1 #LyX 2.2 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
137 \maintain_unincluded_children false
139 \language_package default
142 \font_roman "lmodern" "default"
143 \font_sans "lmss" "default"
144 \font_typewriter "lmtt" "default"
145 \font_math "auto" "auto"
146 \font_default_family default
147 \use_non_tex_fonts false
150 \font_sf_scale 100 100
151 \font_tt_scale 100 100
153 \default_output_format pdf2
155 \bibtex_command default
156 \index_command default
160 \pdf_title "LyX's Math Manual"
161 \pdf_author "LyX Team, Uwe Stöhr"
162 \pdf_subject "LyX-documentation about math"
163 \pdf_keywords "LyX, Mathed"
165 \pdf_bookmarksnumbered true
166 \pdf_bookmarksopen true
167 \pdf_bookmarksopenlevel 1
168 \pdf_breaklinks false
172 \pdf_pdfusetitle false
173 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
176 \use_package amsmath 2
177 \use_package amssymb 2
178 \use_package cancel 0
180 \use_package mathdots 1
181 \use_package mathtools 2
182 \use_package mhchem 1
183 \use_package stackrel 0
184 \use_package stmaryrd 0
185 \use_package undertilde 0
187 \cite_engine_type default
191 \paperorientation portrait
195 \notefontcolor #0000ff
202 \paragraph_separation skip
204 \quotes_language english
207 \paperpagestyle plain
211 \tracking_changes false
212 \output_changes false
215 \html_be_strict false
223 's detailed Math manual
227 by the \SpecialChar LyX
232 \begin_layout Plain Layout
234 If you have comments or error corrections, please send them to the \SpecialChar LyX
239 \begin_inset CommandInset href
241 name "lyx-docs@lists.lyx.org"
242 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
253 \begin_inset Note Note
256 \begin_layout Plain Layout
263 \begin_inset Newline newline
267 \begin_inset Newline newline
275 \begin_layout Standard
276 \begin_inset CommandInset toc
277 LatexCommand tableofcontents
284 \begin_layout Standard
285 \begin_inset Note Note
288 \begin_layout Plain Layout
289 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
292 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
299 If they are not installed the document can be exported anyway but the sections
300 where the packages are required will not appear in the output.
305 ; if it is not installed, this file cannot be exported.
308 \begin_layout Plain Layout
309 The latest PDF-version of this document can be found here:
310 \begin_inset Newline newline
315 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
323 \begin_layout Standard
324 \begin_inset Newpage newpage
330 \begin_layout Section
334 \begin_layout Standard
335 This document explains \SpecialChar LyX
336 's math features and is furthermore a collection
337 of \SpecialChar LaTeX
338 -commands used for mathematical characters and constructs.
339 The explanations are designed for the usage of commands.
340 It is therefore required that you have read the section
351 \begin_layout Standard
352 Most of the characters and many constructs explained in this manual are
353 also accessible via the menu
357 \SpecialChar menuseparator
373 But everybody who has to write lots of formulas will notice that it is
374 much faster to use commands instead of the math toolbar.
375 Therefore this manual is focused on commands but also mentions the correspondin
376 g toolbar buttons when available.
379 \begin_layout Standard
380 If not specially mentioned the commands are only available within formulas.
381 To be able to use all commands explained in this document, the option
385 must be checked in the document settings (menu
387 Document\SpecialChar menuseparator
388 Settings\SpecialChar menuseparator
399 \begin_layout Plain Layout
402 Use AMS math package automatically
408 \begin_layout Plain Layout
417 -math when math constructs are found that are supported by \SpecialChar LyX
426 \begin_layout Standard
427 This document doesn't list all
431 \begin_layout Plain Layout
444 \begin_layout Plain Layout
449 \begin_layout Plain Layout
458 -math commands is in the file
461 \begin_inset CommandInset href
464 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
470 , which is part of every \SpecialChar LaTeX
471 standard installation.
476 for lucidity reasons.
479 \begin_layout Section
483 \begin_layout Standard
484 To create an inline formula
485 \begin_inset Index idx
488 \begin_layout Plain Layout
494 that is embedded into a text line, use one of the shortcuts
500 or the toolbar button
507 \begin_inset Newline newline
510 To create a display style formula
511 \begin_inset Index idx
514 \begin_layout Plain Layout
515 Formula ! display style
520 which will appear bigger, has a different format, and will be in a separate
521 paragraph, use one of these shortcuts:
530 \begin_layout Standard
531 To change a display style formula to an inline formula, set the cursor into
532 the formula and use one of the shortcuts
540 Edit\SpecialChar menuseparator
541 Math\SpecialChar menuseparator
545 The same way is used to change an inline formula to a display style formula.
548 \begin_layout Standard
549 To display parts of an inline formula in the size of a display style formula,
557 \begin_inset Index idx
560 \begin_layout Plain Layout
569 Then a new blue box appears in which the desired formula part is inserted.
572 \begin_layout Standard
573 Only inline formulas are allowed inside tables.
576 \begin_layout Standard
581 can be turned on in the menu
583 View\SpecialChar menuseparator
587 When you click there on
588 \begin_inset Quotes eld
592 \begin_inset Quotes erd
595 the toolbar will be shown permanently at the bottom; this state is visualized
600 menu with a checkmark.
601 When you click in this state again on
602 \begin_inset Quotes eld
606 \begin_inset Quotes erd
617 is only shown when the cursor is within a formula; this state is visualized
618 by the renaming of the menu entry from
619 \begin_inset Quotes eld
623 \begin_inset Quotes erd
627 \begin_inset Quotes eld
635 \begin_inset Quotes erd
641 \begin_layout Standard
644 \begin_inset Index idx
647 \begin_layout Plain Layout
654 is invoked by pressing the toolbar button
662 Insert\SpecialChar menuseparator
674 \begin_layout Standard
675 To change the \SpecialChar LaTeX
677 \begin_inset Index idx
680 \begin_layout Plain Layout
689 Document\SpecialChar menuseparator
690 Settings\SpecialChar menuseparator
700 \begin_layout Standard
701 To edit matrices, case differentiations and multiline formulas subsequently,
704 Edit\SpecialChar menuseparator
709 Edit\SpecialChar menuseparator
711 \begin_inset space \thinspace{}
715 \begin_inset space \thinspace{}
725 When lines and columns are swapped via the menu, the column or line where
726 the cursor is in is exchanged with the column to the right or the line
728 Is the cursor in the last column or row, the exchange is done with the
729 column to the left or the line above.
732 \begin_layout Standard
733 To write text in formulas
737 \begin_layout Plain Layout
738 For multiline formulas the command
745 \begin_inset CommandInset ref
747 reference "subsec:Text-in-multiline"
761 \begin_inset Index idx
764 \begin_layout Plain Layout
771 \begin_inset Index idx
774 \begin_layout Plain Layout
781 This mode is invoked with the shortcut
787 or by the insertion of the command
794 \begin_inset Index idx
797 \begin_layout Plain Layout
806 The text appears black in \SpecialChar LyX
807 and can therefore be distinguished from the
808 other formula parts which appear blue.
809 In the output mathematical text is set upright, in contrary to other formula
813 \begin_layout Subsection*
817 \begin_layout Standard
818 Most of the \SpecialChar LaTeX
819 -commands for math constructs have the following scheme:
822 \begin_layout Standard
838 \begin_layout Standard
839 A command always starts with a backslash
840 \begin_inset Quotes gld
850 \begin_inset Quotes grd
854 To omit optional arguments, also omit the associated brackets.
855 The braces around the required arguments are named in this document as
858 \begin_inset Index idx
861 \begin_layout Plain Layout
869 If you add in a formula a left brace to a command name, \SpecialChar LyX
871 creates a \SpecialChar TeX
873 In all other cases \SpecialChar TeX
874 braces are created in formulas with the command
882 braces appear red in \SpecialChar LyX
883 , in contrary to normal braces which appear blue.
885 mode no command is needed to get \SpecialChar TeX
888 braces don't appear in the output.
891 \begin_layout Standard
892 When commands without arguments, like commands for symbols are entered in
894 mode, a space character must
898 be behind the command to end it.
899 This space doesn't appear in the output.
900 When the space should appear in the output, the space must be followed
901 by a protected space in normal text.
904 \begin_layout Standard
905 A protected space is inserted with
908 arg "command-alternatives space-insert protected ; math-space"
914 \begin_layout Subsection*
915 \begin_inset Newpage newpage
921 \begin_layout Itemize
923 \begin_inset space \textvisiblespace{}
926 denotes a space character to be input.
929 \begin_layout Itemize
931 \begin_inset Formula $\to$
934 denotes the usage of the corresponding arrow key on the keyboard.
939 key can often be used instead of
940 \begin_inset Formula $\to$
944 \begin_inset Formula $\downarrow$
952 \begin_inset Formula $\leftarrow$
956 \begin_inset Formula $\uparrow$
962 \begin_layout Subsection*
966 \begin_layout Standard
968 \begin_inset Float table
974 \begin_layout Plain Layout
976 \begin_inset Caption Standard
978 \begin_layout Plain Layout
979 \begin_inset CommandInset label
981 name "tab:Available-units"
993 \begin_layout Plain Layout
996 <lyxtabular version="3" rows="13" columns="2">
997 <features booktabs="true" tabularvalignment="middle">
998 <column alignment="center" valignment="top">
999 <column alignment="center" valignment="top" width="0pt">
1001 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1004 \begin_layout Plain Layout
1010 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1013 \begin_layout Plain Layout
1021 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1024 \begin_layout Plain Layout
1030 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1033 \begin_layout Plain Layout
1041 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1044 \begin_layout Plain Layout
1050 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1053 \begin_layout Plain Layout
1061 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1064 \begin_layout Plain Layout
1070 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1073 \begin_layout Plain Layout
1075 \begin_inset space \thinspace{}
1079 \begin_inset space \thinspace{}
1089 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1092 \begin_layout Plain Layout
1098 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1101 \begin_layout Plain Layout
1103 \begin_inset space \thinspace{}
1107 \begin_inset space \thinspace{}
1117 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1120 \begin_layout Plain Layout
1126 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1129 \begin_layout Plain Layout
1131 \begin_inset space \thinspace{}
1135 \begin_inset space \thinspace{}
1145 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1148 \begin_layout Plain Layout
1154 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1157 \begin_layout Plain Layout
1159 \begin_inset space \thinspace{}
1163 \begin_inset space \thinspace{}
1173 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1176 \begin_layout Plain Layout
1182 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1185 \begin_layout Plain Layout
1187 \begin_inset space \thinspace{}
1191 \begin_inset space \thinspace{}
1201 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1204 \begin_layout Plain Layout
1210 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1213 \begin_layout Plain Layout
1215 \begin_inset space \thinspace{}
1219 \begin_inset Formula $\approx$
1223 \begin_inset space \thinspace{}
1233 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1236 \begin_layout Plain Layout
1242 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1245 \begin_layout Plain Layout
1247 \begin_inset space \thinspace{}
1251 \begin_inset space \thinspace{}
1261 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1264 \begin_layout Plain Layout
1270 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1273 \begin_layout Plain Layout
1277 \begin_inset Quotes eld
1283 \begin_inset Quotes erd
1293 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1296 \begin_layout Plain Layout
1302 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1305 \begin_layout Plain Layout
1307 \begin_inset Quotes eld
1315 \begin_inset Quotes erd
1325 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1328 \begin_layout Plain Layout
1334 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1337 \begin_layout Plain Layout
1339 \begin_inset space \thinspace{}
1343 \begin_inset Formula $\nicefrac{1}{18}$
1347 \begin_inset space \thinspace{}
1368 \begin_layout Standard
1369 \begin_inset Newpage newpage
1375 \begin_layout Section
1379 \begin_layout Subsection
1381 \begin_inset Index idx
1384 \begin_layout Plain Layout
1391 \begin_inset Index idx
1394 \begin_layout Plain Layout
1401 \begin_inset Index idx
1404 \begin_layout Plain Layout
1409 \begin_layout Plain Layout
1420 \begin_layout Plain Layout
1433 \begin_inset Index idx
1436 \begin_layout Plain Layout
1441 \begin_layout Plain Layout
1452 \begin_layout Plain Layout
1467 \begin_layout Standard
1468 Indices are created with an underscore
1469 \begin_inset Quotes eld
1473 \begin_inset Quotes erd
1476 or via the math toolbar button
1479 arg "math-subscript"
1482 , exponents with a caret
1483 \begin_inset Quotes eld
1487 \begin_inset Quotes erd
1490 or via the math toolbar button
1493 arg "math-superscript"
1497 \begin_inset Separator latexpar
1503 \begin_layout Standard
1505 \begin_inset Tabular
1506 <lyxtabular version="3" rows="4" columns="2">
1507 <features booktabs="true" tabularvalignment="middle">
1508 <column alignment="center" valignment="top" width="0pt">
1509 <column alignment="center" valignment="top" width="0pt">
1511 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1514 \begin_layout Plain Layout
1520 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1523 \begin_layout Plain Layout
1531 <cell alignment="center" valignment="top" usebox="none">
1534 \begin_layout Plain Layout
1540 <cell alignment="center" valignment="top" usebox="none">
1543 \begin_layout Plain Layout
1544 \begin_inset Formula $B_{V}$
1553 <row topspace="1.5mm">
1554 <cell alignment="center" valignment="top" usebox="none">
1557 \begin_layout Plain Layout
1563 <cell alignment="center" valignment="top" usebox="none">
1566 \begin_layout Plain Layout
1567 \begin_inset Formula $B^{V}$
1576 <row topspace="1.5mm">
1577 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1580 \begin_layout Plain Layout
1582 \begin_inset space \textvisiblespace{}
1590 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1593 \begin_layout Plain Layout
1594 \begin_inset Formula $B^{A}$
1610 \begin_layout Standard
1611 As the caret is in some languages an accent, vowels will be accentuated
1612 in this case and not set as exponents
1616 \begin_layout Plain Layout
1617 Depending on the used keyboard settings this can also happen for characters
1624 To get exponents in this case, press
1628 after the caret as in the last example.
1631 \begin_layout Subsection
1633 \begin_inset CommandInset label
1635 name "subsec:Fractions"
1640 \begin_inset Index idx
1643 \begin_layout Plain Layout
1652 \begin_layout Standard
1653 Fractions are generated with the command
1660 \begin_inset Index idx
1663 \begin_layout Plain Layout
1671 or via the math toolbar button
1674 arg "math-insert \\frac"
1678 The font size is adjusted automatically, depending on whether the fraction
1679 is in an inline or display style formula.
1680 With the math toolbar button
1683 arg "math-insert \\frac-square"
1686 you can select different fraction types.
1689 \begin_layout Standard
1697 \begin_inset Index idx
1700 \begin_layout Plain Layout
1708 a fraction can be created that always has the size of a display style formula.
1716 \begin_inset Index idx
1719 \begin_layout Plain Layout
1727 the fraction appears always with the size of an inline formula.
1731 \begin_layout Standard
1732 A line with the fraction
1733 \begin_inset Formula $\frac{1}{2}$
1736 that was created with the command
1745 \begin_layout Standard
1746 A line with the fraction
1747 \begin_inset Formula $\dfrac{1}{2}$
1750 that was created with the command
1757 \begin_inset Separator latexpar
1763 \begin_layout Standard
1765 \begin_inset Tabular
1766 <lyxtabular version="3" rows="4" columns="2">
1767 <features booktabs="true" tabularvalignment="middle">
1768 <column alignment="center" valignment="top" width="0pt">
1769 <column alignment="center" valignment="top" width="0pt">
1771 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1774 \begin_layout Plain Layout
1780 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1783 \begin_layout Plain Layout
1790 <row topspace="1.5mm">
1791 <cell alignment="center" valignment="top" usebox="none">
1794 \begin_layout Plain Layout
1798 \begin_inset space \textvisiblespace{}
1802 \begin_inset Formula $\downarrow$
1810 <cell alignment="center" valignment="top" usebox="none">
1813 \begin_layout Plain Layout
1814 \begin_inset Formula $\frac{A}{B}$
1823 <row topspace="2mm">
1824 <cell alignment="center" valignment="top" usebox="none">
1827 \begin_layout Plain Layout
1831 \begin_inset space \textvisiblespace{}
1835 \begin_inset Formula $\downarrow$
1843 <cell alignment="center" valignment="top" usebox="none">
1846 \begin_layout Plain Layout
1847 \begin_inset Formula $\dfrac{A}{B}$
1856 <row topspace="2mm" bottomspace="1mm">
1857 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1860 \begin_layout Plain Layout
1864 \begin_inset space \textvisiblespace{}
1870 \begin_inset space \textvisiblespace{}
1874 \begin_inset Formula $\downarrow$
1878 \begin_inset Formula $\downarrow\downarrow$
1886 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1889 \begin_layout Plain Layout
1890 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1906 \begin_layout Standard
1907 \begin_inset VSpace bigskip
1911 \begin_inset Newpage newpage
1914 For nested fractions the command
1921 \begin_inset Index idx
1924 \begin_layout Plain Layout
1934 \begin_inset VSpace -3mm
1940 \begin_layout Standard
1941 \begin_inset Formula
1943 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1944 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1952 \begin_layout Standard
1953 The command for the example above is:
1956 \begin_layout Standard
1962 \begin_inset space \textvisiblespace{}
1966 \begin_inset Formula $\downarrow$
1972 \begin_inset space \textvisiblespace{}
1978 \begin_inset space \textvisiblespace{}
1982 \begin_inset Formula $\downarrow$
1986 \begin_inset Formula $\downarrow$
1992 \begin_layout Standard
1993 \begin_inset VSpace medskip
1999 \begin_layout Standard
2006 sets the fraction always in the size of a displayed formula, also when
2007 it is part of another fraction.
2010 \begin_layout Standard
2011 It is possible to specify the alignment of the numerator.
2018 is used to left align it, the command
2031 centers the numerator.
2032 These fractions demonstrate the different alignments:
2035 \begin_layout Standard
2038 \begin_inset Formula
2040 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2048 \begin_layout Standard
2049 \begin_inset Note Greyedout
2052 \begin_layout Plain Layout
2069 are no real \SpecialChar LaTeX
2070 commands but represent the command
2074 cfrac[alignment]{numerator}{denominator}
2077 Therefore you cannot use them in \SpecialChar TeX
2086 \begin_layout Standard
2087 \begin_inset VSpace medskip
2090 It is often advantageous to combine
2103 \begin_inset Formula
2105 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2113 \begin_layout Standard
2114 For inline fractions with a sloped fraction stroke you can use the command
2122 \begin_inset Index idx
2125 \begin_layout Plain Layout
2134 \begin_inset Formula $\nicefrac{5}{31}$
2144 \begin_inset Index idx
2147 \begin_layout Plain Layout
2156 \begin_inset Formula $\unitfrac{5}{31}$
2159 There is furthermore the command
2165 that offers to write a fraction in combination with a number:
2166 \begin_inset Formula $\unitfrac[2]{1}{3}$
2172 \begin_layout Standard
2173 \begin_inset Note Greyedout
2176 \begin_layout Plain Layout
2187 is not a real \SpecialChar LaTeX
2188 command but the command
2189 \begin_inset Newline newline
2196 unitfrac[number]{numerator}{denominator}
2199 Therefore you cannot use it in \SpecialChar TeX
2208 \begin_layout Standard
2209 How to define own fractions where the fraction stroke can be changed, is
2211 \begin_inset CommandInset ref
2213 reference "subsec:Self-defined-Fractions"
2220 \begin_layout Standard
2221 Multiline fractions are explained in
2222 \begin_inset CommandInset ref
2224 reference "subsec:Multiline-Fractions"
2231 \begin_layout Subsection
2233 \begin_inset Index idx
2236 \begin_layout Plain Layout
2245 \begin_layout Standard
2246 Square roots are created with
2253 \begin_inset Index idx
2256 \begin_layout Plain Layout
2264 or the math toolbar button
2267 arg "math-insert \\sqrt"
2270 , all other roots with the command
2277 \begin_inset Index idx
2280 \begin_layout Plain Layout
2288 or with the math toolbar button
2291 arg "math-insert \\root"
2295 \begin_inset Separator latexpar
2301 \begin_layout Standard
2303 \begin_inset Tabular
2304 <lyxtabular version="3" rows="3" columns="2">
2305 <features booktabs="true" tabularvalignment="middle">
2306 <column alignment="center" valignment="top" width="0pt">
2307 <column alignment="center" valignment="top" width="0pt">
2309 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2312 \begin_layout Plain Layout
2318 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2321 \begin_layout Plain Layout
2328 <row topspace="1mm">
2329 <cell alignment="center" valignment="top" usebox="none">
2332 \begin_layout Plain Layout
2336 \begin_inset space \textvisiblespace{}
2344 <cell alignment="center" valignment="top" usebox="none">
2347 \begin_layout Plain Layout
2348 \begin_inset Formula $\sqrt{A-B}$
2357 <row topspace="1mm">
2358 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2361 \begin_layout Plain Layout
2365 \begin_inset space \textvisiblespace{}
2369 \begin_inset Formula $\downarrow$
2377 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2380 \begin_layout Plain Layout
2381 \begin_inset Formula $\sqrt[3]{A-B}$
2397 \begin_layout Standard
2398 A square root can also be created with
2404 when the root index field is left empty.
2407 \begin_layout Standard
2408 With certain indices the distance to the root is too small, like in this
2410 \begin_inset Formula $\sqrt[\beta]{B}$
2414 \begin_inset Newline newline
2418 \begin_inset Formula $\beta$
2422 To avoid this, the commands
2429 \begin_inset Index idx
2432 \begin_layout Plain Layout
2447 \begin_inset Index idx
2450 \begin_layout Plain Layout
2458 are used with the following scheme:
2461 \begin_layout Standard
2475 \begin_layout Standard
2476 Distance is the number of Big Points (unit bp;
2477 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2480 ), that the index should be moved to the left or top, resp..
2481 The commands are written to the index.
2482 This way the command
2483 \begin_inset Newline newline
2493 \begin_inset Formula $\to$
2499 \begin_inset Formula $\to$
2505 \begin_inset space \textvisiblespace{}
2509 \begin_inset Formula $\to$
2513 \begin_inset Newline newline
2518 produces a correct typeset formula:
2519 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2525 \begin_layout Subsection
2526 Binomial Coefficients
2527 \begin_inset Index idx
2530 \begin_layout Plain Layout
2531 Binomial coefficients
2539 \begin_layout Standard
2540 Binomial coefficients are inserted with the command
2547 \begin_inset Index idx
2550 \begin_layout Plain Layout
2558 or with the submenu of the math toolbar button
2561 arg "math-insert \\frac-square"
2577 there are the commands
2584 \begin_inset Index idx
2587 \begin_layout Plain Layout
2602 \begin_inset Index idx
2605 \begin_layout Plain Layout
2614 For other brackets around binomial coeficients there are the commands
2621 \begin_inset Index idx
2624 \begin_layout Plain Layout
2639 \begin_inset Index idx
2642 \begin_layout Plain Layout
2651 \begin_inset Separator latexpar
2657 \begin_layout Standard
2659 \begin_inset Tabular
2660 <lyxtabular version="3" rows="6" columns="2">
2661 <features booktabs="true" tabularvalignment="middle">
2662 <column alignment="center" valignment="top" width="0pt">
2663 <column alignment="center" valignment="top" width="0pt">
2665 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2668 \begin_layout Plain Layout
2674 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2677 \begin_layout Plain Layout
2684 <row topspace="1mm">
2685 <cell alignment="center" valignment="top" usebox="none">
2688 \begin_layout Plain Layout
2692 \begin_inset space \textvisiblespace{}
2696 \begin_inset Formula $\downarrow$
2704 <cell alignment="center" valignment="top" usebox="none">
2707 \begin_layout Plain Layout
2708 \begin_inset Formula $\binom{A}{B}$
2717 <row topspace="2mm">
2718 <cell alignment="center" valignment="top" usebox="none">
2721 \begin_layout Plain Layout
2725 \begin_inset space \textvisiblespace{}
2729 \begin_inset Formula $\downarrow$
2737 <cell alignment="center" valignment="top" usebox="none">
2740 \begin_layout Plain Layout
2741 \begin_inset Formula $\dbinom{A}{B}$
2750 <row topspace="2mm" bottomspace="0.5mm">
2751 <cell alignment="center" valignment="top" usebox="none">
2754 \begin_layout Plain Layout
2758 \begin_inset space \textvisiblespace{}
2762 \begin_inset Formula $\downarrow$
2770 <cell alignment="center" valignment="top" usebox="none">
2773 \begin_layout Plain Layout
2774 \begin_inset Formula $\tbinom{A}{B}$
2783 <row topspace="1mm">
2784 <cell alignment="center" valignment="top" topline="true" usebox="none">
2787 \begin_layout Plain Layout
2791 \begin_inset space \textvisiblespace{}
2795 \begin_inset Formula $\downarrow$
2803 <cell alignment="center" valignment="top" topline="true" usebox="none">
2806 \begin_layout Plain Layout
2807 \begin_inset Formula ${A \brack B}$
2816 <row topspace="2mm" bottomspace="0.5mm">
2817 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2820 \begin_layout Plain Layout
2824 \begin_inset space \textvisiblespace{}
2828 \begin_inset Formula $\downarrow$
2836 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2839 \begin_layout Plain Layout
2840 \begin_inset Formula ${A \brace B}$
2856 \begin_layout Subsection
2857 Case Differentiations
2858 \begin_inset Index idx
2861 \begin_layout Plain Layout
2862 Case differentiations
2870 \begin_layout Standard
2872 \begin_inset Tabular
2873 <lyxtabular version="3" rows="3" columns="2">
2874 <features booktabs="true" tabularvalignment="middle">
2875 <column alignment="center" valignment="top" width="0pt">
2876 <column alignment="center" valignment="top" width="0pt">
2878 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2881 \begin_layout Plain Layout
2887 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2890 \begin_layout Plain Layout
2898 <cell alignment="center" valignment="top" usebox="none">
2901 \begin_layout Plain Layout
2905 \begin_inset space \textvisiblespace{}
2909 \begin_inset Formula $\to$
2913 \begin_inset Index idx
2916 \begin_layout Plain Layout
2929 <cell alignment="center" valignment="top" usebox="none">
2932 \begin_layout Plain Layout
2933 \begin_inset Formula $\begin{cases}
2943 <row topspace="1.5mm">
2944 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2947 \begin_layout Plain Layout
2951 \begin_inset space \textvisiblespace{}
2957 arg "newline-insert newline"
2965 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2968 \begin_layout Plain Layout
2969 \begin_inset Formula $\begin{cases}
2970 A & \textrm{for }x>0\\
2971 B & \textrm{for }x=0
2988 \begin_layout Standard
2995 or pressing the math toolbar button
2998 arg "math-insert \\cases"
3001 you can create new lines with the shortcut
3004 arg "newline-insert newline"
3007 or the table toolbar button
3010 arg "tabular-feature append-row"
3016 \begin_layout Standard
3023 is also available via the menu
3025 Insert\SpecialChar menuseparator
3026 Math\SpecialChar menuseparator
3032 \begin_layout Subsection
3034 \begin_inset Index idx
3037 \begin_layout Plain Layout
3046 \begin_layout Standard
3054 \begin_inset Index idx
3057 \begin_layout Plain Layout
3065 every character can be displayed canceled.
3066 The characters are quasi accentuated by a slash.
3067 \begin_inset Separator latexpar
3073 \begin_layout Standard
3075 \begin_inset Tabular
3076 <lyxtabular version="3" rows="4" columns="2">
3077 <features booktabs="true" tabularvalignment="middle">
3078 <column alignment="center" valignment="top" width="0pt">
3079 <column alignment="center" valignment="top" width="0pt">
3081 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3084 \begin_layout Plain Layout
3090 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3093 \begin_layout Plain Layout
3101 <cell alignment="center" valignment="top" usebox="none">
3104 \begin_layout Plain Layout
3112 <cell alignment="center" valignment="top" usebox="none">
3115 \begin_layout Plain Layout
3116 \begin_inset Formula $\not=$
3126 <cell alignment="center" valignment="top" usebox="none">
3129 \begin_layout Plain Layout
3139 <cell alignment="center" valignment="top" usebox="none">
3142 \begin_layout Plain Layout
3143 \begin_inset Formula $\not\le$
3153 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3156 \begin_layout Plain Layout
3166 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3169 \begin_layout Plain Layout
3170 \begin_inset Formula $\not\parallel$
3186 \begin_layout Standard
3187 The last example shows that not all negations look good.
3188 Therefore there are special commands for some negations (see
3189 \begin_inset CommandInset ref
3191 reference "subsec:Mathematical-Symbols"
3196 \begin_inset CommandInset ref
3198 reference "sec:Relations"
3205 \begin_layout Subsection
3207 \begin_inset CommandInset label
3209 name "subsec:Placeholders"
3214 \begin_inset Index idx
3217 \begin_layout Plain Layout
3224 \begin_inset Index idx
3227 \begin_layout Plain Layout
3228 Chemical characters ! Isotopes
3234 \begin_inset Index idx
3237 \begin_layout Plain Layout
3242 \begin_layout Plain Layout
3253 \begin_layout Plain Layout
3268 \begin_layout Standard
3270 \begin_inset space \thinspace{}
3274 \begin_inset space \space{}
3281 \begin_layout Plain Layout
3282 Typesetting isotopes and chemical symbols is described in
3283 \begin_inset CommandInset ref
3285 reference "subsec:Chemical-Symbols-and"
3294 the following problem occurs:
3295 \begin_inset Separator latexpar
3301 \begin_layout Standard
3303 \begin_inset Tabular
3304 <lyxtabular version="3" rows="2" columns="2">
3305 <features booktabs="true" tabularvalignment="middle">
3306 <column alignment="center" valignment="top" width="0pt">
3307 <column alignment="center" valignment="top" width="0pt">
3309 <cell alignment="center" valignment="top" usebox="none">
3312 \begin_layout Plain Layout
3313 Indices created with sub- and superscripts:
3318 <cell alignment="center" valignment="top" usebox="none">
3321 \begin_layout Plain Layout
3322 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3331 <row topspace="1.5mm">
3332 <cell alignment="center" valignment="top" usebox="none">
3335 \begin_layout Plain Layout
3341 <cell alignment="center" valignment="top" usebox="none">
3344 \begin_layout Plain Layout
3345 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3361 \begin_layout Standard
3362 The shorter index is by default placed below or above the first character
3363 of the longer index.
3364 To avoid this there is the command
3371 \begin_inset Index idx
3374 \begin_layout Plain Layout
3382 or the math toolbar button
3383 \begin_inset space \thinspace{}
3390 \begin_layout Plain Layout
3391 can be found in the submenu of the toolbar button
3394 arg "math-insert \\space"
3408 that creates one or more phantom characters.
3415 a small blue box appears that is superposed with two red arrows.
3416 The arrows indicate that the complete width and height of the box content
3417 will be created as placeholder.
3418 Phantom characters are accordingly placeholders with the size of the characters.
3419 \begin_inset Separator latexpar
3425 \begin_layout Standard
3427 \begin_inset Tabular
3428 <lyxtabular version="3" rows="4" columns="2">
3429 <features booktabs="true" tabularvalignment="middle">
3430 <column alignment="center" valignment="top" width="0pt">
3431 <column alignment="center" valignment="top" width="0pt">
3433 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3436 \begin_layout Plain Layout
3442 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3445 \begin_layout Plain Layout
3452 <row topspace="1.5mm">
3453 <cell alignment="center" valignment="top" usebox="none">
3456 \begin_layout Plain Layout
3458 \begin_inset space \textvisiblespace{}
3464 \begin_inset space \textvisiblespace{}
3468 \begin_inset Formula $\to$
3472 \begin_inset space \textvisiblespace{}
3480 <cell alignment="center" valignment="top" usebox="none">
3483 \begin_layout Plain Layout
3484 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3493 <row topspace="1.5mm" bottomspace="0.5mm">
3494 <cell alignment="center" valignment="top" usebox="none">
3497 \begin_layout Plain Layout
3499 \begin_inset space \textvisiblespace{}
3505 \begin_inset space \textvisiblespace{}
3509 \begin_inset Formula $\to$
3513 \begin_inset space \textvisiblespace{}
3521 <cell alignment="center" valignment="top" usebox="none">
3524 \begin_layout Plain Layout
3525 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3534 <row topspace="1.5mm" bottomspace="0.5mm">
3535 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3538 \begin_layout Plain Layout
3542 \begin_inset space \textvisiblespace{}
3548 \begin_inset space \textvisiblespace{}
3552 \begin_inset Formula $\to$
3556 \begin_inset space \textvisiblespace{}
3564 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3567 \begin_layout Plain Layout
3568 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3584 \begin_layout Standard
3585 Furthermore there are the commands
3592 \begin_inset Index idx
3595 \begin_layout Plain Layout
3616 \begin_inset Index idx
3619 \begin_layout Plain Layout
3640 creates only space for the maximal height of the characters in the box
3641 but not for its width.
3648 creates only space for the width of the box content.
3649 Therefore the boxes of both commands have only one red arrow.
3652 \begin_layout Standard
3653 For example the command
3658 \begin_inset space \textvisiblespace{}
3665 creates space for the height of the integral sign,
3669 \begin_layout Plain Layout
3676 creates an integral sign, see
3677 \begin_inset CommandInset ref
3679 reference "subsec:Big-Operators"
3688 because this is the larger character.
3689 An example application is in
3690 \begin_inset CommandInset ref
3692 reference "subsec:Multiline-Brackets"
3699 \begin_layout Standard
3700 Placeholders can also be used for text when they are inserted via the menu
3703 Insert\SpecialChar menuseparator
3704 Formatting\SpecialChar menuseparator
3710 \begin_layout Standard
3712 \begin_inset Newline newline
3716 \begin_inset Phantom Phantom
3719 \begin_layout Plain Layout
3728 \begin_layout Subsection
3730 \begin_inset Index idx
3733 \begin_layout Plain Layout
3740 \begin_inset Index idx
3743 \begin_layout Plain Layout
3744 Formula ! underlined
3752 \begin_layout Standard
3754 \begin_inset Tabular
3755 <lyxtabular version="3" rows="4" columns="2">
3756 <features booktabs="true" tabularvalignment="middle">
3757 <column alignment="center" valignment="top" width="0pt">
3758 <column alignment="center" valignment="top" width="0pt">
3760 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3763 \begin_layout Plain Layout
3769 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3772 \begin_layout Plain Layout
3779 <row topspace="2mm">
3780 <cell alignment="center" valignment="top" usebox="none">
3783 \begin_layout Plain Layout
3787 \begin_inset space \textvisiblespace{}
3791 \begin_inset Index idx
3794 \begin_layout Plain Layout
3807 <cell alignment="center" valignment="top" usebox="none">
3810 \begin_layout Plain Layout
3811 \begin_inset Formula $\overline{A+B}$
3820 <row bottomspace="1mm">
3821 <cell alignment="center" valignment="top" usebox="none">
3824 \begin_layout Plain Layout
3828 \begin_inset space \textvisiblespace{}
3832 \begin_inset Index idx
3835 \begin_layout Plain Layout
3848 <cell alignment="center" valignment="top" usebox="none">
3851 \begin_layout Plain Layout
3852 \begin_inset Formula $\underline{A+B}$
3861 <row topspace="2mm" bottomspace="1mm">
3862 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3865 \begin_layout Plain Layout
3869 \begin_inset space \textvisiblespace{}
3875 \begin_inset space \textvisiblespace{}
3883 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3886 \begin_layout Plain Layout
3887 \begin_inset Formula $\overline{\underline{A+B}}$
3903 \begin_layout Standard
3904 In the last example it doesn't matter if first
3919 \begin_layout Standard
3920 To double underline use
3929 \begin_layout Standard
3930 It is possible to place up to 6 lines above or below characters.
3933 \begin_layout Standard
3934 \begin_inset VSpace bigskip
3937 Custom lines can be created using the command
3944 \begin_inset Index idx
3947 \begin_layout Plain Layout
3955 which has the following scheme:
3958 \begin_layout Standard
3963 rule[vertical offset]{length}{thickness}
3966 \begin_layout Standard
3967 The optional vertical offset shifts the line upwards (or downwards, when
3968 the value is negative).
3970 \begin_inset CommandInset ref
3972 reference "tab:Available-units"
3976 can be used for the values.
3977 Here are two example lines created with the commands
3978 \begin_inset Newline newline
3985 rule[-2ex]{3cm}{2pt}
3996 \begin_layout Standard
3998 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4004 \begin_layout Standard
4011 can also be used for text when a line is inserted via the menu
4013 Insert\SpecialChar menuseparator
4014 Formatting\SpecialChar menuseparator
4016 \begin_inset space ~
4024 \begin_layout Standard
4026 \begin_inset CommandInset line
4037 \begin_layout Subsection
4039 \begin_inset CommandInset label
4041 name "subsec:Ellipses"
4046 \begin_inset Index idx
4049 \begin_layout Plain Layout
4058 \begin_layout Standard
4059 There are different types of ellipses available.
4063 \begin_layout Plain Layout
4064 In the math toolbar in the submenu of the button
4067 arg "math-insert \\ldots"
4075 For listings dots at the baseline are used (
4082 \begin_inset Index idx
4085 \begin_layout Plain Layout
4093 ), while for operations dots are needed that are on the same height as the
4101 \begin_inset Index idx
4104 \begin_layout Plain Layout
4113 When using the command
4120 \begin_inset Index idx
4123 \begin_layout Plain Layout
4131 , \SpecialChar LaTeX
4132 decides on the basis of the next character what type is used.
4133 \begin_inset Separator latexpar
4139 \begin_layout Standard
4141 \begin_inset Tabular
4142 <lyxtabular version="3" rows="9" columns="2">
4143 <features booktabs="true" tabularvalignment="middle">
4144 <column alignment="center" valignment="top" width="0pt">
4145 <column alignment="center" valignment="top" width="0pt">
4147 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4150 \begin_layout Plain Layout
4156 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4159 \begin_layout Plain Layout
4167 <cell alignment="center" valignment="top" usebox="none">
4170 \begin_layout Plain Layout
4172 \begin_inset space \textvisiblespace{}
4178 \begin_inset space \textvisiblespace{}
4186 <cell alignment="center" valignment="top" usebox="none">
4189 \begin_layout Plain Layout
4190 \begin_inset Formula $A_{1},\dots,A_{n}$
4200 <cell alignment="center" valignment="top" usebox="none">
4203 \begin_layout Plain Layout
4205 \begin_inset space \textvisiblespace{}
4211 \begin_inset space \textvisiblespace{}
4219 <cell alignment="center" valignment="top" usebox="none">
4222 \begin_layout Plain Layout
4223 \begin_inset Formula $A_{1}+\dots+A_{n}$
4233 <cell alignment="center" valignment="top" usebox="none">
4236 \begin_layout Plain Layout
4238 \begin_inset space \textvisiblespace{}
4244 \begin_inset space \textvisiblespace{}
4252 <cell alignment="center" valignment="top" usebox="none">
4255 \begin_layout Plain Layout
4256 \begin_inset Formula $A_{1},\ldots,A_{n}$
4266 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4269 \begin_layout Plain Layout
4271 \begin_inset space \textvisiblespace{}
4277 \begin_inset space \textvisiblespace{}
4285 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4288 \begin_layout Plain Layout
4289 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4299 <cell alignment="center" valignment="top" usebox="none">
4302 \begin_layout Plain Layout
4310 <cell alignment="center" valignment="top" usebox="none">
4313 \begin_layout Plain Layout
4314 \begin_inset Formula $\vdots$
4324 <cell alignment="center" valignment="top" usebox="none">
4327 \begin_layout Plain Layout
4335 <cell alignment="center" valignment="top" usebox="none">
4338 \begin_layout Plain Layout
4339 \begin_inset Formula $\ddots$
4349 <cell alignment="center" valignment="top" usebox="none">
4352 \begin_layout Plain Layout
4360 <cell alignment="center" valignment="top" usebox="none">
4363 \begin_layout Plain Layout
4364 \begin_inset Formula $\iddots$
4374 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4377 \begin_layout Plain Layout
4379 \begin_inset space \thinspace{}
4382 matrix with the different dots
4387 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4390 \begin_layout Plain Layout
4391 \begin_inset Formula $\begin{array}{ccc}
4392 A_{11} & \cdots & A_{1m}\\
4393 \vdots & \ddots & \vdots\\
4394 A_{n1} & \cdots & A_{nm}
4411 \begin_layout Standard
4412 The ellipses available in menu
4414 Insert\SpecialChar menuseparator
4416 \begin_inset space ~
4430 \begin_layout Standard
4431 \begin_inset VSpace medskip
4440 , one of the options
4442 Use mathdots package (automatically)
4444 must be set in the document settings under
4447 \begin_inset space ~
4453 \begin_inset Newline newline
4458 Use mathdots package
4460 will improve the appearance of all dots in the documents if their font
4461 style or size is not the default.
