1 #LyX 2.1 created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % solves the following problem:
27 % If the dection number consits of too many numerals the section heading
28 % will be printed in the TOC without a space between it and the section number.
29 % As solution more space between the number and the heading is inserted:
30 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
31 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
33 % increase link area for cross-references and autoname them,
34 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
35 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
36 \addto\extrasenglish{%
37 \renewcommand*{\equationautorefname}[1]{}%
38 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
39 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
40 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
43 % don't load packages twice
44 % see first footnote in sec. 9.3
45 \@ifundefined{textcolor}{\usepackage{color}}{}
47 % the pages of the TOC are numbered roman
48 % and a PDF-bookmark for the TOC is added
50 \let\myTOC\tableofcontents
51 \renewcommand{\tableofcontents}{%
53 \pdfbookmark[1]{\contentsname}{}
56 \pagenumbering{arabic}}
58 % insert additional vertical space of 1.5 mm between footnotes,
60 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
62 % provides caption formatting
63 \setkomafont{captionlabel}{\bfseries}
65 % enables calculation of values
68 % for multiple columns used in sec. 24.7
74 % for the Fourier transformation symbol
77 % define a color, used in sec.9.3
78 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
80 % declare operators (see sec. 10.4 and sec. 15.2)
81 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
82 \DeclareMathOperator{\sgn}{sgn}
84 % example definitions for sec. 20.1
85 \newcommand{\gr}{\Longrightarrow}
86 \newcommand{\us}[1]{\underline{#1}}
87 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
88 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
89 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
91 % example macro from sec. 19.4
92 %\def\tagform@#1{\maketag@@@{|#1|}}
94 % macro from sec. 10.2
95 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
96 \def\mathclap {\mathpalette \mathclapinternal}
97 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
100 % ------------------------------------
101 % used to check for needed LaTeX packages
104 % check for package undertilde
105 % used for the command \utilde
106 \newboolean{undertilde}
107 \IfFileExists{undertilde.sty}
108 {\usepackage{undertilde}
109 \setboolean{undertilde}{true}}
110 {\setboolean{undertilde}{false}}
112 % check for package eurosym
113 % used for the Euro symbol
115 \IfFileExists{eurosym.sty}
116 {\usepackage[gennarrow]{eurosym}
117 \setboolean{eurosym}{true}}
118 {\setboolean{eurosym}{false}}
120 % check for package braket
121 % used for physical vectors
123 \IfFileExists{braket.sty}
125 \setboolean{braket}{true}}
126 {\setboolean{braket}{false}}
128 % check for package cancel
130 \IfFileExists{cancel.sty}
132 \setboolean{cancel}{true}}
133 {\setboolean{cancel}{false}}
135 % check for package upgreek
137 \IfFileExists{upgreek.sty}
138 {\usepackage{upgreek}
139 \setboolean{upgreek}{true}}
140 {\setboolean{upgreek}{false}}
142 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
143 \use_default_options false
144 \maintain_unincluded_children false
146 \language_package default
151 \font_typewriter default
153 \font_default_family default
154 \use_non_tex_fonts false
160 \default_output_format default
162 \bibtex_command default
163 \index_command default
167 \pdf_title "LyX's Math Manual"
168 \pdf_author "LyX Team, Uwe Stöhr"
169 \pdf_subject "LyX-documentation about math"
170 \pdf_keywords "LyX, Mathed"
172 \pdf_bookmarksnumbered true
173 \pdf_bookmarksopen true
174 \pdf_bookmarksopenlevel 1
175 \pdf_breaklinks false
179 \pdf_pdfusetitle false
180 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
183 \use_package amsmath 2
184 \use_package amssymb 2
185 \use_package cancel 0
187 \use_package mathdots 1
188 \use_package mathtools 0
189 \use_package mhchem 1
190 \use_package stackrel 0
191 \use_package stmaryrd 0
192 \use_package undertilde 0
194 \cite_engine_type default
198 \paperorientation portrait
202 \notefontcolor #0000ff
209 \paragraph_separation skip
211 \quotes_language english
214 \paperpagestyle plain
218 \tracking_changes false
219 \output_changes false
222 \html_be_strict false
228 LyX's detailed Math manual
236 \begin_layout Plain Layout
238 If you have comments or error corrections, please send them to the LyX Documenta
242 \begin_inset CommandInset href
244 name "lyx-docs@lists.lyx.org"
245 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
256 \begin_inset Note Note
259 \begin_layout Plain Layout
266 \begin_inset Newline newline
270 \begin_inset Newline newline
278 \begin_layout Standard
279 \begin_inset CommandInset toc
280 LatexCommand tableofcontents
287 \begin_layout Standard
288 \begin_inset Note Note
291 \begin_layout Plain Layout
292 To export this document to PDF, PS or DVI the LaTeX-packages
294 braket, cancel, eurosym, mathdots, mhchem, undertilde
301 If they are not installed the document can be exported anyway but the sections
302 where the packages are required will not appear in the output.
307 ; if it is not installed, this file cannot be exported.
310 \begin_layout Plain Layout
311 The latest PDF-version of this document can be found here:
312 \begin_inset Newline newline
317 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
325 \begin_layout Standard
326 \begin_inset Newpage newpage
332 \begin_layout Section
336 \begin_layout Standard
337 This document explains LyX's math features and is furthermore a collection
338 of LaTeX-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 LyX.
425 \begin_layout Standard
426 This document doesn't list all
430 \begin_layout Plain Layout
443 \begin_layout Plain Layout
448 \begin_layout Plain Layout
457 -math commands is in the file
460 \begin_inset CommandInset href
463 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
469 , which is part of every LaTeX standard installation.
474 for lucidity reasons.
477 \begin_layout Section
481 \begin_layout Standard
482 To create an inline formula
483 \begin_inset Index idx
486 \begin_layout Plain Layout
492 that is embedded into a text line, use one of the shortcuts
498 or the toolbar button
499 \begin_inset Graphics
500 filename ../images/math-mode.png
506 \begin_inset Newline newline
509 To create a display style formula
510 \begin_inset Index idx
513 \begin_layout Plain Layout
514 Formula ! display style
519 which will appear bigger, has a different format, and will be in a separate
520 paragraph, use one of these shortcuts:
529 \begin_layout Standard
530 To change a display style formula to an inline formula, set the cursor into
531 the formula and use one of the shortcuts
539 Edit\SpecialChar \menuseparator
540 Math\SpecialChar \menuseparator
544 The same way is used to change an inline formula to a display style formula.
547 \begin_layout Standard
548 To display parts of an inline formula in the size of a display style formula,
556 \begin_inset Index idx
559 \begin_layout Plain Layout
568 Then a new blue box appears in which the desired formula part is inserted.
571 \begin_layout Standard
572 Only inline formulas are allowed inside tables.
575 \begin_layout Standard
580 can be turned on in the menu
582 View\SpecialChar \menuseparator
586 When you click there on
587 \begin_inset Quotes eld
591 \begin_inset Quotes erd
594 the toolbar will be shown permanently at the bottom; this state is visualized
599 menu with a checkmark.
600 When you click in this state again on
601 \begin_inset Quotes eld
605 \begin_inset Quotes erd
616 is only shown when the cursor is within a formula; this state is visualized
617 by the renaming of the menu entry from
618 \begin_inset Quotes eld
622 \begin_inset Quotes erd
626 \begin_inset Quotes eld
634 \begin_inset Quotes erd
640 \begin_layout Standard
642 \begin_inset Index idx
645 \begin_layout Plain Layout
651 is invoked by pressing the toolbar button
652 \begin_inset Graphics
653 filename ../images/ert-insert.png
660 Insert\SpecialChar \menuseparator
665 \begin_layout Plain Layout
681 \begin_inset Note Note
684 \begin_layout Plain Layout
685 In LyX there are three
686 \begin_inset Quotes eld
690 \begin_inset Quotes erd
693 that appear in the output with sub- and superscript letters: TeX, LaTeX
697 \begin_layout Plain Layout
698 To avoid that these names are recognized as proper names, a TeX-brace pair
707 \begin_layout Standard
708 To change the LaTeX-preamble
709 \begin_inset Index idx
712 \begin_layout Plain Layout
720 Document\SpecialChar \menuseparator
721 Settings\SpecialChar \menuseparator
726 \begin_layout Plain Layout
742 \begin_layout Standard
743 To edit matrices, case differentiations and multiline formulas subsequently,
746 Edit\SpecialChar \menuseparator
751 Edit\SpecialChar \menuseparator
753 \begin_inset space \thinspace{}
757 \begin_inset space \thinspace{}
767 When lines and columns are swapped via the menu, the column or line where
768 the cursor is in is exchanged with the column to the right or the line
770 Is the cursor in the last column or row, the exchange is done with the
771 column to the left or the line above.
774 \begin_layout Standard
775 To write text in formulas
779 \begin_layout Plain Layout
780 For multiline formulas the command
787 \begin_inset CommandInset ref
789 reference "sub:Text-in-multiline"
803 \begin_inset Index idx
806 \begin_layout Plain Layout
813 \begin_inset Index idx
816 \begin_layout Plain Layout
823 This mode is invoked with the shortcut
829 or by the insertion of the command
836 \begin_inset Index idx
839 \begin_layout Plain Layout
848 The text appears black in LyX and can therefore be distinguished from the
849 other formula parts which appear blue.
850 In the output mathematical text is set upright, in contrary to other formula
854 \begin_layout Subsection*
858 \begin_layout Standard
859 Most of the LaTeX-commands for math constructs have the following scheme:
862 \begin_layout Standard
878 \begin_layout Standard
879 A command always starts with a backslash
880 \begin_inset Quotes gld
890 \begin_inset Quotes grd
894 To omit optional arguments, also omit the associated brackets.
895 The braces around the required arguments are named in this document as
897 \begin_inset Index idx
900 \begin_layout Plain Layout
907 If you add in a formula a left brace to a command name, LyX automatically
909 In all other cases TeX-braces are created in formulas with the command
917 TeX-braces appear red in LyX, in contrary to normal braces which appear
919 In TeX-mode no command is needed to get TeX-braces.
920 TeX-braces don't appear in the output.
923 \begin_layout Standard
924 When commands without arguments, like commands for symbols are entered in
925 TeX-mode, a space character must
929 be behind the command to end it.
930 This space doesn't appear in the output.
931 When the space should appear in the output, the space must be followed
932 by a protected space in normal text.
935 \begin_layout Standard
936 A protected space is inserted with
939 arg "command-alternatives space-insert protected ; math-space"
945 \begin_layout Subsection*
946 \begin_inset Newpage newpage
952 \begin_layout Itemize
954 \begin_inset space \textvisiblespace{}
957 denotes a space character to be input.
960 \begin_layout Itemize
962 \begin_inset Formula $\to$
965 denotes the usage of the corresponding arrow key on the keyboard.
970 key can often be used instead of
971 \begin_inset Formula $\to$
975 \begin_inset Formula $\downarrow$
983 \begin_inset Formula $\leftarrow$
987 \begin_inset Formula $\uparrow$
993 \begin_layout Subsection*
997 \begin_layout Standard
999 \begin_inset Float table
1005 \begin_layout Plain Layout
1007 \begin_inset Caption Standard
1009 \begin_layout Plain Layout
1010 \begin_inset CommandInset label
1012 name "tab:Available-units"
1024 \begin_layout Plain Layout
1026 \begin_inset Tabular
1027 <lyxtabular version="3" rows="13" columns="2">
1028 <features rotate="0" tabularvalignment="middle">
1029 <column alignment="center" valignment="top">
1030 <column alignment="center" valignment="top">
1032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1035 \begin_layout Plain Layout
1041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1044 \begin_layout Plain Layout
1052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1055 \begin_layout Plain Layout
1061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1064 \begin_layout Plain Layout
1072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1075 \begin_layout Plain Layout
1081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1084 \begin_layout Plain Layout
1092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1095 \begin_layout Plain Layout
1101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1104 \begin_layout Plain Layout
1106 \begin_inset space \thinspace{}
1110 \begin_inset space \thinspace{}
1120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1123 \begin_layout Plain Layout
1129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1132 \begin_layout Plain Layout
1134 \begin_inset space \thinspace{}
1138 \begin_inset space \thinspace{}
1148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1151 \begin_layout Plain Layout
1157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1160 \begin_layout Plain Layout
1162 \begin_inset space \thinspace{}
1166 \begin_inset space \thinspace{}
1176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1179 \begin_layout Plain Layout
1185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1188 \begin_layout Plain Layout
1190 \begin_inset space \thinspace{}
1194 \begin_inset space \thinspace{}
1204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1207 \begin_layout Plain Layout
1213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1216 \begin_layout Plain Layout
1218 \begin_inset space \thinspace{}
1222 \begin_inset space \thinspace{}
1232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1235 \begin_layout Plain Layout
1241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1244 \begin_layout Plain Layout
1246 \begin_inset space \thinspace{}
1250 \begin_inset Formula $\approx$
1254 \begin_inset space \thinspace{}
1264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1267 \begin_layout Plain Layout
1273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1276 \begin_layout Plain Layout
1278 \begin_inset space \thinspace{}
1282 \begin_inset space \thinspace{}
1292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1295 \begin_layout Plain Layout
1301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1304 \begin_layout Plain Layout
1308 \begin_inset Quotes eld
1314 \begin_inset Quotes erd
1324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1327 \begin_layout Plain Layout
1333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1336 \begin_layout Plain Layout
1338 \begin_inset Quotes eld
1346 \begin_inset Quotes erd
1356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1359 \begin_layout Plain Layout
1365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1368 \begin_layout Plain Layout
1370 \begin_inset space \thinspace{}
1374 \begin_inset Formula $\nicefrac{1}{18}$
1378 \begin_inset space \thinspace{}
1399 \begin_layout Standard
1400 \begin_inset Newpage newpage
1406 \begin_layout Section
1410 \begin_layout Subsection
1412 \begin_inset Index idx
1415 \begin_layout Plain Layout
1422 \begin_inset Index idx
1425 \begin_layout Plain Layout
1432 \begin_inset Index idx
1435 \begin_layout Plain Layout
1440 \begin_layout Plain Layout
1451 \begin_layout Plain Layout
1464 \begin_inset Index idx
1467 \begin_layout Plain Layout
1472 \begin_layout Plain Layout
1483 \begin_layout Plain Layout
1498 \begin_layout Standard
1499 Indices are created with an underscore
1500 \begin_inset Quotes eld
1504 \begin_inset Quotes erd
1507 or via the math toolbar button
1508 \begin_inset Graphics
1509 filename ../images/math-subscript.png
1514 , exponents with a caret
1515 \begin_inset Quotes eld
1519 \begin_inset Quotes erd
1522 or via the math toolbar button
1523 \begin_inset Graphics
1524 filename ../images/math-superscript.png
1532 \begin_layout Standard
1534 \begin_inset Tabular
1535 <lyxtabular version="3" rows="4" columns="2">
1536 <features rotate="0" tabularvalignment="middle">
1537 <column alignment="center" valignment="top" width="0pt">
1538 <column alignment="center" valignment="top" width="0pt">
1540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1543 \begin_layout Plain Layout
1549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1552 \begin_layout Plain Layout
1554 \begin_inset Note Note
1557 \begin_layout Plain Layout
1564 is only used as spacer.
1576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1579 \begin_layout Plain Layout
1585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1588 \begin_layout Plain Layout
1589 \begin_inset Formula $B_{V}$
1599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1602 \begin_layout Plain Layout
1608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1611 \begin_layout Plain Layout
1612 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1625 \begin_layout Plain Layout
1627 \begin_inset space \textvisiblespace{}
1635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1638 \begin_layout Plain Layout
1639 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1655 \begin_layout Standard
1656 As the caret is in some languages an accent, vowels will be accentuated
1657 in this case and not set as exponents
1661 \begin_layout Plain Layout
1662 Depending on the used keyboard settings this can also happen for characters
1669 To get exponents in this case, press
1673 after the caret as in the last example.
1676 \begin_layout Subsection
1678 \begin_inset CommandInset label
1680 name "sub:Fractions"
1685 \begin_inset Index idx
1688 \begin_layout Plain Layout
1697 \begin_layout Standard
1698 Fractions are generated with the command
1705 \begin_inset Index idx
1708 \begin_layout Plain Layout
1716 or via the math toolbar button
1717 \begin_inset Graphics
1718 filename ../images/math/frac.png
1724 The font size is adjusted automatically, depending on whether the fraction
1725 is in an inline or display style formula.
1726 With the math toolbar button
1727 \begin_inset Graphics
1728 filename ../images/math/frac-square.png
1733 you can select different fraction types.
1736 \begin_layout Standard
1744 \begin_inset Index idx
1747 \begin_layout Plain Layout
1755 a fraction can be created that always has the size of a display style formula.
1763 \begin_inset Index idx
1766 \begin_layout Plain Layout
1774 the fraction appears always with the size of an inline formula.
1778 \begin_layout Standard
1779 A line with the fraction
1780 \begin_inset Formula $\frac{1}{2}$
1783 that was created with the command
1792 \begin_layout Standard
1793 A line with the fraction
1794 \begin_inset Formula $\dfrac{1}{2}$
1797 that was created with the command
1806 \begin_layout Standard
1808 \begin_inset Tabular
1809 <lyxtabular version="3" rows="4" columns="2">
1810 <features rotate="0" tabularvalignment="middle">
1811 <column alignment="center" valignment="top" width="0pt">
1812 <column alignment="center" valignment="top" width="0pt">
1814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1817 \begin_layout Plain Layout
1823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1826 \begin_layout Plain Layout
1828 \begin_inset Note Note
1831 \begin_layout Plain Layout
1838 is only used as spacer.
1850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1853 \begin_layout Plain Layout
1857 \begin_inset space \textvisiblespace{}
1861 \begin_inset Formula $\downarrow$
1869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1872 \begin_layout Plain Layout
1873 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1886 \begin_layout Plain Layout
1890 \begin_inset space \textvisiblespace{}
1894 \begin_inset Formula $\downarrow$
1902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1905 \begin_layout Plain Layout
1906 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1919 \begin_layout Plain Layout
1923 \begin_inset space \textvisiblespace{}
1929 \begin_inset space \textvisiblespace{}
1933 \begin_inset Formula $\downarrow$
1937 \begin_inset Formula $\downarrow\downarrow$
1945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1948 \begin_layout Plain Layout
1949 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
1965 \begin_layout Standard
1966 \begin_inset VSpace bigskip
1970 \begin_inset Newpage newpage
1973 For nested fractions the command
1980 \begin_inset Index idx
1983 \begin_layout Plain Layout
1993 \begin_inset VSpace -3mm
1999 \begin_layout Standard
2000 \begin_inset Formula
2002 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2003 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2011 \begin_layout Standard
2012 The command for the example above is:
2015 \begin_layout Standard
2021 \begin_inset space \textvisiblespace{}
2025 \begin_inset Formula $\downarrow$
2031 \begin_inset space \textvisiblespace{}
2037 \begin_inset space \textvisiblespace{}
2041 \begin_inset Formula $\downarrow$
2045 \begin_inset Formula $\downarrow$
2051 \begin_layout Standard
2052 \begin_inset VSpace medskip
2058 \begin_layout Standard
2065 sets the fraction always in the size of a displayed formula, also when
2066 it is part of another fraction.
2069 \begin_layout Standard
2070 It is possible to specify the alignment of the numerator.
2077 is used to left align it, the command
2090 centers the numerator.
2091 These fractions demonstrate the different alignments:
2094 \begin_layout Standard
2097 \begin_inset Formula
2099 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2107 \begin_layout Standard
2108 \begin_inset Note Greyedout
2111 \begin_layout Plain Layout
2128 are no real LaTeX commands but represent the command
2132 cfrac[alignment]{numerator}{denominator}
2135 Therefore you cannot use them in TeX code.
2143 \begin_layout Standard
2144 \begin_inset VSpace medskip
2147 It is often advantageous to combine
2160 \begin_inset Formula
2162 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2170 \begin_layout Standard
2171 For inline fractions with a sloped fraction stroke you can use the command
2179 \begin_inset Index idx
2182 \begin_layout Plain Layout
2191 \begin_inset Formula $\nicefrac{5}{31}$
2201 \begin_inset Index idx
2204 \begin_layout Plain Layout
2213 \begin_inset Formula $\unitfrac{5}{31}$
2216 There is furthermore the command
2222 that offers to write a fraction in combination with a number:
2223 \begin_inset Formula $\unitfrac[2]{1}{3}$
2229 \begin_layout Standard
2230 \begin_inset Note Greyedout
2233 \begin_layout Plain Layout
2244 is not a real LaTeX command but the command
2245 \begin_inset Newline newline
2252 unitfrac[number]{numerator}{denominator}
2255 Therefore you cannot use it in TeX code.
2263 \begin_layout Standard
2264 How to define own fractions where the fraction stroke can be changed, is
2266 \begin_inset CommandInset ref
2268 reference "sub:Self-defined-Fractions"
2275 \begin_layout Standard
2276 \begin_inset Newpage newpage
2282 \begin_layout Subsection
2284 \begin_inset Index idx
2287 \begin_layout Plain Layout
2296 \begin_layout Standard
2297 Square roots are created with
2304 \begin_inset Index idx
2307 \begin_layout Plain Layout
2315 or the math toolbar button
2316 \begin_inset Graphics
2317 filename ../images/math/sqrt.png
2322 , all other roots with the command
2329 \begin_inset Index idx
2332 \begin_layout Plain Layout
2340 or with the math toolbar button
2341 \begin_inset Graphics
2342 filename ../images/math/root.png
2350 \begin_layout Standard
2352 \begin_inset Tabular
2353 <lyxtabular version="3" rows="3" columns="2">
2354 <features rotate="0" tabularvalignment="middle">
2355 <column alignment="center" valignment="top" width="0pt">
2356 <column alignment="center" valignment="top" width="0pt">
2358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2361 \begin_layout Plain Layout
2367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2370 \begin_layout Plain Layout
2372 \begin_inset Note Note
2375 \begin_layout Plain Layout
2382 is only used as spacer.
2394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2397 \begin_layout Plain Layout
2401 \begin_inset space \textvisiblespace{}
2409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2412 \begin_layout Plain Layout
2413 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2423 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2426 \begin_layout Plain Layout
2430 \begin_inset space \textvisiblespace{}
2434 \begin_inset Formula $\downarrow$
2442 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2445 \begin_layout Plain Layout
2446 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2462 \begin_layout Standard
2463 A square root can also be created with
2469 when the root index field is left empty.
2472 \begin_layout Standard
2473 With certain indices the distance to the root is too small, like in this
2475 \begin_inset Formula $\sqrt[\beta]{B}$
2479 \begin_inset Newline newline
2483 \begin_inset Formula $\beta$
2487 To avoid this, the commands
2494 \begin_inset Index idx
2497 \begin_layout Plain Layout
2512 \begin_inset Index idx
2515 \begin_layout Plain Layout
2523 are used with the following scheme:
2526 \begin_layout Standard
2540 \begin_layout Standard
2541 Distance is the number of Big Points (unit bp;
2542 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2545 ), that the index should be moved to the left or top, resp..
2546 The commands are written to the index.
2547 This way the command
2548 \begin_inset Newline newline
2558 \begin_inset Formula $\to$
2564 \begin_inset Formula $\to$
2570 \begin_inset space \textvisiblespace{}
2574 \begin_inset Formula $\to$
2578 \begin_inset Newline newline
2583 produces a correct typeset formula:
2584 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2590 \begin_layout Subsection
2591 Binomial Coefficients
2592 \begin_inset Index idx
2595 \begin_layout Plain Layout
2596 Binomial coefficients
2604 \begin_layout Standard
2605 Binomial coefficients are inserted with the command
2612 \begin_inset Index idx
2615 \begin_layout Plain Layout
2623 or with the submenu of the math toolbar button
2624 \begin_inset Graphics
2625 filename ../images/math/frac-square.png
2643 there are the commands
2650 \begin_inset Index idx
2653 \begin_layout Plain Layout
2668 \begin_inset Index idx
2671 \begin_layout Plain Layout
2680 For other brackets around binomial coeficients there are the commands
2687 \begin_inset Index idx
2690 \begin_layout Plain Layout
2705 \begin_inset Index idx
2708 \begin_layout Plain Layout
2719 \begin_layout Standard
2721 \begin_inset Tabular
2722 <lyxtabular version="3" rows="6" columns="2">
2723 <features rotate="0" tabularvalignment="middle">
2724 <column alignment="center" valignment="top" width="0pt">
2725 <column alignment="center" valignment="top" width="0pt">
2727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2730 \begin_layout Plain Layout
2736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2739 \begin_layout Plain Layout
2741 \begin_inset Note Note
2744 \begin_layout Plain Layout
2751 is only used as spacer.
2763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2766 \begin_layout Plain Layout
2770 \begin_inset space \textvisiblespace{}
2774 \begin_inset Formula $\downarrow$
2782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2785 \begin_layout Plain Layout
2786 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2799 \begin_layout Plain Layout
2803 \begin_inset space \textvisiblespace{}
2807 \begin_inset Formula $\downarrow$
2815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2818 \begin_layout Plain Layout
2819 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2832 \begin_layout Plain Layout
2836 \begin_inset space \textvisiblespace{}
2840 \begin_inset Formula $\downarrow$
2848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2851 \begin_layout Plain Layout
2852 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2865 \begin_layout Plain Layout
2869 \begin_inset space \textvisiblespace{}
2873 \begin_inset Formula $\downarrow$
2881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2884 \begin_layout Plain Layout
2885 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2898 \begin_layout Plain Layout
2902 \begin_inset space \textvisiblespace{}
2906 \begin_inset Formula $\downarrow$
2914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2917 \begin_layout Plain Layout
2918 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
2934 \begin_layout Subsection
2935 Case Differentiations
2936 \begin_inset Index idx
2939 \begin_layout Plain Layout
2940 Case differentiations
2948 \begin_layout Standard
2950 \begin_inset Tabular
2951 <lyxtabular version="3" rows="3" columns="2">
2952 <features rotate="0" tabularvalignment="middle">
2953 <column alignment="center" valignment="top" width="0pt">
2954 <column alignment="center" valignment="top" width="0pt">
2956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2959 \begin_layout Plain Layout
2965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2968 \begin_layout Plain Layout
2976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2979 \begin_layout Plain Layout
2983 \begin_inset space \textvisiblespace{}
2987 \begin_inset Formula $\to$
2991 \begin_inset Index idx
2994 \begin_layout Plain Layout
3007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3010 \begin_layout Plain Layout
3011 \begin_inset Formula $\begin{cases}
3022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3025 \begin_layout Plain Layout
3029 \begin_inset space \textvisiblespace{}
3035 arg "newline-insert newline"
3043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3046 \begin_layout Plain Layout
3047 \begin_inset Formula $\begin{cases}
3048 A & \textrm{for }x>0\\
3049 B & \textrm{for }x=0
3066 \begin_layout Standard
3073 or pressing the math toolbar button
3074 \begin_inset Graphics
3075 filename ../images/math/cases.png
3080 you can create new lines with the shortcut
3083 arg "newline-insert newline"
3086 or the table toolbar button
3087 \begin_inset Graphics
3088 filename ../images/tabular-feature_append-row.png
3096 \begin_layout Standard
3103 is also available via the menu
3105 Insert\SpecialChar \menuseparator
3106 Math\SpecialChar \menuseparator
3112 \begin_layout Subsection
3114 \begin_inset Index idx
3117 \begin_layout Plain Layout
3126 \begin_layout Standard
3134 \begin_inset Index idx
3137 \begin_layout Plain Layout
3145 every character can be displayed canceled.
3146 The characters are quasi accentuated by a slash.
3149 \begin_layout Standard
3151 \begin_inset Tabular
3152 <lyxtabular version="3" rows="4" columns="2">
3153 <features rotate="0" tabularvalignment="middle">
3154 <column alignment="center" valignment="top" width="0pt">
3155 <column alignment="center" valignment="top" width="0pt">
3157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3160 \begin_layout Plain Layout
3166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3169 \begin_layout Plain Layout
3177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3180 \begin_layout Plain Layout
3188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3191 \begin_layout Plain Layout
3192 \begin_inset Formula $\not=$
3202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3205 \begin_layout Plain Layout
3215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3218 \begin_layout Plain Layout
3219 \begin_inset Formula $\not\le$
3229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3232 \begin_layout Plain Layout
3242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3245 \begin_layout Plain Layout
3246 \begin_inset Formula $\not\parallel$
3262 \begin_layout Standard
3263 The last example shows that not all negations look good.
3264 Therefore there are special commands for some negations (see
3265 \begin_inset CommandInset ref
3267 reference "sub:Mathematical-Symbols"
3272 \begin_inset CommandInset ref
3274 reference "sec:Relations"
3281 \begin_layout Subsection
3283 \begin_inset CommandInset label
3285 name "sub:Placeholders"
3290 \begin_inset Index idx
3293 \begin_layout Plain Layout
3300 \begin_inset Index idx
3303 \begin_layout Plain Layout
3304 Chemical characters ! Isotopes
3310 \begin_inset Index idx
3313 \begin_layout Plain Layout
3318 \begin_layout Plain Layout
3329 \begin_layout Plain Layout
3344 \begin_layout Standard
3346 \begin_inset space \thinspace{}
3350 \begin_inset space \space{}
3357 \begin_layout Plain Layout
3358 Typesetting isotopes and chemical symbols is described in
3359 \begin_inset CommandInset ref
3361 reference "sub:Chemical-Symbols-and"
3370 the following problem occurs:
3373 \begin_layout Standard
3375 \begin_inset Tabular
3376 <lyxtabular version="3" rows="2" columns="2">
3377 <features rotate="0" tabularvalignment="middle">
3378 <column alignment="center" valignment="top" width="0pt">
3379 <column alignment="center" valignment="top" width="0pt">
3381 <cell alignment="center" valignment="top" usebox="none">
3384 \begin_layout Plain Layout
3385 Indices created with sub- and superscripts:
3390 <cell alignment="center" valignment="top" usebox="none">
3393 \begin_layout Plain Layout
3394 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3404 <cell alignment="center" valignment="top" usebox="none">
3407 \begin_layout Plain Layout
3413 <cell alignment="center" valignment="top" usebox="none">
3416 \begin_layout Plain Layout
3417 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3431 \begin_inset Note Note
3434 \begin_layout Plain Layout
3441 is only used as spacer.
3449 \begin_layout Standard
3450 The shorter index is by default placed below or above the first character
3451 of the longer index.
3452 To avoid this there is the command
3459 \begin_inset Index idx
3462 \begin_layout Plain Layout
3470 or the math toolbar button
3471 \begin_inset space \thinspace{}
3478 \begin_layout Plain Layout
3479 can be found in the submenu of the toolbar button
3480 \begin_inset Graphics
3481 filename ../images/math/space.png
3492 \begin_inset Graphics
3493 filename ../images/math/phantom.png
3498 that creates one or more phantom characters.
3505 a small blue box appears that is superposed with two red arrows.
3506 The arrows indicate that the complete width and height of the box content
3507 will be created as placeholder.
3508 Phantom characters are accordingly placeholders with the size of the characters.
3511 \begin_layout Standard
3513 \begin_inset Tabular
3514 <lyxtabular version="3" rows="4" columns="2">
3515 <features rotate="0" tabularvalignment="middle">
3516 <column alignment="center" valignment="top">
3517 <column alignment="center" valignment="top">
3519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3522 \begin_layout Plain Layout
3528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3531 \begin_layout Plain Layout
3533 \begin_inset Note Note
3536 \begin_layout Plain Layout
3543 is only used as spacer.
3555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3558 \begin_layout Plain Layout
3560 \begin_inset space \textvisiblespace{}
3566 \begin_inset space \textvisiblespace{}
3570 \begin_inset Formula $\to$
3574 \begin_inset space \textvisiblespace{}
3582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3585 \begin_layout Plain Layout
3586 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3599 \begin_layout Plain Layout
3601 \begin_inset space \textvisiblespace{}
3607 \begin_inset space \textvisiblespace{}
3611 \begin_inset Formula $\to$
3615 \begin_inset space \textvisiblespace{}
3623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3626 \begin_layout Plain Layout
3627 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3640 \begin_layout Plain Layout
3644 \begin_inset space \textvisiblespace{}
3650 \begin_inset space \textvisiblespace{}
3654 \begin_inset Formula $\to$
3658 \begin_inset space \textvisiblespace{}
3666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3669 \begin_layout Plain Layout
3670 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3686 \begin_layout Standard
3687 Furthermore there are the commands
3694 \begin_inset Index idx
3697 \begin_layout Plain Layout
3706 \begin_inset space ~
3710 \begin_inset Graphics
3711 filename ../images/math/vphantom.png
3723 \begin_inset Index idx
3726 \begin_layout Plain Layout
3735 \begin_inset space ~
3739 \begin_inset Graphics
3740 filename ../images/math/hphantom.png
3752 creates only space for the maximal height of the characters in the box
3753 but not for its width.
3760 creates only space for the width of the box content.
3761 Therefore the boxes of both commands have only one red arrow.
3764 \begin_layout Standard
3765 For example the command
3770 \begin_inset space \textvisiblespace{}
3777 creates space for the height of the integral sign,
3781 \begin_layout Plain Layout
3788 creates an integral sign, see
3789 \begin_inset CommandInset ref
3791 reference "sub:Big-Operators"
3800 because this is the larger character.
3801 An example application is in
3802 \begin_inset CommandInset ref
3804 reference "sub:Multiline-Brackets"
3811 \begin_layout Standard
3812 Placeholders can also be used for text when they are inserted via the menu
3815 Insert\SpecialChar \menuseparator
3816 Formatting\SpecialChar \menuseparator
3822 \begin_layout Standard
3824 \begin_inset Newline newline
3828 \begin_inset Phantom Phantom
3831 \begin_layout Plain Layout
3840 \begin_layout Subsection
3842 \begin_inset Index idx
3845 \begin_layout Plain Layout
3852 \begin_inset Index idx
3855 \begin_layout Plain Layout
3856 Formula ! underlined
3864 \begin_layout Standard
3866 \begin_inset Tabular
3867 <lyxtabular version="3" rows="4" columns="2">
3868 <features rotate="0" tabularvalignment="middle">
3869 <column alignment="center" valignment="top" width="0pt">
3870 <column alignment="center" valignment="top" width="0pt">
3872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3875 \begin_layout Plain Layout
3881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3884 \begin_layout Plain Layout
3886 \begin_inset Note Note
3889 \begin_layout Plain Layout
3896 is only used as spacer.
3908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3911 \begin_layout Plain Layout
3915 \begin_inset space \textvisiblespace{}
3919 \begin_inset Index idx
3922 \begin_layout Plain Layout
3935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3938 \begin_layout Plain Layout
3939 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3949 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
3952 \begin_layout Plain Layout
3956 \begin_inset space \textvisiblespace{}
3960 \begin_inset Index idx
3963 \begin_layout Plain Layout
3976 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
3979 \begin_layout Plain Layout
3980 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3993 \begin_layout Plain Layout
3997 \begin_inset space \textvisiblespace{}
4003 \begin_inset space \textvisiblespace{}
4011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4014 \begin_layout Plain Layout
4015 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4031 \begin_layout Standard
4032 In the last example it doesn't matter if first
4047 \begin_layout Standard
4048 To double underline use
4057 \begin_layout Standard
4058 It is possible to place up to 6 lines above or below characters.
4061 \begin_layout Standard
4062 \begin_inset VSpace bigskip
4065 Custom lines can be created using the command
4072 \begin_inset Index idx
4075 \begin_layout Plain Layout
4083 which has the following scheme:
4086 \begin_layout Standard
4091 rule[vertical offset]{length}{thickness}
4094 \begin_layout Standard
4095 The optional vertical offset shifts the line upwards (or downwards, when
4096 the value is negative).
4098 \begin_inset CommandInset ref
4100 reference "tab:Available-units"
4104 can be used for the values.
4105 Here are two example lines created with the commands
4106 \begin_inset Newline newline
4113 rule[-2ex]{3cm}{2pt}
4124 \begin_layout Standard
4126 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4132 \begin_layout Standard
4139 can also be used for text when a line is inserted via the menu
4141 Insert\SpecialChar \menuseparator
4142 Formatting\SpecialChar \menuseparator
4144 \begin_inset space ~
4152 \begin_layout Standard
4154 \begin_inset CommandInset line
4165 \begin_layout Subsection
4167 \begin_inset CommandInset label
4174 \begin_inset Index idx
4177 \begin_layout Plain Layout
4186 \begin_layout Standard
4187 There are different types of ellipses available.
4191 \begin_layout Plain Layout
4192 In the math toolbar in the submenu of the button
4193 \begin_inset Graphics
4194 filename ../images/math/ldots.png
4204 For listings dots at the baseline are used (
4211 \begin_inset Index idx
4214 \begin_layout Plain Layout
4222 ), while for operations dots are needed that are on the same height as the
4230 \begin_inset Index idx
4233 \begin_layout Plain Layout
4242 When using the command
4249 \begin_inset Index idx
4252 \begin_layout Plain Layout
4260 , LaTeX decides on the basis of the next character what type is used.
