size as
19177 \begin_layout Standard
19178 A size command is inserted in \SpecialChar TeX
19179 mode before the formula and sets the size
19180 for all following formula and text characters.
19181 To switch back to the initial size, the command
19187 is inserted behind the formula in \SpecialChar TeX
19191 \begin_layout Standard
19192 Within a formula the size can be changed using the following size commands
19193 or the toolbar button
19196 arg "math-insert \\style"
19202 \begin_layout Standard
19205 \begin_inset Tabular
19206 <lyxtabular version="3" rows="5" columns="2">
19207 <features booktabs="true" tabularvalignment="middle">
19208 <column alignment="center" valignment="top" width="0pt">
19209 <column alignment="center" valignment="top">
19211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19214 \begin_layout Plain Layout
19220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19223 \begin_layout Plain Layout
19231 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19234 \begin_layout Plain Layout
19238 \begin_inset Index idx
19241 \begin_layout Plain Layout
19254 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19257 \begin_layout Plain Layout
19258 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19267 <row topspace="1mm">
19268 <cell alignment="center" valignment="top" usebox="none">
19271 \begin_layout Plain Layout
19279 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19282 \begin_layout Plain Layout
19283 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19293 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19296 \begin_layout Plain Layout
19304 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19307 \begin_layout Plain Layout
19308 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19318 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19321 \begin_layout Plain Layout
19329 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19332 \begin_layout Plain Layout
19333 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19349 \begin_layout Standard
19350 After entering these commands, a blue box appears in which the formula parts
19354 \begin_layout Standard
19355 There is a further method to change the font size, that though only works
19356 for symbols or letters in mathematical text.
19357 To use it, one of the above text size commands is inserted in mathematical
19359 All following characters until the end of the mathematical text or until
19360 another size command will have the selected size.
19362 \begin_inset VSpace -2mm
19368 \begin_layout Standard
19372 \begin_layout Plain Layout
19382 \begin_inset Formula
19384 A=\frac{B}{c}\cdot\maltese
19390 \begin_inset Formula
19392 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19401 \begin_layout Plain Layout
19413 \begin_layout Standard
19414 \begin_inset VSpace medskip
19417 Before both formulas the command
19424 The command for the second formula is:
19425 \begin_inset Newline newline
19433 \begin_inset space \textvisiblespace{}
19439 \begin_inset space \textvisiblespace{}
19445 \begin_inset space \textvisiblespace{}
19451 \begin_inset space \textvisiblespace{}
19455 \begin_inset Formula $\to$
19459 \begin_inset Formula $\to$
19463 \begin_inset Newline newline
19467 \begin_inset space \hspace*{}
19478 \begin_inset space \textvisiblespace{}
19484 \begin_inset space \textvisiblespace{}
19490 \begin_inset space \textvisiblespace{}
19496 \begin_layout Standard
19497 If a symbol cannot be displayed in different sizes, it will always be displayed
19498 in the default size.
19501 \begin_layout Section
19503 \begin_inset Index idx
19506 \begin_layout Plain Layout
19515 \begin_layout Standard
19516 Greek letters can also be inserted via the toolbar button
19519 arg "math-insert \\alpha"
19523 All international typesetting norms purport that Greek letters in math
19524 have to be typeset italic/slanted.
19525 In some languages, like French or Russian, they are nevertheless sometimes
19529 \begin_layout Subsection
19531 \begin_inset Index idx
19534 \begin_layout Plain Layout
19535 Greek letters ! small
19543 \begin_layout Standard
19544 \begin_inset space \hfill{}
19548 \begin_inset Tabular
19549 <lyxtabular version="3" rows="11" columns="2">
19550 <features booktabs="true" tabularvalignment="middle">
19551 <column alignment="center" valignment="top" width="0pt">
19552 <column alignment="center" valignment="top" width="0pt">
19554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19557 \begin_layout Plain Layout
19563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19566 \begin_layout Plain Layout
19574 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19577 \begin_layout Plain Layout
19585 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19588 \begin_layout Plain Layout
19589 \begin_inset Formula $\alpha$
19599 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19602 \begin_layout Plain Layout
19610 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19613 \begin_layout Plain Layout
19614 \begin_inset Formula $\beta$
19624 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19627 \begin_layout Plain Layout
19635 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19638 \begin_layout Plain Layout
19639 \begin_inset Formula $\gamma$
19649 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19652 \begin_layout Plain Layout
19660 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19663 \begin_layout Plain Layout
19664 \begin_inset Formula $\delta$
19674 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19677 \begin_layout Plain Layout
19685 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19688 \begin_layout Plain Layout
19689 \begin_inset Formula $\epsilon$
19699 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19702 \begin_layout Plain Layout
19710 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19713 \begin_layout Plain Layout
19714 \begin_inset Formula $\varepsilon$
19724 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19727 \begin_layout Plain Layout
19735 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19738 \begin_layout Plain Layout
19739 \begin_inset Formula $\zeta$
19749 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19752 \begin_layout Plain Layout
19760 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19763 \begin_layout Plain Layout
19764 \begin_inset Formula $\eta$
19774 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19777 \begin_layout Plain Layout
19785 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19788 \begin_layout Plain Layout
19789 \begin_inset Formula $\theta$
19799 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19802 \begin_layout Plain Layout
19810 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19813 \begin_layout Plain Layout
19814 \begin_inset Formula $\vartheta$
19828 \begin_inset space \hfill{}
19832 \begin_inset Tabular
19833 <lyxtabular version="3" rows="12" columns="2">
19834 <features booktabs="true" tabularvalignment="middle">
19835 <column alignment="center" valignment="top" width="0pt">
19836 <column alignment="center" valignment="top" width="0pt">
19838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19841 \begin_layout Plain Layout
19847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19850 \begin_layout Plain Layout
19858 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19861 \begin_layout Plain Layout
19869 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19872 \begin_layout Plain Layout
19873 \begin_inset Formula $\iota$
19883 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19886 \begin_layout Plain Layout
19894 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19897 \begin_layout Plain Layout
19898 \begin_inset Formula $\kappa$
19908 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19911 \begin_layout Plain Layout
19919 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19922 \begin_layout Plain Layout
19923 \begin_inset Formula $\varkappa$
19933 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19936 \begin_layout Plain Layout
19944 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19947 \begin_layout Plain Layout
19948 \begin_inset Formula $\lambda$
19958 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19961 \begin_layout Plain Layout
19969 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19972 \begin_layout Plain Layout
19973 \begin_inset Formula $\mu$
19983 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19986 \begin_layout Plain Layout
19994 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19997 \begin_layout Plain Layout
19998 \begin_inset Formula $\nu$
20008 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20011 \begin_layout Plain Layout
20019 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20022 \begin_layout Plain Layout
20023 \begin_inset Formula $\xi$
20033 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20036 \begin_layout Plain Layout
20042 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20045 \begin_layout Plain Layout
20046 \begin_inset Formula $o$
20056 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20059 \begin_layout Plain Layout
20067 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20070 \begin_layout Plain Layout
20071 \begin_inset Formula $\pi$
20081 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20084 \begin_layout Plain Layout
20092 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20095 \begin_layout Plain Layout
20096 \begin_inset Formula $\varpi$
20106 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20109 \begin_layout Plain Layout
20117 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20120 \begin_layout Plain Layout
20121 \begin_inset Formula $\rho$
20135 \begin_inset space \hfill{}
20139 \begin_inset Tabular
20140 <lyxtabular version="3" rows="11" columns="2">
20141 <features booktabs="true" tabularvalignment="middle">
20142 <column alignment="center" valignment="top" width="0pt">
20143 <column alignment="center" valignment="top" width="0pt">
20145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20148 \begin_layout Plain Layout
20154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20157 \begin_layout Plain Layout
20165 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20168 \begin_layout Plain Layout
20176 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20179 \begin_layout Plain Layout
20180 \begin_inset Formula $\varrho$
20190 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20193 \begin_layout Plain Layout
20201 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20204 \begin_layout Plain Layout
20205 \begin_inset Formula $\sigma$
20215 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20218 \begin_layout Plain Layout
20226 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20229 \begin_layout Plain Layout
20230 \begin_inset Formula $\varsigma$
20240 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20243 \begin_layout Plain Layout
20251 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20254 \begin_layout Plain Layout
20255 \begin_inset Formula $\tau$
20265 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20268 \begin_layout Plain Layout
20276 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20279 \begin_layout Plain Layout
20280 \begin_inset Formula $\upsilon$
20290 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20293 \begin_layout Plain Layout
20301 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20304 \begin_layout Plain Layout
20305 \begin_inset Formula $\phi$
20315 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20318 \begin_layout Plain Layout
20326 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20329 \begin_layout Plain Layout
20330 \begin_inset Formula $\varphi$
20340 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20343 \begin_layout Plain Layout
20351 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20354 \begin_layout Plain Layout
20355 \begin_inset Formula $\chi$
20365 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20368 \begin_layout Plain Layout
20376 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20379 \begin_layout Plain Layout
20380 \begin_inset Formula $\psi$
20390 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20393 \begin_layout Plain Layout
20401 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20404 \begin_layout Plain Layout
20405 \begin_inset Formula $\omega$
20419 \begin_inset space \hfill{}
20425 \begin_layout Standard
20426 \begin_inset VSpace medskip
20432 \begin_layout Standard
20433 How to create special upright Greek letters is explained in
20434 \begin_inset CommandInset ref
20436 reference "subsec:Upright-small-Greek"
20443 \begin_layout Subsection
20445 \begin_inset Index idx
20448 \begin_layout Plain Layout
20449 Greek letters ! big
20457 \begin_layout Standard
20458 \begin_inset space \hfill{}
20462 \begin_inset Tabular
20463 <lyxtabular version="3" rows="7" columns="2">
20464 <features booktabs="true" tabularvalignment="middle">
20465 <column alignment="center" valignment="top" width="0pt">
20466 <column alignment="center" valignment="top" width="0pt">
20468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20471 \begin_layout Plain Layout
20477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20480 \begin_layout Plain Layout
20488 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20491 \begin_layout Plain Layout
20499 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20502 \begin_layout Plain Layout
20503 \begin_inset Formula $\Gamma$
20513 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20516 \begin_layout Plain Layout
20524 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20527 \begin_layout Plain Layout
20528 \begin_inset Formula $\Delta$
20538 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20541 \begin_layout Plain Layout
20549 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20552 \begin_layout Plain Layout
20553 \begin_inset Formula $\Theta$
20563 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20566 \begin_layout Plain Layout
20574 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20577 \begin_layout Plain Layout
20578 \begin_inset Formula $\Lambda$
20588 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20591 \begin_layout Plain Layout
20599 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20602 \begin_layout Plain Layout
20603 \begin_inset Formula $\Xi$
20613 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20616 \begin_layout Plain Layout
20624 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20627 \begin_layout Plain Layout
20628 \begin_inset Formula $\Pi$
20642 \begin_inset space \hfill{}
20646 \begin_inset Tabular
20647 <lyxtabular version="3" rows="6" columns="2">
20648 <features booktabs="true" tabularvalignment="middle">
20649 <column alignment="center" valignment="top" width="0pt">
20650 <column alignment="center" valignment="top" width="0pt">
20652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20655 \begin_layout Plain Layout
20661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20664 \begin_layout Plain Layout
20672 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20675 \begin_layout Plain Layout
20683 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20686 \begin_layout Plain Layout
20687 \begin_inset Formula $\Sigma$
20697 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20700 \begin_layout Plain Layout
20708 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20711 \begin_layout Plain Layout
20712 \begin_inset Formula $\Upsilon$
20722 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20725 \begin_layout Plain Layout
20733 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20736 \begin_layout Plain Layout
20737 \begin_inset Formula $\Phi$
20747 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20750 \begin_layout Plain Layout
20758 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20761 \begin_layout Plain Layout
20762 \begin_inset Formula $\Psi$
20772 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20775 \begin_layout Plain Layout
20783 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20786 \begin_layout Plain Layout
20787 \begin_inset Formula $\Omega$
20801 \begin_inset space \hfill{}
20807 \begin_layout Standard
20808 \begin_inset VSpace medskip
20811 That the big Greek letters appear upright is caused by a design bug when
20814 To get correct italic big letters, begin every command with
20819 For example the command
20826 \begin_inset Formula $\varGamma$
20830 Another way is to load the package
20838 \begin_layout Plain Layout
20843 is part of the \SpecialChar LaTeX
20849 \begin_inset Index idx
20852 \begin_layout Plain Layout
20857 \begin_layout Plain Layout
20877 \begin_inset Index idx
20880 \begin_layout Plain Layout
20886 with the \SpecialChar LaTeX
20890 \begin_layout Standard
20895 usepackage{fixmath}
20898 \begin_layout Standard
20899 Then all big Greek letters in a document will automatically be typeset italic.
20902 \begin_layout Subsection
20904 \begin_inset Index idx
20907 \begin_layout Plain Layout
20908 Greek letters ! bold
20916 \begin_layout Standard
20917 Greek letters cannot be set with different font styles like Latin letters.
20918 They can only be made bold with the command
20925 \begin_inset Index idx
20928 \begin_layout Plain Layout
20939 \begin_layout Standard
20941 \begin_inset Tabular
20942 <lyxtabular version="3" rows="3" columns="2">
20943 <features booktabs="true" tabularvalignment="middle">
20944 <column alignment="center" valignment="top" width="0pt">
20945 <column alignment="center" valignment="top">
20947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20950 \begin_layout Plain Layout
20956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20959 \begin_layout Plain Layout
20967 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20970 \begin_layout Plain Layout
20982 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20985 \begin_layout Plain Layout
20986 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20996 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20999 \begin_layout Plain Layout
21011 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21014 \begin_layout Plain Layout
21015 \begin_inset Formula $\theta\boldsymbol{\theta}$
21031 \begin_layout Section
21036 \begin_layout Plain Layout
21049 \begin_layout Plain Layout
21050 A list with all symbols of most of the \SpecialChar LaTeX
21051 -packages can be found in
21052 \begin_inset CommandInset citation
21068 \begin_layout Plain Layout
21076 \begin_inset Note Note
21079 \begin_layout Plain Layout
21082 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21085 \begin_layout Plain Layout
21088 texorpdfstring is in section
21089 \begin_inset CommandInset ref
21091 reference "subsec:Formulas-in-Section"
21101 \begin_inset Index idx
21104 \begin_layout Plain Layout
21113 \begin_layout Standard
21114 Many of the symbols listed in this section can also be inserted via the
21118 arg "math-insert \\nabla"
21124 arg "math-insert \\digamma"
21130 \begin_layout Subsection
21131 Mathematical Symbols
21132 \begin_inset CommandInset label
21134 name "subsec:Mathematical-Symbols"
21139 \begin_inset Index idx
21142 \begin_layout Plain Layout
21143 Symbols ! mathematical
21151 \begin_layout Standard
21152 \begin_inset Tabular
21153 <lyxtabular version="3" rows="10" columns="2">
21154 <features booktabs="true" tabularvalignment="middle">
21155 <column alignment="center" valignment="top" width="0pt">
21156 <column alignment="center" valignment="top" width="0pt">
21158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21161 \begin_layout Plain Layout
21167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21170 \begin_layout Plain Layout
21178 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21181 \begin_layout Plain Layout
21189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21192 \begin_layout Plain Layout
21193 \begin_inset Formula $\neg$
21203 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21206 \begin_layout Plain Layout
21214 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21217 \begin_layout Plain Layout
21218 \begin_inset Formula $\Im$
21228 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21231 \begin_layout Plain Layout
21239 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21242 \begin_layout Plain Layout
21243 \begin_inset Formula $\Re$
21253 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21256 \begin_layout Plain Layout
21264 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21267 \begin_layout Plain Layout
21268 \begin_inset Formula $\aleph$
21278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21281 \begin_layout Plain Layout
21289 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21292 \begin_layout Plain Layout
21293 \begin_inset Formula $\partial$
21303 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21306 \begin_layout Plain Layout
21314 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21317 \begin_layout Plain Layout
21318 \begin_inset Formula $\infty$
21328 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21331 \begin_layout Plain Layout
21339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21342 \begin_layout Plain Layout
21343 \begin_inset Formula $\wp$
21353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21356 \begin_layout Plain Layout
21364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21367 \begin_layout Plain Layout
21368 \begin_inset Formula $\imath$
21378 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21381 \begin_layout Plain Layout
21389 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21392 \begin_layout Plain Layout
21393 \begin_inset Formula $\jmath$
21407 \begin_inset space \hfill{}
21411 \begin_inset Tabular
21412 <lyxtabular version="3" rows="10" columns="2">
21413 <features booktabs="true" tabularvalignment="middle">
21414 <column alignment="center" valignment="top" width="0pt">
21415 <column alignment="center" valignment="top" width="0pt">
21417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21420 \begin_layout Plain Layout
21426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21429 \begin_layout Plain Layout
21431 \begin_inset Note Note
21434 \begin_layout Plain Layout
21441 is only used as spacer.