4464 \begin_layout Standard
4465 \begin_inset VSpace medskip
4468 Specially for matrices there are ellipses that span over several columns.
4469 They are created with the command
4476 \begin_inset Index idx
4479 \begin_layout Plain Layout
4487 , that has the following scheme:
4490 \begin_layout Standard
4495 hdotsfor[distance]{number of columns}
4498 \begin_layout Standard
4499 The number of columns specifies how many columns should be spanned.
4500 Distance is a factor for the distance between the dots.
4503 \begin_layout Standard
4504 In the following matrix the command
4510 was inserted in the first box of the second line, to get an ellipsis with
4511 a dot distance twice as long as with the command
4518 \begin_inset Formula
4520 \left(\begin{array}{cccc}
4529 Note that the matrix fields that should be spanned must be empty, otherwise
4530 you get \SpecialChar LaTeX
4534 \begin_layout Standard
4535 \begin_inset VSpace bigskip
4538 Furthermore you can fill with the command
4545 \begin_inset Index idx
4548 \begin_layout Plain Layout
4556 the rest of a line with dots.
4557 The effect of these commands is the same as with
4564 \begin_inset CommandInset ref
4566 reference "subsec:Variable-Space"
4573 \begin_layout Standard
4574 For example the command
4579 \begin_inset space \textvisiblespace{}
4587 \begin_layout Standard
4588 \begin_inset Formula $A\dotfill B$
4594 \begin_layout Standard
4601 there is for a line the command
4608 \begin_inset Index idx
4611 \begin_layout Plain Layout
4622 \begin_layout Standard
4623 \begin_inset Formula $A\hrulefill B$
4629 \begin_layout Standard
4630 To use the commands for text, they have to be inserted in \SpecialChar TeX
4634 \begin_layout Section
4636 \begin_inset CommandInset label
4643 \begin_inset Index idx
4646 \begin_layout Plain Layout
4655 \begin_layout Standard
4656 Matrices can be inserted via the math toolbar button
4659 arg "dialog-show mathmatrix"
4664 Insert\SpecialChar menuseparator
4665 Math\SpecialChar menuseparator
4669 In the matrix dialog you can specify the number of columns and rows, the
4670 alignment and the decoration.
4671 The vertical alignment is only of importance for matrices in inline formulas:
4674 \begin_layout Standard
4675 The first matrix is top
4676 \begin_inset Formula $\begin{array}[t]{cccc}
4684 \begin_inset Formula $\begin{array}{cccc}
4691 and the third bottom
4692 \begin_inset Formula $\begin{array}[b]{cccc}
4702 \begin_layout Standard
4703 The horizontal alignment specifies how the column entries should be aligned.
4704 It is set by entering a letter for every column.
4709 denotes left aligned,
4718 To create for example a 4
4723 \begin_inset space ~
4726 matrix where the first column is left aligned, the second and third are
4727 centered and the last one is right aligned, one enters for the horizontal
4733 Normally in a matrix all columns are centered, therefore the default for
4741 \begin_layout Standard
4742 Horizontal alignment:
4745 \begin_layout Standard
4751 \begin_inset Formula $\begin{array}{lll}
4763 \begin_inset Formula $\begin{array}{ccc}
4775 \begin_inset Formula $\begin{array}{rrr}
4785 \begin_layout Standard
4786 To add or delete rows and columns subsequently, the math toolbar buttons
4790 arg "tabular-feature append-row"
4796 arg "tabular-feature delete-row"
4800 \begin_inset space \thinspace{}
4805 Edit\SpecialChar menuseparator
4809 New rows can also be created with
4812 arg "newline-insert newline"
4818 \begin_layout Standard
4819 \begin_inset VSpace bigskip
4826 adds parentheses in the selected style around the matrix.
4827 Alternatively, parentheses can can either be created with the commands
4835 \begin_inset Index idx
4838 \begin_layout Plain Layout
4853 \begin_inset Index idx
4856 \begin_layout Plain Layout
4867 \begin_inset space ~
4873 \begin_inset CommandInset ref
4875 reference "subsec:Automatic-Bracket-Size"
4879 , or by using the following commands:
4880 \begin_inset VSpace medskip
4886 \begin_layout Standard
4887 \begin_inset space \hfill{}
4891 \begin_inset Tabular
4892 <lyxtabular version="3" rows="4" columns="2">
4893 <features booktabs="true" tabularvalignment="middle">
4894 <column alignment="center" valignment="top" width="0pt">
4895 <column alignment="center" valignment="top">
4897 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4900 \begin_layout Plain Layout
4906 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4909 \begin_layout Plain Layout
4916 <row topspace="1.5mm">
4917 <cell alignment="center" valignment="top" usebox="none">
4920 \begin_layout Plain Layout
4924 \begin_inset space \textvisiblespace{}
4932 \begin_inset space \thinspace{}
4940 <cell alignment="center" valignment="top" usebox="none">
4943 \begin_layout Plain Layout
4944 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4945 0 & \textrm{-}\mathrm{i}\\
4947 \end{array}\end{bmatrix}$
4956 <row topspace="1.5mm" bottomspace="0.5mm">
4957 <cell alignment="center" valignment="top" usebox="none">
4960 \begin_layout Plain Layout
4964 \begin_inset space \textvisiblespace{}
4972 \begin_inset space \thinspace{}
4980 <cell alignment="center" valignment="top" usebox="none">
4983 \begin_layout Plain Layout
4984 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
4985 0 & \textrm{-}\mathrm{i}\\
4987 \end{array}\end{Bmatrix}$
4997 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5000 \begin_layout Plain Layout
5004 \begin_inset space \textvisiblespace{}
5012 \begin_inset space \thinspace{}
5020 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5023 \begin_layout Plain Layout
5024 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5025 0 & \textrm{-}\mathrm{i}\\
5027 \end{array}\end{pmatrix}$
5041 \begin_inset space \hfill{}
5045 \begin_inset Tabular
5046 <lyxtabular version="3" rows="4" columns="2">
5047 <features booktabs="true" tabularvalignment="middle">
5048 <column alignment="center" valignment="top" width="0pt">
5049 <column alignment="center" valignment="top">
5051 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5054 \begin_layout Plain Layout
5060 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5063 \begin_layout Plain Layout
5070 <row topspace="1.5mm">
5071 <cell alignment="center" valignment="top" usebox="none">
5074 \begin_layout Plain Layout
5078 \begin_inset space \textvisiblespace{}
5086 \begin_inset space \thinspace{}
5094 <cell alignment="center" valignment="top" usebox="none">
5097 \begin_layout Plain Layout
5098 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5099 0 & \textrm{-}\mathrm{i}\\
5101 \end{array}\end{vmatrix}$
5110 <row topspace="1.5mm" bottomspace="0.5mm">
5111 <cell alignment="center" valignment="top" usebox="none">
5114 \begin_layout Plain Layout
5118 \begin_inset space \textvisiblespace{}
5126 \begin_inset space \thinspace{}
5134 <cell alignment="center" valignment="top" usebox="none">
5137 \begin_layout Plain Layout
5138 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5139 0 & \textrm{-}\mathrm{i}\\
5141 \end{array}\end{Vmatrix}$
5151 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5154 \begin_layout Plain Layout
5158 \begin_inset space \textvisiblespace{}
5166 \begin_inset space \thinspace{}
5174 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5177 \begin_layout Plain Layout
5178 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5179 0 & \textrm{-}\mathrm{i}\\
5181 \end{array}\end{matrix}$
5195 \begin_inset space \hfill{}
5201 \begin_layout Standard
5202 \begin_inset VSpace medskip
5206 \begin_inset space \thinspace{}
5210 \begin_inset space \space{}
5219 is inserted, a blue box appears between two vertical lines where the matrix
5221 \begin_inset Newline newline
5224 Note that decorated matrices ignore the vertical alignment.
5227 \begin_layout Standard
5228 \begin_inset VSpace bigskip
5231 As all multiline formulas are matrices, the length
5238 \begin_inset Index idx
5241 \begin_layout Plain Layout
5249 that is described in
5250 \begin_inset CommandInset ref
5252 reference "subsec:Column-Separation"
5256 can also be used to change the column separation of matrices.
5259 \begin_layout Standard
5260 To change the row separation, the command
5267 \begin_inset Index idx
5270 \begin_layout Plain Layout
5279 It is used as follows:
5282 \begin_layout Standard
5289 arraystretch}{stretch factor}
5290 \begin_inset Index idx
5293 \begin_layout Plain Layout
5304 \begin_layout Standard
5311 assigns the stretch factor to the predefined command
5319 \begin_inset space \thinspace{}
5323 \begin_inset space \space{}
5326 the row separation, use the factor 2.
5327 This is then used for all following matrices.
5328 To go back to the original separation, assign the factor 1 to
5337 \begin_layout Standard
5338 To set matrices into a text line, the command
5345 \begin_inset Index idx
5348 \begin_layout Plain Layout
5357 When it is inserted a blue box with two dashed lines appears.
5358 In this box the matrix is inserted.
5361 \begin_layout Standard
5363 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5365 \end{smallmatrix}\right)$
5371 \begin_layout Section
5372 Brackets and Delimiters
5373 \begin_inset Index idx
5376 \begin_layout Plain Layout
5383 \begin_inset Index idx
5386 \begin_layout Plain Layout
5395 \begin_layout Subsection
5396 Vertical Brackets and Delimiters
5397 \begin_inset Index idx
5400 \begin_layout Plain Layout
5409 \begin_layout Standard
5410 \begin_inset space \hfill{}
5414 \begin_inset Tabular
5415 <lyxtabular version="3" rows="9" columns="2">
5416 <features booktabs="true" tabularvalignment="middle">
5417 <column alignment="center" valignment="top" width="0pt">
5418 <column alignment="center" valignment="top" width="0pt">
5420 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5423 \begin_layout Plain Layout
5429 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5432 \begin_layout Plain Layout
5440 <cell alignment="center" valignment="top" usebox="none">
5443 \begin_layout Plain Layout
5449 <cell alignment="center" valignment="top" usebox="none">
5452 \begin_layout Plain Layout
5453 \begin_inset Formula $($
5463 <cell alignment="center" valignment="top" usebox="none">
5466 \begin_layout Plain Layout
5472 <cell alignment="center" valignment="top" usebox="none">
5475 \begin_layout Plain Layout
5476 \begin_inset Formula $\{$
5486 <cell alignment="center" valignment="top" usebox="none">
5489 \begin_layout Plain Layout
5495 <cell alignment="center" valignment="top" usebox="none">
5498 \begin_layout Plain Layout
5499 \begin_inset Formula $[$
5509 <cell alignment="center" valignment="top" usebox="none">
5512 \begin_layout Plain Layout
5520 <cell alignment="center" valignment="top" usebox="none">
5523 \begin_layout Plain Layout
5524 \begin_inset Formula $\langle$
5534 <cell alignment="center" valignment="top" usebox="none">
5537 \begin_layout Plain Layout
5545 <cell alignment="center" valignment="top" usebox="none">
5548 \begin_layout Plain Layout
5549 \begin_inset Formula $\lceil$
5559 <cell alignment="center" valignment="top" usebox="none">
5562 \begin_layout Plain Layout
5570 <cell alignment="center" valignment="top" usebox="none">
5573 \begin_layout Plain Layout
5574 \begin_inset Formula $\lfloor$
5584 <cell alignment="center" valignment="top" usebox="none">
5587 \begin_layout Plain Layout
5593 <cell alignment="center" valignment="top" usebox="none">
5596 \begin_layout Plain Layout
5597 \begin_inset Formula $/$
5607 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5610 \begin_layout Plain Layout
5616 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5619 \begin_layout Plain Layout
5620 \begin_inset Formula $|$
5634 \begin_inset space \hfill{}
5638 \begin_inset Tabular
5639 <lyxtabular version="3" rows="9" columns="2">
5640 <features booktabs="true" tabularvalignment="middle">
5641 <column alignment="center" valignment="top" width="0pt">
5642 <column alignment="center" valignment="top" width="0pt">
5644 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5647 \begin_layout Plain Layout
5653 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5656 \begin_layout Plain Layout
5664 <cell alignment="center" valignment="top" usebox="none">
5667 \begin_layout Plain Layout
5673 <cell alignment="center" valignment="top" usebox="none">
5676 \begin_layout Plain Layout
5677 \begin_inset Formula $)$
5687 <cell alignment="center" valignment="top" usebox="none">
5690 \begin_layout Plain Layout
5696 <cell alignment="center" valignment="top" usebox="none">
5699 \begin_layout Plain Layout
5700 \begin_inset Formula $\}$
5710 <cell alignment="center" valignment="top" usebox="none">
5713 \begin_layout Plain Layout
5719 <cell alignment="center" valignment="top" usebox="none">
5722 \begin_layout Plain Layout
5723 \begin_inset Formula $]$
5733 <cell alignment="center" valignment="top" usebox="none">
5736 \begin_layout Plain Layout
5744 <cell alignment="center" valignment="top" usebox="none">
5747 \begin_layout Plain Layout
5748 \begin_inset Formula $\rangle$
5758 <cell alignment="center" valignment="top" usebox="none">
5761 \begin_layout Plain Layout
5769 <cell alignment="center" valignment="top" usebox="none">
5772 \begin_layout Plain Layout
5773 \begin_inset Formula $\rceil$
5783 <cell alignment="center" valignment="top" usebox="none">
5786 \begin_layout Plain Layout
5794 <cell alignment="center" valignment="top" usebox="none">
5797 \begin_layout Plain Layout
5798 \begin_inset Formula $\rfloor$
5808 <cell alignment="center" valignment="top" usebox="none">
5811 \begin_layout Plain Layout
5821 <cell alignment="center" valignment="top" usebox="none">
5824 \begin_layout Plain Layout
5825 \begin_inset Formula $\backslash$
5835 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5838 \begin_layout Plain Layout
5846 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5849 \begin_layout Plain Layout
5850 \begin_inset Formula $\|$
5864 \begin_inset space \hfill{}
5870 \begin_layout Standard
5873 \begin_inset Note Greyedout
5876 \begin_layout Plain Layout
5889 \begin_inset Index idx
5892 \begin_layout Plain Layout
5900 must be used for the backslash, because the command
5908 produces a line break there.
5916 \begin_layout Standard
5917 For all characters listed above the size can be adjusted with the commands
5918 described in the following two subsections.
5919 When using these commands, the characters < and > can directly be used
5920 instead of the commands
5935 \begin_layout Subsubsection
5937 \begin_inset CommandInset label
5939 name "subsec:Manual-Bracket-Size"
5944 \begin_inset Index idx
5947 \begin_layout Plain Layout
5948 Bracket size ! manual
5956 \begin_layout Standard
5957 The bracket size can be specified manually by the \SpecialChar LaTeX
5965 \begin_inset Index idx
5968 \begin_layout Plain Layout
6001 denotes the smallest and
6007 the largest bracket size.
6010 \begin_layout Standard
6011 These commands are used to emphasize levels of brackets:
6012 \begin_inset Separator latexpar
6018 \begin_layout Standard
6020 \begin_inset Tabular
6021 <lyxtabular version="3" rows="2" columns="2">
6022 <features booktabs="true" tabularvalignment="middle">
6023 <column alignment="center" valignment="top" width="0pt">
6024 <column alignment="center" valignment="top" width="0pt">
6026 <cell alignment="center" valignment="top" usebox="none">
6029 \begin_layout Plain Layout
6030 all brackets in the same size:
6035 <cell alignment="center" valignment="top" usebox="none">
6038 \begin_layout Plain Layout
6039 \begin_inset Formula $((A+B)(A-B))^{C}$
6048 <row topspace="2mm">
6049 <cell alignment="center" valignment="top" usebox="none">
6052 \begin_layout Plain Layout
6058 <cell alignment="center" valignment="top" usebox="none">
6061 \begin_layout Plain Layout
6062 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6078 \begin_layout Standard
6079 For the second formula the command
6086 \begin_inset space \textvisiblespace{}
6094 \begin_layout Standard
6095 Here is an overview about all bracket sizes:
6096 \begin_inset Separator latexpar
6102 \begin_layout Standard
6119 \begin_inset space \textvisiblespace{}
6127 \begin_inset space \textvisiblespace{}
6131 \begin_inset space \textvisiblespace{}
6141 \begin_layout Standard
6143 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6149 \begin_layout Standard
6156 -commands there is the variant
6163 \begin_inset Index idx
6166 \begin_layout Plain Layout
6174 that adds a bit more space between the bracket and its content, and the
6188 \begin_inset Index idx
6191 \begin_layout Plain Layout
6201 , that don't add additional space.
6206 at the end of the command
6212 is for a left bracket; for a right bracket this will be replaced by an
6218 A left or right bracket can each be an opening or closing bracket.
6221 \begin_layout Standard
6222 In the following table is a comparison of the variants:
6223 \begin_inset Separator latexpar
6229 \begin_layout Standard
6231 \begin_inset Tabular
6232 <lyxtabular version="3" rows="5" columns="2">
6233 <features booktabs="true" tabularvalignment="middle">
6234 <column alignment="center" valignment="top" width="0pt">
6235 <column alignment="center" valignment="middle">
6237 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6240 \begin_layout Plain Layout
6246 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6249 \begin_layout Plain Layout
6256 <row topspace="2mm">
6257 <cell alignment="center" valignment="top" usebox="none">
6260 \begin_layout Plain Layout
6270 \begin_inset space \textvisiblespace{}
6280 <cell alignment="center" valignment="top" usebox="none">
6283 \begin_layout Plain Layout
6284 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6293 <row topspace="2mm">
6294 <cell alignment="center" valignment="top" usebox="none">
6297 \begin_layout Plain Layout
6307 \begin_inset space \textvisiblespace{}
6317 <cell alignment="center" valignment="top" usebox="none">
6320 \begin_layout Plain Layout
6321 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6330 <row topspace="2mm" bottomspace="0.5mm">
6331 <cell alignment="center" valignment="top" usebox="none">
6334 \begin_layout Plain Layout
6344 \begin_inset space \textvisiblespace{}
6354 <cell alignment="center" valignment="top" usebox="none">
6357 \begin_layout Plain Layout
6358 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6367 <row topspace="1.5mm" bottomspace="0.5mm">
6368 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6371 \begin_layout Plain Layout
6383 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6386 \begin_layout Plain Layout
6387 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6403 \begin_layout Subsubsection
6404 Automatic Bracket Size
6405 \begin_inset CommandInset label
6407 name "subsec:Automatic-Bracket-Size"
6412 \begin_inset Index idx
6415 \begin_layout Plain Layout
6416 Bracket size ! automatic
6424 \begin_layout Standard
6425 Brackets with variable size can be inserted with the commands
6432 \begin_inset Index idx
6435 \begin_layout Plain Layout
6450 \begin_inset Index idx
6453 \begin_layout Plain Layout
6461 or via the math toolbar button
6464 arg "dialog-show mathdelimiter"
6480 the wanted bracket must be inserted.
6481 The bracket size will then automatically be calculated for the output.
6482 \begin_inset Separator latexpar
6488 \begin_layout Standard
6490 normal bracket: The command
6497 \begin_inset space \textvisiblespace{}
6501 \begin_inset Formula $\downarrow$
6505 \begin_inset space \textvisiblespace{}
6511 \begin_inset Formula
6521 \begin_layout Standard
6523 multiline bracket: The command
6532 \begin_inset space \textvisiblespace{}
6536 \begin_inset Formula $\downarrow$
6540 \begin_inset space \textvisiblespace{}
6548 \begin_inset Formula
6550 \ln\left(\frac{A}{C}\right)
6558 \begin_layout Standard
6574 \begin_inset space ~
6580 This has the advantage that you can see in \SpecialChar LyX
6581 immediately the real bracket
6582 size and that the matching right bracket will be created too.
6583 \begin_inset Newline newline
6586 The command for the last example would then be:
6597 \begin_inset space \textvisiblespace{}
6601 \begin_inset Formula $\downarrow$
6607 \begin_layout Standard
6608 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6609 For example the command
6616 \begin_inset space \textvisiblespace{}
6620 \begin_inset Formula $\downarrow$
6624 \begin_inset space \textvisiblespace{}
6634 \begin_inset Formula
6636 \left.\frac{A}{B}\right\}
6655 will be converted by \SpecialChar LyX
6656 to brackets in the right size when the document is
6657 reloaded and an omitted bracket will appear as dashed line.
6660 \begin_layout Standard
6661 \begin_inset VSpace bigskip
6664 Because all popular \SpecialChar LaTeX
6665 distributions use e\SpecialChar TeX
6666 , an extension to \SpecialChar LaTeX
6675 \begin_inset Index idx
6678 \begin_layout Plain Layout
6686 is additionally available for all brackets and limits.
6687 With this command the height of the following character is adapted to the
6688 one of the surrounding brackets, what is e.
6689 \begin_inset space \thinspace{}
6693 \begin_inset space \space{}
6696 needed for physical vectors:
6697 \begin_inset Formula
6699 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6704 For physical vectors there is a special \SpecialChar LaTeX
6705 -package, described in
6706 \begin_inset CommandInset ref
6708 reference "subsec:Physical-Vectors"
6715 \begin_layout Subsection
6717 \begin_inset Index idx
6720 \begin_layout Plain Layout
6721 Brackets ! horizontal
6729 \begin_layout Standard
6731 \begin_inset Tabular
6732 <lyxtabular version="3" rows="4" columns="2">
6733 <features booktabs="true" tabularvalignment="middle">
6734 <column alignment="center" valignment="top" width="0pt">
6735 <column alignment="center" valignment="top" width="0pt">
6737 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6740 \begin_layout Plain Layout
6746 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6749 \begin_layout Plain Layout
6757 <cell alignment="center" valignment="top" usebox="none">
6760 \begin_layout Plain Layout
6764 \begin_inset space \textvisiblespace{}
6768 \begin_inset space \textvisiblespace{}
6772 \begin_inset Index idx
6775 \begin_layout Plain Layout
6788 <cell alignment="center" valignment="top" usebox="none">
6791 \begin_layout Plain Layout
6792 \begin_inset Formula $\overbrace{A+B}^{3}$
6801 <row topspace="2mm">
6802 <cell alignment="center" valignment="top" usebox="none">
6805 \begin_layout Plain Layout
6809 \begin_inset space \textvisiblespace{}
6813 \begin_inset space \textvisiblespace{}
6817 \begin_inset Index idx
6820 \begin_layout Plain Layout
6833 <cell alignment="center" valignment="top" usebox="none">
6836 \begin_layout Plain Layout
6837 \begin_inset Formula $\underbrace{A+B}_{5}$
6847 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6850 \begin_layout Plain Layout
6854 \begin_inset space \textvisiblespace{}
6860 \begin_inset space \textvisiblespace{}
6864 \begin_inset space \textvisiblespace{}
6868 \begin_inset space \textvisiblespace{}
6872 \begin_inset space \textvisiblespace{}
6876 \begin_inset space \textvisiblespace{}
6880 \begin_inset space \textvisiblespace{}
6888 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6891 \begin_layout Plain Layout
6892 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6908 \begin_layout Standard
6909 In the last example it doesn't matter if
6921 is inserted at first.
6924 \begin_layout Standard
6925 \begin_inset VSpace medskip
6931 \begin_layout Standard
6932 If you set in the document settings under
6935 \begin_inset space ~
6945 \begin_inset Index idx
6948 \begin_layout Plain Layout
6949 Packages ! mathtools
6957 \begin_inset space ~
6962 , you have access to square backets:
6963 \begin_inset Separator latexpar
6969 \begin_layout Standard
6971 \begin_inset Tabular
6972 <lyxtabular version="3" rows="4" columns="2">
6973 <features booktabs="true" tabularvalignment="middle">
6974 <column alignment="center" valignment="top" width="0pt">
6975 <column alignment="center" valignment="top" width="0pt">
6977 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6980 \begin_layout Plain Layout
6986 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6989 \begin_layout Plain Layout
6997 <cell alignment="center" valignment="top" usebox="none">
7000 \begin_layout Plain Layout
7028 \begin_inset space \textvisiblespace{}
7032 \begin_inset Index idx
7035 \begin_layout Plain Layout
7048 <cell alignment="center" valignment="top" usebox="none">
7051 \begin_layout Plain Layout
7052 \begin_inset Formula $\overbracket{A+B}^{3}$
7061 <row topspace="2mm">
7062 <cell alignment="center" valignment="top" usebox="none">
7065 \begin_layout Plain Layout
7093 \begin_inset space \textvisiblespace{}
7097 \begin_inset Index idx
7100 \begin_layout Plain Layout
7125 <cell alignment="center" valignment="top" usebox="none">
7128 \begin_layout Plain Layout
7129 \begin_inset Formula $\underbracket{A+B}_{5}$
7139 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7142 \begin_layout Plain Layout
7148 \begin_inset space \textvisiblespace{}
7152 \begin_inset space \textvisiblespace{}
7156 \begin_inset space \textvisiblespace{}
7160 \begin_inset space \textvisiblespace{}
7164 \begin_inset space \textvisiblespace{}
7172 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7175 \begin_layout Plain Layout
7176 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7192 \begin_layout Standard
7205 you can change the thickness of the bracket's stroke by specifying the
7206 desired thickness in square brackets behind the command:
7207 \begin_inset Separator latexpar
7213 \begin_layout Standard
7215 \begin_inset Tabular
7216 <lyxtabular version="3" rows="3" columns="2">
7217 <features booktabs="true" tabularvalignment="middle">
7218 <column alignment="center" valignment="top" width="0pt">
7219 <column alignment="center" valignment="top" width="0pt">
7221 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7224 \begin_layout Plain Layout
7230 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7233 \begin_layout Plain Layout
7241 <cell alignment="center" valignment="top" usebox="none">
7244 \begin_layout Plain Layout
7274 \begin_inset space \textvisiblespace{}
7282 <cell alignment="center" valignment="top" usebox="none">
7285 \begin_layout Plain Layout
7286 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7295 <row topspace="2mm">
7296 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7299 \begin_layout Plain Layout
7329 \begin_inset space \textvisiblespace{}
7337 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7340 \begin_layout Plain Layout
7341 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7357 \begin_layout Standard
7358 \begin_inset VSpace bigskip
7361 When brackets should overlap each other, multiline formulas, as described
7363 \begin_inset CommandInset ref
7365 reference "sec:Multiline-Formulas"
7370 \begin_inset Formula
7372 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7373 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7378 In the first row the formula is inserted together with the first brace.
7379 It is hereby important that the space command
7383 \begin_layout Plain Layout
7384 Space commands are explained in
7385 \begin_inset CommandInset ref
7387 reference "subsec:Predefined-Space"
7402 is inserted before the first
7403 \begin_inset Formula $d$
7406 , because the brace that ends behind the
7407 \begin_inset Formula $q$
7410 prevents that the following
7411 \begin_inset Quotes eld
7415 \begin_inset Quotes erd
7418 is surrounded by space.
7422 \begin_layout Plain Layout
7423 because a bracket is not handled as a character, see
7424 \begin_inset CommandInset ref
7426 reference "subsec:Binary-Operators"
7435 In the second row the second brace is inserted.
7436 As it should begin before the
7437 \begin_inset Formula $b$
7452 \begin_layout Plain Layout
7460 \begin_inset CommandInset ref
7462 reference "subsec:Placeholders"
7471 This space is needed because the
7472 \begin_inset Quotes eld
7476 \begin_inset Quotes erd
7479 is also surrounded by space in the formula.
7480 The brace is placed under the command
7489 \begin_layout Standard
7490 It gets more complicated when brackets overlap each other above and under
7491 the formula, like in the following example:
7495 \begin_layout Plain Layout
7507 \begin_inset Formula
7509 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7510 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7519 \begin_layout Plain Layout
7530 The first formula row is the same as the second row of the previous example,
7531 with the difference that the brace is above.
7532 The second row contains the formula together with the second brace.
7533 To avoid that there is space between the upper brace in the first row and
7534 the formula, the row spacing needs to be reduced.
7535 This is not easily possible due to a bug in \SpecialChar LyX
7540 \begin_layout Plain Layout
7541 \begin_inset CommandInset href
7543 name "LyX-bug #1505"
7544 target "http://www.lyx.org/trac/ticket/1505"
7553 As a solution for the problem, the global formula row separation
7560 \begin_inset Index idx
7563 \begin_layout Plain Layout
7571 must be changed to -6
7572 \begin_inset space \thinspace{}
7575 pt before the formula with the command
7591 is set back after the formula to the standard value of 3
7592 \begin_inset space \thinspace{}
7595 pt using the same command.
7596 More about the row separation in formulas is explained in
7597 \begin_inset CommandInset ref
7599 reference "subsec:Line-Separation"
7606 \begin_layout Section
7608 \begin_inset Index idx
7611 \begin_layout Plain Layout
7620 \begin_layout Standard
7621 Arrows can be inserted via the math toolbar button
7624 arg "math-insert \\leftarrow"
7627 or the commands listed in the following subsections.
7630 \begin_layout Subsection
7632 \begin_inset Index idx
7635 \begin_layout Plain Layout
7644 \begin_layout Standard
7645 \begin_inset space \hfill{}
7649 \begin_inset Tabular
7650 <lyxtabular version="3" rows="8" columns="2">
7651 <features booktabs="true" tabularvalignment="middle">
7652 <column alignment="center" valignment="top" width="0pt">
7653 <column alignment="center" valignment="top" width="0pt">
7655 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7658 \begin_layout Plain Layout
7664 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7667 \begin_layout Plain Layout
7675 <cell alignment="center" valignment="top" usebox="none">
7678 \begin_layout Plain Layout
7686 <cell alignment="center" valignment="top" usebox="none">
7689 \begin_layout Plain Layout
7690 \begin_inset Formula $\gets$
7700 <cell alignment="center" valignment="top" usebox="none">
7703 \begin_layout Plain Layout
7711 <cell alignment="center" valignment="top" usebox="none">
7714 \begin_layout Plain Layout
7715 \begin_inset Formula $\Leftarrow$
7725 <cell alignment="center" valignment="top" usebox="none">
7728 \begin_layout Plain Layout
7736 <cell alignment="center" valignment="top" usebox="none">
7739 \begin_layout Plain Layout
7740 \begin_inset Formula $\longleftarrow$
7750 <cell alignment="center" valignment="top" usebox="none">
7753 \begin_layout Plain Layout
7761 <cell alignment="center" valignment="top" usebox="none">
7764 \begin_layout Plain Layout
7765 \begin_inset Formula $\Longleftarrow$
7775 <cell alignment="center" valignment="top" usebox="none">
7778 \begin_layout Plain Layout
7786 <cell alignment="center" valignment="top" usebox="none">
7789 \begin_layout Plain Layout
7790 \begin_inset Formula $\leftharpoonup$
7800 <cell alignment="center" valignment="top" usebox="none">
7803 \begin_layout Plain Layout
7811 <cell alignment="center" valignment="top" usebox="none">
7814 \begin_layout Plain Layout
7815 \begin_inset Formula $\leftharpoondown$
7825 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7828 \begin_layout Plain Layout
7836 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7839 \begin_layout Plain Layout
7840 \begin_inset Formula $\hookleftarrow$
7854 \begin_inset space \hfill{}
7858 \begin_inset Tabular
7859 <lyxtabular version="3" rows="8" columns="2">
7860 <features booktabs="true" tabularvalignment="middle">
7861 <column alignment="center" valignment="top" width="0pt">
7862 <column alignment="center" valignment="top" width="0pt">
7864 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7867 \begin_layout Plain Layout
7873 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7876 \begin_layout Plain Layout
7884 <cell alignment="center" valignment="top" usebox="none">
7887 \begin_layout Plain Layout
7895 <cell alignment="center" valignment="top" usebox="none">
7898 \begin_layout Plain Layout
7899 \begin_inset Formula $\to$
7909 <cell alignment="center" valignment="top" usebox="none">
7912 \begin_layout Plain Layout
7920 <cell alignment="center" valignment="top" usebox="none">
7923 \begin_layout Plain Layout
7924 \begin_inset Formula $\Rightarrow$
7934 <cell alignment="center" valignment="top" usebox="none">
7937 \begin_layout Plain Layout
7945 <cell alignment="center" valignment="top" usebox="none">
7948 \begin_layout Plain Layout
7949 \begin_inset Formula $\longrightarrow$
7959 <cell alignment="center" valignment="top" usebox="none">
7962 \begin_layout Plain Layout
7970 <cell alignment="center" valignment="top" usebox="none">
7973 \begin_layout Plain Layout
7974 \begin_inset Formula $\Longrightarrow$
7984 <cell alignment="center" valignment="top" usebox="none">
7987 \begin_layout Plain Layout
7995 <cell alignment="center" valignment="top" usebox="none">
7998 \begin_layout Plain Layout
7999 \begin_inset Formula $\rightharpoonup$
8009 <cell alignment="center" valignment="top" usebox="none">
8012 \begin_layout Plain Layout
8020 <cell alignment="center" valignment="top" usebox="none">
8023 \begin_layout Plain Layout
8024 \begin_inset Formula $\rightharpoondown$
8034 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8037 \begin_layout Plain Layout
8045 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8048 \begin_layout Plain Layout
8049 \begin_inset Formula $\hookrightarrow$
8063 \begin_inset space \hfill{}
8069 \begin_layout Standard
8070 \begin_inset space \hfill{}
8074 \begin_inset Tabular
8075 <lyxtabular version="3" rows="6" columns="2">
8076 <features booktabs="true" tabularvalignment="middle">
8077 <column alignment="center" valignment="top" width="0pt">
8078 <column alignment="center" valignment="top" width="0pt">
8080 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8083 \begin_layout Plain Layout
8089 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8092 \begin_layout Plain Layout
8100 <cell alignment="center" valignment="top" usebox="none">
8103 \begin_layout Plain Layout
8111 <cell alignment="center" valignment="top" usebox="none">
8114 \begin_layout Plain Layout
8115 \begin_inset Formula $\leftrightarrow$
8125 <cell alignment="center" valignment="top" usebox="none">
8128 \begin_layout Plain Layout
8136 <cell alignment="center" valignment="top" usebox="none">
8139 \begin_layout Plain Layout
8140 \begin_inset Formula $\Leftrightarrow$
8150 <cell alignment="center" valignment="top" usebox="none">
8153 \begin_layout Plain Layout
8161 <cell alignment="center" valignment="top" usebox="none">
8164 \begin_layout Plain Layout
8165 \begin_inset Formula $\longleftrightarrow$
8175 <cell alignment="center" valignment="top" usebox="none">
8178 \begin_layout Plain Layout
8186 <cell alignment="center" valignment="top" usebox="none">
8189 \begin_layout Plain Layout
8190 \begin_inset Formula $\Longleftrightarrow$
8200 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8203 \begin_layout Plain Layout
8211 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8214 \begin_layout Plain Layout
8215 \begin_inset Formula $\rightleftharpoons$
8229 \begin_inset space \hspace{}
8234 \begin_inset space \hfill{}
8238 \begin_inset Tabular
8239 <lyxtabular version="3" rows="5" columns="2">
8240 <features booktabs="true" tabularvalignment="middle">
8241 <column alignment="center" valignment="top" width="0pt">
8242 <column alignment="center" valignment="top" width="0pt">
8244 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8247 \begin_layout Plain Layout
8253 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8256 \begin_layout Plain Layout
8264 <cell alignment="center" valignment="top" usebox="none">
8267 \begin_layout Plain Layout
8275 <cell alignment="center" valignment="top" usebox="none">
8278 \begin_layout Plain Layout
8279 \begin_inset Formula $\mapsto$
8289 <cell alignment="center" valignment="top" usebox="none">
8292 \begin_layout Plain Layout
8300 <cell alignment="center" valignment="top" usebox="none">
8303 \begin_layout Plain Layout
8304 \begin_inset Formula $\longmapsto$
8314 <cell alignment="center" valignment="top" usebox="none">
8317 \begin_layout Plain Layout
8325 <cell alignment="center" valignment="top" usebox="none">
8328 \begin_layout Plain Layout
8329 \begin_inset Formula $\leadsto$
8339 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8342 \begin_layout Plain Layout
8350 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8353 \begin_layout Plain Layout
8354 \begin_inset Formula $\dasharrow$
8368 \begin_inset space \hfill{}
8374 \begin_layout Standard
8375 \begin_inset VSpace medskip
8378 Arrows used as accents like e.
8379 \begin_inset space \thinspace{}
8383 \begin_inset space \space{}
8386 vector arrows are listed in
8387 \begin_inset CommandInset ref
8389 reference "sec:Accents"
8396 \begin_layout Standard
8397 \begin_inset VSpace bigskip
8400 Furthermore there are the labeled arrows
8401 \begin_inset Index idx
8404 \begin_layout Plain Layout
8417 \begin_inset Index idx
8420 \begin_layout Plain Layout
8435 \begin_inset Index idx
8438 \begin_layout Plain Layout
8445 \begin_layout Plain Layout
8460 When inserting one of these commands in a formula, an arrow with two blue
8461 boxes appear where the label can be inserted.