4263 \begin_layout Standard
4265 \begin_inset Tabular
4266 <lyxtabular version="3" rows="9" columns="2">
4267 <features rotate="0" tabularvalignment="middle">
4268 <column alignment="center" valignment="top" width="0pt">
4269 <column alignment="center" valignment="top" width="0pt">
4271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4274 \begin_layout Plain Layout
4280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4283 \begin_layout Plain Layout
4291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4294 \begin_layout Plain Layout
4296 \begin_inset space \textvisiblespace{}
4302 \begin_inset space \textvisiblespace{}
4310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4313 \begin_layout Plain Layout
4314 \begin_inset Formula $A_{1},\dots,A_{n}$
4324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4327 \begin_layout Plain Layout
4329 \begin_inset space \textvisiblespace{}
4335 \begin_inset space \textvisiblespace{}
4343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4346 \begin_layout Plain Layout
4347 \begin_inset Formula $A_{1}+\dots+A_{n}$
4357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4360 \begin_layout Plain Layout
4362 \begin_inset space \textvisiblespace{}
4368 \begin_inset space \textvisiblespace{}
4376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4379 \begin_layout Plain Layout
4380 \begin_inset Formula $A_{1},\ldots,A_{n}$
4390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4393 \begin_layout Plain Layout
4395 \begin_inset space \textvisiblespace{}
4401 \begin_inset space \textvisiblespace{}
4409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4412 \begin_layout Plain Layout
4413 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4426 \begin_layout Plain Layout
4434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4437 \begin_layout Plain Layout
4438 \begin_inset Formula $\vdots$
4448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4451 \begin_layout Plain Layout
4459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4462 \begin_layout Plain Layout
4463 \begin_inset Formula $\ddots$
4473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4476 \begin_layout Plain Layout
4484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4487 \begin_layout Plain Layout
4488 \begin_inset Formula $\iddots$
4498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4501 \begin_layout Plain Layout
4503 \begin_inset space \thinspace{}
4506 matrix with the different dots
4511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4514 \begin_layout Plain Layout
4515 \begin_inset Formula $\begin{array}{ccc}
4516 A_{11} & \cdots & A_{1m}\\
4517 \vdots & \ddots & \vdots\\
4518 A_{n1} & \cdots & A_{nm}
4535 \begin_layout Standard
4536 The ellipses available in menu
4538 Insert\SpecialChar \menuseparator
4540 \begin_inset space ~
4554 \begin_layout Standard
4555 \begin_inset VSpace medskip
4564 , one of the options
4566 Use mathdots package (automatically)
4568 must be set in the document settings under
4571 \begin_inset space ~
4577 \begin_inset Newline newline
4582 Use mathdots package
4584 will improve the appearance of all dots in the documents if their font
4585 style or size is not the default.
4588 \begin_layout Standard
4589 \begin_inset VSpace medskip
4592 Specially for matrices there are ellipses that span over several columns.
4593 They are created with the command
4600 \begin_inset Index idx
4603 \begin_layout Plain Layout
4611 , that has the following scheme:
4614 \begin_layout Standard
4619 hdotsfor[distance]{number of columns}
4622 \begin_layout Standard
4623 The number of columns specifies how many columns should be spanned.
4624 Distance is a factor for the distance between the dots.
4627 \begin_layout Standard
4628 In the following matrix the command
4634 was inserted in the first box of the second line, to get an ellipsis with
4635 a dot distance twice as long as with the command
4642 \begin_inset Formula
4644 \left(\begin{array}{cccc}
4653 Note that the matrix fields that should be spanned must be empty, otherwise
4654 you get LaTeX-errors.
4657 \begin_layout Standard
4658 \begin_inset VSpace bigskip
4661 Furthermore you can fill with the command
4668 \begin_inset Index idx
4671 \begin_layout Plain Layout
4679 the rest of a line with dots.
4680 The effect of these commands is the same as with
4687 \begin_inset CommandInset ref
4689 reference "sub:Variable-Space"
4696 \begin_layout Standard
4697 For example the command
4702 \begin_inset space \textvisiblespace{}
4710 \begin_layout Standard
4711 \begin_inset Formula $A\dotfill B$
4717 \begin_layout Standard
4724 there is for a line the command
4731 \begin_inset Index idx
4734 \begin_layout Plain Layout
4745 \begin_layout Standard
4746 \begin_inset Formula $A\hrulefill B$
4752 \begin_layout Standard
4753 To use the commands for text, they have to be inserted in TeX-mode.
4756 \begin_layout Section
4758 \begin_inset CommandInset label
4765 \begin_inset Index idx
4768 \begin_layout Plain Layout
4777 \begin_layout Standard
4778 Matrices can be inserted via the math toolbar button
4779 \begin_inset Graphics
4780 filename ../images/dialog-show_mathmatrix.png
4787 Insert\SpecialChar \menuseparator
4788 Math\SpecialChar \menuseparator
4792 In the matrix dialog you can specify the number of columns and rows, the
4793 alignment and the decoration.
4794 The vertical alignment is only of importance for matrices in inline formulas:
4797 \begin_layout Standard
4798 The first matrix is top
4799 \begin_inset Formula $\begin{array}[t]{cccc}
4807 \begin_inset Formula $\begin{array}{cccc}
4814 and the third bottom
4815 \begin_inset Formula $\begin{array}[b]{cccc}
4825 \begin_layout Standard
4826 The horizontal alignment specifies how the column entries should be aligned.
4827 It is set by entering a letter for every column.
4832 denotes left aligned,
4841 To create for example a 4
4846 \begin_inset space ~
4849 matrix where the first column is left aligned, the second and third are
4850 centered and the last one is right aligned, one enters for the horizontal
4856 Normally in a matrix all columns are centered, therefore the default for
4864 \begin_layout Standard
4865 Horizontal alignment:
4868 \begin_layout Standard
4874 \begin_inset Formula $\begin{array}{lll}
4886 \begin_inset Formula $\begin{array}{ccc}
4898 \begin_inset Formula $\begin{array}{rrr}
4908 \begin_layout Standard
4909 To add or delete rows and columns subsequently, the math toolbar buttons
4911 \begin_inset Graphics
4912 filename ../images/tabular-feature_append-row.png
4918 \begin_inset Graphics
4919 filename ../images/tabular-feature_delete-row.png
4925 \begin_inset space \thinspace{}
4930 Edit\SpecialChar \menuseparator
4934 New rows can also be created with
4937 arg "newline-insert newline"
4943 \begin_layout Standard
4944 \begin_inset VSpace bigskip
4951 adds parentheses in the selected style around the matrix.
4952 Alternatively, parentheses can can either be created with the commands
4960 \begin_inset Index idx
4963 \begin_layout Plain Layout
4978 \begin_inset Index idx
4981 \begin_layout Plain Layout
4992 \begin_inset space ~
4998 \begin_inset CommandInset ref
5000 reference "sub:Automatic-Bracket-Size"
5004 , or by using the following commands:
5005 \begin_inset VSpace medskip
5011 \begin_layout Standard
5012 \begin_inset space \hfill{}
5016 \begin_inset Tabular
5017 <lyxtabular version="3" rows="4" columns="2">
5018 <features rotate="0" tabularvalignment="middle">
5019 <column alignment="center" valignment="top">
5020 <column alignment="center" valignment="top">
5022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5025 \begin_layout Plain Layout
5031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5034 \begin_layout Plain Layout
5036 \begin_inset Note Note
5039 \begin_layout Plain Layout
5046 is only used as spacer.
5058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5061 \begin_layout Plain Layout
5065 \begin_inset space \textvisiblespace{}
5073 \begin_inset space \thinspace{}
5081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5084 \begin_layout Plain Layout
5085 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5086 0 & \textrm{-}\mathrm{i}\\
5088 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5101 \begin_layout Plain Layout
5105 \begin_inset space \textvisiblespace{}
5113 \begin_inset space \thinspace{}
5121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5124 \begin_layout Plain Layout
5125 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5126 0 & \textrm{-}\mathrm{i}\\
5128 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5141 \begin_layout Plain Layout
5145 \begin_inset space \textvisiblespace{}
5153 \begin_inset space \thinspace{}
5161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5164 \begin_layout Plain Layout
5165 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5166 0 & \textrm{-}\mathrm{i}\\
5168 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5182 \begin_inset space \hfill{}
5186 \begin_inset Tabular
5187 <lyxtabular version="3" rows="4" columns="2">
5188 <features rotate="0" tabularvalignment="middle">
5189 <column alignment="center" valignment="top">
5190 <column alignment="center" valignment="top">
5192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5195 \begin_layout Plain Layout
5201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5204 \begin_layout Plain Layout
5212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5215 \begin_layout Plain Layout
5219 \begin_inset space \textvisiblespace{}
5227 \begin_inset space \thinspace{}
5235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5238 \begin_layout Plain Layout
5239 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5240 0 & \textrm{-}\mathrm{i}\\
5242 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5255 \begin_layout Plain Layout
5259 \begin_inset space \textvisiblespace{}
5267 \begin_inset space \thinspace{}
5275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5278 \begin_layout Plain Layout
5279 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5280 0 & \textrm{-}\mathrm{i}\\
5282 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5295 \begin_layout Plain Layout
5299 \begin_inset space \textvisiblespace{}
5307 \begin_inset space \thinspace{}
5315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5318 \begin_layout Plain Layout
5319 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5320 0 & \textrm{-}\mathrm{i}\\
5322 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5336 \begin_inset space \hfill{}
5342 \begin_layout Standard
5343 \begin_inset VSpace medskip
5347 \begin_inset space \thinspace{}
5351 \begin_inset space \space{}
5360 is inserted, a blue box appears between two vertical lines where the matrix
5362 \begin_inset Newline newline
5365 Note that decorated matrices ignore the vertical alignment.
5368 \begin_layout Standard
5369 \begin_inset VSpace bigskip
5372 As all multiline formulas are matrices, the length
5379 \begin_inset Index idx
5382 \begin_layout Plain Layout
5390 that is described in
5391 \begin_inset CommandInset ref
5393 reference "sub:Column-Separation"
5397 can also be used to change the column separation of matrices.
5400 \begin_layout Standard
5401 To change the row separation, the command
5408 \begin_inset Index idx
5411 \begin_layout Plain Layout
5420 It is used as follows:
5423 \begin_layout Standard
5430 arraystretch}{stretch factor}
5431 \begin_inset Index idx
5434 \begin_layout Plain Layout
5445 \begin_layout Standard
5452 assigns the stretch factor to the predefined command
5460 \begin_inset space \thinspace{}
5464 \begin_inset space \space{}
5467 the row separation, use the factor 2.
5468 This is then used for all following matrices.
5469 To go back to the original separation, assign the factor 1 to
5478 \begin_layout Standard
5479 To set matrices into a text line, the command
5486 \begin_inset Index idx
5489 \begin_layout Plain Layout
5498 When it is inserted a blue box with two dashed lines appears.
5499 In this box the matrix is inserted.
5502 \begin_layout Standard
5504 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5506 \end{smallmatrix}\right)$
5512 \begin_layout Section
5513 Brackets and Delimiters
5514 \begin_inset Index idx
5517 \begin_layout Plain Layout
5524 \begin_inset Index idx
5527 \begin_layout Plain Layout
5536 \begin_layout Subsection
5537 Vertical Brackets and Delimiters
5538 \begin_inset Index idx
5541 \begin_layout Plain Layout
5550 \begin_layout Standard
5551 \begin_inset space \hfill{}
5555 \begin_inset Tabular
5556 <lyxtabular version="3" rows="9" columns="2">
5557 <features rotate="0" tabularvalignment="middle">
5558 <column alignment="center" valignment="top" width="0pt">
5559 <column alignment="center" valignment="top" width="0pt">
5561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5564 \begin_layout Plain Layout
5570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5573 \begin_layout Plain Layout
5581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5584 \begin_layout Plain Layout
5590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5593 \begin_layout Plain Layout
5594 \begin_inset Formula $($
5604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5607 \begin_layout Plain Layout
5613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5616 \begin_layout Plain Layout
5617 \begin_inset Formula $\{$
5627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5630 \begin_layout Plain Layout
5636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5639 \begin_layout Plain Layout
5640 \begin_inset Formula $[$
5650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5653 \begin_layout Plain Layout
5661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5664 \begin_layout Plain Layout
5665 \begin_inset Formula $\langle$
5675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5678 \begin_layout Plain Layout
5686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5689 \begin_layout Plain Layout
5690 \begin_inset Formula $\lceil$
5700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5703 \begin_layout Plain Layout
5711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5714 \begin_layout Plain Layout
5715 \begin_inset Formula $\lfloor$
5725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5728 \begin_layout Plain Layout
5734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5737 \begin_layout Plain Layout
5738 \begin_inset Formula $/$
5748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5751 \begin_layout Plain Layout
5757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5760 \begin_layout Plain Layout
5761 \begin_inset Formula $|$
5775 \begin_inset space \hfill{}
5779 \begin_inset Tabular
5780 <lyxtabular version="3" rows="9" columns="2">
5781 <features rotate="0" tabularvalignment="middle">
5782 <column alignment="center" valignment="top" width="0pt">
5783 <column alignment="center" valignment="top" width="0pt">
5785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5788 \begin_layout Plain Layout
5794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5797 \begin_layout Plain Layout
5805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5808 \begin_layout Plain Layout
5814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5817 \begin_layout Plain Layout
5818 \begin_inset Formula $)$
5828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5831 \begin_layout Plain Layout
5837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5840 \begin_layout Plain Layout
5841 \begin_inset Formula $\}$
5851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5854 \begin_layout Plain Layout
5860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5863 \begin_layout Plain Layout
5864 \begin_inset Formula $]$
5874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5877 \begin_layout Plain Layout
5885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5888 \begin_layout Plain Layout
5889 \begin_inset Formula $\rangle$
5899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5902 \begin_layout Plain Layout
5910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5913 \begin_layout Plain Layout
5914 \begin_inset Formula $\rceil$
5924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5927 \begin_layout Plain Layout
5935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5938 \begin_layout Plain Layout
5939 \begin_inset Formula $\rfloor$
5949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5952 \begin_layout Plain Layout
5962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5965 \begin_layout Plain Layout
5966 \begin_inset Formula $\backslash$
5976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5979 \begin_layout Plain Layout
5987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5990 \begin_layout Plain Layout
5991 \begin_inset Formula $\|$
6005 \begin_inset space \hfill{}
6011 \begin_layout Standard
6014 \begin_inset Note Greyedout
6017 \begin_layout Plain Layout
6022 In TeX-mode the command
6029 \begin_inset Index idx
6032 \begin_layout Plain Layout
6040 must be used for the backslash, because the command
6048 produces a line break there.
6056 \begin_layout Standard
6057 For all characters listed above the size can be adjusted with the commands
6058 described in the following two subsections.
6059 When using these commands, the characters < and > can directly be used
6060 instead of the commands
6075 \begin_layout Subsubsection
6077 \begin_inset CommandInset label
6079 name "sub:Manual-Bracket-Size"
6084 \begin_inset Index idx
6087 \begin_layout Plain Layout
6088 Bracket size ! manual
6096 \begin_layout Standard
6097 The bracket size can be specified manually by the LaTeX-commands
6104 \begin_inset Index idx
6107 \begin_layout Plain Layout
6140 denotes the smallest and
6146 the largest bracket size.
6149 \begin_layout Standard
6150 These commands are used to emphasize levels of brackets:
6153 \begin_layout Standard
6155 \begin_inset Tabular
6156 <lyxtabular version="3" rows="2" columns="2">
6157 <features rotate="0" tabularvalignment="middle">
6158 <column alignment="center" valignment="top" width="0pt">
6159 <column alignment="center" valignment="top" width="0pt">
6161 <cell alignment="center" valignment="top" usebox="none">
6164 \begin_layout Plain Layout
6165 all brackets in the same size:
6170 <cell alignment="center" valignment="top" usebox="none">
6173 \begin_layout Plain Layout
6174 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6184 <cell alignment="center" valignment="top" usebox="none">
6187 \begin_layout Plain Layout
6193 <cell alignment="center" valignment="top" usebox="none">
6196 \begin_layout Plain Layout
6197 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6211 \begin_inset Note Note
6214 \begin_layout Plain Layout
6221 is only used as spacer.
6229 \begin_layout Standard
6230 For the second formula the command
6237 \begin_inset space \textvisiblespace{}
6245 \begin_layout Standard
6246 Here is an overview about all bracket sizes:
6249 \begin_layout Standard
6266 \begin_inset space \textvisiblespace{}
6274 \begin_inset space \textvisiblespace{}
6278 \begin_inset space \textvisiblespace{}
6288 \begin_layout Standard
6290 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6296 \begin_layout Standard
6303 -commands there is the variant
6310 \begin_inset Index idx
6313 \begin_layout Plain Layout
6321 that adds a bit more space between the bracket and its content, and the
6335 \begin_inset Index idx
6338 \begin_layout Plain Layout
6348 , that don't add additional space.
6353 at the end of the command
6359 is for a left bracket; for a right bracket this will be replaced by an
6365 A left or right bracket can each be an opening or closing bracket.
6368 \begin_layout Standard
6369 In the following table is a comparison of the variants:
6372 \begin_layout Standard
6374 \begin_inset Tabular
6375 <lyxtabular version="3" rows="5" columns="2">
6376 <features rotate="0" tabularvalignment="middle">
6377 <column alignment="center" valignment="middle">
6378 <column alignment="center" valignment="middle">
6380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6383 \begin_layout Plain Layout
6389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6392 \begin_layout Plain Layout
6394 \begin_inset Note Note
6397 \begin_layout Plain Layout
6404 is only used as spacer.
6416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6419 \begin_layout Plain Layout
6429 \begin_inset space \textvisiblespace{}
6439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6442 \begin_layout Plain Layout
6443 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6456 \begin_layout Plain Layout
6466 \begin_inset space \textvisiblespace{}
6476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6479 \begin_layout Plain Layout
6480 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6493 \begin_layout Plain Layout
6503 \begin_inset space \textvisiblespace{}
6513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6516 \begin_layout Plain Layout
6517 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6530 \begin_layout Plain Layout
6542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6545 \begin_layout Plain Layout
6546 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6562 \begin_layout Subsubsection
6563 Automatic Bracket Size
6564 \begin_inset CommandInset label
6566 name "sub:Automatic-Bracket-Size"
6571 \begin_inset Index idx
6574 \begin_layout Plain Layout
6575 Bracket size ! automatic
6583 \begin_layout Standard
6584 Brackets with variable size can be inserted with the commands
6591 \begin_inset Index idx
6594 \begin_layout Plain Layout
6609 \begin_inset Index idx
6612 \begin_layout Plain Layout
6620 or via the math toolbar button
6621 \begin_inset Graphics
6622 filename ../images/dialog-show_mathdelimiter.png
6640 the wanted bracket must be inserted.
6641 The bracket size will then automatically be calculated for the output.
6644 \begin_layout Standard
6646 normal bracket: The command
6653 \begin_inset space \textvisiblespace{}
6657 \begin_inset Formula $\downarrow$
6661 \begin_inset space \textvisiblespace{}
6667 \begin_inset Formula
6677 \begin_layout Standard
6679 multiline bracket: The command
6688 \begin_inset space \textvisiblespace{}
6692 \begin_inset Formula $\downarrow$
6696 \begin_inset space \textvisiblespace{}
6704 \begin_inset Formula
6706 \ln\left(\frac{A}{C}\right)
6714 \begin_layout Standard
6730 \begin_inset space ~
6736 This has the advantage that you can see in LyX immediately the real bracket
6737 size and that the matching right bracket will be created too.
6738 \begin_inset Newline newline
6741 The command for the last example would then be:
6752 \begin_inset space \textvisiblespace{}
6756 \begin_inset Formula $\downarrow$
6762 \begin_layout Standard
6763 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6764 For example the command
6771 \begin_inset space \textvisiblespace{}
6775 \begin_inset Formula $\downarrow$
6779 \begin_inset space \textvisiblespace{}
6789 \begin_inset Formula
6791 \left.\frac{A}{B}\right\}
6810 will be converted by LyX to brackets in the right size when the document
6811 is reloaded and an omitted bracket will appear as dashed line.
6814 \begin_layout Standard
6815 \begin_inset VSpace bigskip
6818 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6826 \begin_inset Index idx
6829 \begin_layout Plain Layout
6837 is additionally available for all brackets and limits.
6838 With this command the height of the following character is adapted to the
6839 one of the surrounding brackets, what is e.
6840 \begin_inset space \thinspace{}
6844 \begin_inset space \space{}
6847 needed for physical vectors:
6848 \begin_inset Formula
6850 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
6855 For physical vectors there is a special LaTeX-package, described in
6856 \begin_inset CommandInset ref
6858 reference "sub:Physical-Vectors"
6865 \begin_layout Subsection
6867 \begin_inset Index idx
6870 \begin_layout Plain Layout
6871 Brackets ! horizontal
6879 \begin_layout Standard
6881 \begin_inset Tabular
6882 <lyxtabular version="3" rows="4" columns="2">
6883 <features rotate="0" tabularvalignment="middle">
6884 <column alignment="center" valignment="top" width="0pt">
6885 <column alignment="center" valignment="top" width="0pt">
6887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6890 \begin_layout Plain Layout
6892 \begin_inset Note Note
6895 \begin_layout Plain Layout
6902 is only used as spacer.
6912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6915 \begin_layout Plain Layout
6923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6926 \begin_layout Plain Layout
6930 \begin_layout Plain Layout
6942 \begin_inset space \textvisiblespace{}
6946 \begin_inset space \textvisiblespace{}
6953 \begin_layout Plain Layout
6961 \begin_inset Index idx
6964 \begin_layout Plain Layout
6977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6980 \begin_layout Plain Layout
6981 \begin_inset Formula $\overbrace{A+B}^{3}$
6991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6994 \begin_layout Plain Layout
6998 \begin_layout Plain Layout
7010 \begin_inset space \textvisiblespace{}
7014 \begin_inset space \textvisiblespace{}
7021 \begin_layout Plain Layout
7029 \begin_inset Index idx
7032 \begin_layout Plain Layout
7045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7048 \begin_layout Plain Layout
7049 \begin_inset Formula $\underbrace{A+B}_{5}$
7059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7062 \begin_layout Plain Layout
7066 \begin_inset space \textvisiblespace{}
7072 \begin_inset space \textvisiblespace{}
7076 \begin_inset space \textvisiblespace{}
7080 \begin_inset space \textvisiblespace{}
7084 \begin_inset space \textvisiblespace{}
7088 \begin_inset space \textvisiblespace{}
7092 \begin_inset space \textvisiblespace{}
7100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7103 \begin_layout Plain Layout
7104 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7120 \begin_layout Standard
7121 In the last example it doesn't matter if
7133 is inserted at first.
7136 \begin_layout Standard
7137 \begin_inset VSpace bigskip
7140 When brackets are needed that overlap each other, multiline formulas, as
7142 \begin_inset CommandInset ref
7144 reference "sec:Multiline-Formulas"
7149 \begin_inset Formula
7151 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7152 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7157 In the first row the formula is inserted together with the first brace.
7158 It is hereby important that the space command
7162 \begin_layout Plain Layout
7163 Space commands are explained in
7164 \begin_inset CommandInset ref
7166 reference "sub:Predefined-Space"
7181 is inserted before the first
7182 \begin_inset Formula $d$
7185 , because the brace that ends behind the
7186 \begin_inset Formula $q$
7189 prevents that the following
7190 \begin_inset Quotes eld
7194 \begin_inset Quotes erd
7197 is surrounded by space.
7201 \begin_layout Plain Layout
7202 because a bracket is not handled as a character, see
7203 \begin_inset CommandInset ref
7205 reference "sub:Binary-Operators"
7214 In the second row the second brace is inserted.
7215 As it should begin before the
7216 \begin_inset Formula $b$
7231 \begin_layout Plain Layout
7239 \begin_inset CommandInset ref
7241 reference "sub:Placeholders"
7250 This space is needed because the
7251 \begin_inset Quotes eld
7255 \begin_inset Quotes erd
7258 is also surrounded by space in the formula.
7259 The brace is placed under the command
7268 \begin_layout Standard
7269 It gets more complicated when brackets overlap each other, like in the following
7274 \begin_layout Plain Layout
7286 \begin_inset Formula
7288 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7289 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7298 \begin_layout Plain Layout
7309 The first formula row is the same as the second row of the previous example,
7310 with the difference that the brace is above.
7311 The second row contains the formula together with the second brace.
7312 To avoid that there is space between the upper brace in the first row and
7313 the formula, the row spacing needs to be reduced.
7314 This is not easily possible due to a bug in LyX
7318 \begin_layout Plain Layout
7319 \begin_inset CommandInset href
7321 name "LyX-bug #1505"
7322 target "http://www.lyx.org/trac/ticket/1505"
7332 As a solution for the problem, the global formula row separation
7339 \begin_inset Index idx
7342 \begin_layout Plain Layout
7350 must be changed to -6
7351 \begin_inset space \thinspace{}
7354 pt before the formula with the command
7369 is set back after the formula to the standard value of 3
7370 \begin_inset space \thinspace{}
7373 pt using the same command.
7374 More about the row separation in formulas is explained in
7375 \begin_inset CommandInset ref
7377 reference "sub:Line-Separation"
7384 \begin_layout Section
7386 \begin_inset Index idx
7389 \begin_layout Plain Layout
7398 \begin_layout Standard
7399 Arrows can be inserted via the math toolbar button
7400 \begin_inset Graphics
7401 filename ../images/math/leftarrow.png
7406 or the commands listed in the following subsections.
7409 \begin_layout Subsection
7411 \begin_inset Index idx
7414 \begin_layout Plain Layout
7423 \begin_layout Standard
7424 \begin_inset space \hfill{}
7428 \begin_inset Tabular
7429 <lyxtabular version="3" rows="8" columns="2">
7430 <features rotate="0" tabularvalignment="middle">
7431 <column alignment="center" valignment="top" width="0pt">
7432 <column alignment="center" valignment="top" width="0pt">
7434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7437 \begin_layout Plain Layout
7443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7446 \begin_layout Plain Layout
7454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7457 \begin_layout Plain Layout
7465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7468 \begin_layout Plain Layout
7469 \begin_inset Formula $\gets$
7479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7482 \begin_layout Plain Layout
7490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7493 \begin_layout Plain Layout
7494 \begin_inset Formula $\Leftarrow$
7504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7507 \begin_layout Plain Layout
7515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7518 \begin_layout Plain Layout
7519 \begin_inset Formula $\longleftarrow$
7529 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7532 \begin_layout Plain Layout
7540 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7543 \begin_layout Plain Layout
7544 \begin_inset Formula $\Longleftarrow$
7554 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7557 \begin_layout Plain Layout
7565 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7568 \begin_layout Plain Layout
7569 \begin_inset Formula $\leftharpoonup$
7579 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7582 \begin_layout Plain Layout
7590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7593 \begin_layout Plain Layout
7594 \begin_inset Formula $\leftharpoondown$
7604 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7607 \begin_layout Plain Layout
7615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7618 \begin_layout Plain Layout
7619 \begin_inset Formula $\hookleftarrow$
7633 \begin_inset space \hfill{}
7637 \begin_inset Tabular
7638 <lyxtabular version="3" rows="8" columns="2">
7639 <features rotate="0" tabularvalignment="middle">
7640 <column alignment="center" valignment="top" width="0pt">
7641 <column alignment="center" valignment="top" width="0pt">
7643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7646 \begin_layout Plain Layout
7652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7655 \begin_layout Plain Layout
7663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7666 \begin_layout Plain Layout
7674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7677 \begin_layout Plain Layout
7678 \begin_inset Formula $\to$
7688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7691 \begin_layout Plain Layout
7699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7702 \begin_layout Plain Layout
7703 \begin_inset Formula $\Rightarrow$
7713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7716 \begin_layout Plain Layout
7724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7727 \begin_layout Plain Layout
7728 \begin_inset Formula $\longrightarrow$
7738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7741 \begin_layout Plain Layout
7749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7752 \begin_layout Plain Layout
7753 \begin_inset Formula $\Longrightarrow$
7763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7766 \begin_layout Plain Layout
7774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7777 \begin_layout Plain Layout
7778 \begin_inset Formula $\rightharpoonup$
7788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7791 \begin_layout Plain Layout
7799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7802 \begin_layout Plain Layout
7803 \begin_inset Formula $\rightharpoondown$
7813 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7816 \begin_layout Plain Layout
7824 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7827 \begin_layout Plain Layout
7828 \begin_inset Formula $\hookrightarrow$
7842 \begin_inset space \hfill{}
7848 \begin_layout Standard
7849 \begin_inset space \hfill{}
7853 \begin_inset Tabular
7854 <lyxtabular version="3" rows="6" columns="2">
7855 <features rotate="0" tabularvalignment="middle">
7856 <column alignment="center" valignment="top" width="0pt">
7857 <column alignment="center" valignment="top" width="0pt">
7859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7862 \begin_layout Plain Layout
7868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7871 \begin_layout Plain Layout
7879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7882 \begin_layout Plain Layout
7890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7893 \begin_layout Plain Layout
7894 \begin_inset Formula $\leftrightarrow$
7904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7907 \begin_layout Plain Layout
7915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7918 \begin_layout Plain Layout
7919 \begin_inset Formula $\Leftrightarrow$
7929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7932 \begin_layout Plain Layout
7940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7943 \begin_layout Plain Layout
7944 \begin_inset Formula $\longleftrightarrow$
7954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7957 \begin_layout Plain Layout
7965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7968 \begin_layout Plain Layout
7969 \begin_inset Formula $\Longleftrightarrow$
7979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7982 \begin_layout Plain Layout
7990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7993 \begin_layout Plain Layout
7994 \begin_inset Formula $\rightleftharpoons$
8008 \begin_inset space \hspace{}
8013 \begin_inset space \hfill{}
8017 \begin_inset Tabular
8018 <lyxtabular version="3" rows="5" columns="2">
8019 <features rotate="0" tabularvalignment="middle">
8020 <column alignment="center" valignment="top" width="0pt">
8021 <column alignment="center" valignment="top" width="0pt">
8023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8026 \begin_layout Plain Layout
8032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8035 \begin_layout Plain Layout
8043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8046 \begin_layout Plain Layout
8054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8057 \begin_layout Plain Layout
8058 \begin_inset Formula $\mapsto$
8068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8071 \begin_layout Plain Layout
8079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8082 \begin_layout Plain Layout
8083 \begin_inset Formula $\longmapsto$
8093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8096 \begin_layout Plain Layout
8104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8107 \begin_layout Plain Layout
8108 \begin_inset Formula $\leadsto$
8118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8121 \begin_layout Plain Layout
8129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8132 \begin_layout Plain Layout
8133 \begin_inset Formula $\dasharrow$
8147 \begin_inset space \hfill{}
8153 \begin_layout Standard
8154 \begin_inset VSpace medskip
8157 Arrows used as accents like e.
8158 \begin_inset space \thinspace{}
8162 \begin_inset space \space{}
8165 vector arrows are listed in
8166 \begin_inset CommandInset ref
8168 reference "sec:Accents"
8175 \begin_layout Standard
8176 \begin_inset VSpace bigskip
8179 Furthermore there are the labeled arrows
8180 \begin_inset Index idx
8183 \begin_layout Plain Layout
8196 \begin_inset Index idx
8199 \begin_layout Plain Layout
8214 \begin_inset Index idx
8217 \begin_layout Plain Layout
8224 \begin_layout Plain Layout
8239 When inserting one of these commands in a formula, an arrow with two blue
8240 boxes appear where the label can be inserted.
8241 The length of the arrow adapts to the label width.
8244 \begin_layout Standard
8246 \begin_inset Tabular
8247 <lyxtabular version="3" rows="3" columns="2">
8248 <features rotate="0" tabularvalignment="middle">
8249 <column alignment="center" valignment="top" width="0pt">
8250 <column alignment="center" valignment="top" width="0pt">
8252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8255 \begin_layout Plain Layout
8261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8264 \begin_layout Plain Layout
8266 \begin_inset Note Note
8269 \begin_layout Plain Layout
8276 is only used as spacer.
8288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8291 \begin_layout Plain Layout
8295 \begin_inset space \textvisiblespace{}
8299 \begin_inset Formula $\downarrow$
8303 \begin_inset Formula $\to$
8311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8314 \begin_layout Plain Layout
8315 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8328 \begin_layout Plain Layout
8332 \begin_inset space \textvisiblespace{}
8336 \begin_inset Formula $\downarrow$
8340 \begin_inset Formula $\to$
8348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8351 \begin_layout Plain Layout
8352 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8368 \begin_layout Subsection
8369 Vertical and diagonal Arrows
8370 \begin_inset Index idx
8373 \begin_layout Plain Layout
8380 \begin_inset Index idx
8383 \begin_layout Plain Layout
8392 \begin_layout Standard
8393 \begin_inset space \hfill{}
8397 \begin_inset Tabular
8398 <lyxtabular version="3" rows="7" columns="2">
8399 <features rotate="0" tabularvalignment="middle">
8400 <column alignment="center" valignment="top" width="0pt">
8401 <column alignment="center" valignment="top" width="0pt">
8403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8406 \begin_layout Plain Layout
8412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8415 \begin_layout Plain Layout
8423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8426 \begin_layout Plain Layout
8434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8437 \begin_layout Plain Layout
8438 \begin_inset Formula $\uparrow$
8448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8451 \begin_layout Plain Layout
8459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8462 \begin_layout Plain Layout
8463 \begin_inset Formula $\Uparrow$
8473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8476 \begin_layout Plain Layout
8484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8487 \begin_layout Plain Layout
8488 \begin_inset Formula $\updownarrow$
8498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8501 \begin_layout Plain Layout
8509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8512 \begin_layout Plain Layout
8513 \begin_inset Formula $\Updownarrow$
8523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8526 \begin_layout Plain Layout
8534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8537 \begin_layout Plain Layout
8538 \begin_inset Formula $\Downarrow$
8548 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8551 \begin_layout Plain Layout
8559 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8562 \begin_layout Plain Layout
8563 \begin_inset Formula $\downarrow$
8577 \begin_inset space \hfill{}
8581 \begin_inset Tabular
8582 <lyxtabular version="3" rows="5" columns="2">
8583 <features rotate="0" tabularvalignment="middle">
8584 <column alignment="center" valignment="top" width="0pt">
8585 <column alignment="center" valignment="top" width="0pt">
8587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8590 \begin_layout Plain Layout
8596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8599 \begin_layout Plain Layout
8607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8610 \begin_layout Plain Layout
8618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8621 \begin_layout Plain Layout
8622 \begin_inset Formula $\nearrow$
8632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8635 \begin_layout Plain Layout
8643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8646 \begin_layout Plain Layout
8647 \begin_inset Formula $\searrow$
8657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8660 \begin_layout Plain Layout
8668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8671 \begin_layout Plain Layout
8672 \begin_inset Formula $\swarrow$
8682 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8685 \begin_layout Plain Layout
8693 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8696 \begin_layout Plain Layout
8697 \begin_inset Formula $\nwarrow$
8711 \begin_inset space \hfill{}
8717 \begin_layout Standard
8718 \begin_inset VSpace medskip
8721 Vertical arrows can be used also as delimiters together with the commands
8723 \begin_inset CommandInset ref
8725 reference "sub:Manual-Bracket-Size"
8730 \begin_inset CommandInset ref
8732 reference "sub:Automatic-Bracket-Size"
8739 \begin_layout Section
8741 \begin_inset CommandInset label
8748 \begin_inset Index idx
8751 \begin_layout Plain Layout
8760 \begin_layout Standard
8761 Accents can be inserted via the math toolbar button
8762 \begin_inset Graphics
8763 filename ../images/math/hat.png
8768 or the commands listed in the following subsections.
8771 \begin_layout Subsection
8772 Accents for one Character
8776 \begin_layout Plain Layout
8789 \begin_layout Plain Layout
8791 \begin_inset CommandInset ref
8793 reference "sub:Accents-in-Text"
8806 \begin_layout Plain Layout
8814 \begin_inset Note Note
8817 \begin_layout Plain Layout
8824 is used to avoid that the footnote appears in the PDF-bookmark.
8827 \begin_layout Plain Layout
8835 \begin_inset CommandInset ref
8837 reference "sub:Formulas-in-Section"
8847 \begin_inset CommandInset label
8849 name "sub:Accents-for-one"
8854 \begin_inset Index idx
8857 \begin_layout Plain Layout
8858 Accents ! for one character
8866 \begin_layout Standard
8867 \begin_inset space \hfill{}
8871 \begin_inset Tabular
8872 <lyxtabular version="3" rows="8" columns="2">
8873 <features rotate="0" tabularvalignment="middle">
8874 <column alignment="center" valignment="top" width="0pt">
8875 <column alignment="center" valignment="top" width="0pt">
8877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8880 \begin_layout Plain Layout
8886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8889 \begin_layout Plain Layout
8891 \begin_inset Note Note
8894 \begin_layout Plain Layout
8901 is only used as spacer.