21453 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21456 \begin_layout Plain Layout
21464 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21467 \begin_layout Plain Layout
21468 \begin_inset Formula $\forall$
21478 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21481 \begin_layout Plain Layout
21489 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21492 \begin_layout Plain Layout
21493 \begin_inset Formula $\exists$
21503 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21506 \begin_layout Plain Layout
21514 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21517 \begin_layout Plain Layout
21518 \begin_inset Formula $\nexists$
21528 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21531 \begin_layout Plain Layout
21539 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21542 \begin_layout Plain Layout
21543 \begin_inset Formula $\emptyset$
21553 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21556 \begin_layout Plain Layout
21564 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21567 \begin_layout Plain Layout
21568 \begin_inset Formula $\varnothing$
21578 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21581 \begin_layout Plain Layout
21589 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21592 \begin_layout Plain Layout
21593 \begin_inset Formula $\dag$
21603 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21606 \begin_layout Plain Layout
21614 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21617 \begin_layout Plain Layout
21618 \begin_inset Formula $\ddag$
21628 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21631 \begin_layout Plain Layout
21639 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21642 \begin_layout Plain Layout
21646 \begin_layout Plain Layout
21656 \begin_inset Formula $\complement$
21663 \begin_layout Plain Layout
21677 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21680 \begin_layout Plain Layout
21688 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21691 \begin_layout Plain Layout
21692 \begin_inset Formula $\Bbbk$
21706 \begin_inset space \hfill{}
21710 \begin_inset Tabular
21711 <lyxtabular version="3" rows="10" columns="2">
21712 <features booktabs="true" tabularvalignment="middle">
21713 <column alignment="center" valignment="top" width="0pt">
21714 <column alignment="center" valignment="top" width="0pt">
21716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21719 \begin_layout Plain Layout
21725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21728 \begin_layout Plain Layout
21736 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21739 \begin_layout Plain Layout
21747 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21750 \begin_layout Plain Layout
21751 \begin_inset Formula $\prime$
21761 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21764 \begin_layout Plain Layout
21772 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21775 \begin_layout Plain Layout
21776 \begin_inset Formula $\backprime$
21786 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21789 \begin_layout Plain Layout
21797 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21800 \begin_layout Plain Layout
21801 \begin_inset Formula $\mho$
21811 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21814 \begin_layout Plain Layout
21822 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21825 \begin_layout Plain Layout
21826 \begin_inset Formula $\triangle$
21836 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21839 \begin_layout Plain Layout
21847 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21850 \begin_layout Plain Layout
21851 \begin_inset Formula $\angle$
21861 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21864 \begin_layout Plain Layout
21872 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21875 \begin_layout Plain Layout
21876 \begin_inset Formula $\measuredangle$
21886 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21889 \begin_layout Plain Layout
21897 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21900 \begin_layout Plain Layout
21901 \begin_inset Formula $\sphericalangle$
21911 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21914 \begin_layout Plain Layout
21922 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21925 \begin_layout Plain Layout
21926 \begin_inset Formula $\top$
21936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21939 \begin_layout Plain Layout
21947 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21950 \begin_layout Plain Layout
21951 \begin_inset Formula $\bot$
21967 \begin_layout Subsection
21968 Miscellaneous Symbols
21969 \begin_inset CommandInset label
21971 name "subsec:Miscellaneous-Symbols"
21976 \begin_inset Index idx
21979 \begin_layout Plain Layout
21980 Symbols ! miscellaneous
21988 \begin_layout Standard
21991 \begin_inset Tabular
21992 <lyxtabular version="3" rows="10" columns="2">
21993 <features booktabs="true" tabularvalignment="middle">
21994 <column alignment="center" valignment="top" width="0pt">
21995 <column alignment="center" valignment="top" width="0pt">
21997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22000 \begin_layout Plain Layout
22006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22009 \begin_layout Plain Layout
22017 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22020 \begin_layout Plain Layout
22028 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22031 \begin_layout Plain Layout
22032 \begin_inset Formula $\flat$
22042 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22045 \begin_layout Plain Layout
22053 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22056 \begin_layout Plain Layout
22057 \begin_inset Formula $\natural$
22067 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22070 \begin_layout Plain Layout
22078 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22081 \begin_layout Plain Layout
22082 \begin_inset Formula $\sharp$
22092 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22095 \begin_layout Plain Layout
22103 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22106 \begin_layout Plain Layout
22107 \begin_inset Formula $\surd$
22117 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22120 \begin_layout Plain Layout
22128 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22131 \begin_layout Plain Layout
22132 \begin_inset Formula $\checkmark$
22142 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22145 \begin_layout Plain Layout
22153 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22156 \begin_layout Plain Layout
22157 \begin_inset Formula $\yen$
22167 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22170 \begin_layout Plain Layout
22178 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22181 \begin_layout Plain Layout
22182 \begin_inset Formula $\pounds$
22192 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22195 \begin_layout Plain Layout
22201 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22204 \begin_layout Plain Layout
22205 \begin_inset Formula $\$$
22215 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22218 \begin_layout Plain Layout
22224 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22227 \begin_layout Plain Layout
22228 \begin_inset Formula $§$
22242 \begin_inset space \hfill{}
22246 \begin_inset Tabular
22247 <lyxtabular version="3" rows="10" columns="2">
22248 <features booktabs="true" tabularvalignment="middle">
22249 <column alignment="center" valignment="top" width="0pt">
22250 <column alignment="center" valignment="top">
22252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22255 \begin_layout Plain Layout
22261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22264 \begin_layout Plain Layout
22272 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22275 \begin_layout Plain Layout
22283 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22286 \begin_layout Plain Layout
22287 \begin_inset Formula $\hbar$
22297 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22300 \begin_layout Plain Layout
22308 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22311 \begin_layout Plain Layout
22312 \begin_inset Formula $\hslash$
22322 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22325 \begin_layout Plain Layout
22333 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22336 \begin_layout Plain Layout
22337 \begin_inset Formula $\clubsuit$
22347 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22350 \begin_layout Plain Layout
22358 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22361 \begin_layout Plain Layout
22362 \begin_inset Formula $\spadesuit$
22372 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22375 \begin_layout Plain Layout
22383 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22386 \begin_layout Plain Layout
22387 \begin_inset Formula $\bigstar$
22397 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22400 \begin_layout Plain Layout
22408 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22411 \begin_layout Plain Layout
22412 \begin_inset Formula $\blacklozenge$
22422 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22425 \begin_layout Plain Layout
22433 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22436 \begin_layout Plain Layout
22437 \begin_inset Formula $\blacktriangle$
22447 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22450 \begin_layout Plain Layout
22458 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22461 \begin_layout Plain Layout
22462 \begin_inset Formula $\blacktriangledown$
22472 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22475 \begin_layout Plain Layout
22483 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22486 \begin_layout Plain Layout
22487 \begin_inset Formula $\bullet$
22501 \begin_inset space \hfill{}
22505 \begin_inset Tabular
22506 <lyxtabular version="3" rows="10" columns="2">
22507 <features booktabs="true" tabularvalignment="middle">
22508 <column alignment="center" valignment="top" width="0pt">
22509 <column alignment="center" valignment="top" width="0pt">
22511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22514 \begin_layout Plain Layout
22520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22523 \begin_layout Plain Layout
22531 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22534 \begin_layout Plain Layout
22542 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22545 \begin_layout Plain Layout
22546 \begin_inset Formula $\diamondsuit$
22556 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22559 \begin_layout Plain Layout
22567 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22570 \begin_layout Plain Layout
22571 \begin_inset Formula $\Diamond$
22581 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22584 \begin_layout Plain Layout
22592 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22595 \begin_layout Plain Layout
22596 \begin_inset Formula $\heartsuit$
22606 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22609 \begin_layout Plain Layout
22617 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22620 \begin_layout Plain Layout
22621 \begin_inset Formula $\P$
22631 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22634 \begin_layout Plain Layout
22642 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22645 \begin_layout Plain Layout
22646 \begin_inset Formula $\copyright$
22656 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22659 \begin_layout Plain Layout
22667 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22670 \begin_layout Plain Layout
22671 \begin_inset Formula $\circledR$
22681 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22684 \begin_layout Plain Layout
22692 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22695 \begin_layout Plain Layout
22696 \begin_inset Formula $\maltese$
22706 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22709 \begin_layout Plain Layout
22717 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22720 \begin_layout Plain Layout
22721 \begin_inset Formula $\diagup$
22731 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22734 \begin_layout Plain Layout
22742 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22745 \begin_layout Plain Layout
22746 \begin_inset Formula $\diagdown$
22762 \begin_layout Standard
22763 \begin_inset VSpace medskip
22769 \begin_layout Standard
22770 Some symbols can be displayed in different sizes, see
22771 \begin_inset CommandInset ref
22773 reference "subsec:Font-Sizes"
22780 \begin_layout Subsection
22782 \begin_inset Index idx
22785 \begin_layout Plain Layout
22786 Symbols ! Euro-symbol
22792 \begin_inset Index idx
22795 \begin_layout Plain Layout
22802 \begin_layout Plain Layout
22819 \begin_layout Standard
22820 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22826 \begin_inset Index idx
22829 \begin_layout Plain Layout
22835 must be installed and loaded with the \SpecialChar LaTeX
22839 \begin_layout Standard
22844 usepackage[gennarrow]{eurosym}
22847 \begin_layout Standard
22848 The Euro symbol can now be inserted with the command
22855 \begin_inset Index idx
22858 \begin_layout Plain Layout
22869 \begin_layout Standard
22870 The Euro symbol can directly be inserted with the € key in mathematical
22871 text, without having
22886 can also be inserted in \SpecialChar TeX
22888 The official currency symbol can then be inserted with the command
22895 \begin_inset Index idx
22898 \begin_layout Plain Layout
22906 , that is only available in \SpecialChar TeX
22910 \begin_layout Standard
22914 \begin_layout Plain Layout
22924 \begin_inset Note Note
22927 \begin_layout Plain Layout
22928 The following table will only be displayed when the \SpecialChar LaTeX
22941 \begin_layout Standard
22942 An overview about the different Euro symbols:
22945 \begin_layout Standard
22947 \begin_inset Tabular
22948 <lyxtabular version="3" rows="4" columns="3">
22949 <features booktabs="true" tabularvalignment="middle">
22950 <column alignment="center" valignment="top" width="0pt">
22951 <column alignment="center" valignment="top" width="0pt">
22952 <column alignment="center" valignment="top" width="0pt">
22954 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22957 \begin_layout Plain Layout
22961 \begin_layout Plain Layout
22965 cmidrule[0.08em]{2-3}
22975 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22978 \begin_layout Plain Layout
22984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22987 \begin_layout Plain Layout
22995 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22998 \begin_layout Plain Layout
23004 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23007 \begin_layout Plain Layout
23015 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23018 \begin_layout Plain Layout
23019 \begin_inset Formula $\euro$
23029 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23032 \begin_layout Plain Layout
23038 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23041 \begin_layout Plain Layout
23047 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23050 \begin_layout Plain Layout
23051 \begin_inset Formula $\mbox{€}$
23061 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23064 \begin_layout Plain Layout
23071 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23074 \begin_layout Plain Layout
23082 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23085 \begin_layout Plain Layout
23089 \begin_layout Plain Layout
23109 \begin_inset Note Note
23112 \begin_layout Plain Layout
23119 is used here only for table borders.
23129 manual for details.
23137 \begin_layout Standard
23141 \begin_layout Plain Layout
23151 \begin_inset Note Note
23154 \begin_layout Plain Layout
23155 The following will be displayed when the \SpecialChar LaTeX
23168 \begin_layout Standard
23169 You need to install the \SpecialChar LaTeX
23174 to see the rest of this subsection in the output.
23177 \begin_layout Standard
23181 \begin_layout Plain Layout
23193 \begin_layout Section
23195 \begin_inset CommandInset label
23197 name "sec:Relations"
23202 \begin_inset Index idx
23205 \begin_layout Plain Layout
23212 \begin_inset Index idx
23215 \begin_layout Plain Layout
23220 \begin_layout Plain Layout
23231 \begin_layout Plain Layout
23246 \begin_layout Standard
23247 All following relations can also be inserted via the toolbar button
23250 arg "math-insert \\leq"
23256 \begin_layout Standard
23257 \begin_inset Tabular
23258 <lyxtabular version="3" rows="17" columns="2">
23259 <features booktabs="true" tabularvalignment="middle">
23260 <column alignment="center" valignment="top" width="0pt">
23261 <column alignment="center" valignment="top" width="0pt">
23263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23266 \begin_layout Plain Layout
23272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23275 \begin_layout Plain Layout
23283 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23286 \begin_layout Plain Layout
23292 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23295 \begin_layout Plain Layout
23296 \begin_inset Formula $<$
23306 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23309 \begin_layout Plain Layout
23317 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23320 \begin_layout Plain Layout
23321 \begin_inset Formula $\le$
23331 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23334 \begin_layout Plain Layout
23342 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23345 \begin_layout Plain Layout
23346 \begin_inset Formula $\ll$
23356 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23359 \begin_layout Plain Layout
23367 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23370 \begin_layout Plain Layout
23371 \begin_inset Formula $\prec$
23381 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23384 \begin_layout Plain Layout
23392 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23395 \begin_layout Plain Layout
23396 \begin_inset Formula $\preceq$
23406 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23409 \begin_layout Plain Layout
23417 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23420 \begin_layout Plain Layout
23421 \begin_inset Formula $\subset$
23431 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23434 \begin_layout Plain Layout
23442 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23445 \begin_layout Plain Layout
23446 \begin_inset Formula $\subseteq$
23456 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23459 \begin_layout Plain Layout
23467 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23470 \begin_layout Plain Layout
23471 \begin_inset Formula $\sqsubseteq$
23481 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23484 \begin_layout Plain Layout
23492 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23495 \begin_layout Plain Layout
23496 \begin_inset Formula $\in$
23506 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23509 \begin_layout Plain Layout
23517 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23520 \begin_layout Plain Layout
23521 \begin_inset Formula $\vdash$
23531 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23534 \begin_layout Plain Layout
23542 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23545 \begin_layout Plain Layout
23546 \begin_inset Formula $\smile$
23556 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23559 \begin_layout Plain Layout
23567 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23570 \begin_layout Plain Layout
23571 \begin_inset Formula $\lhd$
23581 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23584 \begin_layout Plain Layout
23592 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23595 \begin_layout Plain Layout
23596 \begin_inset Formula $\unlhd$
23606 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23609 \begin_layout Plain Layout
23617 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23620 \begin_layout Plain Layout
23621 \begin_inset Formula $\gtrless$
23631 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23634 \begin_layout Plain Layout
23642 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23645 \begin_layout Plain Layout
23646 \begin_inset Formula $\mid$
23656 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23659 \begin_layout Plain Layout
23667 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23670 \begin_layout Plain Layout
23671 \begin_inset Formula $\nmid$
23685 \begin_inset space \hfill{}
23689 \begin_inset Tabular
23690 <lyxtabular version="3" rows="17" columns="2">
23691 <features booktabs="true" tabularvalignment="middle">
23692 <column alignment="center" valignment="top" width="0pt">
23693 <column alignment="center" valignment="top" width="0pt">
23695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23698 \begin_layout Plain Layout
23704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23707 \begin_layout Plain Layout
23715 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23718 \begin_layout Plain Layout
23724 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23727 \begin_layout Plain Layout
23728 \begin_inset Formula $=$
23738 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23741 \begin_layout Plain Layout
23749 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23752 \begin_layout Plain Layout
23753 \begin_inset Formula $\not=$
23763 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23766 \begin_layout Plain Layout
23774 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23777 \begin_layout Plain Layout
23778 \begin_inset Formula $\equiv$
23788 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23791 \begin_layout Plain Layout
23799 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23802 \begin_layout Plain Layout
23803 \begin_inset Formula $\sim$
23813 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23816 \begin_layout Plain Layout
23824 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23827 \begin_layout Plain Layout
23828 \begin_inset Formula $\simeq$
23838 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23841 \begin_layout Plain Layout
23849 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23852 \begin_layout Plain Layout
23853 \begin_inset Formula $\approx$
23863 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23866 \begin_layout Plain Layout
23874 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23877 \begin_layout Plain Layout
23878 \begin_inset Formula $\cong$
23888 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23891 \begin_layout Plain Layout
23899 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23902 \begin_layout Plain Layout
23903 \begin_inset Formula $\bowtie$
23913 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23916 \begin_layout Plain Layout
23924 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23927 \begin_layout Plain Layout
23928 \begin_inset Formula $\notin$
23938 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23941 \begin_layout Plain Layout
23949 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23952 \begin_layout Plain Layout
23953 \begin_inset Formula $\perp$
23963 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23966 \begin_layout Plain Layout
23974 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23977 \begin_layout Plain Layout
23978 \begin_inset Formula $\propto$
23988 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23991 \begin_layout Plain Layout
23999 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24002 \begin_layout Plain Layout
24003 \begin_inset Formula $\asymp$
24013 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24016 \begin_layout Plain Layout
24024 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24027 \begin_layout Plain Layout
24028 \begin_inset Formula $\doteq$
24038 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24041 \begin_layout Plain Layout
24049 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24052 \begin_layout Plain Layout
24053 \begin_inset Formula $\circeq$
24063 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24066 \begin_layout Plain Layout
24074 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24077 \begin_layout Plain Layout
24078 \begin_inset Formula $\models$
24088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24091 \begin_layout Plain Layout
24099 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24102 \begin_layout Plain Layout
24103 \begin_inset Formula $\widehat{=}$
24117 \begin_inset space \hfill{}
24121 \begin_inset Tabular
24122 <lyxtabular version="3" rows="17" columns="2">
24123 <features booktabs="true" tabularvalignment="middle">
24124 <column alignment="center" valignment="top" width="0pt">
24125 <column alignment="center" valignment="top" width="0pt">
24127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24130 \begin_layout Plain Layout
24136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24139 \begin_layout Plain Layout
24147 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24150 \begin_layout Plain Layout
24156 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24159 \begin_layout Plain Layout
24160 \begin_inset Formula $>$
24170 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24173 \begin_layout Plain Layout
24181 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24184 \begin_layout Plain Layout
24185 \begin_inset Formula $\ge$
24195 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24198 \begin_layout Plain Layout
24206 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24209 \begin_layout Plain Layout
24210 \begin_inset Formula $\gg$
24220 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24223 \begin_layout Plain Layout
24231 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24234 \begin_layout Plain Layout
24235 \begin_inset Formula $\succ$
24245 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24248 \begin_layout Plain Layout
24256 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24259 \begin_layout Plain Layout
24260 \begin_inset Formula $\succeq$
24270 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24273 \begin_layout Plain Layout
24281 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24284 \begin_layout Plain Layout
24285 \begin_inset Formula $\supset$
24295 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24298 \begin_layout Plain Layout
24306 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24309 \begin_layout Plain Layout
24310 \begin_inset Formula $\supseteq$
24320 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24323 \begin_layout Plain Layout
24331 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24334 \begin_layout Plain Layout
24335 \begin_inset Formula $\sqsupseteq$
24345 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24348 \begin_layout Plain Layout
24356 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24359 \begin_layout Plain Layout
24360 \begin_inset Formula $\ni$
24370 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24373 \begin_layout Plain Layout
24381 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24384 \begin_layout Plain Layout
24385 \begin_inset Formula $\dashv$
24395 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24398 \begin_layout Plain Layout
24406 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24409 \begin_layout Plain Layout
24410 \begin_inset Formula $\frown$
24420 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24423 \begin_layout Plain Layout
24431 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24434 \begin_layout Plain Layout
24435 \begin_inset Formula $\rhd$
24445 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24448 \begin_layout Plain Layout
24456 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24459 \begin_layout Plain Layout
24460 \begin_inset Formula $\unrhd$
24470 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24473 \begin_layout Plain Layout
24481 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24484 \begin_layout Plain Layout
24485 \begin_inset Formula $\lessgtr$
24495 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24498 \begin_layout Plain Layout
24506 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24509 \begin_layout Plain Layout
24510 \begin_inset Formula $\parallel$
24520 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24523 \begin_layout Plain Layout
24531 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24534 \begin_layout Plain Layout
24535 \begin_inset Formula $\nparallel$
24551 \begin_layout Standard
24552 \begin_inset VSpace medskip
24567 are bigger than the equal looking operators
24582 \begin_layout Standard
24584 supports also many special relations.
24585 Use the toolbar button
24588 arg "math-insert \\leqq"
24591 to see a list of these relations.