8462 The length of the arrow adapts to the label width.
8465 \begin_layout Standard
8467 \begin_inset Tabular
8468 <lyxtabular version="3" rows="3" columns="2">
8469 <features booktabs="true" tabularvalignment="middle">
8470 <column alignment="center" valignment="top" width="0pt">
8471 <column alignment="center" valignment="top" width="0pt">
8473 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8476 \begin_layout Plain Layout
8482 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8485 \begin_layout Plain Layout
8493 <cell alignment="center" valignment="top" usebox="none">
8496 \begin_layout Plain Layout
8500 \begin_inset space \textvisiblespace{}
8504 \begin_inset Formula $\downarrow$
8508 \begin_inset Formula $\to$
8516 <cell alignment="center" valignment="top" usebox="none">
8519 \begin_layout Plain Layout
8520 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8529 <row topspace="2mm">
8530 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8533 \begin_layout Plain Layout
8537 \begin_inset space \textvisiblespace{}
8541 \begin_inset Formula $\downarrow$
8545 \begin_inset Formula $\to$
8553 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8556 \begin_layout Plain Layout
8557 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8573 \begin_layout Standard
8574 \begin_inset VSpace medskip
8580 \begin_layout Standard
8581 If you set in the document settings under
8584 \begin_inset space ~
8594 \begin_inset Index idx
8597 \begin_layout Plain Layout
8598 Packages ! mathtools
8606 \begin_inset space ~
8611 , you have access to the following labeled arrows:
8614 \begin_layout Standard
8615 \begin_inset Newpage newpage
8619 \begin_inset Separator latexpar
8625 \begin_layout Standard
8627 \begin_inset space \hspace*{\fill}
8631 \begin_inset Tabular
8632 <lyxtabular version="3" rows="7" columns="2">
8633 <features booktabs="true" tabularvalignment="middle">
8634 <column alignment="center" valignment="top" width="0pt">
8635 <column alignment="center" valignment="top" width="0pt">
8637 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8640 \begin_layout Plain Layout
8646 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8649 \begin_layout Plain Layout
8657 <cell alignment="center" valignment="top" usebox="none">
8660 \begin_layout Plain Layout
8680 <cell alignment="center" valignment="top" usebox="none">
8683 \begin_layout Plain Layout
8684 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8693 <row topspace="2mm">
8694 <cell alignment="center" valignment="top" usebox="none">
8697 \begin_layout Plain Layout
8717 <cell alignment="center" valignment="top" usebox="none">
8720 \begin_layout Plain Layout
8721 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8730 <row topspace="2mm">
8731 <cell alignment="center" valignment="top" usebox="none">
8734 \begin_layout Plain Layout
8754 <cell alignment="center" valignment="top" usebox="none">
8757 \begin_layout Plain Layout
8758 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8767 <row topspace="2mm">
8768 <cell alignment="center" valignment="top" usebox="none">
8771 \begin_layout Plain Layout
8791 <cell alignment="center" valignment="top" usebox="none">
8794 \begin_layout Plain Layout
8795 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8804 <row topspace="2mm">
8805 <cell alignment="center" valignment="top" usebox="none">
8808 \begin_layout Plain Layout
8828 <cell alignment="center" valignment="top" usebox="none">
8831 \begin_layout Plain Layout
8832 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8841 <row topspace="2mm">
8842 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8845 \begin_layout Plain Layout
8865 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8868 \begin_layout Plain Layout
8869 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8883 \begin_inset space \hspace*{\fill}
8887 \begin_inset Tabular
8888 <lyxtabular version="3" rows="7" columns="2">
8889 <features booktabs="true" tabularvalignment="middle">
8890 <column alignment="center" valignment="top" width="0pt">
8891 <column alignment="center" valignment="top" width="0pt">
8893 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8896 \begin_layout Plain Layout
8902 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8905 \begin_layout Plain Layout
8913 <cell alignment="center" valignment="top" usebox="none">
8916 \begin_layout Plain Layout
8936 <cell alignment="center" valignment="top" usebox="none">
8939 \begin_layout Plain Layout
8940 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8949 <row topspace="2mm">
8950 <cell alignment="center" valignment="top" usebox="none">
8953 \begin_layout Plain Layout
8973 <cell alignment="center" valignment="top" usebox="none">
8976 \begin_layout Plain Layout
8977 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8986 <row topspace="2mm">
8987 <cell alignment="center" valignment="top" usebox="none">
8990 \begin_layout Plain Layout
9010 <cell alignment="center" valignment="top" usebox="none">
9013 \begin_layout Plain Layout
9014 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
9023 <row topspace="2mm">
9024 <cell alignment="center" valignment="top" usebox="none">
9027 \begin_layout Plain Layout
9047 <cell alignment="center" valignment="top" usebox="none">
9050 \begin_layout Plain Layout
9051 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9060 <row topspace="2mm">
9061 <cell alignment="center" valignment="top" usebox="none">
9064 \begin_layout Plain Layout
9084 <cell alignment="center" valignment="top" usebox="none">
9087 \begin_layout Plain Layout
9088 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9097 <row topspace="2mm">
9098 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9101 \begin_layout Plain Layout
9121 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9124 \begin_layout Plain Layout
9125 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9139 \begin_inset space \hspace*{\fill}
9145 \begin_layout Standard
9146 The command scheme is for all these arrows:
9147 \begin_inset Separator latexpar
9153 \begin_layout Standard
9155 \begin_inset Tabular
9156 <lyxtabular version="3" rows="2" columns="2">
9157 <features booktabs="true" tabularvalignment="middle">
9158 <column alignment="center" valignment="top" width="0pt">
9159 <column alignment="center" valignment="top" width="0pt">
9161 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9164 \begin_layout Plain Layout
9170 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9173 \begin_layout Plain Layout
9180 <row bottomspace="0.5mm">
9181 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9184 \begin_layout Plain Layout
9187 xleftrightarrow[x=a]
9190 \begin_inset Formula $\to$
9198 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9201 \begin_layout Plain Layout
9202 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9218 \begin_layout Subsection
9219 Vertical and diagonal Arrows
9220 \begin_inset Index idx
9223 \begin_layout Plain Layout
9230 \begin_inset Index idx
9233 \begin_layout Plain Layout
9242 \begin_layout Standard
9243 \begin_inset space \hfill{}
9247 \begin_inset Tabular
9248 <lyxtabular version="3" rows="7" columns="2">
9249 <features booktabs="true" tabularvalignment="middle">
9250 <column alignment="center" valignment="top" width="0pt">
9251 <column alignment="center" valignment="top" width="0pt">
9253 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9256 \begin_layout Plain Layout
9262 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9265 \begin_layout Plain Layout
9273 <cell alignment="center" valignment="top" usebox="none">
9276 \begin_layout Plain Layout
9284 <cell alignment="center" valignment="top" usebox="none">
9287 \begin_layout Plain Layout
9288 \begin_inset Formula $\uparrow$
9298 <cell alignment="center" valignment="top" usebox="none">
9301 \begin_layout Plain Layout
9309 <cell alignment="center" valignment="top" usebox="none">
9312 \begin_layout Plain Layout
9313 \begin_inset Formula $\Uparrow$
9323 <cell alignment="center" valignment="top" usebox="none">
9326 \begin_layout Plain Layout
9334 <cell alignment="center" valignment="top" usebox="none">
9337 \begin_layout Plain Layout
9338 \begin_inset Formula $\updownarrow$
9348 <cell alignment="center" valignment="top" usebox="none">
9351 \begin_layout Plain Layout
9359 <cell alignment="center" valignment="top" usebox="none">
9362 \begin_layout Plain Layout
9363 \begin_inset Formula $\Updownarrow$
9373 <cell alignment="center" valignment="top" usebox="none">
9376 \begin_layout Plain Layout
9384 <cell alignment="center" valignment="top" usebox="none">
9387 \begin_layout Plain Layout
9388 \begin_inset Formula $\Downarrow$
9398 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9401 \begin_layout Plain Layout
9409 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9412 \begin_layout Plain Layout
9413 \begin_inset Formula $\downarrow$
9427 \begin_inset space \hfill{}
9431 \begin_inset Tabular
9432 <lyxtabular version="3" rows="5" columns="2">
9433 <features booktabs="true" tabularvalignment="middle">
9434 <column alignment="center" valignment="top" width="0pt">
9435 <column alignment="center" valignment="top" width="0pt">
9437 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9440 \begin_layout Plain Layout
9446 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9449 \begin_layout Plain Layout
9457 <cell alignment="center" valignment="top" usebox="none">
9460 \begin_layout Plain Layout
9468 <cell alignment="center" valignment="top" usebox="none">
9471 \begin_layout Plain Layout
9472 \begin_inset Formula $\nearrow$
9482 <cell alignment="center" valignment="top" usebox="none">
9485 \begin_layout Plain Layout
9493 <cell alignment="center" valignment="top" usebox="none">
9496 \begin_layout Plain Layout
9497 \begin_inset Formula $\searrow$
9507 <cell alignment="center" valignment="top" usebox="none">
9510 \begin_layout Plain Layout
9518 <cell alignment="center" valignment="top" usebox="none">
9521 \begin_layout Plain Layout
9522 \begin_inset Formula $\swarrow$
9532 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9535 \begin_layout Plain Layout
9543 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9546 \begin_layout Plain Layout
9547 \begin_inset Formula $\nwarrow$
9561 \begin_inset space \hfill{}
9567 \begin_layout Standard
9568 \begin_inset VSpace medskip
9571 Vertical arrows can be used also as delimiters together with the commands
9573 \begin_inset CommandInset ref
9575 reference "subsec:Manual-Bracket-Size"
9580 \begin_inset CommandInset ref
9582 reference "subsec:Automatic-Bracket-Size"
9589 \begin_layout Section
9591 \begin_inset CommandInset label
9598 \begin_inset Index idx
9601 \begin_layout Plain Layout
9610 \begin_layout Standard
9611 Accents can be inserted via the math toolbar button
9614 arg "math-insert \\hat"
9617 or the commands listed in the following subsections.
9620 \begin_layout Subsection
9621 Accents for one Character
9625 \begin_layout Plain Layout
9638 \begin_layout Plain Layout
9640 \begin_inset CommandInset ref
9642 reference "subsec:Accents-in-Text"
9655 \begin_layout Plain Layout
9663 \begin_inset Note Note
9666 \begin_layout Plain Layout
9673 is used to avoid that the footnote appears in the PDF-bookmark.
9676 \begin_layout Plain Layout
9684 \begin_inset CommandInset ref
9686 reference "subsec:Formulas-in-Section"
9696 \begin_inset CommandInset label
9698 name "subsec:Accents-for-one"
9703 \begin_inset Index idx
9706 \begin_layout Plain Layout
9707 Accents ! for one character
9715 \begin_layout Standard
9716 \begin_inset space \hfill{}
9720 \begin_inset Tabular
9721 <lyxtabular version="3" rows="8" columns="2">
9722 <features booktabs="true" tabularvalignment="middle">
9723 <column alignment="center" valignment="top" width="0pt">
9724 <column alignment="center" valignment="top" width="0pt">
9726 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9729 \begin_layout Plain Layout
9735 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9738 \begin_layout Plain Layout
9745 <row topspace="1.5mm">
9746 <cell alignment="center" valignment="top" usebox="none">
9749 \begin_layout Plain Layout
9753 \begin_inset space \textvisiblespace{}
9761 <cell alignment="center" valignment="top" usebox="none">
9764 \begin_layout Plain Layout
9765 \begin_inset Formula $\dot{A}$
9774 <row topspace="1.5mm">
9775 <cell alignment="center" valignment="top" usebox="none">
9778 \begin_layout Plain Layout
9782 \begin_inset space \textvisiblespace{}
9790 <cell alignment="center" valignment="top" usebox="none">
9793 \begin_layout Plain Layout
9794 \begin_inset Formula $\ddot{A}$
9803 <row topspace="1.5mm">
9804 <cell alignment="center" valignment="top" usebox="none">
9807 \begin_layout Plain Layout
9811 \begin_inset space \textvisiblespace{}
9819 <cell alignment="center" valignment="top" usebox="none">
9822 \begin_layout Plain Layout
9823 \begin_inset Formula $\dddot{A}$
9832 <row topspace="1.5mm">
9833 <cell alignment="center" valignment="top" usebox="none">
9836 \begin_layout Plain Layout
9840 \begin_inset space \textvisiblespace{}
9848 <cell alignment="center" valignment="top" usebox="none">
9851 \begin_layout Plain Layout
9852 \begin_inset Formula $\ddddot{A}$
9861 <row topspace="1.5mm">
9862 <cell alignment="center" valignment="top" usebox="none">
9865 \begin_layout Plain Layout
9869 \begin_inset space \textvisiblespace{}
9873 \begin_inset Index idx
9876 \begin_layout Plain Layout
9887 <cell alignment="center" valignment="top" usebox="none">
9890 \begin_layout Plain Layout
9891 \begin_inset Formula $\vec{A}$
9900 <row topspace="1.5mm">
9901 <cell alignment="center" valignment="top" usebox="none">
9904 \begin_layout Plain Layout
9908 \begin_inset space \textvisiblespace{}
9916 <cell alignment="center" valignment="top" usebox="none">
9919 \begin_layout Plain Layout
9920 \begin_inset Formula $\bar{A}$
9929 <row topspace="1.5mm">
9930 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9933 \begin_layout Plain Layout
9937 \begin_inset space \textvisiblespace{}
9945 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9948 \begin_layout Plain Layout
9949 \begin_inset Formula $\mathring{A}$
9963 \begin_inset space \hfill{}
9967 \begin_inset Tabular
9968 <lyxtabular version="3" rows="7" columns="2">
9969 <features booktabs="true" tabularvalignment="middle">
9970 <column alignment="center" valignment="top" width="0pt">
9971 <column alignment="center" valignment="top" width="0pt">
9973 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9976 \begin_layout Plain Layout
9982 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9985 \begin_layout Plain Layout
9992 <row topspace="1.5mm">
9993 <cell alignment="center" valignment="top" usebox="none">
9996 \begin_layout Plain Layout
10000 \begin_inset space \textvisiblespace{}
10008 <cell alignment="center" valignment="top" usebox="none">
10011 \begin_layout Plain Layout
10012 \begin_inset Formula $\tilde{A}$
10021 <row topspace="1.5mm">
10022 <cell alignment="center" valignment="top" usebox="none">
10025 \begin_layout Plain Layout
10029 \begin_inset space \textvisiblespace{}
10037 <cell alignment="center" valignment="top" usebox="none">
10040 \begin_layout Plain Layout
10041 \begin_inset Formula $\hat{A}$
10050 <row topspace="1.5mm">
10051 <cell alignment="center" valignment="top" usebox="none">
10054 \begin_layout Plain Layout
10058 \begin_inset space \textvisiblespace{}
10066 <cell alignment="center" valignment="top" usebox="none">
10069 \begin_layout Plain Layout
10070 \begin_inset Formula $\check{A}$
10079 <row topspace="1.5mm">
10080 <cell alignment="center" valignment="top" usebox="none">
10083 \begin_layout Plain Layout
10087 \begin_inset space \textvisiblespace{}
10095 <cell alignment="center" valignment="top" usebox="none">
10098 \begin_layout Plain Layout
10099 \begin_inset Formula $\acute{A}$
10108 <row topspace="1.5mm">
10109 <cell alignment="center" valignment="top" usebox="none">
10112 \begin_layout Plain Layout
10116 \begin_inset space \textvisiblespace{}
10124 <cell alignment="center" valignment="top" usebox="none">
10127 \begin_layout Plain Layout
10128 \begin_inset Formula $\grave{A}$
10137 <row topspace="1.5mm">
10138 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10141 \begin_layout Plain Layout
10145 \begin_inset space \textvisiblespace{}
10153 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10156 \begin_layout Plain Layout
10157 \begin_inset Formula $\breve{A}$
10171 \begin_inset space \hfill{}
10177 \begin_layout Standard
10178 \begin_inset VSpace bigskip
10184 \begin_layout Standard
10185 You can directly insert accents like é to formulas.
10187 will transform them to the corresponding accent command.
10189 \begin_inset Index idx
10192 \begin_layout Plain Layout
10198 it is better to insert a quotation mark before the vowel.
10199 These two characters are then treated by \SpecialChar LaTeX
10204 character when the formula part with the umlaut is marked as German.
10212 \begin_inset Quotes eld
10216 \begin_inset Quotes erd
10219 umlauts are created as demonstrated in the following example:
10222 \begin_layout Standard
10223 \begin_inset VSpace -2mm
10229 \begin_layout Standard
10231 \begin_inset Tabular
10232 <lyxtabular version="3" rows="3" columns="2">
10233 <features booktabs="true" tabularvalignment="middle">
10234 <column alignment="center" valignment="top" width="0pt">
10235 <column alignment="center" valignment="top">
10237 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10240 \begin_layout Plain Layout
10246 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10249 \begin_layout Plain Layout
10257 <cell alignment="center" valignment="top" usebox="none">
10260 \begin_layout Plain Layout
10261 \begin_inset Quotes grd
10269 <cell alignment="center" valignment="top" usebox="none">
10272 \begin_layout Plain Layout
10273 \begin_inset space \hspace{}
10280 \begin_inset Formula $"i$
10289 <row topspace="1.5mm">
10290 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10293 \begin_layout Plain Layout
10297 \begin_inset space \textvisiblespace{}
10305 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10308 \begin_layout Plain Layout
10309 \begin_inset Formula $\ddot{i}$
10325 \begin_layout Standard
10326 Another advantage to
10332 is that umlauts can directly be converted to mathematical text because
10333 the accent commands above are
10339 in mathematical text
10342 To convert an accented character to mathematical text, only the character
10343 under the accent may be converted.
10344 This applies also for all other conversions, e.
10345 \begin_inset space \thinspace{}
10349 \begin_inset space \space{}
10355 \begin_layout Standard
10356 In mathematical text, umlauts and other accented characters can directly
10360 \begin_layout Standard
10361 \begin_inset VSpace bigskip
10367 \begin_layout Standard
10369 also supports a tilde under the character if the \SpecialChar LaTeX
10375 \begin_inset Index idx
10378 \begin_layout Plain Layout
10379 Packages ! undertilde
10384 is installed on your system:
10387 \begin_layout Standard
10391 \begin_layout Plain Layout
10401 \begin_inset Note Note
10404 \begin_layout Plain Layout
10405 The following table will only be displayed when the \SpecialChar LaTeX
10416 \begin_inset Separator latexpar
10422 \begin_layout Standard
10425 \begin_inset Tabular
10426 <lyxtabular version="3" rows="2" columns="2">
10427 <features booktabs="true" tabularvalignment="middle">
10428 <column alignment="center" valignment="top" width="0pt">
10429 <column alignment="center" valignment="top" width="0pt">
10431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10434 \begin_layout Plain Layout
10440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10443 \begin_layout Plain Layout
10451 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10454 \begin_layout Plain Layout
10458 \begin_inset space \textvisiblespace{}
10466 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10469 \begin_layout Plain Layout
10470 \begin_inset Formula $\utilde{A}$
10486 \begin_layout Standard
10490 \begin_layout Plain Layout
10500 \begin_inset Note Note
10503 \begin_layout Plain Layout
10504 The following will be displayed when the \SpecialChar LaTeX
10517 \begin_layout Standard
10518 You need to install the \SpecialChar LaTeX
10523 to see the rest of this subsection in the output.
10526 \begin_layout Standard
10530 \begin_layout Plain Layout
10542 \begin_layout Standard
10543 \begin_inset Newpage newpage
10549 \begin_layout Subsection
10550 Accents for several Characters
10551 \begin_inset Index idx
10554 \begin_layout Plain Layout
10555 Accents ! for several characters
10563 \begin_layout Standard
10564 \begin_inset space \hfill{}
10568 \begin_inset Tabular
10569 <lyxtabular version="3" rows="5" columns="2">
10570 <features booktabs="true" tabularvalignment="middle">
10571 <column alignment="center" valignment="top" width="0pt">
10572 <column alignment="center" valignment="top" width="0pt">
10574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10577 \begin_layout Plain Layout
10583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10586 \begin_layout Plain Layout
10593 <row topspace="1.5mm">
10594 <cell alignment="center" valignment="top" usebox="none">
10597 \begin_layout Plain Layout
10601 \begin_inset space \textvisiblespace{}
10609 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10612 \begin_layout Plain Layout
10613 \begin_inset Formula $\overleftarrow{A=B}$
10622 <row topspace="1.5mm">
10623 <cell alignment="center" valignment="top" usebox="none">
10626 \begin_layout Plain Layout
10630 \begin_inset space \textvisiblespace{}
10638 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10641 \begin_layout Plain Layout
10642 \begin_inset Formula $\underleftarrow{A=B}$
10651 <row topspace="1.5mm">
10652 <cell alignment="center" valignment="top" usebox="none">
10655 \begin_layout Plain Layout
10659 \begin_inset space \textvisiblespace{}
10667 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10670 \begin_layout Plain Layout
10671 \begin_inset Formula $\overleftrightarrow{A=B}$
10680 <row topspace="1.5mm" bottomspace="1mm">
10681 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10684 \begin_layout Plain Layout
10687 underleftrightarrow
10688 \begin_inset space \textvisiblespace{}
10696 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10699 \begin_layout Plain Layout
10700 \begin_inset Formula $\underleftrightarrow{A=B}$
10714 \begin_inset space \hfill{}
10718 \begin_inset Tabular
10719 <lyxtabular version="3" rows="5" columns="2">
10720 <features booktabs="true" tabularvalignment="middle">
10721 <column alignment="center" valignment="top" width="0pt">
10722 <column alignment="center" valignment="top" width="0pt">
10724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10727 \begin_layout Plain Layout
10733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10736 \begin_layout Plain Layout
10743 <row topspace="1.5mm">
10744 <cell alignment="center" valignment="top" usebox="none">
10747 \begin_layout Plain Layout
10751 \begin_inset space \textvisiblespace{}
10759 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10762 \begin_layout Plain Layout
10763 \begin_inset Formula $\overrightarrow{A=B}$
10772 <row topspace="1.5mm">
10773 <cell alignment="center" valignment="top" usebox="none">
10776 \begin_layout Plain Layout
10780 \begin_inset space \textvisiblespace{}
10788 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10791 \begin_layout Plain Layout
10792 \begin_inset Formula $\underrightarrow{A=B}$
10801 <row topspace="1.5mm">
10802 <cell alignment="center" valignment="top" usebox="none">
10805 \begin_layout Plain Layout
10809 \begin_inset space \textvisiblespace{}
10817 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10820 \begin_layout Plain Layout
10821 \begin_inset Formula $\widetilde{A=B}$
10830 <row topspace="1.5mm" bottomspace="1mm">
10831 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10834 \begin_layout Plain Layout
10838 \begin_inset space \textvisiblespace{}
10846 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10849 \begin_layout Plain Layout
10850 \begin_inset Formula $\widehat{A=B}$
10864 \begin_inset space \hfill{}
10870 \begin_layout Standard
10871 \begin_inset VSpace medskip
10874 With these commands as many characters as you like can be accented.
10887 will only be set in the output with a length of three characters, as shown
10888 in the following example:
10889 \begin_inset Formula
10891 \widetilde{A+B=C-D}
10899 \begin_layout Standard
10907 \begin_inset Index idx
10910 \begin_layout Plain Layout
10925 \begin_inset Index idx
10928 \begin_layout Plain Layout
10936 described in the previous subsection it is also possible to accent several
10943 \begin_inset space \textvisiblespace{}
10947 \begin_inset Formula $\downarrow$
10953 \begin_inset Formula
10955 \underset{***}{A=B}
10963 \begin_layout Section
10965 \begin_inset CommandInset label
10967 name "subsec:Space"
10972 \begin_inset Index idx
10975 \begin_layout Plain Layout
10984 \begin_layout Subsection
10986 \begin_inset CommandInset label
10988 name "subsec:Predefined-Space"
10993 \begin_inset Index idx
10996 \begin_layout Plain Layout
10997 Space ! horizontal ! predefined
11005 \begin_layout Standard
11006 Sometimes it is necessary to insert horizontal space into a formula.
11007 This is done by inserting a protected space (shortcut
11010 arg "command-alternatives space-insert protected ; math-space"
11015 \begin_inset Quotes eld
11021 \begin_inset space \textvisiblespace{}
11027 \begin_inset Quotes erd
11030 appears and by pressing
11034 several times one can select one of eight different space sizes.
11035 The spaces can also be inserted using the math toolbar button
11038 arg "math-insert \\space"
11041 or special commands.
11042 Independent from the inserted command, one can select the size again by
11048 \begin_inset Separator latexpar
11054 \begin_layout Standard
11057 \begin_inset Tabular
11058 <lyxtabular version="3" rows="6" columns="3">
11059 <features booktabs="true" tabularvalignment="middle">
11060 <column alignment="center" valignment="top">
11061 <column alignment="center" valignment="top" width="15col%">
11062 <column alignment="center" valignment="top">
11064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11067 \begin_layout Plain Layout
11073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11076 \begin_layout Plain Layout
11086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11089 \begin_layout Plain Layout
11097 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11100 \begin_layout Plain Layout
11108 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11111 \begin_layout Plain Layout
11117 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11120 \begin_layout Plain Layout
11121 \begin_inset Formula $A\,B$
11131 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11134 \begin_layout Plain Layout
11142 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11145 \begin_layout Plain Layout
11151 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11154 \begin_layout Plain Layout
11155 \begin_inset Formula $A\:B$
11165 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11168 \begin_layout Plain Layout
11176 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11179 \begin_layout Plain Layout
11185 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11188 \begin_layout Plain Layout
11189 \begin_inset Formula $A\;B$
11199 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11202 \begin_layout Plain Layout
11210 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11213 \begin_layout Plain Layout
11219 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11222 \begin_layout Plain Layout
11223 \begin_inset Formula $A\quad B$
11233 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11236 \begin_layout Plain Layout
11244 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11247 \begin_layout Plain Layout
11253 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11256 \begin_layout Plain Layout
11257 \begin_inset Formula $A\qquad B$
11271 \begin_inset space \hfill{}
11275 \begin_inset Tabular
11276 <lyxtabular version="3" rows="6" columns="3">
11277 <features booktabs="true" tabularvalignment="middle">
11278 <column alignment="center" valignment="top">
11279 <column alignment="center" valignment="top" width="15col%">
11280 <column alignment="center" valignment="top">
11282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11285 \begin_layout Plain Layout
11291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11294 \begin_layout Plain Layout
11304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11307 \begin_layout Plain Layout
11315 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11318 \begin_layout Plain Layout
11326 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11329 \begin_layout Plain Layout
11335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11338 \begin_layout Plain Layout
11339 \begin_inset Formula $A\hfill B$
11349 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11352 \begin_layout Plain Layout
11360 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11363 \begin_layout Plain Layout
11369 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11372 \begin_layout Plain Layout
11373 \begin_inset Formula $A\hspace*{1em}B$
11383 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11386 \begin_layout Plain Layout
11394 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11397 \begin_layout Plain Layout
11403 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11406 \begin_layout Plain Layout
11407 \begin_inset Formula $A\hspace{1em}B$
11417 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11420 \begin_layout Plain Layout
11424 \begin_inset space \textvisiblespace{}
11432 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11435 \begin_layout Plain Layout
11441 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11444 \begin_layout Plain Layout
11445 \begin_inset Formula $A\ B$
11455 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11458 \begin_layout Plain Layout
11466 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11469 \begin_layout Plain Layout
11475 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11478 \begin_layout Plain Layout
11479 \begin_inset Formula $A\!B$
11495 \begin_layout Standard
11497 \begin_inset space ~
11501 \begin_inset space \thinspace{}
11505 \begin_inset space \thinspace{}
11508 7 are variable spaces which are explained in
11509 \begin_inset CommandInset ref
11511 reference "subsec:Variable-Space"
11517 \begin_inset space ~
11520 9 seems to produce no space.
11521 It is displayed red in \SpecialChar LyX
11522 contrary to the other sizes, because it is a negative
11524 There are two more negative spaces:
11525 \begin_inset Separator latexpar
11531 \begin_layout Standard
11533 \begin_inset Tabular
11534 <lyxtabular version="3" rows="3" columns="3">
11535 <features booktabs="true" tabularvalignment="middle">
11536 <column alignment="center" valignment="middle" width="6.8cm">
11537 <column alignment="center" valignment="top" width="0pt">
11538 <column alignment="center" valignment="top" width="0pt">
11540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11543 \begin_layout Plain Layout
11549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11552 \begin_layout Plain Layout
11560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11563 \begin_layout Plain Layout
11573 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11576 \begin_layout Plain Layout
11581 keystrokes after inserting the protected space
11586 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11589 \begin_layout Plain Layout
11595 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11598 \begin_layout Plain Layout
11606 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11609 \begin_layout Plain Layout
11615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11618 \begin_layout Plain Layout
11619 \begin_inset Formula $A\negmedspace B$
11627 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11630 \begin_layout Plain Layout
11631 \begin_inset Formula $A\negthickspace B$
11647 \begin_layout Standard
11648 Negative spaces can lead to characters overlapping each other.
11649 Thus they can be used to enforce ligatures, which are e.
11650 \begin_inset space \thinspace{}
11654 \begin_inset space \space{}
11657 useful for summation operators:
11658 \begin_inset Separator latexpar
11664 \begin_layout Standard
11666 \begin_inset Tabular
11667 <lyxtabular version="3" rows="3" columns="2">
11668 <features booktabs="true" tabularvalignment="middle">
11669 <column alignment="center" valignment="top" width="0pt">
11670 <column alignment="center" valignment="top">
11672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11675 \begin_layout Plain Layout
11681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11684 \begin_layout Plain Layout
11692 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11695 \begin_layout Plain Layout
11701 \begin_inset space \textvisiblespace{}
11709 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11712 \begin_layout Plain Layout
11713 \begin_inset Formula $\sum\sum f_{kl}$
11723 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11726 \begin_layout Plain Layout
11734 \begin_inset space \textvisiblespace{}
11742 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11745 \begin_layout Plain Layout
11746 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11762 \begin_layout Standard
11764 \begin_inset VSpace medskip
11770 \begin_layout Standard
11772 Relations like for example equal signs, are always surrounded by space.
11773 To suppress this, the equal sign is placed into a \SpecialChar TeX
11775 The following example demonstrates this:
11776 \begin_inset Separator latexpar
11782 \begin_layout Standard
11784 \begin_inset Tabular
11785 <lyxtabular version="3" rows="2" columns="2">
11786 <features tabularvalignment="middle">
11787 <column alignment="center" valignment="top" width="0pt">
11788 <column alignment="center" valignment="top" width="0pt">
11790 <cell alignment="center" valignment="top" usebox="none">
11793 \begin_layout Plain Layout
11799 <cell alignment="center" valignment="top" usebox="none">
11802 \begin_layout Plain Layout
11803 \begin_inset Formula $A=B$
11813 <cell alignment="center" valignment="top" usebox="none">
11816 \begin_layout Plain Layout
11817 equation without space
11822 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11825 \begin_layout Plain Layout
11826 \begin_inset Formula $A{=}B$
11842 \begin_layout Standard
11844 The command for the last formula is:
11849 \begin_inset Formula $\to$
11855 \begin_layout Standard
11856 \begin_inset VSpace bigskip
11862 \begin_layout Standard
11863 Spaces are needed for physical units, because the space between the value
11864 and the unit is the smallest one and not a normal space.
11865 For units in text, the smallest space is inserted via the menu
11867 Insert\SpecialChar menuseparator
11868 Formatting\SpecialChar menuseparator
11870 \begin_inset space ~
11878 arg "space-insert thin"
11884 \begin_layout Standard
11885 An example to visualize the difference:
11888 \begin_layout Standard
11889 \begin_inset Tabular
11890 <lyxtabular version="3" rows="2" columns="2">
11891 <features tabularvalignment="middle">
11892 <column alignment="left" valignment="top">
11893 <column alignment="left" valignment="top">
11895 <cell alignment="center" valignment="top" usebox="none">
11898 \begin_layout Plain Layout
11900 \begin_inset Formula $\cdot$
11908 <cell alignment="center" valignment="top" usebox="none">
11911 \begin_layout Plain Layout
11912 space between value and unit
11919 <cell alignment="center" valignment="top" usebox="none">
11922 \begin_layout Plain Layout
11924 \begin_inset space \thinspace{}
11928 \begin_inset Formula $\cdot$
11936 <cell alignment="center" valignment="top" usebox="none">
11939 \begin_layout Plain Layout
11940 smallest space between value and unit
11953 \begin_layout Subsection
11958 \begin_layout Plain Layout
11971 \begin_layout Plain Layout
11972 for vertical space in formulas see
11973 \begin_inset CommandInset ref
11975 reference "subsec:Line-Separation"
11988 \begin_layout Plain Layout
11996 \begin_inset Note Note
11999 \begin_layout Plain Layout
12002 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12005 \begin_layout Plain Layout
12008 texorpdfstring is in section
12009 \begin_inset CommandInset ref
12011 reference "subsec:Formulas-in-Section"
12021 \begin_inset CommandInset label
12023 name "subsec:Variable-Space"
12028 \begin_inset Index idx
12031 \begin_layout Plain Layout
12032 Space ! horizontal ! variable
12040 \begin_layout Standard
12041 Space with a defined length can be inserted with the command
12048 \begin_inset Index idx
12051 \begin_layout Plain Layout
12061 \begin_inset Quotes eld
12067 \begin_inset space \textvisiblespace{}
12073 \begin_inset Quotes erd
12077 The length can be specified by left-clicking on the
12078 \begin_inset Quotes eld
12084 \begin_inset space \textvisiblespace{}
12090 \begin_inset Quotes erd
12094 The length may also be negative.
12095 When a space would be the first character in a line it would be omitted.
12096 To force its output use the command
12108 or left-click on the
12109 \begin_inset Quotes eld
12115 \begin_inset space \textvisiblespace{}
12121 \begin_inset Quotes erd
12124 and check the option
12129 \begin_inset Newline newline
12132 To insert as much space as is available, the command
12139 \begin_inset Index idx
12142 \begin_layout Plain Layout
12153 \begin_layout Standard
12155 \begin_inset Tabular
12156 <lyxtabular version="3" rows="4" columns="2">
12157 <features booktabs="true" tabularvalignment="middle">
12158 <column alignment="center" valignment="top" width="0pt">
12159 <column alignment="center" valignment="top">
12161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12164 \begin_layout Plain Layout
12172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12175 \begin_layout Plain Layout
12183 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12186 \begin_layout Plain Layout
12190 \begin_inset space \textvisiblespace{}
12196 \begin_inset space \thinspace{}
12204 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12207 \begin_layout Plain Layout
12208 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12218 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12221 \begin_layout Plain Layout
12225 \begin_inset space \textvisiblespace{}
12231 \begin_inset space \thinspace{}
12239 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12242 \begin_layout Plain Layout
12243 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12256 \begin_layout Plain Layout
12260 \begin_inset space \textvisiblespace{}
12268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12271 \begin_layout Plain Layout
12272 \begin_inset Formula $A=A\hfill B=B$
12288 \begin_layout Standard
12289 In the last example the available space is given by the longest column entry
12291 In an inline formula the space depends on the length of the line in which
12299 Thus, when the line uses the full width, no space will be created.
12306 only has an effect on displayed formulas when the formula style
12311 (Formula styles are explained in
12312 \begin_inset CommandInset ref
12314 reference "sec:Formula-Styles"
12321 \begin_layout Standard
12328 , there are the commands
12340 that fill the space with a pattern, see
12341 \begin_inset CommandInset ref
12343 reference "subsec:Ellipses"
12350 \begin_layout Standard
12351 For text, variable space can be inserted via the menu
12353 Insert\SpecialChar menuseparator
12354 Formatting\SpecialChar menuseparator
12356 \begin_inset space ~
12364 \begin_layout Standard
12365 This is a line with
12366 \begin_inset space \hspace{}
12371 \begin_inset space \thinspace{}
12377 \begin_layout Standard
12378 This is a line with
12379 \begin_inset space \hfill{}
12385 \begin_layout Subsection
12386 Space besides inline Formulas
12387 \begin_inset Index idx
12390 \begin_layout Plain Layout
12391 Space ! besides inline formulas
12399 \begin_layout Standard
12400 The space that surrounds inline formulas can be adjusted with the length
12408 \begin_inset Index idx
12411 \begin_layout Plain Layout
12420 The value of a length is set with the command
12427 \begin_inset Index idx
12430 \begin_layout Plain Layout
12438 which has the following scheme:
12441 \begin_layout Standard
12446 setlength{length name}{value}
12449 \begin_layout Standard
12457 \begin_inset space \thinspace{}
12463 \begin_layout Standard
12473 \begin_layout Standard
12474 is inserted in \SpecialChar TeX
12477 \begin_inset space \thinspace{}
12480 mm space will now be set around all inline formulas:
12484 \begin_layout Plain Layout
12498 \begin_layout Standard
12499 This is a line with an inline formula
12500 \begin_inset Formula $A=B$
12504 \begin_inset space \thinspace{}
12507 mm surrounding space.
12511 \begin_layout Plain Layout
12525 \begin_layout Standard
12526 To return to the predefined value,
12532 is set to the value 0
12533 \begin_inset space \thinspace{}
12539 \begin_layout Standard
12540 \begin_inset Newpage newpage
12546 \begin_layout Section
12548 \begin_inset Index idx
12551 \begin_layout Plain Layout
12558 \begin_inset Index idx
12561 \begin_layout Plain Layout
12566 \begin_layout Plain Layout
12577 \begin_layout Plain Layout
12592 \begin_layout Standard
12593 Boxes for text are described in chapter
12600 \begin_inset space ~
12608 \begin_layout Subsection
12610 \begin_inset CommandInset label
12612 name "subsec:Boxes-with-Frame"
12617 \begin_inset Index idx
12620 \begin_layout Plain Layout
12629 \begin_layout Standard
12630 It is possible to frame a formula or part of one with the commands
12637 \begin_inset Index idx
12640 \begin_layout Plain Layout
12655 \begin_inset Index idx
12658 \begin_layout Plain Layout
12669 \begin_layout Standard
12670 When one of these commands is inserted in a formula, a blue box appears
12671 within a frame to enter formula parts.
12678 an additional formula has to be created by
12682 within this box, because the box content will otherwise be treated as mathemati
12690 is used, a new formula is automatically created inside the frame.
12693 \begin_layout Standard
12700 is not suitable to frame displayed formulas because the formula will always
12701 be set in the size of the text.
12708 is in contrary not suitable to frame inline formulas, because the formula
12709 will always be set in the size of a displayed formula.
12712 \begin_layout Standard
12726 \begin_inset Index idx
12729 \begin_layout Plain Layout
12737 where additionally the frame width and the alignment can be specified.
12744 is used in the following scheme:
12747 \begin_layout Standard
12752 framebox[frame width][position]{box content}
12755 \begin_layout Standard
12756 The position can either be
12773 right aligns the formula in the box.
12774 When no position is given, the formula will be centered.
12775 \begin_inset Newline newline
12778 If no width is given, also no position can be given.
12779 In this case the frame width is adjusted to the box content like for
12788 \begin_layout Standard
12795 is inserted, a box appears containing three blue boxes.
12796 The first two boxes are surrounded by brackets and denote the two optional
12798 The third box is for formula parts like for
12805 \begin_inset Separator latexpar
12811 \begin_layout Standard
12813 \begin_inset Tabular
12814 <lyxtabular version="3" rows="5" columns="2">
12815 <features booktabs="true" tabularvalignment="middle">
12816 <column alignment="center" valignment="top" width="0pt">
12817 <column alignment="center" valignment="top">
12819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12822 \begin_layout Plain Layout
12828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12831 \begin_layout Plain Layout
12838 <row topspace="1.5mm">
12839 <cell alignment="center" valignment="top" usebox="none">
12842 \begin_layout Plain Layout
12846 \begin_inset space \textvisiblespace{}
12856 \begin_inset space \textvisiblespace{}
12864 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12867 \begin_layout Plain Layout
12868 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12877 <row topspace="1.5mm">
12878 <cell alignment="center" valignment="top" usebox="none">
12881 \begin_layout Plain Layout
12885 \begin_inset space \textvisiblespace{}
12891 \begin_inset space \textvisiblespace{}
12899 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12902 \begin_layout Plain Layout
12903 \begin_inset Formula $\boxed{\int A=B}$
12912 <row topspace="1.5mm">
12913 <cell alignment="center" valignment="top" usebox="none">
12916 \begin_layout Plain Layout
12920 \begin_inset space \textvisiblespace{}
12928 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12931 \begin_layout Plain Layout
12932 \begin_inset Formula $A+\fbox{B}$
12941 <row topspace="1.5mm" bottomspace="1mm">
12942 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12945 \begin_layout Plain Layout
12949 \begin_inset space \textvisiblespace{}
12953 \begin_inset Formula $\to$
12957 \begin_inset Formula $\to$
12967 \begin_inset space \textvisiblespace{}
12971 \begin_inset Formula $\downarrow$
12979 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12982 \begin_layout Plain Layout
12983 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12999 \begin_layout Standard
13000 The frame thickness can also be adjusted.
13001 To do this the following commands have to be inserted in \SpecialChar TeX
13006 \begin_layout Standard
13016 \begin_inset Quotes eld
13020 \begin_inset Quotes erd
13034 \begin_inset Quotes eld
13038 \begin_inset Quotes erd
13044 \begin_layout Standard
13045 \begin_inset Quotes eld
13049 \begin_inset Quotes erd
13052 specifies the minimal distance between the frame and the first character
13054 An example for this is the following framed formula:
13058 \begin_layout Plain Layout
13070 \begin_inset Formula
13077 Before this formula the commands
13080 \begin_layout Standard
13102 \begin_layout Standard
13103 were inserted in \SpecialChar TeX
13105 The given values are used for all following boxes.
13108 \begin_layout Standard
13109 To return to the standard frame size, the command
13112 \begin_layout Standard
13137 \begin_layout Plain Layout
13151 \begin_layout Standard
13152 is inserted in \SpecialChar TeX
13153 mode before the next formula.
13156 \begin_layout Subsection
13157 Boxes without Frame
13158 \begin_inset CommandInset label
13160 name "subsec:Boxes-without-Frame"
13165 \begin_inset Index idx
13168 \begin_layout Plain Layout
13169 Boxes ! without frame
13177 \begin_layout Standard
13178 For boxes without a frame there are the following box commands:
13185 \begin_inset Index idx
13188 \begin_layout Plain Layout
13203 \begin_inset Index idx
13206 \begin_layout Plain Layout
13221 \begin_inset Index idx
13224 \begin_layout Plain Layout
13235 \begin_layout Standard
13242 a box can be super- or subscripted.
13243 But in contrary to normal super- and subscripting, the characters in the
13244 box keep their font size.
13251 is used in the following scheme:
13254 \begin_layout Standard
13259 raisebox{height}{box content}
13262 \begin_layout Standard
13263 When the box should contain a formula, an extra formula is needed like for
13274 \begin_inset Note Greyedout
13277 \begin_layout Plain Layout
13288 this extra formula is created by pressing
13292 twice instead of once because \SpecialChar LyX
13293 doesn't yet support
13307 \begin_inset Separator latexpar
13313 \begin_layout Standard
13315 \begin_inset Tabular
13316 <lyxtabular version="3" rows="4" columns="2">
13317 <features booktabs="true" tabularvalignment="middle">
13318 <column alignment="center" valignment="top" width="0pt">
13319 <column alignment="center" valignment="top">
13321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13324 \begin_layout Plain Layout
13330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13333 \begin_layout Plain Layout
13341 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13344 \begin_layout Plain Layout
13348 \begin_inset Formula $\to$
13354 \begin_inset Formula $\to$
13362 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13365 \begin_layout Plain Layout
13366 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13376 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13379 \begin_layout Plain Layout
13383 \begin_inset Formula $\to$
13389 \begin_inset Formula $\to$
13397 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13400 \begin_layout Plain Layout
13401 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13414 \begin_layout Plain Layout
13418 \begin_inset Formula $\to$
13434 \begin_inset space \textvisiblespace{}
13442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13445 \begin_layout Plain Layout
13446 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13462 \begin_layout Standard
13487 , with the difference that there is no frame.
13490 \begin_layout Subsection
13492 \begin_inset CommandInset label
13494 name "subsec:Colored-Boxes"
13499 \begin_inset Index idx
13502 \begin_layout Plain Layout
13511 \begin_layout Standard
13512 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13521 \begin_layout Plain Layout
13522 The \SpecialChar LaTeX
13527 is part of every \SpecialChar LaTeX
13528 standard installation.