8913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8916 \begin_layout Plain Layout
8920 \begin_inset space \textvisiblespace{}
8928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8931 \begin_layout Plain Layout
8932 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
8942 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8945 \begin_layout Plain Layout
8949 \begin_inset space \textvisiblespace{}
8957 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8960 \begin_layout Plain Layout
8961 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
8971 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8974 \begin_layout Plain Layout
8978 \begin_inset space \textvisiblespace{}
8986 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8989 \begin_layout Plain Layout
8990 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9000 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9003 \begin_layout Plain Layout
9007 \begin_inset space \textvisiblespace{}
9015 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9018 \begin_layout Plain Layout
9019 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9029 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9032 \begin_layout Plain Layout
9036 \begin_inset space \textvisiblespace{}
9040 \begin_inset Index idx
9043 \begin_layout Plain Layout
9054 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9057 \begin_layout Plain Layout
9058 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9068 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9071 \begin_layout Plain Layout
9075 \begin_inset space \textvisiblespace{}
9083 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9086 \begin_layout Plain Layout
9087 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9097 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9100 \begin_layout Plain Layout
9104 \begin_inset space \textvisiblespace{}
9112 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9115 \begin_layout Plain Layout
9116 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9130 \begin_inset space \hfill{}
9134 \begin_inset Tabular
9135 <lyxtabular version="3" rows="7" columns="2">
9136 <features rotate="0" tabularvalignment="middle">
9137 <column alignment="center" valignment="top" width="0pt">
9138 <column alignment="center" valignment="top" width="0pt">
9140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9143 \begin_layout Plain Layout
9149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9152 \begin_layout Plain Layout
9160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9163 \begin_layout Plain Layout
9167 \begin_inset space \textvisiblespace{}
9175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9178 \begin_layout Plain Layout
9179 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9189 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9192 \begin_layout Plain Layout
9196 \begin_inset space \textvisiblespace{}
9204 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9207 \begin_layout Plain Layout
9208 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9218 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9221 \begin_layout Plain Layout
9225 \begin_inset space \textvisiblespace{}
9233 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9236 \begin_layout Plain Layout
9237 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9247 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9250 \begin_layout Plain Layout
9254 \begin_inset space \textvisiblespace{}
9262 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9265 \begin_layout Plain Layout
9266 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9279 \begin_layout Plain Layout
9283 \begin_inset space \textvisiblespace{}
9291 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9294 \begin_layout Plain Layout
9295 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9305 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9308 \begin_layout Plain Layout
9312 \begin_inset space \textvisiblespace{}
9320 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9323 \begin_layout Plain Layout
9324 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9338 \begin_inset space \hfill{}
9344 \begin_layout Standard
9345 \begin_inset VSpace bigskip
9351 \begin_layout Standard
9352 You can directly insert accents like é to formulas.
9353 LyX will transform them to the corresponding accent command.
9355 \begin_inset Index idx
9358 \begin_layout Plain Layout
9364 it is better to insert a quotation mark before the vowel.
9365 These two characters are then treated by LaTeX as
9369 character when the formula part with the umlaut is marked as German.
9377 \begin_inset Quotes eld
9381 \begin_inset Quotes erd
9384 umlauts are created as demonstrated in the following example:
9387 \begin_layout Standard
9388 \begin_inset VSpace -2mm
9394 \begin_layout Standard
9396 \begin_inset Tabular
9397 <lyxtabular version="3" rows="3" columns="2">
9398 <features rotate="0" tabularvalignment="middle">
9399 <column alignment="center" valignment="top">
9400 <column alignment="center" valignment="top">
9402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9405 \begin_layout Plain Layout
9411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9414 \begin_layout Plain Layout
9416 \begin_inset Note Note
9419 \begin_layout Plain Layout
9427 \begin_inset space \thinspace{}
9430 pt space are only used as spacer.
9442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9445 \begin_layout Plain Layout
9448 \begin_inset Quotes grd
9456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9459 \begin_layout Plain Layout
9460 \begin_inset space \hspace{}
9467 \begin_inset Formula $"i$
9477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9480 \begin_layout Plain Layout
9484 \begin_inset space \textvisiblespace{}
9492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9495 \begin_layout Plain Layout
9496 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9512 \begin_layout Standard
9513 Another advantage to
9519 is that umlauts can directly be converted to mathematical text because
9520 the accent commands above are
9526 in mathematical text
9529 To convert an accented character to mathematical text, only the character
9530 under the accent may be converted.
9531 This applies also for all other conversions, e.
9532 \begin_inset space \thinspace{}
9536 \begin_inset space \space{}
9542 \begin_layout Standard
9543 In mathematical text, umlauts and other accented characters can directly
9547 \begin_layout Standard
9548 \begin_inset VSpace bigskip
9554 \begin_layout Standard
9555 LyX also supports a tilde under the character if the LaTeX-package
9560 \begin_inset Index idx
9563 \begin_layout Plain Layout
9564 Packages ! undertilde
9569 is installed on your system:
9572 \begin_layout Standard
9576 \begin_layout Plain Layout
9586 \begin_inset Note Note
9589 \begin_layout Plain Layout
9590 The following table will only be displayed when the LaTeX-package
9602 \begin_layout Standard
9605 \begin_inset Tabular
9606 <lyxtabular version="3" rows="2" columns="2">
9607 <features rotate="0" tabularvalignment="middle">
9608 <column alignment="center" valignment="top" width="0pt">
9609 <column alignment="center" valignment="top" width="0pt">
9611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9614 \begin_layout Plain Layout
9620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9623 \begin_layout Plain Layout
9631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9634 \begin_layout Plain Layout
9638 \begin_inset space \textvisiblespace{}
9646 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9649 \begin_layout Plain Layout
9650 \begin_inset Formula $\raisebox{5mm}{}\utilde{A}$
9666 \begin_layout Standard
9670 \begin_layout Plain Layout
9680 \begin_inset Note Note
9683 \begin_layout Plain Layout
9684 The following will be displayed when the LaTeX-package
9696 \begin_layout Standard
9697 You need to install the LaTeX-package
9701 to see the rest of this subsection in the output.
9704 \begin_layout Standard
9708 \begin_layout Plain Layout
9720 \begin_layout Subsection
9721 Accents for several Characters
9722 \begin_inset Index idx
9725 \begin_layout Plain Layout
9726 Accents ! for several characters
9734 \begin_layout Standard
9735 \begin_inset space \hfill{}
9739 \begin_inset Tabular
9740 <lyxtabular version="3" rows="5" columns="2">
9741 <features rotate="0" tabularvalignment="middle">
9742 <column alignment="center" valignment="top" width="0pt">
9743 <column alignment="center" valignment="top" width="0pt">
9745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9748 \begin_layout Plain Layout
9754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9757 \begin_layout Plain Layout
9759 \begin_inset Note Note
9762 \begin_layout Plain Layout
9769 is only used as spacer.
9781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9784 \begin_layout Plain Layout
9788 \begin_inset space \textvisiblespace{}
9796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9799 \begin_layout Plain Layout
9800 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9810 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9813 \begin_layout Plain Layout
9817 \begin_inset space \textvisiblespace{}
9825 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9828 \begin_layout Plain Layout
9829 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9839 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9842 \begin_layout Plain Layout
9846 \begin_inset space \textvisiblespace{}
9854 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9857 \begin_layout Plain Layout
9858 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9871 \begin_layout Plain Layout
9875 \begin_inset space \textvisiblespace{}
9883 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9886 \begin_layout Plain Layout
9887 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9901 \begin_inset space \hfill{}
9905 \begin_inset Tabular
9906 <lyxtabular version="3" rows="5" columns="2">
9907 <features rotate="0" tabularvalignment="middle">
9908 <column alignment="center" valignment="top" width="0pt">
9909 <column alignment="center" valignment="top" width="0pt">
9911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9914 \begin_layout Plain Layout
9920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9923 \begin_layout Plain Layout
9931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9934 \begin_layout Plain Layout
9938 \begin_inset space \textvisiblespace{}
9946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9949 \begin_layout Plain Layout
9950 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9960 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9963 \begin_layout Plain Layout
9967 \begin_inset space \textvisiblespace{}
9975 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9978 \begin_layout Plain Layout
9979 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9989 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9992 \begin_layout Plain Layout
9996 \begin_inset space \textvisiblespace{}
10004 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10007 \begin_layout Plain Layout
10008 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10018 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10021 \begin_layout Plain Layout
10025 \begin_inset space \textvisiblespace{}
10033 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10036 \begin_layout Plain Layout
10037 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10051 \begin_inset space \hfill{}
10057 \begin_layout Standard
10058 \begin_inset VSpace medskip
10061 With these commands as many characters as you like can be accented.
10074 will only be set in the output with a length of three characters, as shown
10075 in the following example:
10076 \begin_inset Formula
10078 \widetilde{A+B=C-D}
10086 \begin_layout Standard
10094 \begin_inset Index idx
10097 \begin_layout Plain Layout
10112 \begin_inset Index idx
10115 \begin_layout Plain Layout
10123 described in the previous subsection it is also possible to accent several
10130 \begin_inset space \textvisiblespace{}
10134 \begin_inset Formula $\downarrow$
10140 \begin_inset Formula
10142 \underset{***}{A=B}
10150 \begin_layout Standard
10151 \begin_inset Newpage newpage
10157 \begin_layout Section
10159 \begin_inset CommandInset label
10166 \begin_inset Index idx
10169 \begin_layout Plain Layout
10178 \begin_layout Subsection
10180 \begin_inset CommandInset label
10182 name "sub:Predefined-Space"
10187 \begin_inset Index idx
10190 \begin_layout Plain Layout
10191 Space ! horizontal ! predefined
10199 \begin_layout Standard
10200 Sometimes it is necessary to insert horizontal space into a formula.
10201 This is done by inserting a protected space (shortcut
10204 arg "command-alternatives space-insert protected ; math-space"
10209 \begin_inset Quotes eld
10215 \begin_inset space \textvisiblespace{}
10221 \begin_inset Quotes erd
10224 appears and by pressing
10228 several times one can select one of eight different space sizes.
10229 The spaces can also be inserted using the math toolbar button
10230 \begin_inset Graphics
10231 filename ../images/math/space.png
10236 or special commands.
10237 Independent from the inserted command, one can select the size again by
10245 \begin_layout Standard
10248 \begin_inset VSpace -5mm
10252 \begin_inset Tabular
10253 <lyxtabular version="3" rows="3" columns="7">
10254 <features rotate="0" tabularvalignment="middle">
10255 <column alignment="center" valignment="middle" width="6.8cm">
10256 <column alignment="center" valignment="top">
10257 <column alignment="center" valignment="top">
10258 <column alignment="center" valignment="top">
10259 <column alignment="center" valignment="top">
10260 <column alignment="center" valignment="top">
10261 <column alignment="center" valignment="top">
10263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10266 \begin_layout Plain Layout
10272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10275 \begin_layout Plain Layout
10283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10286 \begin_layout Plain Layout
10294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10297 \begin_layout Plain Layout
10305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10308 \begin_layout Plain Layout
10316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10319 \begin_layout Plain Layout
10327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10330 \begin_layout Plain Layout
10340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10343 \begin_layout Plain Layout
10348 keystrokes after inserting the protected space
10353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10356 \begin_layout Plain Layout
10362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10365 \begin_layout Plain Layout
10371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10374 \begin_layout Plain Layout
10380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10383 \begin_layout Plain Layout
10389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10392 \begin_layout Plain Layout
10398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10401 \begin_layout Plain Layout
10409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10412 \begin_layout Plain Layout
10418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10421 \begin_layout Plain Layout
10422 \begin_inset Formula $A\, B$
10430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10433 \begin_layout Plain Layout
10434 \begin_inset Formula $A\: B$
10442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10445 \begin_layout Plain Layout
10446 \begin_inset Formula $A\; B$
10454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10457 \begin_layout Plain Layout
10458 \begin_inset Formula $A\quad B$
10466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10469 \begin_layout Plain Layout
10470 \begin_inset Formula $A\qquad B$
10478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10481 \begin_layout Plain Layout
10482 \begin_inset Formula $A\! B$
10498 \begin_layout Standard
10499 The last size seem to produce no space.
10500 It is displayed red in LyX contrary to the other sizes, because it is a
10502 There are two more negative spaces:
10505 \begin_layout Standard
10507 \begin_inset Tabular
10508 <lyxtabular version="3" rows="3" columns="3">
10509 <features rotate="0" tabularvalignment="middle">
10510 <column alignment="center" valignment="middle" width="6.8cm">
10511 <column alignment="center" valignment="top" width="0pt">
10512 <column alignment="center" valignment="top" width="0pt">
10514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10517 \begin_layout Plain Layout
10523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10526 \begin_layout Plain Layout
10534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10537 \begin_layout Plain Layout
10547 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10550 \begin_layout Plain Layout
10555 keystrokes after inserting the protected space
10560 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10563 \begin_layout Plain Layout
10569 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10572 \begin_layout Plain Layout
10580 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10583 \begin_layout Plain Layout
10589 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10592 \begin_layout Plain Layout
10593 \begin_inset Formula $A\negmedspace B$
10601 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10604 \begin_layout Plain Layout
10605 \begin_inset Formula $A\negthickspace B$
10621 \begin_layout Standard
10622 Negative spaces can lead to characters overlapping each other.
10623 Thus they can be used to enforce ligatures, which are e.
10624 \begin_inset space \thinspace{}
10628 \begin_inset space \space{}
10631 useful for summation operators:
10634 \begin_layout Standard
10636 \begin_inset Tabular
10637 <lyxtabular version="3" rows="3" columns="2">
10638 <features rotate="0" tabularvalignment="middle">
10639 <column alignment="center" valignment="top">
10640 <column alignment="center" valignment="top">
10642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10645 \begin_layout Plain Layout
10651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10654 \begin_layout Plain Layout
10656 \begin_inset Note Note
10659 \begin_layout Plain Layout
10666 is only used as spacer.
10678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10681 \begin_layout Plain Layout
10687 \begin_inset space \textvisiblespace{}
10695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10698 \begin_layout Plain Layout
10699 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10712 \begin_layout Plain Layout
10720 \begin_inset space \textvisiblespace{}
10728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10731 \begin_layout Plain Layout
10732 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10748 \begin_layout Standard
10749 Relations like for example equal signs, are always surrounded by space.
10750 To suppress this, the equal sign is placed into a TeX-brace.
10751 The following example demonstrates this:
10754 \begin_layout Standard
10756 \begin_inset Tabular
10757 <lyxtabular version="3" rows="2" columns="2">
10758 <features rotate="0" tabularvalignment="middle">
10759 <column alignment="center" valignment="top" width="0pt">
10760 <column alignment="center" valignment="top" width="0pt">
10762 <cell alignment="center" valignment="top" usebox="none">
10765 \begin_layout Plain Layout
10771 <cell alignment="center" valignment="top" usebox="none">
10774 \begin_layout Plain Layout
10775 \begin_inset Formula $A=B$
10785 <cell alignment="center" valignment="top" usebox="none">
10788 \begin_layout Plain Layout
10789 \begin_inset Note Note
10792 \begin_layout Plain Layout
10799 is only used as spacer.
10805 \begin_inset Formula $\raisebox{5mm}{}$
10808 equation without space
10813 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
10816 \begin_layout Plain Layout
10817 \begin_inset Formula $A{=}B$
10833 \begin_layout Standard
10835 The command for the last formula is:
10840 \begin_inset Formula $\to$
10846 \begin_layout Standard
10847 \begin_inset VSpace bigskip
10850 Spaces are needed for physical units, because the space between the value
10851 and the unit is the smallest one and not a normal space.
10852 For units in text, the smallest space is inserted via the menu
10854 Insert\SpecialChar \menuseparator
10855 Formatting\SpecialChar \menuseparator
10857 \begin_inset space ~
10865 arg "space-insert thin"
10871 \begin_layout Standard
10872 An example to visualize the difference:
10875 \begin_layout Standard
10876 \begin_inset Tabular
10877 <lyxtabular version="3" rows="2" columns="2">
10878 <features rotate="0" tabularvalignment="middle">
10879 <column alignment="left" valignment="top">
10880 <column alignment="left" valignment="top">
10882 <cell alignment="center" valignment="top" usebox="none">
10885 \begin_layout Plain Layout
10887 \begin_inset Formula $\cdot$
10895 <cell alignment="center" valignment="top" usebox="none">
10898 \begin_layout Plain Layout
10899 space between value and unit
10906 <cell alignment="center" valignment="top" usebox="none">
10909 \begin_layout Plain Layout
10911 \begin_inset space \thinspace{}
10915 \begin_inset Formula $\cdot$
10923 <cell alignment="center" valignment="top" usebox="none">
10926 \begin_layout Plain Layout
10927 smallest space between value and unit
10940 \begin_layout Subsection
10945 \begin_layout Plain Layout
10958 \begin_layout Plain Layout
10959 for vertical space in formulas see
10960 \begin_inset CommandInset ref
10962 reference "sub:Line-Separation"
10975 \begin_layout Plain Layout
10983 \begin_inset Note Note
10986 \begin_layout Plain Layout
10989 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
10992 \begin_layout Plain Layout
10995 texorpdfstring is in section
10996 \begin_inset CommandInset ref
10998 reference "sub:Formulas-in-Section"
11008 \begin_inset CommandInset label
11010 name "sub:Variable-Space"
11015 \begin_inset Index idx
11018 \begin_layout Plain Layout
11019 Space ! horizontal ! variable
11027 \begin_layout Standard
11028 Space with a defined length can be inserted with the command
11035 \begin_inset Index idx
11038 \begin_layout Plain Layout
11048 \begin_inset Quotes eld
11054 \begin_inset space \textvisiblespace{}
11060 \begin_inset Quotes erd
11064 The length can be specified by left-clicking on the
11065 \begin_inset Quotes eld
11071 \begin_inset space \textvisiblespace{}
11077 \begin_inset Quotes erd
11081 The length may also be negative.
11082 To insert as much space as is available, the command
11089 \begin_inset Index idx
11092 \begin_layout Plain Layout
11103 \begin_layout Standard
11104 \begin_inset VSpace -1mm
11110 \begin_layout Standard
11112 \begin_inset Tabular
11113 <lyxtabular version="3" rows="4" columns="2">
11114 <features rotate="0" tabularvalignment="middle">
11115 <column alignment="center" valignment="top">
11116 <column alignment="center" valignment="top">
11118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11121 \begin_layout Plain Layout
11129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11132 \begin_layout Plain Layout
11140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11143 \begin_layout Plain Layout
11147 \begin_inset space \textvisiblespace{}
11151 \begin_inset Formula $\to$
11157 \begin_inset space \thinspace{}
11165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11168 \begin_layout Plain Layout
11169 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11182 \begin_layout Plain Layout
11186 \begin_inset space \textvisiblespace{}
11190 \begin_inset Formula $\to$
11196 \begin_inset space \thinspace{}
11204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11207 \begin_layout Plain Layout
11208 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11221 \begin_layout Plain Layout
11225 \begin_inset space \textvisiblespace{}
11233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11236 \begin_layout Plain Layout
11237 \begin_inset Formula $A=A\hfill B=B$
11253 \begin_layout Standard
11254 In the last example the available space is given by the longest column entry
11256 In an inline formula the space depends on the length of the line in which
11264 Thus, when the line uses the full width, no space will be created.
11271 only has an effect on displayed formulas when the formula style
11276 (Formula styles are explained in
11277 \begin_inset CommandInset ref
11279 reference "sec:Formula-Styles"
11286 \begin_layout Standard
11293 , there are the commands
11305 that fill the space with a pattern, see
11306 \begin_inset CommandInset ref
11308 reference "sub:Ellipses"
11315 \begin_layout Standard
11316 For text, variable space can be inserted via the menu
11318 Insert\SpecialChar \menuseparator
11319 Formatting\SpecialChar \menuseparator
11321 \begin_inset space ~
11329 \begin_layout Standard
11330 This is a line with
11331 \begin_inset space \hspace{}
11336 \begin_inset space \thinspace{}
11342 \begin_layout Standard
11343 This is a line with
11344 \begin_inset space \hfill{}
11350 \begin_layout Subsection
11351 Space besides inline Formulas
11352 \begin_inset Index idx
11355 \begin_layout Plain Layout
11356 Space ! besides inline formulas
11364 \begin_layout Standard
11365 The space that surrounds inline formulas can be adjusted with the length
11373 \begin_inset Index idx
11376 \begin_layout Plain Layout
11385 The value of a length is set with the command
11392 \begin_inset Index idx
11395 \begin_layout Plain Layout
11403 which has the following scheme:
11406 \begin_layout Standard
11411 setlength{length name}{value}
11414 \begin_layout Standard
11422 \begin_inset space \thinspace{}
11428 \begin_layout Standard
11438 \begin_layout Standard
11439 is inserted in TeX-mode.
11441 \begin_inset space \thinspace{}
11444 mm space will now be set around all inline formulas:
11448 \begin_layout Plain Layout
11462 \begin_layout Standard
11463 This is a line with an inline formula
11464 \begin_inset Formula $A=B$
11468 \begin_inset space \thinspace{}
11471 mm surrounding space.
11475 \begin_layout Plain Layout
11489 \begin_layout Standard
11490 To return to the predefined value,
11496 is set to the value 0
11497 \begin_inset space \thinspace{}
11503 \begin_layout Section
11505 \begin_inset Index idx
11508 \begin_layout Plain Layout
11515 \begin_inset Index idx
11518 \begin_layout Plain Layout
11523 \begin_layout Plain Layout
11534 \begin_layout Plain Layout
11549 \begin_layout Standard
11550 Boxes for text are described in chapter
11557 \begin_inset space ~
11565 \begin_layout Subsection
11567 \begin_inset CommandInset label
11569 name "sub:Boxes-with-Frame"
11574 \begin_inset Index idx
11577 \begin_layout Plain Layout
11586 \begin_layout Standard
11587 It is possible to frame a formula or part of one with the commands
11594 \begin_inset Index idx
11597 \begin_layout Plain Layout
11612 \begin_inset Index idx
11615 \begin_layout Plain Layout
11626 \begin_layout Standard
11627 When one of these commands is inserted in a formula, a blue box appears
11628 within a frame to enter formula parts.
11635 an additional formula has to be created by
11639 within this box, because the box content will otherwise be treated as mathemati
11647 is used, a new formula is automatically created inside the frame.
11650 \begin_layout Standard
11657 is not suitable to frame displayed formulas because the formula will always
11658 be set in the size of the text.
11665 is in contrary not suitable to frame inline formulas, because the formula
11666 will always be set in the size of a displayed formula.
11669 \begin_layout Standard
11683 \begin_inset Index idx
11686 \begin_layout Plain Layout
11694 where additionally the frame width and the alignment can be specified.
11701 is used in the following scheme:
11704 \begin_layout Standard
11709 framebox[frame width][position]{box content}
11712 \begin_layout Standard
11713 The position can either be
11730 right aligns the formula in the box.
11731 When no position is given, the formula will be centered.
11732 \begin_inset Newline newline
11735 If no width is given, also no position can be given.
11736 In this case the frame width is adjusted to the box content like for
11745 \begin_layout Standard
11752 is inserted, a box appears containing three blue boxes.
11753 The first two boxes are surrounded by brackets and denote the two optional
11755 The third box is for formula parts like for
11764 \begin_layout Standard
11765 \begin_inset Newpage newpage
11771 \begin_layout Standard
11773 \begin_inset Tabular
11774 <lyxtabular version="3" rows="5" columns="2">
11775 <features rotate="0" tabularvalignment="middle">
11776 <column alignment="center" valignment="top">
11777 <column alignment="center" valignment="top">
11779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11782 \begin_layout Plain Layout
11788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11791 \begin_layout Plain Layout
11793 \begin_inset Note Note
11796 \begin_layout Plain Layout
11803 is only used as spacer.
11815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11818 \begin_layout Plain Layout
11822 \begin_inset space \textvisiblespace{}
11832 \begin_inset space \textvisiblespace{}
11840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11843 \begin_layout Plain Layout
11844 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
11854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11857 \begin_layout Plain Layout
11861 \begin_inset space \textvisiblespace{}
11867 \begin_inset space \textvisiblespace{}
11875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11878 \begin_layout Plain Layout
11879 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
11889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11892 \begin_layout Plain Layout
11896 \begin_inset space \textvisiblespace{}
11904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11907 \begin_layout Plain Layout
11908 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
11918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11921 \begin_layout Plain Layout
11925 \begin_inset space \textvisiblespace{}
11929 \begin_inset Formula $\to$
11933 \begin_inset Formula $\to$
11943 \begin_inset space \textvisiblespace{}
11947 \begin_inset Formula $\downarrow$
11955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11958 \begin_layout Plain Layout
11959 \begin_inset Formula $\raisebox{6mm}{}$
11963 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
11967 \begin_inset Formula $\raisebox{-4mm}{}$
11983 \begin_layout Standard
11984 The frame thickness can also be adjusted.
11985 To do this the following commands have to be inserted in TeX-mode before
11989 \begin_layout Standard
11999 \begin_inset Quotes eld
12003 \begin_inset Quotes erd
12017 \begin_inset Quotes eld
12021 \begin_inset Quotes erd
12027 \begin_layout Standard
12028 \begin_inset Quotes eld
12032 \begin_inset Quotes erd
12035 specifies the minimal distance between the frame and the first character
12037 An example for this is the following framed formula:
12041 \begin_layout Plain Layout
12053 \begin_inset Formula
12060 Before this formula the commands
12063 \begin_layout Standard
12085 \begin_layout Standard
12086 were inserted in TeX-mode.
12087 The given values are used for all following boxes.
12090 \begin_layout Standard
12091 To return to the standard frame size, the command
12094 \begin_layout Standard
12119 \begin_layout Plain Layout
12133 \begin_layout Standard
12134 is inserted in TeX-mode before the next formula.
12137 \begin_layout Subsection
12138 Boxes without Frame
12139 \begin_inset CommandInset label
12141 name "sub:Boxes-without-Frame"
12146 \begin_inset Index idx
12149 \begin_layout Plain Layout
12150 Boxes ! without frame
12158 \begin_layout Standard
12159 For boxes without a frame there are the following box commands:
12166 \begin_inset Index idx
12169 \begin_layout Plain Layout
12184 \begin_inset Index idx
12187 \begin_layout Plain Layout
12202 \begin_inset Index idx
12205 \begin_layout Plain Layout
12216 \begin_layout Standard
12223 a box can be super- or subscripted.
12224 But in contrary to normal super- and subscripting, the characters in the
12225 box keep their font size.
12232 is used in the following scheme:
12235 \begin_layout Standard
12240 raisebox{height}{box content}
12243 \begin_layout Standard
12244 When the box should contain a formula, an extra formula is needed like for
12255 \begin_inset Note Greyedout
12258 \begin_layout Plain Layout
12269 this extra formula is created by pressing
12273 twice instead of once because LyX doesn't yet support
12287 \begin_layout Standard
12289 \begin_inset Tabular
12290 <lyxtabular version="3" rows="4" columns="2">
12291 <features rotate="0" tabularvalignment="middle">
12292 <column alignment="center" valignment="top">
12293 <column alignment="center" valignment="top">
12295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12298 \begin_layout Plain Layout
12304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12307 \begin_layout Plain Layout
12315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12318 \begin_layout Plain Layout
12322 \begin_inset Formula $\to$
12328 \begin_inset Formula $\to$
12336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12339 \begin_layout Plain Layout
12340 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12353 \begin_layout Plain Layout
12357 \begin_inset Formula $\to$
12363 \begin_inset Formula $\to$
12371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12374 \begin_layout Plain Layout
12375 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12388 \begin_layout Plain Layout
12392 \begin_inset Formula $\to$
12408 \begin_inset space \textvisiblespace{}
12416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12419 \begin_layout Plain Layout
12420 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
12436 \begin_layout Standard
12461 , with the difference that there is no frame.
12464 \begin_layout Subsection
12466 \begin_inset CommandInset label
12468 name "sub:Colored-Boxes"
12473 \begin_inset Index idx
12476 \begin_layout Plain Layout
12485 \begin_layout Standard
12486 To be able to use all commands explained in this section, the LaTeX-package
12495 \begin_layout Plain Layout
12500 is part of every LaTeX standard installation.
12506 \begin_inset Index idx
12509 \begin_layout Plain Layout
12515 has to be loaded in the LaTeX-preamble with the line
12519 \begin_layout Plain Layout
12520 When text is colored somewhere in the document with a predefined color,
12521 LyX loads the LaTeX-package
12526 Thus it is possible that the package is loaded twice, but this does not
12533 \begin_inset Note Note
12536 \begin_layout Plain Layout
12537 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12546 \begin_layout Standard
12554 \begin_layout Standard
12555 \begin_inset VSpace medskip
12558 To color boxes, the command
12565 \begin_inset Index idx
12568 \begin_layout Plain Layout
12576 is used in the following scheme:
12579 \begin_layout Standard
12584 colorbox{color}{box content}
12587 \begin_layout Standard
12588 The box content can also be a box and a
12594 can also be part of another box (see the 2nd and 3rd example).
12595 When the box should contain a formula, an extra formula has to be created,
12596 the same way as for
12606 \begin_layout Plain Layout
12607 This also applies for the command
12621 \begin_layout Standard
12622 One of the following predefined colors can be chosen:
12625 \begin_layout Standard
12659 \begin_layout Standard
12661 \begin_inset Tabular
12662 <lyxtabular version="3" rows="4" columns="2">
12663 <features rotate="0" tabularvalignment="middle">
12664 <column alignment="center" valignment="top">
12665 <column alignment="center" valignment="top">
12667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12670 \begin_layout Plain Layout
12676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12679 \begin_layout Plain Layout
12681 \begin_inset Note Note
12684 \begin_layout Plain Layout
12691 is only used as spacer.
12703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12706 \begin_layout Plain Layout
12710 \begin_inset Formula $\to$
12720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12723 \begin_layout Plain Layout
12724 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12737 \begin_layout Plain Layout
12741 \begin_inset Formula $\to$
12749 \begin_inset space \textvisiblespace{}
12757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12760 \begin_layout Plain Layout
12761 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
12771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12774 \begin_layout Plain Layout
12778 \begin_inset space \textvisiblespace{}
12784 \begin_inset Formula $\to$
12800 \begin_inset space \textvisiblespace{}
12808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12811 \begin_layout Plain Layout
12812 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
12828 \begin_layout Standard
12835 only colors the box but not the characters in the box.
12836 To color all characters, the whole formula is highlighted and the desired
12837 color is chosen in the
12840 \begin_inset space ~
12846 The dialog can be called with the toolbar button
12847 \begin_inset Graphics
12848 filename ../images/dialog-show_character.png
12855 Edit\SpecialChar \menuseparator
12857 \begin_inset space ~
12860 Style\SpecialChar \menuseparator
12864 The formula number then has the same color as the formula.
12865 When the formula number should get another color than the formula characters,
12866 the color must be changed within the formula.
12869 \begin_layout Standard
12873 \begin_layout Standard
12876 \begin_inset Formula
12878 \int A=B\label{eq:red}
12886 \begin_inset Formula
12888 \textcolor{red}{\int A=B}\label{eq:redgreen}
12896 \begin_layout Standard
12898 \begin_inset CommandInset ref
12904 is completely colored red.
12905 \begin_inset Newline newline
12909 \begin_inset CommandInset ref
12911 reference "eq:redgreen"
12915 was first completely colored green to set the color for the formula number.
12916 Subsequently the formula characters were colored red.
12919 \begin_layout Standard
12920 \begin_inset VSpace bigskip
12923 To color the frame different than the rest of the box, the command
12930 \begin_inset Index idx
12933 \begin_layout Plain Layout
12941 is used in the following scheme:
12944 \begin_layout Standard
12949 fcolorbox{frame color}{color}{box content}
12952 \begin_layout Standard
12959 is an extension of the command
12966 The frame width is set, like for
12989 \begin_layout Plain Layout
13001 \begin_inset Formula
13003 \fcolorbox{cyan}{magenta}{A=B}
13012 \begin_layout Plain Layout
13026 \begin_layout Standard
13027 This formula was created with the command
13028 \begin_inset Newline newline
13036 \begin_inset Formula $\to$
13042 \begin_inset Formula $\to$
13052 \begin_layout Standard
13053 \begin_inset VSpace bigskip
13056 To use other colors than the predefined ones, they have to be defined first.
13059 \begin_layout Standard
13060 One can for example define the color
13061 \begin_inset Quotes eld
13069 \begin_inset Quotes erd
13072 with the LaTeX-preamble line:
13075 \begin_layout Standard
13080 definecolor{darkgreen}{cmyk}{0.5,
13095 \begin_inset Index idx
13098 \begin_layout Plain Layout
13109 \begin_layout Standard
13114 is the color space that denotes the colors
13131 The four comma separated numbers are the portion factor for the corresponding
13132 colors of the color space.
13133 The factors can be in the range of 0
13134 \begin_inset space \thinspace{}
13138 \begin_inset space \thinspace{}
13146 also the color space
13150 can be used for definitions.
13167 , so that there are in this case three portion factors for the corresponding
13169 Furthermore there is the color space
13173 with one portion factor for the gray value.
13176 \begin_layout Standard
13177 As example a framed box with the new defined color
13181 where the characters have been colored
13186 \begin_inset Formula
13188 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
13196 \begin_layout Standard
13197 Self-defined colors can also be used for text with the help of the command
13205 \begin_inset Index idx
13208 \begin_layout Plain Layout
13217 \begin_layout Standard
13221 \begin_layout Plain Layout
13225 textcolor{darkgreen}{
13231 \begin_inset Quotes eld
13235 \begin_inset Quotes erd
13242 \begin_layout Plain Layout
13252 \begin_layout Standard
13260 \begin_inset Index idx
13263 \begin_layout Plain Layout
13271 is used in the scheme
13275 textcolor{color}{characters to color}
13280 \begin_layout Subsection
13282 \begin_inset CommandInset label
13284 name "sub:Paragraph-Boxes"
13289 \begin_inset Index idx
13292 \begin_layout Plain Layout
13293 Boxes ! as paragraph
13301 \begin_layout Standard
13302 A box that can contain several lines and paragraphs, a so-called paragraph
13303 box (parbox), can be created with the menu
13305 Insert\SpecialChar \menuseparator
13308 or the toolbar button
13309 \begin_inset Graphics
13310 filename ../images/box-insert.png
13318 \begin_layout Standard
13319 The following example shows a framed parbox in a line:
13322 \begin_layout Standard
13323 \begin_inset VSpace medskip
13327 \begin_inset Box Boxed
13337 height_special "totalheight"
13340 \begin_layout Plain Layout
13341 This is a paragraph box.
13343 \begin_inset space \thinspace{}
13346 cm long and can also contain formulas:
13347 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13358 \begin_layout Standard
13359 \begin_inset VSpace medskip
13365 \begin_layout Standard
13366 Such a box is created by right-clicking on the gray box inset.
13367 A dialog pops up showing the box properties.
13381 \begin_inset space \thinspace{}
13386 Vertical Box Alignment
13391 \begin_layout Standard
13392 \begin_inset VSpace medskip
13395 In LaTeX a parbox is created with the command
13402 \begin_inset Index idx
13405 \begin_layout Plain Layout
13413 which has the following scheme:
13416 \begin_layout Standard
13421 parbox[position]{width}{box content}
13424 \begin_layout Standard
13439 \begin_inset Quotes eld
13443 \begin_inset Quotes erd
13446 means that the box is aligned within the surrounding text with its last
13453 \begin_inset Quotes eld
13457 \begin_inset Quotes erd
13460 this is done with the first line.
13461 When no position is given, the box will be vertically centered, see section
13469 \begin_inset space ~
13474 manual for examples.
13477 \begin_layout Standard
13478 \begin_inset VSpace bigskip
13481 To frame formulas completely, including the formula number, the formula
13482 must be set into a parbox.
13483 To do this, the command
13497 is inserted in TeX-mode before the formula.
13505 \begin_inset Index idx
13508 \begin_layout Plain Layout
13516 is hereby the line width set for the document.
13517 Because the frame is outside the parbox, 2
13518 \begin_inset space \thinspace{}
13521 times the frame separation and the frame thickness must be subtracted from
13523 As this is not automatically done by LyX due to a bug
13527 \begin_layout Plain Layout
13528 \begin_inset CommandInset href
13530 name "LyX-bug #4483"
13531 target "http://www.lyx.org/trac/ticket/4483"
13540 , TeX-mode has to be used.
13541 To be able to multiply and subtract in arguments, the LaTeX-package
13549 \begin_layout Plain Layout
13554 is part of every LaTeX standard installation.
