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.
15545 The command scheme is:
15548 \begin_layout Standard
15564 \begin_layout Standard
15571 must always be before the operator.
15572 You can decorate with several characters and even with other operators
15574 To place for example only characters behind a big operator, write nothing
15575 between the first braces but don't omit the braces.
15578 \begin_layout Standard
15579 For example the command
15584 \begin_inset Formula $\to$
15594 \begin_inset Formula $\to$
15600 \begin_inset space \textvisiblespace{}
15610 \begin_inset Formula
15612 \sideset{}{'}\sum_{k=1}^{n}
15620 \begin_layout Standard
15621 \begin_inset Note Greyedout
15624 \begin_layout Plain Layout
15631 can only be used to decorate big operators, binary operators are not allowed.
15639 \begin_layout Standard
15652 can also be used to decorate symbols and characters.
15653 For example, the command
15658 \begin_inset space \textvisiblespace{}
15664 \begin_inset space \textvisiblespace{}
15670 \begin_inset Formula $\uparrow$
15678 \begin_inset Formula
15680 \overset{a}{\maltese}
15688 \begin_layout Subsection
15690 \begin_inset CommandInset label
15692 name "sub:Binary-Operators"
15697 \begin_inset Index idx
15700 \begin_layout Plain Layout
15709 \begin_layout Standard
15710 Binary operators are surrounded by space when there is a character before
15712 \begin_inset VSpace medskip
15718 \begin_layout Standard
15719 \begin_inset space \hfill{}
15723 \begin_inset Tabular
15724 <lyxtabular version="3" rows="13" columns="2">
15725 <features rotate="0" tabularvalignment="middle">
15726 <column alignment="center" valignment="top" width="0pt">
15727 <column alignment="center" valignment="top" width="0pt">
15729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15732 \begin_layout Plain Layout
15734 \begin_inset Note Note
15737 \begin_layout Plain Layout
15744 is only used as spacer.
15754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15757 \begin_layout Plain Layout
15765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15768 \begin_layout Plain Layout
15774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15777 \begin_layout Plain Layout
15778 \begin_inset Formula $+$
15788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15791 \begin_layout Plain Layout
15797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15800 \begin_layout Plain Layout
15801 \begin_inset Formula $-$
15811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15814 \begin_layout Plain Layout
15822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15825 \begin_layout Plain Layout
15826 \begin_inset Formula $\pm$
15836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15839 \begin_layout Plain Layout
15847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15850 \begin_layout Plain Layout
15851 \begin_inset Formula $\mp$
15861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15864 \begin_layout Plain Layout
15872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15875 \begin_layout Plain Layout
15876 \begin_inset Formula $\cdot$
15886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15889 \begin_layout Plain Layout
15897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15900 \begin_layout Plain Layout
15901 \begin_inset Formula $\times$
15911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15914 \begin_layout Plain Layout
15922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15925 \begin_layout Plain Layout
15926 \begin_inset Formula $\div$
15936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15939 \begin_layout Plain Layout
15943 \begin_layout Plain Layout
15956 \begin_layout Plain Layout
15968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15971 \begin_layout Plain Layout
15972 \begin_inset Formula $*$
15982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15985 \begin_layout Plain Layout
15993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15996 \begin_layout Plain Layout
15997 \begin_inset Formula $\star$
16007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16010 \begin_layout Plain Layout
16018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16021 \begin_layout Plain Layout
16022 \begin_inset Formula $\circ$
16032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16035 \begin_layout Plain Layout
16043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16046 \begin_layout Plain Layout
16047 \begin_inset Formula $\diamond$
16057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16060 \begin_layout Plain Layout
16068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16071 \begin_layout Plain Layout
16072 \begin_inset Formula $\bullet$
16086 \begin_inset space \hfill{}
16090 \begin_inset Tabular
16091 <lyxtabular version="3" rows="13" columns="2">
16092 <features rotate="0" tabularvalignment="middle">
16093 <column alignment="center" valignment="top" width="0pt">
16094 <column alignment="center" valignment="top" width="0pt">
16096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16099 \begin_layout Plain Layout
16105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16108 \begin_layout Plain Layout
16116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16119 \begin_layout Plain Layout
16127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16130 \begin_layout Plain Layout
16131 \begin_inset Formula $\nabla$
16141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16144 \begin_layout Plain Layout
16152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16155 \begin_layout Plain Layout
16156 \begin_inset Formula $\bigtriangledown$
16166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16169 \begin_layout Plain Layout
16177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16180 \begin_layout Plain Layout
16181 \begin_inset Formula $\bigtriangleup$
16191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16194 \begin_layout Plain Layout
16202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16205 \begin_layout Plain Layout
16206 \begin_inset Formula $\Box$
16216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16219 \begin_layout Plain Layout
16227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16230 \begin_layout Plain Layout
16231 \begin_inset Formula $\cap$
16241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16244 \begin_layout Plain Layout
16252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16255 \begin_layout Plain Layout
16256 \begin_inset Formula $\cup$
16266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16269 \begin_layout Plain Layout
16277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16280 \begin_layout Plain Layout
16281 \begin_inset Formula $\dagger$
16291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16294 \begin_layout Plain Layout
16302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16305 \begin_layout Plain Layout
16306 \begin_inset Formula $\ddagger$
16316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16319 \begin_layout Plain Layout
16327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16330 \begin_layout Plain Layout
16331 \begin_inset Formula $\wr$
16341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16344 \begin_layout Plain Layout
16352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16355 \begin_layout Plain Layout
16356 \begin_inset Formula $\bigcirc$
16366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16369 \begin_layout Plain Layout
16377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16380 \begin_layout Plain Layout
16381 \begin_inset Formula $\wedge$
16391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16394 \begin_layout Plain Layout
16402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16405 \begin_layout Plain Layout
16406 \begin_inset Formula $\vee$
16420 \begin_inset space \hfill{}
16424 \begin_inset Tabular
16425 <lyxtabular version="3" rows="13" columns="2">
16426 <features rotate="0" tabularvalignment="middle">
16427 <column alignment="center" valignment="top" width="0pt">
16428 <column alignment="center" valignment="top" width="0pt">
16430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16433 \begin_layout Plain Layout
16439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16442 \begin_layout Plain Layout
16450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16453 \begin_layout Plain Layout
16461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16464 \begin_layout Plain Layout
16465 \begin_inset Formula $\oplus$
16475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16478 \begin_layout Plain Layout
16486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16489 \begin_layout Plain Layout
16490 \begin_inset Formula $\ominus$
16500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16503 \begin_layout Plain Layout
16511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16514 \begin_layout Plain Layout
16515 \begin_inset Formula $\otimes$
16525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16528 \begin_layout Plain Layout
16536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16539 \begin_layout Plain Layout
16540 \begin_inset Formula $\oslash$
16550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16553 \begin_layout Plain Layout
16561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16564 \begin_layout Plain Layout
16565 \begin_inset Formula $\odot$
16575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16578 \begin_layout Plain Layout
16586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16589 \begin_layout Plain Layout
16590 \begin_inset Formula $\amalg$
16600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16603 \begin_layout Plain Layout
16611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16614 \begin_layout Plain Layout
16615 \begin_inset Formula $\uplus$
16625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16628 \begin_layout Plain Layout
16636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16639 \begin_layout Plain Layout
16640 \begin_inset Formula $\setminus$
16650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16653 \begin_layout Plain Layout
16661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16664 \begin_layout Plain Layout
16665 \begin_inset Formula $\sqcap$
16675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16678 \begin_layout Plain Layout
16686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16689 \begin_layout Plain Layout
16690 \begin_inset Formula $\sqcup$
16700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16703 \begin_layout Plain Layout
16711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16714 \begin_layout Plain Layout
16715 \begin_inset Formula $\triangleleft$
16725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16728 \begin_layout Plain Layout
16736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16739 \begin_layout Plain Layout
16740 \begin_inset Formula $\triangleright$
16754 \begin_inset space \hfill{}
16760 \begin_layout Standard
16761 All binary operators can also be inserted via the math toolbar button
16762 \begin_inset Graphics
16763 filename ../images/math/pm.png
16771 \begin_layout Standard
16772 To typeset the Laplace operator also
16789 \begin_inset Formula $\nabla^{2}$
16792 ) can be used instead of
16801 \begin_layout Standard
16808 Insert\SpecialChar \menuseparator
16820 \begin_layout Subsection
16821 Self-defined Operators
16822 \begin_inset CommandInset label
16824 name "sub:Self-defined-Operators"
16829 \begin_inset Index idx
16832 \begin_layout Plain Layout
16833 Operators ! self-defined
16841 \begin_layout Standard
16842 With the help of the command
16846 DeclareMathOperator
16849 \begin_inset Index idx
16852 \begin_layout Plain Layout
16857 DeclareMathOperator
16862 custom operators can be defined in the LaTeX-preamble.