13534 \begin_inset Index idx
13537 \begin_layout Plain Layout
13543 has to be loaded in the \SpecialChar LaTeX
13544 -preamble with the line
13548 \begin_layout Plain Layout
13549 When text is colored somewhere in the document with a predefined color,
13551 loads the \SpecialChar LaTeX
13557 Thus it is possible that the package is loaded twice, but this does not
13564 \begin_inset Note Note
13567 \begin_layout Plain Layout
13568 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13577 \begin_layout Standard
13585 \begin_layout Standard
13586 \begin_inset VSpace medskip
13589 To color boxes, the command
13596 \begin_inset Index idx
13599 \begin_layout Plain Layout
13607 is used in the following scheme:
13610 \begin_layout Standard
13615 colorbox{color}{box content}
13618 \begin_layout Standard
13619 The box content can also be a box and a
13625 can also be part of another box (see the 2nd and 3rd example).
13626 When the box should contain a formula, an extra formula has to be created,
13627 the same way as for
13637 \begin_layout Plain Layout
13638 This also applies for the command
13652 \begin_layout Standard
13653 One of the following predefined colors can be chosen:
13656 \begin_layout Standard
13690 \begin_inset Separator latexpar
13696 \begin_layout Standard
13698 \begin_inset Tabular
13699 <lyxtabular version="3" rows="4" columns="2">
13700 <features booktabs="true" tabularvalignment="middle">
13701 <column alignment="center" valignment="top" width="0pt">
13702 <column alignment="center" valignment="top">
13704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13707 \begin_layout Plain Layout
13713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13716 \begin_layout Plain Layout
13724 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13727 \begin_layout Plain Layout
13731 \begin_inset Formula $\to$
13741 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13744 \begin_layout Plain Layout
13745 \begin_inset Formula $\colorbox{yellow}{A=B}$
13754 <row topspace="1.5mm">
13755 <cell alignment="center" valignment="top" usebox="none">
13758 \begin_layout Plain Layout
13762 \begin_inset Formula $\to$
13770 \begin_inset space \textvisiblespace{}
13778 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13781 \begin_layout Plain Layout
13782 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13791 <row topspace="1.5mm" bottomspace="1mm">
13792 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13795 \begin_layout Plain Layout
13799 \begin_inset space \textvisiblespace{}
13805 \begin_inset Formula $\to$
13821 \begin_inset space \textvisiblespace{}
13829 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13832 \begin_layout Plain Layout
13833 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13849 \begin_layout Standard
13856 only colors the box but not the characters in the box.
13857 To color all characters, the whole formula is highlighted and the desired
13858 color is chosen in the
13861 \begin_inset space ~
13867 The dialog can be called with the toolbar button
13870 arg "dialog-show character"
13875 Edit\SpecialChar menuseparator
13877 \begin_inset space ~
13880 Style\SpecialChar menuseparator
13884 The formula number then has the same color as the formula.
13885 When the formula number should get another color than the formula characters,
13886 the color must be changed within the formula.
13889 \begin_layout Standard
13893 \begin_layout Standard
13896 \begin_inset Formula
13898 \int A=B\label{eq:red}
13906 \begin_inset Formula
13908 \textcolor{red}{\int A=B}\label{eq:redgreen}
13916 \begin_layout Standard
13918 \begin_inset CommandInset ref
13924 is completely colored red.
13925 \begin_inset Newline newline
13929 \begin_inset CommandInset ref
13931 reference "eq:redgreen"
13935 was first completely colored green to set the color for the formula number.
13936 Subsequently the formula characters were colored red.
13939 \begin_layout Standard
13940 \begin_inset VSpace bigskip
13943 To color the frame different than the rest of the box, the command
13950 \begin_inset Index idx
13953 \begin_layout Plain Layout
13961 is used in the following scheme:
13964 \begin_layout Standard
13969 fcolorbox{frame color}{color}{box content}
13972 \begin_layout Standard
13979 is an extension of the command
13986 The frame width is set, like for
14009 \begin_layout Plain Layout
14021 \begin_inset Formula
14023 \fcolorbox{cyan}{magenta}{A=B}
14032 \begin_layout Plain Layout
14046 \begin_layout Standard
14047 This formula was created with the command
14048 \begin_inset Newline newline
14056 \begin_inset Formula $\to$
14062 \begin_inset Formula $\to$
14072 \begin_layout Standard
14073 \begin_inset VSpace bigskip
14076 To use other colors than the predefined ones, they have to be defined first.
14079 \begin_layout Standard
14080 One can for example define the color
14081 \begin_inset Quotes eld
14089 \begin_inset Quotes erd
14092 with the \SpecialChar LaTeX
14096 \begin_layout Standard
14101 definecolor{darkgreen}{cmyk}{0.5,
14116 \begin_inset Index idx
14119 \begin_layout Plain Layout
14130 \begin_layout Standard
14135 is the color space that denotes the colors
14152 The four comma separated numbers are the portion factor for the corresponding
14153 colors of the color space.
14154 The factors can be in the range of 0
14155 \begin_inset space \thinspace{}
14159 \begin_inset space \thinspace{}
14167 also the color space
14171 can be used for definitions.
14188 , so that there are in this case three portion factors for the corresponding
14190 Furthermore there is the color space
14194 with one portion factor for the gray value.
14197 \begin_layout Standard
14198 As example a framed box with the new defined color
14202 where the characters have been colored
14207 \begin_inset Formula
14209 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14217 \begin_layout Standard
14218 Self-defined colors can also be used for text with the help of the command
14226 \begin_inset Index idx
14229 \begin_layout Plain Layout
14238 \begin_layout Standard
14242 \begin_layout Plain Layout
14246 textcolor{darkgreen}{
14252 \begin_inset Quotes eld
14256 \begin_inset Quotes erd
14263 \begin_layout Plain Layout
14273 \begin_layout Standard
14281 \begin_inset Index idx
14284 \begin_layout Plain Layout
14292 is used in the scheme
14296 textcolor{color}{characters to color}
14301 \begin_layout Subsection
14303 \begin_inset CommandInset label
14305 name "subsec:Paragraph-Boxes"
14310 \begin_inset Index idx
14313 \begin_layout Plain Layout
14314 Boxes ! as paragraph
14322 \begin_layout Standard
14323 A box that can contain several lines and paragraphs, a so-called paragraph
14324 box (parbox), can be created with the menu
14326 Insert\SpecialChar menuseparator
14329 or the toolbar button
14338 \begin_layout Standard
14339 The following example shows a framed parbox in a line:
14342 \begin_layout Standard
14343 \begin_inset VSpace medskip
14347 \begin_inset Box Boxed
14357 height_special "totalheight"
14362 backgroundcolor "none"
14365 \begin_layout Plain Layout
14366 This is a paragraph box.
14368 \begin_inset space \thinspace{}
14371 cm long and can also contain formulas:
14372 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14383 \begin_layout Standard
14384 \begin_inset VSpace medskip
14390 \begin_layout Standard
14391 Such a box is created by right-clicking on the gray box inset.
14392 A dialog pops up showing the box properties.
14406 \begin_inset space \thinspace{}
14411 Vertical Box Alignment
14416 \begin_layout Standard
14417 \begin_inset VSpace medskip
14420 In \SpecialChar LaTeX
14421 a parbox is created with the command
14428 \begin_inset Index idx
14431 \begin_layout Plain Layout
14439 which has the following scheme:
14442 \begin_layout Standard
14447 parbox[position]{width}{box content}
14450 \begin_layout Standard
14465 \begin_inset Quotes eld
14469 \begin_inset Quotes erd
14472 means that the box is aligned within the surrounding text with its last
14479 \begin_inset Quotes eld
14483 \begin_inset Quotes erd
14486 this is done with the first line.
14487 When no position is given, the box will be vertically centered, see section
14495 \begin_inset space ~
14500 manual for examples.
14503 \begin_layout Standard
14504 \begin_inset VSpace bigskip
14507 To frame formulas completely, including the formula number, the formula
14508 must be set into a parbox.
14509 To do this, the command
14523 is inserted in \SpecialChar TeX
14524 mode before the formula.
14532 \begin_inset Index idx
14535 \begin_layout Plain Layout
14543 is hereby the line width set for the document.
14544 Because the frame is outside the parbox, 2
14545 \begin_inset space \thinspace{}
14548 times the frame separation and the frame thickness must be subtracted from
14550 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14559 \begin_layout Plain Layout
14564 is part of every \SpecialChar LaTeX
14565 standard installation.
14571 \begin_inset Index idx
14574 \begin_layout Plain Layout
14580 must be loaded in the \SpecialChar LaTeX
14581 -preamble with the line
14584 \begin_layout Standard
14592 \begin_layout Standard
14593 Behind the formula both boxes are closed by entering
14597 in \SpecialChar TeX
14599 Here is an example:
14603 \begin_layout Plain Layout
14617 \begin_layout Standard
14621 \begin_layout Plain Layout
14639 \begin_inset Formula
14641 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14650 \begin_layout Plain Layout
14661 \begin_layout Plain Layout
14675 \begin_layout Standard
14676 \begin_inset VSpace medskip
14679 As a parbox is used as the argument of
14685 , there is in this case no difference between
14700 \begin_layout Standard
14701 \begin_inset VSpace bigskip
14704 Paragraph boxes are very useful to comment formulas directly.
14711 is used in combination with the command
14725 \begin_inset CommandInset ref
14727 reference "subsec:User-defined-Numbering"
14734 \begin_layout Standard
14735 An example of a formula commented with
14744 \begin_layout Standard
14748 \begin_layout Plain Layout
14761 This is a description.
14762 It is distinctly separated from the formula and multiline.
14766 \begin_layout Plain Layout
14778 \begin_layout Standard
14779 Such a formula must be inserted completely in \SpecialChar TeX
14780 mode because \SpecialChar LyX
14782 support the command
14789 The formula is created with the following command sequence:
14792 \begin_layout Standard
14805 is inserted in \SpecialChar TeX
14810 \begin_layout Plain Layout
14811 When the formula style
14823 can also be replaced by
14830 (formula styles see
14831 \begin_inset CommandInset ref
14833 reference "sec:Formula-Styles"
14842 Then the description follows as normal text and finally
14848 is inserted in \SpecialChar TeX
14862 hereby create a displayed formula.
14865 \begin_layout Standard
14872 can be seen in this example that was
14873 \begin_inset Quotes eld
14877 \begin_inset Quotes erd
14880 using the mathematical textmode:
14881 \begin_inset Formula
14883 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14891 \begin_layout Section
14893 \begin_inset Index idx
14896 \begin_layout Plain Layout
14905 \begin_layout Subsection
14907 \begin_inset CommandInset label
14909 name "subsec:Big-Operators"
14914 \begin_inset Index idx
14917 \begin_layout Plain Layout
14924 \begin_inset Index idx
14927 \begin_layout Plain Layout
14934 \begin_inset Index idx
14937 \begin_layout Plain Layout
14946 \begin_layout Standard
14947 To be able to use all integral operators listed here, the option
14949 Use esint package automatically
14951 must be set in the document settings under
14954 \begin_inset space ~
14962 \begin_layout Standard
14963 \begin_inset space \hfill{}
14967 \begin_inset Tabular
14968 <lyxtabular version="3" rows="11" columns="2">
14969 <features booktabs="true" tabularvalignment="middle">
14970 <column alignment="center" valignment="top" width="0pt">
14971 <column alignment="center" valignment="top" width="0pt">
14973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14976 \begin_layout Plain Layout
14982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14985 \begin_layout Plain Layout
14993 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14996 \begin_layout Plain Layout
15000 \begin_inset Index idx
15003 \begin_layout Plain Layout
15016 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15019 \begin_layout Plain Layout
15020 \begin_inset Formula $\int$
15030 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15033 \begin_layout Plain Layout
15041 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15044 \begin_layout Plain Layout
15045 \begin_inset Formula $\oint$
15055 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15058 \begin_layout Plain Layout
15066 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15069 \begin_layout Plain Layout
15070 \begin_inset Formula $\ointctrclockwise$
15080 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15083 \begin_layout Plain Layout
15091 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15094 \begin_layout Plain Layout
15095 \begin_inset Formula $\ointclockwise$
15105 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15108 \begin_layout Plain Layout
15116 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15119 \begin_layout Plain Layout
15120 \begin_inset Formula $\sqint$
15130 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15133 \begin_layout Plain Layout
15141 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15144 \begin_layout Plain Layout
15146 \begin_inset Formula $\fint$
15156 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15159 \begin_layout Plain Layout
15167 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15170 \begin_layout Plain Layout
15172 \begin_inset Formula $\landupint$
15182 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15185 \begin_layout Plain Layout
15193 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15196 \begin_layout Plain Layout
15198 \begin_inset Formula $\landdownint$
15208 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15211 \begin_layout Plain Layout
15219 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15222 \begin_layout Plain Layout
15223 \begin_inset Formula $\bigcap$
15233 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15236 \begin_layout Plain Layout
15244 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15247 \begin_layout Plain Layout
15248 \begin_inset Formula $\bigcup$
15262 \begin_inset space \hfill{}
15266 \begin_inset Tabular
15267 <lyxtabular version="3" rows="11" columns="2">
15268 <features booktabs="true" tabularvalignment="middle">
15269 <column alignment="center" valignment="top" width="0pt">
15270 <column alignment="center" valignment="top" width="0pt">
15272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15275 \begin_layout Plain Layout
15281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15284 \begin_layout Plain Layout
15292 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15295 \begin_layout Plain Layout
15299 \begin_inset Index idx
15302 \begin_layout Plain Layout
15315 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15318 \begin_layout Plain Layout
15319 \begin_inset Formula $\sum$
15329 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15332 \begin_layout Plain Layout
15336 \begin_inset Index idx
15339 \begin_layout Plain Layout
15346 \begin_layout Plain Layout
15365 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15368 \begin_layout Plain Layout
15369 \begin_inset Formula $\prod$
15379 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15382 \begin_layout Plain Layout
15390 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15393 \begin_layout Plain Layout
15394 \begin_inset Formula $\coprod$
15404 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15407 \begin_layout Plain Layout
15415 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15418 \begin_layout Plain Layout
15419 \begin_inset Formula $\bigodot$
15429 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15432 \begin_layout Plain Layout
15440 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15443 \begin_layout Plain Layout
15444 \begin_inset Formula $\bigotimes$
15454 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15457 \begin_layout Plain Layout
15465 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15468 \begin_layout Plain Layout
15469 \begin_inset Formula $\bigoplus$
15479 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15482 \begin_layout Plain Layout
15490 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15493 \begin_layout Plain Layout
15494 \begin_inset Formula $\bigwedge$
15504 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15507 \begin_layout Plain Layout
15515 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15518 \begin_layout Plain Layout
15519 \begin_inset Formula $\bigvee$
15529 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15532 \begin_layout Plain Layout
15540 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15543 \begin_layout Plain Layout
15544 \begin_inset Formula $\bigsqcup$
15554 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15557 \begin_layout Plain Layout
15565 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15568 \begin_layout Plain Layout
15569 \begin_inset Formula $\biguplus$
15583 \begin_inset space \hfill{}
15589 \begin_layout Standard
15590 All big operators can also be inserted via the math toolbar button
15593 arg "math-insert \\intop"
15599 \begin_layout Standard
15600 The operators are called big because they are bigger than the sometimes
15601 equal looking binary operators.
15602 All big operators can have limits as described in the next subsection.
15605 \begin_layout Standard
15606 For all integral operators there is a second version available, ending in
15624 These operators are different from
15631 \begin_inset space \space{}
15634 in the style the operator limits are displayed, see
15635 \begin_inset CommandInset ref
15637 reference "subsec:Operator-Limits"
15645 \begin_layout Subsubsection*
15646 Advice for Integrals
15649 \begin_layout Standard
15654 in an integral is an operator, that therefore has to be set upright.
15655 This is done by highlighting the
15659 and using the keyboard shortcut
15669 \begin_layout Plain Layout
15675 \begin_inset CommandInset ref
15677 reference "subsec:Font-Styles"
15687 Finally the smallest space is inserted before the
15691 , as this is usual for operators.
15695 \begin_layout Standard
15697 \begin_inset Formula $\int A(x)dx$
15701 \begin_inset Newline newline
15705 \begin_inset Phantom HPhantom
15708 \begin_layout Plain Layout
15715 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15721 \begin_layout Standard
15722 For multiple integrals there are the following commands:
15723 \begin_inset VSpace medskip
15729 \begin_layout Standard
15730 \begin_inset space \hfill{}
15734 \begin_inset Tabular
15735 <lyxtabular version="3" rows="4" columns="2">
15736 <features booktabs="true" tabularvalignment="middle">
15737 <column alignment="center" valignment="top" width="0pt">
15738 <column alignment="center" valignment="top" width="0pt">
15740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15743 \begin_layout Plain Layout
15749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15752 \begin_layout Plain Layout
15759 <row bottomspace="1mm">
15760 <cell alignment="center" valignment="top" usebox="none">
15763 \begin_layout Plain Layout
15771 <cell alignment="center" valignment="top" usebox="none">
15774 \begin_layout Plain Layout
15775 \begin_inset Formula $\iint$
15784 <row bottomspace="1mm">
15785 <cell alignment="center" valignment="top" usebox="none">
15788 \begin_layout Plain Layout
15796 <cell alignment="center" valignment="top" usebox="none">
15799 \begin_layout Plain Layout
15800 \begin_inset Formula $\oiint$
15809 <row bottomspace="1mm">
15810 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15813 \begin_layout Plain Layout
15821 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15824 \begin_layout Plain Layout
15825 \begin_inset Formula $\sqiint$
15839 \begin_inset space \hfill{}
15843 \begin_inset Tabular
15844 <lyxtabular version="3" rows="4" columns="2">
15845 <features booktabs="true" tabularvalignment="middle">
15846 <column alignment="center" valignment="top" width="0pt">
15847 <column alignment="center" valignment="top" width="0pt">
15849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15852 \begin_layout Plain Layout
15858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15861 \begin_layout Plain Layout
15868 <row bottomspace="1mm">
15869 <cell alignment="center" valignment="top" usebox="none">
15872 \begin_layout Plain Layout
15880 <cell alignment="center" valignment="top" usebox="none">
15883 \begin_layout Plain Layout
15884 \begin_inset Formula $\iiint$
15893 <row bottomspace="1mm">
15894 <cell alignment="center" valignment="top" usebox="none">
15897 \begin_layout Plain Layout
15905 <cell alignment="center" valignment="top" usebox="none">
15908 \begin_layout Plain Layout
15909 \begin_inset Formula $\iiiint$
15918 <row bottomspace="1mm">
15919 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15922 \begin_layout Plain Layout
15930 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15933 \begin_layout Plain Layout
15934 \begin_inset Formula $\dotsint$
15948 \begin_inset space \hfill{}
15954 \begin_layout Subsection
15956 \begin_inset CommandInset label
15958 name "subsec:Operator-Limits"
15963 \begin_inset Index idx
15966 \begin_layout Plain Layout
15975 \begin_layout Standard
15976 Limits are created by super- and subscripts:
15977 \begin_inset Separator latexpar
15983 \begin_layout Standard
15985 \begin_inset Tabular
15986 <lyxtabular version="3" rows="2" columns="2">
15987 <features booktabs="true" tabularvalignment="middle">
15988 <column alignment="center" valignment="top" width="0pt">
15989 <column alignment="center" valignment="top" width="0pt">
15991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15994 \begin_layout Plain Layout
16000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16003 \begin_layout Plain Layout
16011 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16014 \begin_layout Plain Layout
16020 \begin_inset space \textvisiblespace{}
16024 \begin_inset Formula $\to$
16028 \begin_inset Formula $\to$
16036 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16039 \begin_layout Plain Layout
16040 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
16056 \begin_layout Standard
16057 Limits of inline formulas are set right beside the operator.
16058 Limits in displayed formulas are set above or below the operator, except
16059 for integral limits.
16062 \begin_layout Standard
16063 To force that the limits are set beside the operator, the cursor is set
16064 directly behind the operator and the limits type is changed with the menu
16067 Edit\SpecialChar menuseparator
16068 Math\SpecialChar menuseparator
16087 \begin_layout Standard
16088 The default limits type is this:
16089 \begin_inset Formula
16091 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16096 This is how it looks when the limits type was changed to
16103 \begin_inset Formula
16105 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16110 For integrals, except those ending with
16126 etc., the limits are by default set beside the operator.
16127 But for multiple integrals the limits are often set below the operator.
16128 In the following example the limits type was therefore set to
16132 and so set below the integrals:
16133 \begin_inset Formula
16135 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16143 \begin_layout Standard
16144 \begin_inset VSpace medskip
16147 To specify conditions for limits, the commands
16154 \begin_inset Index idx
16157 \begin_layout Plain Layout
16172 \begin_inset Index idx
16175 \begin_layout Plain Layout
16184 To create for example this expression
16185 \begin_inset Formula
16187 \sum_{\begin{subarray}{c}
16191 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16199 \begin_layout Standard
16200 the following has to be done:
16201 \begin_inset Newline newline
16213 \begin_inset space \textvisiblespace{}
16219 One is now in a blue box under the summation operator and insert there
16225 \begin_inset space \textvisiblespace{}
16231 The blue box is now within a purple box and now several lines can be written
16233 A new line is created by inserting a line break (
16236 arg "newline-insert newline"
16241 \begin_inset Newline newline
16246 0<k<1000 Ctrl+Return
16247 \begin_inset Newline newline
16252 is typed in, a new box appears below for the new line.
16255 \begin_layout Standard
16256 The alignment of the lines can be changed to left aligned with the
16266 Edit\SpecialChar menuseparator
16270 To get right alignment,
16275 \begin_inset space \textvisiblespace{}
16280 is inserted at the beginning of the line.
16283 \begin_layout Standard
16296 with the difference that the lines are always centered.
16299 \begin_layout Standard
16300 \begin_inset VSpace bigskip
16304 \begin_inset CommandInset ref
16306 reference "eq:substack"
16310 there can be too much space beside an operator, because the characters
16311 following the operator are set beside the limits.
16312 To avoid this the command
16319 \begin_inset Index idx
16322 \begin_layout Plain Layout
16331 To activate it, set in the document settings under
16334 \begin_inset space ~
16344 \begin_inset Index idx
16347 \begin_layout Plain Layout
16348 Packages ! mathtools
16356 \begin_inset space ~
16368 sets the space besides the operator to 0
16369 \begin_inset space \thinspace{}
16373 \begin_inset Newline newline
16377 \begin_inset CommandInset ref
16379 reference "eq:substack"
16383 , one uses the command
16386 \begin_layout Standard
16394 \begin_layout Standard
16395 and inserts the operator with its limits into the braces.
16396 Behind the brace one continues the formula:
16397 \begin_inset Formula
16399 \smashoperator{\sum_{\begin{subarray}{c}
16403 \end{subarray}}^{n}}k^{-2}
16411 \begin_layout Standard
16412 It is possible to set the space of only one side of the operator to 0
16413 \begin_inset space \thinspace{}
16417 To do this write either
16436 stands for the left and
16440 for the right side of the operator.
16441 Here is an example of the possible
16450 \begin_layout Standard
16451 \begin_inset Formula
16453 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}
16461 \begin_layout Standard
16462 \begin_inset VSpace bigskip
16468 \begin_layout Standard
16469 When several consecutive operators have limits the typesetting of the limits
16470 looks often imperfect in the output, see this example:
16471 \begin_inset Formula
16473 \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}
16478 To improve the typesetting set in the document settings under
16481 \begin_inset space ~
16491 \begin_inset Index idx
16494 \begin_layout Plain Layout
16495 Packages ! mathtools
16503 \begin_inset space ~
16509 Then insert into your formula the command
16516 \begin_inset Index idx
16519 \begin_layout Plain Layout
16527 directly before the first operator.
16528 The example will then look like this:
16529 \begin_inset Formula
16531 \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}
16539 \begin_layout Standard
16540 \begin_inset VSpace bigskip
16543 How to use one limit for several operators is described in
16544 \begin_inset CommandInset ref
16546 reference "subsec:Self-defined-Operators"
16553 \begin_layout Subsection
16554 Decoration for Operators
16555 \begin_inset Index idx
16558 \begin_layout Plain Layout
16559 Operators ! Decoration
16567 \begin_layout Standard
16575 \begin_inset Index idx
16578 \begin_layout Plain Layout
16593 \begin_inset Index idx
16596 \begin_layout Plain Layout
16604 characters can be placed above or below an operator, respectively.
16612 \begin_inset Index idx
16615 \begin_layout Plain Layout
16623 characters can be set before and behind a big operator.
16626 \begin_layout Standard
16628 \begin_inset space ~
16640 \begin_layout Itemize
16647 is used to set characters at the corners of the operator
16650 \begin_layout Itemize
16657 is used to set characters before and/or behind the operator (this variant
16658 represents \SpecialChar LaTeX
16668 \begin_layout Itemize
16675 is used to set characters at the left corners and/or behind the operator
16678 \begin_layout Itemize
16685 is used to set characters at the right corners and/or before the operator
16688 \begin_layout Standard
16689 For example the command
16694 \begin_inset space \textvisiblespace{}
16700 \begin_inset space \textvisiblespace{}
16704 \begin_inset Formula $\to$
16708 \begin_inset Formula $\to$
16712 \begin_inset space \textvisiblespace{}
16722 \begin_inset Formula
16724 \sideset{}{'}\sum_{k=1}^{n}
16732 \begin_layout Standard
16733 \begin_inset Note Greyedout
16736 \begin_layout Plain Layout
16743 can only be used to decorate big operators, binary operators are not allowed.
16751 \begin_layout Standard
16764 can also be used to decorate symbols and characters.
16765 For example, the command
16770 \begin_inset space \textvisiblespace{}
16776 \begin_inset space \textvisiblespace{}
16782 \begin_inset Formula $\uparrow$
16790 \begin_inset Formula
16792 \overset{a}{\maltese}
16800 \begin_layout Subsection
16802 \begin_inset CommandInset label
16804 name "subsec:Binary-Operators"
16809 \begin_inset Index idx
16812 \begin_layout Plain Layout
16821 \begin_layout Standard
16822 Binary operators are surrounded by space when there is a character before
16824 \begin_inset VSpace medskip
16830 \begin_layout Standard
16831 \begin_inset Tabular
16832 <lyxtabular version="3" rows="13" columns="2">
16833 <features booktabs="true" tabularvalignment="middle">
16834 <column alignment="center" valignment="top" width="0pt">
16835 <column alignment="center" valignment="top" width="0pt">
16837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16840 \begin_layout Plain Layout
16842 \begin_inset Note Note
16845 \begin_layout Plain Layout
16852 is only used as spacer.
16862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16865 \begin_layout Plain Layout
16873 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16876 \begin_layout Plain Layout
16882 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16885 \begin_layout Plain Layout
16886 \begin_inset Formula $+$
16896 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16899 \begin_layout Plain Layout
16905 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16908 \begin_layout Plain Layout
16909 \begin_inset Formula $-$
16919 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16922 \begin_layout Plain Layout
16930 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16933 \begin_layout Plain Layout
16934 \begin_inset Formula $\pm$
16944 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16947 \begin_layout Plain Layout
16955 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16958 \begin_layout Plain Layout
16959 \begin_inset Formula $\mp$
16969 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16972 \begin_layout Plain Layout
16980 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16983 \begin_layout Plain Layout
16984 \begin_inset Formula $\cdot$
16994 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16997 \begin_layout Plain Layout
17005 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17008 \begin_layout Plain Layout
17009 \begin_inset Formula $\times$
17019 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17022 \begin_layout Plain Layout
17030 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17033 \begin_layout Plain Layout
17034 \begin_inset Formula $\div$
17044 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17047 \begin_layout Plain Layout
17051 \begin_layout Plain Layout
17064 \begin_layout Plain Layout
17076 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17079 \begin_layout Plain Layout
17080 \begin_inset Formula $*$
17090 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17093 \begin_layout Plain Layout
17101 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17104 \begin_layout Plain Layout
17105 \begin_inset Formula $\star$
17115 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17118 \begin_layout Plain Layout
17126 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17129 \begin_layout Plain Layout
17130 \begin_inset Formula $\circ$
17140 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17143 \begin_layout Plain Layout
17151 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17154 \begin_layout Plain Layout
17155 \begin_inset Formula $\diamond$
17165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17168 \begin_layout Plain Layout
17176 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17179 \begin_layout Plain Layout
17180 \begin_inset Formula $\bullet$
17194 \begin_inset space \hfill{}
17198 \begin_inset Tabular
17199 <lyxtabular version="3" rows="13" columns="2">
17200 <features booktabs="true" tabularvalignment="middle">
17201 <column alignment="center" valignment="top" width="0pt">
17202 <column alignment="center" valignment="top" width="0pt">
17204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17207 \begin_layout Plain Layout
17213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17216 \begin_layout Plain Layout
17224 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17227 \begin_layout Plain Layout
17235 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17238 \begin_layout Plain Layout
17239 \begin_inset Formula $\nabla$
17249 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17252 \begin_layout Plain Layout
17260 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17263 \begin_layout Plain Layout
17264 \begin_inset Formula $\bigtriangledown$
17274 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17277 \begin_layout Plain Layout
17285 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17288 \begin_layout Plain Layout
17289 \begin_inset Formula $\bigtriangleup$
17299 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17302 \begin_layout Plain Layout
17310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17313 \begin_layout Plain Layout
17314 \begin_inset Formula $\Box$
17324 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17327 \begin_layout Plain Layout
17335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17338 \begin_layout Plain Layout
17339 \begin_inset Formula $\cap$
17349 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17352 \begin_layout Plain Layout
17360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17363 \begin_layout Plain Layout
17364 \begin_inset Formula $\cup$
17374 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17377 \begin_layout Plain Layout
17385 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17388 \begin_layout Plain Layout
17389 \begin_inset Formula $\dagger$
17399 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17402 \begin_layout Plain Layout
17410 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17413 \begin_layout Plain Layout
17414 \begin_inset Formula $\ddagger$
17424 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17427 \begin_layout Plain Layout
17435 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17438 \begin_layout Plain Layout
17439 \begin_inset Formula $\wr$
17449 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17452 \begin_layout Plain Layout
17460 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17463 \begin_layout Plain Layout
17464 \begin_inset Formula $\bigcirc$
17474 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17477 \begin_layout Plain Layout
17485 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17488 \begin_layout Plain Layout
17489 \begin_inset Formula $\wedge$
17499 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17502 \begin_layout Plain Layout
17510 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17513 \begin_layout Plain Layout
17514 \begin_inset Formula $\vee$
17528 \begin_inset space \hfill{}
17532 \begin_inset Tabular
17533 <lyxtabular version="3" rows="13" columns="2">
17534 <features booktabs="true" tabularvalignment="middle">
17535 <column alignment="center" valignment="top" width="0pt">
17536 <column alignment="center" valignment="top" width="0pt">
17538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17541 \begin_layout Plain Layout
17547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17550 \begin_layout Plain Layout
17558 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17561 \begin_layout Plain Layout
17569 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17572 \begin_layout Plain Layout
17573 \begin_inset Formula $\oplus$
17583 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17586 \begin_layout Plain Layout
17594 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17597 \begin_layout Plain Layout
17598 \begin_inset Formula $\ominus$
17608 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17611 \begin_layout Plain Layout
17619 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17622 \begin_layout Plain Layout
17623 \begin_inset Formula $\otimes$
17633 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17636 \begin_layout Plain Layout
17644 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17647 \begin_layout Plain Layout
17648 \begin_inset Formula $\oslash$
17658 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17661 \begin_layout Plain Layout
17669 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17672 \begin_layout Plain Layout
17673 \begin_inset Formula $\odot$
17683 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17686 \begin_layout Plain Layout
17694 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17697 \begin_layout Plain Layout
17698 \begin_inset Formula $\amalg$
17708 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17711 \begin_layout Plain Layout
17719 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17722 \begin_layout Plain Layout
17723 \begin_inset Formula $\uplus$
17733 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17736 \begin_layout Plain Layout
17744 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17747 \begin_layout Plain Layout
17748 \begin_inset Formula $\setminus$
17758 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17761 \begin_layout Plain Layout
17769 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17772 \begin_layout Plain Layout
17773 \begin_inset Formula $\sqcap$
17783 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17786 \begin_layout Plain Layout
17794 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17797 \begin_layout Plain Layout
17798 \begin_inset Formula $\sqcup$
17808 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17811 \begin_layout Plain Layout
17819 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17822 \begin_layout Plain Layout
17823 \begin_inset Formula $\triangleleft$
17833 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17836 \begin_layout Plain Layout
17844 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17847 \begin_layout Plain Layout
17848 \begin_inset Formula $\triangleright$
17864 \begin_layout Standard
17865 All binary operators can also be inserted via the math toolbar button
17868 arg "math-insert \\pm"
17874 \begin_layout Standard
17875 To typeset the Laplace operator also
17892 \begin_inset Formula $\nabla^{2}$
17895 ) can be used instead of
17904 \begin_layout Standard
17911 Insert\SpecialChar menuseparator
17923 \begin_layout Subsection
17924 Self-defined Operators
17925 \begin_inset CommandInset label
17927 name "subsec:Self-defined-Operators"
17932 \begin_inset Index idx
17935 \begin_layout Plain Layout
17936 Operators ! self-defined
17944 \begin_layout Standard
17945 With the help of the command
17949 DeclareMathOperator
17952 \begin_inset Index idx
17955 \begin_layout Plain Layout
17960 DeclareMathOperator
17965 custom operators can be defined in the \SpecialChar LaTeX
17967 Its command scheme is:
17970 \begin_layout Standard
17975 DeclareMathOperator{new command}{display}
17978 \begin_layout Standard
17979 Display can be characters or symbols that define how the operator looks
17981 To define a big operator a * is set behind the command.
17982 All self-defined big operators can have limits as described in
17983 \begin_inset CommandInset ref
17985 reference "subsec:Operator-Limits"
17992 \begin_layout Standard
17993 For example the \SpecialChar LaTeX
17997 \begin_layout Standard
18002 DeclareMathOperator*{
18009 \begin_layout Standard
18010 defines the command
18016 , that inserts a big operator consisting of the lozenge symbol from
18017 \begin_inset CommandInset ref
18019 reference "subsec:Miscellaneous-Symbols"
18024 \begin_inset Formula
18026 \Lozenge_{n=1}^{\infty}
18031 The command for this formula is:
18042 \begin_inset Formula $\to$
18048 \begin_layout Standard
18049 \begin_inset VSpace bigskip
18052 When self-defined operators are not used several times in the document,
18053 they can also be defined with the commands
18060 \begin_inset Index idx
18063 \begin_layout Plain Layout
18078 \begin_inset Index idx
18081 \begin_layout Plain Layout
18089 , which have the following scheme:
18092 \begin_layout Standard
18106 \begin_layout Standard
18113 defines big operators,
18122 \begin_layout Standard
18130 \begin_inset space \thinspace{}
18134 \begin_inset space \space{}
18137 be used to use one limit for several operators:
18140 \begin_layout Standard
18141 \begin_inset Formula
18143 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18151 \begin_layout Standard
18152 The command for the formula above is:
18153 \begin_inset Newline newline
18169 \begin_inset space \textvisiblespace{}
18175 \begin_inset Formula $\to$
18181 \begin_inset space \textvisiblespace{}
18189 \begin_layout Section
18191 \begin_inset Index idx
18194 \begin_layout Plain Layout
18203 \begin_layout Subsection
18205 \begin_inset CommandInset label
18207 name "subsec:Font-Styles"
18212 \begin_inset Index idx
18215 \begin_layout Plain Layout
18224 \begin_layout Standard
18225 Latin letters in formulas can be set in one of the following font styles:
18228 \begin_layout Standard
18230 \begin_inset space \hfill{}
18234 \begin_inset Tabular
18235 <lyxtabular version="3" rows="6" columns="2">
18236 <features booktabs="true" tabularvalignment="middle">
18237 <column alignment="center" valignment="top" width="0pt">
18238 <column alignment="center" valignment="top">
18240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18243 \begin_layout Plain Layout
18249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18252 \begin_layout Plain Layout
18260 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18263 \begin_layout Plain Layout
18269 \begin_inset space \textvisiblespace{}
18279 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18282 \begin_layout Plain Layout
18283 \begin_inset Formula $\mathbb{ABC}$
18293 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18296 \begin_layout Plain Layout
18302 \begin_inset space \textvisiblespace{}
18312 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18315 \begin_layout Plain Layout
18316 \begin_inset Formula $\mathbf{AbC}$
18326 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18329 \begin_layout Plain Layout
18335 \begin_inset space \textvisiblespace{}
18345 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18348 \begin_layout Plain Layout
18349 \begin_inset Formula $\boldsymbol{AbC}$
18359 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18362 \begin_layout Plain Layout
18368 \begin_inset space \textvisiblespace{}
18378 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18381 \begin_layout Plain Layout
18382 \begin_inset Formula $\mathcal{ABC}$
18392 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18395 \begin_layout Plain Layout
18401 \begin_inset space \textvisiblespace{}
18411 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18414 \begin_layout Plain Layout
18415 \begin_inset Formula $\mathfrak{AbC}$
18429 \begin_inset space \hfill{}
18433 \begin_inset Tabular
18434 <lyxtabular version="3" rows="6" columns="2">
18435 <features booktabs="true" tabularvalignment="middle">
18436 <column alignment="center" valignment="top" width="0pt">
18437 <column alignment="center" valignment="top">
18439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18442 \begin_layout Plain Layout
18448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18451 \begin_layout Plain Layout
18459 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18462 \begin_layout Plain Layout
18468 \begin_inset space \textvisiblespace{}
18478 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18481 \begin_layout Plain Layout
18482 \begin_inset Formula $\mathit{AbC}$
18492 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18495 \begin_layout Plain Layout
18501 \begin_inset space \textvisiblespace{}
18511 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18514 \begin_layout Plain Layout
18515 \begin_inset Formula $\mathrm{AbC}$
18525 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18528 \begin_layout Plain Layout
18534 \begin_inset space \textvisiblespace{}
18544 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18547 \begin_layout Plain Layout
18548 \begin_inset Formula $\mathsf{AbC}$
18558 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18561 \begin_layout Plain Layout
18567 \begin_inset space \textvisiblespace{}
18577 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18580 \begin_layout Plain Layout
18581 \begin_inset Formula $\mathtt{AbC}$
18591 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18594 \begin_layout Plain Layout
18600 \begin_inset space \textvisiblespace{}
18610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18613 \begin_layout Plain Layout
18614 \begin_inset Formula $\mathscr{ABC}$
18628 \begin_inset space \hfill{}
18634 \begin_layout Standard
18635 \begin_inset Note Greyedout
18638 \begin_layout Plain Layout
18661 can only be used for big letters.
18669 \begin_layout Standard
18670 Predefined is the style
18679 \begin_layout Standard
18680 The style commands work also for letters in mathematical constructs:
18681 \begin_inset Formula
18683 \mathfrak{A=\frac{b}{C}}
18691 \begin_layout Standard
18692 Characters in mathematical text don't appear in a math font style but in
18693 the text font style
18700 That their style can't be set correctly via the text style dialog is a
18701 bug in \SpecialChar LyX
18706 \begin_layout Plain Layout
18707 \begin_inset CommandInset href
18709 name "LyX-bug #4629"
18710 target "http://www.lyx.org/trac/ticket/4629"
18722 \begin_layout Standard
18723 Instead of the style commands the dialog
18725 Edit\SpecialChar menuseparator
18726 Math\SpecialChar menuseparator
18729 or the toolbar button
18732 arg "math-insert \\font"
18738 \begin_layout Subsection
18740 \begin_inset CommandInset label
18742 name "subsec:Bold-Formulas"
18747 \begin_inset Index idx
18750 \begin_layout Plain Layout
18759 \begin_layout Standard
18760 To make a complete formula bold, the command
18766 from the previous subsection cannot be used, because it doesn't work for
18767 small Greek letters.