24594 \begin_layout Standard
24595 Relations are, in contrary to symbols, always surrounded by space.
24598 \begin_layout Standard
24599 Relations with labels can be created with the command
24606 \begin_inset Index idx
24609 \begin_layout Plain Layout
24620 \begin_layout Standard
24622 \begin_inset Tabular
24623 <lyxtabular version="3" rows="2" columns="2">
24624 <features booktabs="true" tabularvalignment="middle">
24625 <column alignment="center" valignment="top" width="0pt">
24626 <column alignment="center" valignment="top">
24628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24631 \begin_layout Plain Layout
24637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24640 \begin_layout Plain Layout
24647 <row topspace="1.5mm">
24648 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24651 \begin_layout Plain Layout
24655 \begin_inset space \textvisiblespace{}
24663 \begin_inset space \textvisiblespace{}
24667 \begin_inset Formula $\downarrow$
24673 \begin_inset space \textvisiblespace{}
24677 \begin_inset space \textvisiblespace{}
24685 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24688 \begin_layout Plain Layout
24689 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24705 \begin_layout Section
24709 \begin_layout Subsection
24710 Predefined Functions
24711 \begin_inset CommandInset label
24713 name "subsec:Predefined-Functions"
24718 \begin_inset Index idx
24721 \begin_layout Plain Layout
24722 Functions ! predefined
24730 \begin_layout Standard
24731 In general, variables are set
24735 in mathematical expressions, but not function names, because
24736 \begin_inset Formula $sin$
24739 could be misunderstood as
24740 \begin_inset Formula $s\cdot i\cdot n$
24744 Therefore there are predefined functions which are additionally a bit separated
24746 They are inserted as commands starting with a backslash before their name.
24749 \begin_layout Standard
24751 \begin_inset Tabular
24752 <lyxtabular version="3" rows="2" columns="2">
24753 <features booktabs="true" tabularvalignment="middle">
24754 <column alignment="center" valignment="top" width="0pt">
24755 <column alignment="center" valignment="top" width="0pt">
24757 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24760 \begin_layout Plain Layout
24766 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24769 \begin_layout Plain Layout
24777 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24780 \begin_layout Plain Layout
24786 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24789 \begin_layout Plain Layout
24790 \begin_inset Formula $Asin(x)+B$
24804 \begin_inset space \quad{}
24808 \begin_inset Tabular
24809 <lyxtabular version="3" rows="2" columns="2">
24810 <features booktabs="true" tabularvalignment="middle">
24811 <column alignment="center" valignment="top" width="0pt">
24812 <column alignment="center" valignment="top" width="0pt">
24814 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24817 \begin_layout Plain Layout
24823 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24826 \begin_layout Plain Layout
24834 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24837 \begin_layout Plain Layout
24845 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24848 \begin_layout Plain Layout
24849 \begin_inset Formula $A\sin(x)+B$
24865 \begin_layout Standard
24866 The following functions are predefined:
24869 \begin_layout Standard
24870 \begin_inset VSpace -2mm
24876 \begin_layout Standard
24878 \begin_inset Tabular
24879 <lyxtabular version="3" rows="9" columns="4">
24880 <features booktabs="true" tabularvalignment="middle">
24881 <column alignment="center" valignment="top" width="0pt">
24882 <column alignment="center" valignment="top" width="0pt">
24883 <column alignment="center" valignment="top" width="0pt">
24884 <column alignment="center" valignment="top" width="0pt">
24886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24889 \begin_layout Plain Layout
24895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24898 \begin_layout Plain Layout
24904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24907 \begin_layout Plain Layout
24913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24916 \begin_layout Plain Layout
24924 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24927 \begin_layout Plain Layout
24935 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24938 \begin_layout Plain Layout
24946 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24949 \begin_layout Plain Layout
24957 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24960 \begin_layout Plain Layout
24970 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24973 \begin_layout Plain Layout
24981 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24984 \begin_layout Plain Layout
24992 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24995 \begin_layout Plain Layout
25003 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25006 \begin_layout Plain Layout
25016 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25019 \begin_layout Plain Layout
25027 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25030 \begin_layout Plain Layout
25038 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25041 \begin_layout Plain Layout
25049 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25052 \begin_layout Plain Layout
25062 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25065 \begin_layout Plain Layout
25073 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25076 \begin_layout Plain Layout
25084 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25087 \begin_layout Plain Layout
25095 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25098 \begin_layout Plain Layout
25108 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25111 \begin_layout Plain Layout
25119 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25122 \begin_layout Plain Layout
25130 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25133 \begin_layout Plain Layout
25141 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25144 \begin_layout Plain Layout
25154 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25157 \begin_layout Plain Layout
25165 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25168 \begin_layout Plain Layout
25176 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25179 \begin_layout Plain Layout
25187 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25190 \begin_layout Plain Layout
25200 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25203 \begin_layout Plain Layout
25211 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25214 \begin_layout Plain Layout
25222 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25225 \begin_layout Plain Layout
25233 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25236 \begin_layout Plain Layout
25246 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25249 \begin_layout Plain Layout
25257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25260 \begin_layout Plain Layout
25268 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25271 \begin_layout Plain Layout
25279 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25282 \begin_layout Plain Layout
25298 \begin_layout Standard
25299 They can also be inserted with the math toolbar button
25302 arg "math-insert \\functions"
25308 \begin_layout Subsection
25309 Self-defined Functions
25310 \begin_inset Index idx
25313 \begin_layout Plain Layout
25314 Functions ! self-defined
25322 \begin_layout Standard
25323 To use a function that is not predefined, like for example the sign function
25324 sgn(x), there are two possibilities:
25327 \begin_layout Itemize
25328 Define the function by inserting the following line to the \SpecialChar LaTeX
25333 \begin_layout Plain Layout
25338 DeclareMathOperator
25341 \begin_inset CommandInset ref
25343 reference "subsec:Self-defined-Operators"
25353 \begin_inset Newline newline
25357 \begin_inset VSpace -3mm
25361 \begin_inset Newline newline
25368 DeclareMathOperator{
25373 \begin_inset Index idx
25376 \begin_layout Plain Layout
25381 DeclareMathOperator
25387 \begin_inset Newline newline
25391 \begin_inset VSpace -2mm
25395 \begin_inset Newline newline
25398 Now the new defined function can be called with the command
25407 \begin_layout Itemize
25408 Write the formula as usual, mark the formula name, in our example the letters
25413 , and change it to mathematical text.
25414 Finally, a space is inserted between prefactor and function.
25417 \begin_layout Standard
25418 The result is the same with both methods as with a predefined function
25422 \begin_layout Plain Layout
25423 In \SpecialChar LyX
25424 self-defined functions are displayed red, predefined ones black.
25432 \begin_layout Standard
25434 \begin_inset Tabular
25435 <lyxtabular version="3" rows="3" columns="2">
25436 <features booktabs="true" tabularvalignment="middle">
25437 <column alignment="center" valignment="top" width="0pt">
25438 <column alignment="center" valignment="top" width="0pt">
25440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25443 \begin_layout Plain Layout
25449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25452 \begin_layout Plain Layout
25460 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25463 \begin_layout Plain Layout
25471 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25474 \begin_layout Plain Layout
25475 \begin_inset Formula $A\sgn(x)+B$
25485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25488 \begin_layout Plain Layout
25492 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25503 \begin_layout Plain Layout
25504 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25520 \begin_layout Standard
25521 The first method is more suitable when the self-defined function should
25522 be used several times.
25525 \begin_layout Subsection
25527 \begin_inset Index idx
25530 \begin_layout Plain Layout
25539 \begin_layout Standard
25540 For limits, in addition to the commands
25547 \begin_inset Index idx
25550 \begin_layout Plain Layout
25570 the following functions are defined:
25573 \begin_layout Standard
25575 \begin_inset Tabular
25576 <lyxtabular version="3" rows="5" columns="2">
25577 <features booktabs="true" tabularvalignment="middle">
25578 <column alignment="center" valignment="top" width="0pt">
25579 <column alignment="center" valignment="top" width="0pt">
25581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25584 \begin_layout Plain Layout
25590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25593 \begin_layout Plain Layout
25601 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25604 \begin_layout Plain Layout
25612 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25615 \begin_layout Plain Layout
25616 \begin_inset Formula $\varliminf$
25625 <row topspace="1.5mm">
25626 <cell alignment="center" valignment="top" usebox="none">
25629 \begin_layout Plain Layout
25637 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25640 \begin_layout Plain Layout
25641 \begin_inset Formula $\varlimsup$
25650 <row topspace="1.5mm">
25651 <cell alignment="center" valignment="top" usebox="none">
25654 \begin_layout Plain Layout
25662 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25665 \begin_layout Plain Layout
25666 \begin_inset Formula $\varprojlim$
25675 <row topspace="1.5mm" bottomspace="1mm">
25676 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25679 \begin_layout Plain Layout
25687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25690 \begin_layout Plain Layout
25691 \begin_inset Formula $\varinjlim$
25707 \begin_layout Standard
25708 \begin_inset VSpace medskip
25711 The limit is created by inserting a subscript.
25712 It is set right beside the function in an inline formula:
25715 \begin_layout Standard
25717 \begin_inset Tabular
25718 <lyxtabular version="3" rows="2" columns="2">
25719 <features booktabs="true" tabularvalignment="middle">
25720 <column alignment="center" valignment="top" width="0pt">
25721 <column alignment="center" valignment="top" width="0pt">
25723 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25726 \begin_layout Plain Layout
25732 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25735 \begin_layout Plain Layout
25743 <cell alignment="center" valignment="top" usebox="none">
25746 \begin_layout Plain Layout
25752 \begin_inset space \textvisiblespace{}
25756 \begin_inset space \textvisiblespace{}
25764 <cell alignment="center" valignment="top" usebox="none">
25767 \begin_layout Plain Layout
25768 \begin_inset Formula $\lim_{x\to A}x=B$
25784 \begin_layout Standard
25785 In a displayed formula the limit is set below the formula, as usual:
25786 \begin_inset Formula
25796 \begin_layout Standard
25797 \begin_inset VSpace medskip
25803 \begin_layout Standard
25804 How to adjust the typesetting of the limits see
25805 \begin_inset CommandInset ref
25807 reference "subsec:Operator-Limits"
25814 \begin_layout Subsection
25816 \begin_inset Index idx
25819 \begin_layout Plain Layout
25820 Functions ! modulo-
25828 \begin_layout Standard
25829 The modulo-function is special, because it exists in four variants.
25830 The variants in a displayed formula are:
25831 \begin_inset Formula
25833 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25834 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25835 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25836 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25837 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25845 \begin_layout Standard
25846 In an inline formula less space is set before the function names for all
25848 By default the modulo-functions take only the first following character
25850 To use more than one character, one has to put them into \SpecialChar TeX
25852 \begin_inset Formula
25854 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25855 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25856 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25864 \begin_layout Section
25866 \begin_inset Index idx
25869 \begin_layout Plain Layout
25878 \begin_layout Standard
25879 The characters ^ and _ would normally create a superscript and subscript,
25881 To get these characters you have to insert them with a leading
25886 \begin_layout Standard
25889 \begin_inset Tabular
25890 <lyxtabular version="3" rows="3" columns="2">
25891 <features booktabs="true" tabularvalignment="middle">
25892 <column alignment="left" valignment="top" width="0pt">
25893 <column alignment="block" valignment="top">
25895 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25898 \begin_layout Plain Layout
25904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25907 \begin_layout Plain Layout
25915 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25918 \begin_layout Plain Layout
25922 \begin_inset space \textvisiblespace{}
25930 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25933 \begin_layout Plain Layout
25934 \begin_inset Formula $\mathcircumflex$
25944 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25947 \begin_layout Plain Layout
25955 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25958 \begin_layout Plain Layout
25959 \begin_inset Formula $\_$
25975 \begin_layout Subsection
25976 Special Characters in Mathematical Text
25979 \begin_layout Standard
25980 The following commands can only be used in mathematical text or in \SpecialChar TeX
25984 \begin_layout Standard
25985 \begin_inset space \hfill{}
25989 \begin_inset Tabular
25990 <lyxtabular version="3" rows="8" columns="2">
25991 <features booktabs="true" tabularvalignment="middle">
25992 <column alignment="left" valignment="top" width="0pt">
25993 <column alignment="block" valignment="top">
25995 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25998 \begin_layout Plain Layout
26004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26007 \begin_layout Plain Layout
26015 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26018 \begin_layout Plain Layout
26026 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26029 \begin_layout Plain Layout
26030 \begin_inset Formula $\textrm{œ}$
26040 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26043 \begin_layout Plain Layout
26051 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26054 \begin_layout Plain Layout
26055 \begin_inset Formula $\textrm{Œ}$
26065 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26068 \begin_layout Plain Layout
26076 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26079 \begin_layout Plain Layout
26080 \begin_inset Formula $\textrm{æ}$
26090 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26093 \begin_layout Plain Layout
26101 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26104 \begin_layout Plain Layout
26105 \begin_inset Formula $\textrm{Æ}$
26115 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26118 \begin_layout Plain Layout
26126 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26129 \begin_layout Plain Layout
26130 \begin_inset Formula $\textrm{å}$
26140 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26143 \begin_layout Plain Layout
26151 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26154 \begin_layout Plain Layout
26155 \begin_inset Formula $\textrm{Å}$
26165 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26168 \begin_layout Plain Layout
26176 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26179 \begin_layout Plain Layout
26180 \begin_inset Formula $\textrm{ı}$
26194 \begin_inset space \hfill{}
26198 \begin_inset Tabular
26199 <lyxtabular version="3" rows="8" columns="2">
26200 <features booktabs="true" tabularvalignment="middle">
26201 <column alignment="left" valignment="top" width="0pt">
26202 <column alignment="center" valignment="top">
26204 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26207 \begin_layout Plain Layout
26209 \begin_inset Note Note
26212 \begin_layout Plain Layout
26214 \begin_inset space \thinspace{}
26217 mm is used for separation, because otherwise the output will be ¡ and ¿
26228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26231 \begin_layout Plain Layout
26239 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26242 \begin_layout Plain Layout
26250 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26253 \begin_layout Plain Layout
26254 \begin_inset Formula $\textrm{ø}$
26264 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26267 \begin_layout Plain Layout
26275 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26278 \begin_layout Plain Layout
26279 \begin_inset Formula $\textrm{Ø}$
26289 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26292 \begin_layout Plain Layout
26300 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26303 \begin_layout Plain Layout
26304 \begin_inset Formula $\textrm{ł}$
26314 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26317 \begin_layout Plain Layout
26325 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26328 \begin_layout Plain Layout
26329 \begin_inset Formula $\textrm{Ł}$
26339 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26342 \begin_layout Plain Layout
26344 \begin_inset space \hspace{}
26349 \begin_inset space \textvisiblespace{}
26357 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26360 \begin_layout Plain Layout
26361 \begin_inset Formula $\textrm{!`}$
26371 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26374 \begin_layout Plain Layout
26376 \begin_inset space \hspace{}
26381 \begin_inset space \textvisiblespace{}
26389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26392 \begin_layout Plain Layout
26393 \begin_inset Formula $\textrm{?`}$
26403 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26406 \begin_layout Plain Layout
26414 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26417 \begin_layout Plain Layout
26418 \begin_inset Formula $\textrm{ȷ}$
26432 \begin_inset space \hfill{}
26438 \begin_layout Standard
26440 \begin_inset Formula $\textrm{\textrm{Å}}$
26444 \begin_inset Formula $\textrm{\textrm{Ø}}$
26447 can also be inserted via the math toolbar button
26450 arg "math-insert \\digamma"
26456 \begin_layout Standard
26457 An exception are the commands
26460 \begin_inset space \hspace{}
26469 \begin_inset space \hspace{}
26475 , because they can be inserted in \SpecialChar LyX
26479 \begin_layout Subsection
26481 \begin_inset CommandInset label
26483 name "subsec:Accents-in-Text"
26488 \begin_inset Index idx
26491 \begin_layout Plain Layout
26500 \begin_layout Standard
26501 With the following commands all letters can be accented.
26502 The commands must be inserted in \SpecialChar TeX
26506 \begin_layout Standard
26507 \begin_inset space \hfill{}
26511 \begin_inset Tabular
26512 <lyxtabular version="3" rows="8" columns="2">
26513 <features booktabs="true" tabularvalignment="middle">
26514 <column alignment="left" valignment="top" width="0pt">
26515 <column alignment="block" valignment="top">
26517 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26520 \begin_layout Plain Layout
26526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26529 \begin_layout Plain Layout
26537 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26540 \begin_layout Plain Layout
26544 \begin_inset Quotes grd
26552 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26555 \begin_layout Plain Layout
26559 \begin_layout Plain Layout
26575 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26578 \begin_layout Plain Layout
26586 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26589 \begin_layout Plain Layout
26593 \begin_layout Plain Layout
26609 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26612 \begin_layout Plain Layout
26616 \begin_inset space \textvisiblespace{}
26624 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26627 \begin_layout Plain Layout
26631 \begin_layout Plain Layout
26647 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26650 \begin_layout Plain Layout
26658 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26661 \begin_layout Plain Layout
26665 \begin_layout Plain Layout
26681 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26684 \begin_layout Plain Layout
26688 \begin_inset space \textvisiblespace{}
26696 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26699 \begin_layout Plain Layout
26703 \begin_layout Plain Layout
26719 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26722 \begin_layout Plain Layout
26726 \begin_inset space \textvisiblespace{}
26734 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26737 \begin_layout Plain Layout
26741 \begin_layout Plain Layout
26757 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26760 \begin_layout Plain Layout
26764 \begin_inset space \textvisiblespace{}
26772 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26775 \begin_layout Plain Layout
26779 \begin_layout Plain Layout
26799 \begin_inset space \hfill{}
26803 \begin_inset Tabular
26804 <lyxtabular version="3" rows="8" columns="2">
26805 <features booktabs="true" tabularvalignment="middle">
26806 <column alignment="left" valignment="top" width="0pt">
26807 <column alignment="center" valignment="top">
26809 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26812 \begin_layout Plain Layout
26818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26821 \begin_layout Plain Layout
26829 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26832 \begin_layout Plain Layout
26836 \begin_inset space \textvisiblespace{}
26844 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26847 \begin_layout Plain Layout
26851 \begin_layout Plain Layout
26867 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26870 \begin_layout Plain Layout
26878 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26881 \begin_layout Plain Layout
26885 \begin_layout Plain Layout
26901 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26904 \begin_layout Plain Layout
26908 \begin_inset Index idx
26911 \begin_layout Plain Layout
26922 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26925 \begin_layout Plain Layout
26929 \begin_layout Plain Layout
26945 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26948 \begin_layout Plain Layout
26956 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26959 \begin_layout Plain Layout
26963 \begin_layout Plain Layout
26979 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26982 \begin_layout Plain Layout
26986 \begin_inset space \textvisiblespace{}
26994 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26997 \begin_layout Plain Layout
27001 \begin_layout Plain Layout
27017 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27020 \begin_layout Plain Layout
27024 \begin_inset space \textvisiblespace{}
27032 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27035 \begin_layout Plain Layout
27039 \begin_layout Plain Layout
27055 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27058 \begin_layout Plain Layout
27062 \begin_inset space \textvisiblespace{}
27070 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27073 \begin_layout Plain Layout
27077 \begin_layout Plain Layout
27097 \begin_inset space \hfill{}
27103 \begin_layout Standard
27104 \begin_inset VSpace medskip
27113 also two different characters can be accented.
27119 \begin_inset space \textvisiblespace{}
27128 \begin_layout Plain Layout
27140 \begin_layout Standard
27153 can in combination with vowels directly be inserted with the keyboard without
27154 using \SpecialChar TeX
27156 The same applies for the tilde
27160 \begin_layout Plain Layout
27161 This only applies for keyboards where the tilde is defined as accent.
27170 in combination with
27185 \begin_layout Standard
27228 and accents that are inserted directly with the keyboard are also available
27229 in mathematical text.
27230 For the other accents there are special math commands to be used in formulas,
27232 \begin_inset CommandInset ref
27234 reference "subsec:Accents-for-one"
27241 \begin_layout Standard
27242 \begin_inset VSpace bigskip
27245 Furthermore, with the command
27252 \begin_inset Index idx
27255 \begin_layout Plain Layout
27263 all numbers and letters can be set into a circle, quasi accented with a
27264 circle, similar to the copyright symbol.
27267 \begin_layout Standard
27269 \begin_inset Tabular
27270 <lyxtabular version="3" rows="3" columns="2">
27271 <features booktabs="true" tabularvalignment="middle">
27272 <column alignment="center" valignment="top" width="0pt">
27273 <column alignment="center" valignment="top">
27275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27278 \begin_layout Plain Layout
27284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27287 \begin_layout Plain Layout
27295 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27298 \begin_layout Plain Layout
27306 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27309 \begin_layout Plain Layout
27313 \begin_layout Plain Layout
27328 <row topspace="1mm">
27329 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27332 \begin_layout Plain Layout
27343 raisebox{-1.5pt}{W}}
27348 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27351 \begin_layout Plain Layout
27355 \begin_layout Plain Layout
27385 \begin_layout Standard
27386 One has to take care that the character fits in the circle.
27397 \begin_layout Plain Layout
27399 \begin_inset CommandInset ref
27401 reference "subsec:Font-Sizes"
27410 specifies thereby the size of the circle.
27421 \begin_layout Plain Layout
27423 \begin_inset CommandInset ref
27425 reference "subsec:Boxes-without-Frame"
27434 the character can be centered.
27437 \begin_layout Subsection
27439 \begin_inset Index idx
27442 \begin_layout Plain Layout
27451 \begin_layout Standard
27452 Old-style figures (also known as old-style numerals) are created with the
27460 \begin_inset Index idx
27463 \begin_layout Plain Layout
27472 The command can be used in formulas and in \SpecialChar TeX
27474 The command scheme is:
27477 \begin_layout Standard
27482 oldstylenums{number}
27485 \begin_layout Standard
27490 oldstylenums{0123456789
27493 \begin_inset Formula $\oldstylenums{0123456789}$
27499 \begin_layout Section
27501 \begin_inset CommandInset label
27503 name "sec:Formula-Styles"
27508 \begin_inset Index idx
27511 \begin_layout Plain Layout
27520 \begin_layout Itemize
27521 There are two different alignment styles:
27525 \begin_layout Description
27526 Centered is the predefined standard.
27529 \begin_layout Description
27530 Indented this can be set using the menu
27532 Document\SpecialChar menuseparator
27538 \begin_inset space ~
27544 \begin_layout Standard
27549 is used, the indentation can be adjusted.