16863 Its command scheme is:
16866 \begin_layout Standard
16871 DeclareMathOperator{new command}{display}
16874 \begin_layout Standard
16875 Display can be characters or symbols that define how the operator looks
16877 To define a big operator a * is set behind the command.
16878 All self-defined big operators can have limits as described in
16879 \begin_inset CommandInset ref
16881 reference "sub:Operator-Limits"
16888 \begin_layout Standard
16889 For example the LaTeX-preamble line
16892 \begin_layout Standard
16897 DeclareMathOperator*{
16904 \begin_layout Standard
16905 defines the command
16911 , that inserts a big operator consisting of the lozenge symbol from
16912 \begin_inset CommandInset ref
16914 reference "sub:Miscellaneous-Symbols"
16919 \begin_inset Formula
16921 \Lozenge_{n=1}^{\infty}
16926 The command for this formula is:
16937 \begin_inset Formula $\to$
16943 \begin_layout Standard
16944 \begin_inset VSpace bigskip
16947 When self-defined operators are not used several times in the document,
16948 they can also be defined with the commands
16955 \begin_inset Index idx
16958 \begin_layout Plain Layout
16973 \begin_inset Index idx
16976 \begin_layout Plain Layout
16984 , which have the following scheme:
16987 \begin_layout Standard
17001 \begin_layout Standard
17008 defines big operators,
17017 \begin_layout Standard
17025 \begin_inset space \thinspace{}
17029 \begin_inset space \space{}
17032 be used to use one limit for several operators:
17035 \begin_layout Standard
17036 \begin_inset Formula
17038 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
17046 \begin_layout Standard
17047 The command for the formula above is:
17048 \begin_inset Newline newline
17064 \begin_inset space \textvisiblespace{}
17070 \begin_inset Formula $\to$
17076 \begin_inset space \textvisiblespace{}
17084 \begin_layout Section
17086 \begin_inset Index idx
17089 \begin_layout Plain Layout
17098 \begin_layout Subsection
17100 \begin_inset CommandInset label
17102 name "sub:Font-Styles"
17107 \begin_inset Index idx
17110 \begin_layout Plain Layout
17119 \begin_layout Standard
17120 Latin letters in formulas can be set in one of the following font styles:
17121 \begin_inset VSpace -2mm
17127 \begin_layout Standard
17129 \begin_inset Tabular
17130 <lyxtabular version="3" rows="7" columns="3">
17131 <features rotate="0" tabularvalignment="middle">
17132 <column alignment="center" valignment="top">
17133 <column alignment="center" valignment="top">
17134 <column alignment="center" valignment="top">
17136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17139 \begin_layout Plain Layout
17145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17148 \begin_layout Plain Layout
17154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17157 \begin_layout Plain Layout
17165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17168 \begin_layout Plain Layout
17174 \begin_inset space \textvisiblespace{}
17184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17187 \begin_layout Plain Layout
17188 \begin_inset Formula $\mathbb{ABC}$
17196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17199 \begin_layout Plain Layout
17212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17215 \begin_layout Plain Layout
17221 \begin_inset space \textvisiblespace{}
17231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17234 \begin_layout Plain Layout
17235 \begin_inset Formula $\mathbf{AbC}$
17243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17246 \begin_layout Plain Layout
17259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17262 \begin_layout Plain Layout
17268 \begin_inset space \textvisiblespace{}
17278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17281 \begin_layout Plain Layout
17282 \begin_inset Formula $\boldsymbol{AbC}$
17290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17293 \begin_layout Plain Layout
17296 arg "font-boldsymbol"
17306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17309 \begin_layout Plain Layout
17315 \begin_inset space \textvisiblespace{}
17325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17328 \begin_layout Plain Layout
17329 \begin_inset Formula $\mathcal{ABC}$
17337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17340 \begin_layout Plain Layout
17353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17356 \begin_layout Plain Layout
17362 \begin_inset space \textvisiblespace{}
17372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17375 \begin_layout Plain Layout
17376 \begin_inset Formula $\mathfrak{AbC}$
17384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17387 \begin_layout Plain Layout
17395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17398 \begin_layout Plain Layout
17404 \begin_inset space \textvisiblespace{}
17414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17417 \begin_layout Plain Layout
17418 \begin_inset Formula $\mathscr{AbC}$
17426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17429 \begin_layout Plain Layout
17443 \begin_layout Standard
17445 \begin_inset Tabular
17446 <lyxtabular version="3" rows="5" columns="3">
17447 <features rotate="0" tabularvalignment="middle">
17448 <column alignment="center" valignment="top">
17449 <column alignment="center" valignment="top">
17450 <column alignment="center" valignment="top">
17452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17455 \begin_layout Plain Layout
17461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17464 \begin_layout Plain Layout
17470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17473 \begin_layout Plain Layout
17481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17484 \begin_layout Plain Layout
17490 \begin_inset space \textvisiblespace{}
17500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17503 \begin_layout Plain Layout
17504 \begin_inset Formula $\mathit{AbC}$
17512 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17515 \begin_layout Plain Layout
17523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17526 \begin_layout Plain Layout
17532 \begin_inset space \textvisiblespace{}
17542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17545 \begin_layout Plain Layout
17546 \begin_inset Formula $\mathrm{AbC}$
17554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17557 \begin_layout Plain Layout
17570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17573 \begin_layout Plain Layout
17579 \begin_inset space \textvisiblespace{}
17589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17592 \begin_layout Plain Layout
17593 \begin_inset Formula $\mathsf{AbC}$
17601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17604 \begin_layout Plain Layout
17617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17620 \begin_layout Plain Layout
17626 \begin_inset space \textvisiblespace{}
17636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17639 \begin_layout Plain Layout
17640 \begin_inset Formula $\mathtt{AbC}$
17648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17651 \begin_layout Plain Layout
17654 arg "font-typewriter"
17670 \begin_layout Standard
17671 \begin_inset Note Greyedout
17674 \begin_layout Plain Layout
17691 can only be used for big letters.
17699 \begin_layout Standard
17700 Predefined is the style
17709 \begin_layout Standard
17710 The style commands work also for letters in mathematical constructs:
17711 \begin_inset Formula
17713 \mathfrak{A=\frac{b}{C}}
17721 \begin_layout Standard
17722 Characters in mathematical text don't appear in a math font style but in
17723 the text font style
17730 That their style can't be set correctly via the text style dialog is a
17735 \begin_layout Plain Layout
17736 \begin_inset CommandInset href
17738 name "LyX-bug #4629"
17739 target "http://www.lyx.org/trac/ticket/4629"
17751 \begin_layout Standard
17752 Instead of the style commands the dialog
17754 Edit\SpecialChar \menuseparator
17755 Math\SpecialChar \menuseparator
17758 or the toolbar button
17759 \begin_inset Graphics
17760 filename ../images/math/font.png
17768 \begin_layout Subsection
17770 \begin_inset CommandInset label
17772 name "sub:Bold-Formulas"
17777 \begin_inset Index idx
17780 \begin_layout Plain Layout
17789 \begin_layout Standard
17790 To make a complete formula bold, the command
17796 from the previous subsection cannot be used, because it doesn't work for
17797 small Greek letters.
17798 Furthermore it prints Latin letters always upright, like in the following
17802 \begin_layout Standard
17803 \begin_inset Formula
17805 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
17813 \begin_layout Standard
17814 To display the formula correctly, the command
17821 \begin_inset Formula
17823 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
17828 It is also possible to set the formula in a
17830 boldmath environment
17833 This environment is created by inserting the command
17840 \begin_inset Index idx
17843 \begin_layout Plain Layout
17852 To end the environment, the command
17859 \begin_inset Index idx
17862 \begin_layout Plain Layout
17870 is inserted in TeX-mode.
17874 \begin_layout Plain Layout
17884 \begin_inset Formula
17886 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
17895 \begin_layout Plain Layout
17907 \begin_layout Subsection
17909 \begin_inset Index idx
17912 \begin_layout Plain Layout
17921 \begin_layout Standard
17922 Formulas can be colored like normal text: Highlight a formula or a formula
17928 Here is a formula in magenta:
17929 \begin_inset Formula
17931 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
17939 \begin_layout Standard
17940 You can also define your own colors as described in
17941 \begin_inset CommandInset ref
17943 reference "sub:Colored-Boxes"
17948 They can be used with the TeX code command
17955 \begin_inset Index idx
17958 \begin_layout Plain Layout
17969 \begin_layout Standard
17974 textcolor{color}{characters or formula}
17977 \begin_layout Standard
17978 The following example was colored completely dark green and partly red:
17981 \begin_layout Standard
17985 \begin_layout Plain Layout
17989 textcolor{darkgreen}{
17995 \begin_inset Formula
17997 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
18006 \begin_layout Plain Layout
18016 \begin_layout Standard
18017 Due to a bug in LyX only complete formulas can be colored with self-defined
18022 \begin_layout Plain Layout
18023 \begin_inset CommandInset href
18025 name "LyX-bug #5269"
18026 target "http://www.lyx.org/trac/ticket/5269"
18038 \begin_layout Subsection
18040 \begin_inset CommandInset label
18042 name "sub:Font-Sizes"
18047 \begin_inset Index idx
18050 \begin_layout Plain Layout
18059 \begin_layout Standard
18060 For characters in formulas there are, analog to characters in text, the
18061 following size commands:
18064 \begin_layout Standard
18108 \begin_inset Newline newline
18130 \begin_layout Standard
18131 The size produced by the commands depends on the document font size, which
18132 corresponds to the command
18139 The other commands produce smaller or larger sizes than
18146 The font size can however not exceed a certain value.
18147 Is for example the document font size 12
18148 \begin_inset space \thinspace{}
18157 switches to the same size as
18167 \begin_layout Standard
18168 A size command is inserted in TeX-mode before the formula and sets the size
18169 for all following formula and text characters.