18768 Furthermore it prints Latin letters always upright, like in the following
18772 \begin_layout Standard
18773 \begin_inset Formula
18775 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18783 \begin_layout Standard
18784 To display the formula correctly, the command
18791 \begin_inset Formula
18793 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18798 It is also possible to set the formula in a
18800 boldmath environment
18803 This environment is created by inserting the command
18810 \begin_inset Index idx
18813 \begin_layout Plain Layout
18821 in \SpecialChar TeX
18823 To end the environment, the command
18830 \begin_inset Index idx
18833 \begin_layout Plain Layout
18841 is inserted in \SpecialChar TeX
18846 \begin_layout Plain Layout
18856 \begin_inset Formula
18858 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18867 \begin_layout Plain Layout
18879 \begin_layout Subsection
18881 \begin_inset Index idx
18884 \begin_layout Plain Layout
18893 \begin_layout Standard
18894 Formulas can be colored like normal text: Highlight a formula or a formula
18900 Here is a formula in magenta:
18901 \begin_inset Formula
18903 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18911 \begin_layout Standard
18912 You can also define your own colors as described in
18913 \begin_inset CommandInset ref
18915 reference "subsec:Colored-Boxes"
18920 They can be used with the \SpecialChar TeX
18928 \begin_inset Index idx
18931 \begin_layout Plain Layout
18942 \begin_layout Standard
18947 textcolor{color}{characters or formula}
18950 \begin_layout Standard
18951 The following example was colored completely dark green and partly red:
18954 \begin_layout Standard
18958 \begin_layout Plain Layout
18962 textcolor{darkgreen}{
18968 \begin_inset Formula
18970 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
18979 \begin_layout Plain Layout
18989 \begin_layout Standard
18990 Due to a bug in \SpecialChar LyX
18991 only complete formulas can be colored with self-defined
18996 \begin_layout Plain Layout
18997 \begin_inset CommandInset href
18999 name "LyX-bug #5269"
19000 target "http://www.lyx.org/trac/ticket/5269"
19012 \begin_layout Subsection
19014 \begin_inset CommandInset label
19016 name "subsec:Font-Sizes"
19021 \begin_inset Index idx
19024 \begin_layout Plain Layout
19033 \begin_layout Standard
19034 For characters in formulas there are, analog to characters in text, the
19035 following size commands:
19038 \begin_layout Standard
19082 \begin_inset Newline newline
19104 \begin_layout Standard
19105 The size produced by the commands depends on the document font size, which
19106 corresponds to the command
19113 The other commands produce smaller or larger sizes than
19120 The font size can however not exceed a certain value.
19121 Is for example the document font size 12
19122 \begin_inset space \thinspace{}
19131 switches to the same size as
19141 \begin_layout Standard
19142 A size command is inserted in \SpecialChar TeX
19143 mode before the formula and sets the size
19144 for all following formula and text characters.
19145 To switch back to the initial size, the command
19151 is inserted behind the formula in \SpecialChar TeX
19155 \begin_layout Standard
19156 Within a formula the size can be changed using the following size commands
19157 or the toolbar button
19160 arg "math-insert \\style"
19164 \begin_inset Separator latexpar
19170 \begin_layout Standard
19173 \begin_inset Tabular
19174 <lyxtabular version="3" rows="5" columns="2">
19175 <features booktabs="true" tabularvalignment="middle">
19176 <column alignment="center" valignment="top" width="0pt">
19177 <column alignment="center" valignment="top">
19179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19182 \begin_layout Plain Layout
19188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19191 \begin_layout Plain Layout
19199 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19202 \begin_layout Plain Layout
19206 \begin_inset Index idx
19209 \begin_layout Plain Layout
19222 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19225 \begin_layout Plain Layout
19226 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19235 <row topspace="1mm">
19236 <cell alignment="center" valignment="top" usebox="none">
19239 \begin_layout Plain Layout
19247 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19250 \begin_layout Plain Layout
19251 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19261 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19264 \begin_layout Plain Layout
19272 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19275 \begin_layout Plain Layout
19276 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19286 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19289 \begin_layout Plain Layout
19297 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19300 \begin_layout Plain Layout
19301 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19317 \begin_layout Standard
19318 After entering these commands, a blue box appears in which the formula parts
19322 \begin_layout Standard
19323 There is a further method to change the font size, that though only works
19324 for symbols or letters in mathematical text.
19325 To use it, one of the above text size commands is inserted in mathematical
19327 All following characters until the end of the mathematical text or until
19328 another size command will have the selected size.
19330 \begin_inset VSpace -2mm
19336 \begin_layout Standard
19340 \begin_layout Plain Layout
19350 \begin_inset Formula
19352 A=\frac{B}{c}\cdot\maltese
19358 \begin_inset Formula
19360 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19369 \begin_layout Plain Layout
19381 \begin_layout Standard
19382 \begin_inset VSpace medskip
19385 Before both formulas the command
19392 The command for the second formula is:
19393 \begin_inset Newline newline
19401 \begin_inset space \textvisiblespace{}
19407 \begin_inset space \textvisiblespace{}
19413 \begin_inset space \textvisiblespace{}
19419 \begin_inset space \textvisiblespace{}
19423 \begin_inset Formula $\to$
19427 \begin_inset Formula $\to$
19431 \begin_inset Newline newline
19435 \begin_inset space \hspace*{}
19446 \begin_inset space \textvisiblespace{}
19452 \begin_inset space \textvisiblespace{}
19458 \begin_inset space \textvisiblespace{}
19464 \begin_layout Standard
19465 If a symbol cannot be displayed in different sizes, it will always be displayed
19466 in the default size.
19469 \begin_layout Section
19471 \begin_inset Index idx
19474 \begin_layout Plain Layout
19483 \begin_layout Standard
19484 Greek letters can also be inserted via the toolbar button
19487 arg "math-insert \\alpha"
19491 All international typesetting norms purport that Greek letters in math
19492 have to be typeset italic/slanted.
19493 In some languages, like French or Russian, they are nevertheless sometimes
19497 \begin_layout Subsection
19499 \begin_inset Index idx
19502 \begin_layout Plain Layout
19503 Greek letters ! small
19511 \begin_layout Standard
19512 \begin_inset space \hfill{}
19516 \begin_inset Tabular
19517 <lyxtabular version="3" rows="11" columns="2">
19518 <features booktabs="true" tabularvalignment="middle">
19519 <column alignment="center" valignment="top" width="0pt">
19520 <column alignment="center" valignment="top" width="0pt">
19522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19525 \begin_layout Plain Layout
19531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19534 \begin_layout Plain Layout
19542 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19545 \begin_layout Plain Layout
19553 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19556 \begin_layout Plain Layout
19557 \begin_inset Formula $\alpha$
19567 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19570 \begin_layout Plain Layout
19578 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19581 \begin_layout Plain Layout
19582 \begin_inset Formula $\beta$
19592 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19595 \begin_layout Plain Layout
19603 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19606 \begin_layout Plain Layout
19607 \begin_inset Formula $\gamma$
19617 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19620 \begin_layout Plain Layout
19628 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19631 \begin_layout Plain Layout
19632 \begin_inset Formula $\delta$
19642 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19645 \begin_layout Plain Layout
19653 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19656 \begin_layout Plain Layout
19657 \begin_inset Formula $\epsilon$
19667 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19670 \begin_layout Plain Layout
19678 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19681 \begin_layout Plain Layout
19682 \begin_inset Formula $\varepsilon$
19692 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19695 \begin_layout Plain Layout
19703 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19706 \begin_layout Plain Layout
19707 \begin_inset Formula $\zeta$
19717 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19720 \begin_layout Plain Layout
19728 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19731 \begin_layout Plain Layout
19732 \begin_inset Formula $\eta$
19742 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19745 \begin_layout Plain Layout
19753 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19756 \begin_layout Plain Layout
19757 \begin_inset Formula $\theta$
19767 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19770 \begin_layout Plain Layout
19778 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19781 \begin_layout Plain Layout
19782 \begin_inset Formula $\vartheta$
19796 \begin_inset space \hfill{}
19800 \begin_inset Tabular
19801 <lyxtabular version="3" rows="12" columns="2">
19802 <features booktabs="true" tabularvalignment="middle">
19803 <column alignment="center" valignment="top" width="0pt">
19804 <column alignment="center" valignment="top" width="0pt">
19806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19809 \begin_layout Plain Layout
19815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19818 \begin_layout Plain Layout
19826 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19829 \begin_layout Plain Layout
19837 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19840 \begin_layout Plain Layout
19841 \begin_inset Formula $\iota$
19851 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19854 \begin_layout Plain Layout
19862 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19865 \begin_layout Plain Layout
19866 \begin_inset Formula $\kappa$
19876 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19879 \begin_layout Plain Layout
19887 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19890 \begin_layout Plain Layout
19891 \begin_inset Formula $\varkappa$
19901 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19904 \begin_layout Plain Layout
19912 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19915 \begin_layout Plain Layout
19916 \begin_inset Formula $\lambda$
19926 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19929 \begin_layout Plain Layout
19937 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19940 \begin_layout Plain Layout
19941 \begin_inset Formula $\mu$
19951 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19954 \begin_layout Plain Layout
19962 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19965 \begin_layout Plain Layout
19966 \begin_inset Formula $\nu$
19976 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19979 \begin_layout Plain Layout
19987 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19990 \begin_layout Plain Layout
19991 \begin_inset Formula $\xi$
20001 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20004 \begin_layout Plain Layout
20010 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20013 \begin_layout Plain Layout
20014 \begin_inset Formula $o$
20024 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20027 \begin_layout Plain Layout
20035 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20038 \begin_layout Plain Layout
20039 \begin_inset Formula $\pi$
20049 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20052 \begin_layout Plain Layout
20060 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20063 \begin_layout Plain Layout
20064 \begin_inset Formula $\varpi$
20074 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20077 \begin_layout Plain Layout
20085 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20088 \begin_layout Plain Layout
20089 \begin_inset Formula $\rho$
20103 \begin_inset space \hfill{}
20107 \begin_inset Tabular
20108 <lyxtabular version="3" rows="11" columns="2">
20109 <features booktabs="true" tabularvalignment="middle">
20110 <column alignment="center" valignment="top" width="0pt">
20111 <column alignment="center" valignment="top" width="0pt">
20113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20116 \begin_layout Plain Layout
20122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20125 \begin_layout Plain Layout
20133 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20136 \begin_layout Plain Layout
20144 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20147 \begin_layout Plain Layout
20148 \begin_inset Formula $\varrho$
20158 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20161 \begin_layout Plain Layout
20169 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20172 \begin_layout Plain Layout
20173 \begin_inset Formula $\sigma$
20183 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20186 \begin_layout Plain Layout
20194 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20197 \begin_layout Plain Layout
20198 \begin_inset Formula $\varsigma$
20208 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20211 \begin_layout Plain Layout
20219 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20222 \begin_layout Plain Layout
20223 \begin_inset Formula $\tau$
20233 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20236 \begin_layout Plain Layout
20244 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20247 \begin_layout Plain Layout
20248 \begin_inset Formula $\upsilon$
20258 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20261 \begin_layout Plain Layout
20269 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20272 \begin_layout Plain Layout
20273 \begin_inset Formula $\phi$
20283 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20286 \begin_layout Plain Layout
20294 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20297 \begin_layout Plain Layout
20298 \begin_inset Formula $\varphi$
20308 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20311 \begin_layout Plain Layout
20319 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20322 \begin_layout Plain Layout
20323 \begin_inset Formula $\chi$
20333 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20336 \begin_layout Plain Layout
20344 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20347 \begin_layout Plain Layout
20348 \begin_inset Formula $\psi$
20358 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20361 \begin_layout Plain Layout
20369 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20372 \begin_layout Plain Layout
20373 \begin_inset Formula $\omega$
20387 \begin_inset space \hfill{}
20393 \begin_layout Standard
20394 \begin_inset VSpace medskip
20400 \begin_layout Standard
20401 How to create special upright Greek letters is explained in
20402 \begin_inset CommandInset ref
20404 reference "subsec:Upright-small-Greek"
20411 \begin_layout Subsection
20413 \begin_inset Index idx
20416 \begin_layout Plain Layout
20417 Greek letters ! big
20425 \begin_layout Standard
20426 \begin_inset space \hfill{}
20430 \begin_inset Tabular
20431 <lyxtabular version="3" rows="7" columns="2">
20432 <features booktabs="true" tabularvalignment="middle">
20433 <column alignment="center" valignment="top" width="0pt">
20434 <column alignment="center" valignment="top" width="0pt">
20436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20439 \begin_layout Plain Layout
20445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20448 \begin_layout Plain Layout
20456 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20459 \begin_layout Plain Layout
20467 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20470 \begin_layout Plain Layout
20471 \begin_inset Formula $\Gamma$
20481 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20484 \begin_layout Plain Layout
20492 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20495 \begin_layout Plain Layout
20496 \begin_inset Formula $\Delta$
20506 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20509 \begin_layout Plain Layout
20517 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20520 \begin_layout Plain Layout
20521 \begin_inset Formula $\Theta$
20531 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20534 \begin_layout Plain Layout
20542 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20545 \begin_layout Plain Layout
20546 \begin_inset Formula $\Lambda$
20556 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20559 \begin_layout Plain Layout
20567 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20570 \begin_layout Plain Layout
20571 \begin_inset Formula $\Xi$
20581 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20584 \begin_layout Plain Layout
20592 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20595 \begin_layout Plain Layout
20596 \begin_inset Formula $\Pi$
20610 \begin_inset space \hfill{}
20614 \begin_inset Tabular
20615 <lyxtabular version="3" rows="6" columns="2">
20616 <features booktabs="true" tabularvalignment="middle">
20617 <column alignment="center" valignment="top" width="0pt">
20618 <column alignment="center" valignment="top" width="0pt">
20620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20623 \begin_layout Plain Layout
20629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20632 \begin_layout Plain Layout
20640 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20643 \begin_layout Plain Layout
20651 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20654 \begin_layout Plain Layout
20655 \begin_inset Formula $\Sigma$
20665 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20668 \begin_layout Plain Layout
20676 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20679 \begin_layout Plain Layout
20680 \begin_inset Formula $\Upsilon$
20690 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20693 \begin_layout Plain Layout
20701 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20704 \begin_layout Plain Layout
20705 \begin_inset Formula $\Phi$
20715 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20718 \begin_layout Plain Layout
20726 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20729 \begin_layout Plain Layout
20730 \begin_inset Formula $\Psi$
20740 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20743 \begin_layout Plain Layout
20751 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20754 \begin_layout Plain Layout
20755 \begin_inset Formula $\Omega$
20769 \begin_inset space \hfill{}
20775 \begin_layout Standard
20776 \begin_inset VSpace medskip
20779 That the big Greek letters appear upright is caused by a design bug when
20782 To get correct italic big letters, begin every command with
20787 For example the command
20794 \begin_inset Formula $\varGamma$
20798 Another way is to load the package
20806 \begin_layout Plain Layout
20811 is part of the \SpecialChar LaTeX
20817 \begin_inset Index idx
20820 \begin_layout Plain Layout
20825 \begin_layout Plain Layout
20845 \begin_inset Index idx
20848 \begin_layout Plain Layout
20854 with the \SpecialChar LaTeX
20858 \begin_layout Standard
20863 usepackage{fixmath}
20866 \begin_layout Standard
20867 Then all big Greek letters in a document will automatically be typeset italic.
20870 \begin_layout Subsection
20872 \begin_inset Index idx
20875 \begin_layout Plain Layout
20876 Greek letters ! bold
20884 \begin_layout Standard
20885 Greek letters cannot be set with different font styles like Latin letters.
20886 They can only be made bold with the command
20893 \begin_inset Index idx
20896 \begin_layout Plain Layout
20905 \begin_inset Separator latexpar
20911 \begin_layout Standard
20913 \begin_inset Tabular
20914 <lyxtabular version="3" rows="3" columns="2">
20915 <features booktabs="true" tabularvalignment="middle">
20916 <column alignment="center" valignment="top" width="0pt">
20917 <column alignment="center" valignment="top">
20919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20922 \begin_layout Plain Layout
20928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20931 \begin_layout Plain Layout
20939 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20942 \begin_layout Plain Layout
20954 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20957 \begin_layout Plain Layout
20958 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20968 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20971 \begin_layout Plain Layout
20983 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20986 \begin_layout Plain Layout
20987 \begin_inset Formula $\theta\boldsymbol{\theta}$
21003 \begin_layout Section
21008 \begin_layout Plain Layout
21021 \begin_layout Plain Layout
21022 A list with all symbols of most of the \SpecialChar LaTeX
21023 -packages can be found in
21024 \begin_inset CommandInset citation
21039 \begin_layout Plain Layout
21047 \begin_inset Note Note
21050 \begin_layout Plain Layout
21053 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21056 \begin_layout Plain Layout
21059 texorpdfstring is in section
21060 \begin_inset CommandInset ref
21062 reference "subsec:Formulas-in-Section"
21072 \begin_inset Index idx
21075 \begin_layout Plain Layout
21084 \begin_layout Standard
21085 Many of the symbols listed in this section can also be inserted via the
21089 arg "math-insert \\nabla"
21095 arg "math-insert \\digamma"
21101 \begin_layout Subsection
21102 Mathematical Symbols
21103 \begin_inset CommandInset label
21105 name "subsec:Mathematical-Symbols"
21110 \begin_inset Index idx
21113 \begin_layout Plain Layout
21114 Symbols ! mathematical
21122 \begin_layout Standard
21123 \begin_inset Tabular
21124 <lyxtabular version="3" rows="10" columns="2">
21125 <features booktabs="true" tabularvalignment="middle">
21126 <column alignment="center" valignment="top" width="0pt">
21127 <column alignment="center" valignment="top" width="0pt">
21129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21132 \begin_layout Plain Layout
21138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21141 \begin_layout Plain Layout
21149 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21152 \begin_layout Plain Layout
21160 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21163 \begin_layout Plain Layout
21164 \begin_inset Formula $\neg$
21174 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21177 \begin_layout Plain Layout
21185 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21188 \begin_layout Plain Layout
21189 \begin_inset Formula $\Im$
21199 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21202 \begin_layout Plain Layout
21210 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21213 \begin_layout Plain Layout
21214 \begin_inset Formula $\Re$
21224 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21227 \begin_layout Plain Layout
21235 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21238 \begin_layout Plain Layout
21239 \begin_inset Formula $\aleph$
21249 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21252 \begin_layout Plain Layout
21260 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21263 \begin_layout Plain Layout
21264 \begin_inset Formula $\partial$
21274 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21277 \begin_layout Plain Layout
21285 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21288 \begin_layout Plain Layout
21289 \begin_inset Formula $\infty$
21299 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21302 \begin_layout Plain Layout
21310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21313 \begin_layout Plain Layout
21314 \begin_inset Formula $\wp$
21324 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21327 \begin_layout Plain Layout
21335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21338 \begin_layout Plain Layout
21339 \begin_inset Formula $\imath$
21349 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21352 \begin_layout Plain Layout
21360 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21363 \begin_layout Plain Layout
21364 \begin_inset Formula $\jmath$
21378 \begin_inset space \hfill{}
21382 \begin_inset Tabular
21383 <lyxtabular version="3" rows="10" columns="2">
21384 <features booktabs="true" tabularvalignment="middle">
21385 <column alignment="center" valignment="top" width="0pt">
21386 <column alignment="center" valignment="top" width="0pt">
21388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21391 \begin_layout Plain Layout
21397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21400 \begin_layout Plain Layout
21402 \begin_inset Note Note
21405 \begin_layout Plain Layout
21412 is only used as spacer.
21424 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21427 \begin_layout Plain Layout
21435 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21438 \begin_layout Plain Layout
21439 \begin_inset Formula $\forall$
21449 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21452 \begin_layout Plain Layout
21460 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21463 \begin_layout Plain Layout
21464 \begin_inset Formula $\exists$
21474 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21477 \begin_layout Plain Layout
21485 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21488 \begin_layout Plain Layout
21489 \begin_inset Formula $\nexists$
21499 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21502 \begin_layout Plain Layout
21510 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21513 \begin_layout Plain Layout
21514 \begin_inset Formula $\emptyset$
21524 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21527 \begin_layout Plain Layout
21535 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21538 \begin_layout Plain Layout
21539 \begin_inset Formula $\varnothing$
21549 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21552 \begin_layout Plain Layout
21560 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21563 \begin_layout Plain Layout
21564 \begin_inset Formula $\dag$
21574 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21577 \begin_layout Plain Layout
21585 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21588 \begin_layout Plain Layout
21589 \begin_inset Formula $\ddag$
21599 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21602 \begin_layout Plain Layout
21610 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21613 \begin_layout Plain Layout
21617 \begin_layout Plain Layout
21627 \begin_inset Formula $\complement$
21634 \begin_layout Plain Layout
21648 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21651 \begin_layout Plain Layout
21659 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21662 \begin_layout Plain Layout
21663 \begin_inset Formula $\Bbbk$
21677 \begin_inset space \hfill{}
21681 \begin_inset Tabular
21682 <lyxtabular version="3" rows="10" columns="2">
21683 <features booktabs="true" tabularvalignment="middle">
21684 <column alignment="center" valignment="top" width="0pt">
21685 <column alignment="center" valignment="top" width="0pt">
21687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21690 \begin_layout Plain Layout
21696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21699 \begin_layout Plain Layout
21707 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21710 \begin_layout Plain Layout
21718 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21721 \begin_layout Plain Layout
21722 \begin_inset Formula $\prime$
21732 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21735 \begin_layout Plain Layout
21743 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21746 \begin_layout Plain Layout
21747 \begin_inset Formula $\backprime$
21757 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21760 \begin_layout Plain Layout
21768 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21771 \begin_layout Plain Layout
21772 \begin_inset Formula $\mho$
21782 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21785 \begin_layout Plain Layout
21793 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21796 \begin_layout Plain Layout
21797 \begin_inset Formula $\triangle$
21807 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21810 \begin_layout Plain Layout
21818 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21821 \begin_layout Plain Layout
21822 \begin_inset Formula $\angle$
21832 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21835 \begin_layout Plain Layout
21843 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21846 \begin_layout Plain Layout
21847 \begin_inset Formula $\measuredangle$
21857 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21860 \begin_layout Plain Layout
21868 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21871 \begin_layout Plain Layout
21872 \begin_inset Formula $\sphericalangle$
21882 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21885 \begin_layout Plain Layout
21893 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21896 \begin_layout Plain Layout
21897 \begin_inset Formula $\top$
21907 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21910 \begin_layout Plain Layout
21918 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21921 \begin_layout Plain Layout
21922 \begin_inset Formula $\bot$
21938 \begin_layout Standard
21939 \begin_inset Newpage newpage
21945 \begin_layout Subsection
21946 Miscellaneous Symbols
21947 \begin_inset CommandInset label
21949 name "subsec:Miscellaneous-Symbols"
21954 \begin_inset Index idx
21957 \begin_layout Plain Layout
21958 Symbols ! miscellaneous
21966 \begin_layout Standard
21969 \begin_inset Tabular
21970 <lyxtabular version="3" rows="10" columns="2">
21971 <features booktabs="true" tabularvalignment="middle">
21972 <column alignment="center" valignment="top" width="0pt">
21973 <column alignment="center" valignment="top" width="0pt">
21975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21978 \begin_layout Plain Layout
21984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21987 \begin_layout Plain Layout
21995 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21998 \begin_layout Plain Layout
22006 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22009 \begin_layout Plain Layout
22010 \begin_inset Formula $\flat$
22020 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22023 \begin_layout Plain Layout
22031 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22034 \begin_layout Plain Layout
22035 \begin_inset Formula $\natural$
22045 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22048 \begin_layout Plain Layout
22056 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22059 \begin_layout Plain Layout
22060 \begin_inset Formula $\sharp$
22070 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22073 \begin_layout Plain Layout
22081 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22084 \begin_layout Plain Layout
22085 \begin_inset Formula $\surd$
22095 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22098 \begin_layout Plain Layout
22106 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22109 \begin_layout Plain Layout
22110 \begin_inset Formula $\checkmark$
22120 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22123 \begin_layout Plain Layout
22131 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22134 \begin_layout Plain Layout
22135 \begin_inset Formula $\yen$
22145 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22148 \begin_layout Plain Layout
22156 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22159 \begin_layout Plain Layout
22160 \begin_inset Formula $\pounds$
22170 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22173 \begin_layout Plain Layout
22179 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22182 \begin_layout Plain Layout
22183 \begin_inset Formula $\$$
22193 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22196 \begin_layout Plain Layout
22202 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22205 \begin_layout Plain Layout
22206 \begin_inset Formula $§$
22220 \begin_inset space \hfill{}
22224 \begin_inset Tabular
22225 <lyxtabular version="3" rows="10" columns="2">
22226 <features booktabs="true" tabularvalignment="middle">
22227 <column alignment="center" valignment="top" width="0pt">
22228 <column alignment="center" valignment="top">
22230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22233 \begin_layout Plain Layout
22239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22242 \begin_layout Plain Layout
22250 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22253 \begin_layout Plain Layout
22261 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22264 \begin_layout Plain Layout
22265 \begin_inset Formula $\hbar$
22275 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22278 \begin_layout Plain Layout
22286 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22289 \begin_layout Plain Layout
22290 \begin_inset Formula $\hslash$
22300 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22303 \begin_layout Plain Layout
22311 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22314 \begin_layout Plain Layout
22315 \begin_inset Formula $\clubsuit$
22325 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22328 \begin_layout Plain Layout
22336 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22339 \begin_layout Plain Layout
22340 \begin_inset Formula $\spadesuit$
22350 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22353 \begin_layout Plain Layout
22361 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22364 \begin_layout Plain Layout
22365 \begin_inset Formula $\bigstar$
22375 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22378 \begin_layout Plain Layout
22386 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22389 \begin_layout Plain Layout
22390 \begin_inset Formula $\blacklozenge$
22400 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22403 \begin_layout Plain Layout
22411 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22414 \begin_layout Plain Layout
22415 \begin_inset Formula $\blacktriangle$
22425 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22428 \begin_layout Plain Layout
22436 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22439 \begin_layout Plain Layout
22440 \begin_inset Formula $\blacktriangledown$
22450 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22453 \begin_layout Plain Layout
22461 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22464 \begin_layout Plain Layout
22465 \begin_inset Formula $\bullet$
22479 \begin_inset space \hfill{}
22483 \begin_inset Tabular
22484 <lyxtabular version="3" rows="10" columns="2">
22485 <features booktabs="true" tabularvalignment="middle">
22486 <column alignment="center" valignment="top" width="0pt">
22487 <column alignment="center" valignment="top" width="0pt">
22489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22492 \begin_layout Plain Layout
22498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22501 \begin_layout Plain Layout
22509 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22512 \begin_layout Plain Layout
22520 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22523 \begin_layout Plain Layout
22524 \begin_inset Formula $\diamondsuit$
22534 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22537 \begin_layout Plain Layout
22545 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22548 \begin_layout Plain Layout
22549 \begin_inset Formula $\Diamond$
22559 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22562 \begin_layout Plain Layout
22570 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22573 \begin_layout Plain Layout
22574 \begin_inset Formula $\heartsuit$
22584 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22587 \begin_layout Plain Layout
22595 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22598 \begin_layout Plain Layout
22599 \begin_inset Formula $\P$
22609 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22612 \begin_layout Plain Layout
22620 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22623 \begin_layout Plain Layout
22624 \begin_inset Formula $\copyright$
22634 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22637 \begin_layout Plain Layout
22645 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22648 \begin_layout Plain Layout
22649 \begin_inset Formula $\circledR$
22659 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22662 \begin_layout Plain Layout
22670 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22673 \begin_layout Plain Layout
22674 \begin_inset Formula $\maltese$
22684 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22687 \begin_layout Plain Layout
22695 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22698 \begin_layout Plain Layout
22699 \begin_inset Formula $\diagup$
22709 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22712 \begin_layout Plain Layout
22720 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22723 \begin_layout Plain Layout
22724 \begin_inset Formula $\diagdown$
22740 \begin_layout Standard
22741 \begin_inset VSpace medskip
22747 \begin_layout Standard
22748 Some symbols can be displayed in different sizes, see
22749 \begin_inset CommandInset ref
22751 reference "subsec:Font-Sizes"
22758 \begin_layout Subsection
22760 \begin_inset Index idx
22763 \begin_layout Plain Layout
22764 Symbols ! Euro-symbol
22770 \begin_inset Index idx
22773 \begin_layout Plain Layout
22780 \begin_layout Plain Layout
22797 \begin_layout Standard
22798 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22804 \begin_inset Index idx
22807 \begin_layout Plain Layout
22813 must be installed and loaded with the \SpecialChar LaTeX
22817 \begin_layout Standard
22822 usepackage[gennarrow]{eurosym}
22825 \begin_layout Standard
22826 The Euro symbol can now be inserted with the command
22833 \begin_inset Index idx
22836 \begin_layout Plain Layout
22847 \begin_layout Standard
22848 The Euro symbol can directly be inserted with the € key in mathematical
22849 text, without having
22864 can also be inserted in \SpecialChar TeX
22866 The official currency symbol can then be inserted with the command
22873 \begin_inset Index idx
22876 \begin_layout Plain Layout
22884 , that is only available in \SpecialChar TeX
22888 \begin_layout Standard
22892 \begin_layout Plain Layout
22902 \begin_inset Note Note
22905 \begin_layout Plain Layout
22906 The following table will only be displayed when the \SpecialChar LaTeX
22919 \begin_layout Standard
22920 An overview about the different Euro symbols:
22921 \begin_inset Separator latexpar
22927 \begin_layout Standard
22929 \begin_inset Tabular
22930 <lyxtabular version="3" rows="4" columns="3">
22931 <features booktabs="true" tabularvalignment="middle">
22932 <column alignment="center" valignment="top" width="0pt">
22933 <column alignment="center" valignment="top" width="0pt">
22934 <column alignment="center" valignment="top" width="0pt">
22936 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22939 \begin_layout Plain Layout
22943 \begin_layout Plain Layout
22947 cmidrule[0.08em]{2-3}
22957 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22960 \begin_layout Plain Layout
22966 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22969 \begin_layout Plain Layout
22977 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22980 \begin_layout Plain Layout
22986 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22989 \begin_layout Plain Layout
22997 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23000 \begin_layout Plain Layout
23001 \begin_inset Formula $\euro$
23011 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23014 \begin_layout Plain Layout
23020 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23023 \begin_layout Plain Layout
23029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23032 \begin_layout Plain Layout
23033 \begin_inset Formula $\mbox{€}$
23043 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23046 \begin_layout Plain Layout
23053 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23056 \begin_layout Plain Layout
23064 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23067 \begin_layout Plain Layout
23071 \begin_layout Plain Layout
23091 \begin_inset Note Note
23094 \begin_layout Plain Layout
23101 is used here only for table borders.
23111 manual for details.
23119 \begin_layout Standard
23123 \begin_layout Plain Layout
23133 \begin_inset Note Note
23136 \begin_layout Plain Layout
23137 The following will be displayed when the \SpecialChar LaTeX
23150 \begin_layout Standard
23151 You need to install the \SpecialChar LaTeX
23156 to see the rest of this subsection in the output.
23159 \begin_layout Standard
23163 \begin_layout Plain Layout
23175 \begin_layout Standard
23176 \begin_inset Newpage newpage
23182 \begin_layout Section
23184 \begin_inset CommandInset label
23186 name "sec:Relations"
23191 \begin_inset Index idx
23194 \begin_layout Plain Layout
23201 \begin_inset Index idx
23204 \begin_layout Plain Layout
23209 \begin_layout Plain Layout
23220 \begin_layout Plain Layout
23235 \begin_layout Standard
23236 All following relations can also be inserted via the toolbar button
23239 arg "math-insert \\leq"
23245 \begin_layout Standard
23246 \begin_inset Tabular
23247 <lyxtabular version="3" rows="17" columns="2">
23248 <features booktabs="true" tabularvalignment="middle">
23249 <column alignment="center" valignment="top" width="0pt">
23250 <column alignment="center" valignment="top" width="0pt">
23252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23255 \begin_layout Plain Layout
23261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23264 \begin_layout Plain Layout
23272 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23275 \begin_layout Plain Layout
23281 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23284 \begin_layout Plain Layout
23285 \begin_inset Formula $<$
23295 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23298 \begin_layout Plain Layout
23306 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23309 \begin_layout Plain Layout
23310 \begin_inset Formula $\le$
23320 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23323 \begin_layout Plain Layout
23331 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23334 \begin_layout Plain Layout
23335 \begin_inset Formula $\ll$
23345 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23348 \begin_layout Plain Layout
23356 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23359 \begin_layout Plain Layout
23360 \begin_inset Formula $\prec$
23370 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23373 \begin_layout Plain Layout
23381 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23384 \begin_layout Plain Layout
23385 \begin_inset Formula $\preceq$
23395 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23398 \begin_layout Plain Layout
23406 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23409 \begin_layout Plain Layout
23410 \begin_inset Formula $\subset$
23420 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23423 \begin_layout Plain Layout
23431 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23434 \begin_layout Plain Layout
23435 \begin_inset Formula $\subseteq$
23445 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23448 \begin_layout Plain Layout
23456 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23459 \begin_layout Plain Layout
23460 \begin_inset Formula $\sqsubseteq$
23470 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23473 \begin_layout Plain Layout
23481 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23484 \begin_layout Plain Layout
23485 \begin_inset Formula $\in$
23495 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23498 \begin_layout Plain Layout
23506 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23509 \begin_layout Plain Layout
23510 \begin_inset Formula $\vdash$
23520 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23523 \begin_layout Plain Layout
23531 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23534 \begin_layout Plain Layout
23535 \begin_inset Formula $\smile$
23545 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23548 \begin_layout Plain Layout
23556 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23559 \begin_layout Plain Layout
23560 \begin_inset Formula $\lhd$
23570 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23573 \begin_layout Plain Layout
23581 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23584 \begin_layout Plain Layout
23585 \begin_inset Formula $\unlhd$
23595 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23598 \begin_layout Plain Layout
23606 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23609 \begin_layout Plain Layout
23610 \begin_inset Formula $\gtrless$
23620 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23623 \begin_layout Plain Layout
23631 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23634 \begin_layout Plain Layout
23635 \begin_inset Formula $\mid$
23645 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23648 \begin_layout Plain Layout
23656 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23659 \begin_layout Plain Layout
23660 \begin_inset Formula $\nmid$
23674 \begin_inset space \hfill{}
23678 \begin_inset Tabular
23679 <lyxtabular version="3" rows="17" columns="2">
23680 <features booktabs="true" tabularvalignment="middle">
23681 <column alignment="center" valignment="top" width="0pt">
23682 <column alignment="center" valignment="top" width="0pt">
23684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23687 \begin_layout Plain Layout
23693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23696 \begin_layout Plain Layout
23704 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23707 \begin_layout Plain Layout
23713 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23716 \begin_layout Plain Layout
23717 \begin_inset Formula $=$
23727 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23730 \begin_layout Plain Layout
23738 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23741 \begin_layout Plain Layout
23742 \begin_inset Formula $\not=$
23752 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23755 \begin_layout Plain Layout
23763 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23766 \begin_layout Plain Layout
23767 \begin_inset Formula $\equiv$
23777 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23780 \begin_layout Plain Layout
23788 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23791 \begin_layout Plain Layout
23792 \begin_inset Formula $\sim$
23802 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23805 \begin_layout Plain Layout
23813 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23816 \begin_layout Plain Layout
23817 \begin_inset Formula $\simeq$
23827 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23830 \begin_layout Plain Layout
23838 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23841 \begin_layout Plain Layout
23842 \begin_inset Formula $\approx$
23852 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23855 \begin_layout Plain Layout
23863 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23866 \begin_layout Plain Layout
23867 \begin_inset Formula $\cong$
23877 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23880 \begin_layout Plain Layout
23888 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23891 \begin_layout Plain Layout
23892 \begin_inset Formula $\bowtie$
23902 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23905 \begin_layout Plain Layout
23913 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23916 \begin_layout Plain Layout
23917 \begin_inset Formula $\notin$
23927 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23930 \begin_layout Plain Layout
23938 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23941 \begin_layout Plain Layout
23942 \begin_inset Formula $\perp$
23952 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23955 \begin_layout Plain Layout
23963 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23966 \begin_layout Plain Layout
23967 \begin_inset Formula $\propto$
23977 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23980 \begin_layout Plain Layout
23988 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23991 \begin_layout Plain Layout
23992 \begin_inset Formula $\asymp$
24002 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24005 \begin_layout Plain Layout
24013 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24016 \begin_layout Plain Layout
24017 \begin_inset Formula $\doteq$
24027 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24030 \begin_layout Plain Layout
24038 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24041 \begin_layout Plain Layout
24042 \begin_inset Formula $\circeq$
24052 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24055 \begin_layout Plain Layout
24063 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24066 \begin_layout Plain Layout
24067 \begin_inset Formula $\models$
24077 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24080 \begin_layout Plain Layout
24088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24091 \begin_layout Plain Layout
24092 \begin_inset Formula $\widehat{=}$
24106 \begin_inset space \hfill{}
24110 \begin_inset Tabular
24111 <lyxtabular version="3" rows="17" columns="2">
24112 <features booktabs="true" tabularvalignment="middle">
24113 <column alignment="center" valignment="top" width="0pt">
24114 <column alignment="center" valignment="top" width="0pt">
24116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24119 \begin_layout Plain Layout
24125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24128 \begin_layout Plain Layout
24136 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24139 \begin_layout Plain Layout
24145 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24148 \begin_layout Plain Layout
24149 \begin_inset Formula $>$
24159 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24162 \begin_layout Plain Layout
24170 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24173 \begin_layout Plain Layout
24174 \begin_inset Formula $\ge$
24184 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24187 \begin_layout Plain Layout
24195 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24198 \begin_layout Plain Layout
24199 \begin_inset Formula $\gg$
24209 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24212 \begin_layout Plain Layout
24220 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24223 \begin_layout Plain Layout
24224 \begin_inset Formula $\succ$
24234 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24237 \begin_layout Plain Layout
24245 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24248 \begin_layout Plain Layout
24249 \begin_inset Formula $\succeq$
24259 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24262 \begin_layout Plain Layout
24270 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24273 \begin_layout Plain Layout
24274 \begin_inset Formula $\supset$
24284 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24287 \begin_layout Plain Layout
24295 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24298 \begin_layout Plain Layout
24299 \begin_inset Formula $\supseteq$
24309 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24312 \begin_layout Plain Layout
24320 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24323 \begin_layout Plain Layout
24324 \begin_inset Formula $\sqsupseteq$
24334 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24337 \begin_layout Plain Layout
24345 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24348 \begin_layout Plain Layout
24349 \begin_inset Formula $\ni$
24359 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24362 \begin_layout Plain Layout
24370 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24373 \begin_layout Plain Layout
24374 \begin_inset Formula $\dashv$
24384 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24387 \begin_layout Plain Layout
24395 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24398 \begin_layout Plain Layout
24399 \begin_inset Formula $\frown$
24409 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24412 \begin_layout Plain Layout
24420 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24423 \begin_layout Plain Layout
24424 \begin_inset Formula $\rhd$
24434 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24437 \begin_layout Plain Layout
24445 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24448 \begin_layout Plain Layout
24449 \begin_inset Formula $\unrhd$
24459 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24462 \begin_layout Plain Layout
24470 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24473 \begin_layout Plain Layout
24474 \begin_inset Formula $\lessgtr$
24484 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24487 \begin_layout Plain Layout
24495 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24498 \begin_layout Plain Layout
24499 \begin_inset Formula $\parallel$
24509 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24512 \begin_layout Plain Layout
24520 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24523 \begin_layout Plain Layout
24524 \begin_inset Formula $\nparallel$
24540 \begin_layout Standard
24541 \begin_inset VSpace medskip
24556 are bigger than the equal looking operators
24571 \begin_layout Standard
24573 supports also many special relations.
24574 Use the toolbar button
24577 arg "math-insert \\leqq"
24580 to see a list of these relations.