13560 \begin_inset Index idx
13563 \begin_layout Plain Layout
13569 must be loaded in the LaTeX-preamble with the line
13572 \begin_layout Standard
13580 \begin_layout Standard
13581 Behind the formula both boxes are closed by entering
13586 Here is an example:
13590 \begin_layout Plain Layout
13604 \begin_layout Standard
13608 \begin_layout Plain Layout
13626 \begin_inset Formula
13628 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
13637 \begin_layout Plain Layout
13648 \begin_layout Plain Layout
13662 \begin_layout Standard
13663 \begin_inset VSpace medskip
13666 As a parbox is used as the argument of
13672 , there is in this case no difference between
13687 \begin_layout Standard
13688 \begin_inset VSpace bigskip
13691 Paragraph boxes are very useful to comment formulas directly.
13698 is used in combination with the command
13712 \begin_inset CommandInset ref
13714 reference "sub:User-defined-Numbering"
13721 \begin_layout Standard
13722 An example of a formula commented with
13731 \begin_layout Standard
13735 \begin_layout Plain Layout
13748 This is a description.
13749 It is distinctly separated from the formula and multiline.
13753 \begin_layout Plain Layout
13765 \begin_layout Standard
13766 Such a formula must be inserted completely in TeX-mode because LyX does
13767 not yet support the command
13774 The formula is created with the following command sequence:
13777 \begin_layout Standard
13790 is inserted in TeX-mode.
13794 \begin_layout Plain Layout
13795 When the formula style
13807 can also be replaced by
13814 (formula styles see
13815 \begin_inset CommandInset ref
13817 reference "sec:Formula-Styles"
13826 Then the description follows as normal text and finally
13832 is inserted in TeX-mode.
13845 hereby create a displayed formula.
13848 \begin_layout Standard
13855 can be seen in this example that was
13856 \begin_inset Quotes eld
13860 \begin_inset Quotes erd
13863 using the mathematical textmode:
13864 \begin_inset Formula
13866 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
13874 \begin_layout Section
13876 \begin_inset Index idx
13879 \begin_layout Plain Layout
13888 \begin_layout Subsection
13890 \begin_inset CommandInset label
13892 name "sub:Big-Operators"
13897 \begin_inset Index idx
13900 \begin_layout Plain Layout
13907 \begin_inset Index idx
13910 \begin_layout Plain Layout
13917 \begin_inset Index idx
13920 \begin_layout Plain Layout
13929 \begin_layout Standard
13930 To be able to use all integral operators listed here, the option
13932 Use esint package automatically
13934 must be set in the document settings under
13937 \begin_inset space ~
13945 \begin_layout Standard
13946 \begin_inset space \hfill{}
13950 \begin_inset Tabular
13951 <lyxtabular version="3" rows="11" columns="2">
13952 <features rotate="0" tabularvalignment="middle">
13953 <column alignment="center" valignment="top" width="0pt">
13954 <column alignment="center" valignment="top" width="0pt">
13956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13959 \begin_layout Plain Layout
13965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13968 \begin_layout Plain Layout
13976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13979 \begin_layout Plain Layout
13983 \begin_inset Index idx
13986 \begin_layout Plain Layout
13999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14002 \begin_layout Plain Layout
14003 \begin_inset Formula $\int$
14013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14016 \begin_layout Plain Layout
14024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14027 \begin_layout Plain Layout
14028 \begin_inset Formula $\oint$
14038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14041 \begin_layout Plain Layout
14049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14052 \begin_layout Plain Layout
14053 \begin_inset Formula $\ointctrclockwise$
14063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14066 \begin_layout Plain Layout
14074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14077 \begin_layout Plain Layout
14078 \begin_inset Formula $\ointclockwise$
14088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14091 \begin_layout Plain Layout
14099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14102 \begin_layout Plain Layout
14103 \begin_inset Formula $\sqint$
14113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14116 \begin_layout Plain Layout
14124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14127 \begin_layout Plain Layout
14129 \begin_inset Formula $\fint$
14139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14142 \begin_layout Plain Layout
14150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14153 \begin_layout Plain Layout
14155 \begin_inset Formula $\landupint$
14165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14168 \begin_layout Plain Layout
14176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14179 \begin_layout Plain Layout
14181 \begin_inset Formula $\landdownint$
14191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14194 \begin_layout Plain Layout
14202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14205 \begin_layout Plain Layout
14206 \begin_inset Formula $\bigcap$
14216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14219 \begin_layout Plain Layout
14227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14230 \begin_layout Plain Layout
14231 \begin_inset Formula $\bigcup$
14245 \begin_inset space \hfill{}
14249 \begin_inset Tabular
14250 <lyxtabular version="3" rows="11" columns="2">
14251 <features rotate="0" tabularvalignment="middle">
14252 <column alignment="center" valignment="top" width="0pt">
14253 <column alignment="center" valignment="top" width="0pt">
14255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14258 \begin_layout Plain Layout
14264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14267 \begin_layout Plain Layout
14275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14278 \begin_layout Plain Layout
14282 \begin_inset Index idx
14285 \begin_layout Plain Layout
14298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14301 \begin_layout Plain Layout
14302 \begin_inset Formula $\sum$
14312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14315 \begin_layout Plain Layout
14319 \begin_inset Index idx
14322 \begin_layout Plain Layout
14329 \begin_layout Plain Layout
14348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14351 \begin_layout Plain Layout
14352 \begin_inset Formula $\prod$
14362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14365 \begin_layout Plain Layout
14373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14376 \begin_layout Plain Layout
14377 \begin_inset Formula $\coprod$
14387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14390 \begin_layout Plain Layout
14398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14401 \begin_layout Plain Layout
14402 \begin_inset Formula $\bigodot$
14412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14415 \begin_layout Plain Layout
14423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14426 \begin_layout Plain Layout
14427 \begin_inset Formula $\bigotimes$
14437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14440 \begin_layout Plain Layout
14448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14451 \begin_layout Plain Layout
14452 \begin_inset Formula $\bigoplus$
14462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14465 \begin_layout Plain Layout
14473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14476 \begin_layout Plain Layout
14477 \begin_inset Formula $\bigwedge$
14487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14490 \begin_layout Plain Layout
14498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14501 \begin_layout Plain Layout
14502 \begin_inset Formula $\bigvee$
14512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14515 \begin_layout Plain Layout
14523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14526 \begin_layout Plain Layout
14527 \begin_inset Formula $\bigsqcup$
14537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14540 \begin_layout Plain Layout
14548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14551 \begin_layout Plain Layout
14552 \begin_inset Formula $\biguplus$
14566 \begin_inset space \hfill{}
14572 \begin_layout Standard
14573 All big operators can also be inserted via the math toolbar button
14574 \begin_inset Graphics
14575 filename ../images/math/intop.png
14583 \begin_layout Standard
14584 The operators are called big because they are bigger than the sometimes
14585 equal looking binary operators.
14586 All big operators can have limits as described in the next subsection.
14589 \begin_layout Standard
14590 For all integral operators there is a second version available, ending in
14608 These operators are different from
14615 \begin_inset space \space{}
14618 in the style the operator limits are displayed, see
14619 \begin_inset CommandInset ref
14621 reference "sub:Operator-Limits"
14629 \begin_layout Subsubsection*
14630 Advice for Integrals
14633 \begin_layout Standard
14638 in an integral is an operator, that therefore has to be set upright.
14639 This is done by highlighting the
14643 and using the keyboard shortcut
14653 \begin_layout Plain Layout
14659 \begin_inset CommandInset ref
14661 reference "sub:Font-Styles"
14671 Finally the smallest space is inserted before the
14675 , as this is usual for operators.
14679 \begin_layout Standard
14681 \begin_inset Formula $\int A(x)dx$
14685 \begin_inset Newline newline
14689 \begin_inset Phantom HPhantom
14692 \begin_layout Plain Layout
14699 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14705 \begin_layout Standard
14706 For multiple integrals there are the following commands:
14707 \begin_inset VSpace medskip
14713 \begin_layout Standard
14714 \begin_inset space \hfill{}
14718 \begin_inset Tabular
14719 <lyxtabular version="3" rows="4" columns="2">
14720 <features rotate="0" tabularvalignment="middle">
14721 <column alignment="center" valignment="top">
14722 <column alignment="center" valignment="top">
14724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14727 \begin_layout Plain Layout
14733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14736 \begin_layout Plain Layout
14738 \begin_inset Note Note
14741 \begin_layout Plain Layout
14748 is only used as spacer.
14760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14763 \begin_layout Plain Layout
14771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14774 \begin_layout Plain Layout
14775 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
14785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14788 \begin_layout Plain Layout
14796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14799 \begin_layout Plain Layout
14800 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
14810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14813 \begin_layout Plain Layout
14821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14824 \begin_layout Plain Layout
14825 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
14839 \begin_inset space \hfill{}
14843 \begin_inset Tabular
14844 <lyxtabular version="3" rows="4" columns="2">
14845 <features rotate="0" tabularvalignment="middle">
14846 <column alignment="center" valignment="top">
14847 <column alignment="center" valignment="top">
14849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14852 \begin_layout Plain Layout
14858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14861 \begin_layout Plain Layout
14869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14872 \begin_layout Plain Layout
14880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14883 \begin_layout Plain Layout
14884 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
14894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14897 \begin_layout Plain Layout
14905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14908 \begin_layout Plain Layout
14909 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
14919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14922 \begin_layout Plain Layout
14930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14933 \begin_layout Plain Layout
14934 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
14948 \begin_inset space \hfill{}
14954 \begin_layout Standard
14955 \begin_inset Newpage newpage
14961 \begin_layout Subsection
14963 \begin_inset CommandInset label
14965 name "sub:Operator-Limits"
14970 \begin_inset Index idx
14973 \begin_layout Plain Layout
14982 \begin_layout Standard
14983 Limits are created by super- and subscripts:
14986 \begin_layout Standard
14988 \begin_inset Tabular
14989 <lyxtabular version="3" rows="2" columns="2">
14990 <features rotate="0" tabularvalignment="middle">
14991 <column alignment="center" valignment="top" width="0pt">
14992 <column alignment="center" valignment="top" width="0pt">
14994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14997 \begin_layout Plain Layout
15003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15006 \begin_layout Plain Layout
15008 \begin_inset Note Note
15011 \begin_layout Plain Layout
15018 is only used as spacer.
15030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15033 \begin_layout Plain Layout
15039 \begin_inset space \textvisiblespace{}
15043 \begin_inset Formula $\to$
15047 \begin_inset Formula $\to$
15055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15058 \begin_layout Plain Layout
15059 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15075 \begin_layout Standard
15076 Limits of inline formulas are set right beside the operator.
15077 Limits in displayed formulas are set above or below the operator, except
15078 for integral limits.
15081 \begin_layout Standard
15082 To force that the limits are set beside the operator, the cursor is set
15083 directly behind the operator and the limits type is changed with the menu
15086 Edit\SpecialChar \menuseparator
15087 Math\SpecialChar \menuseparator
15106 \begin_layout Standard
15107 The default limits type is this:
15108 \begin_inset Formula
15110 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
15115 This is how it looks when the limits type was changed to
15122 \begin_inset Formula
15124 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
15129 For integrals, except those ending with
15145 etc., the limits are by default set beside the operator.
15146 But for multiple integrals the limits are often set below the operator.
15147 In the following example the limits type was therefore set to
15151 and so set below the integrals:
15152 \begin_inset Formula
15154 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
15162 \begin_layout Standard
15163 \begin_inset VSpace medskip
15166 To specify conditions for limits, the commands
15173 \begin_inset Index idx
15176 \begin_layout Plain Layout
15191 \begin_inset Index idx
15194 \begin_layout Plain Layout
15203 To create for example this expression
15204 \begin_inset Formula
15206 \sum_{\begin{subarray}{c}
15210 \end{subarray}}^{n}k^{-2}\label{eq:substack}
15218 \begin_layout Standard
15219 the following has to be done:
15220 \begin_inset Newline newline
15232 \begin_inset space \textvisiblespace{}
15238 One is now in a blue box under the summation operator and insert there
15244 \begin_inset space \textvisiblespace{}
15250 The blue box is now within a purple box and now several lines can be written
15252 A new line is created by inserting a line break (
15255 arg "newline-insert newline"
15260 \begin_inset Newline newline
15265 0<k<1000 Ctrl+Return
15266 \begin_inset Newline newline
15271 is typed in, a new box appears below for the new line.
15274 \begin_layout Standard
15275 The alignment of the lines can be changed to left aligned with the
15285 Edit\SpecialChar \menuseparator
15289 To get right alignment,
15294 \begin_inset space \textvisiblespace{}
15299 is inserted at the beginning of the line.
15302 \begin_layout Standard
15315 with the difference that the lines are always centered.
15318 \begin_layout Standard
15319 \begin_inset VSpace bigskip
15323 \begin_inset CommandInset ref
15325 reference "eq:substack"
15329 there can be too much space beside an operator, because the characters
15330 following the operator are set beside the limits.
15333 \begin_layout Standard
15334 To avoid this, the following macro can be used in the LaTeX-preamble:
15337 \begin_layout Standard
15351 \begin_inset Newline newline
15363 \begin_inset Newline newline
15370 mathclapinternal #1#2{
15374 mathsurround =0pt #1{#2}$}}
15377 \begin_layout Standard
15378 This defines the command
15385 \begin_inset Index idx
15388 \begin_layout Plain Layout
15396 that sets the width of the limit to 0
15397 \begin_inset space \thinspace{}
15401 The command scheme is
15404 \begin_layout Standard
15412 \begin_layout Standard
15413 where the limit can consist of several conditions.
15416 \begin_layout Standard
15418 \begin_inset CommandInset ref
15420 reference "eq:substack"
15424 , one uses the command
15427 \begin_layout Standard
15437 \begin_inset space \textvisiblespace{}
15440 0<k<1000 Ctrl+Return
15443 \begin_layout Standard
15444 to create the lower limit.
15445 The summand is now directly behind the summation operator:
15446 \begin_inset Formula
15448 \sum_{\mathclap{\substack{0<k<1000\\
15460 \begin_layout Standard
15461 \begin_inset VSpace bigskip
15464 How to use one limit for several operators is described in
15465 \begin_inset CommandInset ref
15467 reference "sub:Self-defined-Operators"
15474 \begin_layout Subsection
15475 Decoration for Operators
15476 \begin_inset Index idx
15479 \begin_layout Plain Layout
15480 Operators ! Decoration
15488 \begin_layout Standard
15496 \begin_inset Index idx
15499 \begin_layout Plain Layout
15514 \begin_inset Index idx
15517 \begin_layout Plain Layout
15525 characters can be placed above or below an operator, respectively.
15533 \begin_inset Index idx
15536 \begin_layout Plain Layout
15544 characters can be set before and behind a big operator.
15547 \begin_layout Standard
15549 \begin_inset space ~
15561 \begin_layout Itemize
15568 is used to set characters at the corners of the operator
15571 \begin_layout Itemize
15578 is used to set characters before and/or behind the operator (this variant
15579 represents LaTeX's original
15588 \begin_layout Itemize
15595 is used to set characters at the left corners and/or behind the operator
15598 \begin_layout Itemize
15605 is used to set characters at the right corners and/or before the operator
15608 \begin_layout Standard
15609 For example the command
15614 \begin_inset space \textvisiblespace{}
15620 \begin_inset space \textvisiblespace{}
15624 \begin_inset Formula $\to$
15628 \begin_inset Formula $\to$
15632 \begin_inset space \textvisiblespace{}
15642 \begin_inset Formula
15644 \sideset{}{'}\sum_{k=1}^{n}
15652 \begin_layout Standard
15653 \begin_inset Note Greyedout
15656 \begin_layout Plain Layout
15663 can only be used to decorate big operators, binary operators are not allowed.
15671 \begin_layout Standard
15684 can also be used to decorate symbols and characters.
15685 For example, the command
15690 \begin_inset space \textvisiblespace{}
15696 \begin_inset space \textvisiblespace{}
15702 \begin_inset Formula $\uparrow$
15710 \begin_inset Formula
15712 \overset{a}{\maltese}
15720 \begin_layout Subsection
15722 \begin_inset CommandInset label
15724 name "sub:Binary-Operators"
15729 \begin_inset Index idx
15732 \begin_layout Plain Layout
15741 \begin_layout Standard
15742 Binary operators are surrounded by space when there is a character before
15744 \begin_inset VSpace medskip
15750 \begin_layout Standard
15751 \begin_inset space \hfill{}
15755 \begin_inset Tabular
15756 <lyxtabular version="3" rows="13" columns="2">
15757 <features rotate="0" tabularvalignment="middle">
15758 <column alignment="center" valignment="top" width="0pt">
15759 <column alignment="center" valignment="top" width="0pt">
15761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15764 \begin_layout Plain Layout
15766 \begin_inset Note Note
15769 \begin_layout Plain Layout
15776 is only used as spacer.
15786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15789 \begin_layout Plain Layout
15797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15800 \begin_layout Plain Layout
15806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15809 \begin_layout Plain Layout
15810 \begin_inset Formula $+$
15820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15823 \begin_layout Plain Layout
15829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15832 \begin_layout Plain Layout
15833 \begin_inset Formula $-$
15843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15846 \begin_layout Plain Layout
15854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15857 \begin_layout Plain Layout
15858 \begin_inset Formula $\pm$
15868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15871 \begin_layout Plain Layout
15879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15882 \begin_layout Plain Layout
15883 \begin_inset Formula $\mp$
15893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15896 \begin_layout Plain Layout
15904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15907 \begin_layout Plain Layout
15908 \begin_inset Formula $\cdot$
15918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15921 \begin_layout Plain Layout
15929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15932 \begin_layout Plain Layout
15933 \begin_inset Formula $\times$
15943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15946 \begin_layout Plain Layout
15954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15957 \begin_layout Plain Layout
15958 \begin_inset Formula $\div$
15968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15971 \begin_layout Plain Layout
15975 \begin_layout Plain Layout
15988 \begin_layout Plain Layout
16000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16003 \begin_layout Plain Layout
16004 \begin_inset Formula $*$
16014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16017 \begin_layout Plain Layout
16025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16028 \begin_layout Plain Layout
16029 \begin_inset Formula $\star$
16039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16042 \begin_layout Plain Layout
16050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16053 \begin_layout Plain Layout
16054 \begin_inset Formula $\circ$
16064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16067 \begin_layout Plain Layout
16075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16078 \begin_layout Plain Layout
16079 \begin_inset Formula $\diamond$
16089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16092 \begin_layout Plain Layout
16100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16103 \begin_layout Plain Layout
16104 \begin_inset Formula $\bullet$
16118 \begin_inset space \hfill{}
16122 \begin_inset Tabular
16123 <lyxtabular version="3" rows="13" columns="2">
16124 <features rotate="0" tabularvalignment="middle">
16125 <column alignment="center" valignment="top" width="0pt">
16126 <column alignment="center" valignment="top" width="0pt">
16128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16131 \begin_layout Plain Layout
16137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16140 \begin_layout Plain Layout
16148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16151 \begin_layout Plain Layout
16159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16162 \begin_layout Plain Layout
16163 \begin_inset Formula $\nabla$
16173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16176 \begin_layout Plain Layout
16184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16187 \begin_layout Plain Layout
16188 \begin_inset Formula $\bigtriangledown$
16198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16201 \begin_layout Plain Layout
16209 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16212 \begin_layout Plain Layout
16213 \begin_inset Formula $\bigtriangleup$
16223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16226 \begin_layout Plain Layout
16234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16237 \begin_layout Plain Layout
16238 \begin_inset Formula $\Box$
16248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16251 \begin_layout Plain Layout
16259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16262 \begin_layout Plain Layout
16263 \begin_inset Formula $\cap$
16273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16276 \begin_layout Plain Layout
16284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16287 \begin_layout Plain Layout
16288 \begin_inset Formula $\cup$
16298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16301 \begin_layout Plain Layout
16309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16312 \begin_layout Plain Layout
16313 \begin_inset Formula $\dagger$
16323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16326 \begin_layout Plain Layout
16334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16337 \begin_layout Plain Layout
16338 \begin_inset Formula $\ddagger$
16348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16351 \begin_layout Plain Layout
16359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16362 \begin_layout Plain Layout
16363 \begin_inset Formula $\wr$
16373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16376 \begin_layout Plain Layout
16384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16387 \begin_layout Plain Layout
16388 \begin_inset Formula $\bigcirc$
16398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16401 \begin_layout Plain Layout
16409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16412 \begin_layout Plain Layout
16413 \begin_inset Formula $\wedge$
16423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16426 \begin_layout Plain Layout
16434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16437 \begin_layout Plain Layout
16438 \begin_inset Formula $\vee$
16452 \begin_inset space \hfill{}
16456 \begin_inset Tabular
16457 <lyxtabular version="3" rows="13" columns="2">
16458 <features rotate="0" tabularvalignment="middle">
16459 <column alignment="center" valignment="top" width="0pt">
16460 <column alignment="center" valignment="top" width="0pt">
16462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16465 \begin_layout Plain Layout
16471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16474 \begin_layout Plain Layout
16482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16485 \begin_layout Plain Layout
16493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16496 \begin_layout Plain Layout
16497 \begin_inset Formula $\oplus$
16507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16510 \begin_layout Plain Layout
16518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16521 \begin_layout Plain Layout
16522 \begin_inset Formula $\ominus$
16532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16535 \begin_layout Plain Layout
16543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16546 \begin_layout Plain Layout
16547 \begin_inset Formula $\otimes$
16557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16560 \begin_layout Plain Layout
16568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16571 \begin_layout Plain Layout
16572 \begin_inset Formula $\oslash$
16582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16585 \begin_layout Plain Layout
16593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16596 \begin_layout Plain Layout
16597 \begin_inset Formula $\odot$
16607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16610 \begin_layout Plain Layout
16618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16621 \begin_layout Plain Layout
16622 \begin_inset Formula $\amalg$
16632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16635 \begin_layout Plain Layout
16643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16646 \begin_layout Plain Layout
16647 \begin_inset Formula $\uplus$
16657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16660 \begin_layout Plain Layout
16668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16671 \begin_layout Plain Layout
16672 \begin_inset Formula $\setminus$
16682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16685 \begin_layout Plain Layout
16693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16696 \begin_layout Plain Layout
16697 \begin_inset Formula $\sqcap$
16707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16710 \begin_layout Plain Layout
16718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16721 \begin_layout Plain Layout
16722 \begin_inset Formula $\sqcup$
16732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16735 \begin_layout Plain Layout
16743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16746 \begin_layout Plain Layout
16747 \begin_inset Formula $\triangleleft$
16757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16760 \begin_layout Plain Layout
16768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16771 \begin_layout Plain Layout
16772 \begin_inset Formula $\triangleright$
16786 \begin_inset space \hfill{}
16792 \begin_layout Standard
16793 All binary operators can also be inserted via the math toolbar button
16794 \begin_inset Graphics
16795 filename ../images/math/pm.png
16803 \begin_layout Standard
16804 To typeset the Laplace operator also
16821 \begin_inset Formula $\nabla^{2}$
16824 ) can be used instead of
16833 \begin_layout Standard
16840 Insert\SpecialChar \menuseparator
16852 \begin_layout Subsection
16853 Self-defined Operators
16854 \begin_inset CommandInset label
16856 name "sub:Self-defined-Operators"
16861 \begin_inset Index idx
16864 \begin_layout Plain Layout
16865 Operators ! self-defined
16873 \begin_layout Standard
16874 With the help of the command
16878 DeclareMathOperator
16881 \begin_inset Index idx
16884 \begin_layout Plain Layout
16889 DeclareMathOperator
16894 custom operators can be defined in the LaTeX-preamble.
16895 Its command scheme is:
16898 \begin_layout Standard
16903 DeclareMathOperator{new command}{display}
16906 \begin_layout Standard
16907 Display can be characters or symbols that define how the operator looks
16909 To define a big operator a * is set behind the command.
16910 All self-defined big operators can have limits as described in
16911 \begin_inset CommandInset ref
16913 reference "sub:Operator-Limits"
16920 \begin_layout Standard
16921 For example the LaTeX-preamble line
16924 \begin_layout Standard
16929 DeclareMathOperator*{
16936 \begin_layout Standard
16937 defines the command
16943 , that inserts a big operator consisting of the lozenge symbol from
16944 \begin_inset CommandInset ref
16946 reference "sub:Miscellaneous-Symbols"
16951 \begin_inset Formula
16953 \Lozenge_{n=1}^{\infty}
16958 The command for this formula is:
16969 \begin_inset Formula $\to$
16975 \begin_layout Standard
16976 \begin_inset VSpace bigskip
16979 When self-defined operators are not used several times in the document,
16980 they can also be defined with the commands
16987 \begin_inset Index idx
16990 \begin_layout Plain Layout
17005 \begin_inset Index idx
17008 \begin_layout Plain Layout
17016 , which have the following scheme:
17019 \begin_layout Standard
17033 \begin_layout Standard
17040 defines big operators,
17049 \begin_layout Standard
17057 \begin_inset space \thinspace{}
17061 \begin_inset space \space{}
17064 be used to use one limit for several operators:
17067 \begin_layout Standard
17068 \begin_inset Formula
17070 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
17078 \begin_layout Standard
17079 The command for the formula above is:
17080 \begin_inset Newline newline
17096 \begin_inset space \textvisiblespace{}
17102 \begin_inset Formula $\to$
17108 \begin_inset space \textvisiblespace{}
17116 \begin_layout Section
17118 \begin_inset Index idx
17121 \begin_layout Plain Layout
17130 \begin_layout Subsection
17132 \begin_inset CommandInset label
17134 name "sub:Font-Styles"
17139 \begin_inset Index idx
17142 \begin_layout Plain Layout
17151 \begin_layout Standard
17152 Latin letters in formulas can be set in one of the following font styles:
17153 \begin_inset VSpace -2mm
17159 \begin_layout Standard
17161 \begin_inset Tabular
17162 <lyxtabular version="3" rows="7" columns="3">
17163 <features rotate="0" tabularvalignment="middle">
17164 <column alignment="center" valignment="top">
17165 <column alignment="center" valignment="top">
17166 <column alignment="center" valignment="top">
17168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17171 \begin_layout Plain Layout
17177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17180 \begin_layout Plain Layout
17186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17189 \begin_layout Plain Layout
17197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17200 \begin_layout Plain Layout
17206 \begin_inset space \textvisiblespace{}
17216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17219 \begin_layout Plain Layout
17220 \begin_inset Formula $\mathbb{ABC}$
17228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17231 \begin_layout Plain Layout
17244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17247 \begin_layout Plain Layout
17253 \begin_inset space \textvisiblespace{}
17263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17266 \begin_layout Plain Layout
17267 \begin_inset Formula $\mathbf{AbC}$
17275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17278 \begin_layout Plain Layout
17291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17294 \begin_layout Plain Layout
17300 \begin_inset space \textvisiblespace{}
17310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17313 \begin_layout Plain Layout
17314 \begin_inset Formula $\boldsymbol{AbC}$
17322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17325 \begin_layout Plain Layout
17328 arg "font-boldsymbol"
17338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17341 \begin_layout Plain Layout
17347 \begin_inset space \textvisiblespace{}
17357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17360 \begin_layout Plain Layout
17361 \begin_inset Formula $\mathcal{ABC}$
17369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17372 \begin_layout Plain Layout
17385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17388 \begin_layout Plain Layout
17394 \begin_inset space \textvisiblespace{}
17404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17407 \begin_layout Plain Layout
17408 \begin_inset Formula $\mathfrak{AbC}$
17416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17419 \begin_layout Plain Layout
17427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17430 \begin_layout Plain Layout
17436 \begin_inset space \textvisiblespace{}
17446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17449 \begin_layout Plain Layout
17450 \begin_inset Formula $\mathscr{AbC}$
17458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17461 \begin_layout Plain Layout
17475 \begin_layout Standard
17477 \begin_inset Tabular
17478 <lyxtabular version="3" rows="5" columns="3">
17479 <features rotate="0" tabularvalignment="middle">
17480 <column alignment="center" valignment="top">
17481 <column alignment="center" valignment="top">
17482 <column alignment="center" valignment="top">
17484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17487 \begin_layout Plain Layout
17493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17496 \begin_layout Plain Layout
17502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17505 \begin_layout Plain Layout
17513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17516 \begin_layout Plain Layout
17522 \begin_inset space \textvisiblespace{}
17532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17535 \begin_layout Plain Layout
17536 \begin_inset Formula $\mathit{AbC}$
17544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17547 \begin_layout Plain Layout
17555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17558 \begin_layout Plain Layout
17564 \begin_inset space \textvisiblespace{}
17574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17577 \begin_layout Plain Layout
17578 \begin_inset Formula $\mathrm{AbC}$
17586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17589 \begin_layout Plain Layout
17602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17605 \begin_layout Plain Layout
17611 \begin_inset space \textvisiblespace{}
17621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17624 \begin_layout Plain Layout
17625 \begin_inset Formula $\mathsf{AbC}$
17633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17636 \begin_layout Plain Layout
17649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17652 \begin_layout Plain Layout
17658 \begin_inset space \textvisiblespace{}
17668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17671 \begin_layout Plain Layout
17672 \begin_inset Formula $\mathtt{AbC}$
17680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17683 \begin_layout Plain Layout
17686 arg "font-typewriter"
17702 \begin_layout Standard
17703 \begin_inset Note Greyedout
17706 \begin_layout Plain Layout
17723 can only be used for big letters.
17731 \begin_layout Standard
17732 Predefined is the style
17741 \begin_layout Standard
17742 The style commands work also for letters in mathematical constructs:
17743 \begin_inset Formula
17745 \mathfrak{A=\frac{b}{C}}
17753 \begin_layout Standard
17754 Characters in mathematical text don't appear in a math font style but in
17755 the text font style
17762 That their style can't be set correctly via the text style dialog is a
17767 \begin_layout Plain Layout
17768 \begin_inset CommandInset href
17770 name "LyX-bug #4629"
17771 target "http://www.lyx.org/trac/ticket/4629"
17783 \begin_layout Standard
17784 Instead of the style commands the dialog
17786 Edit\SpecialChar \menuseparator
17787 Math\SpecialChar \menuseparator
17790 or the toolbar button
17791 \begin_inset Graphics
17792 filename ../images/math/font.png
17800 \begin_layout Subsection
17802 \begin_inset CommandInset label
17804 name "sub:Bold-Formulas"
17809 \begin_inset Index idx
17812 \begin_layout Plain Layout
17821 \begin_layout Standard
17822 To make a complete formula bold, the command
17828 from the previous subsection cannot be used, because it doesn't work for
17829 small Greek letters.
17830 Furthermore it prints Latin letters always upright, like in the following
17834 \begin_layout Standard
17835 \begin_inset Formula
17837 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
17845 \begin_layout Standard
17846 To display the formula correctly, the command
17853 \begin_inset Formula
17855 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
17860 It is also possible to set the formula in a
17862 boldmath environment
17865 This environment is created by inserting the command
17872 \begin_inset Index idx
17875 \begin_layout Plain Layout
17884 To end the environment, the command
17891 \begin_inset Index idx
17894 \begin_layout Plain Layout
17902 is inserted in TeX-mode.
17906 \begin_layout Plain Layout
17916 \begin_inset Formula
17918 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
17927 \begin_layout Plain Layout
17939 \begin_layout Subsection
17941 \begin_inset Index idx
17944 \begin_layout Plain Layout
17953 \begin_layout Standard
17954 Formulas can be colored like normal text: Highlight a formula or a formula
17960 Here is a formula in magenta:
17961 \begin_inset Formula
17963 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
17971 \begin_layout Standard
17972 You can also define your own colors as described in
17973 \begin_inset CommandInset ref
17975 reference "sub:Colored-Boxes"
17980 They can be used with the TeX code command
17987 \begin_inset Index idx
17990 \begin_layout Plain Layout
18001 \begin_layout Standard
18006 textcolor{color}{characters or formula}
18009 \begin_layout Standard
18010 The following example was colored completely dark green and partly red:
18013 \begin_layout Standard
18017 \begin_layout Plain Layout
18021 textcolor{darkgreen}{
18027 \begin_inset Formula
18029 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
18038 \begin_layout Plain Layout
18048 \begin_layout Standard
18049 Due to a bug in LyX only complete formulas can be colored with self-defined
18054 \begin_layout Plain Layout
18055 \begin_inset CommandInset href
18057 name "LyX-bug #5269"
18058 target "http://www.lyx.org/trac/ticket/5269"
18070 \begin_layout Subsection
18072 \begin_inset CommandInset label
18074 name "sub:Font-Sizes"
18079 \begin_inset Index idx
18082 \begin_layout Plain Layout
18091 \begin_layout Standard
18092 For characters in formulas there are, analog to characters in text, the
18093 following size commands:
18096 \begin_layout Standard
18140 \begin_inset Newline newline
18162 \begin_layout Standard
18163 The size produced by the commands depends on the document font size, which
18164 corresponds to the command
18171 The other commands produce smaller or larger sizes than
18178 The font size can however not exceed a certain value.
18179 Is for example the document font size 12
18180 \begin_inset space \thinspace{}
18189 switches to the same size as
18199 \begin_layout Standard
18200 A size command is inserted in TeX-mode before the formula and sets the size
18201 for all following formula and text characters.
18202 To switch back to the initial size, the command
18208 is inserted behind the formula in TeX-mode.
18211 \begin_layout Standard
18212 Within a formula the size can be changed using the following size commands:
18215 \begin_layout Standard
18218 \begin_inset Tabular
18219 <lyxtabular version="3" rows="5" columns="2">
18220 <features rotate="0" tabularvalignment="middle">
18221 <column alignment="center" valignment="top">
18222 <column alignment="center" valignment="top">
18224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18227 \begin_layout Plain Layout
18233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18236 \begin_layout Plain Layout
18238 \begin_inset Note Note
18241 \begin_layout Plain Layout
18248 is only used as spacer.
18260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18263 \begin_layout Plain Layout
18267 \begin_inset Index idx
18270 \begin_layout Plain Layout
18283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18286 \begin_layout Plain Layout
18287 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
18297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18300 \begin_layout Plain Layout
18308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18311 \begin_layout Plain Layout
18312 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
18322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18325 \begin_layout Plain Layout
18333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18336 \begin_layout Plain Layout
18337 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18350 \begin_layout Plain Layout
18358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18361 \begin_layout Plain Layout
18362 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18378 \begin_layout Standard
18379 After entering these commands, a blue box appears in which the formula parts
18383 \begin_layout Standard
18384 There is a further method to change the font size, that though only works
18385 for symbols or letters in mathematical text.
18386 To use it, one of the above text size commands is inserted in mathematical
18388 All following characters until the end of the mathematical text or until
18389 another size command will have the selected size.
18391 \begin_inset VSpace -2mm
18397 \begin_layout Standard
18401 \begin_layout Plain Layout
18411 \begin_inset Formula
18413 A=\frac{B}{c}\cdot\maltese
18419 \begin_inset Formula
18421 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
18430 \begin_layout Plain Layout
18442 \begin_layout Standard
18443 \begin_inset VSpace medskip
18446 Before both formulas the command
18453 The command for the second formula is:
18454 \begin_inset Newline newline
18462 \begin_inset space \textvisiblespace{}
18468 \begin_inset space \textvisiblespace{}
18474 \begin_inset space \textvisiblespace{}
18480 \begin_inset space \textvisiblespace{}
18484 \begin_inset Formula $\to$
18488 \begin_inset Formula $\to$
18492 \begin_inset Newline newline
18496 \begin_inset space \hspace*{}
18507 \begin_inset space \textvisiblespace{}
18513 \begin_inset space \textvisiblespace{}
18519 \begin_inset space \textvisiblespace{}
18525 \begin_layout Standard
18526 If a symbol cannot be displayed in different sizes, it will always be displayed
18527 in the default size.
18530 \begin_layout Section
18532 \begin_inset Index idx
18535 \begin_layout Plain Layout
18544 \begin_layout Standard
18545 Greek letters can also be inserted via the toolbar button
18546 \begin_inset Graphics
18547 filename ../images/math/alpha.png
18553 All international typesetting norms purport that Greek letters in math
18554 have to be typeset italic/slanted.