18170 To switch back to the initial size, the command
18176 is inserted behind the formula in TeX-mode.
18179 \begin_layout Standard
18180 Within a formula the size can be changed using the following size commands:
18183 \begin_layout Standard
18186 \begin_inset Tabular
18187 <lyxtabular version="3" rows="5" columns="2">
18188 <features rotate="0" tabularvalignment="middle">
18189 <column alignment="center" valignment="top">
18190 <column alignment="center" valignment="top">
18192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18195 \begin_layout Plain Layout
18201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18204 \begin_layout Plain Layout
18206 \begin_inset Note Note
18209 \begin_layout Plain Layout
18216 is only used as spacer.
18228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18231 \begin_layout Plain Layout
18235 \begin_inset Index idx
18238 \begin_layout Plain Layout
18251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18254 \begin_layout Plain Layout
18255 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
18265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18268 \begin_layout Plain Layout
18276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18279 \begin_layout Plain Layout
18280 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
18290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18293 \begin_layout Plain Layout
18301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18304 \begin_layout Plain Layout
18305 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18318 \begin_layout Plain Layout
18326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18329 \begin_layout Plain Layout
18330 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18346 \begin_layout Standard
18347 After entering these commands, a blue box appears in which the formula parts
18351 \begin_layout Standard
18352 There is a further method to change the font size, that though only works
18353 for symbols or letters in mathematical text.
18354 To use it, one of the above text size commands is inserted in mathematical
18356 All following characters until the end of the mathematical text or until
18357 another size command will have the selected size.
18359 \begin_inset VSpace -2mm
18365 \begin_layout Standard
18369 \begin_layout Plain Layout
18379 \begin_inset Formula
18381 A=\frac{B}{c}\cdot\maltese
18387 \begin_inset Formula
18389 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
18398 \begin_layout Plain Layout
18410 \begin_layout Standard
18411 \begin_inset VSpace medskip
18414 Before both formulas the command
18421 The command for the second formula is:
18422 \begin_inset Newline newline
18430 \begin_inset space \textvisiblespace{}
18436 \begin_inset space \textvisiblespace{}
18442 \begin_inset space \textvisiblespace{}
18448 \begin_inset space \textvisiblespace{}
18452 \begin_inset Formula $\to$
18456 \begin_inset Formula $\to$
18460 \begin_inset Newline newline
18464 \begin_inset space \hspace*{}
18475 \begin_inset space \textvisiblespace{}
18481 \begin_inset space \textvisiblespace{}
18487 \begin_inset space \textvisiblespace{}
18493 \begin_layout Standard
18494 If a symbol cannot be displayed in different sizes, it will always be displayed
18495 in the default size.
18498 \begin_layout Section
18500 \begin_inset Index idx
18503 \begin_layout Plain Layout
18512 \begin_layout Standard
18513 Greek letters can also be inserted via the toolbar button
18514 \begin_inset Graphics
18515 filename ../images/math/alpha.png
18521 All international typesetting norms purport that Greek letters in math
18522 have to be typeset italic/slanted.
18523 In some languages, like French or Russian, they are nevertheless sometimes
18527 \begin_layout Subsection
18529 \begin_inset Index idx
18532 \begin_layout Plain Layout
18533 Greek letters ! small
18541 \begin_layout Standard
18542 \begin_inset space \hfill{}
18546 \begin_inset Tabular
18547 <lyxtabular version="3" rows="11" columns="2">
18548 <features rotate="0" tabularvalignment="middle">
18549 <column alignment="center" valignment="top" width="0pt">
18550 <column alignment="center" valignment="top" width="0pt">
18552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18555 \begin_layout Plain Layout
18561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18564 \begin_layout Plain Layout
18572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18575 \begin_layout Plain Layout
18583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18586 \begin_layout Plain Layout
18587 \begin_inset Formula $\alpha$
18597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18600 \begin_layout Plain Layout
18608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18611 \begin_layout Plain Layout
18612 \begin_inset Formula $\beta$
18622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18625 \begin_layout Plain Layout
18633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18636 \begin_layout Plain Layout
18637 \begin_inset Formula $\gamma$
18647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18650 \begin_layout Plain Layout
18658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18661 \begin_layout Plain Layout
18662 \begin_inset Formula $\delta$
18672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18675 \begin_layout Plain Layout
18683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18686 \begin_layout Plain Layout
18687 \begin_inset Formula $\epsilon$
18697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18700 \begin_layout Plain Layout
18708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18711 \begin_layout Plain Layout
18712 \begin_inset Formula $\varepsilon$
18722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18725 \begin_layout Plain Layout
18733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18736 \begin_layout Plain Layout
18737 \begin_inset Formula $\zeta$
18747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18750 \begin_layout Plain Layout
18758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18761 \begin_layout Plain Layout
18762 \begin_inset Formula $\eta$
18772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18775 \begin_layout Plain Layout
18783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18786 \begin_layout Plain Layout
18787 \begin_inset Formula $\theta$
18797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18800 \begin_layout Plain Layout
18808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18811 \begin_layout Plain Layout
18812 \begin_inset Formula $\vartheta$
18826 \begin_inset space \hfill{}
18830 \begin_inset Tabular
18831 <lyxtabular version="3" rows="12" columns="2">
18832 <features rotate="0" tabularvalignment="middle">
18833 <column alignment="center" valignment="top" width="0pt">
18834 <column alignment="center" valignment="top" width="0pt">
18836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18839 \begin_layout Plain Layout
18845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18848 \begin_layout Plain Layout
18856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18859 \begin_layout Plain Layout
18867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18870 \begin_layout Plain Layout
18871 \begin_inset Formula $\iota$
18881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18884 \begin_layout Plain Layout
18892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18895 \begin_layout Plain Layout
18896 \begin_inset Formula $\kappa$
18906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18909 \begin_layout Plain Layout
18917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18920 \begin_layout Plain Layout
18921 \begin_inset Formula $\varkappa$
18931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18934 \begin_layout Plain Layout
18942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18945 \begin_layout Plain Layout
18946 \begin_inset Formula $\lambda$
18956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18959 \begin_layout Plain Layout
18967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18970 \begin_layout Plain Layout
18971 \begin_inset Formula $\mu$
18981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18984 \begin_layout Plain Layout
18992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18995 \begin_layout Plain Layout
18996 \begin_inset Formula $\nu$
19006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19009 \begin_layout Plain Layout
19017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19020 \begin_layout Plain Layout
19021 \begin_inset Formula $\xi$
19031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19034 \begin_layout Plain Layout
19040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19043 \begin_layout Plain Layout
19044 \begin_inset Formula $o$
19054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19057 \begin_layout Plain Layout
19065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19068 \begin_layout Plain Layout
19069 \begin_inset Formula $\pi$
19079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19082 \begin_layout Plain Layout
19090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19093 \begin_layout Plain Layout
19094 \begin_inset Formula $\varpi$
19104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19107 \begin_layout Plain Layout
19115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19118 \begin_layout Plain Layout
19119 \begin_inset Formula $\rho$
19133 \begin_inset space \hfill{}
19137 \begin_inset Tabular
19138 <lyxtabular version="3" rows="11" columns="2">
19139 <features rotate="0" tabularvalignment="middle">
19140 <column alignment="center" valignment="top" width="0pt">
19141 <column alignment="center" valignment="top" width="0pt">
19143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19146 \begin_layout Plain Layout
19152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19155 \begin_layout Plain Layout
19163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19166 \begin_layout Plain Layout
19174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19177 \begin_layout Plain Layout
19178 \begin_inset Formula $\varrho$
19188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19191 \begin_layout Plain Layout
19199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19202 \begin_layout Plain Layout
19203 \begin_inset Formula $\sigma$
19213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19216 \begin_layout Plain Layout
19224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19227 \begin_layout Plain Layout
19228 \begin_inset Formula $\varsigma$
19238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19241 \begin_layout Plain Layout
19249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19252 \begin_layout Plain Layout
19253 \begin_inset Formula $\tau$
19263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19266 \begin_layout Plain Layout
19274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19277 \begin_layout Plain Layout
19278 \begin_inset Formula $\upsilon$