27550 The default value depends on the used document class.
27554 \begin_layout Itemize
27555 And two different numbering styles that can be set in the menu
27557 Document\SpecialChar menuseparator
27563 \begin_inset space ~
27572 \begin_layout Description
27573 Right is in most cases the default.
27576 \begin_layout Description
27581 \begin_layout Standard
27582 The chosen styles are used for all displayed formulas of the document.
27583 When both, centered and indented formulas should be created in a document,
27589 The indented formulas are then set in a flalign environment, see
27590 \begin_inset CommandInset ref
27592 reference "subsec:Flalign-Environment"
27599 \begin_layout Section
27601 \begin_inset CommandInset label
27603 name "sec:Multiline-Formulas"
27608 \begin_inset Index idx
27611 \begin_layout Plain Layout
27612 Formula ! multiline
27620 \begin_layout Subsection
27624 \begin_layout Standard
27625 In \SpecialChar LyX
27626 multiline formulas are created by pressing
27629 arg "newline-insert newline"
27633 This creates either an
27637 that is described in
27638 \begin_inset CommandInset ref
27640 reference "subsec:Standard-align-Environment"
27644 or, when automatically loading the package
27648 is disabled in the document settings, an
27650 eqnarray environment
27652 that is described in
27653 \begin_inset CommandInset ref
27655 reference "subsec:Eqnarray-Environment"
27660 The align environment is recommended because it provides in any case a
27661 typographically correct output.
27664 \begin_layout Standard
27665 There are other multiline formula environments that can be created via the
27668 Insert\SpecialChar menuseparator
27672 These environments are described in the following sections.
27675 \begin_layout Standard
27676 In all multiline formula environments a new line is created by pressing
27680 arg "newline-insert newline"
27684 To add or delete lines, the math toolbar buttons
27687 arg "tabular-feature append-row"
27693 arg "tabular-feature delete-row"
27696 , respectively, or the menu
27698 Edit\SpecialChar menuseparator
27704 \begin_layout Subsubsection
27706 \begin_inset CommandInset label
27708 name "subsec:Line-Separation"
27713 \begin_inset Index idx
27716 \begin_layout Plain Layout
27717 Formula ! multiline ! Line separation
27725 \begin_layout Standard
27726 There is sometimes not enough space in multiline formulas between the lines:
27727 \begin_inset Formula
27729 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}\\
27730 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
27738 \begin_layout Standard
27739 In \SpecialChar LaTeX
27740 additional line space is specified as optional argument of the new line
27742 This is not yet possible in \SpecialChar LyX
27747 \begin_layout Plain Layout
27749 \begin_inset CommandInset href
27751 name "LyX-bug #1505"
27752 target "http://www.lyx.org/trac/ticket/1505"
27762 , therefore the whole formula must be inserted in \SpecialChar TeX
27764 To add in our example space, the command
27772 is inserted at the end of the first line.
27777 \begin_layout Plain Layout
27784 \begin_layout Plain Layout
27786 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27789 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27796 \begin_layout Plain Layout
27800 left(B^{2}+x_{0}^{2}
27808 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27813 \begin_layout Plain Layout
27825 \begin_layout Standard
27826 \begin_inset VSpace bigskip
27829 To set the line separation for all lines in a formula, the length
27836 \begin_inset Index idx
27839 \begin_layout Plain Layout
27849 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27860 \begin_inset space \thinspace{}
27865 \begin_inset space \thinspace{}
27868 mm additional line separation as in the previous example, the command
27871 \begin_layout Standard
27881 \begin_layout Standard
27882 is inserted in \SpecialChar TeX
27883 mode before the formula.
27884 This requires that the \SpecialChar LaTeX
27893 \begin_layout Plain Layout
27898 is part of every \SpecialChar LaTeX
27899 standard installation.
27905 \begin_inset Index idx
27908 \begin_layout Plain Layout
27914 was loaded in \SpecialChar LaTeX
27915 -preamble with the line
27918 \begin_layout Standard
27926 \begin_layout Standard
27931 \begin_layout Plain Layout
27943 \begin_inset Formula
27945 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}\\
27946 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
27954 \begin_layout Standard
27958 \begin_layout Plain Layout
27969 To get back to the predefined distance,
27975 is set to the value 3
27976 \begin_inset space \thinspace{}
27982 \begin_layout Subsubsection
27984 \begin_inset CommandInset label
27986 name "subsec:Column-Separation"
27991 \begin_inset Index idx
27994 \begin_layout Plain Layout
27995 Formula ! multiline ! Column separation
28003 \begin_layout Standard
28004 Multiline formulas form a matrix.
28005 A formula in the eqnarray environment is for example a matrix with three
28007 By changing the column separation in this environment, the space beside
28008 the relation sign can be changed.
28011 \begin_layout Standard
28012 The column separation is specified with the length
28019 \begin_inset Index idx
28022 \begin_layout Plain Layout
28031 \begin_inset Newline newline
28034 column separation = 2
28035 \begin_inset space \thinspace{}
28045 \begin_inset Newline newline
28051 \begin_layout Standard
28061 \begin_layout Standard
28062 inserted in \SpecialChar TeX
28063 mode, sets for all following formulas a column separation of
28065 \begin_inset space \thinspace{}
28069 To get back to the predefined distance,
28076 \begin_inset space \thinspace{}
28082 \begin_layout Standard
28084 \begin_inset space \thinspace{}
28087 cm column separation:
28091 \begin_layout Plain Layout
28103 \begin_inset Formula
28111 A formula with the predefined column separation for matrices of 10
28112 \begin_inset space \thinspace{}
28119 \begin_layout Plain Layout
28131 \begin_inset Formula
28142 \begin_layout Standard
28143 \begin_inset Newpage newpage
28149 \begin_layout Subsubsection
28151 \begin_inset Index idx
28154 \begin_layout Plain Layout
28163 \begin_layout Standard
28164 Long formulas can be typeset using these methods:
28167 \begin_layout Itemize
28168 When one side of the equation is much shorter than the line width, this
28169 one is chosen for the left side and the right side is typeset over two
28171 \begin_inset Formula
28173 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 \\
28174 & & -\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}
28179 The minus sign at the beginning of the second line does normally not appear
28180 as an operator because it is the first character of the line.
28181 Thus it would not be surrounded by space and could not be distinguished
28182 from the fraction bar.
28184 \begin_inset space \thinspace{}
28187 pt space was inserted behind the minus sign with the command
28197 \begin_layout Plain Layout
28205 \begin_inset CommandInset ref
28207 reference "subsec:Variable-Space"
28217 \begin_inset Index idx
28220 \begin_layout Plain Layout
28231 \begin_layout Itemize
28232 When both sides of the equation are too long, the command
28239 \begin_inset Index idx
28242 \begin_layout Plain Layout
28251 It is inserted in the first column of the first line and causes all further
28252 insertions to overwrite the following columns:
28253 \begin_inset Formula
28255 \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 \\
28256 & & -\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 \\
28257 & & =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}
28262 After the insertion of
28268 , the cursor is in a purple box that is a bit shifted to the left from the
28270 In this the formula is inserted.
28271 \begin_inset Newline newline
28274 The content of the further lines is inserted to the second or another formula
28276 The greater the column number where it was inserted, the larger the indentation.
28277 \begin_inset VSpace medskip
28281 \begin_inset Newline newline
28285 \begin_inset Note Greyedout
28288 \begin_layout Plain Layout
28289 Note the following when using
28298 \begin_layout Itemize
28299 The formula doesn't use the full page width.
28301 \begin_inset space \thinspace{}
28305 \begin_inset space \space{}
28309 \begin_inset Formula $-B^{2}$
28312 is added to the first line in the above example, it would have been outside
28314 To better use the width, negative space can be inserted at the beginning
28318 \begin_layout Itemize
28319 Due to a bug in \SpecialChar LyX
28320 the cursor cannot be set with the mouse into the first
28325 \begin_layout Plain Layout
28326 \begin_inset CommandInset href
28328 name "LyX-bug #1429"
28329 target "http://www.lyx.org/trac/ticket/1429"
28339 One can only set the cursor at the beginning of the line and move it with
28348 \begin_layout Itemize
28349 Other methods to set long formulas are offered by the environments described
28351 \begin_inset CommandInset ref
28353 reference "subsec:Multline-Environment"
28358 \begin_inset CommandInset ref
28360 reference "subsec:Multiline-Formula-Parts"
28367 \begin_layout Subsubsection
28368 Multiline Fractions
28369 \begin_inset CommandInset label
28371 name "subsec:Multiline-Fractions"
28376 \begin_inset Index idx
28379 \begin_layout Plain Layout
28380 Fractions ! multiline
28388 \begin_layout Standard
28389 There are cases where the denominator and/or the numerator of a fraction
28390 is so long that the fraction does not fit into one line.
28391 It is then necessary to add a line break within the fraction.
28392 This can be done using the command
28399 \begin_inset Index idx
28402 \begin_layout Plain Layout
28411 To activate it, set in the document settings under
28414 \begin_inset space ~
28424 \begin_inset Index idx
28427 \begin_layout Plain Layout
28428 Packages ! mathtools
28436 \begin_inset space ~
28451 \begin_layout Standard
28456 splitfrac{first line}{second line}
28459 \begin_layout Standard
28460 and is used as denominator and/or numerator:
28463 \begin_layout Standard
28464 \begin_inset Formula
28466 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}
28471 The command for the first numerator above is:
28474 \begin_layout Standard
28479 splitfrac{xy+xy+xy+xy+xy
28480 \begin_inset space \textvisiblespace{}
28488 \begin_layout Subsubsection
28490 \begin_inset CommandInset label
28492 name "subsec:Multiline-Brackets"
28497 \begin_inset Index idx
28500 \begin_layout Plain Layout
28501 Brackets ! for multiline expressions
28509 \begin_layout Standard
28510 For brackets spanning multiple lines the following problem occurs:
28511 \begin_inset Formula
28513 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28514 & & \left.\cdots+B-D\right]
28522 \begin_layout Standard
28523 The closing bracket is smaller than the opening bracket because brackets
28524 with variable size may not span multiple lines.
28527 \begin_layout Standard
28528 To set the bracket size for the second line correctly, the first line is
28536 \begin_inset Index idx
28539 \begin_layout Plain Layout
28547 and the second line with
28555 \begin_layout Plain Layout
28569 \begin_inset CommandInset ref
28571 reference "subsec:Automatic-Bracket-Size"
28583 \begin_inset Index idx
28586 \begin_layout Plain Layout
28609 \begin_inset space \textvisiblespace{}
28619 \begin_inset space \textvisiblespace{}
28629 \begin_inset space \textvisiblespace{}
28635 \begin_inset Formula $\downarrow$
28641 \begin_inset Index idx
28644 \begin_layout Plain Layout
28652 is inserted, because the multiplication operator with its limits is the
28653 largest symbol in the first line and this should be the size for the bracket
28654 in the second line.
28657 \begin_layout Standard
28658 The result is this:
28659 \begin_inset Formula
28661 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28662 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28670 \begin_layout Subsection
28674 \begin_layout Standard
28675 Align environments can be used for every kind of multiline formulas.
28676 They are especially useful to set several formulas side by side.
28679 \begin_layout Standard
28680 Align environments consist of columns.
28681 The odd columns are right aligned, the even ones left aligned.
28682 Every line in an Align environment can be numbered.
28685 \begin_layout Standard
28686 Align environments are created via the menu
28688 Insert\SpecialChar menuseparator
28694 Edit\SpecialChar menuseparator
28695 Math\SpecialChar menuseparator
28696 Change Formula Type
28698 already existing formulas can be converted to Align environments.
28701 \begin_layout Standard
28702 To add or delete columns, the math toolbar buttons
28705 arg "tabular-feature append-column"
28711 arg "tabular-feature delete-column"
28714 , respectively, or the menu
28716 Edit\SpecialChar menuseparator
28722 \begin_layout Subsubsection
28723 Standard align Environment
28724 \begin_inset CommandInset label
28726 name "subsec:Standard-align-Environment"
28731 \begin_inset Index idx
28734 \begin_layout Plain Layout
28735 Formula ! multiline ! align environment
28743 \begin_layout Standard
28744 This Align environment is created by pressing
28747 arg "newline-insert newline"
28750 in a formula or by the menu
28752 Insert\SpecialChar menuseparator
28753 Math\SpecialChar menuseparator
28754 AMS align Environment
28759 \begin_layout Standard
28760 An example for two formulas set side by side, that are created with a four
28761 column align environment:
28762 \begin_inset Formula
28764 A & =\sin(B) & C & =D\\
28765 C & \ne A & B & \ne D
28770 As it can be seen, the formulas in this environment are placed so as if
28779 \begin_layout Plain Layout
28787 \begin_inset CommandInset ref
28789 reference "subsec:Variable-Space"
28800 before the first and after every even column.
28801 When the formula style
28807 \begin_layout Plain Layout
28809 \begin_inset CommandInset ref
28811 reference "sec:Formula-Styles"
28822 is used, the formula is set without the
28828 before the first column.
28831 \begin_layout Subsubsection
28832 Alignat Environment
28833 \begin_inset Index idx
28836 \begin_layout Plain Layout
28837 Formula ! multiline ! alignat environment
28845 \begin_layout Standard
28846 The alignat environment has no predefined column separation.
28847 It can be inserted manually with the spaces that are described
28848 \begin_inset CommandInset ref
28850 reference "subsec:Space"
28857 \begin_layout Standard
28858 The above example in the alignat environment where 1
28859 \begin_inset space \thinspace{}
28862 cm space was inserted at the beginning of the second formula:
28863 \begin_inset Formula
28864 \begin{alignat*}{2}
28865 A & =\sin(B) & \hspace{1cm}C & =D\\
28866 C & \ne A & B & \ne D
28871 Because the column separation can be set separately for every column, this
28872 environment is especially suitable to set three and more formulas side
28876 \begin_layout Subsubsection
28877 Flalign Environment
28878 \begin_inset CommandInset label
28880 name "subsec:Flalign-Environment"
28885 \begin_inset Index idx
28888 \begin_layout Plain Layout
28889 Formula ! multiline ! flalign environment
28897 \begin_layout Standard
28898 In this environment the first two columns are always set as much as possible
28899 to the left and the last two ones to the right.
28901 \begin_inset Formula
28903 A & =1 & B & =2 & C & =3\\
28904 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28912 \begin_layout Standard
28913 By creating a flalign environment with an odd number of columns where an
28914 empty \SpecialChar TeX
28915 brace is inserted to the last column, several formulas in a document
28916 can be set to the left, although the formula style
28921 As example the indented formula
28922 \begin_inset CommandInset ref
28924 reference "eq:VolInt"
28929 \begin_inset Formula
28931 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
28936 The first two columns contain the formula.
28937 To indent it as with the formula style
28942 \begin_inset space \thinspace{}
28945 pt space was inserted at the beginning of the first column.
28948 \begin_layout Subsection
28949 Eqnarray Environment
28950 \begin_inset CommandInset label
28952 name "subsec:Eqnarray-Environment"
28957 \begin_inset Index idx
28960 \begin_layout Plain Layout
28961 Formula ! multiline ! eqnarray environment
28969 \begin_layout Standard
28970 When this environment has been created, three blue boxes appear.
28971 The content of the first box is right aligned, the content of the last
28973 The content of the middle box appears centered and a bit smaller, because
28974 it is designed to insert there only relation characters.
28975 \begin_inset Formula
28977 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28987 \begin_layout Subsection
28989 \begin_inset Index idx
28992 \begin_layout Plain Layout
28993 Formula ! multiline ! gather environment
29001 \begin_layout Standard
29002 This environment consists of only one centered column.
29003 Every line can be numbered.
29004 \begin_inset Formula
29015 \begin_layout Subsection
29016 Multline Environment
29017 \begin_inset CommandInset label
29019 name "subsec:Multline-Environment"
29024 \begin_inset Index idx
29027 \begin_layout Plain Layout
29028 Formula ! multiline ! multline environment
29036 \begin_layout Standard
29037 The multline environment consists, like the gather environment, of only
29039 But the first line is left aligned, the last one right aligned.
29040 All other lines are centered.
29041 Therefore this environment is suitable for long formulas.
29043 \begin_inset CommandInset ref
29045 reference "eq:lefteqn"
29049 in the multline environment:
29050 \begin_inset Formula
29052 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}\\
29053 -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}\\
29054 =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}}
29062 \begin_layout Standard
29063 In the output only the last (first) line of a multline environment appears
29064 numbered when the document numbering is right (left).
29068 \begin_layout Plain Layout
29069 numbering styles see
29070 \begin_inset CommandInset ref
29072 reference "sec:Formula-Styles"
29084 \begin_layout Standard
29092 \begin_inset Index idx
29095 \begin_layout Plain Layout
29110 \begin_inset Index idx
29113 \begin_layout Plain Layout
29121 a centered line can be right or left aligned, respectively.
29122 The commands are used as follows:
29125 \begin_layout Standard
29130 shoveright{line content}
29136 shoveleft{line content}
29139 \begin_layout Standard
29140 \begin_inset VSpace medskip
29150 \begin_inset Index idx
29153 \begin_layout Plain Layout
29161 specifies the distance of the first line from the left page margin.
29162 Predefined is the length 0
29163 \begin_inset space \thinspace{}
29169 \begin_layout Standard
29170 As example the above formula where the command
29173 \begin_layout Standard
29183 \begin_layout Standard
29184 was inserted in \SpecialChar TeX
29189 \begin_layout Plain Layout
29201 \begin_inset Formula
29203 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}\\
29204 \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}}\\
29205 =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}}
29214 \begin_layout Plain Layout
29225 The second line was left aligned using
29234 \begin_layout Subsection
29235 Multiline Formula Parts
29236 \begin_inset CommandInset label
29238 name "subsec:Multiline-Formula-Parts"
29243 \begin_inset Index idx
29246 \begin_layout Plain Layout
29247 Formula ! multiline ! formula parts
29255 \begin_layout Standard
29256 To display only parts of a formula with multiple lines, one of the following
29257 environments is used:
29274 They can be inserted via the menu
29276 Insert\SpecialChar menuseparator
29279 or by using the commands described in this section.
29282 \begin_layout Standard
29283 The first three have the same properties as the corresponding multiline
29284 formula environments, but it is possible to set further formula parts beside
29287 \begin_inset Formula
29289 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29290 \Delta E\Delta t & \ge\frac{\hbar}{2}
29292 \right\} \textrm{Uncertainty relations}
29300 \begin_layout Standard
29301 To get this formula, a displayed formula is created where the command
29308 \begin_inset Index idx
29311 \begin_layout Plain Layout
29320 A purple box appears around the blue formula box where now columns and
29321 lines can be added.
29322 Outside the multiline environment other formula parts can be set, like
29326 \begin_layout Standard
29327 The aligned environment is also suitable for long formulas whose lines are
29328 horizontally aligned.
29329 Using aligned in a displayed formula has the advantage that the formula
29330 number is vertically centered behind the lines.
29332 \begin_inset CommandInset ref
29334 reference "eq:shortlong"
29338 in the aligned environment:
29339 \begin_inset Formula
29341 \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}|}\\
29342 & -\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}|}
29351 \begin_layout Standard
29352 To use the environments
29371 \begin_inset Index idx
29374 \begin_layout Plain Layout
29389 \begin_inset Index idx
29392 \begin_layout Plain Layout
29407 \begin_inset Index idx
29410 \begin_layout Plain Layout
29418 are inserted, respectively.
29419 The split environment has the same properties as the aligned environment
29420 but it can only have two columns.
29423 \begin_layout Subsection
29424 Text in multiline Formulas
29425 \begin_inset CommandInset label
29427 name "subsec:Text-in-multiline"
29432 \begin_inset Index idx
29435 \begin_layout Plain Layout
29442 \begin_inset Index idx
29445 \begin_layout Plain Layout
29446 Formula ! multiline ! text
29454 \begin_layout Standard
29455 In the Align environments, and the multline and gather environment, text
29456 can be inserted that will appear in a separate line and doesn't affect
29457 the column alignment.
29458 To do this, the command
29465 \begin_inset Index idx
29468 \begin_layout Plain Layout
29476 is used in the following scheme:
29479 \begin_layout Standard
29487 \begin_layout Standard
29488 The text should not be longer than a line because it cannot be hyphenated.
29489 As \SpecialChar LyX
29490 doesn't yet support
29496 directly, the text is written as mathematical text.
29503 must hereby be at the beginning of a line and appears in the output above
29505 An example where the text was inserted at the beginning of the second line:
29506 \begin_inset Formula
29508 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29509 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29517 \begin_layout Standard
29524 always creates some vertical space between the text and the formula lines.