24583 \begin_layout Standard
24584 Relations are, in contrary to symbols, always surrounded by space.
24587 \begin_layout Standard
24588 Relations with labels can be created with the command
24595 \begin_inset Index idx
24598 \begin_layout Plain Layout
24607 \begin_inset Separator latexpar
24613 \begin_layout Standard
24615 \begin_inset Tabular
24616 <lyxtabular version="3" rows="2" columns="2">
24617 <features booktabs="true" tabularvalignment="middle">
24618 <column alignment="center" valignment="top" width="0pt">
24619 <column alignment="center" valignment="top">
24621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24624 \begin_layout Plain Layout
24630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24633 \begin_layout Plain Layout
24640 <row topspace="1.5mm">
24641 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24644 \begin_layout Plain Layout
24648 \begin_inset space \textvisiblespace{}
24656 \begin_inset space \textvisiblespace{}
24660 \begin_inset Formula $\downarrow$
24666 \begin_inset space \textvisiblespace{}
24670 \begin_inset space \textvisiblespace{}
24678 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24681 \begin_layout Plain Layout
24682 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24698 \begin_layout Section
24702 \begin_layout Subsection
24703 Predefined Functions
24704 \begin_inset CommandInset label
24706 name "subsec:Predefined-Functions"
24711 \begin_inset Index idx
24714 \begin_layout Plain Layout
24715 Functions ! predefined
24723 \begin_layout Standard
24724 In general, variables are set
24728 in mathematical expressions, but not function names, because
24729 \begin_inset Formula $sin$
24732 could be misunderstood as
24733 \begin_inset Formula $s\cdot i\cdot n$
24737 Therefore there are predefined functionswhich are additionally a bit separated
24739 They are inserted as commands starting with a backslash before their name.
24740 \begin_inset Separator latexpar
24746 \begin_layout Standard
24748 \begin_inset Tabular
24749 <lyxtabular version="3" rows="2" columns="2">
24750 <features booktabs="true" tabularvalignment="middle">
24751 <column alignment="center" valignment="top" width="0pt">
24752 <column alignment="center" valignment="top" width="0pt">
24754 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24757 \begin_layout Plain Layout
24763 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24766 \begin_layout Plain Layout
24774 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24777 \begin_layout Plain Layout
24783 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24786 \begin_layout Plain Layout
24787 \begin_inset Formula $Asin(x)+B$
24801 \begin_inset space \quad{}
24805 \begin_inset Tabular
24806 <lyxtabular version="3" rows="2" columns="2">
24807 <features booktabs="true" tabularvalignment="middle">
24808 <column alignment="center" valignment="top" width="0pt">
24809 <column alignment="center" valignment="top" width="0pt">
24811 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24814 \begin_layout Plain Layout
24820 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24823 \begin_layout Plain Layout
24831 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24834 \begin_layout Plain Layout
24842 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24845 \begin_layout Plain Layout
24846 \begin_inset Formula $A\sin(x)+B$
24862 \begin_layout Standard
24863 The following functions are predefined:
24866 \begin_layout Standard
24867 \begin_inset VSpace -2mm
24873 \begin_layout Standard
24875 \begin_inset Tabular
24876 <lyxtabular version="3" rows="9" columns="4">
24877 <features booktabs="true" tabularvalignment="middle">
24878 <column alignment="center" valignment="top" width="0pt">
24879 <column alignment="center" valignment="top" width="0pt">
24880 <column alignment="center" valignment="top" width="0pt">
24881 <column alignment="center" valignment="top" width="0pt">
24883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24886 \begin_layout Plain Layout
24892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24895 \begin_layout Plain Layout
24901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24904 \begin_layout Plain Layout
24910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24913 \begin_layout Plain Layout
24921 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24924 \begin_layout Plain Layout
24932 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24935 \begin_layout Plain Layout
24943 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24946 \begin_layout Plain Layout
24954 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24957 \begin_layout Plain Layout
24967 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24970 \begin_layout Plain Layout
24978 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24981 \begin_layout Plain Layout
24989 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24992 \begin_layout Plain Layout
25000 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25003 \begin_layout Plain Layout
25013 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25016 \begin_layout Plain Layout
25024 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25027 \begin_layout Plain Layout
25035 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25038 \begin_layout Plain Layout
25046 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25049 \begin_layout Plain Layout
25059 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25062 \begin_layout Plain Layout
25070 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25073 \begin_layout Plain Layout
25081 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25084 \begin_layout Plain Layout
25092 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25095 \begin_layout Plain Layout
25105 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25108 \begin_layout Plain Layout
25116 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25119 \begin_layout Plain Layout
25127 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25130 \begin_layout Plain Layout
25138 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25141 \begin_layout Plain Layout
25151 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25154 \begin_layout Plain Layout
25162 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25165 \begin_layout Plain Layout
25173 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25176 \begin_layout Plain Layout
25184 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25187 \begin_layout Plain Layout
25197 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25200 \begin_layout Plain Layout
25208 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25211 \begin_layout Plain Layout
25219 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25222 \begin_layout Plain Layout
25230 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25233 \begin_layout Plain Layout
25243 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25246 \begin_layout Plain Layout
25254 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25257 \begin_layout Plain Layout
25265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25268 \begin_layout Plain Layout
25276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25279 \begin_layout Plain Layout
25295 \begin_layout Standard
25296 They can also be inserted with the math toolbar button
25299 arg "math-insert \\functions"
25305 \begin_layout Subsection
25306 Self-defined Functions
25307 \begin_inset Index idx
25310 \begin_layout Plain Layout
25311 Functions ! self-defined
25319 \begin_layout Standard
25320 To use a function that is not predefined, like for example the sign function
25321 sgn(x), there are two possibilities:
25324 \begin_layout Itemize
25325 Define the function by inserting the following line to the \SpecialChar LaTeX
25330 \begin_layout Plain Layout
25335 DeclareMathOperator
25338 \begin_inset CommandInset ref
25340 reference "subsec:Self-defined-Operators"
25350 \begin_inset Newline newline
25354 \begin_inset VSpace -3mm
25358 \begin_inset Newline newline
25365 DeclareMathOperator{
25370 \begin_inset Index idx
25373 \begin_layout Plain Layout
25378 DeclareMathOperator
25384 \begin_inset Newline newline
25388 \begin_inset VSpace -2mm
25392 \begin_inset Newline newline
25395 Now the new defined function can be called with the command
25404 \begin_layout Itemize
25405 Write the formula as usual, mark the formula name, in our example the letters
25410 , and change it to mathematical text.
25411 Finally, a space is inserted between prefactor and function.
25414 \begin_layout Standard
25415 The result is the same with both methods as with a predefined function
25419 \begin_layout Plain Layout
25420 In \SpecialChar LyX
25421 self-defined functions are displayed red, predefined ones black.
25427 \begin_inset Separator latexpar
25433 \begin_layout Standard
25435 \begin_inset Tabular
25436 <lyxtabular version="3" rows="3" columns="2">
25437 <features booktabs="true" tabularvalignment="middle">
25438 <column alignment="center" valignment="top" width="0pt">
25439 <column alignment="center" valignment="top" width="0pt">
25441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25444 \begin_layout Plain Layout
25450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25453 \begin_layout Plain Layout
25461 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25464 \begin_layout Plain Layout
25472 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25475 \begin_layout Plain Layout
25476 \begin_inset Formula $A\sgn(x)+B$
25486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25489 \begin_layout Plain Layout
25493 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25504 \begin_layout Plain Layout
25505 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25521 \begin_layout Standard
25522 The first method is more suitable when the self-defined function should
25523 be used several times.
25526 \begin_layout Subsection
25528 \begin_inset Index idx
25531 \begin_layout Plain Layout
25540 \begin_layout Standard
25541 For limits, in addition to the commands
25548 \begin_inset Index idx
25551 \begin_layout Plain Layout
25571 the following functions are defined:
25572 \begin_inset Separator latexpar
25578 \begin_layout Standard
25580 \begin_inset Tabular
25581 <lyxtabular version="3" rows="5" columns="2">
25582 <features booktabs="true" tabularvalignment="middle">
25583 <column alignment="center" valignment="top" width="0pt">
25584 <column alignment="center" valignment="top" width="0pt">
25586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25589 \begin_layout Plain Layout
25595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25598 \begin_layout Plain Layout
25606 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25609 \begin_layout Plain Layout
25617 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25620 \begin_layout Plain Layout
25621 \begin_inset Formula $\varliminf$
25630 <row topspace="1.5mm">
25631 <cell alignment="center" valignment="top" usebox="none">
25634 \begin_layout Plain Layout
25642 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25645 \begin_layout Plain Layout
25646 \begin_inset Formula $\varlimsup$
25655 <row topspace="1.5mm">
25656 <cell alignment="center" valignment="top" usebox="none">
25659 \begin_layout Plain Layout
25667 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25670 \begin_layout Plain Layout
25671 \begin_inset Formula $\varprojlim$
25680 <row topspace="1.5mm" bottomspace="1mm">
25681 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25684 \begin_layout Plain Layout
25692 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25695 \begin_layout Plain Layout
25696 \begin_inset Formula $\varinjlim$
25712 \begin_layout Standard
25713 \begin_inset VSpace medskip
25716 The limit is created by inserting a subscript.
25717 It is set right beside the function in an inline formula:
25720 \begin_layout Standard
25722 \begin_inset Tabular
25723 <lyxtabular version="3" rows="2" columns="2">
25724 <features booktabs="true" tabularvalignment="middle">
25725 <column alignment="center" valignment="top" width="0pt">
25726 <column alignment="center" valignment="top" width="0pt">
25728 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25731 \begin_layout Plain Layout
25737 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25740 \begin_layout Plain Layout
25748 <cell alignment="center" valignment="top" usebox="none">
25751 \begin_layout Plain Layout
25757 \begin_inset space \textvisiblespace{}
25761 \begin_inset space \textvisiblespace{}
25769 <cell alignment="center" valignment="top" usebox="none">
25772 \begin_layout Plain Layout
25773 \begin_inset Formula $\lim_{x\to A}x=B$
25789 \begin_layout Standard
25790 In a displayed formula the limit is set below the formula, as usual:
25791 \begin_inset Formula
25801 \begin_layout Standard
25802 \begin_inset VSpace medskip
25808 \begin_layout Standard
25809 How to adjust the typesetting of the limits see
25810 \begin_inset CommandInset ref
25812 reference "subsec:Operator-Limits"
25819 \begin_layout Subsection
25821 \begin_inset Index idx
25824 \begin_layout Plain Layout
25825 Functions ! modulo-
25833 \begin_layout Standard
25834 The modulo-function is special, because it exists in four variants.
25835 The variants in a displayed formula are:
25836 \begin_inset Formula
25838 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25839 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25840 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25841 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25842 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25850 \begin_layout Standard
25851 In an inline formula less space is set before the function names for all
25853 By default the modulo-functions take only the first following character
25855 To use more than one character, one has to put them into \SpecialChar TeX
25857 \begin_inset Formula
25859 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25860 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25861 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25869 \begin_layout Section
25871 \begin_inset Index idx
25874 \begin_layout Plain Layout
25883 \begin_layout Standard
25884 The characters ^ and _ would normally create a superscript and subscript,
25886 To get these characters you have to insert them with a leading
25889 \begin_inset Separator latexpar
25895 \begin_layout Standard
25898 \begin_inset Tabular
25899 <lyxtabular version="3" rows="3" columns="2">
25900 <features booktabs="true" tabularvalignment="middle">
25901 <column alignment="left" valignment="top" width="0pt">
25902 <column alignment="block" valignment="top">
25904 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25907 \begin_layout Plain Layout
25913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25916 \begin_layout Plain Layout
25924 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25927 \begin_layout Plain Layout
25931 \begin_inset space \textvisiblespace{}
25939 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25942 \begin_layout Plain Layout
25943 \begin_inset Formula $\mathcircumflex$
25953 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25956 \begin_layout Plain Layout
25964 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25967 \begin_layout Plain Layout
25968 \begin_inset Formula $\_$
25984 \begin_layout Subsection
25985 Special Characters in Mathematical Text
25988 \begin_layout Standard
25989 The following commands can only be used in mathematical text or in \SpecialChar TeX
25993 \begin_layout Standard
25994 \begin_inset space \hfill{}
25998 \begin_inset Tabular
25999 <lyxtabular version="3" rows="8" columns="2">
26000 <features booktabs="true" tabularvalignment="middle">
26001 <column alignment="left" valignment="top" width="0pt">
26002 <column alignment="block" valignment="top">
26004 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26007 \begin_layout Plain Layout
26013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26016 \begin_layout Plain Layout
26024 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26027 \begin_layout Plain Layout
26035 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26038 \begin_layout Plain Layout
26039 \begin_inset Formula $\textrm{œ}$
26049 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26052 \begin_layout Plain Layout
26060 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26063 \begin_layout Plain Layout
26064 \begin_inset Formula $\textrm{Œ}$
26074 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26077 \begin_layout Plain Layout
26085 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26088 \begin_layout Plain Layout
26089 \begin_inset Formula $\textrm{æ}$
26099 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26102 \begin_layout Plain Layout
26110 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26113 \begin_layout Plain Layout
26114 \begin_inset Formula $\textrm{Æ}$
26124 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26127 \begin_layout Plain Layout
26135 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26138 \begin_layout Plain Layout
26139 \begin_inset Formula $\textrm{å}$
26149 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26152 \begin_layout Plain Layout
26156 \begin_inset Index idx
26159 \begin_layout Plain Layout
26166 \begin_layout Plain Layout
26187 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26190 \begin_layout Plain Layout
26191 \begin_inset Formula $\textrm{Å}$
26201 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26204 \begin_layout Plain Layout
26212 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26215 \begin_layout Plain Layout
26216 \begin_inset Formula $\textrm{ı}$
26230 \begin_inset space \hfill{}
26234 \begin_inset Tabular
26235 <lyxtabular version="3" rows="8" columns="2">
26236 <features booktabs="true" tabularvalignment="middle">
26237 <column alignment="left" valignment="top" width="0pt">
26238 <column alignment="center" valignment="top">
26240 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26243 \begin_layout Plain Layout
26245 \begin_inset Note Note
26248 \begin_layout Plain Layout
26250 \begin_inset space \thinspace{}
26253 mm is used for separation, because otherwise the output will be ¡ and ¿
26264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26267 \begin_layout Plain Layout
26275 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26278 \begin_layout Plain Layout
26286 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26289 \begin_layout Plain Layout
26290 \begin_inset Formula $\textrm{ø}$
26300 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26303 \begin_layout Plain Layout
26311 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26314 \begin_layout Plain Layout
26315 \begin_inset Formula $\textrm{Ø}$
26325 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26328 \begin_layout Plain Layout
26336 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26339 \begin_layout Plain Layout
26340 \begin_inset Formula $\textrm{ł}$
26350 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26353 \begin_layout Plain Layout
26361 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26364 \begin_layout Plain Layout
26365 \begin_inset Formula $\textrm{Ł}$
26375 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26378 \begin_layout Plain Layout
26380 \begin_inset space \hspace{}
26385 \begin_inset space \textvisiblespace{}
26393 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26396 \begin_layout Plain Layout
26397 \begin_inset Formula $\textrm{!`}$
26407 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26410 \begin_layout Plain Layout
26412 \begin_inset space \hspace{}
26417 \begin_inset space \textvisiblespace{}
26425 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26428 \begin_layout Plain Layout
26429 \begin_inset Formula $\textrm{?`}$
26439 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26442 \begin_layout Plain Layout
26450 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26453 \begin_layout Plain Layout
26454 \begin_inset Formula $\textrm{ȷ}$
26468 \begin_inset space \hfill{}
26474 \begin_layout Standard
26476 \begin_inset Formula $\textrm{\textrm{Å}}$
26480 \begin_inset Formula $\textrm{\textrm{Ø}}$
26483 can also be inserted via the math toolbar button
26486 arg "math-insert \\digamma"
26492 \begin_layout Standard
26493 An exception are the commands
26496 \begin_inset space \hspace{}
26505 \begin_inset space \hspace{}
26511 , because they can be inserted in \SpecialChar LyX
26515 \begin_layout Subsection
26517 \begin_inset CommandInset label
26519 name "subsec:Accents-in-Text"
26524 \begin_inset Index idx
26527 \begin_layout Plain Layout
26536 \begin_layout Standard
26537 With the following commands all letters can be accented.
26538 The commands must be inserted in \SpecialChar TeX
26542 \begin_layout Standard
26543 \begin_inset space \hfill{}
26547 \begin_inset Tabular
26548 <lyxtabular version="3" rows="8" columns="2">
26549 <features booktabs="true" tabularvalignment="middle">
26550 <column alignment="left" valignment="top" width="0pt">
26551 <column alignment="block" valignment="top">
26553 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26556 \begin_layout Plain Layout
26562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26565 \begin_layout Plain Layout
26573 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26576 \begin_layout Plain Layout
26580 \begin_inset Quotes grd
26588 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26591 \begin_layout Plain Layout
26595 \begin_layout Plain Layout
26611 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26614 \begin_layout Plain Layout
26622 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26625 \begin_layout Plain Layout
26629 \begin_layout Plain Layout
26645 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26648 \begin_layout Plain Layout
26652 \begin_inset space \textvisiblespace{}
26660 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26663 \begin_layout Plain Layout
26667 \begin_layout Plain Layout
26683 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26686 \begin_layout Plain Layout
26694 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26697 \begin_layout Plain Layout
26701 \begin_layout Plain Layout
26717 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26720 \begin_layout Plain Layout
26724 \begin_inset space \textvisiblespace{}
26732 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26735 \begin_layout Plain Layout
26739 \begin_layout Plain Layout
26755 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26758 \begin_layout Plain Layout
26762 \begin_inset space \textvisiblespace{}
26770 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26773 \begin_layout Plain Layout
26777 \begin_layout Plain Layout
26793 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26796 \begin_layout Plain Layout
26800 \begin_inset space \textvisiblespace{}
26808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26811 \begin_layout Plain Layout
26815 \begin_layout Plain Layout
26835 \begin_inset space \hfill{}
26839 \begin_inset Tabular
26840 <lyxtabular version="3" rows="8" columns="2">
26841 <features booktabs="true" tabularvalignment="middle">
26842 <column alignment="left" valignment="top" width="0pt">
26843 <column alignment="center" valignment="top">
26845 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26848 \begin_layout Plain Layout
26854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26857 \begin_layout Plain Layout
26865 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26868 \begin_layout Plain Layout
26872 \begin_inset space \textvisiblespace{}
26880 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26883 \begin_layout Plain Layout
26887 \begin_layout Plain Layout
26903 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26906 \begin_layout Plain Layout
26914 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26917 \begin_layout Plain Layout
26921 \begin_layout Plain Layout
26937 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26940 \begin_layout Plain Layout
26944 \begin_inset Index idx
26947 \begin_layout Plain Layout
26958 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26961 \begin_layout Plain Layout
26965 \begin_layout Plain Layout
26981 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26984 \begin_layout Plain Layout
26992 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26995 \begin_layout Plain Layout
26999 \begin_layout Plain Layout
27015 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27018 \begin_layout Plain Layout
27022 \begin_inset space \textvisiblespace{}
27030 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27033 \begin_layout Plain Layout
27037 \begin_layout Plain Layout
27053 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27056 \begin_layout Plain Layout
27060 \begin_inset space \textvisiblespace{}
27068 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27071 \begin_layout Plain Layout
27075 \begin_layout Plain Layout
27091 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27094 \begin_layout Plain Layout
27098 \begin_inset space \textvisiblespace{}
27106 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27109 \begin_layout Plain Layout
27113 \begin_layout Plain Layout
27133 \begin_inset space \hfill{}
27139 \begin_layout Standard
27140 \begin_inset VSpace medskip
27149 also two different characters can be accented.
27155 \begin_inset space \textvisiblespace{}
27164 \begin_layout Plain Layout
27176 \begin_layout Standard
27189 can in combination with vowels directly be inserted with the keyboard without
27190 using \SpecialChar TeX
27192 The same applies for the tilde
27196 \begin_layout Plain Layout
27197 This only applies for keyboards where the tilde is defined as accent.
27206 in combination with
27221 \begin_layout Standard
27264 and accents that are inserted directly with the keyboard are also available
27265 in mathematical text.
27266 For the other accents there are special math commands to be used in formulas,
27268 \begin_inset CommandInset ref
27270 reference "subsec:Accents-for-one"
27277 \begin_layout Standard
27278 \begin_inset VSpace bigskip
27281 Furthermore, with the command
27288 \begin_inset Index idx
27291 \begin_layout Plain Layout
27299 all numbers and letters can be set into a circle, quasi accented with a
27300 circle, similar to the copyright symbol.
27303 \begin_layout Standard
27305 \begin_inset Tabular
27306 <lyxtabular version="3" rows="3" columns="2">
27307 <features booktabs="true" tabularvalignment="middle">
27308 <column alignment="center" valignment="top" width="0pt">
27309 <column alignment="center" valignment="top">
27311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27314 \begin_layout Plain Layout
27320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27323 \begin_layout Plain Layout
27331 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27334 \begin_layout Plain Layout
27342 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27345 \begin_layout Plain Layout
27349 \begin_layout Plain Layout
27364 <row topspace="1mm">
27365 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27368 \begin_layout Plain Layout
27379 raisebox{-1.5pt}{W}}
27384 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27387 \begin_layout Plain Layout
27391 \begin_layout Plain Layout
27421 \begin_layout Standard
27422 One has to take care that the character fits in the circle.
27433 \begin_layout Plain Layout
27435 \begin_inset CommandInset ref
27437 reference "subsec:Font-Sizes"
27446 specifies thereby the size of the circle.
27457 \begin_layout Plain Layout
27459 \begin_inset CommandInset ref
27461 reference "subsec:Boxes-without-Frame"
27470 the character can be centered.
27473 \begin_layout Subsection
27475 \begin_inset Index idx
27478 \begin_layout Plain Layout
27487 \begin_layout Standard
27488 Old-style figures (also known as old-style numerals) are created with the
27496 \begin_inset Index idx
27499 \begin_layout Plain Layout
27508 The command can be used in formulas and in \SpecialChar TeX
27510 The command scheme is:
27513 \begin_layout Standard
27518 oldstylenums{number}
27521 \begin_layout Standard
27526 oldstylenums{0123456789
27529 \begin_inset Formula $\oldstylenums{0123456789}$
27535 \begin_layout Section
27537 \begin_inset CommandInset label
27539 name "sec:Formula-Styles"
27544 \begin_inset Index idx
27547 \begin_layout Plain Layout
27556 \begin_layout Itemize
27557 There are two different alignment styles:
27558 \begin_inset Separator latexpar
27565 \begin_layout Description
27566 Centered is the predefined standard
27569 \begin_layout Description
27570 Indented for this the option
27574 must be inserted in the menu
27576 Document\SpecialChar menuseparator
27582 \begin_inset space ~
27588 \begin_layout Standard
27593 is used, the indentation can be adjusted with the length
27600 \begin_inset Index idx
27603 \begin_layout Plain Layout
27612 Should the distance be 15
27613 \begin_inset space \thinspace{}
27616 mm, the following command line is inserted in the \SpecialChar LaTeX
27620 \begin_layout Standard
27630 \begin_layout Standard
27631 When no length is specified, the predefined value of 30
27632 \begin_inset space \thinspace{}
27639 \begin_layout Itemize
27640 And two different numbering styles:
27641 \begin_inset Separator latexpar
27648 \begin_layout Description
27649 Right is the predefined standard
27652 \begin_layout Description
27653 Left for this the option
27657 must be inserted in the menu
27659 Document\SpecialChar menuseparator
27665 \begin_inset space ~
27672 \begin_layout Standard
27681 can also be used together.
27682 In this case both options are inserted, separated by a comma.
27685 \begin_layout Standard
27686 The chosen styles are used for all displayed formulas of the document.
27687 When both, centered and indented formulas should be created in a document,
27693 The indented formulas are then set in a flalign environment, see
27694 \begin_inset CommandInset ref
27696 reference "subsec:Flalign-Environment"
27703 \begin_layout Section
27705 \begin_inset CommandInset label
27707 name "sec:Multiline-Formulas"
27712 \begin_inset Index idx
27715 \begin_layout Plain Layout
27716 Formula ! multiline
27724 \begin_layout Subsection
27728 \begin_layout Standard
27729 In \SpecialChar LyX
27730 multiline formulas are created by pressing
27733 arg "newline-insert newline"
27737 This creates either an
27741 that is described in
27742 \begin_inset CommandInset ref
27744 reference "subsec:Standard-align-Environment"
27748 or, when automatically loading the package
27752 is disabled in the document settings, an
27754 eqnarray environment
27756 that is described in
27757 \begin_inset CommandInset ref
27759 reference "subsec:Eqnarray-Environment"
27764 The align environment is recommended because it provides in any case a
27765 typographically correct output.
27768 \begin_layout Standard
27769 There are other multiline formula environments that can be created via the
27772 Insert\SpecialChar menuseparator
27776 These environments are described in the following sections.
27779 \begin_layout Standard
27780 In all multiline formula environments a new line is created by pressing
27784 arg "newline-insert newline"
27788 To add or delete lines, the math toolbar buttons
27791 arg "tabular-feature append-row"
27797 arg "tabular-feature delete-row"
27800 , respectively, or the menu
27802 Edit\SpecialChar menuseparator
27808 \begin_layout Subsubsection
27810 \begin_inset CommandInset label
27812 name "subsec:Line-Separation"
27817 \begin_inset Index idx
27820 \begin_layout Plain Layout
27821 Formula ! multiline ! Line separation
27829 \begin_layout Standard
27830 There is sometimes not enough space in multiline formulas between the lines:
27831 \begin_inset Formula
27833 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}\\
27834 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
27842 \begin_layout Standard
27843 In \SpecialChar LaTeX
27844 additional line space is specified as optional argument of the new line
27846 This is not yet possible in \SpecialChar LyX
27851 \begin_layout Plain Layout
27853 \begin_inset CommandInset href
27855 name "LyX-bug #1505"
27856 target "http://www.lyx.org/trac/ticket/1505"
27865 , therefore the whole formula must be inserted in \SpecialChar TeX
27867 To add in our example space, the command
27875 is inserted at the end of the first line.
27880 \begin_layout Plain Layout
27887 \begin_layout Plain Layout
27889 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27892 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27899 \begin_layout Plain Layout
27903 left(B^{2}+x_{0}^{2}
27911 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27916 \begin_layout Plain Layout
27928 \begin_layout Standard
27929 \begin_inset VSpace bigskip
27932 To set the line separation for all lines in a formula, the length
27939 \begin_inset Index idx
27942 \begin_layout Plain Layout
27952 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27963 \begin_inset space \thinspace{}
27968 \begin_inset space \thinspace{}
27971 mm additional line separation as in the previous example, the command
27974 \begin_layout Standard
27984 \begin_layout Standard
27985 is inserted in \SpecialChar TeX
27986 mode before the formula.
27987 This requires that the \SpecialChar LaTeX
27996 \begin_layout Plain Layout
28001 is part of every \SpecialChar LaTeX
28002 standard installation.
28008 \begin_inset Index idx
28011 \begin_layout Plain Layout
28017 was loaded in \SpecialChar LaTeX
28018 -preamble with the line
28021 \begin_layout Standard
28029 \begin_layout Standard
28034 \begin_layout Plain Layout
28046 \begin_inset Formula
28048 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}\\
28049 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
28057 \begin_layout Standard
28061 \begin_layout Plain Layout
28072 To get back to the predefined distance,
28078 is set to the value 3
28079 \begin_inset space \thinspace{}
28085 \begin_layout Subsubsection
28087 \begin_inset CommandInset label
28089 name "subsec:Column-Separation"
28094 \begin_inset Index idx
28097 \begin_layout Plain Layout
28098 Formula ! multiline ! Column separation
28106 \begin_layout Standard
28107 Multiline formulas form a matrix.
28108 A formula in the eqnarray environment is for example a matrix with three
28110 By changing the column separation in this environment, the space beside
28111 the relation sign can be changed.
28114 \begin_layout Standard
28115 The column separation is specified with the length
28122 \begin_inset Index idx
28125 \begin_layout Plain Layout
28134 \begin_inset Newline newline
28137 column separation = 2
28138 \begin_inset space \thinspace{}
28148 \begin_inset Newline newline
28154 \begin_layout Standard
28164 \begin_layout Standard
28165 inserted in \SpecialChar TeX
28166 mode, sets for all following formulas a column separation of
28168 \begin_inset space \thinspace{}
28172 To get back to the predefined distance,
28179 \begin_inset space \thinspace{}
28185 \begin_layout Standard
28187 \begin_inset space \thinspace{}
28190 cm column separation:
28194 \begin_layout Plain Layout
28206 \begin_inset Formula
28214 A formula with the predefined column separation for matrices of 10
28215 \begin_inset space \thinspace{}
28222 \begin_layout Plain Layout
28234 \begin_inset Formula
28245 \begin_layout Subsubsection
28247 \begin_inset Index idx
28250 \begin_layout Plain Layout
28259 \begin_layout Standard
28260 Long formulas can be typeset using these methods:
28263 \begin_layout Itemize
28264 When one side of the equation is much shorter than the line width, this
28265 one is chosen for the left side and the right side is typeset over two
28267 \begin_inset Formula
28269 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 \\
28270 & & -\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}
28275 The minus sign at the beginning of the second line does normally not appear
28276 as an operator because it is the first character of the line.
28277 Thus it would not be surrounded by space and could not be distinguished
28278 from the fraction bar.
28280 \begin_inset space \thinspace{}
28283 pt space was inserted behind the minus sign with the command
28293 \begin_layout Plain Layout
28301 \begin_inset CommandInset ref
28303 reference "subsec:Variable-Space"
28313 \begin_inset Index idx
28316 \begin_layout Plain Layout
28327 \begin_layout Itemize
28328 When both sides of the equation are too long, the command
28335 \begin_inset Index idx
28338 \begin_layout Plain Layout
28347 It is inserted in the first column of the first line and causes all further
28348 insertions to overwrite the following columns:
28349 \begin_inset Formula
28351 \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 \\
28352 & & -\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 \\
28353 & & =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}
28358 After the insertion of
28364 , the cursor is in a purple box that is a bit shifted to the left from the
28366 In this the formula is inserted.
28367 \begin_inset Newline newline
28370 The content of the further lines is inserted to the second or another formula
28372 The greater the column number where it was inserted, the larger the indentation.
28373 \begin_inset VSpace medskip
28377 \begin_inset Newline newline
28381 \begin_inset Note Greyedout
28384 \begin_layout Plain Layout
28385 Note the following when using
28394 \begin_layout Itemize
28395 The formula doesn't use the full page width.
28397 \begin_inset space \thinspace{}
28401 \begin_inset space \space{}
28405 \begin_inset Formula $-B^{2}$
28408 is added to the first line in the above example, it would have been outside
28410 To better use the width, negative space can be inserted at the beginning
28414 \begin_layout Itemize
28415 Due to a bug in \SpecialChar LyX
28416 the cursor cannot be set with the mouse into the first
28421 \begin_layout Plain Layout
28422 \begin_inset CommandInset href
28424 name "LyX-bug #1429"
28425 target "http://www.lyx.org/trac/ticket/1429"
28434 One can only set the cursor at the beginning of the line and move it with
28443 \begin_layout Itemize
28444 Other methods to set long formulas are offered by the environments described
28446 \begin_inset CommandInset ref
28448 reference "subsec:Multline-Environment"
28453 \begin_inset CommandInset ref
28455 reference "subsec:Multiline-Formula-Parts"
28462 \begin_layout Subsubsection
28463 Multiline Fractions
28464 \begin_inset CommandInset label
28466 name "subsec:Multiline-Fractions"
28471 \begin_inset Index idx
28474 \begin_layout Plain Layout
28475 Fractions ! multiline
28483 \begin_layout Standard
28484 There are cases where the denominator and/or the numerator of a fraction
28485 is so long that the fraction does not fit into one line.
28486 It is then necessary to add a line break within the fraction.
28487 This can be done using the command
28494 \begin_inset Index idx
28497 \begin_layout Plain Layout
28506 To activate it, set in the document settings under
28509 \begin_inset space ~
28519 \begin_inset Index idx
28522 \begin_layout Plain Layout
28523 Packages ! mathtools
28531 \begin_inset space ~
28546 \begin_layout Standard
28551 splitfrac{first line}{second line}
28554 \begin_layout Standard
28555 and is used as denominator and/or numerator:
28558 \begin_layout Standard
28559 \begin_inset Formula
28561 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}
28566 The command for the first numerator above is:
28569 \begin_layout Standard
28574 splitfrac{xy+xy+xy+xy+xy
28575 \begin_inset space \textvisiblespace{}
28583 \begin_layout Subsubsection
28585 \begin_inset CommandInset label
28587 name "subsec:Multiline-Brackets"
28592 \begin_inset Index idx
28595 \begin_layout Plain Layout
28596 Brackets ! for multiline expressions
28604 \begin_layout Standard
28605 For brackets spanning multiple lines the following problem occurs:
28606 \begin_inset Formula
28608 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28609 & & \left.\cdots+B-D\right]
28617 \begin_layout Standard
28618 The closing bracket is smaller than the opening bracket because brackets
28619 with variable size may not span multiple lines.
28622 \begin_layout Standard
28623 To set the bracket size for the second line correctly, the first line is
28631 \begin_inset Index idx
28634 \begin_layout Plain Layout
28642 and the second line with
28650 \begin_layout Plain Layout
28664 \begin_inset CommandInset ref
28666 reference "subsec:Automatic-Bracket-Size"
28678 \begin_inset Index idx
28681 \begin_layout Plain Layout
28704 \begin_inset space \textvisiblespace{}
28714 \begin_inset space \textvisiblespace{}
28724 \begin_inset space \textvisiblespace{}
28730 \begin_inset Formula $\downarrow$
28736 \begin_inset Index idx
28739 \begin_layout Plain Layout
28747 is inserted, because the multiplication operator with its limits is the
28748 largest symbol in the first line and this should be the size for the bracket
28749 in the second line.
28752 \begin_layout Standard
28753 The result is this:
28754 \begin_inset Formula
28756 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28757 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28765 \begin_layout Subsection
28769 \begin_layout Standard
28770 Align environments can be used for every kind of multiline formulas.
28771 They are especially useful to set several formulas side by side.
28774 \begin_layout Standard
28775 Align environments consist of columns.
28776 The odd columns are right aligned, the even ones left aligned.
28777 Every line in an Align environment can be numbered.
28780 \begin_layout Standard
28781 Align environments are created via the menu
28783 Insert\SpecialChar menuseparator
28789 Edit\SpecialChar menuseparator
28790 Math\SpecialChar menuseparator
28791 Change Formula Type
28793 already existing formulas can be converted to Align environments.
28796 \begin_layout Standard
28797 To add or delete columns, the math toolbar buttons
28800 arg "tabular-feature append-column"
28806 arg "tabular-feature delete-column"
28809 , respectively, or the menu
28811 Edit\SpecialChar menuseparator
28817 \begin_layout Subsubsection
28818 Standard align Environment
28819 \begin_inset CommandInset label
28821 name "subsec:Standard-align-Environment"
28826 \begin_inset Index idx
28829 \begin_layout Plain Layout
28830 Formula ! multiline ! align environment
28838 \begin_layout Standard
28839 This Align environment is created by pressing
28842 arg "newline-insert newline"
28845 in a formula or by the menu
28847 Insert\SpecialChar menuseparator
28848 Math\SpecialChar menuseparator
28849 AMS align Environment
28854 \begin_layout Standard
28855 An example for two formulas set side by side, that are created with a four
28856 column align environment:
28857 \begin_inset Formula
28859 A & =\sin(B) & C & =D\\
28860 C & \ne A & B & \ne D
28865 As it can be seen, the formulas in this environment are placed so as if
28874 \begin_layout Plain Layout
28882 \begin_inset CommandInset ref
28884 reference "subsec:Variable-Space"
28895 before the first and after every even column.
28896 When the formula style
28902 \begin_layout Plain Layout
28904 \begin_inset CommandInset ref
28906 reference "sec:Formula-Styles"
28917 is used, the formula is set without the
28923 before the first column.
28926 \begin_layout Subsubsection
28927 Alignat Environment
28928 \begin_inset Index idx
28931 \begin_layout Plain Layout
28932 Formula ! multiline ! alignat environment
28940 \begin_layout Standard
28941 The alignat environment has no predefined column separation.
28942 It can be inserted manually with the spaces that are described
28943 \begin_inset CommandInset ref
28945 reference "subsec:Space"
28952 \begin_layout Standard
28953 The above example in the alignat environment where 1
28954 \begin_inset space \thinspace{}
28957 cm space was inserted at the beginning of the second formula:
28958 \begin_inset Formula
28959 \begin{alignat*}{2}
28960 A & =\sin(B) & \hspace{1cm}C & =D\\
28961 C & \ne A & B & \ne D
28966 Because the column separation can be set separately for every column, this
28967 environment is especially suitable to set three and more formulas side
28971 \begin_layout Subsubsection
28972 Flalign Environment
28973 \begin_inset CommandInset label
28975 name "subsec:Flalign-Environment"
28980 \begin_inset Index idx
28983 \begin_layout Plain Layout
28984 Formula ! multiline ! flalign environment
28992 \begin_layout Standard
28993 In this environment the first two columns are always set as much as possible
28994 to the left and the last two ones to the right.
28996 \begin_inset Formula
28998 A & =1 & B & =2 & C & =3\\
28999 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29007 \begin_layout Standard
29008 By creating a flalign environment with an odd number of columns where an
29009 empty \SpecialChar TeX
29010 brace is inserted to the last column, several formulas in a document
29011 can be set to the left, although the formula style
29016 As example the indented formula
29017 \begin_inset CommandInset ref
29019 reference "eq:VolInt"
29024 \begin_inset Formula
29026 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29031 The first two columns contain the formula.
29032 To indent it as with the formula style
29037 \begin_inset space \thinspace{}
29040 pt space was inserted at the beginning of the first column.
29043 \begin_layout Subsection
29044 Eqnarray Environment
29045 \begin_inset CommandInset label
29047 name "subsec:Eqnarray-Environment"
29052 \begin_inset Index idx
29055 \begin_layout Plain Layout
29056 Formula ! multiline ! eqnarray environment
29064 \begin_layout Standard
29065 When this environment has been created, three blue boxes appear.
29066 The content of the first box is right aligned, the content of the last
29068 The content of the middle box appears centered and a bit smaller, because
29069 it is designed to insert there only relation characters.
29070 \begin_inset Formula
29072 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29082 \begin_layout Subsection
29084 \begin_inset Index idx
29087 \begin_layout Plain Layout
29088 Formula ! multiline ! gather environment
29096 \begin_layout Standard
29097 This environment consists of only one centered column.
29098 Every line can be numbered.
29099 \begin_inset Formula
29110 \begin_layout Subsection
29111 Multline Environment
29112 \begin_inset CommandInset label
29114 name "subsec:Multline-Environment"
29119 \begin_inset Index idx
29122 \begin_layout Plain Layout
29123 Formula ! multiline ! multline environment
29131 \begin_layout Standard
29132 The multline environment consists, like the gather environment, of only
29134 But the first line is left aligned, the last one right aligned.
29135 All other lines are centered.
29136 Therefore this environment is suitable for long formulas.
29138 \begin_inset CommandInset ref
29140 reference "eq:lefteqn"
29144 in the multline environment:
29145 \begin_inset Formula
29147 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}\\
29148 -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}\\
29149 =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}}
29157 \begin_layout Standard
29158 In the output only the last (first) line of a multline environment appears
29159 numbered when the document numbering is right (left).
29163 \begin_layout Plain Layout
29164 numbering styles see
29165 \begin_inset CommandInset ref
29167 reference "sec:Formula-Styles"
29179 \begin_layout Standard
29187 \begin_inset Index idx
29190 \begin_layout Plain Layout
29205 \begin_inset Index idx
29208 \begin_layout Plain Layout
29216 a centered line can be right or left aligned, respectively.
29217 The commands are used as follows:
29220 \begin_layout Standard
29225 shoveright{line content}
29231 shoveleft{line content}
29234 \begin_layout Standard
29235 \begin_inset VSpace medskip
29245 \begin_inset Index idx
29248 \begin_layout Plain Layout
29256 specifies the distance of the first line from the left page margin.
29257 Predefined is the length 0
29258 \begin_inset space \thinspace{}
29264 \begin_layout Standard
29265 As example the above formula where the command
29268 \begin_layout Standard
29278 \begin_layout Standard
29279 was inserted in \SpecialChar TeX
29284 \begin_layout Plain Layout
29296 \begin_inset Formula
29298 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}\\
29299 \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}}\\
29300 =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}}
29309 \begin_layout Plain Layout
29320 The second line was left aligned using
29329 \begin_layout Subsection
29330 Multiline Formula Parts
29331 \begin_inset CommandInset label
29333 name "subsec:Multiline-Formula-Parts"
29338 \begin_inset Index idx
29341 \begin_layout Plain Layout
29342 Formula ! multiline ! formula parts
29350 \begin_layout Standard
29351 To display only parts of a formula with multiple lines, one of the following
29352 environments is used:
29369 They can be inserted via the menu
29371 Insert\SpecialChar menuseparator
29374 or by using the commands described in this section.
29377 \begin_layout Standard
29378 The first three have the same properties as the corresponding multiline
29379 formula environments, but it is possible to set further formula parts beside
29382 \begin_inset Formula
29384 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29385 \Delta E\Delta t & \ge\frac{\hbar}{2}
29387 \right\} \textrm{Uncertainty relations}
29395 \begin_layout Standard
29396 To get this formula, a displayed formula is created where the command
29403 \begin_inset Index idx
29406 \begin_layout Plain Layout
29415 A purple box appears around the blue formula box where now columns and
29416 lines can be added.
29417 Outside the multiline environment other formula parts can be set, like
29421 \begin_layout Standard
29422 The aligned environment is also suitable for long formulas whose lines are
29423 horizontally aligned.
29424 Using aligned in a displayed formula has the advantage that the formula
29425 number is vertically centered behind the lines.
29427 \begin_inset CommandInset ref
29429 reference "eq:shortlong"
29433 in the aligned environment:
29434 \begin_inset Formula
29436 \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}|}\\
29437 & -\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}|}
29446 \begin_layout Standard
29447 To use the environments
29466 \begin_inset Index idx
29469 \begin_layout Plain Layout
29484 \begin_inset Index idx
29487 \begin_layout Plain Layout
29502 \begin_inset Index idx
29505 \begin_layout Plain Layout
29513 are inserted, respectively.
29514 The split environment has the same properties as the aligned environment
29515 but it can only have two columns.