19288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19291 \begin_layout Plain Layout
19299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19302 \begin_layout Plain Layout
19303 \begin_inset Formula $\phi$
19313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19316 \begin_layout Plain Layout
19324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19327 \begin_layout Plain Layout
19328 \begin_inset Formula $\varphi$
19338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19341 \begin_layout Plain Layout
19349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19352 \begin_layout Plain Layout
19353 \begin_inset Formula $\chi$
19363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19366 \begin_layout Plain Layout
19374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19377 \begin_layout Plain Layout
19378 \begin_inset Formula $\psi$
19388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19391 \begin_layout Plain Layout
19399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19402 \begin_layout Plain Layout
19403 \begin_inset Formula $\omega$
19417 \begin_inset space \hfill{}
19423 \begin_layout Standard
19424 \begin_inset VSpace medskip
19430 \begin_layout Standard
19431 How to create special upright Greek letters is explained in
19432 \begin_inset CommandInset ref
19434 reference "sub:Upright-small-Greek"
19441 \begin_layout Subsection
19443 \begin_inset Index idx
19446 \begin_layout Plain Layout
19447 Greek letters ! big
19455 \begin_layout Standard
19456 \begin_inset space \hfill{}
19460 \begin_inset Tabular
19461 <lyxtabular version="3" rows="7" columns="2">
19462 <features rotate="0" tabularvalignment="middle">
19463 <column alignment="center" valignment="top" width="0pt">
19464 <column alignment="center" valignment="top" width="0pt">
19466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19469 \begin_layout Plain Layout
19475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19478 \begin_layout Plain Layout
19486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19489 \begin_layout Plain Layout
19497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19500 \begin_layout Plain Layout
19501 \begin_inset Formula $\Gamma$
19511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19514 \begin_layout Plain Layout
19522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19525 \begin_layout Plain Layout
19526 \begin_inset Formula $\Delta$
19536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19539 \begin_layout Plain Layout
19547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19550 \begin_layout Plain Layout
19551 \begin_inset Formula $\Theta$
19561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19564 \begin_layout Plain Layout
19572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19575 \begin_layout Plain Layout
19576 \begin_inset Formula $\Lambda$
19586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19589 \begin_layout Plain Layout
19597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19600 \begin_layout Plain Layout
19601 \begin_inset Formula $\Xi$
19611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19614 \begin_layout Plain Layout
19622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19625 \begin_layout Plain Layout
19626 \begin_inset Formula $\Pi$
19640 \begin_inset space \hfill{}
19644 \begin_inset Tabular
19645 <lyxtabular version="3" rows="6" columns="2">
19646 <features rotate="0" tabularvalignment="middle">
19647 <column alignment="center" valignment="top" width="0pt">
19648 <column alignment="center" valignment="top" width="0pt">
19650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19653 \begin_layout Plain Layout
19659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19662 \begin_layout Plain Layout
19670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19673 \begin_layout Plain Layout
19681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19684 \begin_layout Plain Layout
19685 \begin_inset Formula $\Sigma$
19695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19698 \begin_layout Plain Layout
19706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19709 \begin_layout Plain Layout
19710 \begin_inset Formula $\Upsilon$
19720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19723 \begin_layout Plain Layout
19731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19734 \begin_layout Plain Layout
19735 \begin_inset Formula $\Phi$
19745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19748 \begin_layout Plain Layout
19756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19759 \begin_layout Plain Layout
19760 \begin_inset Formula $\Psi$
19770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19773 \begin_layout Plain Layout
19781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19784 \begin_layout Plain Layout
19785 \begin_inset Formula $\Omega$
19799 \begin_inset space \hfill{}
19805 \begin_layout Standard
19806 \begin_inset VSpace medskip
19809 That the big Greek letters appear upright is caused by a design bug when
19811 To get correct italic big letters, begin every command with
19816 For example the command
19823 \begin_inset Formula $\varGamma$
19827 Another way is to load the package
19835 \begin_layout Plain Layout
19840 is part of the LaTeX-package
19845 \begin_inset Index idx
19848 \begin_layout Plain Layout
19853 \begin_layout Plain Layout
19873 \begin_inset Index idx
19876 \begin_layout Plain Layout
19882 with the LaTeX-preamble line
19885 \begin_layout Standard
19890 usepackage{fixmath}
19893 \begin_layout Standard
19894 Then all big Greek letters in a document will automatically be typeset italic.
19897 \begin_layout Subsection
19899 \begin_inset Index idx
19902 \begin_layout Plain Layout
19903 Greek letters ! bold
19911 \begin_layout Standard
19912 Greek letters cannot be set with different font styles like Latin letters.
19913 They can only be made bold with the command
19920 \begin_inset Index idx
19923 \begin_layout Plain Layout
19934 \begin_layout Standard
19936 \begin_inset Tabular
19937 <lyxtabular version="3" rows="3" columns="2">
19938 <features rotate="0" tabularvalignment="middle">
19939 <column alignment="center" valignment="top">
19940 <column alignment="center" valignment="top">
19942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19945 \begin_layout Plain Layout
19951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19954 \begin_layout Plain Layout
19962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19965 \begin_layout Plain Layout
19977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19980 \begin_layout Plain Layout
19981 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
19991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19994 \begin_layout Plain Layout
20006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20009 \begin_layout Plain Layout
20010 \begin_inset Formula $\theta\boldsymbol{\theta}$
20026 \begin_layout Section
20031 \begin_layout Plain Layout
20044 \begin_layout Plain Layout
20045 A list with all symbols of most of the LaTeX-packages can be found in
20046 \begin_inset CommandInset citation
20061 \begin_layout Plain Layout
20069 \begin_inset Note Note
20072 \begin_layout Plain Layout
20075 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20078 \begin_layout Plain Layout
20081 texorpdfstring is in section
20082 \begin_inset CommandInset ref
20084 reference "sub:Formulas-in-Section"
20094 \begin_inset Index idx
20097 \begin_layout Plain Layout
20106 \begin_layout Standard
20107 Many of the symbols listed in this section can also be inserted via the
20109 \begin_inset Graphics
20110 filename ../images/math/nabla.png
20116 \begin_inset Graphics
20117 filename ../images/math/digamma.png
20125 \begin_layout Subsection
20126 Mathematical Symbols
20127 \begin_inset CommandInset label
20129 name "sub:Mathematical-Symbols"
20134 \begin_inset Index idx
20137 \begin_layout Plain Layout
20138 Symbols ! mathematical
20146 \begin_layout Standard
20147 \begin_inset space \hfill{}
20151 \begin_inset Tabular
20152 <lyxtabular version="3" rows="10" columns="2">
20153 <features rotate="0" tabularvalignment="middle">
20154 <column alignment="center" valignment="top" width="0pt">
20155 <column alignment="center" valignment="top" width="0pt">
20157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20160 \begin_layout Plain Layout
20166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20169 \begin_layout Plain Layout
20177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20180 \begin_layout Plain Layout
20188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20191 \begin_layout Plain Layout
20192 \begin_inset Formula $\neg$
20202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20205 \begin_layout Plain Layout
20213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20216 \begin_layout Plain Layout
20217 \begin_inset Formula $\Im$
20227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20230 \begin_layout Plain Layout
20238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20241 \begin_layout Plain Layout
20242 \begin_inset Formula $\Re$
20252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20255 \begin_layout Plain Layout
20263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20266 \begin_layout Plain Layout
20267 \begin_inset Formula $\aleph$
20277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20280 \begin_layout Plain Layout
20288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20291 \begin_layout Plain Layout
20292 \begin_inset Formula $\partial$
20302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20305 \begin_layout Plain Layout
20313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20316 \begin_layout Plain Layout
20317 \begin_inset Formula $\infty$
20327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20330 \begin_layout Plain Layout
20338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20341 \begin_layout Plain Layout
20342 \begin_inset Formula $\wp$
20352 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20355 \begin_layout Plain Layout
20363 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20366 \begin_layout Plain Layout
20367 \begin_inset Formula $\imath$
20377 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20380 \begin_layout Plain Layout
20388 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20391 \begin_layout Plain Layout
20392 \begin_inset Formula $\jmath$
20406 \begin_inset space \hfill{}
20410 \begin_inset Tabular
20411 <lyxtabular version="3" rows="10" columns="2">
20412 <features rotate="0" tabularvalignment="middle">
20413 <column alignment="center" valignment="top" width="0pt">
20414 <column alignment="center" valignment="top" width="0pt">
20416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20419 \begin_layout Plain Layout
20425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20428 \begin_layout Plain Layout
20430 \begin_inset Note Note
20433 \begin_layout Plain Layout
20440 is only used as spacer.