29525 To avoid this space, set in the document settings under
29528 \begin_inset space ~
29538 \begin_inset Index idx
29541 \begin_layout Plain Layout
29542 Packages ! mathtools
29550 \begin_inset space ~
29556 Then you can use the command
29563 \begin_inset Index idx
29566 \begin_layout Plain Layout
29583 \begin_layout Standard
29584 \begin_inset Formula
29586 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29587 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29595 \begin_layout Section
29597 \begin_inset Index idx
29600 \begin_layout Plain Layout
29607 \begin_inset Index idx
29610 \begin_layout Plain Layout
29611 Formula ! numbering|see
29615 \begin_layout Plain Layout
29626 \begin_layout Plain Layout
29641 \begin_layout Subsection
29645 \begin_layout Standard
29646 Numbered formulas can be created with the menu
29648 Insert\SpecialChar menuseparator
29649 Math\SpecialChar menuseparator
29651 \begin_inset space ~
29659 \begin_inset space ~
29665 Existing formulas can be numbered with the menu
29667 Edit\SpecialChar menuseparator
29668 Math\SpecialChar menuseparator
29670 \begin_inset space ~
29678 arg "math-number-toggle"
29682 The formula number is displayed in \SpecialChar LyX
29683 behind the formula as a number sign
29685 The number sign is replaced in the output by the formula number.
29688 \begin_layout Standard
29689 When numbering is turned on in multiline formulas, all lines will be numbered.
29690 But the numbering can be controlled with the menu
29692 Edit\SpecialChar menuseparator
29693 Math\SpecialChar menuseparator
29695 \begin_inset space ~
29699 \begin_inset space ~
29703 \begin_inset space ~
29711 arg "math-number-line-toggle"
29717 \begin_layout Standard
29718 Except for inline formulas, all formulas can be numbered with two different
29720 \begin_inset CommandInset ref
29722 reference "sec:Formula-Styles"
29729 \begin_layout Subsection
29731 \begin_inset Index idx
29734 \begin_layout Plain Layout
29735 Cross-references ! to formulas
29743 \begin_layout Standard
29744 All labeled formulas can be cross-referenced.
29745 A label is added by the menu
29747 Insert\SpecialChar menuseparator
29750 or the toolbar button
29757 The cursor must hereby be inside a displayed formula.
29758 Alternatively you can right-click on the formula and choose
29763 A dialog pops up displaying the prefix
29768 The label is inserted there behind the prefix.
29769 The predefined prefix means
29770 \begin_inset Quotes eld
29774 \begin_inset Quotes erd
29777 and makes it easier to find labels in large documents because it marks
29778 it as formula label to divide it from e.
29779 \begin_inset space \thinspace{}
29783 \begin_inset space \space{}
29787 To change a label, the menu
29789 Insert\SpecialChar menuseparator
29792 is used again or you right-click on a formula and then on
29799 \begin_layout Standard
29800 The name of the label is displayed in \SpecialChar LyX
29801 within two parentheses behind formula.
29802 A formula with a label is always numbered.
29805 \begin_layout Standard
29806 Cross-references are inserted via the menu
29808 Insert\SpecialChar menuseparator
29811 or with the toolbar button
29814 arg "dialog-show-new-inset ref"
29818 A formula cross-reference appears in the output as formula number.
29819 When in the cross-reference dialog window the format
29823 is chosen, the cross-reference appears in the output as formula number
29825 \begin_inset Newline newline
29828 By right-clicking on a cross-reference in \SpecialChar LyX
29829 , one jumps to the formula that
29833 \begin_layout Standard
29834 Here are as examples cross-references to formulas of the following subsections:
29835 \begin_inset Note Note
29838 \begin_layout Plain Layout
29839 Note the different cross-reference types.
29847 \begin_layout Standard
29849 \begin_inset CommandInset ref
29856 \begin_inset CommandInset ref
29864 \begin_inset CommandInset ref
29870 ) big Latin letters are used for the numbering in contrary to (
29871 \begin_inset CommandInset ref
29880 \begin_layout Standard
29881 \begin_inset VSpace medskip
29884 When the argument of
29892 \begin_layout Plain Layout
29900 \begin_inset CommandInset ref
29902 reference "subsec:User-defined-Numbering"
29913 contains a box like in
29914 \begin_inset CommandInset ref
29916 reference "subsec:Paragraph-Boxes"
29920 , the formula cannot be referenced.
29923 \begin_layout Subsection
29925 \begin_inset Index idx
29928 \begin_layout Plain Layout
29929 Formula numbering ! subnumbering
29937 \begin_layout Standard
29938 Formulas can be numbered as subequations.
29939 To activate this feature, add the module
29943 to the document in the menu
29945 Document\SpecialChar menuseparator
29946 Settings\SpecialChar menuseparator
29950 To insert subequations use the menu
29952 Insert\SpecialChar menuseparator
29953 Custom Insets\SpecialChar menuseparator
29959 \begin_layout Standard
29960 The equations to be subnumbered are put into the
29966 \begin_inset Formula
29974 \begin_inset VSpace -5mm
29978 \begin_inset Flex Subequations
29981 \begin_layout Plain Layout
29982 \begin_inset Formula
29990 \begin_inset Formula
30005 \begin_layout Standard
30006 Every formula in the
30010 inset will be subnumbered with a, b, c, \SpecialChar ldots
30012 For multiline formulas every line will be subnumbered.
30015 \begin_layout Standard
30016 Referencing subequations work like for normal equations:
30017 \begin_inset CommandInset ref
30024 \begin_inset CommandInset ref
30031 If you want to reference the subequations collectively, insert a label
30032 as first thing in the
30038 \begin_inset CommandInset ref
30040 reference "eq:Here-is-an"
30050 \begin_layout Standard
30051 By inserting subequations vertical space is added before it.
30052 To remove this, insert -5
30053 \begin_inset space \thinspace{}
30056 mm vertical space right before the
30061 If the formula style
30067 \begin_layout Plain Layout
30069 \begin_inset CommandInset ref
30071 reference "sec:Formula-Styles"
30083 \begin_inset space \thinspace{}
30089 \begin_layout Standard
30090 To get another subnumber instead of small Latin letters, insert this command
30091 as \SpecialChar TeX
30092 code before the equations in the
30099 \begin_layout Standard
30108 theparentequation -
30113 \begin_layout Standard
30120 creates hereby the parent number and
30126 adds a small Roman number as subnumber.
30127 For more information about the customization of the numbering, see
30128 \begin_inset CommandInset ref
30130 reference "subsec:Numbering-with-Roman"
30137 \begin_layout Standard
30138 Here is an example for a multiline formula where the numbering is customized
30139 and turned off for the second line:
30140 \begin_inset Flex Subequations
30143 \begin_layout Plain Layout
30144 \begin_inset CommandInset label
30146 name "eq:Here-is-an"
30154 \begin_layout Plain Layout
30162 theparentequation -
30170 \begin_inset Formula
30172 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
30173 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30174 & = & B^{2}-2BZ+Z^{2}
30187 \begin_layout Subsection
30188 Numbering with Roman Numbers and Letters
30189 \begin_inset CommandInset label
30191 name "subsec:Numbering-with-Roman"
30196 \begin_inset Index idx
30199 \begin_layout Plain Layout
30200 Formula numbering ! with letters
30206 \begin_inset Index idx
30209 \begin_layout Plain Layout
30210 Formula numbering ! with Roman numbers
30218 \begin_layout Standard
30219 Formulas can also be numbered with Roman numbers and Latin letters.
30220 To number for example with small Roman numbers, the command
30223 \begin_layout Standard
30235 \begin_layout Standard
30236 is inserted before the formula in \SpecialChar TeX
30245 \begin_inset Index idx
30248 \begin_layout Plain Layout
30256 redefines the predefined command
30272 \begin_layout Plain Layout
30279 has the same scheme like the command
30285 that is described in
30286 \begin_inset CommandInset ref
30288 reference "subsec:The-Command-newcommand"
30301 is the formula counter.
30308 is used as prefix for a counter, the value of the counter is output as
30310 When a formula is numbered, \SpecialChar LaTeX
30311 sets internally the command
30317 behind the formula.
30323 \begin_inset Index idx
30326 \begin_layout Plain Layout
30336 outputs the counter as small Roman number.
30339 \begin_layout Standard
30340 All formulas behind the command
30350 are now numbered Roman.
30351 To switch to numbering with big Roman numbers, the command is inserted
30365 \begin_inset Index idx
30368 \begin_layout Plain Layout
30380 \begin_inset Quotes eld
30384 \begin_inset Quotes erd
30387 with small Latin letters there is the command
30394 \begin_inset Index idx
30397 \begin_layout Plain Layout
30405 , for big ones there is the command
30412 \begin_inset Index idx
30415 \begin_layout Plain Layout
30428 \begin_layout Standard
30429 \begin_inset Note Greyedout
30432 \begin_layout Plain Layout
30439 \begin_inset space ~
30442 formulas can be numbered with Latin letters in one document.
30450 \begin_layout Standard
30454 \begin_layout Plain Layout
30470 \begin_layout Standard
30471 \begin_inset Formula
30473 A=\textrm{small roman}
30482 \begin_layout Plain Layout
30496 \begin_inset Formula
30498 B=\textrm{big Roman}\label{eq:Rom}
30507 \begin_layout Plain Layout
30521 \begin_inset Formula
30523 C=\textrm{small Latin}
30532 \begin_layout Plain Layout
30546 \begin_inset Formula
30548 D=\textrm{big Latin}\label{eq:Lat}
30556 \begin_layout Standard
30557 To switch back to the default numbering, insert the command:
30560 \begin_layout Standard
30570 \begin_inset Index idx
30573 \begin_layout Plain Layout
30584 \begin_layout Standard
30588 \begin_layout Plain Layout
30602 \begin_inset Formula
30612 \begin_layout Standard
30613 \begin_inset VSpace medskip
30616 As you see, formulas are numbered serially independent from the numbering
30618 When then numbering should start with
30619 \begin_inset Quotes eld
30623 \begin_inset Quotes erd
30626 when the style is changed, new equation counters have to be defined.
30627 A description about this can be found in the file
30628 \begin_inset CommandInset href
30630 name "Formula-numbering.lyx"
30631 target "run:Formula-numbering.lyx"
30639 \begin_layout Subsection
30640 User-defined Numbering
30641 \begin_inset CommandInset label
30643 name "subsec:User-defined-Numbering"
30648 \begin_inset Index idx
30651 \begin_layout Plain Layout
30652 Formula numbering ! user-defined
30660 \begin_layout Standard
30661 \begin_inset Index idx
30664 \begin_layout Plain Layout
30665 Formula numbering ! self-defined delimiters
30670 With the standard numbering parentheses are set around the formula number.
30671 To replace the parentheses for example by vertical bars, the following
30672 line is added to the \SpecialChar LaTeX
30676 \begin_layout Standard
30688 \begin_inset Note Note
30691 \begin_layout Plain Layout
30692 This macro is already declared in the \SpecialChar LaTeX
30693 -preamble for testing.
30694 To activate it, remove the percent sign at the beginning.
30702 \begin_layout Standard
30703 To use other characters, the vertical bars besides the
30707 are replaced by one ore more characters.
30708 To get only the formula number the vertical bars are omitted.
30711 \begin_layout Standard
30712 \begin_inset VSpace bigskip
30715 When there should be an expression of your choice instead of the consecutive
30716 formula number in parentheses behind the formula, the command
30723 \begin_inset Index idx
30726 \begin_layout Plain Layout
30735 \begin_inset Formula
30737 A+B=C\tag{something}\label{eq:tag}
30742 In this example the command
30747 \begin_inset space \textvisiblespace{}
30752 was inserted in the formula.
30755 \begin_layout Standard
30761 \begin_inset space \textvisiblespace{}
30766 is inserted instead, the star prevents the parentheses around the expression:
30767 \begin_inset Formula
30769 A+B=C\tag*{something}
30777 \begin_layout Standard
30778 \begin_inset VSpace bigskip
30781 To restart the formula numbering with new document parts or sections, the
30782 following command is used:
30785 \begin_layout Standard
30790 @addtoreset{equation}{part}
30793 \begin_inset Index idx
30796 \begin_layout Plain Layout
30801 \begin_layout Plain Layout
30812 \begin_layout Plain Layout
30825 \begin_layout Plain Layout
30836 \begin_layout Plain Layout
30849 \begin_inset Newline newline
30853 \begin_inset Newline newline
30860 @addtoreset{equation}{section}
30863 \begin_layout Standard
30864 To be able to use these commands in \SpecialChar TeX
30866 \begin_inset Quotes eld
30870 \begin_inset Quotes erd
30873 character has to be made
30874 \begin_inset Quotes eld
30878 \begin_inset Quotes erd
30881 for \SpecialChar LaTeX
30896 So the command sequence in \SpecialChar TeX
30900 \begin_layout Standard
30906 \begin_inset Newline newline
30911 @addtoreset{equation}{section}
30912 \begin_inset Newline newline
30920 \begin_layout Standard
30921 In the \SpecialChar LaTeX
30934 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30938 \begin_layout Standard
30953 \begin_layout Plain Layout
30958 is part of the \SpecialChar LaTeX
30964 \begin_inset Index idx
30967 \begin_layout Plain Layout
30968 Packages ! carlisle
30973 that is part of every \SpecialChar LaTeX
30974 standard installation.
30980 \begin_inset Index idx
30983 \begin_layout Plain Layout
30984 Packages ! remreset
30989 has to be loaded in the \SpecialChar LaTeX
30990 -preamble with the line
30993 \begin_layout Standard
30998 usepackage{remreset}
31001 \begin_layout Standard
31009 \begin_inset Index idx
31012 \begin_layout Plain Layout
31017 \begin_layout Plain Layout
31028 \begin_layout Plain Layout
31041 \begin_layout Plain Layout
31052 \begin_layout Plain Layout
31064 can be used with the same scheme as
31073 \begin_layout Standard
31074 \begin_inset VSpace bigskip
31077 Sometimes formulas should be numbered in the following form:
31080 \begin_layout Standard
31083 (section number.formula number)
31086 \begin_layout Standard
31087 The formula number should start with every section with
31088 \begin_inset Quotes eld
31092 \begin_inset Quotes erd
31098 \begin_layout Standard
31099 For this case there is the command
31106 \begin_inset Index idx
31109 \begin_layout Plain Layout
31117 , which is used with the following scheme:
31120 \begin_layout Standard
31125 numberwithin{counter}{sectioning}
31128 \begin_layout Standard
31129 Counter denotes what kind of numbering is affected, sectioning denotes what
31130 number is before the dot.
31133 \begin_layout Standard
31134 Thus in our case the following \SpecialChar LaTeX
31135 preamble or \SpecialChar TeX
31139 \begin_layout Standard
31144 numberwithin{equation}{section}
31147 \begin_layout Standard
31148 This is the result:
31152 \begin_layout Plain Layout
31156 numberwithin{equation}{section}
31162 \begin_inset Formula
31172 \begin_layout Standard
31174 \begin_inset space \thinspace{}
31178 \begin_inset space \space{}
31181 tables so that the number of the part is the sectioning,
31182 \begin_inset Newline newline
31189 numberwithin{table}{part}
31194 \begin_layout Standard
31195 To go back to the standard numbering or to prevent this kind of numbering
31196 when it is defined by the document class, the following command is inserted
31197 as \SpecialChar TeX
31198 code or to the \SpecialChar LaTeX
31202 \begin_layout Standard
31212 \begin_inset Index idx
31215 \begin_layout Plain Layout
31229 \begin_layout Plain Layout
31245 \begin_inset Newline newline
31253 \begin_inset Newline newline
31265 \begin_layout Standard
31272 uses internally the command
31278 , described above, that also needs to be reverted.
31282 \begin_layout Plain Layout
31289 \begin_layout Plain Layout
31293 @removefromreset{equation}{section}
31296 \begin_layout Plain Layout
31308 \begin_layout Section
31309 Chemical Symbols and Equations
31310 \begin_inset CommandInset label
31312 name "subsec:Chemical-Symbols-and"
31317 \begin_inset Index idx
31320 \begin_layout Plain Layout
31321 Chemical characters ! Symbols
31327 \begin_inset Index idx
31330 \begin_layout Plain Layout
31337 \begin_inset Index idx
31340 \begin_layout Plain Layout
31349 \begin_layout Standard
31350 An example text from chemistry:
31353 \begin_layout Quote
31355 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31358 -ion reacts with two
31359 \begin_inset Formula $\mathrm{Na^{+}}$
31362 -ions to sodium sulfate
31363 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31367 The chemical equation for this is:
31368 \begin_inset Formula
31370 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31378 \begin_layout Standard
31379 This chemical equation can directly be created as formula.
31380 To avoid that the symbols appear italic, everything is highlighted and
31381 changed by the shortcut
31387 to the upright font style.
31391 \begin_layout Plain Layout
31397 \begin_inset CommandInset ref
31399 reference "subsec:Font-Styles"
31411 \begin_layout Standard
31412 A more convenient way to typeset chemical formulas is to use the command
31420 \begin_inset Index idx
31423 \begin_layout Plain Layout
31431 that is available when the \SpecialChar LaTeX
31437 \begin_inset Index idx
31440 \begin_layout Plain Layout
31453 to a formula a new blue box appears where chemical formulas can be inserted
31454 in an intuitive way.
31457 \begin_layout Standard
31459 \begin_inset Tabular
31460 <lyxtabular version="3" rows="10" columns="2">
31461 <features booktabs="true" tabularvalignment="middle">
31462 <column alignment="center" valignment="top" width="0pt">
31463 <column alignment="center" valignment="top">
31465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31468 \begin_layout Plain Layout
31474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31477 \begin_layout Plain Layout
31485 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31488 \begin_layout Plain Layout
31492 \begin_inset space \textvisiblespace{}
31500 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31503 \begin_layout Plain Layout
31504 \begin_inset Formula $\ce{H2CO3}$
31513 <row topspace="1.5mm">
31514 <cell alignment="center" valignment="top" usebox="none">
31517 \begin_layout Plain Layout
31521 \begin_inset space \textvisiblespace{}
31529 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31532 \begin_layout Plain Layout
31533 \begin_inset Formula $\ce{SO4^{2-}}$
31542 <row topspace="1.5mm">
31543 <cell alignment="center" valignment="top" usebox="none">
31546 \begin_layout Plain Layout
31550 \begin_inset space \textvisiblespace{}
31558 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31561 \begin_layout Plain Layout
31562 \begin_inset Formula $\ce{(NH4)2S}$
31571 <row topspace="1.5mm">
31572 <cell alignment="center" valignment="top" usebox="none">
31575 \begin_layout Plain Layout
31579 \begin_inset space \textvisiblespace{}
31587 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31590 \begin_layout Plain Layout
31591 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31600 <row topspace="1.5mm">
31601 <cell alignment="center" valignment="top" usebox="none">
31604 \begin_layout Plain Layout
31608 \begin_inset space \textvisiblespace{}
31614 \begin_inset space \textvisiblespace{}
31620 \begin_inset space \textvisiblespace{}
31628 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31631 \begin_layout Plain Layout
31632 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31641 <row topspace="1.5mm">
31642 <cell alignment="center" valignment="top" usebox="none">
31645 \begin_layout Plain Layout
31649 \begin_inset space \textvisiblespace{}
31653 \begin_inset Formula $\downarrow$
31657 \begin_inset Formula $\to$
31665 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31668 \begin_layout Plain Layout
31669 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31679 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31682 \begin_layout Plain Layout
31686 \begin_inset space \textvisiblespace{}
31692 \begin_inset space \textvisiblespace{}
31698 \begin_inset space \textvisiblespace{}
31706 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31709 \begin_layout Plain Layout
31710 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31723 \begin_layout Plain Layout
31727 \begin_inset space \textvisiblespace{}
31731 \begin_inset space \textvisiblespace{}
31735 \begin_inset space \textvisiblespace{}
31739 \begin_inset space \textvisiblespace{}
31743 \begin_inset space \textvisiblespace{}
31751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31754 \begin_layout Plain Layout
31755 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31764 <row topspace="1.5mm">
31765 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31768 \begin_layout Plain Layout
31772 \begin_inset space \textvisiblespace{}
31776 \begin_inset space \textvisiblespace{}
31780 \begin_inset space \textvisiblespace{}
31784 \begin_inset space \textvisiblespace{}
31792 \begin_inset space \textvisiblespace{}
31800 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31803 \begin_layout Plain Layout
31804 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
31820 \begin_layout Standard
31821 \begin_inset Note Greyedout
31824 \begin_layout Plain Layout
31830 It is not possible in \SpecialChar LyX
31831 to use the character ^ to get an up-arrow as described
31837 One instead uses a negative thin space followed by the command
31844 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
31855 \begin_layout Standard
31862 the command for equation
31863 \begin_inset space ~
31867 \begin_inset CommandInset ref
31869 reference "eq:chem-reaction"
31874 \begin_inset Newline newline
31882 \begin_inset space \textvisiblespace{}
31886 \begin_inset space \textvisiblespace{}
31890 \begin_inset space \textvisiblespace{}
31894 \begin_inset space \textvisiblespace{}
31898 \begin_inset space \textvisiblespace{}
31902 \begin_inset space \textvisiblespace{}
31908 \begin_layout Standard
31909 To create multiline chemical equations first a multiline formula is created
31911 \begin_inset CommandInset ref
31913 reference "sec:Multiline-Formulas"
31918 Afterwards the command
31924 is used in every small blue box of the formula.