29518 \begin_layout Subsection
29519 Text in multiline Formulas
29520 \begin_inset CommandInset label
29522 name "subsec:Text-in-multiline"
29527 \begin_inset Index idx
29530 \begin_layout Plain Layout
29537 \begin_inset Index idx
29540 \begin_layout Plain Layout
29541 Formula ! multiline ! text
29549 \begin_layout Standard
29550 In the Align environments, and the multline and gather environment, text
29551 can be inserted that will appear in a separate line and doesn't affect
29552 the column alignment.
29553 To do this, the command
29560 \begin_inset Index idx
29563 \begin_layout Plain Layout
29571 is used in the following scheme:
29574 \begin_layout Standard
29582 \begin_layout Standard
29583 The text should not be longer than a line because it cannot be hyphenated.
29584 As \SpecialChar LyX
29585 doesn't yet support
29591 directly, the text is written as mathematical text.
29598 must hereby be at the beginning of a line and appears in the output above
29600 An example where the text was inserted at the beginning of the second line:
29601 \begin_inset Formula
29603 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29604 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29612 \begin_layout Standard
29619 always creates some vertical space between the text and the formula lines.
29620 To avoid this space, set in the document settings under
29623 \begin_inset space ~
29633 \begin_inset Index idx
29636 \begin_layout Plain Layout
29637 Packages ! mathtools
29645 \begin_inset space ~
29651 Then you can use the command
29658 \begin_inset Index idx
29661 \begin_layout Plain Layout
29678 \begin_layout Standard
29679 \begin_inset Formula
29681 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29682 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29690 \begin_layout Section
29692 \begin_inset Index idx
29695 \begin_layout Plain Layout
29702 \begin_inset Index idx
29705 \begin_layout Plain Layout
29706 Formula ! numbering|see
29710 \begin_layout Plain Layout
29721 \begin_layout Plain Layout
29736 \begin_layout Subsection
29740 \begin_layout Standard
29741 Numbered formulas can be created with the menu
29743 Insert\SpecialChar menuseparator
29744 Math\SpecialChar menuseparator
29746 \begin_inset space ~
29754 \begin_inset space ~
29760 Existing formulas can be numbered with the menu
29762 Edit\SpecialChar menuseparator
29763 Math\SpecialChar menuseparator
29765 \begin_inset space ~
29773 arg "math-number-toggle"
29777 The formula number is displayed in \SpecialChar LyX
29778 behind the formula as a number sign
29780 The number sign is replaced in the output by the formula number.
29783 \begin_layout Standard
29784 When numbering is turned on in multiline formulas, all lines will be numbered.
29785 But the numbering can be controlled with the menu
29787 Edit\SpecialChar menuseparator
29788 Math\SpecialChar menuseparator
29790 \begin_inset space ~
29794 \begin_inset space ~
29798 \begin_inset space ~
29806 arg "math-number-line-toggle"
29812 \begin_layout Standard
29813 Except for inline formulas, all formulas can be numbered with two different
29815 \begin_inset CommandInset ref
29817 reference "sec:Formula-Styles"
29824 \begin_layout Subsection
29826 \begin_inset Index idx
29829 \begin_layout Plain Layout
29830 Cross-references ! to formulas
29838 \begin_layout Standard
29839 All labeled formulas can be cross-referenced.
29840 A label is added by the menu
29842 Insert\SpecialChar menuseparator
29845 or the toolbar button
29852 The cursor must hereby be inside a displayed formula.
29853 Alternatively you can right-click on the formula and choose
29858 A dialog pops up displaying the prefix
29863 The label is inserted there behind the prefix.
29864 The predefined prefix means
29865 \begin_inset Quotes eld
29869 \begin_inset Quotes erd
29872 and makes it easier to find labels in large documents because it marks
29873 it as formula label to divide it from e.
29874 \begin_inset space \thinspace{}
29878 \begin_inset space \space{}
29882 To change a label, the menu
29884 Insert\SpecialChar menuseparator
29887 is used again or you right-click on a formula and then on
29894 \begin_layout Standard
29895 The name of the label is displayed in \SpecialChar LyX
29896 within two parentheses behind formula.
29897 A formula with a label is always numbered.
29900 \begin_layout Standard
29901 Cross-references are inserted via the menu
29903 Insert\SpecialChar menuseparator
29906 or with the toolbar button
29909 arg "dialog-show-new-inset ref"
29913 A formula cross-reference appears in the output as formula number.
29914 When in the cross-reference dialog window the format
29918 is chosen, the cross-reference appears in the output as formula number
29920 \begin_inset Newline newline
29923 By right-clicking on a cross-reference in \SpecialChar LyX
29924 , one jumps to the formula that
29928 \begin_layout Standard
29929 Here are as examples cross-references to formulas of the following subsections:
29930 \begin_inset Note Note
29933 \begin_layout Plain Layout
29934 Note the different cross-reference types.
29942 \begin_layout Standard
29944 \begin_inset CommandInset ref
29951 \begin_inset CommandInset ref
29959 \begin_inset CommandInset ref
29965 ) big Latin letters are used for the numbering in contrary to (
29966 \begin_inset CommandInset ref
29975 \begin_layout Standard
29976 \begin_inset VSpace medskip
29979 When the argument of
29987 \begin_layout Plain Layout
29995 \begin_inset CommandInset ref
29997 reference "subsec:User-defined-Numbering"
30008 contains a box like in
30009 \begin_inset CommandInset ref
30011 reference "subsec:Paragraph-Boxes"
30015 , the formula cannot be referenced.
30018 \begin_layout Subsection
30020 \begin_inset Index idx
30023 \begin_layout Plain Layout
30024 Formula numbering ! subnumbering
30032 \begin_layout Standard
30033 With the help of the commands
30037 begin{subequations}
30045 formulas can be subnumbered.
30046 Both commands are inserted in \SpecialChar TeX
30050 \begin_layout Standard
30052 \begin_inset Formula
30063 \begin_layout Plain Layout
30067 begin{subequations}
30073 \begin_inset VSpace -5mm
30077 \begin_inset Formula
30085 \begin_inset Formula
30095 \begin_layout Standard
30099 \begin_layout Plain Layout
30111 \begin_layout Standard
30112 To create the example, the following is done:
30115 \begin_layout Enumerate
30116 first formula is inserted
30119 \begin_layout Enumerate
30124 begin{subequations}
30125 \begin_inset Newline newline
30130 is inserted after the first formula
30133 \begin_layout Enumerate
30134 second formula is inserted
30137 \begin_layout Enumerate
30138 third formula is inserted
30141 \begin_layout Enumerate
30148 is inserted after the third formula
30151 \begin_layout Standard
30152 Every formula between the commands
30164 will be subnumbered with a, b, c, \SpecialChar ldots
30166 For multiline formulas every line will be subnumbered.
30169 \begin_layout Standard
30170 Referencing subequations work like for normal equations:
30171 \begin_inset CommandInset ref
30178 \begin_inset CommandInset ref
30185 If you want to reference the subequations collectively, insert a label
30190 begin{subequations}
30194 \begin_inset CommandInset ref
30196 reference "eq:Here-is-an"
30203 \begin_layout Standard
30204 By inserting commands in \SpecialChar TeX
30205 mode, a space is created between the first two
30208 \begin_inset space \thinspace{}
30211 mm vertical space is inserted after the command
30215 begin{subequations}
30218 When the formula style
30224 \begin_layout Plain Layout
30226 \begin_inset CommandInset ref
30228 reference "sec:Formula-Styles"
30240 \begin_inset space \thinspace{}
30243 mm space is inserted instead.
30246 \begin_layout Standard
30247 To get another subnumber instead of small Latin letters, insert this command
30252 begin{subequations}
30257 \begin_layout Standard
30266 theparentequation -
30271 \begin_layout Standard
30278 creates hereby the parent number and
30284 adds a small Roman number as subnumber.
30285 For more information about the customization of the numbering, see
30286 \begin_inset CommandInset ref
30288 reference "subsec:Numbering-with-Roman"
30295 \begin_layout Standard
30296 Here is an example for a multiline formula where the numbering is customized
30297 and turned off for the second line:
30301 \begin_layout Plain Layout
30305 begin{subequations}
30311 \begin_inset CommandInset label
30313 name "eq:Here-is-an"
30321 \begin_layout Plain Layout
30329 theparentequation -
30337 \begin_inset Formula
30339 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
30340 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30341 & = & B^{2}-2BZ+Z^{2}
30350 \begin_layout Plain Layout
30362 \begin_layout Subsection
30363 User-defined Numbering
30364 \begin_inset CommandInset label
30366 name "subsec:User-defined-Numbering"
30371 \begin_inset Index idx
30374 \begin_layout Plain Layout
30375 Formula numbering ! user-defined
30383 \begin_layout Standard
30384 \begin_inset Index idx
30387 \begin_layout Plain Layout
30388 Formula numbering ! self-defined delimiters
30393 With the standard numbering parentheses are set around the formula number.
30394 To replace the parentheses for example by vertical bars, the following
30395 line is added to the \SpecialChar LaTeX
30399 \begin_layout Standard
30411 \begin_inset Note Note
30414 \begin_layout Plain Layout
30415 This macro is already declared in the \SpecialChar LaTeX
30416 -preamble for testing.
30417 To activate it, remove the percent sign at the beginning.
30425 \begin_layout Standard
30426 To use other characters, the vertical bars besides the
30430 are replaced by one ore more characters.
30431 To get only the formula number the vertical bars are omitted.
30434 \begin_layout Standard
30435 \begin_inset VSpace bigskip
30438 When there should be an expression of your choice instead of the consecutive
30439 formula number in parentheses behind the formula, the command
30446 \begin_inset Index idx
30449 \begin_layout Plain Layout
30458 \begin_inset Formula
30460 A+B=C\tag{something}\label{eq:tag}
30465 In this example the command
30470 \begin_inset space \textvisiblespace{}
30475 was inserted in the formula.
30478 \begin_layout Standard
30484 \begin_inset space \textvisiblespace{}
30489 is inserted instead, the star prevents the parentheses around the expression:
30490 \begin_inset Formula
30492 A+B=C\tag*{something}
30500 \begin_layout Standard
30501 \begin_inset VSpace bigskip
30504 To restart the formula numbering with new document parts or sections, the
30505 following command is used:
30508 \begin_layout Standard
30513 @addtoreset{equation}{part}
30516 \begin_inset Index idx
30519 \begin_layout Plain Layout
30524 \begin_layout Plain Layout
30535 \begin_layout Plain Layout
30548 \begin_layout Plain Layout
30559 \begin_layout Plain Layout
30572 \begin_inset Newline newline
30576 \begin_inset Newline newline
30583 @addtoreset{equation}{section}
30586 \begin_layout Standard
30587 To be able to use these commands in \SpecialChar TeX
30589 \begin_inset Quotes eld
30593 \begin_inset Quotes erd
30596 character has to be made
30597 \begin_inset Quotes eld
30601 \begin_inset Quotes erd
30604 for \SpecialChar LaTeX
30619 So the command sequence in \SpecialChar TeX
30623 \begin_layout Standard
30629 \begin_inset Newline newline
30634 @addtoreset{equation}{section}
30635 \begin_inset Newline newline
30643 \begin_layout Standard
30644 In the \SpecialChar LaTeX
30657 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30661 \begin_layout Standard
30676 \begin_layout Plain Layout
30681 is part of the \SpecialChar LaTeX
30687 \begin_inset Index idx
30690 \begin_layout Plain Layout
30691 Packages ! carlisle
30696 that is part of every \SpecialChar LaTeX
30697 standard installation.
30703 \begin_inset Index idx
30706 \begin_layout Plain Layout
30707 Packages ! remreset
30712 has to be loaded in the \SpecialChar LaTeX
30713 -preamble with the line
30716 \begin_layout Standard
30721 usepackage{remreset}
30724 \begin_layout Standard
30732 \begin_inset Index idx
30735 \begin_layout Plain Layout
30740 \begin_layout Plain Layout
30751 \begin_layout Plain Layout
30764 \begin_layout Plain Layout
30775 \begin_layout Plain Layout
30787 can be used with the same scheme as
30796 \begin_layout Standard
30797 \begin_inset VSpace bigskip
30800 Sometimes formulas should be numbered in the following form:
30803 \begin_layout Standard
30806 (section number.formula number)
30809 \begin_layout Standard
30810 The formula number should start with every section with
30811 \begin_inset Quotes eld
30815 \begin_inset Quotes erd
30821 \begin_layout Standard
30822 For this case there is the command
30829 \begin_inset Index idx
30832 \begin_layout Plain Layout
30840 , which is used with the following scheme:
30843 \begin_layout Standard
30848 numberwithin{counter}{sectioning}
30851 \begin_layout Standard
30852 Counter denotes what kind of numbering is affected, sectioning denotes what
30853 number is before the dot.
30856 \begin_layout Standard
30857 Thus in our case the following \SpecialChar LaTeX
30858 preamble or \SpecialChar TeX
30862 \begin_layout Standard
30867 numberwithin{equation}{section}
30870 \begin_layout Standard
30871 This is the result:
30875 \begin_layout Plain Layout
30879 numberwithin{equation}{section}
30885 \begin_inset Formula
30895 \begin_layout Standard
30897 \begin_inset space \thinspace{}
30901 \begin_inset space \space{}
30904 tables so that the number of the part is the sectioning,
30905 \begin_inset Newline newline
30912 numberwithin{table}{part}
30917 \begin_layout Standard
30918 To go back to the standard numbering or to prevent this kind of numbering
30919 when it is defined by the document class, the following command is inserted
30920 as \SpecialChar TeX
30921 code or to the \SpecialChar LaTeX
30925 \begin_layout Standard
30935 \begin_inset Index idx
30938 \begin_layout Plain Layout
30952 \begin_layout Plain Layout
30968 \begin_inset Newline newline
30976 \begin_inset Newline newline
30988 \begin_layout Standard
30995 uses internally the command
31001 , described above, that also needs to be reverted.
31005 \begin_layout Plain Layout
31012 \begin_layout Plain Layout
31016 @removefromreset{equation}{section}
31019 \begin_layout Plain Layout
31031 \begin_layout Subsection
31032 Numbering with Roman Numbers and Letters
31033 \begin_inset CommandInset label
31035 name "subsec:Numbering-with-Roman"
31040 \begin_inset Index idx
31043 \begin_layout Plain Layout
31044 Formula numbering ! with letters
31050 \begin_inset Index idx
31053 \begin_layout Plain Layout
31054 Formula numbering ! with Roman numbers
31062 \begin_layout Standard
31063 Formulas can also be numbered with Roman numbers and Latin letters.
31064 To number for example with small Roman numbers, the command
31067 \begin_layout Standard
31079 \begin_layout Standard
31080 is inserted before the formula in \SpecialChar TeX
31089 \begin_inset Index idx
31092 \begin_layout Plain Layout
31100 redefines the predefined command
31116 \begin_layout Plain Layout
31123 has the same scheme like the command
31129 that is described in
31130 \begin_inset CommandInset ref
31132 reference "subsec:The-Command-newcommand"
31145 is the formula counter.
31152 is used as prefix for a counter, the value of the counter is output as
31154 When a formula is numbered, \SpecialChar LaTeX
31155 sets internally the command
31161 behind the formula.
31167 \begin_inset Index idx
31170 \begin_layout Plain Layout
31180 outputs the counter as small Roman number.
31183 \begin_layout Standard
31184 All formulas behind the command
31194 are now numbered Roman.
31195 To switch to numbering with big Roman numbers, the command is inserted
31209 \begin_inset Index idx
31212 \begin_layout Plain Layout
31224 \begin_inset Quotes eld
31228 \begin_inset Quotes erd
31231 with small Latin letters there is the command
31238 \begin_inset Index idx
31241 \begin_layout Plain Layout
31249 , for big ones there is the command
31256 \begin_inset Index idx
31259 \begin_layout Plain Layout
31272 \begin_layout Standard
31273 \begin_inset Note Greyedout
31276 \begin_layout Plain Layout
31283 \begin_inset space ~
31286 formulas can be numbered with Latin letters in one document.
31294 \begin_layout Standard
31298 \begin_layout Plain Layout
31314 \begin_layout Standard
31315 \begin_inset Formula
31317 A=\textrm{small roman}
31326 \begin_layout Plain Layout
31340 \begin_inset Formula
31342 B=\textrm{big Roman}\label{eq:Rom}
31351 \begin_layout Plain Layout
31365 \begin_inset Formula
31367 C=\textrm{small Latin}
31376 \begin_layout Plain Layout
31390 \begin_inset Formula
31392 D=\textrm{big Latin}\label{eq:Lat}
31400 \begin_layout Standard
31401 To switch back to the default numbering, insert the command:
31404 \begin_layout Standard
31414 \begin_inset Index idx
31417 \begin_layout Plain Layout
31428 \begin_layout Standard
31432 \begin_layout Plain Layout
31446 \begin_inset Formula
31456 \begin_layout Standard
31457 \begin_inset VSpace medskip
31460 As you see, formulas are numbered serially independent from the numbering
31462 When then numbering should start with
31463 \begin_inset Quotes eld
31467 \begin_inset Quotes erd
31470 when the style is changed, new equation counters have to be defined.
31471 A description about this can be found in the file
31472 \begin_inset CommandInset href
31474 name "Formula-numbering.lyx"
31475 target "run:Formula-numbering.lyx"
31482 \begin_layout Section
31483 Chemical Symbols and Equations
31484 \begin_inset CommandInset label
31486 name "subsec:Chemical-Symbols-and"
31491 \begin_inset Index idx
31494 \begin_layout Plain Layout
31495 Chemical characters ! Symbols
31501 \begin_inset Index idx
31504 \begin_layout Plain Layout
31511 \begin_inset Index idx
31514 \begin_layout Plain Layout
31523 \begin_layout Standard
31524 An example text from chemistry:
31527 \begin_layout Quote
31529 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31532 -ion reacts with two
31533 \begin_inset Formula $\mathrm{Na^{+}}$
31536 -ions to sodium sulfate
31537 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31541 The chemical equation for this is:
31542 \begin_inset Formula
31544 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31552 \begin_layout Standard
31553 This chemical equation can directly be created as formula.
31554 To avoid that the symbols appear italic, everything is highlighted and
31555 changed by the shortcut
31561 to the upright font style.
31565 \begin_layout Plain Layout
31571 \begin_inset CommandInset ref
31573 reference "subsec:Font-Styles"
31585 \begin_layout Standard
31586 A more convenient way to typeset chemical formulas is to use the command
31594 \begin_inset Index idx
31597 \begin_layout Plain Layout
31605 that is available when the \SpecialChar LaTeX
31611 \begin_inset Index idx
31614 \begin_layout Plain Layout
31627 to a formula a new blue box appears where chemical formulas can be inserted
31628 in an intuitive way.
31629 \begin_inset Separator latexpar
31635 \begin_layout Standard
31637 \begin_inset Tabular
31638 <lyxtabular version="3" rows="10" columns="2">
31639 <features booktabs="true" tabularvalignment="middle">
31640 <column alignment="center" valignment="top" width="0pt">
31641 <column alignment="center" valignment="top">
31643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31646 \begin_layout Plain Layout
31652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31655 \begin_layout Plain Layout
31663 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31666 \begin_layout Plain Layout
31670 \begin_inset space \textvisiblespace{}
31678 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31681 \begin_layout Plain Layout
31682 \begin_inset Formula $\ce{H2CO3}$
31691 <row topspace="1.5mm">
31692 <cell alignment="center" valignment="top" usebox="none">
31695 \begin_layout Plain Layout
31699 \begin_inset space \textvisiblespace{}
31707 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31710 \begin_layout Plain Layout
31711 \begin_inset Formula $\ce{SO4^{2-}}$
31720 <row topspace="1.5mm">
31721 <cell alignment="center" valignment="top" usebox="none">
31724 \begin_layout Plain Layout
31728 \begin_inset space \textvisiblespace{}
31736 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31739 \begin_layout Plain Layout
31740 \begin_inset Formula $\ce{(NH4)2S}$
31749 <row topspace="1.5mm">
31750 <cell alignment="center" valignment="top" usebox="none">
31753 \begin_layout Plain Layout
31757 \begin_inset space \textvisiblespace{}
31765 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31768 \begin_layout Plain Layout
31769 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31778 <row topspace="1.5mm">
31779 <cell alignment="center" valignment="top" usebox="none">
31782 \begin_layout Plain Layout
31786 \begin_inset space \textvisiblespace{}
31792 \begin_inset space \textvisiblespace{}
31798 \begin_inset space \textvisiblespace{}
31806 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31809 \begin_layout Plain Layout
31810 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31819 <row topspace="1.5mm">
31820 <cell alignment="center" valignment="top" usebox="none">
31823 \begin_layout Plain Layout
31827 \begin_inset space \textvisiblespace{}
31831 \begin_inset Formula $\downarrow$
31835 \begin_inset Formula $\to$
31843 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31846 \begin_layout Plain Layout
31847 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31857 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31860 \begin_layout Plain Layout
31864 \begin_inset space \textvisiblespace{}
31870 \begin_inset space \textvisiblespace{}
31876 \begin_inset space \textvisiblespace{}
31884 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31887 \begin_layout Plain Layout
31888 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31901 \begin_layout Plain Layout
31905 \begin_inset space \textvisiblespace{}
31909 \begin_inset space \textvisiblespace{}
31913 \begin_inset space \textvisiblespace{}
31917 \begin_inset space \textvisiblespace{}
31921 \begin_inset space \textvisiblespace{}
31929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31932 \begin_layout Plain Layout
31933 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31942 <row topspace="1.5mm">
31943 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31946 \begin_layout Plain Layout
31950 \begin_inset space \textvisiblespace{}
31954 \begin_inset space \textvisiblespace{}
31958 \begin_inset space \textvisiblespace{}
31962 \begin_inset space \textvisiblespace{}
31970 \begin_inset space \textvisiblespace{}
31978 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31981 \begin_layout Plain Layout
31982 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
31998 \begin_layout Standard
31999 \begin_inset Note Greyedout
32002 \begin_layout Plain Layout
32008 It is not possible in \SpecialChar LyX
32009 to use the character ^ to get an up-arrow as described
32015 One instead uses a negative thin space followed by the command
32022 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32033 \begin_layout Standard
32040 the command for equation
32041 \begin_inset space ~
32045 \begin_inset CommandInset ref
32047 reference "eq:chem-reaction"
32052 \begin_inset Newline newline
32060 \begin_inset space \textvisiblespace{}
32064 \begin_inset space \textvisiblespace{}
32068 \begin_inset space \textvisiblespace{}
32072 \begin_inset space \textvisiblespace{}
32076 \begin_inset space \textvisiblespace{}
32080 \begin_inset space \textvisiblespace{}
32086 \begin_layout Standard
32087 To create multiline chemical equations first a multiline formula is created
32089 \begin_inset CommandInset ref
32091 reference "sec:Multiline-Formulas"
32096 Afterwards the command
32102 is used in every small blue box of the formula.
32104 \begin_inset CommandInset ref
32106 reference "eq:TEOS-reaction-1"
32111 \begin_inset CommandInset ref
32113 reference "eq:TEOS-reaction-2"
32117 are an example of a multi-stage chemical reaction where every equation
32118 has its own number.
32119 \begin_inset Formula
32121 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32122 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32130 \begin_layout Standard
32141 package provides the command
32148 \begin_inset Index idx
32151 \begin_layout Plain Layout
32159 that has to be used for special cases.
32160 For more information about
32166 and more examples have a look at the documentation of
32171 \begin_inset CommandInset citation
32180 \begin_layout Section
32184 \begin_layout Standard
32186 supports two types of commutative diagrams:
32194 that are explained in the following.
32197 \begin_layout Subsection
32199 \begin_inset Index idx
32202 \begin_layout Plain Layout
32211 \begin_layout Standard
32212 Diagrams of this type visualize relations by vertical and horizontal lines
32214 \begin_inset Formula
32216 \begin{CD}A@>>>B@>>>C\\
32227 \begin_layout Standard
32228 To get them, the command
32233 \begin_inset Index idx
32236 \begin_layout Plain Layout
32246 is inserted to a formula.
32247 A blue box appears with two dashed lines where further commands can be
32252 arg "newline-insert newline"
32255 a new line is created.
32256 Horizontal relations are inserted in odd, vertical in even formula lines.
32259 \begin_layout Standard
32260 To create the relations there are the following commands:
32263 \begin_layout Itemize
32268 creates a left arrow,
32279 \begin_layout Itemize
32284 creates an up arrow,
32292 a vertical equal sign
32295 \begin_layout Itemize
32301 is a placeholder for non-existent relations
32304 \begin_layout Standard
32305 All arrows can be labeled as follows:
32308 \begin_layout Itemize
32309 If text inserted between the first and second < or >, resp., it is placed
32311 When it is inserted between the second and third one, it appears under
32315 \begin_layout Itemize
32316 When text for vertical arrows is inserted between the first and second A
32317 or V, resp., it is placed left beside the arrow.
32318 When it is inserted between the second and third one, it appears right
32320 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32324 \begin_layout Standard
32325 As example a diagram with all possible relations:
32328 \begin_layout Standard
32329 \begin_inset Formula
32331 \begin{CD}A@>j>>B@>>k>C@=F\\
32342 \begin_layout Standard
32343 The command for this is:
32344 \begin_inset Newline newline
32352 \begin_inset space \textvisiblespace{}
32355 A@>j>>B@>>k>C@=F Ctrl+Return
32356 \begin_inset Newline newline
32360 \begin_inset Phantom HPhantom
32363 \begin_layout Plain Layout
32369 \begin_inset space \textvisiblespace{}
32382 \begin_inset Formula $\to$
32388 \begin_inset Newline newline
32392 \begin_inset Phantom HPhantom
32395 \begin_layout Plain Layout
32401 \begin_inset space \textvisiblespace{}
32412 \begin_layout Subsection
32414 \begin_inset Index idx
32417 \begin_layout Plain Layout
32418 Diagrams ! xymatrix
32426 \begin_layout Standard
32427 To be able to use xymatrices, the \SpecialChar LaTeX
32433 A xymatrix is created by inserting the command
32440 Then you are able to add new matrix columns and rows like for normal matrices,
32442 \begin_inset CommandInset ref
32444 reference "sec:Matrices"
32451 \begin_layout Standard
32452 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32454 All possibilities to create commutative diagrams and decorations are explained
32459 that you find in the menu
32461 Help\SpecialChar menuseparator
32463 \begin_inset space ~
32471 \begin_layout Subsection
32477 \begin_inset Index idx
32480 \begin_layout Plain Layout
32489 \begin_layout Standard
32494 -diagrams, the \SpecialChar LaTeX
32504 -diagram is created by inserting the command
32511 Then you are able to add new matrix columns and rows like for normal matrices,
32513 \begin_inset CommandInset ref
32515 reference "sec:Matrices"
32522 \begin_layout Standard
32523 Examples how to create
32527 diagrams in \SpecialChar LyX
32530 Feynman-diagram manual
32532 that you find in the menu
32534 Help\SpecialChar menuseparator
32536 \begin_inset space ~
32544 \begin_layout Section
32545 User-defined Commands
32546 \begin_inset Index idx
32549 \begin_layout Plain Layout
32550 User-defined commands
32558 \begin_layout Standard
32559 \begin_inset Note Greyedout
32562 \begin_layout Plain Layout
32567 The names of user-defined commands and macros may only consist of Latin
32576 \begin_layout Subsection
32580 \begin_inset CommandInset label
32582 name "subsec:The-Command-newcommand"
32587 \begin_inset Index idx
32590 \begin_layout Plain Layout
32591 User-defined commands !
32599 \begin_inset Index idx
32602 \begin_layout Plain Layout
32613 \begin_layout Standard
32614 Many \SpecialChar LaTeX
32615 -commands are too long to be used frequently.
32616 But it is possible to define with the command
32622 new shorter commands.
32625 \begin_layout Standard
32626 The command scheme of
32635 \begin_layout Standard
32640 newcommand{new command name}[number of arguments][optional
32645 \begin_inset Newline newline
32649 \begin_inset Phantom HPhantom
32652 \begin_layout Plain Layout
32662 {command definition}
32665 \begin_layout Standard
32666 \begin_inset Note Greyedout
32669 \begin_layout Plain Layout
32674 Assure that the name of the new command is not already used in your document
32675 or by \SpecialChar LaTeX
32676 -packages that you use.
32677 When you for example define the command
32689 , you get an error message because
32695 is already defined as command for
32696 \begin_inset Quotes eld
32700 \begin_inset Formula $\le$
32704 \begin_inset Quotes erd
32715 \begin_layout Standard
32716 The number of arguments is an integer in the range 0
32717 \begin_inset space \thinspace{}
32721 \begin_inset space \thinspace{}
32724 9 and specifies how many arguments the new command should have.
32725 With the optional value a value for an optional argument can be predefined.
32726 When this is done, the
32734 rgument of the new command is automatically an optional one.
32737 \begin_layout Standard
32738 Here are some examples:
32741 \begin_layout Itemize
32742 To define the command
32754 , the \SpecialChar LaTeX
32756 \begin_inset VSpace medskip
32760 \begin_inset Newline newline
32774 \begin_layout Itemize
32775 To define the command
32787 , the argument (that should be underlined) must be taken into account.
32788 For this the preamble line is:
32789 \begin_inset VSpace medskip
32793 \begin_inset Newline newline
32807 \begin_inset VSpace medskip
32811 \begin_inset Newline newline
32818 acts as argument placeholder, the
32822 behind it denotes that it is the placeholder for the first argument.
32825 \begin_layout Itemize
32833 \begin_inset space \thinspace{}
32837 \begin_inset space \space{}
32847 \begin_inset VSpace medskip
32851 \begin_inset Newline newline
32862 framebox#1#2{$#3$}}
32865 \begin_inset VSpace medskip
32869 \begin_inset Newline newline
32872 The two Dollar signs creates the extra formula needed for
32879 \begin_inset CommandInset ref
32881 reference "subsec:Boxes-with-Frame"
32888 \begin_layout Itemize
32889 To create a new command for
32895 where the color for the box need not be specified, the argument for the
32896 color is defined optional:
32897 \begin_inset VSpace medskip
32901 \begin_inset Newline newline
32912 fcolorbox{#2}{#1}{$#3$}}
32915 \begin_inset VSpace medskip
32919 \begin_inset Newline newline
32922 When the color is not specified when using
32928 , the predefined color
32935 \begin_layout Standard
32936 A test of the new defined commands:
32937 \begin_inset Separator latexpar
32943 \begin_layout Standard
32945 \begin_inset Tabular
32946 <lyxtabular version="3" rows="6" columns="2">
32947 <features booktabs="true" tabularvalignment="middle">
32948 <column alignment="center" valignment="top" width="0pt">
32949 <column alignment="center" valignment="top">
32951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32954 \begin_layout Plain Layout
32960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32963 \begin_layout Plain Layout
32971 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32974 \begin_layout Plain Layout
32978 \begin_inset space \textvisiblespace{}
32986 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32989 \begin_layout Plain Layout
32990 \begin_inset Formula $A\gr B$
33000 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33003 \begin_layout Plain Layout
33011 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33014 \begin_layout Plain Layout
33015 \begin_inset Formula $\us{ABcd}$
33024 <row topspace="1mm">
33025 <cell alignment="center" valignment="top" usebox="none">
33028 \begin_layout Plain Layout
33032 \begin_inset Formula $\to$
33038 \begin_inset Formula $\to$
33046 \begin_inset space \textvisiblespace{}
33054 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33057 \begin_layout Plain Layout
33058 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33067 <row topspace="1.5mm">
33068 <cell alignment="center" valignment="top" usebox="none">
33071 \begin_layout Plain Layout
33075 \begin_inset Formula $\to$
33083 \begin_inset space \textvisiblespace{}
33091 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33094 \begin_layout Plain Layout
33095 \begin_inset Formula $\cb{red}{\int A=B}$
33104 <row topspace="1.5mm" bottomspace="1mm">
33105 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33108 \begin_layout Plain Layout
33114 \begin_inset Formula $\to$
33122 \begin_inset space \textvisiblespace{}
33130 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33133 \begin_layout Plain Layout
33134 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33150 \begin_layout Subsection
33152 \begin_inset Index idx
33155 \begin_layout Plain Layout
33156 User-defined commands! Math macros
33162 \begin_inset Index idx
33165 \begin_layout Plain Layout
33174 \begin_layout Standard
33175 User-defined commands are especially convenient for complex expressions.
33176 When you are for example dealing with a document that has quadratic equations,
33177 the same solution type occurs several times.
33178 The general form of a quadratic equation is
33179 \begin_inset Formula
33181 0=\lambda^{2}+p\lambda+q
33186 The general form of the solution is
33187 \begin_inset Formula
33189 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33197 \begin_layout Standard
33198 To define a command for the solution formula where only the three parameters
33200 \begin_inset Formula $\lambda$
33204 \begin_inset Formula $p$
33208 \begin_inset Formula $q$
33211 need to be specified and the index of
33212 \begin_inset Formula $\lambda$
33215 can be given optionally, the \SpecialChar LaTeX
33217 \begin_inset Newline newline
33233 \begin_inset Newline newline
33237 \begin_inset Phantom HPhantom
33240 \begin_layout Plain Layout
33254 frac{#3^{2}}{4}-#4}}
33257 \begin_layout Standard
33258 To create with this the solution formula, the command
33259 \begin_inset Newline newline
33269 \begin_inset Formula $\to$
33275 \begin_inset Formula $\to$
33282 is inserted to a formula
33287 \begin_layout Standard
33288 The definition of the new command is unintuitive because one has to know
33289 the schemes of all used \SpecialChar LaTeX
33291 \begin_inset space \thinspace{}
33295 \begin_inset space \space{}
33298 that a fraction is inserted in \SpecialChar LaTeX
33303 frac{numerator}{denominator}
33306 Furthermore one can easily forget a brace in the definition and cannot
33307 see in \SpecialChar LyX
33308 what the new command is doing.
33309 To avoid these problems \SpecialChar LyX
33310 offers the possibility to use math macros instead
33320 \begin_layout Standard
33321 A math macro is created by using the menu
33323 Insert\SpecialChar menuseparator
33324 Math\SpecialChar menuseparator
33327 or the toolbar button
33330 arg "math-macro newmacroname_newcommand"
33334 The math macro toolbar appears together with the following box where the
33336 \begin_inset Newline newline
33340 \begin_inset space \hspace*{\fill}
33344 \begin_inset Graphics
33345 filename clipart/macrobox.png
33351 \begin_inset space \hspace*{\fill}
33355 \begin_inset Newline newline
33359 \begin_inset FormulaMacro
33360 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33365 newmacroname is the default name of the macro that should be changed to
33366 something sensible.
33367 The wanted formula is inserted in the first blue box.
33368 An argument placeholder is inserted with the command
33375 \begin_inset space \thinspace{}
33379 \begin_inset space \space{}
33388 or by using the macro toolbar button
33391 arg "math-macro-add-param"
33395 Argument placeholders are displayed red.
33397 \begin_inset space ~
33400 arguments are possible.
33401 Optional arguments are created with the toolbar button
33404 arg "math-macro-add-optional-param"
33408 The first non-optional argument can be transformed to an optional one with
33412 arg "math-macro-make-optional"
33416 In the second blue box the appearance of the macro in \SpecialChar LyX
33418 Normally you want to see it as it is defined, so the box is kept empty.
33419 But when you have created a macro that needs lot of space on the screen,
33420 you can insert in the box for example
33421 \begin_inset Newline newline
33451 \begin_inset Newline newline
33456 For the macro only the arguments with the macro name in front of them will
33457 then be displayed in \SpecialChar LyX
33458 , leading to a better overview.
33459 The formula appears in the output as defined in the first box.
33460 \begin_inset Newline newline
33463 The appearance of macros in formulas can furthermore be changed for single
33464 macros by setting the cursor in the macro and using the menu
33466 View\SpecialChar menuseparator
33468 \begin_inset space ~
33472 \begin_inset space ~
33480 \begin_layout Standard
33481 To use a macro, the macro name is inserted as command to a formula, in our
33489 Our macro looks in \SpecialChar LyX
33491 \begin_inset Newline newline
33495 \begin_inset space \hspace*{\fill}
33499 \begin_inset Graphics
33500 filename clipart/macrouse.png
33506 \begin_inset space \hspace*{\fill}
33510 \begin_inset Newline newline
33513 Here is our macro example with the arguments
33514 \begin_inset Formula $x$
33518 \begin_inset Formula $\ln(x)$
33522 \begin_inset Formula $B$
33528 \begin_layout Standard
33529 \begin_inset Formula
33539 \begin_layout Standard
33543 Tools\SpecialChar menuseparator
33544 Preferences\SpecialChar menuseparator
33545 Editing\SpecialChar menuseparator
33548 different styles to edit macros.
33549 To find the style that suits you the most, choose a style and set the cursor
33550 in a macro formula to see the difference.
33553 \begin_layout Standard
33554 A math macro is transformed internally to a
33560 command when exporting the document.
33567 command is not placed in the \SpecialChar LaTeX
33568 -preamble, therefore macros can only be used
33569 in formulas that are in the document below the macro definition box.
33572 \begin_layout Standard
33573 Math macros can also be directly created from a
33580 When writing for example the command
33583 \begin_inset Newline newline
33592 xleftarrow[#2]{#1}}
33593 \begin_inset Newline newline
33598 in \SpecialChar LyX
33599 as normal text, highlighting it completely and using then the shortcut
33604 , the command will be transformed to a math macro.
33605 Using this method you need to be careful that the
33611 command is typed correctly, otherwise you get a faulty macro leading to
33616 \begin_layout Standard
33617 Math macros currently have the problem that further formulas in macro definition
33618 s are handled wrongly.
33619 Therefore the example
33626 \begin_inset CommandInset ref
33628 reference "subsec:The-Command-newcommand"
33632 cannot be created as macro.