18555 In some languages, like French or Russian, they are nevertheless sometimes
18559 \begin_layout Subsection
18561 \begin_inset Index idx
18564 \begin_layout Plain Layout
18565 Greek letters ! small
18573 \begin_layout Standard
18574 \begin_inset space \hfill{}
18578 \begin_inset Tabular
18579 <lyxtabular version="3" rows="11" columns="2">
18580 <features rotate="0" tabularvalignment="middle">
18581 <column alignment="center" valignment="top" width="0pt">
18582 <column alignment="center" valignment="top" width="0pt">
18584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18587 \begin_layout Plain Layout
18593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18596 \begin_layout Plain Layout
18604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18607 \begin_layout Plain Layout
18615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18618 \begin_layout Plain Layout
18619 \begin_inset Formula $\alpha$
18629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18632 \begin_layout Plain Layout
18640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18643 \begin_layout Plain Layout
18644 \begin_inset Formula $\beta$
18654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18657 \begin_layout Plain Layout
18665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18668 \begin_layout Plain Layout
18669 \begin_inset Formula $\gamma$
18679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18682 \begin_layout Plain Layout
18690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18693 \begin_layout Plain Layout
18694 \begin_inset Formula $\delta$
18704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18707 \begin_layout Plain Layout
18715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18718 \begin_layout Plain Layout
18719 \begin_inset Formula $\epsilon$
18729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18732 \begin_layout Plain Layout
18740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18743 \begin_layout Plain Layout
18744 \begin_inset Formula $\varepsilon$
18754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18757 \begin_layout Plain Layout
18765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18768 \begin_layout Plain Layout
18769 \begin_inset Formula $\zeta$
18779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18782 \begin_layout Plain Layout
18790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18793 \begin_layout Plain Layout
18794 \begin_inset Formula $\eta$
18804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18807 \begin_layout Plain Layout
18815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18818 \begin_layout Plain Layout
18819 \begin_inset Formula $\theta$
18829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18832 \begin_layout Plain Layout
18840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18843 \begin_layout Plain Layout
18844 \begin_inset Formula $\vartheta$
18858 \begin_inset space \hfill{}
18862 \begin_inset Tabular
18863 <lyxtabular version="3" rows="12" columns="2">
18864 <features rotate="0" tabularvalignment="middle">
18865 <column alignment="center" valignment="top" width="0pt">
18866 <column alignment="center" valignment="top" width="0pt">
18868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18871 \begin_layout Plain Layout
18877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18880 \begin_layout Plain Layout
18888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18891 \begin_layout Plain Layout
18899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18902 \begin_layout Plain Layout
18903 \begin_inset Formula $\iota$
18913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18916 \begin_layout Plain Layout
18924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18927 \begin_layout Plain Layout
18928 \begin_inset Formula $\kappa$
18938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18941 \begin_layout Plain Layout
18949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18952 \begin_layout Plain Layout
18953 \begin_inset Formula $\varkappa$
18963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18966 \begin_layout Plain Layout
18974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18977 \begin_layout Plain Layout
18978 \begin_inset Formula $\lambda$
18988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18991 \begin_layout Plain Layout
18999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19002 \begin_layout Plain Layout
19003 \begin_inset Formula $\mu$
19013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19016 \begin_layout Plain Layout
19024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19027 \begin_layout Plain Layout
19028 \begin_inset Formula $\nu$
19038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19041 \begin_layout Plain Layout
19049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19052 \begin_layout Plain Layout
19053 \begin_inset Formula $\xi$
19063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19066 \begin_layout Plain Layout
19072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19075 \begin_layout Plain Layout
19076 \begin_inset Formula $o$
19086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19089 \begin_layout Plain Layout
19097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19100 \begin_layout Plain Layout
19101 \begin_inset Formula $\pi$
19111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19114 \begin_layout Plain Layout
19122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19125 \begin_layout Plain Layout
19126 \begin_inset Formula $\varpi$
19136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19139 \begin_layout Plain Layout
19147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19150 \begin_layout Plain Layout
19151 \begin_inset Formula $\rho$
19165 \begin_inset space \hfill{}
19169 \begin_inset Tabular
19170 <lyxtabular version="3" rows="11" columns="2">
19171 <features rotate="0" tabularvalignment="middle">
19172 <column alignment="center" valignment="top" width="0pt">
19173 <column alignment="center" valignment="top" width="0pt">
19175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19178 \begin_layout Plain Layout
19184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19187 \begin_layout Plain Layout
19195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19198 \begin_layout Plain Layout
19206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19209 \begin_layout Plain Layout
19210 \begin_inset Formula $\varrho$
19220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19223 \begin_layout Plain Layout
19231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19234 \begin_layout Plain Layout
19235 \begin_inset Formula $\sigma$
19245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19248 \begin_layout Plain Layout
19256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19259 \begin_layout Plain Layout
19260 \begin_inset Formula $\varsigma$
19270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19273 \begin_layout Plain Layout
19281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19284 \begin_layout Plain Layout
19285 \begin_inset Formula $\tau$
19295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19298 \begin_layout Plain Layout
19306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19309 \begin_layout Plain Layout
19310 \begin_inset Formula $\upsilon$
19320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19323 \begin_layout Plain Layout
19331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19334 \begin_layout Plain Layout
19335 \begin_inset Formula $\phi$
19345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19348 \begin_layout Plain Layout
19356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19359 \begin_layout Plain Layout
19360 \begin_inset Formula $\varphi$
19370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19373 \begin_layout Plain Layout
19381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19384 \begin_layout Plain Layout
19385 \begin_inset Formula $\chi$
19395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19398 \begin_layout Plain Layout
19406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19409 \begin_layout Plain Layout
19410 \begin_inset Formula $\psi$
19420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19423 \begin_layout Plain Layout
19431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19434 \begin_layout Plain Layout
19435 \begin_inset Formula $\omega$
19449 \begin_inset space \hfill{}
19455 \begin_layout Standard
19456 \begin_inset VSpace medskip
19462 \begin_layout Standard
19463 How to create special upright Greek letters is explained in
19464 \begin_inset CommandInset ref
19466 reference "sub:Upright-small-Greek"
19473 \begin_layout Subsection
19475 \begin_inset Index idx
19478 \begin_layout Plain Layout
19479 Greek letters ! big
19487 \begin_layout Standard
19488 \begin_inset space \hfill{}
19492 \begin_inset Tabular
19493 <lyxtabular version="3" rows="7" columns="2">
19494 <features rotate="0" tabularvalignment="middle">
19495 <column alignment="center" valignment="top" width="0pt">
19496 <column alignment="center" valignment="top" width="0pt">
19498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19501 \begin_layout Plain Layout
19507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19510 \begin_layout Plain Layout
19518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19521 \begin_layout Plain Layout
19529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19532 \begin_layout Plain Layout
19533 \begin_inset Formula $\Gamma$
19543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19546 \begin_layout Plain Layout
19554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19557 \begin_layout Plain Layout
19558 \begin_inset Formula $\Delta$
19568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19571 \begin_layout Plain Layout
19579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19582 \begin_layout Plain Layout
19583 \begin_inset Formula $\Theta$
19593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19596 \begin_layout Plain Layout
19604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19607 \begin_layout Plain Layout
19608 \begin_inset Formula $\Lambda$
19618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19621 \begin_layout Plain Layout
19629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19632 \begin_layout Plain Layout
19633 \begin_inset Formula $\Xi$
19643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19646 \begin_layout Plain Layout
19654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19657 \begin_layout Plain Layout
19658 \begin_inset Formula $\Pi$
19672 \begin_inset space \hfill{}
19676 \begin_inset Tabular
19677 <lyxtabular version="3" rows="6" columns="2">
19678 <features rotate="0" tabularvalignment="middle">
19679 <column alignment="center" valignment="top" width="0pt">
19680 <column alignment="center" valignment="top" width="0pt">
19682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19685 \begin_layout Plain Layout
19691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19694 \begin_layout Plain Layout
19702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19705 \begin_layout Plain Layout
19713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19716 \begin_layout Plain Layout
19717 \begin_inset Formula $\Sigma$
19727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19730 \begin_layout Plain Layout
19738 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19741 \begin_layout Plain Layout
19742 \begin_inset Formula $\Upsilon$
19752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19755 \begin_layout Plain Layout
19763 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19766 \begin_layout Plain Layout
19767 \begin_inset Formula $\Phi$
19777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19780 \begin_layout Plain Layout
19788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19791 \begin_layout Plain Layout
19792 \begin_inset Formula $\Psi$
19802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19805 \begin_layout Plain Layout
19813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19816 \begin_layout Plain Layout
19817 \begin_inset Formula $\Omega$
19831 \begin_inset space \hfill{}
19837 \begin_layout Standard
19838 \begin_inset VSpace medskip
19841 That the big Greek letters appear upright is caused by a design bug when
19843 To get correct italic big letters, begin every command with
19848 For example the command
19855 \begin_inset Formula $\varGamma$
19859 Another way is to load the package
19867 \begin_layout Plain Layout
19872 is part of the LaTeX-package
19877 \begin_inset Index idx
19880 \begin_layout Plain Layout
19885 \begin_layout Plain Layout
19905 \begin_inset Index idx
19908 \begin_layout Plain Layout
19914 with the LaTeX-preamble line
19917 \begin_layout Standard
19922 usepackage{fixmath}
19925 \begin_layout Standard
19926 Then all big Greek letters in a document will automatically be typeset italic.
19929 \begin_layout Subsection
19931 \begin_inset Index idx
19934 \begin_layout Plain Layout
19935 Greek letters ! bold
19943 \begin_layout Standard
19944 Greek letters cannot be set with different font styles like Latin letters.
19945 They can only be made bold with the command
19952 \begin_inset Index idx
19955 \begin_layout Plain Layout
19966 \begin_layout Standard
19968 \begin_inset Tabular
19969 <lyxtabular version="3" rows="3" columns="2">
19970 <features rotate="0" tabularvalignment="middle">
19971 <column alignment="center" valignment="top">
19972 <column alignment="center" valignment="top">
19974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19977 \begin_layout Plain Layout
19983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19986 \begin_layout Plain Layout
19994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19997 \begin_layout Plain Layout
20009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20012 \begin_layout Plain Layout
20013 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20026 \begin_layout Plain Layout
20038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20041 \begin_layout Plain Layout
20042 \begin_inset Formula $\theta\boldsymbol{\theta}$
20058 \begin_layout Section
20063 \begin_layout Plain Layout
20076 \begin_layout Plain Layout
20077 A list with all symbols of most of the LaTeX-packages can be found in
20078 \begin_inset CommandInset citation
20093 \begin_layout Plain Layout
20101 \begin_inset Note Note
20104 \begin_layout Plain Layout
20107 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20110 \begin_layout Plain Layout
20113 texorpdfstring is in section
20114 \begin_inset CommandInset ref
20116 reference "sub:Formulas-in-Section"
20126 \begin_inset Index idx
20129 \begin_layout Plain Layout
20138 \begin_layout Standard
20139 Many of the symbols listed in this section can also be inserted via the
20141 \begin_inset Graphics
20142 filename ../images/math/nabla.png
20148 \begin_inset Graphics
20149 filename ../images/math/digamma.png
20157 \begin_layout Subsection
20158 Mathematical Symbols
20159 \begin_inset CommandInset label
20161 name "sub:Mathematical-Symbols"
20166 \begin_inset Index idx
20169 \begin_layout Plain Layout
20170 Symbols ! mathematical
20178 \begin_layout Standard
20179 \begin_inset space \hfill{}
20183 \begin_inset Tabular
20184 <lyxtabular version="3" rows="10" columns="2">
20185 <features rotate="0" tabularvalignment="middle">
20186 <column alignment="center" valignment="top" width="0pt">
20187 <column alignment="center" valignment="top" width="0pt">
20189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20192 \begin_layout Plain Layout
20198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20201 \begin_layout Plain Layout
20209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20212 \begin_layout Plain Layout
20220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20223 \begin_layout Plain Layout
20224 \begin_inset Formula $\neg$
20234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20237 \begin_layout Plain Layout
20245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20248 \begin_layout Plain Layout
20249 \begin_inset Formula $\Im$
20259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20262 \begin_layout Plain Layout
20270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20273 \begin_layout Plain Layout
20274 \begin_inset Formula $\Re$
20284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20287 \begin_layout Plain Layout
20295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20298 \begin_layout Plain Layout
20299 \begin_inset Formula $\aleph$
20309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20312 \begin_layout Plain Layout
20320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20323 \begin_layout Plain Layout
20324 \begin_inset Formula $\partial$
20334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20337 \begin_layout Plain Layout
20345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20348 \begin_layout Plain Layout
20349 \begin_inset Formula $\infty$
20359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20362 \begin_layout Plain Layout
20370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20373 \begin_layout Plain Layout
20374 \begin_inset Formula $\wp$
20384 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20387 \begin_layout Plain Layout
20395 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20398 \begin_layout Plain Layout
20399 \begin_inset Formula $\imath$
20409 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20412 \begin_layout Plain Layout
20420 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20423 \begin_layout Plain Layout
20424 \begin_inset Formula $\jmath$
20438 \begin_inset space \hfill{}
20442 \begin_inset Tabular
20443 <lyxtabular version="3" rows="10" columns="2">
20444 <features rotate="0" tabularvalignment="middle">
20445 <column alignment="center" valignment="top" width="0pt">
20446 <column alignment="center" valignment="top" width="0pt">
20448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20451 \begin_layout Plain Layout
20457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20460 \begin_layout Plain Layout
20462 \begin_inset Note Note
20465 \begin_layout Plain Layout
20472 is only used as spacer.
20484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20487 \begin_layout Plain Layout
20495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20498 \begin_layout Plain Layout
20499 \begin_inset Formula $\forall$
20509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20512 \begin_layout Plain Layout
20520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20523 \begin_layout Plain Layout
20524 \begin_inset Formula $\exists$
20534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20537 \begin_layout Plain Layout
20545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20548 \begin_layout Plain Layout
20549 \begin_inset Formula $\nexists$
20559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20562 \begin_layout Plain Layout
20570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20573 \begin_layout Plain Layout
20574 \begin_inset Formula $\emptyset$
20584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20587 \begin_layout Plain Layout
20595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20598 \begin_layout Plain Layout
20599 \begin_inset Formula $\varnothing$
20609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20612 \begin_layout Plain Layout
20620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20623 \begin_layout Plain Layout
20624 \begin_inset Formula $\dag$
20634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20637 \begin_layout Plain Layout
20645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20648 \begin_layout Plain Layout
20649 \begin_inset Formula $\ddag$
20659 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20662 \begin_layout Plain Layout
20670 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20673 \begin_layout Plain Layout
20677 \begin_layout Plain Layout
20687 \begin_inset Formula $\complement$
20694 \begin_layout Plain Layout
20708 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20711 \begin_layout Plain Layout
20719 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20722 \begin_layout Plain Layout
20723 \begin_inset Formula $\Bbbk$
20737 \begin_inset space \hfill{}
20741 \begin_inset Tabular
20742 <lyxtabular version="3" rows="10" columns="2">
20743 <features rotate="0" tabularvalignment="middle">
20744 <column alignment="center" valignment="top" width="0pt">
20745 <column alignment="center" valignment="top" width="0pt">
20747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20750 \begin_layout Plain Layout
20756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20759 \begin_layout Plain Layout
20767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20770 \begin_layout Plain Layout
20778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20781 \begin_layout Plain Layout
20782 \begin_inset Formula $\prime$
20792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20795 \begin_layout Plain Layout
20803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20806 \begin_layout Plain Layout
20807 \begin_inset Formula $\backprime$
20817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20820 \begin_layout Plain Layout
20828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20831 \begin_layout Plain Layout
20832 \begin_inset Formula $\mho$
20842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20845 \begin_layout Plain Layout
20853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20856 \begin_layout Plain Layout
20857 \begin_inset Formula $\triangle$
20867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20870 \begin_layout Plain Layout
20878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20881 \begin_layout Plain Layout
20882 \begin_inset Formula $\angle$
20892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20895 \begin_layout Plain Layout
20903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20906 \begin_layout Plain Layout
20907 \begin_inset Formula $\measuredangle$
20917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20920 \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
20932 \begin_inset Formula $\sphericalangle$
20942 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20945 \begin_layout Plain Layout
20953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20956 \begin_layout Plain Layout
20957 \begin_inset Formula $\top$
20967 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20970 \begin_layout Plain Layout
20978 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20981 \begin_layout Plain Layout
20982 \begin_inset Formula $\bot$
20996 \begin_inset space \hfill{}
21002 \begin_layout Subsection
21003 Miscellaneous Symbols
21004 \begin_inset CommandInset label
21006 name "sub:Miscellaneous-Symbols"
21011 \begin_inset Index idx
21014 \begin_layout Plain Layout
21015 Symbols ! miscellaneous
21023 \begin_layout Standard
21026 \begin_inset Tabular
21027 <lyxtabular version="3" rows="10" columns="2">
21028 <features rotate="0" tabularvalignment="middle">
21029 <column alignment="center" valignment="top" width="0pt">
21030 <column alignment="center" valignment="top" width="0pt">
21032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21035 \begin_layout Plain Layout
21041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21044 \begin_layout Plain Layout
21052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21055 \begin_layout Plain Layout
21063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21066 \begin_layout Plain Layout
21067 \begin_inset Formula $\flat$
21077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21080 \begin_layout Plain Layout
21088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21091 \begin_layout Plain Layout
21092 \begin_inset Formula $\natural$
21102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21105 \begin_layout Plain Layout
21113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21116 \begin_layout Plain Layout
21117 \begin_inset Formula $\sharp$
21127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21130 \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
21142 \begin_inset Formula $\surd$
21152 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21155 \begin_layout Plain Layout
21163 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21166 \begin_layout Plain Layout
21167 \begin_inset Formula $\checkmark$
21177 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21180 \begin_layout Plain Layout
21188 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21191 \begin_layout Plain Layout
21192 \begin_inset Formula $\yen$
21202 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21205 \begin_layout Plain Layout
21213 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21216 \begin_layout Plain Layout
21217 \begin_inset Formula $\pounds$
21227 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21230 \begin_layout Plain Layout
21236 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21239 \begin_layout Plain Layout
21240 \begin_inset Formula $\$$
21250 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21253 \begin_layout Plain Layout
21259 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21262 \begin_layout Plain Layout
21263 \begin_inset Formula $§$
21277 \begin_inset Tabular
21278 <lyxtabular version="3" rows="10" columns="2">
21279 <features rotate="0" tabularvalignment="middle">
21280 <column alignment="center" valignment="top">
21281 <column alignment="center" valignment="top">
21283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21286 \begin_layout Plain Layout
21292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21295 \begin_layout Plain Layout
21303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21306 \begin_layout Plain Layout
21314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21317 \begin_layout Plain Layout
21318 \begin_inset Formula $\hbar$
21328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21331 \begin_layout Plain Layout
21339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21342 \begin_layout Plain Layout
21343 \begin_inset Formula $\hslash$
21353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21356 \begin_layout Plain Layout
21364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21367 \begin_layout Plain Layout
21368 \begin_inset Formula $\clubsuit$
21378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21381 \begin_layout Plain Layout
21389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21392 \begin_layout Plain Layout
21393 \begin_inset Formula $\spadesuit$
21403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21406 \begin_layout Plain Layout
21414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21417 \begin_layout Plain Layout
21418 \begin_inset Formula $\bigstar$
21428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21431 \begin_layout Plain Layout
21439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21442 \begin_layout Plain Layout
21443 \begin_inset Formula $\blacklozenge$
21453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21456 \begin_layout Plain Layout
21464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21467 \begin_layout Plain Layout
21468 \begin_inset Formula $\blacktriangle$
21478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21481 \begin_layout Plain Layout
21489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21492 \begin_layout Plain Layout
21493 \begin_inset Formula $\blacktriangledown$
21503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21506 \begin_layout Plain Layout
21514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21517 \begin_layout Plain Layout
21518 \begin_inset Formula $\bullet$
21532 \begin_inset Tabular
21533 <lyxtabular version="3" rows="10" columns="2">
21534 <features rotate="0" tabularvalignment="middle">
21535 <column alignment="center" valignment="top" width="0pt">
21536 <column alignment="center" valignment="top" width="0pt">
21538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21541 \begin_layout Plain Layout
21547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21550 \begin_layout Plain Layout
21558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21561 \begin_layout Plain Layout
21569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21572 \begin_layout Plain Layout
21573 \begin_inset Formula $\diamondsuit$
21583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21586 \begin_layout Plain Layout
21594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21597 \begin_layout Plain Layout
21598 \begin_inset Formula $\Diamond$
21608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21611 \begin_layout Plain Layout
21619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21622 \begin_layout Plain Layout
21623 \begin_inset Formula $\heartsuit$
21633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21636 \begin_layout Plain Layout
21644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21647 \begin_layout Plain Layout
21648 \begin_inset Formula $\P$
21658 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21661 \begin_layout Plain Layout
21669 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21672 \begin_layout Plain Layout
21673 \begin_inset Formula $\copyright$
21683 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21686 \begin_layout Plain Layout
21694 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21697 \begin_layout Plain Layout
21698 \begin_inset Formula $\circledR$
21708 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21711 \begin_layout Plain Layout
21719 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21722 \begin_layout Plain Layout
21723 \begin_inset Formula $\maltese$
21733 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21736 \begin_layout Plain Layout
21744 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21747 \begin_layout Plain Layout
21748 \begin_inset Formula $\diagup$
21758 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21761 \begin_layout Plain Layout
21769 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21772 \begin_layout Plain Layout
21773 \begin_inset Formula $\diagdown$
21789 \begin_layout Standard
21790 \begin_inset VSpace medskip
21796 \begin_layout Standard
21797 Some symbols can be displayed in different sizes, see
21798 \begin_inset CommandInset ref
21800 reference "sub:Font-Sizes"
21807 \begin_layout Subsection
21809 \begin_inset Index idx
21812 \begin_layout Plain Layout
21813 Symbols ! Euro-symbol
21819 \begin_inset Index idx
21822 \begin_layout Plain Layout
21829 \begin_layout Plain Layout
21846 \begin_layout Standard
21847 To use the Euro symbol in formulas, the LaTeX-package
21852 \begin_inset Index idx
21855 \begin_layout Plain Layout
21861 must be installed and loaded with the LaTeX-preamble line
21864 \begin_layout Standard
21869 usepackage[gennarrow]{eurosym}
21872 \begin_layout Standard
21873 The Euro symbol can now be inserted with the command
21880 \begin_inset Index idx
21883 \begin_layout Plain Layout
21894 \begin_layout Standard
21895 The Euro symbol can directly be inserted with the € key in mathematical
21896 text, without having
21911 can also be inserted in TeX-mode.
21912 The official currency symbol can then be inserted with the command
21919 \begin_inset Index idx
21922 \begin_layout Plain Layout
21930 , that is only available in TeX-mode.
21933 \begin_layout Standard
21937 \begin_layout Plain Layout
21947 \begin_inset Note Note
21950 \begin_layout Plain Layout
21951 The following table will only be displayed when the LaTeX-package
21963 \begin_layout Standard
21964 An overview about the different Euro symbols:
21967 \begin_layout Standard
21969 \begin_inset Tabular
21970 <lyxtabular version="3" rows="4" columns="3">
21971 <features rotate="0" tabularvalignment="middle">
21972 <column alignment="center" valignment="top" width="0pt">
21973 <column alignment="center" valignment="top" width="0pt">
21974 <column alignment="center" valignment="top" width="0pt">
21976 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
21979 \begin_layout Plain Layout
21985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21988 \begin_layout Plain Layout
21994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21997 \begin_layout Plain Layout
22005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22008 \begin_layout Plain Layout
22014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22017 \begin_layout Plain Layout
22025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22028 \begin_layout Plain Layout
22029 \begin_inset Formula $\euro$
22039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22042 \begin_layout Plain Layout
22048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22051 \begin_layout Plain Layout
22057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22060 \begin_layout Plain Layout
22061 \begin_inset Formula $\mbox{€}$
22071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22074 \begin_layout Plain Layout
22080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22083 \begin_layout Plain Layout
22091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22094 \begin_layout Plain Layout
22098 \begin_layout Plain Layout
22120 \begin_layout Standard
22124 \begin_layout Plain Layout
22134 \begin_inset Note Note
22137 \begin_layout Plain Layout
22138 The following will be displayed when the LaTeX-package
22150 \begin_layout Standard
22151 You need to install the LaTeX-package
22155 to see the rest of this subsection in the output.
22158 \begin_layout Standard
22162 \begin_layout Plain Layout
22174 \begin_layout Section
22176 \begin_inset CommandInset label
22178 name "sec:Relations"
22183 \begin_inset Index idx
22186 \begin_layout Plain Layout
22193 \begin_inset Index idx
22196 \begin_layout Plain Layout
22201 \begin_layout Plain Layout
22212 \begin_layout Plain Layout
22227 \begin_layout Standard
22228 All relations can also be inserted via the toolbar button
22229 \begin_inset Graphics
22230 filename ../images/math/leq.png
22238 \begin_layout Standard
22239 \begin_inset space \hfill{}
22243 \begin_inset Tabular
22244 <lyxtabular version="3" rows="17" columns="2">
22245 <features rotate="0" tabularvalignment="middle">
22246 <column alignment="center" valignment="top" width="0pt">
22247 <column alignment="center" valignment="top" width="0pt">
22249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22252 \begin_layout Plain Layout
22258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22261 \begin_layout Plain Layout
22269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22272 \begin_layout Plain Layout
22278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22281 \begin_layout Plain Layout
22282 \begin_inset Formula $<$
22292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22295 \begin_layout Plain Layout
22303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22306 \begin_layout Plain Layout
22307 \begin_inset Formula $\le$
22317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22320 \begin_layout Plain Layout
22328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22331 \begin_layout Plain Layout
22332 \begin_inset Formula $\ll$
22342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22345 \begin_layout Plain Layout
22353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22356 \begin_layout Plain Layout
22357 \begin_inset Formula $\prec$
22367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22370 \begin_layout Plain Layout
22378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22381 \begin_layout Plain Layout
22382 \begin_inset Formula $\preceq$
22392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22395 \begin_layout Plain Layout
22403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22406 \begin_layout Plain Layout
22407 \begin_inset Formula $\subset$
22417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22420 \begin_layout Plain Layout
22428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22431 \begin_layout Plain Layout
22432 \begin_inset Formula $\subseteq$
22442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22445 \begin_layout Plain Layout
22453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22456 \begin_layout Plain Layout
22457 \begin_inset Formula $\sqsubseteq$
22467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22470 \begin_layout Plain Layout
22478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22481 \begin_layout Plain Layout
22482 \begin_inset Formula $\in$
22492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22495 \begin_layout Plain Layout
22503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22506 \begin_layout Plain Layout
22507 \begin_inset Formula $\vdash$
22517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22520 \begin_layout Plain Layout
22528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22531 \begin_layout Plain Layout
22532 \begin_inset Formula $\smile$
22542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22545 \begin_layout Plain Layout
22553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22556 \begin_layout Plain Layout
22557 \begin_inset Formula $\lhd$
22567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22570 \begin_layout Plain Layout
22578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22581 \begin_layout Plain Layout
22582 \begin_inset Formula $\unlhd$
22592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22595 \begin_layout Plain Layout
22603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22606 \begin_layout Plain Layout
22607 \begin_inset Formula $\gtrless$
22617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22620 \begin_layout Plain Layout
22628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22631 \begin_layout Plain Layout
22632 \begin_inset Formula $\mid$
22642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22645 \begin_layout Plain Layout
22653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22656 \begin_layout Plain Layout
22657 \begin_inset Formula $\nmid$
22671 \begin_inset space \hfill{}
22675 \begin_inset Tabular
22676 <lyxtabular version="3" rows="17" columns="2">
22677 <features rotate="0" tabularvalignment="middle">
22678 <column alignment="center" valignment="top" width="0pt">
22679 <column alignment="center" valignment="top" width="0pt">
22681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22684 \begin_layout Plain Layout
22690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22693 \begin_layout Plain Layout
22701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22704 \begin_layout Plain Layout
22710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22713 \begin_layout Plain Layout
22714 \begin_inset Formula $=$
22724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22727 \begin_layout Plain Layout
22735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22738 \begin_layout Plain Layout
22739 \begin_inset Formula $\not=$
22749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22752 \begin_layout Plain Layout
22760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22763 \begin_layout Plain Layout
22764 \begin_inset Formula $\equiv$
22774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22777 \begin_layout Plain Layout
22785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22788 \begin_layout Plain Layout
22789 \begin_inset Formula $\sim$
22799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22802 \begin_layout Plain Layout
22810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22813 \begin_layout Plain Layout
22814 \begin_inset Formula $\simeq$
22824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22827 \begin_layout Plain Layout
22835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22838 \begin_layout Plain Layout
22839 \begin_inset Formula $\approx$
22849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22852 \begin_layout Plain Layout
22860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22863 \begin_layout Plain Layout
22864 \begin_inset Formula $\cong$
22874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22877 \begin_layout Plain Layout
22885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22888 \begin_layout Plain Layout
22889 \begin_inset Formula $\bowtie$
22899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22902 \begin_layout Plain Layout
22910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22913 \begin_layout Plain Layout
22914 \begin_inset Formula $\notin$
22924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22927 \begin_layout Plain Layout
22935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22938 \begin_layout Plain Layout
22939 \begin_inset Formula $\perp$
22949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22952 \begin_layout Plain Layout
22960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22963 \begin_layout Plain Layout
22964 \begin_inset Formula $\propto$
22974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22977 \begin_layout Plain Layout
22985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22988 \begin_layout Plain Layout
22989 \begin_inset Formula $\asymp$
22999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23002 \begin_layout Plain Layout
23010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23013 \begin_layout Plain Layout
23014 \begin_inset Formula $\doteq$
23024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23027 \begin_layout Plain Layout
23035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23038 \begin_layout Plain Layout
23039 \begin_inset Formula $\circeq$
23049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23052 \begin_layout Plain Layout
23060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23063 \begin_layout Plain Layout
23064 \begin_inset Formula $\models$
23074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23077 \begin_layout Plain Layout
23085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23088 \begin_layout Plain Layout
23089 \begin_inset Formula $\widehat{=}$
23103 \begin_inset space \hfill{}
23107 \begin_inset Tabular
23108 <lyxtabular version="3" rows="17" columns="2">
23109 <features rotate="0" tabularvalignment="middle">
23110 <column alignment="center" valignment="top" width="0pt">
23111 <column alignment="center" valignment="top" width="0pt">
23113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23116 \begin_layout Plain Layout
23122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23125 \begin_layout Plain Layout
23133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23136 \begin_layout Plain Layout
23142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23145 \begin_layout Plain Layout
23146 \begin_inset Formula $>$
23156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23159 \begin_layout Plain Layout
23167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23170 \begin_layout Plain Layout
23171 \begin_inset Formula $\ge$
23181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23184 \begin_layout Plain Layout
23192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23195 \begin_layout Plain Layout
23196 \begin_inset Formula $\gg$
23206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23209 \begin_layout Plain Layout
23217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23220 \begin_layout Plain Layout
23221 \begin_inset Formula $\succ$
23231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23234 \begin_layout Plain Layout
23242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23245 \begin_layout Plain Layout
23246 \begin_inset Formula $\succeq$
23256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23259 \begin_layout Plain Layout
23267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23270 \begin_layout Plain Layout
23271 \begin_inset Formula $\supset$
23281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23284 \begin_layout Plain Layout
23292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23295 \begin_layout Plain Layout
23296 \begin_inset Formula $\supseteq$
23306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23309 \begin_layout Plain Layout
23317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23320 \begin_layout Plain Layout
23321 \begin_inset Formula $\sqsupseteq$
23331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23334 \begin_layout Plain Layout
23342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23345 \begin_layout Plain Layout
23346 \begin_inset Formula $\ni$
23356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23359 \begin_layout Plain Layout
23367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23370 \begin_layout Plain Layout
23371 \begin_inset Formula $\dashv$
23381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23384 \begin_layout Plain Layout
23392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23395 \begin_layout Plain Layout
23396 \begin_inset Formula $\frown$
23406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23409 \begin_layout Plain Layout
23417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23420 \begin_layout Plain Layout
23421 \begin_inset Formula $\rhd$
23431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23434 \begin_layout Plain Layout
23442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23445 \begin_layout Plain Layout
23446 \begin_inset Formula $\unrhd$
23456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23459 \begin_layout Plain Layout
23467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23470 \begin_layout Plain Layout
23471 \begin_inset Formula $\lessgtr$
23481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23484 \begin_layout Plain Layout
23492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23495 \begin_layout Plain Layout
23496 \begin_inset Formula $\parallel$
23506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23509 \begin_layout Plain Layout
23517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23520 \begin_layout Plain Layout
23521 \begin_inset Formula $\nparallel$
23535 \begin_inset space \hfill{}
23541 \begin_layout Standard
23542 \begin_inset VSpace medskip
23557 are bigger than the equal looking operators
23572 \begin_layout Standard
23573 Relations are, in contrary to symbols, always surrounded by space.
23576 \begin_layout Standard
23577 Relations with labels can be created with the command
23584 \begin_inset Index idx
23587 \begin_layout Plain Layout
23598 \begin_layout Standard
23600 \begin_inset Tabular
23601 <lyxtabular version="3" rows="2" columns="2">
23602 <features rotate="0" tabularvalignment="middle">
23603 <column alignment="center" valignment="top">
23604 <column alignment="center" valignment="top">
23606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23609 \begin_layout Plain Layout
23615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23618 \begin_layout Plain Layout
23620 \begin_inset Note Note
23623 \begin_layout Plain Layout
23630 is only used as spacer.
23642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23645 \begin_layout Plain Layout
23649 \begin_inset space \textvisiblespace{}
23657 \begin_inset space \textvisiblespace{}
23661 \begin_inset Formula $\downarrow$
23667 \begin_inset space \textvisiblespace{}
23671 \begin_inset space \textvisiblespace{}
23679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23682 \begin_layout Plain Layout
23683 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23699 \begin_layout Section
23703 \begin_layout Subsection
23704 Predefined Functions
23705 \begin_inset CommandInset label
23707 name "sub:Predefined-Functions"
23712 \begin_inset Index idx
23715 \begin_layout Plain Layout
23716 Functions ! predefined
23724 \begin_layout Standard
23725 In general, variables are set
23729 in mathematical expressions, but not function names, because
23730 \begin_inset Formula $sin$
23733 could be misunderstood as
23734 \begin_inset Formula $s\cdot i\cdot n$
23738 Therefore there are predefined functionswhich are additionally a bit separated
23740 They are inserted as commands starting with a backslash before their name.
23743 \begin_layout Standard
23745 \begin_inset Tabular
23746 <lyxtabular version="3" rows="2" columns="4">
23747 <features rotate="0" tabularvalignment="middle">
23748 <column alignment="center" valignment="top" width="0pt">
23749 <column alignment="center" valignment="top" width="0pt">
23750 <column alignment="center" valignment="top" width="0pt">
23751 <column alignment="center" valignment="top" width="0pt">
23753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23756 \begin_layout Plain Layout
23762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23765 \begin_layout Plain Layout
23771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23774 \begin_layout Plain Layout
23780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23783 \begin_layout Plain Layout
23791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23794 \begin_layout Plain Layout
23800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23803 \begin_layout Plain Layout
23804 \begin_inset Formula $Asin(x)+B$
23812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23815 \begin_layout Plain Layout
23823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23826 \begin_layout Plain Layout
23827 \begin_inset Formula $A\sin(x)+B$
23843 \begin_layout Standard
23844 The following functions are predefined:
23847 \begin_layout Standard
23848 \begin_inset VSpace -2mm
23854 \begin_layout Standard
23856 \begin_inset Tabular
23857 <lyxtabular version="3" rows="9" columns="4">
23858 <features rotate="0" tabularvalignment="middle">
23859 <column alignment="center" valignment="top" width="0pt">
23860 <column alignment="center" valignment="top" width="0pt">
23861 <column alignment="center" valignment="top" width="0pt">
23862 <column alignment="center" valignment="top" width="0pt">
23864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23867 \begin_layout Plain Layout
23873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23876 \begin_layout Plain Layout
23882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23885 \begin_layout Plain Layout
23891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23894 \begin_layout Plain Layout
23902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23905 \begin_layout Plain Layout
23913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23916 \begin_layout Plain Layout
23924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23927 \begin_layout Plain Layout
23935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23938 \begin_layout Plain Layout
23948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23951 \begin_layout Plain Layout
23959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23962 \begin_layout Plain Layout
23970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23973 \begin_layout Plain Layout
23981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23984 \begin_layout Plain Layout
23994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23997 \begin_layout Plain Layout
24005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24008 \begin_layout Plain Layout
24016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24019 \begin_layout Plain Layout
24027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24030 \begin_layout Plain Layout
24040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24043 \begin_layout Plain Layout
24051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24054 \begin_layout Plain Layout
24062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24065 \begin_layout Plain Layout
24073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24076 \begin_layout Plain Layout
24086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24089 \begin_layout Plain Layout
24097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24100 \begin_layout Plain Layout
24108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24111 \begin_layout Plain Layout
24119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24122 \begin_layout Plain Layout
24132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24135 \begin_layout Plain Layout
24143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24146 \begin_layout Plain Layout
24154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24157 \begin_layout Plain Layout
24165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24168 \begin_layout Plain Layout
24178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24181 \begin_layout Plain Layout
24189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24192 \begin_layout Plain Layout
24200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24203 \begin_layout Plain Layout
24211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24214 \begin_layout Plain Layout
24224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24227 \begin_layout Plain Layout
24235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24238 \begin_layout Plain Layout
24246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24249 \begin_layout Plain Layout
24257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24260 \begin_layout Plain Layout
24276 \begin_layout Standard
24277 They can also be inserted with the math toolbar button
24278 \begin_inset Graphics
24279 filename ../images/math/functions.png
24287 \begin_layout Subsection
24288 Self-defined Functions
24289 \begin_inset Index idx
24292 \begin_layout Plain Layout
24293 Functions ! self-defined
24301 \begin_layout Standard
24302 To use a function that is not predefined, like for example the sign function
24303 sgn(x), there are two possibilities:
24306 \begin_layout Itemize
24307 Define the function by inserting the following line to the LaTeX-preamble
24311 \begin_layout Plain Layout
24316 DeclareMathOperator
24319 \begin_inset CommandInset ref
24321 reference "sub:Self-defined-Operators"
24331 \begin_inset Newline newline
24335 \begin_inset VSpace -3mm
24339 \begin_inset Newline newline
24346 DeclareMathOperator{
24351 \begin_inset Index idx
24354 \begin_layout Plain Layout
24359 DeclareMathOperator
24365 \begin_inset Newline newline
24369 \begin_inset VSpace -2mm
24373 \begin_inset Newline newline
24376 Now the new defined function can be called with the command
24385 \begin_layout Itemize
24386 Write the formula as usual, mark the formula name, in our example the letters
24391 , and change it to mathematical text.