31926 \begin_inset CommandInset ref
31928 reference "eq:TEOS-reaction-1"
31933 \begin_inset CommandInset ref
31935 reference "eq:TEOS-reaction-2"
31939 are an example of a multi-stage chemical reaction where every equation
31940 has its own number.
31941 \begin_inset Formula
31943 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
31944 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
31952 \begin_layout Standard
31963 package provides the command
31970 \begin_inset Index idx
31973 \begin_layout Plain Layout
31981 that has to be used for special cases.
31982 For more information about
31988 and more examples have a look at the documentation of
31993 \begin_inset CommandInset citation
32003 \begin_layout Section
32007 \begin_layout Standard
32009 supports two types of commutative diagrams:
32017 that are explained in the following.
32020 \begin_layout Subsection
32022 \begin_inset Index idx
32025 \begin_layout Plain Layout
32034 \begin_layout Standard
32035 Diagrams of this type visualize relations by vertical and horizontal lines
32037 \begin_inset Formula
32039 \begin{CD}A@>>>B@>>>C\\
32050 \begin_layout Standard
32051 To get them, the command
32056 \begin_inset Index idx
32059 \begin_layout Plain Layout
32069 is inserted to a formula.
32070 A blue box appears with two dashed lines where further commands can be
32075 arg "newline-insert newline"
32078 a new line is created.
32079 Horizontal relations are inserted in odd, vertical in even formula lines.
32082 \begin_layout Standard
32083 To create the relations there are the following commands:
32086 \begin_layout Itemize
32091 creates a left arrow,
32102 \begin_layout Itemize
32107 creates an up arrow,
32115 a vertical equal sign
32118 \begin_layout Itemize
32124 is a placeholder for non-existent relations
32127 \begin_layout Standard
32128 All arrows can be labeled as follows:
32131 \begin_layout Itemize
32132 If text inserted between the first and second < or >, resp., it is placed
32134 When it is inserted between the second and third one, it appears under
32138 \begin_layout Itemize
32139 When text for vertical arrows is inserted between the first and second A
32140 or V, resp., it is placed left beside the arrow.
32141 When it is inserted between the second and third one, it appears right
32143 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32147 \begin_layout Standard
32148 As example a diagram with all possible relations:
32151 \begin_layout Standard
32152 \begin_inset Formula
32154 \begin{CD}A@>j>>B@>>k>C@=F\\
32165 \begin_layout Standard
32166 The command for this is:
32167 \begin_inset Newline newline
32175 \begin_inset space \textvisiblespace{}
32178 A@>j>>B@>>k>C@=F Ctrl+Return
32179 \begin_inset Newline newline
32183 \begin_inset Phantom HPhantom
32186 \begin_layout Plain Layout
32192 \begin_inset space \textvisiblespace{}
32205 \begin_inset Formula $\to$
32211 \begin_inset Newline newline
32215 \begin_inset Phantom HPhantom
32218 \begin_layout Plain Layout
32224 \begin_inset space \textvisiblespace{}
32235 \begin_layout Subsection
32237 \begin_inset Index idx
32240 \begin_layout Plain Layout
32241 Diagrams ! xymatrix
32249 \begin_layout Standard
32250 To be able to use xymatrices, the \SpecialChar LaTeX
32256 A xymatrix is created by inserting the command
32263 Then you are able to add new matrix columns and rows like for normal matrices,
32265 \begin_inset CommandInset ref
32267 reference "sec:Matrices"
32274 \begin_layout Standard
32275 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32277 All possibilities to create commutative diagrams and decorations are explained
32282 that you find in the menu
32284 Help\SpecialChar menuseparator
32286 \begin_inset space ~
32294 \begin_layout Subsection
32300 \begin_inset Index idx
32303 \begin_layout Plain Layout
32312 \begin_layout Standard
32317 -diagrams, the \SpecialChar LaTeX
32327 -diagram is created by inserting the command
32334 Then you are able to add new matrix columns and rows like for normal matrices,
32336 \begin_inset CommandInset ref
32338 reference "sec:Matrices"
32345 \begin_layout Standard
32346 Examples how to create
32350 diagrams in \SpecialChar LyX
32353 Feynman-diagram manual
32355 that you find in the menu
32357 Help\SpecialChar menuseparator
32359 \begin_inset space ~
32367 \begin_layout Section
32368 User-defined Commands
32369 \begin_inset Index idx
32372 \begin_layout Plain Layout
32373 User-defined commands
32381 \begin_layout Standard
32382 \begin_inset Note Greyedout
32385 \begin_layout Plain Layout
32390 The names of user-defined commands and macros may only consist of Latin
32399 \begin_layout Subsection
32403 \begin_inset CommandInset label
32405 name "subsec:The-Command-newcommand"
32410 \begin_inset Index idx
32413 \begin_layout Plain Layout
32414 User-defined commands !
32422 \begin_inset Index idx
32425 \begin_layout Plain Layout
32436 \begin_layout Standard
32437 Many \SpecialChar LaTeX
32438 -commands are too long to be used frequently.
32439 But it is possible to define with the command
32445 new shorter commands.
32448 \begin_layout Standard
32449 The command scheme of
32458 \begin_layout Standard
32463 newcommand{new command name}[number of arguments][optional
32468 \begin_inset Newline newline
32472 \begin_inset Phantom HPhantom
32475 \begin_layout Plain Layout
32485 {command definition}
32488 \begin_layout Standard
32489 \begin_inset Note Greyedout
32492 \begin_layout Plain Layout
32497 Assure that the name of the new command is not already used in your document
32498 or by \SpecialChar LaTeX
32499 -packages that you use.
32500 When you for example define the command
32512 , you get an error message because
32518 is already defined as command for
32519 \begin_inset Quotes eld
32523 \begin_inset Formula $\le$
32527 \begin_inset Quotes erd
32538 \begin_layout Standard
32539 The number of arguments is an integer in the range 0
32540 \begin_inset space \thinspace{}
32544 \begin_inset space \thinspace{}
32547 9 and specifies how many arguments the new command should have.
32548 With the optional value a value for an optional argument can be predefined.
32549 When this is done, the
32557 rgument of the new command is automatically an optional one.
32560 \begin_layout Standard
32561 Here are some examples:
32564 \begin_layout Itemize
32565 To define the command
32577 , the \SpecialChar LaTeX
32579 \begin_inset VSpace medskip
32583 \begin_inset Newline newline
32597 \begin_layout Itemize
32598 To define the command
32610 , the argument (that should be underlined) must be taken into account.
32611 For this the preamble line is:
32612 \begin_inset VSpace medskip
32616 \begin_inset Newline newline
32630 \begin_inset VSpace medskip
32634 \begin_inset Newline newline
32641 acts as argument placeholder, the
32645 behind it denotes that it is the placeholder for the first argument.
32648 \begin_layout Itemize
32656 \begin_inset space \thinspace{}
32660 \begin_inset space \space{}
32670 \begin_inset VSpace medskip
32674 \begin_inset Newline newline
32685 framebox#1#2{$#3$}}
32688 \begin_inset VSpace medskip
32692 \begin_inset Newline newline
32695 The two Dollar signs creates the extra formula needed for
32702 \begin_inset CommandInset ref
32704 reference "subsec:Boxes-with-Frame"
32711 \begin_layout Itemize
32712 To create a new command for
32718 where the color for the box need not be specified, the argument for the
32719 color is defined optional:
32720 \begin_inset VSpace medskip
32724 \begin_inset Newline newline
32735 fcolorbox{#2}{#1}{$#3$}}
32738 \begin_inset VSpace medskip
32742 \begin_inset Newline newline
32745 When the color is not specified when using
32751 , the predefined color
32758 \begin_layout Standard
32759 A test of the new defined commands:
32762 \begin_layout Standard
32764 \begin_inset Tabular
32765 <lyxtabular version="3" rows="6" columns="2">
32766 <features booktabs="true" tabularvalignment="middle">
32767 <column alignment="center" valignment="top" width="0pt">
32768 <column alignment="center" valignment="top">
32770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32773 \begin_layout Plain Layout
32779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32782 \begin_layout Plain Layout
32790 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32793 \begin_layout Plain Layout
32797 \begin_inset space \textvisiblespace{}
32805 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32808 \begin_layout Plain Layout
32809 \begin_inset Formula $A\gr B$
32819 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32822 \begin_layout Plain Layout
32830 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32833 \begin_layout Plain Layout
32834 \begin_inset Formula $\us{ABcd}$
32843 <row topspace="1mm">
32844 <cell alignment="center" valignment="top" usebox="none">
32847 \begin_layout Plain Layout
32851 \begin_inset Formula $\to$
32857 \begin_inset Formula $\to$
32865 \begin_inset space \textvisiblespace{}
32873 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32876 \begin_layout Plain Layout
32877 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
32886 <row topspace="1.5mm">
32887 <cell alignment="center" valignment="top" usebox="none">
32890 \begin_layout Plain Layout
32894 \begin_inset Formula $\to$
32902 \begin_inset space \textvisiblespace{}
32910 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32913 \begin_layout Plain Layout
32914 \begin_inset Formula $\cb{red}{\int A=B}$
32923 <row topspace="1.5mm" bottomspace="1mm">
32924 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
32927 \begin_layout Plain Layout
32933 \begin_inset Formula $\to$
32941 \begin_inset space \textvisiblespace{}
32949 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
32952 \begin_layout Plain Layout
32953 \begin_inset Formula $\cb[green]{red}{\int A=B}$
32969 \begin_layout Subsection
32971 \begin_inset Index idx
32974 \begin_layout Plain Layout
32975 User-defined commands! Math macros
32981 \begin_inset Index idx
32984 \begin_layout Plain Layout
32993 \begin_layout Standard
32994 User-defined commands are especially convenient for complex expressions.
32995 When you are for example dealing with a document that has quadratic equations,
32996 the same solution type occurs several times.
32997 The general form of a quadratic equation is
32998 \begin_inset Formula
33000 0=\lambda^{2}+p\lambda+q
33005 The general form of the solution is
33006 \begin_inset Formula
33008 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33016 \begin_layout Standard
33017 To define a command for the solution formula where only the three parameters
33019 \begin_inset Formula $\lambda$
33023 \begin_inset Formula $p$
33027 \begin_inset Formula $q$
33030 need to be specified and the index of
33031 \begin_inset Formula $\lambda$
33034 can be given optionally, the \SpecialChar LaTeX
33036 \begin_inset Newline newline
33052 \begin_inset Newline newline
33056 \begin_inset Phantom HPhantom
33059 \begin_layout Plain Layout
33073 frac{#3^{2}}{4}-#4}}
33076 \begin_layout Standard
33077 To create with this the solution formula, the command
33078 \begin_inset Newline newline
33088 \begin_inset Formula $\to$
33094 \begin_inset Formula $\to$
33101 is inserted to a formula
33106 \begin_layout Standard
33107 The definition of the new command is unintuitive because one has to know
33108 the schemes of all used \SpecialChar LaTeX
33110 \begin_inset space \thinspace{}
33114 \begin_inset space \space{}
33117 that a fraction is inserted in \SpecialChar LaTeX
33122 frac{numerator}{denominator}
33125 Furthermore one can easily forget a brace in the definition and cannot
33126 see in \SpecialChar LyX
33127 what the new command is doing.
33128 To avoid these problems \SpecialChar LyX
33129 offers the possibility to use math macros instead
33139 \begin_layout Standard
33140 A math macro is created by using the menu
33142 Insert\SpecialChar menuseparator
33143 Math\SpecialChar menuseparator
33146 or the toolbar button
33149 arg "math-macro newmacroname_newcommand"
33153 The math macro toolbar appears together with the following box where the
33155 \begin_inset Newline newline
33159 \begin_inset space \hspace*{\fill}
33163 \begin_inset Graphics
33164 filename clipart/macrobox.png
33170 \begin_inset space \hspace*{\fill}
33174 \begin_inset Newline newline
33178 \begin_inset FormulaMacro
33179 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33184 newmacroname is the default name of the macro that should be changed to
33185 something sensible.
33186 The wanted formula is inserted in the first blue box.
33187 An argument placeholder is inserted with the command
33194 \begin_inset space \thinspace{}
33198 \begin_inset space \space{}
33207 or by using the macro toolbar button
33210 arg "math-macro-add-param"
33214 Argument placeholders are displayed red.
33216 \begin_inset space ~
33219 arguments are possible.
33220 Optional arguments are created with the toolbar button
33223 arg "math-macro-add-optional-param"
33227 The first non-optional argument can be transformed to an optional one with
33231 arg "math-macro-make-optional"
33235 In the second blue box the appearance of the macro in \SpecialChar LyX
33237 Normally you want to see it as it is defined, so the box is kept empty.
33238 But when you have created a macro that needs lot of space on the screen,
33239 you can insert in the box for example
33240 \begin_inset Newline newline
33270 \begin_inset Newline newline
33275 For the macro only the arguments with the macro name in front of them will
33276 then be displayed in \SpecialChar LyX
33277 , leading to a better overview.
33278 The formula appears in the output as defined in the first box.
33279 \begin_inset Newline newline
33282 The appearance of macros in formulas can furthermore be changed for single
33283 macros by setting the cursor in the macro and using the menu
33285 View\SpecialChar menuseparator
33287 \begin_inset space ~
33291 \begin_inset space ~
33299 \begin_layout Standard
33300 To use a macro, the macro name is inserted as command to a formula, in our
33308 Our macro looks in \SpecialChar LyX
33310 \begin_inset Newline newline
33314 \begin_inset space \hspace*{\fill}
33318 \begin_inset Graphics
33319 filename clipart/macrouse.png
33325 \begin_inset space \hspace*{\fill}
33329 \begin_inset Newline newline
33332 Here is our macro example with the arguments
33333 \begin_inset Formula $x$
33337 \begin_inset Formula $\ln(x)$
33341 \begin_inset Formula $B$
33347 \begin_layout Standard
33348 \begin_inset Formula
33358 \begin_layout Standard
33362 Tools\SpecialChar menuseparator
33363 Preferences\SpecialChar menuseparator
33364 Editing\SpecialChar menuseparator
33367 different styles to edit macros.
33368 To find the style that suits you the most, choose a style and set the cursor
33369 in a macro formula to see the difference.
33372 \begin_layout Standard
33373 A math macro is transformed internally to a
33379 command when exporting the document.
33386 command is not placed in the \SpecialChar LaTeX
33387 -preamble, therefore macros can only be used
33388 in formulas that are in the document below the macro definition box.
33391 \begin_layout Standard
33392 Math macros can also be directly created from a
33399 When writing for example the command
33402 \begin_inset Newline newline
33411 xleftarrow[#2]{#1}}
33412 \begin_inset Newline newline
33417 in \SpecialChar LyX
33418 as normal text, highlighting it completely and using then the shortcut
33423 , the command will be transformed to a math macro.
33424 Using this method you need to be careful that the
33430 command is typed correctly, otherwise you get a faulty macro leading to
33435 \begin_layout Standard
33436 Math macros currently have the problem that further formulas in macro definition
33437 s are handled wrongly.
33438 Therefore the example
33445 \begin_inset CommandInset ref
33447 reference "subsec:The-Command-newcommand"
33451 cannot be created as macro.
33454 \begin_layout Standard
33455 When the cursor is in a macro definition box, you will see the macro toolbar
33456 in \SpecialChar LyX
33460 \begin_layout Standard
33461 \begin_inset VSpace defskip
33467 \begin_layout Standard
33468 \begin_inset Graphics
33469 filename clipart/MacroToolbar.png
33474 \begin_inset Index idx
33477 \begin_layout Plain Layout
33486 \begin_layout Standard
33487 \begin_inset VSpace defskip
33493 \begin_layout Standard
33494 The macro toolbar contains from left to right the following buttons:
33497 \begin_layout Standard
33498 \begin_inset VSpace defskip
33504 \begin_layout Standard
33505 \begin_inset Tabular
33506 <lyxtabular version="3" rows="9" columns="2">
33507 <features islongtable="true" longtabularalignment="center">
33508 <column alignment="left" valignment="top">
33509 <column alignment="left" valignment="top" width="85col%">
33510 <row interlinespace="2.5mm">
33511 <cell alignment="center" valignment="top" usebox="none">
33514 \begin_layout Plain Layout
33517 arg "math-macro-remove-param"
33525 <cell alignment="center" valignment="top" usebox="none">
33528 \begin_layout Plain Layout
33531 Edit\SpecialChar menuseparator
33532 Math\SpecialChar menuseparator
33534 \begin_inset space ~
33537 Definition\SpecialChar menuseparator
33538 Remove Last Argument
33544 <row interlinespace="2.5mm">
33545 <cell alignment="center" valignment="top" usebox="none">
33548 \begin_layout Plain Layout
33551 arg "math-macro-add-param"
33559 <cell alignment="center" valignment="top" usebox="none">
33562 \begin_layout Plain Layout
33565 Edit\SpecialChar menuseparator
33566 Math\SpecialChar menuseparator
33568 \begin_inset space ~
33571 Definition\SpecialChar menuseparator
33578 <row interlinespace="2.5mm">
33579 <cell alignment="center" valignment="top" usebox="none">
33582 \begin_layout Plain Layout
33585 arg "math-macro-make-optional"
33593 <cell alignment="center" valignment="top" usebox="none">
33596 \begin_layout Plain Layout
33599 Edit\SpecialChar menuseparator
33600 Math\SpecialChar menuseparator
33602 \begin_inset space ~
33605 Definition\SpecialChar menuseparator
33606 Transform First Non-Optional to
33607 \begin_inset Newline newline
33611 \begin_inset Phantom HPhantom
33614 \begin_layout Plain Layout
33617 Edit\SpecialChar menuseparator
33618 Math\SpecialChar menuseparator
33620 \begin_inset space ~
33623 Definition\SpecialChar menuseparator
33635 <row interlinespace="2.5mm">
33636 <cell alignment="center" valignment="top" usebox="none">
33639 \begin_layout Plain Layout
33642 arg "math-macro-make-nonoptional"
33650 <cell alignment="center" valignment="top" usebox="none">
33653 \begin_layout Plain Layout
33656 Edit\SpecialChar menuseparator
33657 Math\SpecialChar menuseparator
33659 \begin_inset space ~
33662 Definition\SpecialChar menuseparator
33663 Transform Last Optional to
33664 \begin_inset Newline newline
33668 \begin_inset Phantom HPhantom
33671 \begin_layout Plain Layout
33674 Edit\SpecialChar menuseparator
33675 Math\SpecialChar menuseparator
33677 \begin_inset space ~
33680 Definition\SpecialChar menuseparator
33686 Non-Optional Argument
33692 <row interlinespace="2.5mm">
33693 <cell alignment="center" valignment="top" usebox="none">
33696 \begin_layout Plain Layout
33699 arg "math-macro-remove-optional-param"
33707 <cell alignment="center" valignment="top" usebox="none">
33710 \begin_layout Plain Layout
33713 Edit\SpecialChar menuseparator
33714 Math\SpecialChar menuseparator
33716 \begin_inset space ~
33719 Definition\SpecialChar menuseparator
33720 Remove Optional Argument
33726 <row interlinespace="2.5mm">
33727 <cell alignment="center" valignment="top" usebox="none">
33730 \begin_layout Plain Layout
33733 arg "math-macro-add-optional-param"
33741 <cell alignment="center" valignment="top" usebox="none">
33744 \begin_layout Plain Layout
33747 Edit\SpecialChar menuseparator
33748 Math\SpecialChar menuseparator
33750 \begin_inset space ~
33753 Definition\SpecialChar menuseparator
33754 Insert Optional Argument
33760 <row interlinespace="2.5mm">
33761 <cell alignment="center" valignment="top" usebox="none">
33764 \begin_layout Plain Layout
33767 arg "math-macro-remove-greedy-param"
33775 <cell alignment="center" valignment="top" usebox="none">
33778 \begin_layout Plain Layout
33781 Edit\SpecialChar menuseparator
33782 Math\SpecialChar menuseparator
33784 \begin_inset space ~
33787 Definition\SpecialChar menuseparator
33788 Remove Last Argument
33789 \begin_inset Newline newline
33793 \begin_inset Phantom HPhantom
33796 \begin_layout Plain Layout
33799 Edit\SpecialChar menuseparator
33800 Math\SpecialChar menuseparator
33802 \begin_inset space ~
33805 Definition\SpecialChar menuseparator
33811 Spitting Out To The Right
33817 <row interlinespace="2.5mm">
33818 <cell alignment="center" valignment="top" usebox="none">
33821 \begin_layout Plain Layout
33824 arg "math-macro-append-greedy-param"
33832 <cell alignment="center" valignment="top" usebox="none">
33835 \begin_layout Plain Layout
33838 Edit\SpecialChar menuseparator
33839 Math\SpecialChar menuseparator
33841 \begin_inset space ~
33844 Definition\SpecialChar menuseparator
33846 \begin_inset Newline newline
33850 \begin_inset Phantom HPhantom
33853 \begin_layout Plain Layout
33856 Edit\SpecialChar menuseparator
33857 Math\SpecialChar menuseparator
33859 \begin_inset space ~
33862 Definition\SpecialChar menuseparator
33868 Eating From The Right
33874 <row interlinespace="2.5mm">
33875 <cell alignment="center" valignment="top" usebox="none">
33878 \begin_layout Plain Layout
33881 arg "math-macro-add-greedy-optional-param"
33889 <cell alignment="center" valignment="top" usebox="none">
33892 \begin_layout Plain Layout
33895 Edit\SpecialChar menuseparator
33896 Math\SpecialChar menuseparator
33898 \begin_inset space ~
33901 Definition\SpecialChar menuseparator
33902 Append Optional Argument
33903 \begin_inset Newline newline
33907 \begin_inset Phantom HPhantom
33910 \begin_layout Plain Layout
33913 Edit\SpecialChar menuseparator
33914 Math\SpecialChar menuseparator
33916 \begin_inset space ~
33919 Definition\SpecialChar menuseparator
33925 Eating From The Right
33938 \begin_layout Section
33939 Computer Algebra Systems
33942 \begin_layout Standard
33944 offers the exchange between mathematical expressions written in \SpecialChar LyX
33946 editor and external applications or user defined scripts.