20452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20455 \begin_layout Plain Layout
20463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20466 \begin_layout Plain Layout
20467 \begin_inset Formula $\forall$
20477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20480 \begin_layout Plain Layout
20488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20491 \begin_layout Plain Layout
20492 \begin_inset Formula $\exists$
20502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20505 \begin_layout Plain Layout
20513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20516 \begin_layout Plain Layout
20517 \begin_inset Formula $\nexists$
20527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20530 \begin_layout Plain Layout
20538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20541 \begin_layout Plain Layout
20542 \begin_inset Formula $\emptyset$
20552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20555 \begin_layout Plain Layout
20563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20566 \begin_layout Plain Layout
20567 \begin_inset Formula $\varnothing$
20577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20580 \begin_layout Plain Layout
20588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20591 \begin_layout Plain Layout
20592 \begin_inset Formula $\dag$
20602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20605 \begin_layout Plain Layout
20613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20616 \begin_layout Plain Layout
20617 \begin_inset Formula $\ddag$
20627 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20630 \begin_layout Plain Layout
20638 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20641 \begin_layout Plain Layout
20645 \begin_layout Plain Layout
20655 \begin_inset Formula $\complement$
20662 \begin_layout Plain Layout
20676 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20679 \begin_layout Plain Layout
20687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20690 \begin_layout Plain Layout
20691 \begin_inset Formula $\Bbbk$
20705 \begin_inset space \hfill{}
20709 \begin_inset Tabular
20710 <lyxtabular version="3" rows="10" columns="2">
20711 <features rotate="0" tabularvalignment="middle">
20712 <column alignment="center" valignment="top" width="0pt">
20713 <column alignment="center" valignment="top" width="0pt">
20715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20718 \begin_layout Plain Layout
20724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20727 \begin_layout Plain Layout
20735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20738 \begin_layout Plain Layout
20746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20749 \begin_layout Plain Layout
20750 \begin_inset Formula $\prime$
20760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20763 \begin_layout Plain Layout
20771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20774 \begin_layout Plain Layout
20775 \begin_inset Formula $\backprime$
20785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20788 \begin_layout Plain Layout
20796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20799 \begin_layout Plain Layout
20800 \begin_inset Formula $\mho$
20810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20813 \begin_layout Plain Layout
20821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20824 \begin_layout Plain Layout
20825 \begin_inset Formula $\triangle$
20835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20838 \begin_layout Plain Layout
20846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20849 \begin_layout Plain Layout
20850 \begin_inset Formula $\angle$
20860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20863 \begin_layout Plain Layout
20871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20874 \begin_layout Plain Layout
20875 \begin_inset Formula $\measuredangle$
20885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20888 \begin_layout Plain Layout
20896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20899 \begin_layout Plain Layout
20900 \begin_inset Formula $\sphericalangle$
20910 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20913 \begin_layout Plain Layout
20921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20924 \begin_layout Plain Layout
20925 \begin_inset Formula $\top$
20935 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20938 \begin_layout Plain Layout
20946 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20949 \begin_layout Plain Layout
20950 \begin_inset Formula $\bot$
20964 \begin_inset space \hfill{}
20970 \begin_layout Subsection
20971 Miscellaneous Symbols
20972 \begin_inset CommandInset label
20974 name "sub:Miscellaneous-Symbols"
20979 \begin_inset Index idx
20982 \begin_layout Plain Layout
20983 Symbols ! miscellaneous
20991 \begin_layout Standard
20994 \begin_inset Tabular
20995 <lyxtabular version="3" rows="10" columns="2">
20996 <features rotate="0" tabularvalignment="middle">
20997 <column alignment="center" valignment="top" width="0pt">
20998 <column alignment="center" valignment="top" width="0pt">
21000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21003 \begin_layout Plain Layout
21009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21012 \begin_layout Plain Layout
21020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21023 \begin_layout Plain Layout
21031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21034 \begin_layout Plain Layout
21035 \begin_inset Formula $\flat$
21045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21048 \begin_layout Plain Layout
21056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21059 \begin_layout Plain Layout
21060 \begin_inset Formula $\natural$
21070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21073 \begin_layout Plain Layout
21081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21084 \begin_layout Plain Layout
21085 \begin_inset Formula $\sharp$
21095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21098 \begin_layout Plain Layout
21106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21109 \begin_layout Plain Layout
21110 \begin_inset Formula $\surd$
21120 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21123 \begin_layout Plain Layout
21131 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21134 \begin_layout Plain Layout
21135 \begin_inset Formula $\checkmark$
21145 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21148 \begin_layout Plain Layout
21156 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21159 \begin_layout Plain Layout
21160 \begin_inset Formula $\yen$
21170 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21173 \begin_layout Plain Layout
21181 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21184 \begin_layout Plain Layout
21185 \begin_inset Formula $\pounds$
21195 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21198 \begin_layout Plain Layout
21204 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21207 \begin_layout Plain Layout
21208 \begin_inset Formula $\$$
21218 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21221 \begin_layout Plain Layout
21227 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21230 \begin_layout Plain Layout
21231 \begin_inset Formula $§$
21245 \begin_inset Tabular
21246 <lyxtabular version="3" rows="10" columns="2">
21247 <features rotate="0" tabularvalignment="middle">
21248 <column alignment="center" valignment="top">
21249 <column alignment="center" valignment="top">
21251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21254 \begin_layout Plain Layout
21260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21263 \begin_layout Plain Layout
21271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21274 \begin_layout Plain Layout
21282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21285 \begin_layout Plain Layout
21286 \begin_inset Formula $\hbar$
21296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21299 \begin_layout Plain Layout
21307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21310 \begin_layout Plain Layout
21311 \begin_inset Formula $\hslash$
21321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21324 \begin_layout Plain Layout
21332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21335 \begin_layout Plain Layout
21336 \begin_inset Formula $\clubsuit$
21346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21349 \begin_layout Plain Layout
21357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21360 \begin_layout Plain Layout
21361 \begin_inset Formula $\spadesuit$
21371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21374 \begin_layout Plain Layout
21382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21385 \begin_layout Plain Layout
21386 \begin_inset Formula $\bigstar$
21396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21399 \begin_layout Plain Layout
21407 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21410 \begin_layout Plain Layout
21411 \begin_inset Formula $\blacklozenge$
21421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21424 \begin_layout Plain Layout
21432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21435 \begin_layout Plain Layout
21436 \begin_inset Formula $\blacktriangle$
21446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21449 \begin_layout Plain Layout
21457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21460 \begin_layout Plain Layout
21461 \begin_inset Formula $\blacktriangledown$
21471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21474 \begin_layout Plain Layout
21482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21485 \begin_layout Plain Layout
21486 \begin_inset Formula $\bullet$
21500 \begin_inset Tabular
21501 <lyxtabular version="3" rows="10" columns="2">
21502 <features rotate="0" tabularvalignment="middle">
21503 <column alignment="center" valignment="top" width="0pt">
21504 <column alignment="center" valignment="top" width="0pt">
21506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21509 \begin_layout Plain Layout
21515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21518 \begin_layout Plain Layout
21526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21529 \begin_layout Plain Layout
21537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21540 \begin_layout Plain Layout
21541 \begin_inset Formula $\diamondsuit$
21551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21554 \begin_layout Plain Layout
21562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21565 \begin_layout Plain Layout
21566 \begin_inset Formula $\Diamond$
21576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21579 \begin_layout Plain Layout
21587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21590 \begin_layout Plain Layout
21591 \begin_inset Formula $\heartsuit$
21601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21604 \begin_layout Plain Layout
21612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21615 \begin_layout Plain Layout
21616 \begin_inset Formula $\P$
21626 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21629 \begin_layout Plain Layout
21637 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21640 \begin_layout Plain Layout
21641 \begin_inset Formula $\copyright$
21651 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21654 \begin_layout Plain Layout
21662 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21665 \begin_layout Plain Layout
21666 \begin_inset Formula $\circledR$
21676 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21679 \begin_layout Plain Layout
21687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21690 \begin_layout Plain Layout
21691 \begin_inset Formula $\maltese$
21701 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21704 \begin_layout Plain Layout
21712 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21715 \begin_layout Plain Layout
21716 \begin_inset Formula $\diagup$
21726 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21729 \begin_layout Plain Layout
21737 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21740 \begin_layout Plain Layout
21741 \begin_inset Formula $\diagdown$
21757 \begin_layout Standard
21758 \begin_inset VSpace medskip
21764 \begin_layout Standard
21765 Some symbols can be displayed in different sizes, see
21766 \begin_inset CommandInset ref
21768 reference "sub:Font-Sizes"
21775 \begin_layout Subsection
21777 \begin_inset Index idx
21780 \begin_layout Plain Layout
21781 Symbols ! Euro-symbol
21787 \begin_inset Index idx
21790 \begin_layout Plain Layout
21797 \begin_layout Plain Layout
21814 \begin_layout Standard
21815 To use the Euro symbol in formulas, the LaTeX-package
21820 \begin_inset Index idx
21823 \begin_layout Plain Layout
21829 must be installed and loaded with the LaTeX-preamble line
21832 \begin_layout Standard
21837 usepackage[gennarrow]{eurosym}
21840 \begin_layout Standard
21841 The Euro symbol can now be inserted with the command
21848 \begin_inset Index idx
21851 \begin_layout Plain Layout
21862 \begin_layout Standard
21863 The Euro symbol can directly be inserted with the € key in mathematical
21864 text, without having
21879 can also be inserted in TeX-mode.