33635 \begin_layout Standard
33636 When the cursor is in a macro definition box, you will see the macro toolbar
33637 in \SpecialChar LyX
33641 \begin_layout Standard
33642 \begin_inset VSpace defskip
33648 \begin_layout Standard
33649 \begin_inset Graphics
33650 filename clipart/MacroToolbar.png
33655 \begin_inset Index idx
33658 \begin_layout Plain Layout
33667 \begin_layout Standard
33668 \begin_inset VSpace defskip
33674 \begin_layout Standard
33675 The macro toolbar contains from left to right the following buttons:
33678 \begin_layout Standard
33679 \begin_inset VSpace defskip
33685 \begin_layout Standard
33686 \begin_inset Tabular
33687 <lyxtabular version="3" rows="9" columns="2">
33688 <features islongtable="true" longtabularalignment="center">
33689 <column alignment="left" valignment="top">
33690 <column alignment="left" valignment="top" width="85col%">
33691 <row interlinespace="2.5mm">
33692 <cell alignment="center" valignment="top" usebox="none">
33695 \begin_layout Plain Layout
33698 arg "math-macro-remove-param"
33706 <cell alignment="center" valignment="top" usebox="none">
33709 \begin_layout Plain Layout
33712 Edit\SpecialChar menuseparator
33713 Math\SpecialChar menuseparator
33715 \begin_inset space ~
33718 Definition\SpecialChar menuseparator
33719 Remove Last Argument
33725 <row interlinespace="2.5mm">
33726 <cell alignment="center" valignment="top" usebox="none">
33729 \begin_layout Plain Layout
33732 arg "math-macro-add-param"
33740 <cell alignment="center" valignment="top" usebox="none">
33743 \begin_layout Plain Layout
33746 Edit\SpecialChar menuseparator
33747 Math\SpecialChar menuseparator
33749 \begin_inset space ~
33752 Definition\SpecialChar menuseparator
33759 <row interlinespace="2.5mm">
33760 <cell alignment="center" valignment="top" usebox="none">
33763 \begin_layout Plain Layout
33766 arg "math-macro-make-optional"
33774 <cell alignment="center" valignment="top" usebox="none">
33777 \begin_layout Plain Layout
33780 Edit\SpecialChar menuseparator
33781 Math\SpecialChar menuseparator
33783 \begin_inset space ~
33786 Definition\SpecialChar menuseparator
33787 Transform First Non-Optional to
33788 \begin_inset Newline newline
33792 \begin_inset Phantom HPhantom
33795 \begin_layout Plain Layout
33798 Edit\SpecialChar menuseparator
33799 Math\SpecialChar menuseparator
33801 \begin_inset space ~
33804 Definition\SpecialChar menuseparator
33816 <row interlinespace="2.5mm">
33817 <cell alignment="center" valignment="top" usebox="none">
33820 \begin_layout Plain Layout
33823 arg "math-macro-make-nonoptional"
33831 <cell alignment="center" valignment="top" usebox="none">
33834 \begin_layout Plain Layout
33837 Edit\SpecialChar menuseparator
33838 Math\SpecialChar menuseparator
33840 \begin_inset space ~
33843 Definition\SpecialChar menuseparator
33844 Transform Last Optional to
33845 \begin_inset Newline newline
33849 \begin_inset Phantom HPhantom
33852 \begin_layout Plain Layout
33855 Edit\SpecialChar menuseparator
33856 Math\SpecialChar menuseparator
33858 \begin_inset space ~
33861 Definition\SpecialChar menuseparator
33867 Non-Optional Argument
33873 <row interlinespace="2.5mm">
33874 <cell alignment="center" valignment="top" usebox="none">
33877 \begin_layout Plain Layout
33880 arg "math-macro-remove-optional-param"
33888 <cell alignment="center" valignment="top" usebox="none">
33891 \begin_layout Plain Layout
33894 Edit\SpecialChar menuseparator
33895 Math\SpecialChar menuseparator
33897 \begin_inset space ~
33900 Definition\SpecialChar menuseparator
33901 Remove Optional Argument
33907 <row interlinespace="2.5mm">
33908 <cell alignment="center" valignment="top" usebox="none">
33911 \begin_layout Plain Layout
33914 arg "math-macro-add-optional-param"
33922 <cell alignment="center" valignment="top" usebox="none">
33925 \begin_layout Plain Layout
33928 Edit\SpecialChar menuseparator
33929 Math\SpecialChar menuseparator
33931 \begin_inset space ~
33934 Definition\SpecialChar menuseparator
33935 Insert Optional Argument
33941 <row interlinespace="2.5mm">
33942 <cell alignment="center" valignment="top" usebox="none">
33945 \begin_layout Plain Layout
33948 arg "math-macro-remove-greedy-param"
33956 <cell alignment="center" valignment="top" usebox="none">
33959 \begin_layout Plain Layout
33962 Edit\SpecialChar menuseparator
33963 Math\SpecialChar menuseparator
33965 \begin_inset space ~
33968 Definition\SpecialChar menuseparator
33969 Remove Last Argument
33970 \begin_inset Newline newline
33974 \begin_inset Phantom HPhantom
33977 \begin_layout Plain Layout
33980 Edit\SpecialChar menuseparator
33981 Math\SpecialChar menuseparator
33983 \begin_inset space ~
33986 Definition\SpecialChar menuseparator
33992 Spitting Out To The Right
33998 <row interlinespace="2.5mm">
33999 <cell alignment="center" valignment="top" usebox="none">
34002 \begin_layout Plain Layout
34005 arg "math-macro-append-greedy-param"
34013 <cell alignment="center" valignment="top" usebox="none">
34016 \begin_layout Plain Layout
34019 Edit\SpecialChar menuseparator
34020 Math\SpecialChar menuseparator
34022 \begin_inset space ~
34025 Definition\SpecialChar menuseparator
34027 \begin_inset Newline newline
34031 \begin_inset Phantom HPhantom
34034 \begin_layout Plain Layout
34037 Edit\SpecialChar menuseparator
34038 Math\SpecialChar menuseparator
34040 \begin_inset space ~
34043 Definition\SpecialChar menuseparator
34049 Eating From The Right
34055 <row interlinespace="2.5mm">
34056 <cell alignment="center" valignment="top" usebox="none">
34059 \begin_layout Plain Layout
34062 arg "math-macro-add-greedy-optional-param"
34070 <cell alignment="center" valignment="top" usebox="none">
34073 \begin_layout Plain Layout
34076 Edit\SpecialChar menuseparator
34077 Math\SpecialChar menuseparator
34079 \begin_inset space ~
34082 Definition\SpecialChar menuseparator
34083 Append Optional Argument
34084 \begin_inset Newline newline
34088 \begin_inset Phantom HPhantom
34091 \begin_layout Plain Layout
34094 Edit\SpecialChar menuseparator
34095 Math\SpecialChar menuseparator
34097 \begin_inset space ~
34100 Definition\SpecialChar menuseparator
34106 Eating From The Right
34119 \begin_layout Section
34120 Computer Algebra Systems
34123 \begin_layout Standard
34125 offers the exchange between mathematical expressions written in \SpecialChar LyX
34127 editor and external applications or user defined scripts.
34128 Currently supported applications are
34145 Note that the set of supported mathematical constructs is limited only
34146 to very simple cases.
34149 \begin_layout Subsection
34153 \begin_layout Standard
34154 Write some expression in a formula, go to the
34156 Edit\SpecialChar menuseparator
34157 Math\SpecialChar menuseparator
34158 Use Computer Algebra System
34160 menu and choose the application you have installed on the computer.
34161 After that the result of computation should show on the right side of the
34162 expression together with the
34163 \begin_inset Quotes eld
34167 \begin_inset Quotes erd
34173 \begin_layout Standard
34174 Here are few simple examples (with results from
34178 ) to show what kind of computations can be performed:
34181 \begin_layout Itemize
34182 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34188 \begin_layout Itemize
34189 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34195 \begin_layout Itemize
34196 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34202 \begin_layout Itemize
34204 \change_inserted 5863208 1465782906
34205 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
34212 \begin_layout Plain Layout
34214 \change_inserted 5863208 1465782906
34215 Note that one needs to use proper delimiter insets
34216 \begin_inset Formula $\left(\right)$
34219 instead of simple '(' ')' characters.
34230 \begin_layout Itemize
34231 \begin_inset Formula $\det\left[\begin{array}{ccc}
34235 \end{array}\right]=-56$
34241 \begin_layout Itemize
34242 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34248 \begin_layout Standard
34250 \change_inserted 5863208 1465782942
34251 One can also use standard commands known to CAS:
34254 \begin_layout Itemize
34256 \change_inserted 5863208 1465782942
34257 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\it i_{1}}=0}^{\infty}{\frac{4^{-{\it i_{1}}-1}\,\left(x-1\right)^{{\it i_{1}}+1}}{{\it i_{1}}+1}}-\log\left(-1\right)$
34263 \begin_layout Itemize
34265 \change_inserted 5863208 1465782942
34266 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
34274 \begin_layout Subsection
34278 \begin_layout Standard
34279 Currently there is no keyboard shortcut for calling the algebra applications.
34280 One can easily bind a shortcut to the
34294 \begin_inset space \thinspace{}
34298 \begin_inset space \space{}
34305 key inside the math editor.
34310 one would use this shortcut definition command:
34313 \begin_layout Standard
34316 command-alternatives paragraph-break;math-extern maxima
34319 \begin_layout Section
34321 \begin_inset Index idx
34324 \begin_layout Plain Layout
34333 \begin_layout Subsection
34335 \begin_inset Index idx
34338 \begin_layout Plain Layout
34347 \begin_layout Standard
34348 Negative numbers often look ugly in formulas because the minus sign before
34349 the number is set with the same length as the minus operator sign.
34350 When writing the negative number in normal text, the minus sign appears
34354 \begin_layout Standard
34355 Thus, the problem disappears when converting the minus sign to mathematical
34359 \begin_layout Standard
34360 An example to visualize the problem:
34361 \begin_inset Separator latexpar
34367 \begin_layout Standard
34369 \begin_inset Tabular
34370 <lyxtabular version="3" rows="3" columns="2">
34371 <features booktabs="true" tabularvalignment="middle">
34372 <column alignment="right" valignment="top" width="0pt">
34373 <column alignment="left" valignment="top">
34375 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34378 \begin_layout Plain Layout
34384 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34387 \begin_layout Plain Layout
34395 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34398 \begin_layout Plain Layout
34404 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34407 \begin_layout Plain Layout
34408 \begin_inset Formula $x=-2$
34418 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34421 \begin_layout Plain Layout
34427 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34430 \begin_layout Plain Layout
34431 \begin_inset Formula $x=\textrm{-}2$
34447 \begin_layout Subsection
34448 Comma as decimal Separator
34449 \begin_inset Index idx
34452 \begin_layout Plain Layout
34461 \begin_layout Standard
34462 In \SpecialChar LaTeX
34463 a comma inside a formula is used, according to the English convention,
34464 as number group separator.
34465 So there will be space added behind all commas in formulas.
34468 \begin_layout Standard
34469 To avoid this, the comma is highlighted and changed to mathematical text
34479 \begin_layout Standard
34480 To use all formula commas in the document as decimal separator, the file
34489 \begin_layout Plain Layout
34494 is part of the \SpecialChar LaTeX
34500 \begin_inset Index idx
34503 \begin_layout Plain Layout
34508 \begin_layout Plain Layout
34528 \begin_inset Index idx
34531 \begin_layout Plain Layout
34537 is loaded with the \SpecialChar LaTeX
34541 \begin_layout Standard
34549 \begin_layout Subsection
34551 \begin_inset CommandInset label
34553 name "subsec:Physical-Vectors"
34558 \begin_inset Index idx
34561 \begin_layout Plain Layout
34570 \begin_layout Standard
34571 Predefined vectors are offered by the \SpecialChar LaTeX
34577 \begin_inset Index idx
34580 \begin_layout Plain Layout
34586 that is loaded with the \SpecialChar LaTeX
34590 \begin_layout Standard
34598 \begin_layout Standard
34602 \begin_layout Plain Layout
34612 \begin_inset Note Note
34615 \begin_layout Plain Layout
34616 The following table will only be displayed when the \SpecialChar LaTeX
34629 \begin_layout Standard
34630 The following commands are defined:
34631 \begin_inset Separator latexpar
34637 \begin_layout Standard
34639 \begin_inset Tabular
34640 <lyxtabular version="3" rows="4" columns="2">
34641 <features booktabs="true" tabularvalignment="middle">
34642 <column alignment="center" valignment="top" width="0pt">
34643 <column alignment="center" valignment="top">
34645 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34648 \begin_layout Plain Layout
34654 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34657 \begin_layout Plain Layout
34665 <cell alignment="center" valignment="top" usebox="none">
34668 \begin_layout Plain Layout
34678 <cell alignment="center" valignment="top" usebox="none">
34681 \begin_layout Plain Layout
34682 \begin_inset Formula $\Bra{\psi}$
34692 <cell alignment="center" valignment="top" usebox="none">
34695 \begin_layout Plain Layout
34705 <cell alignment="center" valignment="top" usebox="none">
34708 \begin_layout Plain Layout
34709 \begin_inset Formula $\Ket{\psi}$
34719 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34722 \begin_layout Plain Layout
34734 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34737 \begin_layout Plain Layout
34738 \begin_inset Formula $\Braket{\psi|\phi}$
34754 \begin_layout Standard
34761 assures that all vertical bars are set in the size of the surrounding brackets:
34762 \begin_inset Formula
34764 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34773 \begin_layout Plain Layout
34783 \begin_inset Note Note
34786 \begin_layout Plain Layout
34787 The following will be displayed when the \SpecialChar LaTeX
34800 \begin_layout Standard
34801 You need to install the \SpecialChar LaTeX
34806 to see the rest of this subsection in the output.
34809 \begin_layout Standard
34813 \begin_layout Plain Layout
34825 \begin_layout Standard
34832 can also be achieved using the command
34838 , that is described in
34839 \begin_inset CommandInset ref
34841 reference "subsec:Automatic-Bracket-Size"
34848 \begin_layout Subsection
34849 Self-defined Fractions
34850 \begin_inset CommandInset label
34852 name "subsec:Self-defined-Fractions"
34857 \begin_inset Index idx
34860 \begin_layout Plain Layout
34861 Fractions ! self-defined
34869 \begin_layout Standard
34870 To define custom commands for fractions, the command
34877 \begin_inset Index idx
34880 \begin_layout Plain Layout
34887 \begin_layout Plain Layout
34901 is used in the following scheme:
34904 \begin_layout Standard
34917 bracket}{fraction bar thickness}{style}
34918 \begin_inset Newline newline
34922 \begin_inset Phantom HPhantom
34925 \begin_layout Plain Layout
34935 {numerator}{denominator}
34938 \begin_layout Standard
34939 The style is a number in the range of 0
34940 \begin_inset space \thinspace{}
34944 \begin_inset space \thinspace{}
34948 \begin_inset Separator latexpar
34954 \begin_layout Standard
34956 \begin_inset Tabular
34957 <lyxtabular version="3" rows="5" columns="2">
34958 <features booktabs="true" tabularvalignment="middle">
34959 <column alignment="center" valignment="top" width="0pt">
34960 <column alignment="center" valignment="top">
34962 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34965 \begin_layout Plain Layout
34971 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34974 \begin_layout Plain Layout
34982 <cell alignment="center" valignment="top" usebox="none">
34985 \begin_layout Plain Layout
34991 <cell alignment="center" valignment="top" usebox="none">
34994 \begin_layout Plain Layout
34995 display style formula
35002 <cell alignment="center" valignment="top" usebox="none">
35005 \begin_layout Plain Layout
35011 <cell alignment="center" valignment="top" usebox="none">
35014 \begin_layout Plain Layout
35022 <cell alignment="center" valignment="top" usebox="none">
35025 \begin_layout Plain Layout
35031 <cell alignment="center" valignment="top" usebox="none">
35034 \begin_layout Plain Layout
35042 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35045 \begin_layout Plain Layout
35051 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35054 \begin_layout Plain Layout
35068 \begin_layout Standard
35069 When no style is given, the size is adjusted to the surrounding environment
35070 like for the command
35079 \begin_layout Standard
35080 When no fraction bar thickness is given, the predefined value of 0.4
35081 \begin_inset space \thinspace{}
35087 \begin_layout Standard
35088 \begin_inset VSpace medskip
35091 For example, the commands
35104 \begin_inset CommandInset ref
35106 reference "subsec:Fractions"
35110 are defined with the commands
35113 \begin_layout Standard
35122 genfrac{}{}{}{0}{#1}{#2}}
35125 \begin_layout Standard
35129 \begin_layout Standard
35138 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35141 \begin_layout Standard
35142 \begin_inset VSpace medskip
35145 To define a fraction where the fraction bar thickness can be given as optional
35146 argument, the following line is inserted to the \SpecialChar LaTeX
35150 \begin_layout Standard
35159 genfrac{}{}{#1}{}{#2}{#3}}
35162 \begin_layout Standard
35164 \begin_inset Formula
35166 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35167 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35172 As one can see, the distance of the numerator and the denominator to the
35173 fraction bar is round about three times the bar thickness.
35176 \begin_layout Subsection
35178 \begin_inset Index idx
35181 \begin_layout Plain Layout
35190 \begin_layout Standard
35191 There are four ways to cancel formulas or parts of formulas:
35194 \begin_layout Standard
35198 \begin_layout Plain Layout
35208 \begin_inset Note Note
35211 \begin_layout Plain Layout
35212 The following table will only be displayed when the \SpecialChar LaTeX
35223 \begin_inset Separator latexpar
35229 \begin_layout Standard
35231 \begin_inset Tabular
35232 <lyxtabular version="3" rows="5" columns="2">
35233 <features booktabs="true" tabularvalignment="middle">
35234 <column alignment="center" valignment="top" width="0pt">
35235 <column alignment="center" valignment="top">
35237 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35240 \begin_layout Plain Layout
35246 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35249 \begin_layout Plain Layout
35257 <cell alignment="center" valignment="top" usebox="none">
35260 \begin_layout Plain Layout
35264 \begin_inset space \textvisiblespace{}
35270 \begin_inset space \textvisiblespace{}
35278 <cell alignment="center" valignment="top" usebox="none">
35281 \begin_layout Plain Layout
35282 \begin_inset Formula $\cancel{\int A=B}$
35291 <row topspace="1.5mm">
35292 <cell alignment="center" valignment="top" usebox="none">
35295 \begin_layout Plain Layout
35299 \begin_inset space \textvisiblespace{}
35305 \begin_inset space \textvisiblespace{}
35313 <cell alignment="center" valignment="top" usebox="none">
35316 \begin_layout Plain Layout
35317 \begin_inset Formula $\bcancel{\int A=B}$
35326 <row topspace="1.5mm">
35327 <cell alignment="center" valignment="top" usebox="none">
35330 \begin_layout Plain Layout
35334 \begin_inset space \textvisiblespace{}
35340 \begin_inset space \textvisiblespace{}
35348 <cell alignment="center" valignment="top" usebox="none">
35351 \begin_layout Plain Layout
35352 \begin_inset Formula $\xcancel{\int A=B}$
35362 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35365 \begin_layout Plain Layout
35369 \begin_inset space \textvisiblespace{}
35375 \begin_inset space \textvisiblespace{}
35379 \begin_inset Formula $\to$
35387 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35390 \begin_layout Plain Layout
35391 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35407 \begin_layout Standard
35414 is especially suitable to visualize the reduction of fractions within formulas:
35415 \begin_inset Formula
35417 \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}}}
35425 \begin_layout Standard
35426 To change the size of
35433 \begin_inset Quotes eld
35437 \begin_inset Quotes erd
35440 value one can add the \SpecialChar LaTeX
35444 \begin_layout Standard
35449 PassOptionsToPackage{option}{cancel}
35452 \begin_layout Standard
35461 which leads to the same size as for the canceled value, or
35465 which makes is it a bit smaller than normal.
35468 \begin_layout Standard
35469 To color the cancellation bar one adds this command as \SpecialChar TeX
35473 \begin_layout Standard
35485 \begin_layout Standard
35490 can be replaced by a color of your choice.
35493 \begin_layout Standard
35497 \begin_layout Plain Layout
35513 \begin_layout Standard
35514 \begin_inset Formula
35516 \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}}}
35524 \begin_layout Standard
35528 \begin_layout Plain Layout
35542 \begin_inset Note Note
35545 \begin_layout Plain Layout
35554 \begin_layout Standard
35555 For further customizations, see the documentation of the package
35560 \begin_inset CommandInset citation
35567 \begin_inset Index idx
35570 \begin_layout Plain Layout
35579 \begin_layout Standard
35583 \begin_layout Plain Layout
35593 \begin_inset Note Note
35596 \begin_layout Plain Layout
35597 The following will be displayed when the \SpecialChar LaTeX
35610 \begin_layout Standard
35611 You need to install the \SpecialChar LaTeX
35616 to see the rest of this subsection in the output.
35619 \begin_layout Standard
35623 \begin_layout Plain Layout
35635 \begin_layout Subsection
35636 Formulas in Section Headings
35637 \begin_inset CommandInset label
35639 name "subsec:Formulas-in-Section"
35644 \begin_inset Index idx
35647 \begin_layout Plain Layout
35648 Formula ! in section headings
35656 \begin_layout Standard
35657 When formulas are used in section headings, the following has to be taken
35661 \begin_layout Standard
35662 \begin_inset Note Greyedout
35665 \begin_layout Plain Layout
35671 \begin_inset Index idx
35674 \begin_layout Plain Layout
35675 Packages ! hyperref
35680 support is enabled in the document settings dialog under
35683 \begin_inset space ~
35688 , PDF-bookmarks are created for every section heading in the table of contents.
35689 If a section heading contains formulas, they are incorrectly displayed
35690 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35699 \begin_layout Standard
35700 Both problems can be solved by inserting at the end of the section heading
35701 a short title with the menu
35703 Insert\SpecialChar menuseparator
35705 \begin_inset space ~
35711 Short titles are used as alternative for multiline section headings to
35712 keep the table of contents clearly arranged.
35713 Only the short title appears in the table of contents and therefore also
35714 in the PDF-bookmark.
35717 \begin_layout Standard
35718 When formulas should be used in the table of contents but
35722 is used, one can use the following command in \SpecialChar TeX
35726 \begin_layout Standard
35731 texorpdfstring{part}{alternative}
35732 \begin_inset Index idx
35735 \begin_layout Plain Layout
35746 \begin_layout Standard
35747 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35748 This can be characters, formulas, footnotes, but also cross-references.
35749 The alternative is used instead of the part for the bookmark.
35752 \begin_layout Standard
35753 Here are two example headings:
35754 \begin_inset VSpace -3mm
35761 \begin_layout Plain Layout
35773 \begin_layout Subsubsection
35774 Heading without formula in table of contents
35775 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35779 \begin_inset Argument 1
35782 \begin_layout Plain Layout
35783 Heading without formula in table of contents
35791 \begin_layout Subsubsection
35792 Heading with formula in table of contents
35796 \begin_layout Plain Layout
35806 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35813 \begin_layout Plain Layout
35823 \begin_layout Standard
35827 \begin_layout Plain Layout
35836 In the first heading a short title was used, in the second one
35845 \begin_layout Standard
35846 To get the same formatting as for the other headings, the complete heading
35855 \begin_layout Plain Layout
35857 \begin_inset CommandInset ref
35859 reference "subsec:Bold-Formulas"
35871 \begin_layout Subsection
35872 Formulas in multi-column Text
35873 \begin_inset Index idx
35876 \begin_layout Plain Layout
35877 Formula ! in multi-column text
35885 \begin_layout Standard
35886 Formulas in multi-column text are often too wide to fit into a column and
35887 thus need to be set over the whole page width.
35888 This is done by using the \SpecialChar LaTeX
35897 \begin_layout Plain Layout
35902 is part of every \SpecialChar LaTeX
35903 standard installation.
35909 \begin_inset Index idx
35912 \begin_layout Plain Layout
35913 Packages ! multicol
35918 , that is loaded with the \SpecialChar LaTeX
35922 \begin_layout Standard
35927 usepackage{multicol}
35930 \begin_layout Standard
35931 \begin_inset Note Greyedout
35934 \begin_layout Plain Layout
35935 Note that in this case the setting
35938 \begin_inset space ~
35945 Document\SpecialChar menuseparator
35951 \begin_inset space ~
35971 \begin_layout Standard
35972 Before the multi-column text the command
35975 \begin_layout Standard
35980 begin{multicols}{column number}
35983 \begin_layout Standard
35984 is written in \SpecialChar TeX
35986 The column number is a number in the range of 2
35987 \begin_inset space \thinspace{}
35991 \begin_inset space \thinspace{}
35995 Before the formula the multi-column text is ended by inserting the command
35998 \begin_layout Standard
36006 \begin_layout Standard
36007 in \SpecialChar TeX
36011 \begin_layout Standard
36012 Due to the command some space is automatically added before the formula.
36014 \begin_inset space \thinspace{}
36017 mm vertical space is inserted before the formula.
36018 When the formula style
36024 \begin_layout Plain Layout
36026 \begin_inset CommandInset ref
36028 reference "sec:Formula-Styles"
36040 \begin_inset space \thinspace{}
36043 mm space is inserted instead.
36046 \begin_layout Standard
36047 As example a multi-column text with a displayed formula:
36050 \begin_layout Standard
36056 \begin_layout Plain Layout
36060 begin{multicols}{2}
36065 Das Spektrum wird fouriertransformiert.
36066 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36067 , Lösungsmittel) zu trennen.
36068 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36069 nun das Aussehen des Ausgangssignals.
36070 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36071 über alle Phasen integrieren muss.
36073 \begin_inset Formula $S$
36076 unser normiertes Ausgangssignal und
36077 \begin_inset Formula $P$
36080 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36084 \begin_layout Plain Layout
36094 \begin_inset VSpace -6mm
36098 \begin_inset Formula
36100 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36109 \begin_layout Plain Layout
36113 begin{multicols}{2}
36119 \begin_inset Formula $S_{0}$
36122 das Signal ohne Gradient ist und die Normierungsbedingung
36123 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36127 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36129 \begin_inset Formula $\nicefrac{\pi}{2}$
36133 \begin_inset space \thinspace{}
36136 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36137 das Signal zusätzlich abschwächt.
36138 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36140 \begin_inset Formula $T_{2}$
36146 \begin_layout Standard
36152 \begin_layout Plain Layout
36164 \begin_layout Subsection
36165 Formulas with Description of Variables
36166 \begin_inset Index idx
36169 \begin_layout Plain Layout
36170 Formula ! with description of variables
36178 \begin_layout Standard
36179 To describe variables within a formula, like in formula
36180 \begin_inset CommandInset ref
36182 reference "eq:within"
36191 \begin_inset Formula $n$
36195 \begin_inset space ~
36198 matrix is used with left aligned columns for the
36199 \begin_inset Formula $n$
36206 \begin_layout Plain Layout
36208 \begin_inset CommandInset ref
36210 reference "sec:Matrices"
36219 To set the description in a smaller size, before the matrix e.
36220 \begin_inset space \thinspace{}
36224 \begin_inset space \space{}
36237 \begin_layout Plain Layout
36239 \begin_inset CommandInset ref
36241 reference "subsec:Font-Sizes"
36253 \begin_layout Standard
36254 When the formula style
36260 \begin_layout Plain Layout
36262 \begin_inset CommandInset ref
36264 reference "sec:Formula-Styles"
36285 \begin_layout Plain Layout
36292 only works in formulas with the style
36297 \begin_inset CommandInset ref
36299 reference "subsec:Variable-Space"
36308 is inserted before and after the matrix to have the same separation of
36309 the matrix from the equation and the side margin.
36312 \begin_layout Standard
36313 When the formula style
36317 is used, the method described in
36318 \begin_inset CommandInset ref
36320 reference "subsec:Flalign-Environment"
36324 is used to indent formulas.
36326 \begin_inset CommandInset ref
36328 reference "eq:within"
36332 consists of five columns where in the first two columns contain the equation,
36333 the third the matrix and the last one an empty \SpecialChar TeX
36335 \begin_inset Formula
36337 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36338 \rho & \textrm{density}\\
36339 V & \textrm{volume}\\
36340 g & \textrm{gravitational acceleration}
36341 \end{array} & & {}\label{eq:within}
36349 \begin_layout Subsection
36350 Upright small Greek Letters
36351 \begin_inset CommandInset label
36353 name "subsec:Upright-small-Greek"
36358 \begin_inset Index idx
36361 \begin_layout Plain Layout
36362 Greek letters ! upright
36370 \begin_layout Standard
36371 Most of the math fonts only provide italic small Greek letters.
36372 But for symbols of elementary particles like pions and neutrinos, upright
36373 Greek letters are needed.
36382 \begin_layout Plain Layout
36387 is part of the \SpecialChar LaTeX
36393 \begin_inset Index idx
36396 \begin_layout Plain Layout
36401 \begin_layout Plain Layout
36421 \begin_inset Index idx
36424 \begin_layout Plain Layout
36430 that is loaded with the \SpecialChar LaTeX
36434 \begin_layout Standard
36439 usepackage{upgreek}
36442 \begin_layout Standard
36448 \begin_layout Plain Layout
36458 \begin_inset Note Note
36461 \begin_layout Plain Layout
36462 The following table will only be displayed when the \SpecialChar LaTeX
36472 They are created when the command for a small Greek letter is started with
36478 For example the command
36485 \begin_inset Formula $\uptau$
36491 \begin_layout Standard
36492 With these commands reactions of elementary particles can be typeset:
36493 \begin_inset Formula
36495 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36503 \begin_layout Standard
36504 The upright letters are more bold and wider than the italic ones.
36505 They should therefore not be used for units like
36506 \begin_inset Quotes eld
36510 \begin_inset Quotes erd
36516 \begin_layout Standard
36520 \begin_layout Plain Layout
36530 \begin_inset Note Note
36533 \begin_layout Plain Layout
36534 The following will be displayed when the \SpecialChar LaTeX
36547 \begin_layout Standard
36548 You need to install the \SpecialChar LaTeX
36553 to see the rest of this subsection in the output.
36556 \begin_layout Standard
36560 \begin_layout Plain Layout
36572 \begin_layout Subsection
36573 Text Characters in Formulas
36574 \begin_inset Index idx
36577 \begin_layout Plain Layout
36586 \begin_layout Standard
36587 In some cases you might want to insert text characters directly into formulas.
36588 When for example the centered dot · is often used in formulas like
36589 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36592 , one would have to insert the command
36602 \begin_layout Plain Layout
36604 \begin_inset CommandInset ref
36606 reference "subsec:Binary-Operators"
36615 all the time, because this character is defined in all encodings as text
36617 But the encoding can be changed by this \SpecialChar LaTeX
36621 \begin_layout Standard
36626 Declare Inputtext{183}{
36636 f\SpecialChar ligaturebreak
36640 \begin_layout Standard
36641 The character encoding (menu
36643 Document\SpecialChar menuseparator
36644 Settings\SpecialChar menuseparator
36647 ) specifies what character appears when a keyboard key is pressed.
36648 When the key for the character '·' is pressed, internally the command
36655 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36657 With the changed encoding the right command is chosen automatically, depending
36658 on if the character was inserted into a formula or not.
36661 \begin_layout Standard
36662 The encoding of several characters is saved in definition files.
36663 For example the encoding
36667 is defined in the file
36671 which is in the installation folder of \SpecialChar LaTeX
36673 Encodings should only be changed via the \SpecialChar LaTeX
36674 -preamble and not in the definition
36676 Otherwise documents could not be edited by other \SpecialChar LyX
36677 users working on other
36681 \begin_layout Standard
36682 \begin_inset VSpace medskip
36685 Besides the centered dot, in this document the degree sign ° is defined
36686 with the following \SpecialChar LaTeX
36687 -preamble line so that it can be directly inserted into
36691 \begin_layout Standard
36696 DeclareInputtext{176}{
36706 f\SpecialChar ligaturebreak
36710 \begin_layout Subsection
36712 -comments in formulas
36713 \begin_inset Index idx
36716 \begin_layout Plain Layout
36726 \begin_layout Standard
36727 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36729 code of your file with the menu
36731 Insert\SpecialChar menuseparator
36732 Note\SpecialChar menuseparator
36736 This is not possible in a formula but you can insert \SpecialChar LaTeX
36741 \begin_layout Standard
36749 \begin_layout Standard
36750 This creates a box in which you can write your comment.
36751 Due to a bug in \SpecialChar LyX
36756 \begin_layout Plain Layout
36757 \begin_inset CommandInset href
36759 name "LyX-bug #9002"
36760 target "http://www.lyx.org/trac/ticket/9002"
36769 you cannot write normal text inside the comment, even when you use mathematical
36770 text, you will see its \SpecialChar LaTeX
36771 -commands in the \SpecialChar LaTeX
36773 \begin_inset Newline newline
36776 This a formula with a \SpecialChar LaTeX
36778 \begin_inset Formula
36780 A=B%\text{This is the comment}
36788 \begin_layout Standard
36789 \begin_inset Newpage newpage
36795 \begin_layout Section
36798 \begin_inset Index idx
36801 \begin_layout Plain Layout
36810 \begin_layout Standard
36811 This section is a summary of the most important typographic rules, listed
36816 \begin_layout Plain Layout
36817 This collection was partly taken from the German semi-official dictionary
36819 \begin_inset Quotes eld
36823 \begin_inset Quotes erd
36827 \begin_inset CommandInset citation
36833 that lists some of the ISO rules.
36834 More rules are listed in
36835 \begin_inset CommandInset citation
36849 \begin_layout Itemize
36858 \begin_layout Plain Layout
36859 done with font styles, see
36860 \begin_inset CommandInset ref
36862 reference "subsec:Font-Styles"
36871 , no matter if they appear in italic text: 30
36872 \begin_inset space \thinspace{}
36876 \begin_inset Newline newline
36879 Between the value and the unit is the smallest space, see
36880 \begin_inset CommandInset ref
36882 reference "subsec:Predefined-Space"
36887 \begin_inset Newline newline
36890 This convention is automatically fulfilled when the command
36897 When it is entered to a formula, two boxes appear.
36898 In the first one the value is inserted, in the second one the unit, and
36900 \begin_inset Formula $\unit[30]{km/h}$
36904 \begin_inset space \thinspace{}
36914 is not a real \SpecialChar LaTeX
36915 command but the command
36921 , therefore you cannot use it in \SpecialChar TeX
36925 \begin_layout Itemize
36926 Percent and perthousand signs are set like physical units:
36927 \begin_inset Newline newline
36931 \begin_inset space \thinspace{}
36937 \begin_layout Itemize
36938 The degree sign follows directly on the value: 15°, but not when it is used
36940 \begin_inset space \thinspace{}
36946 \begin_layout Itemize
36947 In numbers with more than four digits the smallest space is inserted before
36948 every third digit to group them:
36958 \begin_inset space \thinspace{}
36962 \begin_inset space \thinspace{}
36968 \begin_layout Itemize
36969 For dimensions like 120×90×40
36970 \begin_inset space \thinspace{}
36973 cm the multiplication sign
36974 \begin_inset Quotes eld
36978 \begin_inset Quotes erd
36982 It is available either via the command
36990 Insert\SpecialChar menuseparator
36991 Special Character\SpecialChar menuseparator
36997 \begin_layout Itemize
36998 Functions with names consisting of several letters are set upright to avoid
37000 \begin_inset CommandInset ref
37002 reference "subsec:Predefined-Functions"
37009 \begin_layout Itemize
37010 Indices consisting of several letters, are set upright:
37011 \begin_inset Formula $E_{\mathrm{kin}}$
37015 \begin_inset Newline newline
37018 Components of matrices are set italic:
37019 \begin_inset Formula $\hat{H}_{kl}$
37025 \begin_layout Itemize
37026 The differentiation/integration operator 'd', the Euler's number 'e' and
37027 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37031 \begin_layout Itemize
37032 The character that denotes a
37036 transformation is inserted either by the command
37041 \begin_inset space \textvisiblespace{}
37048 Insert\SpecialChar menuseparator
37049 Special Character\SpecialChar menuseparator
37050 Symbols\SpecialChar menuseparator
37052 \begin_inset space ~
37058 \begin_inset Formula $\mathscr{F}$
37064 \begin_layout Standard
37065 \begin_inset Newpage newpage
37071 \begin_layout Section
37073 \begin_inset Index idx
37076 \begin_layout Plain Layout
37085 \begin_layout Standard
37086 Some characters and symbols can be created with several commands.
37087 Here is a list of the synonym commands:
37090 \begin_layout Standard
37091 \begin_inset VSpace bigskip
37095 \begin_inset space \hfill{}
37099 \begin_inset Tabular
37100 <lyxtabular version="3" rows="12" columns="2">
37101 <features booktabs="true" tabularvalignment="middle">
37102 <column alignment="center" valignment="top" width="0pt">
37103 <column alignment="center" valignment="top" width="0pt">
37105 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37108 \begin_layout Plain Layout
37114 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37117 \begin_layout Plain Layout
37125 <cell alignment="center" valignment="top" usebox="none">
37128 \begin_layout Plain Layout
37136 <cell alignment="center" valignment="top" usebox="none">
37139 \begin_layout Plain Layout
37147 <cell alignment="center" valignment="top" usebox="none">
37150 \begin_layout Plain Layout
37158 <cell alignment="center" valignment="top" usebox="none">
37161 \begin_layout Plain Layout
37171 <cell alignment="center" valignment="top" usebox="none">
37174 \begin_layout Plain Layout
37182 <cell alignment="center" valignment="top" usebox="none">
37185 \begin_layout Plain Layout
37195 <cell alignment="center" valignment="top" usebox="none">
37198 \begin_layout Plain Layout
37206 <cell alignment="center" valignment="top" usebox="none">
37209 \begin_layout Plain Layout
37217 <cell alignment="center" valignment="top" usebox="none">
37220 \begin_layout Plain Layout
37228 <cell alignment="center" valignment="top" usebox="none">
37231 \begin_layout Plain Layout
37239 <cell alignment="center" valignment="top" usebox="none">
37242 \begin_layout Plain Layout
37250 <cell alignment="center" valignment="top" usebox="none">
37253 \begin_layout Plain Layout
37263 <cell alignment="center" valignment="top" usebox="none">
37266 \begin_layout Plain Layout
37274 <cell alignment="center" valignment="top" usebox="none">
37277 \begin_layout Plain Layout
37287 <cell alignment="center" valignment="top" usebox="none">
37290 \begin_layout Plain Layout
37298 <cell alignment="center" valignment="top" usebox="none">
37301 \begin_layout Plain Layout
37311 <cell alignment="center" valignment="top" usebox="none">
37314 \begin_layout Plain Layout
37322 <cell alignment="center" valignment="top" usebox="none">
37325 \begin_layout Plain Layout
37335 <cell alignment="center" valignment="top" usebox="none">
37338 \begin_layout Plain Layout
37346 <cell alignment="center" valignment="top" usebox="none">
37349 \begin_layout Plain Layout
37357 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37360 \begin_layout Plain Layout
37368 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37371 \begin_layout Plain Layout
37383 \begin_inset space \hfill{}
37387 \begin_inset Tabular
37388 <lyxtabular version="3" rows="12" columns="2">
37389 <features booktabs="true" tabularvalignment="middle">
37390 <column alignment="center" valignment="top" width="0pt">
37391 <column alignment="center" valignment="top" width="0pt">
37393 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37396 \begin_layout Plain Layout
37402 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37405 \begin_layout Plain Layout
37413 <cell alignment="center" valignment="top" usebox="none">
37416 \begin_layout Plain Layout
37424 <cell alignment="center" valignment="top" usebox="none">
37427 \begin_layout Plain Layout
37439 <cell alignment="center" valignment="top" usebox="none">
37442 \begin_layout Plain Layout
37450 <cell alignment="center" valignment="top" usebox="none">
37453 \begin_layout Plain Layout
37463 <cell alignment="center" valignment="top" usebox="none">
37466 \begin_layout Plain Layout
37474 <cell alignment="center" valignment="top" usebox="none">
37477 \begin_layout Plain Layout
37487 <cell alignment="center" valignment="top" usebox="none">
37490 \begin_layout Plain Layout
37498 <cell alignment="center" valignment="top" usebox="none">
37501 \begin_layout Plain Layout
37509 <cell alignment="center" valignment="top" usebox="none">
37512 \begin_layout Plain Layout
37520 <cell alignment="center" valignment="top" usebox="none">
37523 \begin_layout Plain Layout
37531 <cell alignment="center" valignment="top" usebox="none">
37534 \begin_layout Plain Layout
37542 <cell alignment="center" valignment="top" usebox="none">
37545 \begin_layout Plain Layout
37555 <cell alignment="center" valignment="top" usebox="none">
37558 \begin_layout Plain Layout
37566 <cell alignment="center" valignment="top" usebox="none">
37569 \begin_layout Plain Layout
37579 <cell alignment="center" valignment="top" usebox="none">
37582 \begin_layout Plain Layout
37590 <cell alignment="center" valignment="top" usebox="none">
37593 \begin_layout Plain Layout
37603 <cell alignment="center" valignment="top" usebox="none">
37606 \begin_layout Plain Layout
37614 <cell alignment="center" valignment="top" usebox="none">
37617 \begin_layout Plain Layout
37627 <cell alignment="center" valignment="top" usebox="none">
37630 \begin_layout Plain Layout
37638 <cell alignment="center" valignment="top" usebox="none">
37641 \begin_layout Plain Layout
37651 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37654 \begin_layout Plain Layout
37662 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37665 \begin_layout Plain Layout
37679 \begin_inset space \hfill{}
37685 \begin_layout Standard
37686 \begin_inset Newpage newpage
37692 \begin_layout Bibliography
37693 \begin_inset CommandInset bibitem
37694 LatexCommand bibitem
37706 The \SpecialChar LaTeX
37710 Addison Wesley, 2004
37713 \begin_layout Bibliography
37714 \begin_inset CommandInset bibitem
37715 LatexCommand bibitem
37721 \begin_inset CommandInset href
37724 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37728 of \SpecialChar LaTeX
37732 \begin_layout Bibliography
37733 \begin_inset CommandInset bibitem
37734 LatexCommand bibitem
37740 \begin_inset CommandInset href
37743 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37751 \begin_layout Plain Layout
37760 -\SpecialChar LaTeX
37764 \begin_layout Bibliography
37765 \begin_inset CommandInset bibitem
37766 LatexCommand bibitem
37772 \begin_inset CommandInset href
37775 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37779 of all symbols available with \SpecialChar LaTeX
37783 \begin_layout Bibliography
37784 \begin_inset CommandInset bibitem
37785 LatexCommand bibitem
37791 \begin_inset CommandInset href
37793 name "Documentation"
37794 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37798 of the \SpecialChar LaTeX
37804 \begin_inset Index idx
37807 \begin_layout Plain Layout
37816 \begin_layout Bibliography
37817 \begin_inset CommandInset bibitem
37818 LatexCommand bibitem
37824 \begin_inset CommandInset href
37826 name "Documentation"
37827 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37831 of the \SpecialChar LaTeX
37837 \begin_inset Index idx
37840 \begin_layout Plain Layout
37841 Packages ! hyperref
37849 \begin_layout Bibliography
37850 \begin_inset CommandInset bibitem
37851 LatexCommand bibitem
37857 \begin_inset CommandInset href
37859 name "Documentation"
37860 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37864 of the \SpecialChar LaTeX
37870 \begin_inset Index idx
37873 \begin_layout Plain Layout
37882 \begin_layout Bibliography
37883 \begin_inset CommandInset bibitem
37884 LatexCommand bibitem
37895 Auflage, Duden 2001
37898 \begin_layout Bibliography
37899 \begin_inset CommandInset bibitem
37900 LatexCommand bibitem
37906 \begin_inset CommandInset href
37909 target "http://physics.nist.gov/Pubs/SP811/sec11.html"
37913 for reviewing manuscripts
37916 \begin_layout Standard
37917 \begin_inset CommandInset index_print
37918 LatexCommand printindex