33947 Currently supported applications are
33964 Note that the set of supported mathematical constructs is limited only
33965 to very simple cases.
33968 \begin_layout Subsection
33972 \begin_layout Standard
33973 Write some expression in a formula, go to the
33975 Edit\SpecialChar menuseparator
33976 Math\SpecialChar menuseparator
33977 Use Computer Algebra System
33979 menu and choose the application you have installed on the computer.
33980 After that the result of computation should show on the right side of the
33981 expression together with the
33982 \begin_inset Quotes eld
33986 \begin_inset Quotes erd
33992 \begin_layout Standard
33993 Here are few simple examples (with results from
33997 ) to show what kind of computations can be performed:
34000 \begin_layout Itemize
34001 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34007 \begin_layout Itemize
34008 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34014 \begin_layout Itemize
34015 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34021 \begin_layout Itemize
34022 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
34026 \begin_inset Newline newline
34030 \begin_inset Note Greyedout
34033 \begin_layout Plain Layout
34038 One needs to use proper delimiter insets
34039 \begin_inset Formula $\left(\right)$
34042 instead of simple '(' ')' characters.
34050 \begin_layout Itemize
34051 \begin_inset Formula $\det\left[\begin{array}{ccc}
34055 \end{array}\right]=-56$
34061 \begin_layout Itemize
34062 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34068 \begin_layout Itemize
34069 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
34075 \begin_layout Itemize
34076 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
34082 \begin_layout Subsection
34086 \begin_layout Standard
34087 Currently there is no keyboard shortcut for calling the algebra applications.
34088 One can easily bind a shortcut to the
34102 \begin_inset space \thinspace{}
34106 \begin_inset space \space{}
34113 key inside the math editor.
34118 one would use this shortcut definition command:
34121 \begin_layout Standard
34124 command-alternatives paragraph-break;math-extern maxima
34127 \begin_layout Section
34129 \begin_inset Index idx
34132 \begin_layout Plain Layout
34141 \begin_layout Subsection
34143 \begin_inset Index idx
34146 \begin_layout Plain Layout
34155 \begin_layout Standard
34156 Negative numbers often look ugly in formulas because the minus sign before
34157 the number is set with the same length as the minus operator sign.
34158 When writing the negative number in normal text, the minus sign appears
34162 \begin_layout Standard
34163 Thus, the problem disappears when converting the minus sign to mathematical
34167 \begin_layout Standard
34168 An example to visualize the problem:
34171 \begin_layout Standard
34173 \begin_inset Tabular
34174 <lyxtabular version="3" rows="3" columns="2">
34175 <features booktabs="true" tabularvalignment="middle">
34176 <column alignment="right" valignment="top" width="0pt">
34177 <column alignment="left" valignment="top">
34179 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34182 \begin_layout Plain Layout
34188 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34191 \begin_layout Plain Layout
34199 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34202 \begin_layout Plain Layout
34208 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34211 \begin_layout Plain Layout
34212 \begin_inset Formula $x=-2$
34222 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34225 \begin_layout Plain Layout
34231 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34234 \begin_layout Plain Layout
34235 \begin_inset Formula $x=\textrm{-}2$
34251 \begin_layout Subsection
34252 Comma as decimal Separator
34253 \begin_inset Index idx
34256 \begin_layout Plain Layout
34265 \begin_layout Standard
34266 In \SpecialChar LaTeX
34267 a comma inside a formula is used, according to the English convention,
34268 as number group separator.
34269 So there will be space added behind all commas in formulas.
34272 \begin_layout Standard
34273 To avoid this, the comma is highlighted and changed to mathematical text
34283 \begin_layout Standard
34284 To use all formula commas in the document as decimal separator, the file
34293 \begin_layout Plain Layout
34298 is part of the \SpecialChar LaTeX
34304 \begin_inset Index idx
34307 \begin_layout Plain Layout
34312 \begin_layout Plain Layout
34332 \begin_inset Index idx
34335 \begin_layout Plain Layout
34341 is loaded with the \SpecialChar LaTeX
34345 \begin_layout Standard
34353 \begin_layout Subsection
34355 \begin_inset CommandInset label
34357 name "subsec:Physical-Vectors"
34362 \begin_inset Index idx
34365 \begin_layout Plain Layout
34374 \begin_layout Standard
34375 Predefined vectors are offered by the \SpecialChar LaTeX
34381 \begin_inset Index idx
34384 \begin_layout Plain Layout
34390 that is loaded with the \SpecialChar LaTeX
34394 \begin_layout Standard
34402 \begin_layout Standard
34406 \begin_layout Plain Layout
34416 \begin_inset Note Note
34419 \begin_layout Plain Layout
34420 The following table will only be displayed when the \SpecialChar LaTeX
34433 \begin_layout Standard
34434 The following commands are defined:
34437 \begin_layout Standard
34439 \begin_inset Tabular
34440 <lyxtabular version="3" rows="4" columns="2">
34441 <features booktabs="true" tabularvalignment="middle">
34442 <column alignment="center" valignment="top" width="0pt">
34443 <column alignment="center" valignment="top">
34445 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34448 \begin_layout Plain Layout
34454 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34457 \begin_layout Plain Layout
34465 <cell alignment="center" valignment="top" usebox="none">
34468 \begin_layout Plain Layout
34478 <cell alignment="center" valignment="top" usebox="none">
34481 \begin_layout Plain Layout
34482 \begin_inset Formula $\Bra{\psi}$
34492 <cell alignment="center" valignment="top" usebox="none">
34495 \begin_layout Plain Layout
34505 <cell alignment="center" valignment="top" usebox="none">
34508 \begin_layout Plain Layout
34509 \begin_inset Formula $\Ket{\psi}$
34519 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34522 \begin_layout Plain Layout
34534 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34537 \begin_layout Plain Layout
34538 \begin_inset Formula $\Braket{\psi|\phi}$
34554 \begin_layout Standard
34561 assures that all vertical bars are set in the size of the surrounding brackets:
34562 \begin_inset Formula
34564 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34573 \begin_layout Plain Layout
34583 \begin_inset Note Note
34586 \begin_layout Plain Layout
34587 The following will be displayed when the \SpecialChar LaTeX
34600 \begin_layout Standard
34601 You need to install the \SpecialChar LaTeX
34606 to see the rest of this subsection in the output.
34609 \begin_layout Standard
34613 \begin_layout Plain Layout
34625 \begin_layout Standard
34632 can also be achieved using the command
34638 , that is described in
34639 \begin_inset CommandInset ref
34641 reference "subsec:Automatic-Bracket-Size"
34648 \begin_layout Subsection
34649 Self-defined Fractions
34650 \begin_inset CommandInset label
34652 name "subsec:Self-defined-Fractions"
34657 \begin_inset Index idx
34660 \begin_layout Plain Layout
34661 Fractions ! self-defined
34669 \begin_layout Standard
34670 To define custom commands for fractions, the command
34677 \begin_inset Index idx
34680 \begin_layout Plain Layout
34687 \begin_layout Plain Layout
34701 is used in the following scheme:
34704 \begin_layout Standard
34717 bracket}{fraction bar thickness}{style}
34718 \begin_inset Newline newline
34722 \begin_inset Phantom HPhantom
34725 \begin_layout Plain Layout
34735 {numerator}{denominator}
34738 \begin_layout Standard
34739 The style is a number in the range of 0
34740 \begin_inset space \thinspace{}
34744 \begin_inset space \thinspace{}
34750 \begin_layout Standard
34752 \begin_inset Tabular
34753 <lyxtabular version="3" rows="5" columns="2">
34754 <features booktabs="true" tabularvalignment="middle">
34755 <column alignment="center" valignment="top" width="0pt">
34756 <column alignment="center" valignment="top">
34758 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34761 \begin_layout Plain Layout
34767 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34770 \begin_layout Plain Layout
34778 <cell alignment="center" valignment="top" usebox="none">
34781 \begin_layout Plain Layout
34787 <cell alignment="center" valignment="top" usebox="none">
34790 \begin_layout Plain Layout
34791 display style formula
34798 <cell alignment="center" valignment="top" usebox="none">
34801 \begin_layout Plain Layout
34807 <cell alignment="center" valignment="top" usebox="none">
34810 \begin_layout Plain Layout
34818 <cell alignment="center" valignment="top" usebox="none">
34821 \begin_layout Plain Layout
34827 <cell alignment="center" valignment="top" usebox="none">
34830 \begin_layout Plain Layout
34838 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34841 \begin_layout Plain Layout
34847 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34850 \begin_layout Plain Layout
34864 \begin_layout Standard
34865 When no style is given, the size is adjusted to the surrounding environment
34866 like for the command
34875 \begin_layout Standard
34876 When no fraction bar thickness is given, the predefined value of 0.4
34877 \begin_inset space \thinspace{}
34883 \begin_layout Standard
34884 \begin_inset VSpace medskip
34887 For example, the commands
34900 \begin_inset CommandInset ref
34902 reference "subsec:Fractions"
34906 are defined with the commands
34909 \begin_layout Standard
34918 genfrac{}{}{}{0}{#1}{#2}}
34921 \begin_layout Standard
34925 \begin_layout Standard
34934 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34937 \begin_layout Standard
34938 \begin_inset VSpace medskip
34941 To define a fraction where the fraction bar thickness can be given as optional
34942 argument, the following line is inserted to the \SpecialChar LaTeX
34946 \begin_layout Standard
34955 genfrac{}{}{#1}{}{#2}{#3}}
34958 \begin_layout Standard
34960 \begin_inset Formula
34962 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34963 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
34968 As one can see, the distance of the numerator and the denominator to the
34969 fraction bar is round about three times the bar thickness.
34972 \begin_layout Subsection
34974 \begin_inset Index idx
34977 \begin_layout Plain Layout
34986 \begin_layout Standard
34987 There are four ways to cancel formulas or parts of formulas:
34990 \begin_layout Standard
34994 \begin_layout Plain Layout
35004 \begin_inset Note Note
35007 \begin_layout Plain Layout
35008 The following table will only be displayed when the \SpecialChar LaTeX
35021 \begin_layout Standard
35023 \begin_inset Tabular
35024 <lyxtabular version="3" rows="5" columns="2">
35025 <features booktabs="true" tabularvalignment="middle">
35026 <column alignment="center" valignment="top" width="0pt">
35027 <column alignment="center" valignment="top">
35029 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35032 \begin_layout Plain Layout
35038 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35041 \begin_layout Plain Layout
35049 <cell alignment="center" valignment="top" usebox="none">
35052 \begin_layout Plain Layout
35056 \begin_inset space \textvisiblespace{}
35062 \begin_inset space \textvisiblespace{}
35070 <cell alignment="center" valignment="top" usebox="none">
35073 \begin_layout Plain Layout
35074 \begin_inset Formula $\cancel{\int A=B}$
35083 <row topspace="1.5mm">
35084 <cell alignment="center" valignment="top" usebox="none">
35087 \begin_layout Plain Layout
35091 \begin_inset space \textvisiblespace{}
35097 \begin_inset space \textvisiblespace{}
35105 <cell alignment="center" valignment="top" usebox="none">
35108 \begin_layout Plain Layout
35109 \begin_inset Formula $\bcancel{\int A=B}$
35118 <row topspace="1.5mm">
35119 <cell alignment="center" valignment="top" usebox="none">
35122 \begin_layout Plain Layout
35126 \begin_inset space \textvisiblespace{}
35132 \begin_inset space \textvisiblespace{}
35140 <cell alignment="center" valignment="top" usebox="none">
35143 \begin_layout Plain Layout
35144 \begin_inset Formula $\xcancel{\int A=B}$
35154 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35157 \begin_layout Plain Layout
35161 \begin_inset space \textvisiblespace{}
35167 \begin_inset space \textvisiblespace{}
35171 \begin_inset Formula $\to$
35179 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35182 \begin_layout Plain Layout
35183 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35199 \begin_layout Standard
35206 is especially suitable to visualize the reduction of fractions within formulas:
35207 \begin_inset Formula
35209 \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}}}
35217 \begin_layout Standard
35218 To change the size of
35225 \begin_inset Quotes eld
35229 \begin_inset Quotes erd
35232 value one can add the \SpecialChar LaTeX
35236 \begin_layout Standard
35241 PassOptionsToPackage{option}{cancel}
35244 \begin_layout Standard
35253 which leads to the same size as for the canceled value, or
35257 which makes is it a bit smaller than normal.
35260 \begin_layout Standard
35261 To color the cancellation bar one adds this command as \SpecialChar TeX
35265 \begin_layout Standard
35277 \begin_layout Standard
35282 can be replaced by a color of your choice.
35285 \begin_layout Standard
35289 \begin_layout Plain Layout
35305 \begin_layout Standard
35306 \begin_inset Formula
35308 \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}}}
35316 \begin_layout Standard
35320 \begin_layout Plain Layout
35334 \begin_inset Note Note
35337 \begin_layout Plain Layout
35346 \begin_layout Standard
35347 For further customizations, see the documentation of the package
35352 \begin_inset CommandInset citation
35360 \begin_inset Index idx
35363 \begin_layout Plain Layout
35372 \begin_layout Standard
35376 \begin_layout Plain Layout
35386 \begin_inset Note Note
35389 \begin_layout Plain Layout
35390 The following will be displayed when the \SpecialChar LaTeX
35403 \begin_layout Standard
35404 You need to install the \SpecialChar LaTeX
35409 to see the rest of this subsection in the output.
35412 \begin_layout Standard
35416 \begin_layout Plain Layout
35428 \begin_layout Subsection
35429 Formulas in Section Headings
35430 \begin_inset CommandInset label
35432 name "subsec:Formulas-in-Section"
35437 \begin_inset Index idx
35440 \begin_layout Plain Layout
35441 Formula ! in section headings
35449 \begin_layout Standard
35450 When formulas are used in section headings, the following has to be taken
35454 \begin_layout Standard
35455 \begin_inset Note Greyedout
35458 \begin_layout Plain Layout
35464 \begin_inset Index idx
35467 \begin_layout Plain Layout
35468 Packages ! hyperref
35473 support is enabled in the document settings dialog under
35476 \begin_inset space ~
35481 , PDF-bookmarks are created for every section heading in the table of contents.
35482 If a section heading contains formulas, they are incorrectly displayed
35483 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35492 \begin_layout Standard
35493 Both problems can be solved by inserting at the end of the section heading
35494 a short title with the menu
35496 Insert\SpecialChar menuseparator
35498 \begin_inset space ~
35504 Short titles are used as alternative for multiline section headings to
35505 keep the table of contents clearly arranged.
35506 Only the short title appears in the table of contents and therefore also
35507 in the PDF-bookmark.
35510 \begin_layout Standard
35511 When formulas should be used in the table of contents but
35515 is used, one can use the following command in \SpecialChar TeX
35519 \begin_layout Standard
35524 texorpdfstring{part}{alternative}
35525 \begin_inset Index idx
35528 \begin_layout Plain Layout
35539 \begin_layout Standard
35540 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35541 This can be characters, formulas, footnotes, but also cross-references.
35542 The alternative is used instead of the part for the bookmark.
35545 \begin_layout Standard
35546 Here are two example headings:
35547 \begin_inset VSpace -3mm
35554 \begin_layout Plain Layout
35566 \begin_layout Subsubsection
35567 Heading without formula in table of contents
35568 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35572 \begin_inset Argument 1
35575 \begin_layout Plain Layout
35576 Heading without formula in table of contents
35584 \begin_layout Subsubsection
35585 Heading with formula in table of contents
35589 \begin_layout Plain Layout
35599 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35606 \begin_layout Plain Layout
35616 \begin_layout Standard
35620 \begin_layout Plain Layout
35629 In the first heading a short title was used, in the second one
35638 \begin_layout Standard
35639 To get the same formatting as for the other headings, the complete heading
35648 \begin_layout Plain Layout
35650 \begin_inset CommandInset ref
35652 reference "subsec:Bold-Formulas"
35664 \begin_layout Subsection
35665 Formulas in multi-column Text
35666 \begin_inset Index idx
35669 \begin_layout Plain Layout
35670 Formula ! in multi-column text
35678 \begin_layout Standard
35679 Formulas in multi-column text are often too wide to fit into a column and
35680 thus need to be set over the whole page width.
35681 This is done by using the \SpecialChar LaTeX
35690 \begin_layout Plain Layout
35695 is part of every \SpecialChar LaTeX
35696 standard installation.