24392 Finally, a space is inserted between prefactor and function.
24395 \begin_layout Standard
24396 The result is the same with both methods as with a predefined function
24400 \begin_layout Plain Layout
24401 In LyX self-defined functions are displayed red, predefined ones black.
24409 \begin_layout Standard
24411 \begin_inset Tabular
24412 <lyxtabular version="3" rows="3" columns="2">
24413 <features rotate="0" tabularvalignment="middle">
24414 <column alignment="center" valignment="top" width="0pt">
24415 <column alignment="center" valignment="top" width="0pt">
24417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24420 \begin_layout Plain Layout
24426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24429 \begin_layout Plain Layout
24437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24440 \begin_layout Plain Layout
24448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24451 \begin_layout Plain Layout
24452 \begin_inset Formula $A\sgn(x)+B$
24462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24465 \begin_layout Plain Layout
24469 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
24477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24480 \begin_layout Plain Layout
24481 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24497 \begin_layout Standard
24498 The first method is more suitable when the self-defined function should
24499 be used several times.
24502 \begin_layout Subsection
24504 \begin_inset Index idx
24507 \begin_layout Plain Layout
24516 \begin_layout Standard
24517 For limits, in addition to the commands
24524 \begin_inset Index idx
24527 \begin_layout Plain Layout
24547 the following functions are defined:
24550 \begin_layout Standard
24552 \begin_inset Tabular
24553 <lyxtabular version="3" rows="5" columns="2">
24554 <features rotate="0" tabularvalignment="middle">
24555 <column alignment="center" valignment="top">
24556 <column alignment="center" valignment="top">
24558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24561 \begin_layout Plain Layout
24567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24570 \begin_layout Plain Layout
24572 \begin_inset Note Note
24575 \begin_layout Plain Layout
24582 is only used as spacer.
24594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24597 \begin_layout Plain Layout
24605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24608 \begin_layout Plain Layout
24609 \begin_inset Formula $\varliminf$
24619 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24622 \begin_layout Plain Layout
24630 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24633 \begin_layout Plain Layout
24634 \begin_inset Formula $\varlimsup$
24644 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24647 \begin_layout Plain Layout
24655 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24658 \begin_layout Plain Layout
24659 \begin_inset Formula $\varprojlim$
24669 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24672 \begin_layout Plain Layout
24680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24683 \begin_layout Plain Layout
24684 \begin_inset Formula $\varinjlim$
24688 \begin_inset Formula $\raisebox{-2.5mm}{}$
24704 \begin_layout Standard
24705 \begin_inset VSpace medskip
24708 The limit is created by inserting a subscript.
24709 It is set right beside the function in an inline formula:
24712 \begin_layout Standard
24714 \begin_inset Tabular
24715 <lyxtabular version="3" rows="2" columns="2">
24716 <features rotate="0" tabularvalignment="middle">
24717 <column alignment="center" valignment="top" width="0pt">
24718 <column alignment="center" valignment="top" width="0pt">
24720 <cell alignment="center" valignment="top" usebox="none">
24723 \begin_layout Plain Layout
24729 <cell alignment="center" valignment="top" usebox="none">
24732 \begin_layout Plain Layout
24733 \begin_inset space \hspace{}
24738 \begin_inset Note Note
24741 \begin_layout Plain Layout
24748 are used here as spacer.
24760 <cell alignment="center" valignment="top" usebox="none">
24763 \begin_layout Plain Layout
24769 \begin_inset space \textvisiblespace{}
24773 \begin_inset space \textvisiblespace{}
24781 <cell alignment="center" valignment="top" usebox="none">
24784 \begin_layout Plain Layout
24785 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
24801 \begin_layout Standard
24802 In a displayed formula the limit is set below the formula, as usual:
24803 \begin_inset Formula
24813 \begin_layout Subsection
24815 \begin_inset Index idx
24818 \begin_layout Plain Layout
24819 Functions ! modulo-
24827 \begin_layout Standard
24828 The modulo-function is special, because it exists in four variants.
24829 The variants in a displayed formula are:
24830 \begin_inset Formula
24832 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
24833 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
24834 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
24835 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
24836 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
24844 \begin_layout Standard
24845 In an inline formula less space is set before the function names for all
24847 By default the modulo-functions take only the first following character
24849 To use more than one character, one has to put them into TeX-braces:
24850 \begin_inset Formula
24852 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
24853 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
24854 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
24862 \begin_layout Section
24864 \begin_inset Index idx
24867 \begin_layout Plain Layout
24876 \begin_layout Subsection
24877 Special Characters in Mathematical Text
24880 \begin_layout Standard
24881 The following commands can only be used in mathematical text or in TeX-mode:
24884 \begin_layout Standard
24885 \begin_inset space \hfill{}
24889 \begin_inset Tabular
24890 <lyxtabular version="3" rows="8" columns="2">
24891 <features rotate="0" tabularvalignment="middle">
24892 <column alignment="block" valignment="top">
24893 <column alignment="block" valignment="top">
24895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24898 \begin_layout Plain Layout
24904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24907 \begin_layout Plain Layout
24915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24918 \begin_layout Plain Layout
24926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24929 \begin_layout Plain Layout
24930 \begin_inset Formula $\textrm{œ}$
24940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24943 \begin_layout Plain Layout
24951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24954 \begin_layout Plain Layout
24955 \begin_inset Formula $\textrm{Œ}$
24965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24968 \begin_layout Plain Layout
24976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24979 \begin_layout Plain Layout
24980 \begin_inset Formula $\textrm{æ}$
24990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24993 \begin_layout Plain Layout
25001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25004 \begin_layout Plain Layout
25005 \begin_inset Formula $\textrm{Æ}$
25015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25018 \begin_layout Plain Layout
25026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25029 \begin_layout Plain Layout
25030 \begin_inset Formula $\textrm{\aa}$
25040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25043 \begin_layout Plain Layout
25047 \begin_inset Index idx
25050 \begin_layout Plain Layout
25057 \begin_layout Plain Layout
25078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25081 \begin_layout Plain Layout
25082 \begin_inset Formula $\textrm{Å}$
25092 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25095 \begin_layout Plain Layout
25103 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25106 \begin_layout Plain Layout
25107 \begin_inset Formula $\textrm{ı}$
25121 \begin_inset space \hfill{}
25125 \begin_inset Tabular
25126 <lyxtabular version="3" rows="8" columns="2">
25127 <features rotate="0" tabularvalignment="middle">
25128 <column alignment="block" valignment="top">
25129 <column alignment="center" valignment="top">
25131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25134 \begin_layout Plain Layout
25136 \begin_inset Note Note
25139 \begin_layout Plain Layout
25141 \begin_inset space \thinspace{}
25144 mm is used for separation, because otherwise the output will be ¡ and ¿
25155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25158 \begin_layout Plain Layout
25166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25169 \begin_layout Plain Layout
25177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25180 \begin_layout Plain Layout
25181 \begin_inset Formula $\textrm{ø}$
25191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25194 \begin_layout Plain Layout
25202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25205 \begin_layout Plain Layout
25206 \begin_inset Formula $\textrm{Ø}$
25216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25219 \begin_layout Plain Layout
25227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25230 \begin_layout Plain Layout
25231 \begin_inset Formula $\textrm{ł}$
25241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25244 \begin_layout Plain Layout
25252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25255 \begin_layout Plain Layout
25256 \begin_inset Formula $\textrm{Ł}$
25266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25269 \begin_layout Plain Layout
25271 \begin_inset space \hspace{}
25276 \begin_inset space \textvisiblespace{}
25284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25287 \begin_layout Plain Layout
25288 \begin_inset Formula $\textrm{!`}$
25298 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25301 \begin_layout Plain Layout
25303 \begin_inset space \hspace{}
25308 \begin_inset space \textvisiblespace{}
25316 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25319 \begin_layout Plain Layout
25320 \begin_inset Formula $\textrm{?`}$
25330 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25333 \begin_layout Plain Layout
25341 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25344 \begin_layout Plain Layout
25345 \begin_inset Formula $\textrm{ȷ}$
25359 \begin_inset space \hfill{}
25365 \begin_layout Standard
25367 \begin_inset Formula $\textrm{\textrm{Å}}$
25371 \begin_inset Formula $\textrm{\textrm{Ø}}$
25374 can also be inserted via the math toolbar button
25375 \begin_inset Graphics
25376 filename ../images/math/digamma.png
25384 \begin_layout Standard
25385 An exception are the commands
25388 \begin_inset space \hspace{}
25397 \begin_inset space \hspace{}
25403 , because they can be inserted in LyX directly to text.
25406 \begin_layout Subsection
25408 \begin_inset CommandInset label
25410 name "sub:Accents-in-Text"
25415 \begin_inset Index idx
25418 \begin_layout Plain Layout
25427 \begin_layout Standard
25428 With the following commands all letters can be accented.
25429 The commands must be inserted in TeX-mode.
25432 \begin_layout Standard
25433 \begin_inset space \hfill{}
25437 \begin_inset Tabular
25438 <lyxtabular version="3" rows="8" columns="2">
25439 <features rotate="0" tabularvalignment="middle">
25440 <column alignment="block" valignment="top">
25441 <column alignment="block" valignment="top">
25443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25446 \begin_layout Plain Layout
25452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25455 \begin_layout Plain Layout
25463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25466 \begin_layout Plain Layout
25470 \begin_inset Quotes grd
25478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25481 \begin_layout Plain Layout
25485 \begin_layout Plain Layout
25501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25504 \begin_layout Plain Layout
25512 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25515 \begin_layout Plain Layout
25519 \begin_layout Plain Layout
25535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25538 \begin_layout Plain Layout
25542 \begin_inset space \textvisiblespace{}
25550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25553 \begin_layout Plain Layout
25557 \begin_layout Plain Layout
25573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25576 \begin_layout Plain Layout
25584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25587 \begin_layout Plain Layout
25591 \begin_layout Plain Layout
25607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25610 \begin_layout Plain Layout
25614 \begin_inset space \textvisiblespace{}
25622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25625 \begin_layout Plain Layout
25629 \begin_layout Plain Layout
25645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25648 \begin_layout Plain Layout
25652 \begin_inset space \textvisiblespace{}
25660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25663 \begin_layout Plain Layout
25667 \begin_layout Plain Layout
25683 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25686 \begin_layout Plain Layout
25690 \begin_inset space \textvisiblespace{}
25698 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25701 \begin_layout Plain Layout
25705 \begin_layout Plain Layout
25725 \begin_inset space \hfill{}
25729 \begin_inset Tabular
25730 <lyxtabular version="3" rows="8" columns="2">
25731 <features rotate="0" tabularvalignment="middle">
25732 <column alignment="block" valignment="top">
25733 <column alignment="center" valignment="top">
25735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25738 \begin_layout Plain Layout
25744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25747 \begin_layout Plain Layout
25755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25758 \begin_layout Plain Layout
25762 \begin_inset space \textvisiblespace{}
25770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25773 \begin_layout Plain Layout
25777 \begin_layout Plain Layout
25793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25796 \begin_layout Plain Layout
25804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25807 \begin_layout Plain Layout
25811 \begin_layout Plain Layout
25827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25830 \begin_layout Plain Layout
25834 \begin_inset Index idx
25837 \begin_layout Plain Layout
25848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25851 \begin_layout Plain Layout
25855 \begin_layout Plain Layout
25871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25874 \begin_layout Plain Layout
25882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25885 \begin_layout Plain Layout
25889 \begin_layout Plain Layout
25905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25908 \begin_layout Plain Layout
25912 \begin_inset space \textvisiblespace{}
25920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25923 \begin_layout Plain Layout
25927 \begin_layout Plain Layout
25943 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25946 \begin_layout Plain Layout
25950 \begin_inset space \textvisiblespace{}
25958 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25961 \begin_layout Plain Layout
25965 \begin_layout Plain Layout
25981 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25984 \begin_layout Plain Layout
25988 \begin_inset space \textvisiblespace{}
25996 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25999 \begin_layout Plain Layout
26003 \begin_layout Plain Layout
26023 \begin_inset space \hfill{}
26029 \begin_layout Standard
26030 \begin_inset VSpace medskip
26039 also two different characters can be accented.
26045 \begin_inset space \textvisiblespace{}
26054 \begin_layout Plain Layout
26066 \begin_layout Standard
26079 can in combination with vowels directly be inserted with the keyboard without
26081 The same applies for the tilde
26085 \begin_layout Plain Layout
26086 This only applies for keyboards where the tilde is defined as accent.
26095 in combination with
26110 \begin_layout Standard
26153 and accents that are inserted directly with the keyboard are also available
26154 in mathematical text.
26155 For the other accents there are special math commands to be used in formulas,
26157 \begin_inset CommandInset ref
26159 reference "sub:Accents-for-one"
26166 \begin_layout Standard
26167 \begin_inset VSpace bigskip
26170 Furthermore, with the command
26177 \begin_inset Index idx
26180 \begin_layout Plain Layout
26188 all numbers and letters can be set into a circle, quasi accented with a
26189 circle, similar to the copyright symbol.
26192 \begin_layout Standard
26194 \begin_inset Tabular
26195 <lyxtabular version="3" rows="3" columns="2">
26196 <features rotate="0" tabularvalignment="middle">
26197 <column alignment="center" valignment="top">
26198 <column alignment="center" valignment="top">
26200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26203 \begin_layout Plain Layout
26209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26212 \begin_layout Plain Layout
26214 \begin_inset Note Note
26217 \begin_layout Plain Layout
26224 is only used as spacer.
26236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26239 \begin_layout Plain Layout
26247 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26250 \begin_layout Plain Layout
26254 \begin_layout Plain Layout
26270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26273 \begin_layout Plain Layout
26284 raisebox{-1.5pt}{W}}
26289 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26292 \begin_layout Plain Layout
26293 \begin_inset Formula $\raisebox{4.5mm}{}$
26300 \begin_layout Plain Layout
26318 \begin_inset Formula $\raisebox{-2mm}{}$
26334 \begin_layout Standard
26335 One has to take care that the character fits in the circle.
26346 \begin_layout Plain Layout
26348 \begin_inset CommandInset ref
26350 reference "sub:Font-Sizes"
26359 specifies thereby the size of the circle.
26370 \begin_layout Plain Layout
26372 \begin_inset CommandInset ref
26374 reference "sub:Boxes-without-Frame"
26383 the character can be centered.
26386 \begin_layout Subsection
26388 \begin_inset Index idx
26391 \begin_layout Plain Layout
26400 \begin_layout Standard
26401 Old-style figures (also known as old-style numerals) are created with the
26409 \begin_inset Index idx
26412 \begin_layout Plain Layout
26421 The command can be used in formulas and in TeX-mode.
26422 The command scheme is:
26425 \begin_layout Standard
26430 oldstylenums{number}
26433 \begin_layout Standard
26438 oldstylenums{0123456789
26441 \begin_inset Formula $\oldstylenums{0123456789}$
26447 \begin_layout Section
26449 \begin_inset CommandInset label
26451 name "sec:Formula-Styles"
26456 \begin_inset Index idx
26459 \begin_layout Plain Layout
26468 \begin_layout Itemize
26469 There are two different alignment styles:
26473 \begin_layout Description
26474 Centered is the predefined standard
26477 \begin_layout Description
26478 Indented for this the option
26482 must be inserted in the menu
26484 Document\SpecialChar \menuseparator
26490 \begin_inset space ~
26496 \begin_layout Standard
26501 is used, the indentation can be adjusted with the length
26508 \begin_inset Index idx
26511 \begin_layout Plain Layout
26520 Should the distance be 15
26521 \begin_inset space \thinspace{}
26524 mm, the following command line is inserted in the LaTeX-preamble
26527 \begin_layout Standard
26537 \begin_layout Standard
26538 When no length is specified, the predefined value of 30
26539 \begin_inset space \thinspace{}
26546 \begin_layout Itemize
26547 And two different numbering styles:
26551 \begin_layout Description
26552 Right is the predefined standard
26555 \begin_layout Description
26556 Left for this the option
26560 must be inserted in the menu
26562 Document\SpecialChar \menuseparator
26568 \begin_inset space ~
26575 \begin_layout Standard
26584 can also be used together.
26585 In this case both options are inserted, separated by a comma.
26588 \begin_layout Standard
26589 The chosen styles are used for all displayed formulas of the document.
26590 When both, centered and indented formulas should be created in a document,
26596 The indented formulas are then set in a flalign environment, see
26597 \begin_inset CommandInset ref
26599 reference "sub:Flalign-Environment"
26606 \begin_layout Section
26608 \begin_inset CommandInset label
26610 name "sec:Multiline-Formulas"
26615 \begin_inset Index idx
26618 \begin_layout Plain Layout
26619 Formula ! multiline
26627 \begin_layout Subsection
26631 \begin_layout Standard
26632 In LyX multiline formulas are created by pressing
26637 arg "newline-insert newline"
26643 This creates either an
26645 eqnarray environment
26647 that is described in
26648 \begin_inset CommandInset ref
26650 reference "sub:Eqnarray-Environment"
26654 or, when the option
26656 Use AMS math package
26658 in the document settings is selected, an
26662 that is described in
26663 \begin_inset CommandInset ref
26665 reference "sub:Standard-align-Environment"
26670 The align environment is recommended because it provides in any case a
26671 typographically correct output.
26674 \begin_layout Standard
26675 There are other multiline formula environments that can be created via the
26678 Insert\SpecialChar \menuseparator
26682 These environments are described in the following sections.
26685 \begin_layout Standard
26686 In all multiline formula environments a new line is created by pressing
26690 arg "newline-insert newline"
26694 To add or delete lines, the math toolbar buttons
26695 \begin_inset Graphics
26696 filename ../images/tabular-feature_append-row.png
26702 \begin_inset Graphics
26703 filename ../images/tabular-feature_delete-row.png
26708 , respectively, or the menu
26710 Edit\SpecialChar \menuseparator
26716 \begin_layout Subsubsection
26718 \begin_inset CommandInset label
26720 name "sub:Line-Separation"
26725 \begin_inset Index idx
26728 \begin_layout Plain Layout
26729 Formula ! multiline ! Line separation
26737 \begin_layout Standard
26738 There is sometimes not enough space in multiline formulas between the lines:
26739 \begin_inset Formula
26741 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}\\
26742 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
26750 \begin_layout Standard
26751 In LaTeX additional line space is specified as optional argument of the
26753 This is not yet possible in LyX
26757 \begin_layout Plain Layout
26759 \begin_inset CommandInset href
26761 name "LyX-bug #1505"
26762 target "http://www.lyx.org/trac/ticket/1505"
26771 , therefore the whole formula must be inserted in TeX-mode.
26772 To add in our example space, the command
26780 is inserted at the end of the first line.
26785 \begin_layout Plain Layout
26792 \begin_layout Plain Layout
26794 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
26797 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
26804 \begin_layout Plain Layout
26808 left(B^{2}+x_{0}^{2}
26816 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
26821 \begin_layout Plain Layout
26833 \begin_layout Standard
26834 \begin_inset VSpace bigskip
26837 To set the line separation for all lines in a formula, the length
26844 \begin_inset Index idx
26847 \begin_layout Plain Layout
26857 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
26868 \begin_inset space \thinspace{}
26873 \begin_inset space \thinspace{}
26876 mm additional line separation as in the previous example, the command
26879 \begin_layout Standard
26889 \begin_layout Standard
26890 is inserted in TeX-mode before the formula.
26891 This requires that the LaTeX-package
26899 \begin_layout Plain Layout
26904 is part of every LaTeX standard installation.
26910 \begin_inset Index idx
26913 \begin_layout Plain Layout
26919 was loaded in LaTeX-preamble with the line
26922 \begin_layout Standard
26930 \begin_layout Standard
26935 \begin_layout Plain Layout
26947 \begin_inset Formula
26949 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}\\
26950 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
26958 \begin_layout Standard
26962 \begin_layout Plain Layout
26973 To get back to the predefined distance,
26979 is set to the value 3
26980 \begin_inset space \thinspace{}
26986 \begin_layout Subsubsection
26988 \begin_inset CommandInset label
26990 name "sub:Column-Separation"
26995 \begin_inset Index idx
26998 \begin_layout Plain Layout
26999 Formula ! multiline ! Column separation
27007 \begin_layout Standard
27008 Multiline formulas form a matrix.
27009 A formula in the eqnarray environment is for example a matrix with three
27011 By changing the column separation in this environment, the space beside
27012 the relation sign can be changed.
27015 \begin_layout Standard
27016 The column separation is specified with the length
27023 \begin_inset Index idx
27026 \begin_layout Plain Layout
27035 \begin_inset Newline newline
27038 column separation = 2
27039 \begin_inset space \thinspace{}
27049 \begin_inset Newline newline
27055 \begin_layout Standard
27065 \begin_layout Standard
27066 inserted in TeX-mode, sets for all following formulas a column separation
27068 \begin_inset space \thinspace{}
27072 To get back to the predefined distance,
27079 \begin_inset space \thinspace{}
27085 \begin_layout Standard
27087 \begin_inset space \thinspace{}
27090 cm column separation:
27094 \begin_layout Plain Layout
27106 \begin_inset Formula
27114 A formula with the predefined column separation for matrices of 10
27115 \begin_inset space \thinspace{}
27122 \begin_layout Plain Layout
27134 \begin_inset Formula
27145 \begin_layout Subsubsection
27147 \begin_inset Index idx
27150 \begin_layout Plain Layout
27159 \begin_layout Standard
27160 Long formulas can be typeset using these methods:
27163 \begin_layout Itemize
27164 When one side of the equation is much shorter than the line width, this
27165 one is chosen for the left side and the right side is typeset over two
27167 \begin_inset Formula
27169 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 \\
27170 & & -\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}
27175 The minus sign at the beginning of the second line does normally not appear
27176 as an operator because it is the first character of the line.
27177 Thus it would not be surrounded by space and could not be distinguished
27178 from the fraction bar.
27180 \begin_inset space \thinspace{}
27183 pt space was inserted behind the minus sign with the command
27193 \begin_layout Plain Layout
27201 \begin_inset CommandInset ref
27203 reference "sub:Variable-Space"
27213 \begin_inset Index idx
27216 \begin_layout Plain Layout
27227 \begin_layout Itemize
27228 When both sides of the equation are too long, the command
27235 \begin_inset Index idx
27238 \begin_layout Plain Layout
27247 It is inserted in the first column of the first line and causes all further
27248 insertions to overwrite the following columns:
27249 \begin_inset Formula
27251 \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 \\
27252 & & -\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 \\
27253 & & =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}
27258 After the insertion of
27264 , the cursor is in a purple box that is a bit shifted to the left from the
27266 In this the formula is inserted.
27267 \begin_inset Newline newline
27270 The content of the further lines is inserted to the second or another formula
27272 The greater the column number where it was inserted, the larger the indentation.
27273 \begin_inset VSpace medskip
27277 \begin_inset Newline newline
27281 \begin_inset Note Greyedout
27284 \begin_layout Plain Layout
27285 Note the following when using
27294 \begin_layout Itemize
27295 The formula doesn't use the full page width.
27297 \begin_inset space \thinspace{}
27301 \begin_inset space \space{}
27305 \begin_inset Formula $-B^{2}$
27308 is added to the first line in the above example, it would have been outside
27310 To better use the width, negative space can be inserted at the beginning
27314 \begin_layout Itemize
27315 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27320 \begin_layout Plain Layout
27321 \begin_inset CommandInset href
27323 name "LyX-bug #1429"
27324 target "http://www.lyx.org/trac/ticket/1429"
27333 One can only set the cursor at the beginning of the line and move it with
27342 \begin_layout Itemize
27343 Other methods to set long formulas are offered by the environments described
27345 \begin_inset CommandInset ref
27347 reference "sub:Multline-Environment"
27352 \begin_inset CommandInset ref
27354 reference "sub:Multiline-Formula-Parts"
27361 \begin_layout Subsubsection
27363 \begin_inset CommandInset label
27365 name "sub:Multiline-Brackets"
27370 \begin_inset Index idx
27373 \begin_layout Plain Layout
27374 Brackets ! for multiline expressions
27382 \begin_layout Standard
27383 For brackets spanning multiple lines the following problem occurs:
27384 \begin_inset Formula
27386 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27387 & & \left.\cdots+B-D\right]
27395 \begin_layout Standard
27396 The closing bracket is smaller than the opening bracket because brackets
27397 with variable size may not span multiple lines.
27400 \begin_layout Standard
27401 To set the bracket size for the second line correctly, the first line is
27409 \begin_inset Index idx
27412 \begin_layout Plain Layout
27420 and the second line with
27428 \begin_layout Plain Layout
27442 \begin_inset CommandInset ref
27444 reference "sub:Automatic-Bracket-Size"
27456 \begin_inset Index idx
27459 \begin_layout Plain Layout
27482 \begin_inset space \textvisiblespace{}
27492 \begin_inset space \textvisiblespace{}
27502 \begin_inset space \textvisiblespace{}
27508 \begin_inset Formula $\downarrow$
27514 \begin_inset Index idx
27517 \begin_layout Plain Layout
27525 is inserted, because the multiplication operator with its limits is the
27526 largest symbol in the first line and this should be the size for the bracket
27527 in the second line.
27530 \begin_layout Standard
27531 The result is this:
27532 \begin_inset Formula
27534 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27535 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
27543 \begin_layout Subsection
27547 \begin_layout Standard
27548 Align environments can be used for every kind of multiline formulas.
27549 They are especially useful to set several formulas side by side.
27552 \begin_layout Standard
27553 Align environments consist of columns.
27554 The odd columns are right aligned, the even ones left aligned.
27555 Every line in an Align environment can be numbered.
27558 \begin_layout Standard
27559 Align environments are created via the menu
27561 Insert\SpecialChar \menuseparator
27567 Edit\SpecialChar \menuseparator
27568 Math\SpecialChar \menuseparator
27569 Change Formula Type
27571 already existing formulas can be converted to Align environments.
27574 \begin_layout Standard
27575 To add or delete columns, the math toolbar buttons
27576 \begin_inset Graphics
27577 filename ../images/tabular-feature_append-column.png
27583 \begin_inset Graphics
27584 filename ../images/tabular-feature_delete-column.png
27589 , respectively, or the menu
27591 Edit\SpecialChar \menuseparator
27597 \begin_layout Subsubsection
27598 Standard align Environment
27599 \begin_inset CommandInset label
27601 name "sub:Standard-align-Environment"
27606 \begin_inset Index idx
27609 \begin_layout Plain Layout
27610 Formula ! multiline ! align environment
27618 \begin_layout Standard
27619 This Align environment is created by pressing
27622 arg "newline-insert newline"
27625 in a formula or by the menu
27627 Insert\SpecialChar \menuseparator
27628 Math\SpecialChar \menuseparator
27629 AMS align Environment
27634 \begin_layout Standard
27635 An example for two formulas set side by side, that are created with a four
27636 column align environment:
27637 \begin_inset Formula
27639 A & =\sin(B) & C & =D\\
27640 C & \ne A & B & \ne D
27645 As it can be seen, the formulas in this environment are placed so as if
27654 \begin_layout Plain Layout
27662 \begin_inset CommandInset ref
27664 reference "sub:Variable-Space"
27675 before the first and after every even column.
27676 When the formula style
27682 \begin_layout Plain Layout
27684 \begin_inset CommandInset ref
27686 reference "sec:Formula-Styles"
27697 is used, the formula is set without the
27703 before the first column.
27706 \begin_layout Subsubsection
27707 Alignat Environment
27708 \begin_inset Index idx
27711 \begin_layout Plain Layout
27712 Formula ! multiline ! alignat environment
27720 \begin_layout Standard
27721 The alignat environment has no predefined column separation.
27722 It can be inserted manually with the spaces that are described
27723 \begin_inset CommandInset ref
27725 reference "sub:Space"
27732 \begin_layout Standard
27733 The above example in the alignat environment where 1
27734 \begin_inset space \thinspace{}
27737 cm space was inserted at the beginning of the second formula:
27738 \begin_inset Formula
27739 \begin{alignat*}{2}
27740 A & =\sin(B) & \hspace{1cm}C & =D\\
27741 C & \ne A & B & \ne D
27746 Because the column separation can be set separately for every column, this
27747 environment is especially suitable to set three and more formulas side
27751 \begin_layout Subsubsection
27752 Flalign Environment
27753 \begin_inset CommandInset label
27755 name "sub:Flalign-Environment"
27760 \begin_inset Index idx
27763 \begin_layout Plain Layout
27764 Formula ! multiline ! flalign environment
27772 \begin_layout Standard
27773 In this environment the first two columns are always set as much as possible
27774 to the left and the last two ones to the right.
27776 \begin_inset Formula
27778 A & =1 & B & =2 & C & =3\\
27779 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
27787 \begin_layout Standard
27788 By creating a flalign environment with an odd number of columns where an
27789 empty TeX-brace is inserted to the last column, several formulas in a document
27790 can be set to the left, although the formula style
27795 As example the indented formula
27796 \begin_inset CommandInset ref
27798 reference "eq:VolInt"
27803 \begin_inset Formula
27805 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
27810 The first two columns contain the formula.
27811 To indent it as with the formula style
27816 \begin_inset space \thinspace{}
27819 pt space was inserted at the beginning of the first column.
27822 \begin_layout Subsection
27823 Eqnarray Environment
27824 \begin_inset CommandInset label
27826 name "sub:Eqnarray-Environment"
27831 \begin_inset Index idx
27834 \begin_layout Plain Layout
27835 Formula ! multiline ! eqnarray environment
27843 \begin_layout Standard
27844 When this environment has been created, three blue boxes appear.
27845 The content of the first box is right aligned, the content of the last
27847 The content of the middle box appears centered and a bit smaller, because
27848 it is designed to insert there only relation characters.
27849 \begin_inset Formula
27851 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
27861 \begin_layout Subsection
27863 \begin_inset Index idx
27866 \begin_layout Plain Layout
27867 Formula ! multiline ! gather environment
27875 \begin_layout Standard
27876 This environment consists of only one centered column.
27877 Every line can be numbered.
27878 \begin_inset Formula
27889 \begin_layout Subsection
27890 Multline Environment
27891 \begin_inset CommandInset label
27893 name "sub:Multline-Environment"
27898 \begin_inset Index idx
27901 \begin_layout Plain Layout
27902 Formula ! multiline ! multline environment
27910 \begin_layout Standard
27911 The multline environment consists, like the gather environment, of only
27913 But the first line is left aligned, the last one right aligned.
27914 All other lines are centered.
27915 Therefore this environment is suitable for long formulas.
27917 \begin_inset CommandInset ref
27919 reference "eq:lefteqn"
27923 in the multline environment:
27924 \begin_inset Formula
27926 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}\\
27927 -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}\\
27928 =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}}
27936 \begin_layout Standard
27937 In the output only the last (first) line of a multline environment appears
27938 numbered when the document numbering is right (left).
27942 \begin_layout Plain Layout
27943 numbering styles see
27944 \begin_inset CommandInset ref
27946 reference "sec:Formula-Styles"
27958 \begin_layout Standard
27966 \begin_inset Index idx
27969 \begin_layout Plain Layout
27984 \begin_inset Index idx
27987 \begin_layout Plain Layout
27995 a centered line can be right or left aligned, respectively.
27996 The commands are used as follows:
27999 \begin_layout Standard
28004 shoveright{line content}
28010 shoveleft{line content}
28013 \begin_layout Standard
28014 \begin_inset VSpace medskip
28024 \begin_inset Index idx
28027 \begin_layout Plain Layout
28035 specifies the distance of the first line from the left page margin.
28036 Predefined is the length 0
28037 \begin_inset space \thinspace{}
28043 \begin_layout Standard
28044 As example the above formula where the command
28047 \begin_layout Standard
28057 \begin_layout Standard
28058 was inserted in TeX-mode before:
28062 \begin_layout Plain Layout
28074 \begin_inset Formula
28076 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}\\
28077 \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}}\\
28078 =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}}
28087 \begin_layout Plain Layout
28098 The second line was left aligned using
28107 \begin_layout Subsection
28108 Multiline Formula Parts
28109 \begin_inset CommandInset label
28111 name "sub:Multiline-Formula-Parts"
28116 \begin_inset Index idx
28119 \begin_layout Plain Layout
28120 Formula ! multiline ! formula parts
28128 \begin_layout Standard
28129 To display only parts of a formula with multiple lines, one of the following
28130 environments is used:
28147 They can be inserted via the menu
28149 Insert\SpecialChar \menuseparator
28152 or by using the commands described in this section.
28155 \begin_layout Standard
28156 The first three have the same properties as the corresponding multiline
28157 formula environments, but it is possible to set further formula parts beside
28160 \begin_inset Formula
28162 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28163 \Delta E\Delta t & \ge\frac{\hbar}{2}
28165 \right\} \textrm{Uncertainty relations}
28173 \begin_layout Standard
28174 To get this formula, a displayed formula is created where the command
28181 \begin_inset Index idx
28184 \begin_layout Plain Layout
28193 A purple box appears around the blue formula box where now columns and
28194 lines can be added.
28195 Outside the multiline environment other formula parts can be set, like
28199 \begin_layout Standard
28200 The aligned environment is also suitable for long formulas whose lines are
28201 horizontally aligned.
28202 Using aligned in a displayed formula has the advantage that the formula
28203 number is vertically centered behind the lines.
28205 \begin_inset CommandInset ref
28207 reference "eq:shortlong"
28211 in the aligned environment:
28212 \begin_inset Formula
28214 \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}|}\\
28215 & -\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}|}
28224 \begin_layout Standard
28225 To use the environments
28244 \begin_inset Index idx
28247 \begin_layout Plain Layout
28262 \begin_inset Index idx
28265 \begin_layout Plain Layout
28280 \begin_inset Index idx
28283 \begin_layout Plain Layout
28291 are inserted, respectively.
28292 The split environment has the same properties as the aligned environment
28293 but it can only have two columns.
28296 \begin_layout Subsection
28297 Text in multiline Formulas
28298 \begin_inset CommandInset label
28300 name "sub:Text-in-multiline"
28305 \begin_inset Index idx
28308 \begin_layout Plain Layout
28315 \begin_inset Index idx
28318 \begin_layout Plain Layout
28319 Formula ! multiline ! text
28327 \begin_layout Standard
28328 In the Align environments, and the multline and gather environment, text
28329 can be inserted that will appear in a separate line and doesn't affect
28330 the column alignment.
28331 To do this, the command
28338 \begin_inset Index idx
28341 \begin_layout Plain Layout
28349 is used in the following scheme:
28352 \begin_layout Standard
28360 \begin_layout Standard
28361 The text should not be longer than a line because it cannot be hyphenated.
28362 As LyX doesn't yet support
28368 directly, the text is written as mathematical text.
28375 must hereby be at the beginning of a line and appears in the output above
28377 An example where the text was inserted at the beginning of the second line:
28378 \begin_inset Formula
28380 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
28381 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
28389 \begin_layout Section
28391 \begin_inset Index idx
28394 \begin_layout Plain Layout
28401 \begin_inset Index idx
28404 \begin_layout Plain Layout
28405 Formula ! numbering|see
28409 \begin_layout Plain Layout
28420 \begin_layout Plain Layout
28435 \begin_layout Subsection
28439 \begin_layout Standard
28440 Numbered formulas can be created with the menu
28442 Insert\SpecialChar \menuseparator
28443 Math\SpecialChar \menuseparator
28445 \begin_inset space ~
28453 \begin_inset space ~
28459 Existing formulas can be numbered with the menu
28461 Edit\SpecialChar \menuseparator
28462 Math\SpecialChar \menuseparator
28464 \begin_inset space ~
28472 arg "math-number-toggle"
28476 The formula number is displayed in LyX behind the formula as a number sign
28478 The number sign is replaced in the output by the formula number.
28481 \begin_layout Standard
28482 When numbering is turned on in multiline formulas, all lines will be numbered.
28483 But the numbering can be controlled with the menu
28485 Edit\SpecialChar \menuseparator
28486 Math\SpecialChar \menuseparator
28488 \begin_inset space ~
28492 \begin_inset space ~
28496 \begin_inset space ~
28504 arg "math-number-line-toggle"
28510 \begin_layout Standard
28511 Except for inline formulas, all formulas can be numbered with two different
28513 \begin_inset CommandInset ref
28515 reference "sec:Formula-Styles"
28522 \begin_layout Subsection
28524 \begin_inset Index idx
28527 \begin_layout Plain Layout
28528 Cross-references ! to formulas
28536 \begin_layout Standard
28537 All labeled formulas can be cross-referenced.
28538 A label is added by the menu
28540 Insert\SpecialChar \menuseparator
28543 or the toolbar button
28544 \begin_inset Graphics
28545 filename ../images/label-insert.png
28551 The cursor must hereby be inside a displayed formula.
28552 Alternatively you can right-click on the formula and choose
28557 A dialog pops up displaying the prefix
28562 The label is inserted there behind the prefix.
28563 The predefined prefix means
28564 \begin_inset Quotes eld
28568 \begin_inset Quotes erd
28571 and makes it easier to find labels in large documents because it marks
28572 it as formula label to divide it from e.