21880 The official currency symbol can then be inserted with the command
21887 \begin_inset Index idx
21890 \begin_layout Plain Layout
21898 , that is only available in TeX-mode.
21901 \begin_layout Standard
21905 \begin_layout Plain Layout
21915 \begin_inset Note Note
21918 \begin_layout Plain Layout
21919 The following table will only be displayed when the LaTeX-package
21931 \begin_layout Standard
21932 An overview about the different Euro symbols:
21935 \begin_layout Standard
21937 \begin_inset Tabular
21938 <lyxtabular version="3" rows="4" columns="3">
21939 <features rotate="0" tabularvalignment="middle">
21940 <column alignment="center" valignment="top" width="0pt">
21941 <column alignment="center" valignment="top" width="0pt">
21942 <column alignment="center" valignment="top" width="0pt">
21944 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
21947 \begin_layout Plain Layout
21953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21956 \begin_layout Plain Layout
21962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21965 \begin_layout Plain Layout
21973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21976 \begin_layout Plain Layout
21982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21985 \begin_layout Plain Layout
21993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21996 \begin_layout Plain Layout
21997 \begin_inset Formula $\euro$
22007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22010 \begin_layout Plain Layout
22016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22019 \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 $\mbox{€}$
22039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22042 \begin_layout Plain Layout
22048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22051 \begin_layout Plain Layout
22059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22062 \begin_layout Plain Layout
22066 \begin_layout Plain Layout
22088 \begin_layout Standard
22092 \begin_layout Plain Layout
22102 \begin_inset Note Note
22105 \begin_layout Plain Layout
22106 The following will be displayed when the LaTeX-package
22118 \begin_layout Standard
22119 You need to install the LaTeX-package
22123 to see the rest of this subsection in the output.
22126 \begin_layout Standard
22130 \begin_layout Plain Layout
22142 \begin_layout Section
22144 \begin_inset CommandInset label
22146 name "sec:Relations"
22151 \begin_inset Index idx
22154 \begin_layout Plain Layout
22161 \begin_inset Index idx
22164 \begin_layout Plain Layout
22169 \begin_layout Plain Layout
22180 \begin_layout Plain Layout
22195 \begin_layout Standard
22196 All relations can also be inserted via the toolbar button
22197 \begin_inset Graphics
22198 filename ../images/math/leq.png
22206 \begin_layout Standard
22207 \begin_inset space \hfill{}
22211 \begin_inset Tabular
22212 <lyxtabular version="3" rows="17" columns="2">
22213 <features rotate="0" tabularvalignment="middle">
22214 <column alignment="center" valignment="top" width="0pt">
22215 <column alignment="center" valignment="top" width="0pt">
22217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22220 \begin_layout Plain Layout
22226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22229 \begin_layout Plain Layout
22237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22240 \begin_layout Plain Layout
22246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22249 \begin_layout Plain Layout
22250 \begin_inset Formula $<$
22260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22263 \begin_layout Plain Layout
22271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22274 \begin_layout Plain Layout
22275 \begin_inset Formula $\le$
22285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22288 \begin_layout Plain Layout
22296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22299 \begin_layout Plain Layout
22300 \begin_inset Formula $\ll$
22310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22313 \begin_layout Plain Layout
22321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22324 \begin_layout Plain Layout
22325 \begin_inset Formula $\prec$
22335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22338 \begin_layout Plain Layout
22346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22349 \begin_layout Plain Layout
22350 \begin_inset Formula $\preceq$
22360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22363 \begin_layout Plain Layout
22371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22374 \begin_layout Plain Layout
22375 \begin_inset Formula $\subset$
22385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22388 \begin_layout Plain Layout
22396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22399 \begin_layout Plain Layout
22400 \begin_inset Formula $\subseteq$
22410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22413 \begin_layout Plain Layout
22421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22424 \begin_layout Plain Layout
22425 \begin_inset Formula $\sqsubseteq$
22435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22438 \begin_layout Plain Layout
22446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22449 \begin_layout Plain Layout
22450 \begin_inset Formula $\in$
22460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22463 \begin_layout Plain Layout
22471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22474 \begin_layout Plain Layout
22475 \begin_inset Formula $\vdash$
22485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22488 \begin_layout Plain Layout
22496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22499 \begin_layout Plain Layout
22500 \begin_inset Formula $\smile$
22510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22513 \begin_layout Plain Layout
22521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22524 \begin_layout Plain Layout
22525 \begin_inset Formula $\lhd$
22535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22538 \begin_layout Plain Layout
22546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22549 \begin_layout Plain Layout
22550 \begin_inset Formula $\unlhd$
22560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22563 \begin_layout Plain Layout
22571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22574 \begin_layout Plain Layout
22575 \begin_inset Formula $\gtrless$
22585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22588 \begin_layout Plain Layout
22596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22599 \begin_layout Plain Layout
22600 \begin_inset Formula $\mid$
22610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22613 \begin_layout Plain Layout
22621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22624 \begin_layout Plain Layout
22625 \begin_inset Formula $\nmid$
22639 \begin_inset space \hfill{}
22643 \begin_inset Tabular
22644 <lyxtabular version="3" rows="17" columns="2">
22645 <features rotate="0" tabularvalignment="middle">
22646 <column alignment="center" valignment="top" width="0pt">
22647 <column alignment="center" valignment="top" width="0pt">
22649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22652 \begin_layout Plain Layout
22658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22661 \begin_layout Plain Layout
22669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22672 \begin_layout Plain Layout
22678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22681 \begin_layout Plain Layout
22682 \begin_inset Formula $=$
22692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22695 \begin_layout Plain Layout
22703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22706 \begin_layout Plain Layout
22707 \begin_inset Formula $\not=$
22717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22720 \begin_layout Plain Layout
22728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22731 \begin_layout Plain Layout
22732 \begin_inset Formula $\equiv$
22742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22745 \begin_layout Plain Layout
22753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22756 \begin_layout Plain Layout
22757 \begin_inset Formula $\sim$
22767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22770 \begin_layout Plain Layout
22778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22781 \begin_layout Plain Layout
22782 \begin_inset Formula $\simeq$
22792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22795 \begin_layout Plain Layout
22803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22806 \begin_layout Plain Layout
22807 \begin_inset Formula $\approx$
22817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22820 \begin_layout Plain Layout
22828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22831 \begin_layout Plain Layout
22832 \begin_inset Formula $\cong$
22842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22845 \begin_layout Plain Layout
22853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22856 \begin_layout Plain Layout
22857 \begin_inset Formula $\bowtie$
22867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22870 \begin_layout Plain Layout
22878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22881 \begin_layout Plain Layout
22882 \begin_inset Formula $\notin$
22892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22895 \begin_layout Plain Layout
22903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22906 \begin_layout Plain Layout
22907 \begin_inset Formula $\perp$
22917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22920 \begin_layout Plain Layout
22928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22931 \begin_layout Plain Layout
22932 \begin_inset Formula $\propto$
22942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22945 \begin_layout Plain Layout
22953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22956 \begin_layout Plain Layout
22957 \begin_inset Formula $\asymp$
22967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22970 \begin_layout Plain Layout
22978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22981 \begin_layout Plain Layout
22982 \begin_inset Formula $\doteq$
22992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22995 \begin_layout Plain Layout
23003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23006 \begin_layout Plain Layout
23007 \begin_inset Formula $\circeq$
23017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23020 \begin_layout Plain Layout
23028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23031 \begin_layout Plain Layout
23032 \begin_inset Formula $\models$
23042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23045 \begin_layout Plain Layout
23053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23056 \begin_layout Plain Layout
23057 \begin_inset Formula $\widehat{=}$
23071 \begin_inset space \hfill{}
23075 \begin_inset Tabular
23076 <lyxtabular version="3" rows="17" columns="2">
23077 <features rotate="0" tabularvalignment="middle">
23078 <column alignment="center" valignment="top" width="0pt">
23079 <column alignment="center" valignment="top" width="0pt">
23081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23084 \begin_layout Plain Layout
23090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23093 \begin_layout Plain Layout
23101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23104 \begin_layout Plain Layout
23110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23113 \begin_layout Plain Layout
23114 \begin_inset Formula $>$
23124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23127 \begin_layout Plain Layout
23135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23138 \begin_layout Plain Layout
23139 \begin_inset Formula $\ge$
23149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23152 \begin_layout Plain Layout
23160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23163 \begin_layout Plain Layout
23164 \begin_inset Formula $\gg$
23174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23177 \begin_layout Plain Layout
23185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23188 \begin_layout Plain Layout
23189 \begin_inset Formula $\succ$
23199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23202 \begin_layout Plain Layout
23210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23213 \begin_layout Plain Layout
23214 \begin_inset Formula $\succeq$
23224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23227 \begin_layout Plain Layout
23235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23238 \begin_layout Plain Layout
23239 \begin_inset Formula $\supset$
23249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23252 \begin_layout Plain Layout
23260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23263 \begin_layout Plain Layout
23264 \begin_inset Formula $\supseteq$
23274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23277 \begin_layout Plain Layout
23285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23288 \begin_layout Plain Layout
23289 \begin_inset Formula $\sqsupseteq$
23299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23302 \begin_layout Plain Layout
23310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23313 \begin_layout Plain Layout
23314 \begin_inset Formula $\ni$
23324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23327 \begin_layout Plain Layout
23335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23338 \begin_layout Plain Layout
23339 \begin_inset Formula $\dashv$
23349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23352 \begin_layout Plain Layout
23360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23363 \begin_layout Plain Layout
23364 \begin_inset Formula $\frown$
23374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23377 \begin_layout Plain Layout
23385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23388 \begin_layout Plain Layout
23389 \begin_inset Formula $\rhd$
23399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23402 \begin_layout Plain Layout
23410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23413 \begin_layout Plain Layout
23414 \begin_inset Formula $\unrhd$
23424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23427 \begin_layout Plain Layout
23435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23438 \begin_layout Plain Layout
23439 \begin_inset Formula $\lessgtr$
23449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23452 \begin_layout Plain Layout
23460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23463 \begin_layout Plain Layout
23464 \begin_inset Formula $\parallel$
23474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23477 \begin_layout Plain Layout
23485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23488 \begin_layout Plain Layout