35702 \begin_inset Index idx
35705 \begin_layout Plain Layout
35706 Packages ! multicol
35711 , that is loaded with the \SpecialChar LaTeX
35715 \begin_layout Standard
35720 usepackage{multicol}
35723 \begin_layout Standard
35724 \begin_inset Note Greyedout
35727 \begin_layout Plain Layout
35728 Note that in this case the setting
35731 \begin_inset space ~
35738 Document\SpecialChar menuseparator
35744 \begin_inset space ~
35764 \begin_layout Standard
35765 Before the multi-column text the command
35768 \begin_layout Standard
35773 begin{multicols}{column number}
35776 \begin_layout Standard
35777 is written in \SpecialChar TeX
35779 The column number is a number in the range of 2
35780 \begin_inset space \thinspace{}
35784 \begin_inset space \thinspace{}
35788 Before the formula the multi-column text is ended by inserting the command
35791 \begin_layout Standard
35799 \begin_layout Standard
35800 in \SpecialChar TeX
35804 \begin_layout Standard
35805 Due to the command some space is automatically added before the formula.
35807 \begin_inset space \thinspace{}
35810 mm vertical space is inserted before the formula.
35811 When the formula style
35817 \begin_layout Plain Layout
35819 \begin_inset CommandInset ref
35821 reference "sec:Formula-Styles"
35833 \begin_inset space \thinspace{}
35836 mm space is inserted instead.
35839 \begin_layout Standard
35840 As example a multi-column text with a displayed formula:
35843 \begin_layout Standard
35849 \begin_layout Plain Layout
35853 begin{multicols}{2}
35858 Das Spektrum wird fouriertransformiert.
35859 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35860 , Lösungsmittel) zu trennen.
35861 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35862 nun das Aussehen des Ausgangssignals.
35863 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35864 über alle Phasen integrieren muss.
35866 \begin_inset Formula $S$
35869 unser normiertes Ausgangssignal und
35870 \begin_inset Formula $P$
35873 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35877 \begin_layout Plain Layout
35887 \begin_inset VSpace -6mm
35891 \begin_inset Formula
35893 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
35902 \begin_layout Plain Layout
35906 begin{multicols}{2}
35912 \begin_inset Formula $S_{0}$
35915 das Signal ohne Gradient ist und die Normierungsbedingung
35916 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35920 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35922 \begin_inset Formula $\nicefrac{\pi}{2}$
35926 \begin_inset space \thinspace{}
35929 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35930 das Signal zusätzlich abschwächt.
35931 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35933 \begin_inset Formula $T_{2}$
35939 \begin_layout Standard
35945 \begin_layout Plain Layout
35957 \begin_layout Subsection
35958 Formulas with Description of Variables
35959 \begin_inset Index idx
35962 \begin_layout Plain Layout
35963 Formula ! with description of variables
35971 \begin_layout Standard
35972 To describe variables within a formula, like in formula
35973 \begin_inset CommandInset ref
35975 reference "eq:within"
35984 \begin_inset Formula $n$
35988 \begin_inset space ~
35991 matrix is used with left aligned columns for the
35992 \begin_inset Formula $n$
35999 \begin_layout Plain Layout
36001 \begin_inset CommandInset ref
36003 reference "sec:Matrices"
36012 To set the description in a smaller size, before the matrix e.
36013 \begin_inset space \thinspace{}
36017 \begin_inset space \space{}
36030 \begin_layout Plain Layout
36032 \begin_inset CommandInset ref
36034 reference "subsec:Font-Sizes"
36046 \begin_layout Standard
36047 When the formula style
36053 \begin_layout Plain Layout
36055 \begin_inset CommandInset ref
36057 reference "sec:Formula-Styles"
36078 \begin_layout Plain Layout
36085 only works in formulas with the style
36090 \begin_inset CommandInset ref
36092 reference "subsec:Variable-Space"
36101 is inserted before and after the matrix to have the same separation of
36102 the matrix from the equation and the side margin.
36105 \begin_layout Standard
36106 When the formula style
36110 is used, the method described in
36111 \begin_inset CommandInset ref
36113 reference "subsec:Flalign-Environment"
36117 is used to indent formulas.
36119 \begin_inset CommandInset ref
36121 reference "eq:within"
36125 consists of five columns where in the first two columns contain the equation,
36126 the third the matrix and the last one an empty \SpecialChar TeX
36128 \begin_inset Formula
36130 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36131 \rho & \textrm{density}\\
36132 V & \textrm{volume}\\
36133 g & \textrm{gravitational acceleration}
36134 \end{array} & & {}\label{eq:within}
36142 \begin_layout Subsection
36143 Upright small Greek Letters
36144 \begin_inset CommandInset label
36146 name "subsec:Upright-small-Greek"
36151 \begin_inset Index idx
36154 \begin_layout Plain Layout
36155 Greek letters ! upright
36163 \begin_layout Standard
36164 Most of the math fonts only provide italic small Greek letters.
36165 But for symbols of elementary particles like pions and neutrinos, upright
36166 Greek letters are needed.
36175 \begin_layout Plain Layout
36180 is part of the \SpecialChar LaTeX
36186 \begin_inset Index idx
36189 \begin_layout Plain Layout
36194 \begin_layout Plain Layout
36214 \begin_inset Index idx
36217 \begin_layout Plain Layout
36223 that is loaded with the \SpecialChar LaTeX
36227 \begin_layout Standard
36232 usepackage{upgreek}
36235 \begin_layout Standard
36241 \begin_layout Plain Layout
36251 \begin_inset Note Note
36254 \begin_layout Plain Layout
36255 The following table will only be displayed when the \SpecialChar LaTeX
36265 They are created when the command for a small Greek letter is started with
36271 For example the command
36278 \begin_inset Formula $\uptau$
36284 \begin_layout Standard
36285 With these commands reactions of elementary particles can be typeset:
36286 \begin_inset Formula
36288 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36296 \begin_layout Standard
36297 The upright letters are more bold and wider than the italic ones.
36298 They should therefore not be used for units like
36299 \begin_inset Quotes eld
36303 \begin_inset Quotes erd
36309 \begin_layout Standard
36313 \begin_layout Plain Layout
36323 \begin_inset Note Note
36326 \begin_layout Plain Layout
36327 The following will be displayed when the \SpecialChar LaTeX
36340 \begin_layout Standard
36341 You need to install the \SpecialChar LaTeX
36346 to see the rest of this subsection in the output.
36349 \begin_layout Standard
36353 \begin_layout Plain Layout
36365 \begin_layout Subsection
36366 Text Characters in Formulas
36367 \begin_inset Index idx
36370 \begin_layout Plain Layout
36379 \begin_layout Standard
36380 In some cases you might want to insert text characters directly into formulas.
36381 When for example the centered dot · is often used in formulas like
36382 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36385 , one would have to insert the command
36395 \begin_layout Plain Layout
36397 \begin_inset CommandInset ref
36399 reference "subsec:Binary-Operators"
36408 all the time, because this character is defined in all encodings as text
36410 But the encoding can be changed by this \SpecialChar LaTeX
36414 \begin_layout Standard
36419 Declare Inputtext{183}{
36429 f\SpecialChar ligaturebreak
36433 \begin_layout Standard
36434 The character encoding (menu
36436 Document\SpecialChar menuseparator
36437 Settings\SpecialChar menuseparator
36440 ) specifies what character appears when a keyboard key is pressed.
36441 When the key for the character '·' is pressed, internally the command
36448 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36450 With the changed encoding the right command is chosen automatically, depending
36451 on if the character was inserted into a formula or not.
36454 \begin_layout Standard
36455 The encoding of several characters is saved in definition files.
36456 For example the encoding
36460 is defined in the file
36464 which is in the installation folder of \SpecialChar LaTeX
36466 Encodings should only be changed via the \SpecialChar LaTeX
36467 -preamble and not in the definition
36469 Otherwise documents could not be edited by other \SpecialChar LyX
36470 users working on other
36474 \begin_layout Standard
36475 \begin_inset VSpace medskip
36478 Besides the centered dot, in this document the degree sign ° is defined
36479 with the following \SpecialChar LaTeX
36480 -preamble line so that it can be directly inserted into
36484 \begin_layout Standard
36489 DeclareInputtext{176}{
36499 f\SpecialChar ligaturebreak
36503 \begin_layout Subsection
36505 -comments in formulas
36506 \begin_inset Index idx
36509 \begin_layout Plain Layout
36519 \begin_layout Standard
36520 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36522 code of your file with the menu
36524 Insert\SpecialChar menuseparator
36525 Note\SpecialChar menuseparator
36529 This is not possible in a formula but you can insert \SpecialChar LaTeX
36534 \begin_layout Standard
36542 \begin_layout Standard
36543 This creates a box in which you can write your comment.
36544 Due to a bug in \SpecialChar LyX
36549 \begin_layout Plain Layout
36550 \begin_inset CommandInset href
36552 name "LyX-bug #9002"
36553 target "http://www.lyx.org/trac/ticket/9002"
36563 you cannot write normal text inside the comment, even when you use mathematical
36564 text, you will see its \SpecialChar LaTeX
36565 -commands in the \SpecialChar LaTeX
36567 \begin_inset Newline newline
36570 This a formula with a \SpecialChar LaTeX
36572 \begin_inset Formula
36574 A=B%\text{This is the comment}
36582 \begin_layout Standard
36583 \begin_inset Newpage newpage
36589 \begin_layout Section
36592 \begin_inset Index idx
36595 \begin_layout Plain Layout
36604 \begin_layout Standard
36605 This section is a summary of the most important typographic rules, listed
36610 \begin_layout Plain Layout
36611 This collection was partly taken from the German semi-official dictionary
36613 \begin_inset Quotes eld
36617 \begin_inset Quotes erd
36621 \begin_inset CommandInset citation
36628 that lists some of the ISO rules.
36629 More rules are listed in
36630 \begin_inset CommandInset citation
36645 \begin_layout Itemize
36654 \begin_layout Plain Layout
36655 done with font styles, see
36656 \begin_inset CommandInset ref
36658 reference "subsec:Font-Styles"
36667 , no matter if they appear in italic text: 30
36668 \begin_inset space \thinspace{}
36672 \begin_inset Newline newline
36675 Between the value and the unit is the smallest space, see
36676 \begin_inset CommandInset ref
36678 reference "subsec:Predefined-Space"
36683 \begin_inset Newline newline
36686 This convention is automatically fulfilled when the command
36693 When it is entered to a formula, two boxes appear.
36694 In the first one the value is inserted, in the second one the unit, and
36696 \begin_inset Formula $\unit[30]{km/h}$
36700 \begin_inset space \thinspace{}
36710 is not a real \SpecialChar LaTeX
36711 command but the command
36717 , therefore you cannot use it in \SpecialChar TeX
36721 \begin_layout Itemize
36722 Percent and perthousand signs are set like physical units:
36723 \begin_inset Newline newline
36727 \begin_inset space \thinspace{}
36733 \begin_layout Itemize
36734 The degree sign follows directly on the value: 15°, but not when it is used
36736 \begin_inset space \thinspace{}
36742 \begin_layout Itemize
36743 In numbers with more than four digits the smallest space is inserted before
36744 every third digit to group them:
36754 \begin_inset space \thinspace{}
36758 \begin_inset space \thinspace{}
36764 \begin_layout Itemize
36765 For dimensions like 120×90×40
36766 \begin_inset space \thinspace{}
36769 cm the multiplication sign
36770 \begin_inset Quotes eld
36774 \begin_inset Quotes erd
36778 It is available either via the command
36786 Insert\SpecialChar menuseparator
36787 Special Character\SpecialChar menuseparator
36793 \begin_layout Itemize
36794 Functions with names consisting of several letters are set upright to avoid
36796 \begin_inset CommandInset ref
36798 reference "subsec:Predefined-Functions"
36805 \begin_layout Itemize
36806 Indices consisting of several letters, are set upright:
36807 \begin_inset Formula $E_{\mathrm{kin}}$
36811 \begin_inset Newline newline
36814 Components of matrices are set italic:
36815 \begin_inset Formula $\hat{H}_{kl}$
36821 \begin_layout Itemize
36822 The differentiation/integration operator 'd', the Euler's number 'e' and
36823 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36827 \begin_layout Itemize
36828 The character that denotes a
36832 transformation is inserted either by the command
36837 \begin_inset space \textvisiblespace{}
36844 Insert\SpecialChar menuseparator
36845 Special Character\SpecialChar menuseparator
36846 Symbols\SpecialChar menuseparator
36848 \begin_inset space ~
36854 \begin_inset Formula $\mathscr{F}$
36860 \begin_layout Standard
36861 \begin_inset Newpage newpage
36867 \begin_layout Section
36869 \begin_inset Index idx
36872 \begin_layout Plain Layout
36881 \begin_layout Standard
36882 Some characters and symbols can be created with several commands.
36883 Here is a list of the synonym commands:
36886 \begin_layout Standard
36887 \begin_inset VSpace bigskip
36891 \begin_inset space \hfill{}
36895 \begin_inset Tabular
36896 <lyxtabular version="3" rows="12" columns="2">
36897 <features booktabs="true" tabularvalignment="middle">
36898 <column alignment="center" valignment="top" width="0pt">
36899 <column alignment="center" valignment="top" width="0pt">
36901 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
36904 \begin_layout Plain Layout
36910 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
36913 \begin_layout Plain Layout
36921 <cell alignment="center" valignment="top" usebox="none">
36924 \begin_layout Plain Layout
36932 <cell alignment="center" valignment="top" usebox="none">
36935 \begin_layout Plain Layout
36943 <cell alignment="center" valignment="top" usebox="none">
36946 \begin_layout Plain Layout
36954 <cell alignment="center" valignment="top" usebox="none">
36957 \begin_layout Plain Layout
36967 <cell alignment="center" valignment="top" usebox="none">
36970 \begin_layout Plain Layout
36978 <cell alignment="center" valignment="top" usebox="none">
36981 \begin_layout Plain Layout
36991 <cell alignment="center" valignment="top" usebox="none">
36994 \begin_layout Plain Layout
37002 <cell alignment="center" valignment="top" usebox="none">
37005 \begin_layout Plain Layout
37013 <cell alignment="center" valignment="top" usebox="none">
37016 \begin_layout Plain Layout
37024 <cell alignment="center" valignment="top" usebox="none">
37027 \begin_layout Plain Layout
37035 <cell alignment="center" valignment="top" usebox="none">
37038 \begin_layout Plain Layout
37046 <cell alignment="center" valignment="top" usebox="none">
37049 \begin_layout Plain Layout
37059 <cell alignment="center" valignment="top" usebox="none">
37062 \begin_layout Plain Layout
37070 <cell alignment="center" valignment="top" usebox="none">
37073 \begin_layout Plain Layout
37083 <cell alignment="center" valignment="top" usebox="none">
37086 \begin_layout Plain Layout
37094 <cell alignment="center" valignment="top" usebox="none">
37097 \begin_layout Plain Layout
37107 <cell alignment="center" valignment="top" usebox="none">
37110 \begin_layout Plain Layout
37118 <cell alignment="center" valignment="top" usebox="none">
37121 \begin_layout Plain Layout
37131 <cell alignment="center" valignment="top" usebox="none">
37134 \begin_layout Plain Layout
37142 <cell alignment="center" valignment="top" usebox="none">
37145 \begin_layout Plain Layout
37153 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37156 \begin_layout Plain Layout
37164 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37167 \begin_layout Plain Layout
37179 \begin_inset space \hfill{}
37183 \begin_inset Tabular
37184 <lyxtabular version="3" rows="12" columns="2">
37185 <features booktabs="true" tabularvalignment="middle">
37186 <column alignment="center" valignment="top" width="0pt">
37187 <column alignment="center" valignment="top" width="0pt">
37189 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37192 \begin_layout Plain Layout
37198 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37201 \begin_layout Plain Layout
37209 <cell alignment="center" valignment="top" usebox="none">
37212 \begin_layout Plain Layout
37220 <cell alignment="center" valignment="top" usebox="none">
37223 \begin_layout Plain Layout
37235 <cell alignment="center" valignment="top" usebox="none">
37238 \begin_layout Plain Layout
37246 <cell alignment="center" valignment="top" usebox="none">
37249 \begin_layout Plain Layout
37259 <cell alignment="center" valignment="top" usebox="none">
37262 \begin_layout Plain Layout
37270 <cell alignment="center" valignment="top" usebox="none">
37273 \begin_layout Plain Layout
37283 <cell alignment="center" valignment="top" usebox="none">
37286 \begin_layout Plain Layout
37294 <cell alignment="center" valignment="top" usebox="none">
37297 \begin_layout Plain Layout
37305 <cell alignment="center" valignment="top" usebox="none">
37308 \begin_layout Plain Layout
37316 <cell alignment="center" valignment="top" usebox="none">
37319 \begin_layout Plain Layout
37327 <cell alignment="center" valignment="top" usebox="none">
37330 \begin_layout Plain Layout
37338 <cell alignment="center" valignment="top" usebox="none">
37341 \begin_layout Plain Layout
37351 <cell alignment="center" valignment="top" usebox="none">
37354 \begin_layout Plain Layout
37362 <cell alignment="center" valignment="top" usebox="none">
37365 \begin_layout Plain Layout
37375 <cell alignment="center" valignment="top" usebox="none">
37378 \begin_layout Plain Layout
37386 <cell alignment="center" valignment="top" usebox="none">
37389 \begin_layout Plain Layout
37399 <cell alignment="center" valignment="top" usebox="none">
37402 \begin_layout Plain Layout
37410 <cell alignment="center" valignment="top" usebox="none">
37413 \begin_layout Plain Layout
37423 <cell alignment="center" valignment="top" usebox="none">
37426 \begin_layout Plain Layout
37434 <cell alignment="center" valignment="top" usebox="none">
37437 \begin_layout Plain Layout
37447 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37450 \begin_layout Plain Layout
37458 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37461 \begin_layout Plain Layout
37475 \begin_inset space \hfill{}
37481 \begin_layout Standard
37482 \begin_inset Newpage newpage
37488 \begin_layout Bibliography
37489 \begin_inset CommandInset bibitem
37490 LatexCommand bibitem
37504 The \SpecialChar LaTeX
37508 Addison Wesley, 2004
37511 \begin_layout Bibliography
37512 \begin_inset CommandInset bibitem
37513 LatexCommand bibitem
37520 \begin_inset CommandInset href
37523 target "https://www.tug.org/~hvoss/PDF/mathmode.pdf"
37528 of \SpecialChar LaTeX
37532 \begin_layout Bibliography
37533 \begin_inset CommandInset bibitem
37534 LatexCommand bibitem
37541 \begin_inset CommandInset href
37544 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37553 \begin_layout Plain Layout
37562 -\SpecialChar LaTeX
37566 \begin_layout Bibliography
37567 \begin_inset CommandInset bibitem
37568 LatexCommand bibitem
37575 \begin_inset CommandInset href
37578 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37583 of all symbols available with \SpecialChar LaTeX
37587 \begin_layout Bibliography
37588 \begin_inset CommandInset bibitem
37589 LatexCommand bibitem
37596 \begin_inset CommandInset href
37598 name "Documentation"
37599 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37604 of the \SpecialChar LaTeX
37610 \begin_inset Index idx
37613 \begin_layout Plain Layout
37622 \begin_layout Bibliography
37623 \begin_inset CommandInset bibitem
37624 LatexCommand bibitem
37631 \begin_inset CommandInset href
37633 name "Documentation"
37634 target "http://mirrors.ctan.org/macros/latex/contrib/hyperref/doc/manual.pdf"
37639 of the \SpecialChar LaTeX
37645 \begin_inset Index idx
37648 \begin_layout Plain Layout
37649 Packages ! hyperref
37657 \begin_layout Bibliography
37658 \begin_inset CommandInset bibitem
37659 LatexCommand bibitem
37666 \begin_inset CommandInset href
37668 name "Documentation"
37669 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37674 of the \SpecialChar LaTeX
37680 \begin_inset Index idx
37683 \begin_layout Plain Layout
37692 \begin_layout Bibliography
37693 \begin_inset CommandInset bibitem
37694 LatexCommand bibitem
37706 Auflage, Duden 2001
37709 \begin_layout Bibliography
37710 \begin_inset CommandInset bibitem
37711 LatexCommand bibitem
37718 \begin_inset CommandInset href
37721 target "http://physics.nist.gov/Pubs/SP811/sec11.html"
37726 for reviewing manuscripts
37729 \begin_layout Standard
37730 \begin_inset CommandInset index_print
37731 LatexCommand printindex