28573 \begin_inset space \thinspace{}
28577 \begin_inset space \space{}
28581 To change a label, the menu
28583 Insert\SpecialChar \menuseparator
28586 is used again or you right-click on a formula and then on
28593 \begin_layout Standard
28594 The name of the label is displayed in LyX within two parentheses behind
28596 A formula with a label is always numbered.
28599 \begin_layout Standard
28600 Cross-references are inserted via the menu
28602 Insert\SpecialChar \menuseparator
28605 or with the toolbar button
28606 \begin_inset Graphics
28607 filename ../images/dialog-show-new-inset_ref.png
28613 A formula cross-reference appears in the output as formula number.
28614 When in the cross-reference dialog window the format
28618 is chosen, the cross-reference appears in the output as formula number
28620 \begin_inset Newline newline
28623 By right-clicking on a cross-reference in LyX, one jumps to the formula
28624 that is referenced.
28627 \begin_layout Standard
28628 Here are as examples cross-references to formulas of the following subsections:
28629 \begin_inset Note Note
28632 \begin_layout Plain Layout
28633 Note the different cross-reference types.
28641 \begin_layout Standard
28643 \begin_inset CommandInset ref
28650 \begin_inset CommandInset ref
28658 \begin_inset CommandInset ref
28664 ) big Latin letters are used for the numbering in contrary to (
28665 \begin_inset CommandInset ref
28674 \begin_layout Standard
28675 \begin_inset VSpace medskip
28678 When the argument of
28686 \begin_layout Plain Layout
28694 \begin_inset CommandInset ref
28696 reference "sub:User-defined-Numbering"
28707 contains a box like in
28708 \begin_inset CommandInset ref
28710 reference "sub:Paragraph-Boxes"
28714 , the formula cannot be referenced.
28717 \begin_layout Subsection
28719 \begin_inset Index idx
28722 \begin_layout Plain Layout
28723 Formula numbering ! subnumbering
28731 \begin_layout Standard
28732 With the help of the commands
28736 begin{subequations}
28744 formulas can be subnumbered.
28745 Both commands are inserted in TeX-mode.
28748 \begin_layout Standard
28750 \begin_inset Formula
28761 \begin_layout Plain Layout
28765 addtocounter{equation}{-1}
28774 \begin_layout Plain Layout
28778 begin{subequations}
28784 \begin_inset VSpace -5mm
28788 \begin_inset Formula
28796 \begin_inset Formula
28806 \begin_layout Standard
28810 \begin_layout Plain Layout
28822 \begin_layout Standard
28823 To create the example, the following is done:
28826 \begin_layout Enumerate
28827 first formula is inserted
28830 \begin_layout Enumerate
28835 addtocounter{equation}{-1}
28837 begin{subequations}
28838 \begin_inset Index idx
28841 \begin_layout Plain Layout
28850 \begin_inset Newline newline
28855 is inserted after the first formula
28858 \begin_layout Enumerate
28859 second formula is inserted
28862 \begin_layout Enumerate
28863 third formula is inserted
28866 \begin_layout Enumerate
28873 is inserted after the third formula
28876 \begin_layout Standard
28877 Every formula between the commands
28889 is subnumbered as a, b,
28890 \begin_inset Newline linebreak
28893 c, \SpecialChar \ldots{}
28894 For multiline formulas every line will be subnumbered.
28895 All subnumbered formulas are treated as
28900 But as every numbered formula increases the counter
28904 by one, the command
28910 is needed to decrease it.
28911 Otherwise the formulas
28912 \begin_inset CommandInset ref
28919 \begin_inset CommandInset ref
28926 \begin_inset CommandInset ref
28932 would be numbered as
28933 \begin_inset CommandInset ref
28940 \begin_inset CommandInset ref
28947 \begin_inset CommandInset ref
28956 \begin_layout Standard
28957 By inserting the commands in TeX-mode, a space is created between the first
28960 \begin_inset space \thinspace{}
28963 mm vertical space is inserted after the command
28967 begin{subequations}
28970 When the formula style
28976 \begin_layout Plain Layout
28978 \begin_inset CommandInset ref
28980 reference "sec:Formula-Styles"
28992 \begin_inset space \thinspace{}
28995 mm space is inserted instead.
28998 \begin_layout Standard
28999 Here is an example for a multiline formula where the numbering was turned
29000 off for the second line:
29004 \begin_layout Plain Layout
29008 begin{subequations}
29014 \begin_inset Formula
29016 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29017 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29018 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
29027 \begin_layout Plain Layout
29039 \begin_layout Subsection
29040 User-defined Numbering
29041 \begin_inset CommandInset label
29043 name "sub:User-defined-Numbering"
29048 \begin_inset Index idx
29051 \begin_layout Plain Layout
29052 Formula numbering ! user-defined
29060 \begin_layout Standard
29061 \begin_inset Index idx
29064 \begin_layout Plain Layout
29065 Formula numbering ! self-defined delimiters
29070 With the standard numbering parentheses are set around the formula number.
29071 To replace the parentheses for example by vertical bars, the following
29072 line is added to the LaTeX-preamble:
29075 \begin_layout Standard
29087 \begin_inset Note Note
29090 \begin_layout Plain Layout
29091 This macro is already declared in the LaTeX-preamble for testing.
29092 To activate it, remove the percent sign at the beginning.
29100 \begin_layout Standard
29101 To use other characters, the vertical bars besides the
29105 are replaced by one ore more characters.
29106 To get only the formula number the vertical bars are omitted.
29109 \begin_layout Standard
29110 \begin_inset VSpace bigskip
29113 When there should be an expression of your choice instead of the consecutive
29114 formula number in parentheses behind the formula, the command
29121 \begin_inset Index idx
29124 \begin_layout Plain Layout
29133 \begin_inset Formula
29135 A+B=C\tag{something}\label{eq:tag}
29140 In this example the command
29145 \begin_inset space \textvisiblespace{}
29150 was inserted in the formula.
29153 \begin_layout Standard
29159 \begin_inset space \textvisiblespace{}
29164 is inserted instead, the star prevents the parentheses around the expression:
29165 \begin_inset Formula
29167 A+B=C\tag*{something}
29175 \begin_layout Standard
29176 \begin_inset VSpace bigskip
29179 To restart the formula numbering with new document parts or sections, the
29180 following command is used:
29183 \begin_layout Standard
29188 @addtoreset{equation}{part}
29191 \begin_inset Index idx
29194 \begin_layout Plain Layout
29199 \begin_layout Plain Layout
29210 \begin_layout Plain Layout
29223 \begin_layout Plain Layout
29234 \begin_layout Plain Layout
29247 \begin_inset Newline newline
29251 \begin_inset Newline newline
29258 @addtoreset{equation}{section}
29261 \begin_layout Standard
29262 To be able to use these commands in TeX-mode, the
29263 \begin_inset Quotes eld
29267 \begin_inset Quotes erd
29270 character has to be made
29271 \begin_inset Quotes eld
29275 \begin_inset Quotes erd
29278 for LaTeX using the command
29292 So the command sequence in TeX-mode is:
29295 \begin_layout Standard
29301 \begin_inset Newline newline
29306 @addtoreset{equation}{section}
29307 \begin_inset Newline newline
29315 \begin_layout Standard
29316 In the LaTeX-preamble
29328 can be omitted as they are automatically internally inserted by LyX.
29331 \begin_layout Standard
29346 \begin_layout Plain Layout
29351 is part of the LaTeX-package
29356 \begin_inset Index idx
29359 \begin_layout Plain Layout
29360 Packages ! carlisle
29365 that is part of every LaTeX standard installation.
29371 \begin_inset Index idx
29374 \begin_layout Plain Layout
29375 Packages ! remreset
29380 has to be loaded in the LaTeX-preamble with the line
29383 \begin_layout Standard
29388 usepackage{remreset}
29391 \begin_layout Standard
29399 \begin_inset Index idx
29402 \begin_layout Plain Layout
29407 \begin_layout Plain Layout
29418 \begin_layout Plain Layout
29431 \begin_layout Plain Layout
29442 \begin_layout Plain Layout
29454 can be used with the same scheme as
29463 \begin_layout Standard
29464 \begin_inset VSpace bigskip
29467 Sometimes formulas should be numbered in the following form:
29470 \begin_layout Standard
29473 (section number.formula number)
29476 \begin_layout Standard
29477 The formula number should start with every section with
29478 \begin_inset Quotes eld
29482 \begin_inset Quotes erd
29488 \begin_layout Standard
29489 For this case there is the command
29496 \begin_inset Index idx
29499 \begin_layout Plain Layout
29507 , which is used with the following scheme:
29510 \begin_layout Standard
29515 numberwithin{counter}{sectioning}
29518 \begin_layout Standard
29519 Counter denotes what kind of numbering is affected, sectioning denotes what
29520 number is before the dot.
29523 \begin_layout Standard
29524 Thus in our case the following LaTeX-preamble or TeX code line is used:
29527 \begin_layout Standard
29532 numberwithin{equation}{section}
29535 \begin_layout Standard
29536 This is the result:
29540 \begin_layout Plain Layout
29544 numberwithin{equation}{section}
29550 \begin_inset Formula
29560 \begin_layout Standard
29562 \begin_inset space \thinspace{}
29566 \begin_inset space \space{}
29569 tables so that the number of the part is the sectioning,
29570 \begin_inset Newline newline
29577 numberwithin{table}{part}
29582 \begin_layout Standard
29583 To go back to the standard numbering or to prevent this kind of numbering
29584 when it is defined by the document class, the following command is inserted
29585 as TeX code or to the LaTeX-preamble:
29588 \begin_layout Standard
29598 \begin_inset Index idx
29601 \begin_layout Plain Layout
29615 \begin_layout Plain Layout
29631 \begin_inset Newline newline
29639 \begin_inset Newline newline
29651 \begin_layout Standard
29658 uses internally the command
29664 , described above, that also needs to be reverted.
29668 \begin_layout Plain Layout
29675 \begin_layout Plain Layout
29679 @removefromreset{equation}{section}
29682 \begin_layout Plain Layout
29694 \begin_layout Subsection
29695 Numbering with Roman Numbers and Letters
29696 \begin_inset Index idx
29699 \begin_layout Plain Layout
29700 Formula numbering ! with letters
29706 \begin_inset Index idx
29709 \begin_layout Plain Layout
29710 Formula numbering ! with Roman numbers
29718 \begin_layout Standard
29719 Formulas can also be numbered with Roman numbers and Latin letters.
29720 To number for example with small Roman numbers, the command
29723 \begin_layout Standard
29735 \begin_layout Standard
29736 is inserted before the formula in TeX-mode.
29744 \begin_inset Index idx
29747 \begin_layout Plain Layout
29755 redefines the predefined command
29771 \begin_layout Plain Layout
29778 has the same scheme like the command
29784 that is described in
29785 \begin_inset CommandInset ref
29787 reference "sub:The-Command-newcommand"
29800 is the formula counter.
29807 is used as prefix for a counter, the value of the counter is output as
29809 When a formula is numbered, LaTeX sets internally the command
29815 behind the formula.
29821 \begin_inset Index idx
29824 \begin_layout Plain Layout
29834 outputs the counter as small Roman number.
29837 \begin_layout Standard
29838 All formulas behind the command
29848 are now numbered Roman.
29849 To switch to numbering with big Roman numbers, the command is inserted
29863 \begin_inset Index idx
29866 \begin_layout Plain Layout
29878 \begin_inset Quotes eld
29882 \begin_inset Quotes erd
29885 with small Latin letters there is the command
29892 \begin_inset Index idx
29895 \begin_layout Plain Layout
29903 , for big ones there is the command
29910 \begin_inset Index idx
29913 \begin_layout Plain Layout
29926 \begin_layout Standard
29927 \begin_inset Note Greyedout
29930 \begin_layout Plain Layout
29937 \begin_inset space ~
29940 formulas can be numbered with Latin letters in one document.
29948 \begin_layout Standard
29952 \begin_layout Plain Layout
29968 \begin_layout Standard
29969 \begin_inset Formula
29971 A=\textrm{small roman}
29980 \begin_layout Plain Layout
29994 \begin_inset Formula
29996 B=\textrm{big Roman}\label{eq:Rom}
30005 \begin_layout Plain Layout
30019 \begin_inset Formula
30021 C=\textrm{small Latin}
30030 \begin_layout Plain Layout
30044 \begin_inset Formula
30046 D=\textrm{big Latin}\label{eq:Lat}
30054 \begin_layout Standard
30055 To switch back to the default numbering, insert the command:
30058 \begin_layout Standard
30068 \begin_inset Index idx
30071 \begin_layout Plain Layout
30082 \begin_layout Standard
30086 \begin_layout Plain Layout
30100 \begin_inset Formula
30110 \begin_layout Standard
30111 \begin_inset VSpace medskip
30114 As you see, formulas are numbered serially independent from the numbering
30116 When then numbering should start with
30117 \begin_inset Quotes eld
30121 \begin_inset Quotes erd
30124 when the style is changed, new equation counters have to be defined.
30125 A description about this can be found in the file
30126 \begin_inset CommandInset href
30128 name "Formula-numbering.lyx"
30129 target "run:Formula-numbering.lyx"
30136 \begin_layout Standard
30137 \begin_inset Newpage newpage
30143 \begin_layout Section
30144 Chemical Symbols and Equations
30145 \begin_inset CommandInset label
30147 name "sub:Chemical-Symbols-and"
30152 \begin_inset Index idx
30155 \begin_layout Plain Layout
30156 Chemical characters ! Symbols
30162 \begin_inset Index idx
30165 \begin_layout Plain Layout
30172 \begin_inset Index idx
30175 \begin_layout Plain Layout
30184 \begin_layout Standard
30185 An example text from chemistry:
30188 \begin_layout Quote
30190 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30193 -ion reacts with two
30194 \begin_inset Formula $\mathrm{Na^{+}}$
30197 -ions to sodium sulfate
30198 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30202 The chemical equation for this is:
30203 \begin_inset Formula
30205 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
30213 \begin_layout Standard
30214 This chemical equation can directly be created as formula.
30215 To avoid that the symbols appear italic, everything is highlighted and
30216 changed by the shortcut
30222 to the upright font style.
30226 \begin_layout Plain Layout
30232 \begin_inset CommandInset ref
30234 reference "sub:Font-Styles"
30246 \begin_layout Standard
30247 A more convenient way to typeset chemical formulas is to use the command
30255 \begin_inset Index idx
30258 \begin_layout Plain Layout
30266 that is available when the LaTeX-package
30271 \begin_inset Index idx
30274 \begin_layout Plain Layout
30287 to a formula a new blue box appears where chemical formulas can be inserted
30288 in an intuitive way.
30291 \begin_layout Standard
30293 \begin_inset Tabular
30294 <lyxtabular version="3" rows="9" columns="2">
30295 <features rotate="0" tabularvalignment="middle">
30296 <column alignment="center" valignment="top">
30297 <column alignment="center" valignment="top">
30299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30302 \begin_layout Plain Layout
30308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30311 \begin_layout Plain Layout
30313 \begin_inset Note Note
30316 \begin_layout Plain Layout
30323 is only used as spacer.
30335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30338 \begin_layout Plain Layout
30342 \begin_inset space \textvisiblespace{}
30350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30353 \begin_layout Plain Layout
30354 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
30364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30367 \begin_layout Plain Layout
30371 \begin_inset space \textvisiblespace{}
30379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30382 \begin_layout Plain Layout
30383 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
30393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30396 \begin_layout Plain Layout
30400 \begin_inset space \textvisiblespace{}
30408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30411 \begin_layout Plain Layout
30412 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
30422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30425 \begin_layout Plain Layout
30429 \begin_inset space \textvisiblespace{}
30437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30440 \begin_layout Plain Layout
30441 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
30451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30454 \begin_layout Plain Layout
30458 \begin_inset space \textvisiblespace{}
30464 \begin_inset space \textvisiblespace{}
30470 \begin_inset space \textvisiblespace{}
30478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30481 \begin_layout Plain Layout
30482 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
30492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30495 \begin_layout Plain Layout
30499 \begin_inset space \textvisiblespace{}
30503 \begin_inset Formula $\downarrow$
30507 \begin_inset Formula $\to$
30515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30518 \begin_layout Plain Layout
30519 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
30529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30532 \begin_layout Plain Layout
30536 \begin_inset space \textvisiblespace{}
30540 \begin_inset space \textvisiblespace{}
30544 \begin_inset space \textvisiblespace{}
30548 \begin_inset space \textvisiblespace{}
30552 \begin_inset space \textvisiblespace{}
30560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30563 \begin_layout Plain Layout
30564 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
30574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30577 \begin_layout Plain Layout
30581 \begin_inset space \textvisiblespace{}
30585 \begin_inset space \textvisiblespace{}
30589 \begin_inset space \textvisiblespace{}
30593 \begin_inset space \textvisiblespace{}
30601 \begin_inset space \textvisiblespace{}
30609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30612 \begin_layout Plain Layout
30613 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
30629 \begin_layout Standard
30630 \begin_inset Note Greyedout
30633 \begin_layout Plain Layout
30639 Inserting a formula to a
30645 box will lead to LaTeX errors due to a LyX bug.
30651 \begin_layout Plain Layout
30652 \begin_inset CommandInset href
30654 name "LyX-bug #8566"
30655 target "http://www.lyx.org/trac/ticket/8566"
30666 In this case TeX code has to be used like for
30680 \begin_layout Plain Layout
30701 \begin_layout Standard
30702 \begin_inset Note Greyedout
30705 \begin_layout Plain Layout
30711 It is not possible in LyX to use the character ^ to get an up-arrow as
30717 One instead uses a negative thin space followed by the command
30724 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
30735 \begin_layout Standard
30742 the command for equation
30743 \begin_inset space ~
30747 \begin_inset CommandInset ref
30749 reference "eq:chem-reaction"
30754 \begin_inset Newline newline
30762 \begin_inset space \textvisiblespace{}
30766 \begin_inset space \textvisiblespace{}
30770 \begin_inset space \textvisiblespace{}
30774 \begin_inset space \textvisiblespace{}
30778 \begin_inset space \textvisiblespace{}
30782 \begin_inset space \textvisiblespace{}
30788 \begin_layout Standard
30789 To create multiline chemical equations first a multiline formula is created
30791 \begin_inset CommandInset ref
30793 reference "sec:Multiline-Formulas"
30798 Afterwards the command
30804 is used in every small blue box of the formula.
30806 \begin_inset CommandInset ref
30808 reference "eq:TEOS-reaction-1"
30813 \begin_inset CommandInset ref
30815 reference "eq:TEOS-reaction-2"
30819 are an example of a multi-stage chemical reaction where every equation
30820 has its own number.
30821 \begin_inset Formula
30823 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
30824 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
30832 \begin_layout Standard
30843 package provides the command
30850 \begin_inset Index idx
30853 \begin_layout Plain Layout
30861 that has to be used for special cases.
30862 For more information about
30868 and more examples have a look at the documentation of
30873 \begin_inset CommandInset citation
30882 \begin_layout Section
30886 \begin_layout Standard
30887 LyX supports two types of commutative diagrams:
30895 that are explained in the following.
30898 \begin_layout Subsection
30900 \begin_inset Index idx
30903 \begin_layout Plain Layout
30912 \begin_layout Standard
30913 Diagrams of this type visualize relations by vertical and horizontal lines
30915 \begin_inset Formula
30917 \begin{CD}A@>>>B@>>>C\\
30928 \begin_layout Standard
30929 To get them, the command
30934 \begin_inset Index idx
30937 \begin_layout Plain Layout
30947 is inserted to a formula.
30948 A blue box appears with two dashed lines where further commands can be
30953 arg "newline-insert newline"
30956 a new line is created.
30957 Horizontal relations are inserted in odd, vertical in even formula lines.
30960 \begin_layout Standard
30961 To create the relations there are the following commands:
30964 \begin_layout Itemize
30969 creates a left arrow,
30980 \begin_layout Itemize
30985 creates an up arrow,
30993 a vertical equal sign
30996 \begin_layout Itemize
31002 is a placeholder for non-existent relations
31005 \begin_layout Standard
31006 All arrows can be labeled as follows:
31009 \begin_layout Itemize
31010 If text inserted between the first and second < or >, resp., it is placed
31012 When it is inserted between the second and third one, it appears under
31016 \begin_layout Itemize
31017 When text for vertical arrows is inserted between the first and second A
31018 or V, resp., it is placed left beside the arrow.
31019 When it is inserted between the second and third one, it appears right
31021 If the text contains an A or V, these letters must be set into a TeX-brace.
31024 \begin_layout Standard
31025 As example a diagram with all possible relations:
31028 \begin_layout Standard
31029 \begin_inset Formula
31031 \begin{CD}A@>j>>B@>>k>C@=F\\
31042 \begin_layout Standard
31043 The command for this is:
31044 \begin_inset Newline newline
31052 \begin_inset space \textvisiblespace{}
31055 A@>j>>B@>>k>C@=F Ctrl+Return
31056 \begin_inset Newline newline
31060 \begin_inset Phantom HPhantom
31063 \begin_layout Plain Layout
31069 \begin_inset space \textvisiblespace{}
31082 \begin_inset Formula $\to$
31088 \begin_inset Newline newline
31092 \begin_inset Phantom HPhantom
31095 \begin_layout Plain Layout
31101 \begin_inset space \textvisiblespace{}
31112 \begin_layout Subsection
31114 \begin_inset Index idx
31117 \begin_layout Plain Layout
31118 Diagrams ! xymatrix
31126 \begin_layout Standard
31127 To be able to use xymatrices, the LaTeX-package
31132 A xymatrix is created by inserting the command
31139 Then you are able to add new matrix columns and rows like for normal matrices,
31141 \begin_inset CommandInset ref
31143 reference "sec:Matrices"
31150 \begin_layout Standard
31151 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31153 All possibilities to create commutative diagrams and decorations are explained
31158 that you find in the menu
31160 Help\SpecialChar \menuseparator
31162 \begin_inset space ~
31170 \begin_layout Subsection
31176 \begin_inset Index idx
31179 \begin_layout Plain Layout
31188 \begin_layout Standard
31193 -diagrams, the LaTeX-package
31202 -diagram is created by inserting the command
31209 Then you are able to add new matrix columns and rows like for normal matrices,
31211 \begin_inset CommandInset ref
31213 reference "sec:Matrices"
31220 \begin_layout Standard
31221 Examples how to create
31225 diagrams in LyX is given in the
31227 Feynman-diagram manual
31229 that you find in the menu
31231 Help\SpecialChar \menuseparator
31233 \begin_inset space ~
31241 \begin_layout Standard
31242 \begin_inset Newpage newpage
31248 \begin_layout Section
31249 User-defined Commands
31250 \begin_inset Index idx
31253 \begin_layout Plain Layout
31254 User-defined commands
31262 \begin_layout Standard
31263 \begin_inset Note Greyedout
31266 \begin_layout Plain Layout
31271 The names of user-defined commands and macros may only consist of Latin
31280 \begin_layout Subsection
31284 \begin_inset CommandInset label
31286 name "sub:The-Command-newcommand"
31291 \begin_inset Index idx
31294 \begin_layout Plain Layout
31295 User-defined commands !
31303 \begin_inset Index idx
31306 \begin_layout Plain Layout
31317 \begin_layout Standard
31318 Many LaTeX-commands are too long to be used frequently.
31319 But it is possible to define with the command
31325 new shorter commands.
31328 \begin_layout Standard
31329 The command scheme of
31338 \begin_layout Standard
31343 newcommand{new command name}[number of arguments][optional
31348 \begin_inset Newline newline
31352 \begin_inset Phantom HPhantom
31355 \begin_layout Plain Layout
31365 {command definition}
31368 \begin_layout Standard
31369 \begin_inset Note Greyedout
31372 \begin_layout Plain Layout
31377 Assure that the name of the new command is not already used in your document
31378 or by LaTeX-packages that you use.
31379 When you for example define the command
31391 , you get an error message because
31397 is already defined as command for
31398 \begin_inset Quotes eld
31402 \begin_inset Formula $\le$
31406 \begin_inset Quotes erd
31417 \begin_layout Standard
31418 The number of arguments is an integer in the range 0
31419 \begin_inset space \thinspace{}
31423 \begin_inset space \thinspace{}
31426 9 and specifies how many arguments the new command should have.
31427 With the optional value a value for an optional argument can be predefined.
31428 When this is done, the
31436 rgument of the new command is automatically an optional one.
31439 \begin_layout Standard
31440 Here are some examples:
31443 \begin_layout Itemize
31444 To define the command
31456 , the LaTeX-preamble line is:
31457 \begin_inset VSpace medskip
31461 \begin_inset Newline newline
31475 \begin_layout Itemize
31476 To define the command
31488 , the argument (that should be underlined) must be taken into account.
31489 For this the preamble line is:
31490 \begin_inset VSpace medskip
31494 \begin_inset Newline newline
31508 \begin_inset VSpace medskip
31512 \begin_inset Newline newline
31519 acts as argument placeholder, the
31523 behind it denotes that it is the placeholder for the first argument.
31526 \begin_layout Itemize
31534 \begin_inset space \thinspace{}
31538 \begin_inset space \space{}
31548 \begin_inset VSpace medskip
31552 \begin_inset Newline newline
31563 framebox#1#2{$#3$}}
31566 \begin_inset VSpace medskip
31570 \begin_inset Newline newline
31573 The two Dollar signs creates the extra formula needed for
31580 \begin_inset CommandInset ref
31582 reference "sub:Boxes-with-Frame"
31589 \begin_layout Itemize
31590 To create a new command for
31596 where the color for the box need not be specified, the argument for the
31597 color is defined optional:
31598 \begin_inset VSpace medskip
31602 \begin_inset Newline newline
31613 fcolorbox{#2}{#1}{$#3$}}
31616 \begin_inset VSpace medskip
31620 \begin_inset Newline newline
31623 When the color is not specified when using
31629 , the predefined color
31636 \begin_layout Standard
31637 A test of the new defined commands:
31640 \begin_layout Standard
31642 \begin_inset Tabular
31643 <lyxtabular version="3" rows="6" columns="2">
31644 <features rotate="0" tabularvalignment="middle">
31645 <column alignment="center" valignment="top">
31646 <column alignment="center" valignment="top">
31648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31651 \begin_layout Plain Layout
31657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31660 \begin_layout Plain Layout
31662 \begin_inset Note Note
31665 \begin_layout Plain Layout
31672 is only used as spacer.
31684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31687 \begin_layout Plain Layout
31691 \begin_inset space \textvisiblespace{}
31699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31702 \begin_layout Plain Layout
31703 \begin_inset Formula $A\gr B$
31713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31716 \begin_layout Plain Layout
31724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31727 \begin_layout Plain Layout
31728 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31741 \begin_layout Plain Layout
31745 \begin_inset Formula $\to$
31751 \begin_inset Formula $\to$
31759 \begin_inset space \textvisiblespace{}
31767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31770 \begin_layout Plain Layout
31771 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31784 \begin_layout Plain Layout
31788 \begin_inset Formula $\to$
31796 \begin_inset space \textvisiblespace{}
31804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31807 \begin_layout Plain Layout
31808 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31821 \begin_layout Plain Layout
31827 \begin_inset Formula $\to$
31835 \begin_inset space \textvisiblespace{}
31843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31846 \begin_layout Plain Layout
31847 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31863 \begin_layout Subsection
31865 \begin_inset Index idx
31868 \begin_layout Plain Layout
31869 User-defined commands! Math macros
31875 \begin_inset Index idx
31878 \begin_layout Plain Layout
31887 \begin_layout Standard
31888 User-defined commands are especially convenient for complex expressions.
31889 When you are for example dealing with a document that has quadratic equations,
31890 the same solution type occurs several times.
31891 The general form of a quadratic equation is
31892 \begin_inset Formula
31894 0=\lambda^{2}+p\lambda+q
31899 The general form of the solution is
31900 \begin_inset Formula
31902 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
31910 \begin_layout Standard
31911 To define a command for the solution formula where only the three parameters
31913 \begin_inset Formula $\lambda$
31917 \begin_inset Formula $p$
31921 \begin_inset Formula $q$
31924 need to be specified and the index of
31925 \begin_inset Formula $\lambda$
31928 can be given optionally, the LaTeX-preamble line is
31929 \begin_inset Newline newline
31945 \begin_inset Newline newline
31949 \begin_inset Phantom HPhantom
31952 \begin_layout Plain Layout
31966 frac{#3^{2}}{4}-#4}}
31969 \begin_layout Standard
31970 To create with this the solution formula, the command
31971 \begin_inset Newline newline
31981 \begin_inset Formula $\to$
31987 \begin_inset Formula $\to$
31994 is inserted to a formula
31999 \begin_layout Standard
32000 The definition of the new command is unintuitive because one has to know
32001 the schemes of all used LaTeX commands, e.
32002 \begin_inset space \thinspace{}
32006 \begin_inset space \space{}
32009 that a fraction is inserted in LaTeX as
32013 frac{numerator}{denominator}
32016 Furthermore one can easily forget a brace in the definition and cannot
32017 see in LyX what the new command is doing.
32018 To avoid these problems LyX offers the possibility to use math macros instead
32028 \begin_layout Standard
32029 A math macro is created by using the menu
32031 Insert\SpecialChar \menuseparator
32032 Math\SpecialChar \menuseparator
32035 or the toolbar button
32036 \begin_inset Graphics
32037 filename ../images/math-macro_newmacroname_newcommand.png
32043 The math macro toolbar appears together with the following box where the
32045 \begin_inset Newline newline
32049 \begin_inset space \hspace*{\fill}
32053 \begin_inset Graphics
32054 filename clipart/macrobox.png
32059 \begin_inset space \hspace*{\fill}
32063 \begin_inset Newline newline
32067 \begin_inset FormulaMacro
32068 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
32073 newmacroname is the default name of the macro that should be changed to
32074 something sensible.
32075 The wanted formula is inserted in the first blue box.
32076 An argument placeholder is inserted with the command
32083 \begin_inset space \thinspace{}
32087 \begin_inset space \space{}
32096 or by using the macro toolbar button
32097 \begin_inset Graphics
32098 filename ../images/math-macro-add-param.png
32104 Argument placeholders are displayed red.
32106 \begin_inset space ~
32109 arguments are possible.
32110 Optional arguments are created with the toolbar button
32111 \begin_inset Graphics
32112 filename ../images/math-macro-add-optional-param.png
32118 The first non-optional argument can be transformed to an optional one with
32120 \begin_inset Graphics
32121 filename ../images/math-macro-make-optional.png
32127 In the second blue box the appearance of the macro in LyX can be defined.
32128 Normally you want to see it as it is defined, so the box is kept empty.
32129 But when you have created a macro that needs lot of space on the screen,
32130 you can insert in the box for example
32131 \begin_inset Newline newline
32161 \begin_inset Newline newline
32166 For the macro only the arguments with the macro name in front of them will
32167 then be displayed in LyX, leading to a better overview.
32168 The formula appears in the output as defined in the first box.
32169 \begin_inset Newline newline
32172 The appearance of macros in formulas can furthermore be changed for single
32173 macros by setting the cursor in the macro and using the menu
32175 View\SpecialChar \menuseparator
32177 \begin_inset space ~
32181 \begin_inset space ~
32189 \begin_layout Standard
32190 To use a macro, the macro name is inserted as command to a formula, in our
32198 Our macro looks in LyX like this:
32199 \begin_inset Newline newline
32203 \begin_inset space \hspace*{\fill}
32207 \begin_inset Graphics
32208 filename clipart/macrouse.png
32213 \begin_inset space \hspace*{\fill}
32217 \begin_inset Newline newline
32220 Here is our macro example with the arguments
32221 \begin_inset Formula $x$
32225 \begin_inset Formula $\ln(x)$
32229 \begin_inset Formula $B$
32235 \begin_layout Standard
32236 \begin_inset Formula
32246 \begin_layout Standard
32247 LyX offers in the menu
32249 Tools\SpecialChar \menuseparator
32250 Preferences\SpecialChar \menuseparator
32251 Editing\SpecialChar \menuseparator
32254 different styles to edit macros.
32255 To find the style that suits you the most, choose a style and set the cursor
32256 in a macro formula to see the difference.
32259 \begin_layout Standard
32260 A math macro is transformed internally to a
32266 command when exporting the document.
32273 command is not placed in the LaTeX-preamble, therefore macros can only
32274 be used in formulas that are in the document below the macro definition
32278 \begin_layout Standard
32279 Math macros can also be directly created from a
32286 When writing for example the command
32289 \begin_inset Newline newline
32298 xleftarrow[#2]{#1}}
32299 \begin_inset Newline newline
32304 in LyX as normal text, highlighting it completely and using then the shortcut
32309 , the command will be transformed to a math macro.
32310 Using this method you need to be careful that the
32316 command is typed correctly, otherwise you get a faulty macro leading to
32320 \begin_layout Standard
32321 Math macros currently have the problem that further formulas in macro definition
32322 s are handled wrongly.
32323 Therefore the example
32330 \begin_inset CommandInset ref
32332 reference "sub:The-Command-newcommand"
32336 cannot be created as macro.