23489 \begin_inset Formula $\nparallel$
23503 \begin_inset space \hfill{}
23509 \begin_layout Standard
23510 \begin_inset VSpace medskip
23525 are bigger than the equal looking operators
23540 \begin_layout Standard
23541 Relations are, in contrary to symbols, always surrounded by space.
23544 \begin_layout Standard
23545 Relations with labels can be created with the command
23552 \begin_inset Index idx
23555 \begin_layout Plain Layout
23566 \begin_layout Standard
23568 \begin_inset Tabular
23569 <lyxtabular version="3" rows="2" columns="2">
23570 <features rotate="0" tabularvalignment="middle">
23571 <column alignment="center" valignment="top">
23572 <column alignment="center" valignment="top">
23574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23577 \begin_layout Plain Layout
23583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23586 \begin_layout Plain Layout
23588 \begin_inset Note Note
23591 \begin_layout Plain Layout
23598 is only used as spacer.
23610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23613 \begin_layout Plain Layout
23617 \begin_inset space \textvisiblespace{}
23625 \begin_inset space \textvisiblespace{}
23629 \begin_inset Formula $\downarrow$
23635 \begin_inset space \textvisiblespace{}
23639 \begin_inset space \textvisiblespace{}
23647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23650 \begin_layout Plain Layout
23651 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23667 \begin_layout Section
23671 \begin_layout Subsection
23672 Predefined Functions
23673 \begin_inset CommandInset label
23675 name "sub:Predefined-Functions"
23680 \begin_inset Index idx
23683 \begin_layout Plain Layout
23684 Functions ! predefined
23692 \begin_layout Standard
23693 In general, variables are set
23697 in mathematical expressions, but not function names, because
23698 \begin_inset Formula $sin$
23701 could be misunderstood as
23702 \begin_inset Formula $s\cdot i\cdot n$
23706 Therefore there are predefined functionswhich are additionally a bit separated
23708 They are inserted as commands starting with a backslash before their name.
23711 \begin_layout Standard
23713 \begin_inset Tabular
23714 <lyxtabular version="3" rows="2" columns="4">
23715 <features rotate="0" tabularvalignment="middle">
23716 <column alignment="center" valignment="top" width="0pt">
23717 <column alignment="center" valignment="top" width="0pt">
23718 <column alignment="center" valignment="top" width="0pt">
23719 <column alignment="center" valignment="top" width="0pt">
23721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23724 \begin_layout Plain Layout
23730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23733 \begin_layout Plain Layout
23739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23742 \begin_layout Plain Layout
23748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23751 \begin_layout Plain Layout
23759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23762 \begin_layout Plain Layout
23768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23771 \begin_layout Plain Layout
23772 \begin_inset Formula $Asin(x)+B$
23780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23783 \begin_layout Plain Layout
23791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23794 \begin_layout Plain Layout
23795 \begin_inset Formula $A\sin(x)+B$
23811 \begin_layout Standard
23812 The following functions are predefined:
23815 \begin_layout Standard
23816 \begin_inset VSpace -2mm
23822 \begin_layout Standard
23824 \begin_inset Tabular
23825 <lyxtabular version="3" rows="9" columns="4">
23826 <features rotate="0" tabularvalignment="middle">
23827 <column alignment="center" valignment="top" width="0pt">
23828 <column alignment="center" valignment="top" width="0pt">
23829 <column alignment="center" valignment="top" width="0pt">
23830 <column alignment="center" valignment="top" width="0pt">
23832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23835 \begin_layout Plain Layout
23841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23844 \begin_layout Plain Layout
23850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23853 \begin_layout Plain Layout
23859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23862 \begin_layout Plain Layout
23870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23873 \begin_layout Plain Layout
23881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23884 \begin_layout Plain Layout
23892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23895 \begin_layout Plain Layout
23903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23906 \begin_layout Plain Layout
23916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23919 \begin_layout Plain Layout
23927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23930 \begin_layout Plain Layout
23938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23941 \begin_layout Plain Layout
23949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23952 \begin_layout Plain Layout
23962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23965 \begin_layout Plain Layout
23973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23976 \begin_layout Plain Layout
23984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23987 \begin_layout Plain Layout
23995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23998 \begin_layout Plain Layout
24008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24011 \begin_layout Plain Layout
24019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24022 \begin_layout Plain Layout
24030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24033 \begin_layout Plain Layout
24041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24044 \begin_layout Plain Layout
24054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24057 \begin_layout Plain Layout
24065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24068 \begin_layout Plain Layout
24076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24079 \begin_layout Plain Layout
24087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24090 \begin_layout Plain Layout
24100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24103 \begin_layout Plain Layout
24111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24114 \begin_layout Plain Layout
24122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24125 \begin_layout Plain Layout
24133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24136 \begin_layout Plain Layout
24146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24149 \begin_layout Plain Layout
24157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24160 \begin_layout Plain Layout
24168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24171 \begin_layout Plain Layout
24179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24182 \begin_layout Plain Layout
24192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24195 \begin_layout Plain Layout
24203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24206 \begin_layout Plain Layout
24214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24217 \begin_layout Plain Layout
24225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24228 \begin_layout Plain Layout
24244 \begin_layout Standard
24245 They can also be inserted with the math toolbar button
24246 \begin_inset Graphics
24247 filename ../images/math/functions.png
24255 \begin_layout Subsection
24256 Self-defined Functions
24257 \begin_inset Index idx
24260 \begin_layout Plain Layout
24261 Functions ! self-defined
24269 \begin_layout Standard
24270 To use a function that is not predefined, like for example the sign function
24271 sgn(x), there are two possibilities:
24274 \begin_layout Itemize
24275 Define the function by inserting the following line to the LaTeX-preamble
24279 \begin_layout Plain Layout
24284 DeclareMathOperator
24287 \begin_inset CommandInset ref
24289 reference "sub:Self-defined-Operators"
24299 \begin_inset Newline newline
24303 \begin_inset VSpace -3mm
24307 \begin_inset Newline newline
24314 DeclareMathOperator{
24319 \begin_inset Index idx
24322 \begin_layout Plain Layout
24327 DeclareMathOperator
24333 \begin_inset Newline newline
24337 \begin_inset VSpace -2mm
24341 \begin_inset Newline newline
24344 Now the new defined function can be called with the command
24353 \begin_layout Itemize
24354 Write the formula as usual, mark the formula name, in our example the letters
24359 , and change it to mathematical text.
24360 Finally, a space is inserted between prefactor and function.
24363 \begin_layout Standard
24364 The result is the same with both methods as with a predefined function
24368 \begin_layout Plain Layout
24369 In LyX self-defined functions are displayed red, predefined ones black.
24377 \begin_layout Standard
24379 \begin_inset Tabular
24380 <lyxtabular version="3" rows="3" columns="2">
24381 <features rotate="0" tabularvalignment="middle">
24382 <column alignment="center" valignment="top" width="0pt">
24383 <column alignment="center" valignment="top" width="0pt">
24385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24388 \begin_layout Plain Layout
24394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24397 \begin_layout Plain Layout
24405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24408 \begin_layout Plain Layout
24416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24419 \begin_layout Plain Layout
24420 \begin_inset Formula $A\sgn(x)+B$
24430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24433 \begin_layout Plain Layout
24437 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
24445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24448 \begin_layout Plain Layout
24449 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24465 \begin_layout Standard
24466 The first method is more suitable when the self-defined function should
24467 be used several times.