32339 \begin_layout Standard
32340 When the cursor is in a macro definition box, you will see the macro toolbar
32344 \begin_layout Standard
32345 \begin_inset VSpace defskip
32351 \begin_layout Standard
32352 \begin_inset Graphics
32353 filename clipart/MacroToolbar.png
32358 \begin_inset Index idx
32361 \begin_layout Plain Layout
32370 \begin_layout Standard
32371 \begin_inset VSpace defskip
32377 \begin_layout Standard
32378 The macro toolbar contains from left to right the following buttons:
32381 \begin_layout Standard
32382 \begin_inset VSpace defskip
32388 \begin_layout Standard
32389 \begin_inset Tabular
32390 <lyxtabular version="3" rows="9" columns="2">
32391 <features rotate="0" islongtable="true" longtabularalignment="center">
32392 <column alignment="left" valignment="top">
32393 <column alignment="left" valignment="top" width="85col%">
32394 <row interlinespace="2.5mm">
32395 <cell alignment="center" valignment="top" usebox="none">
32398 \begin_layout Plain Layout
32399 \begin_inset Graphics
32400 filename ../images/math-macro-remove-param.png
32401 rotateOrigin center
32410 <cell alignment="center" valignment="top" usebox="none">
32413 \begin_layout Plain Layout
32416 Edit\SpecialChar \menuseparator
32417 Math\SpecialChar \menuseparator
32419 \begin_inset space ~
32422 Definition\SpecialChar \menuseparator
32423 Remove Last Argument
32429 <row interlinespace="2.5mm">
32430 <cell alignment="center" valignment="top" usebox="none">
32433 \begin_layout Plain Layout
32434 \begin_inset Graphics
32435 filename ../images/math-macro-add-param.png
32436 rotateOrigin center
32445 <cell alignment="center" valignment="top" usebox="none">
32448 \begin_layout Plain Layout
32451 Edit\SpecialChar \menuseparator
32452 Math\SpecialChar \menuseparator
32454 \begin_inset space ~
32457 Definition\SpecialChar \menuseparator
32464 <row interlinespace="2.5mm">
32465 <cell alignment="center" valignment="top" usebox="none">
32468 \begin_layout Plain Layout
32469 \begin_inset Graphics
32470 filename ../images/math-macro-make-optional.png
32471 rotateOrigin center
32480 <cell alignment="center" valignment="top" usebox="none">
32483 \begin_layout Plain Layout
32486 Edit\SpecialChar \menuseparator
32487 Math\SpecialChar \menuseparator
32489 \begin_inset space ~
32492 Definition\SpecialChar \menuseparator
32493 Make First Non-Optional into
32494 \begin_inset Newline newline
32498 \begin_inset Phantom HPhantom
32501 \begin_layout Plain Layout
32504 Edit\SpecialChar \menuseparator
32505 Math\SpecialChar \menuseparator
32507 \begin_inset space ~
32510 Definition\SpecialChar \menuseparator
32522 <row interlinespace="2.5mm">
32523 <cell alignment="center" valignment="top" usebox="none">
32526 \begin_layout Plain Layout
32527 \begin_inset Graphics
32528 filename ../images/math-macro-make-nonoptional.png
32529 rotateOrigin center
32538 <cell alignment="center" valignment="top" usebox="none">
32541 \begin_layout Plain Layout
32544 Edit\SpecialChar \menuseparator
32545 Math\SpecialChar \menuseparator
32547 \begin_inset space ~
32550 Definition\SpecialChar \menuseparator
32551 Make Last Optional into
32552 \begin_inset Newline newline
32556 \begin_inset Phantom HPhantom
32559 \begin_layout Plain Layout
32562 Edit\SpecialChar \menuseparator
32563 Math\SpecialChar \menuseparator
32565 \begin_inset space ~
32568 Definition\SpecialChar \menuseparator
32574 Non-Optional Argument
32580 <row interlinespace="2.5mm">
32581 <cell alignment="center" valignment="top" usebox="none">
32584 \begin_layout Plain Layout
32585 \begin_inset Graphics
32586 filename ../images/math-macro-remove-optional-param.png
32587 rotateOrigin center
32596 <cell alignment="center" valignment="top" usebox="none">
32599 \begin_layout Plain Layout
32602 Edit\SpecialChar \menuseparator
32603 Math\SpecialChar \menuseparator
32605 \begin_inset space ~
32608 Definition\SpecialChar \menuseparator
32609 Remove Optional Argument
32615 <row interlinespace="2.5mm">
32616 <cell alignment="center" valignment="top" usebox="none">
32619 \begin_layout Plain Layout
32620 \begin_inset Graphics
32621 filename ../images/math-macro-add-optional-param.png
32622 rotateOrigin center
32631 <cell alignment="center" valignment="top" usebox="none">
32634 \begin_layout Plain Layout
32637 Edit\SpecialChar \menuseparator
32638 Math\SpecialChar \menuseparator
32640 \begin_inset space ~
32643 Definition\SpecialChar \menuseparator
32644 Insert Optional Argument
32650 <row interlinespace="2.5mm">
32651 <cell alignment="center" valignment="top" usebox="none">
32654 \begin_layout Plain Layout
32655 \begin_inset Graphics
32656 filename ../images/math-macro-remove-greedy-param.png
32657 rotateOrigin center
32666 <cell alignment="center" valignment="top" usebox="none">
32669 \begin_layout Plain Layout
32672 Edit\SpecialChar \menuseparator
32673 Math\SpecialChar \menuseparator
32675 \begin_inset space ~
32678 Definition\SpecialChar \menuseparator
32679 Remove Last Argument
32680 \begin_inset Newline newline
32684 \begin_inset Phantom HPhantom
32687 \begin_layout Plain Layout
32690 Edit\SpecialChar \menuseparator
32691 Math\SpecialChar \menuseparator
32693 \begin_inset space ~
32696 Definition\SpecialChar \menuseparator
32702 Spitting Out To The Right
32708 <row interlinespace="2.5mm">
32709 <cell alignment="center" valignment="top" usebox="none">
32712 \begin_layout Plain Layout
32713 \begin_inset Graphics
32714 filename ../images/math-macro-append-greedy-param.png
32715 rotateOrigin center
32724 <cell alignment="center" valignment="top" usebox="none">
32727 \begin_layout Plain Layout
32730 Edit\SpecialChar \menuseparator
32731 Math\SpecialChar \menuseparator
32733 \begin_inset space ~
32736 Definition\SpecialChar \menuseparator
32738 \begin_inset Newline newline
32742 \begin_inset Phantom HPhantom
32745 \begin_layout Plain Layout
32748 Edit\SpecialChar \menuseparator
32749 Math\SpecialChar \menuseparator
32751 \begin_inset space ~
32754 Definition\SpecialChar \menuseparator
32760 Eating From The Right
32766 <row interlinespace="2.5mm">
32767 <cell alignment="center" valignment="top" usebox="none">
32770 \begin_layout Plain Layout
32771 \begin_inset Graphics
32772 filename ../images/math-macro-add-greedy-optional-param.png
32773 rotateOrigin center
32782 <cell alignment="center" valignment="top" usebox="none">
32785 \begin_layout Plain Layout
32788 Edit\SpecialChar \menuseparator
32789 Math\SpecialChar \menuseparator
32791 \begin_inset space ~
32794 Definition\SpecialChar \menuseparator
32795 Append Optional Argument
32796 \begin_inset Newline newline
32800 \begin_inset Phantom HPhantom
32803 \begin_layout Plain Layout
32806 Edit\SpecialChar \menuseparator
32807 Math\SpecialChar \menuseparator
32809 \begin_inset space ~
32812 Definition\SpecialChar \menuseparator
32818 Eating From The Right
32831 \begin_layout Section
32832 Computer Algebra Systems
32835 \begin_layout Standard
32836 LyX offers the exchange between mathematical expressions written in LyX's
32837 math editor and external applications or user defined scripts.
32838 Currently supported applications are
32855 Note that the set of supported mathematical constructs is limited only
32856 to very simple cases.
32859 \begin_layout Subsection
32863 \begin_layout Standard
32864 Write some expression in a formula, go to the
32866 Edit\SpecialChar \menuseparator
32867 Math\SpecialChar \menuseparator
32868 Use Computer Algebra System
32870 menu and choose the application you have installed on the computer.
32871 After that the result of computation should show on the right side of the
32872 expression together with the
32873 \begin_inset Quotes eld
32877 \begin_inset Quotes erd
32883 \begin_layout Standard
32884 Here are few simple examples (with results from
32888 ) to show what kind of computations can be performed:
32891 \begin_layout Itemize
32892 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
32898 \begin_layout Itemize
32899 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
32905 \begin_layout Itemize
32906 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
32912 \begin_layout Itemize
32913 \begin_inset Formula $\det\left[\begin{array}{ccc}
32917 \end{array}\right]=-56$
32923 \begin_layout Itemize
32924 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
32930 \begin_layout Subsection
32934 \begin_layout Standard
32935 Currently there is no keyboard shortcut for calling the algebra applications.
32936 One can easily bind a shortcut to the
32940 LyX function (see the
32948 \begin_inset space \thinspace{}
32952 \begin_inset space \space{}
32959 key inside the math editor.
32964 one would use this shortcut definition command:
32967 \begin_layout Standard
32970 command-alternatives break-paragraph;math-extern maxima
32973 \begin_layout Section
32975 \begin_inset Index idx
32978 \begin_layout Plain Layout
32987 \begin_layout Subsection
32989 \begin_inset Index idx
32992 \begin_layout Plain Layout
33001 \begin_layout Standard
33002 Negative numbers often look ugly in formulas because the minus sign before
33003 the number is set with the same length as the minus operator sign.
33004 When writing the negative number in normal text, the minus sign appears
33008 \begin_layout Standard
33009 Thus, the problem disappears when converting the minus sign to mathematical
33013 \begin_layout Standard
33014 An example to visualize the problem:
33017 \begin_layout Standard
33019 \begin_inset Tabular
33020 <lyxtabular version="3" rows="3" columns="2">
33021 <features rotate="0" tabularvalignment="middle">
33022 <column alignment="right" valignment="top">
33023 <column alignment="left" valignment="top">
33025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33028 \begin_layout Plain Layout
33034 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33037 \begin_layout Plain Layout
33045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33048 \begin_layout Plain Layout
33054 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33057 \begin_layout Plain Layout
33058 \begin_inset Formula $x=-2$
33068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33071 \begin_layout Plain Layout
33077 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33080 \begin_layout Plain Layout
33081 \begin_inset Formula $x=\textrm{-}2$
33097 \begin_layout Subsection
33098 Comma as decimal Separator
33099 \begin_inset Index idx
33102 \begin_layout Plain Layout
33111 \begin_layout Standard
33112 In LaTeX a comma inside a formula is used, according to the English convention,
33113 as number group separator.
33114 So there will be space added behind all commas in formulas.
33117 \begin_layout Standard
33118 To avoid this, the comma is highlighted and changed to mathematical text
33128 \begin_layout Standard
33129 To use all formula commas in the document as decimal separator, the file
33138 \begin_layout Plain Layout
33143 is part of the LaTeX-package
33148 \begin_inset Index idx
33151 \begin_layout Plain Layout
33156 \begin_layout Plain Layout
33176 \begin_inset Index idx
33179 \begin_layout Plain Layout
33185 is loaded with the LaTeX-preamble line
33188 \begin_layout Standard
33196 \begin_layout Subsection
33198 \begin_inset CommandInset label
33200 name "sub:Physical-Vectors"
33205 \begin_inset Index idx
33208 \begin_layout Plain Layout
33217 \begin_layout Standard
33218 Predefined vectors are offered by the LaTeX-package
33223 \begin_inset Index idx
33226 \begin_layout Plain Layout
33232 that is loaded with the LaTeX-preamble line
33235 \begin_layout Standard
33243 \begin_layout Standard
33247 \begin_layout Plain Layout
33257 \begin_inset Note Note
33260 \begin_layout Plain Layout
33261 The following table will only be displayed when the LaTeX-package
33273 \begin_layout Standard
33274 The following commands are defined:
33277 \begin_layout Standard
33279 \begin_inset Tabular
33280 <lyxtabular version="3" rows="4" columns="2">
33281 <features rotate="0" tabularvalignment="middle">
33282 <column alignment="center" valignment="top">
33283 <column alignment="center" valignment="top">
33285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33288 \begin_layout Plain Layout
33294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33297 \begin_layout Plain Layout
33305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33308 \begin_layout Plain Layout
33318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33321 \begin_layout Plain Layout
33322 \begin_inset Formula $\Bra{\psi}$
33332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33335 \begin_layout Plain Layout
33345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33348 \begin_layout Plain Layout
33349 \begin_inset Formula $\Ket{\psi}$
33359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33362 \begin_layout Plain Layout
33374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33377 \begin_layout Plain Layout
33378 \begin_inset Formula $\Braket{\psi|\phi}$
33394 \begin_layout Standard
33401 assures that all vertical bars are set in the size of the surrounding brackets:
33402 \begin_inset Formula
33404 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
33413 \begin_layout Plain Layout
33423 \begin_inset Note Note
33426 \begin_layout Plain Layout
33427 The following will be displayed when the LaTeX-package
33439 \begin_layout Standard
33440 You need to install the LaTeX-package
33444 to see the rest of this subsection in the output.
33447 \begin_layout Standard
33451 \begin_layout Plain Layout
33463 \begin_layout Standard
33470 can also be achieved using the command
33476 , that is described in
33477 \begin_inset CommandInset ref
33479 reference "sub:Automatic-Bracket-Size"
33486 \begin_layout Subsection
33487 Self-defined Fractions
33488 \begin_inset CommandInset label
33490 name "sub:Self-defined-Fractions"
33495 \begin_inset Index idx
33498 \begin_layout Plain Layout
33499 Fractions ! self-defined
33507 \begin_layout Standard
33508 To define custom commands for fractions, the command
33515 \begin_inset Index idx
33518 \begin_layout Plain Layout
33525 \begin_layout Plain Layout
33539 is used in the following scheme:
33542 \begin_layout Standard
33555 bracket}{fraction bar thickness}{style}
33556 \begin_inset Newline newline
33560 \begin_inset Phantom HPhantom
33563 \begin_layout Plain Layout
33573 {numerator}{denominator}
33576 \begin_layout Standard
33577 The style is a number in the range of 0
33578 \begin_inset space \thinspace{}
33582 \begin_inset space \thinspace{}
33588 \begin_layout Standard
33590 \begin_inset Tabular
33591 <lyxtabular version="3" rows="5" columns="2">
33592 <features rotate="0" tabularvalignment="middle">
33593 <column alignment="center" valignment="top">
33594 <column alignment="center" valignment="top">
33596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33599 \begin_layout Plain Layout
33605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33608 \begin_layout Plain Layout
33616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33619 \begin_layout Plain Layout
33625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33628 \begin_layout Plain Layout
33629 display style formula
33636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33639 \begin_layout Plain Layout
33645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33648 \begin_layout Plain Layout
33656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33659 \begin_layout Plain Layout
33665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33668 \begin_layout Plain Layout
33676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33679 \begin_layout Plain Layout
33685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33688 \begin_layout Plain Layout
33702 \begin_layout Standard
33703 When no style is given, the size is adjusted to the surrounding environment
33704 like for the command
33713 \begin_layout Standard
33714 When no fraction bar thickness is given, the predefined value of 0.4
33715 \begin_inset space \thinspace{}
33721 \begin_layout Standard
33722 \begin_inset VSpace medskip
33725 For example, the commands
33738 \begin_inset CommandInset ref
33740 reference "sub:Fractions"
33744 are defined with the commands
33747 \begin_layout Standard
33756 genfrac{}{}{}{0}{#1}{#2}}
33759 \begin_layout Standard
33763 \begin_layout Standard
33772 genfrac{(}{)}{0pt}{1}{#1}{#2}}
33775 \begin_layout Standard
33776 \begin_inset VSpace medskip
33779 To define a fraction where the fraction bar thickness can be given as optional
33780 argument, the following line is inserted to the LaTeX-preamble:
33783 \begin_layout Standard
33792 genfrac{}{}{#1}{}{#2}{#3}}
33795 \begin_layout Standard
33797 \begin_inset Formula
33799 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
33800 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
33805 As one can see, the distance of the numerator and the denominator to the
33806 fraction bar is round about three times the bar thickness.
33809 \begin_layout Subsection
33811 \begin_inset Index idx
33814 \begin_layout Plain Layout
33823 \begin_layout Standard
33824 There are four ways to cancel formulas or parts of formulas:
33827 \begin_layout Standard
33831 \begin_layout Plain Layout
33841 \begin_inset Note Note
33844 \begin_layout Plain Layout
33845 The following table will only be displayed when the LaTeX-package
33857 \begin_layout Standard
33859 \begin_inset Tabular
33860 <lyxtabular version="3" rows="5" columns="2">
33861 <features rotate="0" tabularvalignment="middle">
33862 <column alignment="center" valignment="top">
33863 <column alignment="center" valignment="top">
33865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33868 \begin_layout Plain Layout
33874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33877 \begin_layout Plain Layout
33879 \begin_inset Note Note
33882 \begin_layout Plain Layout
33889 are used here as spacer.
33901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33904 \begin_layout Plain Layout
33908 \begin_inset space \textvisiblespace{}
33914 \begin_inset space \textvisiblespace{}
33922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33925 \begin_layout Plain Layout
33926 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33939 \begin_layout Plain Layout
33943 \begin_inset space \textvisiblespace{}
33949 \begin_inset space \textvisiblespace{}
33957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33960 \begin_layout Plain Layout
33961 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33974 \begin_layout Plain Layout
33978 \begin_inset space \textvisiblespace{}
33984 \begin_inset space \textvisiblespace{}
33992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33995 \begin_layout Plain Layout
33996 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
34006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34009 \begin_layout Plain Layout
34013 \begin_inset space \textvisiblespace{}
34019 \begin_inset space \textvisiblespace{}
34023 \begin_inset Formula $\to$
34031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34034 \begin_layout Plain Layout
34035 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34051 \begin_layout Standard
34058 is especially suitable to visualize the reduction of fractions within formulas:
34059 \begin_inset Formula
34061 \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}}}
34069 \begin_layout Standard
34070 To change the size of
34077 \begin_inset Quotes eld
34081 \begin_inset Quotes erd
34084 value one can add the LaTeX-preamble line
34087 \begin_layout Standard
34092 PassOptionsToPackage{option}{cancel}
34095 \begin_layout Standard
34104 which leads to the same size as for the canceled value, or
34108 which makes is it a bit smaller than normal.
34111 \begin_layout Standard
34112 To color the cancellation bar one adds this command as TeX code:
34115 \begin_layout Standard
34127 \begin_layout Standard
34132 can be replaced by a color of your choice.
34135 \begin_layout Standard
34139 \begin_layout Plain Layout
34155 \begin_layout Standard
34156 \begin_inset Formula
34158 \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}}}
34166 \begin_layout Standard
34170 \begin_layout Plain Layout
34184 \begin_inset Note Note
34187 \begin_layout Plain Layout
34196 \begin_layout Standard
34197 For further customizations, see the documentation of the package
34202 \begin_inset CommandInset citation
34209 \begin_inset Index idx
34212 \begin_layout Plain Layout
34221 \begin_layout Standard
34225 \begin_layout Plain Layout
34235 \begin_inset Note Note
34238 \begin_layout Plain Layout
34239 The following will be displayed when the LaTeX-package
34251 \begin_layout Standard
34252 You need to install the LaTeX-package
34256 to see the rest of this subsection in the output.
34259 \begin_layout Standard
34263 \begin_layout Plain Layout
34275 \begin_layout Standard
34276 \begin_inset Newpage newpage
34282 \begin_layout Subsection
34283 Formulas in Section Headings
34284 \begin_inset CommandInset label
34286 name "sub:Formulas-in-Section"
34291 \begin_inset Index idx
34294 \begin_layout Plain Layout
34295 Formula ! in section headings
34303 \begin_layout Standard
34304 When formulas are used in section headings, the following has to be taken
34308 \begin_layout Standard
34309 \begin_inset Note Greyedout
34312 \begin_layout Plain Layout
34318 \begin_inset Index idx
34321 \begin_layout Plain Layout
34322 Packages ! hyperref
34327 support is enabled in the document settings dialog under
34330 \begin_inset space ~
34335 , PDF-bookmarks are created for every section heading in the table of contents.
34336 If a section heading contains formulas, they are incorrectly displayed
34337 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34346 \begin_layout Standard
34347 Both problems can be solved by inserting at the end of the section heading
34348 a short title with the menu
34350 Insert\SpecialChar \menuseparator
34352 \begin_inset space ~
34358 Short titles are used as alternative for multiline section headings to
34359 keep the table of contents clearly arranged.
34360 Only the short title appears in the table of contents and therefore also
34361 in the PDF-bookmark.
34364 \begin_layout Standard
34365 When formulas should be used in the table of contents but
34369 is used, one can use the following command in TeX-mode:
34372 \begin_layout Standard
34377 texorpdfstring{part}{alternative}
34378 \begin_inset Index idx
34381 \begin_layout Plain Layout
34392 \begin_layout Standard
34393 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34394 This can be characters, formulas, footnotes, but also cross-references.
34395 The alternative is used instead of the part for the bookmark.
34398 \begin_layout Standard
34399 Here are two example headings:
34400 \begin_inset VSpace -3mm
34407 \begin_layout Plain Layout
34419 \begin_layout Subsubsection
34420 Heading without formula in table of contents
34421 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34425 \begin_inset Argument 1
34428 \begin_layout Plain Layout
34429 Heading without formula in table of contents
34437 \begin_layout Subsubsection
34438 Heading with formula in table of contents
34442 \begin_layout Plain Layout
34452 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34459 \begin_layout Plain Layout
34469 \begin_layout Standard
34473 \begin_layout Plain Layout
34482 In the first heading a short title was used, in the second one
34491 \begin_layout Standard
34492 To get the same formatting as for the other headings, the complete heading
34501 \begin_layout Plain Layout
34503 \begin_inset CommandInset ref
34505 reference "sub:Bold-Formulas"
34517 \begin_layout Subsection
34518 Formulas in multi-column Text
34519 \begin_inset Index idx
34522 \begin_layout Plain Layout
34523 Formula ! in multi-column text
34531 \begin_layout Standard
34532 Formulas in multi-column text are often too wide to fit into a column and
34533 thus need to be set over the whole page width.
34534 This is done by using the LaTeX-package
34542 \begin_layout Plain Layout
34547 is part of every LaTeX standard installation.
34553 \begin_inset Index idx
34556 \begin_layout Plain Layout
34557 Packages ! multicol
34562 , that is loaded with the LaTeX-preamble line
34565 \begin_layout Standard
34570 usepackage{multicol}
34573 \begin_layout Standard
34574 \begin_inset Note Greyedout
34577 \begin_layout Plain Layout
34578 Note that in this case the setting
34581 \begin_inset space ~
34588 Document\SpecialChar \menuseparator
34594 \begin_inset space ~
34614 \begin_layout Standard
34615 Before the multi-column text the command
34618 \begin_layout Standard
34623 begin{multicols}{column number}
34626 \begin_layout Standard
34627 is written in TeX-mode.
34628 The column number is a number in the range of 2
34629 \begin_inset space \thinspace{}
34633 \begin_inset space \thinspace{}
34637 Before the formula the multi-column text is ended by inserting the command
34640 \begin_layout Standard
34648 \begin_layout Standard
34652 \begin_layout Standard
34653 Due to the command some space is automatically added before the formula.
34655 \begin_inset space \thinspace{}
34658 mm vertical space is inserted before the formula.
34659 When the formula style
34665 \begin_layout Plain Layout
34667 \begin_inset CommandInset ref
34669 reference "sec:Formula-Styles"
34681 \begin_inset space \thinspace{}
34684 mm space is inserted instead.
34687 \begin_layout Standard
34688 As example a multi-column text with a displayed formula:
34691 \begin_layout Standard
34697 \begin_layout Plain Layout
34701 begin{multicols}{2}
34706 Das Spektrum wird fouriertransformiert.
34707 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
34708 , Lösungsmittel) zu trennen.
34709 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
34710 nun das Aussehen des Ausgangssignals.
34711 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
34712 über alle Phasen integrieren muss.
34714 \begin_inset Formula $S$
34717 unser normiertes Ausgangssignal und
34718 \begin_inset Formula $P$
34721 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
34725 \begin_layout Plain Layout
34735 \begin_inset VSpace -6mm
34739 \begin_inset Formula
34741 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
34750 \begin_layout Plain Layout
34754 begin{multicols}{2}
34760 \begin_inset Formula $S_{0}$
34763 das Signal ohne Gradient ist und die Normierungsbedingung
34764 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
34768 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
34770 \begin_inset Formula $\nicefrac{\pi}{2}$
34774 \begin_inset space \thinspace{}
34777 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
34778 das Signal zusätzlich abschwächt.
34779 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
34781 \begin_inset Formula $T_{2}$
34787 \begin_layout Standard
34793 \begin_layout Plain Layout
34805 \begin_layout Subsection
34806 Formulas with Description of Variables
34807 \begin_inset Index idx
34810 \begin_layout Plain Layout
34811 Formula ! with description of variables
34819 \begin_layout Standard
34820 To describe variables within a formula, like in formula
34821 \begin_inset CommandInset ref
34823 reference "eq:within"
34832 \begin_inset Formula $n$
34836 \begin_inset space ~
34839 matrix is used with left aligned columns for the
34840 \begin_inset Formula $n$
34847 \begin_layout Plain Layout
34849 \begin_inset CommandInset ref
34851 reference "sec:Matrices"
34860 To set the description in a smaller size, before the matrix e.
34861 \begin_inset space \thinspace{}
34865 \begin_inset space \space{}
34878 \begin_layout Plain Layout
34880 \begin_inset CommandInset ref
34882 reference "sub:Font-Sizes"
34894 \begin_layout Standard
34895 When the formula style
34901 \begin_layout Plain Layout
34903 \begin_inset CommandInset ref
34905 reference "sec:Formula-Styles"
34926 \begin_layout Plain Layout
34933 only works in formulas with the style
34938 \begin_inset CommandInset ref
34940 reference "sub:Variable-Space"
34949 is inserted before and after the matrix to have the same separation of
34950 the matrix from the equation and the side margin.
34953 \begin_layout Standard
34954 When the formula style
34958 is used, the method described in
34959 \begin_inset CommandInset ref
34961 reference "sub:Flalign-Environment"
34965 is used to indent formulas.
34967 \begin_inset CommandInset ref
34969 reference "eq:within"
34973 consists of five columns where in the first two columns contain the equation,
34974 the third the matrix and the last one an empty TeX-brace.
34975 \begin_inset Formula
34977 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
34978 \rho & \textrm{density}\\
34979 V & \textrm{volume}\\
34980 g & \textrm{gravitational acceleration}
34981 \end{array} & & {}\label{eq:within}
34989 \begin_layout Subsection
34990 Upright small Greek Letters
34991 \begin_inset CommandInset label
34993 name "sub:Upright-small-Greek"
34998 \begin_inset Index idx
35001 \begin_layout Plain Layout
35002 Greek letters ! upright
35010 \begin_layout Standard
35011 Most of the math fonts only provide italic small Greek letters.
35012 But for symbols of elementary particles like pions and neutrinos, upright
35013 Greek letters are needed.
35022 \begin_layout Plain Layout
35027 is part of the LaTeX-package
35032 \begin_inset Index idx
35035 \begin_layout Plain Layout
35040 \begin_layout Plain Layout
35060 \begin_inset Index idx
35063 \begin_layout Plain Layout
35069 that is loaded with the LaTeX-preamble line
35072 \begin_layout Standard
35077 usepackage{upgreek}
35080 \begin_layout Standard
35086 \begin_layout Plain Layout
35096 \begin_inset Note Note
35099 \begin_layout Plain Layout
35100 The following table will only be displayed when the LaTeX-package
35109 They are created when the command for a small Greek letter is started with
35115 For example the command
35122 \begin_inset Formula $\uptau$
35128 \begin_layout Standard
35129 With these commands reactions of elementary particles can be typeset:
35130 \begin_inset Formula
35132 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
35140 \begin_layout Standard
35141 The upright letters are more bold and wider than the italic ones.
35142 They should therefore not be used for units like
35143 \begin_inset Quotes eld
35147 \begin_inset Quotes erd
35153 \begin_layout Standard
35157 \begin_layout Plain Layout
35167 \begin_inset Note Note
35170 \begin_layout Plain Layout
35171 The following will be displayed when the LaTeX-package
35183 \begin_layout Standard
35184 You need to install the LaTeX-package
35188 to see the rest of this subsection in the output.
35191 \begin_layout Standard
35195 \begin_layout Plain Layout
35207 \begin_layout Subsection
35208 Text Characters in Formulas
35209 \begin_inset CommandInset label
35211 name "sub:Text-Characters-in"
35216 \begin_inset Index idx
35219 \begin_layout Plain Layout
35228 \begin_layout Standard
35229 In some cases you might want to insert text characters directly into formulas.
35230 When for example the centered dot · is often used in formulas like
35231 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35234 , one would have to insert the command
35244 \begin_layout Plain Layout
35246 \begin_inset CommandInset ref
35248 reference "sub:Binary-Operators"
35257 all the time, because this character is defined in all encodings as text
35259 But the encoding can be changed by this LaTeX-preamble line:
35262 \begin_layout Standard
35267 Declare Inputtext{183}{
35277 f\SpecialChar \textcompwordmark{}
35281 \begin_layout Standard
35282 The character encoding (menu
35284 Document\SpecialChar \menuseparator
35285 Settings\SpecialChar \menuseparator
35288 ) specifies what character appears when a keyboard key is pressed.
35289 When the key for the character '·' is pressed, internally the command
35296 But this command is not available in a formula so that you would get LaTeX-erro
35298 With the changed encoding the right command is chosen automatically, depending
35299 on if the character was inserted into a formula or not.
35302 \begin_layout Standard
35303 The encoding of several characters is saved in definition files.
35304 For example the encoding
35308 is defined in the file
35312 which is in the installation folder of LaTeX.
35313 Encodings should only be changed via the LaTeX-preamble and not in the
35315 Otherwise documents could not be edited by other LyX users working on other
35319 \begin_layout Standard
35320 \begin_inset VSpace medskip
35323 Besides the centered dot, in this document the degree sign ° is defined
35324 with the following LaTeX-preamble line so that it can be directly inserted
35328 \begin_layout Standard
35333 DeclareInputtext{176}{
35343 f\SpecialChar \textcompwordmark{}
35347 \begin_layout Standard
35348 \begin_inset Newpage newpage
35354 \begin_layout Section
35357 \begin_inset Index idx
35360 \begin_layout Plain Layout
35369 \begin_layout Standard
35370 This section is a summary of the most important typographic rules, listed
35375 \begin_layout Plain Layout
35376 This collection was partly taken from the German semi-official dictionary
35378 \begin_inset Quotes eld
35382 \begin_inset Quotes erd
35386 \begin_inset CommandInset citation
35392 that lists some of the ISO rules.
35393 More rules are listed in
35394 \begin_inset CommandInset citation
35408 \begin_layout Itemize
35417 \begin_layout Plain Layout
35418 done with font styles, see
35419 \begin_inset CommandInset ref
35421 reference "sub:Font-Styles"
35430 , no matter if they appear in italic text: 30
35431 \begin_inset space \thinspace{}
35435 \begin_inset Newline newline
35438 Between the value and the unit is the smallest space, see
35439 \begin_inset CommandInset ref
35441 reference "sub:Predefined-Space"
35446 \begin_inset Newline newline
35449 This convention is automatically fulfilled when the command
35456 When it is entered to a formula, two boxes appear.
35457 In the first one the value is inserted, in the second one the unit, and
35459 \begin_inset Formula $\unit[30]{km/h}$
35463 \begin_inset space \thinspace{}
35473 is not a real LaTeX command but the command
35479 , therefore you cannot use it in TeX code.
35482 \begin_layout Itemize
35483 Percent and perthousand signs are set like physical units:
35484 \begin_inset Newline newline
35488 \begin_inset space \thinspace{}
35494 \begin_layout Itemize
35495 The degree sign follows directly on the value: 15°, but not when it is used
35497 \begin_inset space \thinspace{}
35503 \begin_layout Itemize
35504 In numbers with more than four digits the smallest space is inserted before
35505 every third digit to group them:
35515 \begin_inset space \thinspace{}
35519 \begin_inset space \thinspace{}
35525 \begin_layout Itemize
35526 For dimensions like 120×90×40
35527 \begin_inset space \thinspace{}
35530 cm the multiplication sign
35531 \begin_inset Quotes eld
35535 \begin_inset Quotes erd
35539 It is available either via the command
35547 Insert\SpecialChar \menuseparator
35548 Special Character\SpecialChar \menuseparator
35554 \begin_layout Itemize
35555 Functions with names consisting of several letters are set upright to avoid
35557 \begin_inset CommandInset ref
35559 reference "sub:Predefined-Functions"
35566 \begin_layout Itemize
35567 Indices consisting of several letters, are set upright:
35568 \begin_inset Formula $E_{\mathrm{kin}}$
35572 \begin_inset Newline newline
35575 Components of matrices are set italic:
35576 \begin_inset Formula $\hat{H}_{kl}$
35582 \begin_layout Itemize
35583 The differentiation/integration operator 'd', the Euler's number 'e' and
35584 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35588 \begin_layout Itemize
35589 The character that denotes a
35593 transformation is inserted either by the command
35598 \begin_inset space \textvisiblespace{}
35605 Insert\SpecialChar \menuseparator
35606 Special Character\SpecialChar \menuseparator
35607 Symbols\SpecialChar \menuseparator
35609 \begin_inset space ~
35615 \begin_inset Formula $\mathscr{F}$
35621 \begin_layout Standard
35622 \begin_inset Newpage newpage
35628 \begin_layout Section
35630 \begin_inset Index idx
35633 \begin_layout Plain Layout
35642 \begin_layout Standard
35643 Some characters and symbols can be created with several commands.
35644 Here is a list of the synonym commands:
35647 \begin_layout Standard
35648 \begin_inset VSpace bigskip
35652 \begin_inset space \hfill{}
35656 \begin_inset Tabular
35657 <lyxtabular version="3" rows="12" columns="2">
35658 <features rotate="0" tabularvalignment="middle">
35659 <column alignment="center" valignment="top" width="0pt">
35660 <column alignment="center" valignment="top" width="0pt">
35662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35665 \begin_layout Plain Layout
35671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35674 \begin_layout Plain Layout
35676 \begin_inset Note Note
35679 \begin_layout Plain Layout
35686 is only used as spacer.
35698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35701 \begin_layout Plain Layout
35709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35712 \begin_layout Plain Layout
35716 \begin_layout Plain Layout
35729 \begin_layout Plain Layout
35743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35746 \begin_layout Plain Layout
35754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35757 \begin_layout Plain Layout
35767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35770 \begin_layout Plain Layout
35778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35781 \begin_layout Plain Layout
35791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35794 \begin_layout Plain Layout
35802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35805 \begin_layout Plain Layout
35813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35816 \begin_layout Plain Layout
35824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35827 \begin_layout Plain Layout
35835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35838 \begin_layout Plain Layout
35846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35849 \begin_layout Plain Layout
35859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35862 \begin_layout Plain Layout
35870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35873 \begin_layout Plain Layout
35883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35886 \begin_layout Plain Layout
35894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35897 \begin_layout Plain Layout
35907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35910 \begin_layout Plain Layout
35918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35921 \begin_layout Plain Layout
35931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35934 \begin_layout Plain Layout
35942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35945 \begin_layout Plain Layout
35953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35956 \begin_layout Plain Layout
35964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35967 \begin_layout Plain Layout
35979 \begin_inset space \hfill{}
35983 \begin_inset Tabular
35984 <lyxtabular version="3" rows="12" columns="2">
35985 <features rotate="0" tabularvalignment="middle">
35986 <column alignment="center" valignment="top" width="0pt">
35987 <column alignment="center" valignment="top" width="0pt">
35989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35992 \begin_layout Plain Layout
35998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36001 \begin_layout Plain Layout
36009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36012 \begin_layout Plain Layout
36020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36023 \begin_layout Plain Layout
36035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36038 \begin_layout Plain Layout
36046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36049 \begin_layout Plain Layout
36059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36062 \begin_layout Plain Layout
36070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36073 \begin_layout Plain Layout
36083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36086 \begin_layout Plain Layout
36094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36097 \begin_layout Plain Layout
36105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36108 \begin_layout Plain Layout
36116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36119 \begin_layout Plain Layout
36127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36130 \begin_layout Plain Layout
36138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36141 \begin_layout Plain Layout
36151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36154 \begin_layout Plain Layout
36162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36165 \begin_layout Plain Layout
36175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36178 \begin_layout Plain Layout
36186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36189 \begin_layout Plain Layout
36199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36202 \begin_layout Plain Layout
36210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36213 \begin_layout Plain Layout
36223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36226 \begin_layout Plain Layout
36234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36237 \begin_layout Plain Layout
36247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36250 \begin_layout Plain Layout
36258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36261 \begin_layout Plain Layout
36275 \begin_inset space \hfill{}
36281 \begin_layout Standard
36282 \begin_inset Newpage newpage
36288 \begin_layout Bibliography
36289 \begin_inset CommandInset bibitem
36290 LatexCommand bibitem
36302 The LaTeX Companion
36305 Addison Wesley, 2004
36308 \begin_layout Bibliography
36309 \begin_inset CommandInset bibitem
36310 LatexCommand bibitem
36316 \begin_inset CommandInset href
36319 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
36323 of LaTeX's math abilities
36326 \begin_layout Bibliography
36327 \begin_inset CommandInset bibitem
36328 LatexCommand bibitem
36334 \begin_inset CommandInset href
36337 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
36345 \begin_layout Plain Layout
36357 \begin_layout Bibliography
36358 \begin_inset CommandInset bibitem
36359 LatexCommand bibitem
36365 \begin_inset CommandInset href
36368 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
36372 of all symbols available with LaTeX-packages
36375 \begin_layout Bibliography
36376 \begin_inset CommandInset bibitem
36377 LatexCommand bibitem
36383 \begin_inset CommandInset href
36385 name "Documentation"
36386 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
36390 of the LaTeX-package
36395 \begin_inset Index idx
36398 \begin_layout Plain Layout
36407 \begin_layout Bibliography
36408 \begin_inset CommandInset bibitem
36409 LatexCommand bibitem
36415 \begin_inset CommandInset href
36417 name "Documentation"
36418 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
36422 of the LaTeX-package
36427 \begin_inset Index idx
36430 \begin_layout Plain Layout
36431 Packages ! hyperref
36439 \begin_layout Bibliography
36440 \begin_inset CommandInset bibitem
36441 LatexCommand bibitem
36447 \begin_inset CommandInset href
36449 name "Documentation"
36450 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
36454 of the LaTeX-package
36459 \begin_inset Index idx
36462 \begin_layout Plain Layout
36471 \begin_layout Bibliography
36472 \begin_inset CommandInset bibitem
36473 LatexCommand bibitem
36479 \begin_inset CommandInset href
36482 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
36493 \begin_inset CommandInset ref
36495 reference "sub:Operator-Limits"
36500 \begin_inset Index idx
36503 \begin_layout Plain Layout
36514 \begin_layout Bibliography
36515 \begin_inset CommandInset bibitem
36516 LatexCommand bibitem
36527 Auflage, Duden 2001
36530 \begin_layout Bibliography
36531 \begin_inset CommandInset bibitem
36532 LatexCommand bibitem
36538 \begin_inset CommandInset href
36541 target "http://physics.nist.gov/Document/checklist.pdf"
36545 for reviewing manuscripts
36548 \begin_layout Standard
36549 \begin_inset CommandInset index_print
36550 LatexCommand printindex