24470 \begin_layout Subsection
24472 \begin_inset Index idx
24475 \begin_layout Plain Layout
24484 \begin_layout Standard
24485 For limits, in addition to the commands
24492 \begin_inset Index idx
24495 \begin_layout Plain Layout
24515 the following functions are defined:
24518 \begin_layout Standard
24520 \begin_inset Tabular
24521 <lyxtabular version="3" rows="5" columns="2">
24522 <features rotate="0" tabularvalignment="middle">
24523 <column alignment="center" valignment="top">
24524 <column alignment="center" valignment="top">
24526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24529 \begin_layout Plain Layout
24535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24538 \begin_layout Plain Layout
24540 \begin_inset Note Note
24543 \begin_layout Plain Layout
24550 is only used as spacer.
24562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24565 \begin_layout Plain Layout
24573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24576 \begin_layout Plain Layout
24577 \begin_inset Formula $\varliminf$
24587 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24590 \begin_layout Plain Layout
24598 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24601 \begin_layout Plain Layout
24602 \begin_inset Formula $\varlimsup$
24612 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24615 \begin_layout Plain Layout
24623 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24626 \begin_layout Plain Layout
24627 \begin_inset Formula $\varprojlim$
24637 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24640 \begin_layout Plain Layout
24648 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24651 \begin_layout Plain Layout
24652 \begin_inset Formula $\varinjlim$
24656 \begin_inset Formula $\raisebox{-2.5mm}{}$
24672 \begin_layout Standard
24673 \begin_inset VSpace medskip
24676 The limit is created by inserting a subscript.
24677 It is set right beside the function in an inline formula:
24680 \begin_layout Standard
24682 \begin_inset Tabular
24683 <lyxtabular version="3" rows="2" columns="2">
24684 <features rotate="0" tabularvalignment="middle">
24685 <column alignment="center" valignment="top" width="0pt">
24686 <column alignment="center" valignment="top" width="0pt">
24688 <cell alignment="center" valignment="top" usebox="none">
24691 \begin_layout Plain Layout
24697 <cell alignment="center" valignment="top" usebox="none">
24700 \begin_layout Plain Layout
24701 \begin_inset space \hspace{}
24706 \begin_inset Note Note
24709 \begin_layout Plain Layout
24716 are used here as spacer.
24728 <cell alignment="center" valignment="top" usebox="none">
24731 \begin_layout Plain Layout
24737 \begin_inset space \textvisiblespace{}
24741 \begin_inset space \textvisiblespace{}
24749 <cell alignment="center" valignment="top" usebox="none">
24752 \begin_layout Plain Layout
24753 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
24769 \begin_layout Standard
24770 In a displayed formula the limit is set below the formula, as usual:
24771 \begin_inset Formula
24781 \begin_layout Subsection
24783 \begin_inset Index idx
24786 \begin_layout Plain Layout
24787 Functions ! modulo-
24795 \begin_layout Standard
24796 The modulo-function is special, because it exists in four variants.
24797 The variants in a displayed formula are:
24798 \begin_inset Formula
24800 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
24801 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
24802 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
24803 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
24804 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
24812 \begin_layout Standard
24813 In an inline formula less space is set before the function names for all
24815 By default the modulo-functions take only the first following character
24817 To use more than one character, one has to put them into TeX-braces:
24818 \begin_inset Formula
24820 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
24821 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
24822 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
24830 \begin_layout Section
24832 \begin_inset Index idx
24835 \begin_layout Plain Layout
24844 \begin_layout Subsection
24845 Special Characters in Mathematical Text
24848 \begin_layout Standard
24849 The following commands can only be used in mathematical text or in TeX-mode:
24852 \begin_layout Standard
24853 \begin_inset space \hfill{}
24857 \begin_inset Tabular
24858 <lyxtabular version="3" rows="8" columns="2">
24859 <features rotate="0" tabularvalignment="middle">
24860 <column alignment="block" valignment="top">
24861 <column alignment="block" valignment="top">
24863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24866 \begin_layout Plain Layout
24872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24875 \begin_layout Plain Layout
24883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24886 \begin_layout Plain Layout
24894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24897 \begin_layout Plain Layout
24898 \begin_inset Formula $\textrm{œ}$
24908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24911 \begin_layout Plain Layout
24919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24922 \begin_layout Plain Layout
24923 \begin_inset Formula $\textrm{Œ}$
24933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24936 \begin_layout Plain Layout
24944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24947 \begin_layout Plain Layout
24948 \begin_inset Formula $\textrm{æ}$
24958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24961 \begin_layout Plain Layout
24969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24972 \begin_layout Plain Layout
24973 \begin_inset Formula $\textrm{Æ}$
24983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24986 \begin_layout Plain Layout
24994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24997 \begin_layout Plain Layout
24998 \begin_inset Formula $\textrm{\aa}$
25008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25011 \begin_layout Plain Layout
25015 \begin_inset Index idx
25018 \begin_layout Plain Layout
25025 \begin_layout Plain Layout
25046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25049 \begin_layout Plain Layout
25050 \begin_inset Formula $\textrm{Å}$
25060 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25063 \begin_layout Plain Layout
25071 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25074 \begin_layout Plain Layout
25075 \begin_inset Formula $\textrm{ı}$
25089 \begin_inset space \hfill{}
25093 \begin_inset Tabular
25094 <lyxtabular version="3" rows="8" columns="2">
25095 <features rotate="0" tabularvalignment="middle">
25096 <column alignment="block" valignment="top">
25097 <column alignment="center" valignment="top">
25099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25102 \begin_layout Plain Layout
25104 \begin_inset Note Note
25107 \begin_layout Plain Layout
25109 \begin_inset space \thinspace{}
25112 mm is used for separation, because otherwise the output will be ¡ and ¿
25123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25126 \begin_layout Plain Layout
25134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25137 \begin_layout Plain Layout
25145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25148 \begin_layout Plain Layout
25149 \begin_inset Formula $\textrm{ø}$
25159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25162 \begin_layout Plain Layout
25170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25173 \begin_layout Plain Layout
25174 \begin_inset Formula $\textrm{Ø}$
25184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25187 \begin_layout Plain Layout
25195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25198 \begin_layout Plain Layout
25199 \begin_inset Formula $\textrm{ł}$
25209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25212 \begin_layout Plain Layout
25220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25223 \begin_layout Plain Layout
25224 \begin_inset Formula $\textrm{Ł}$
25234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25237 \begin_layout Plain Layout
25239 \begin_inset space \hspace{}
25244 \begin_inset space \textvisiblespace{}
25252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25255 \begin_layout Plain Layout
25256 \begin_inset Formula $\textrm{!`}$
25266 <cell alignment="center" valignment="top" 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" 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
25309 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25312 \begin_layout Plain Layout
25313 \begin_inset Formula $\textrm{ȷ}$
25327 \begin_inset space \hfill{}
25333 \begin_layout Standard
25335 \begin_inset Formula $\textrm{\textrm{Å}}$
25339 \begin_inset Formula $\textrm{\textrm{Ø}}$
25342 can also be inserted via the math toolbar button
25343 \begin_inset Graphics
25344 filename ../images/math/digamma.png
25352 \begin_layout Standard
25353 An exception are the commands
25356 \begin_inset space \hspace{}
25365 \begin_inset space \hspace{}
25371 , because they can be inserted in LyX directly to text.
25374 \begin_layout Subsection
25376 \begin_inset CommandInset label
25378 name "sub:Accents-in-Text"
25383 \begin_inset Index idx
25386 \begin_layout Plain Layout
25395 \begin_layout Standard
25396 With the following commands all letters can be accented.
25397 The commands must be inserted in TeX-mode.
25400 \begin_layout Standard
25401 \begin_inset space \hfill{}
25405 \begin_inset Tabular
25406 <lyxtabular version="3" rows="8" columns="2">
25407 <features rotate="0" tabularvalignment="middle">
25408 <column alignment="block" valignment="top">
25409 <column alignment="block" valignment="top">
25411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25414 \begin_layout Plain Layout
25420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25423 \begin_layout Plain Layout
25431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25434 \begin_layout Plain Layout
25438 \begin_inset Quotes grd
25446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25449 \begin_layout Plain Layout
25453 \begin_layout Plain Layout
25469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25472 \begin_layout Plain Layout
25480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25483 \begin_layout Plain Layout
25487 \begin_layout Plain Layout
25503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25506 \begin_layout Plain Layout
25510 \begin_inset space \textvisiblespace{}
25518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25521 \begin_layout Plain Layout
25525 \begin_layout Plain Layout
25541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25544 \begin_layout Plain Layout
25552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25555 \begin_layout Plain Layout
25559 \begin_layout Plain Layout
25575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25578 \begin_layout Plain Layout
25582 \begin_inset space \textvisiblespace{}
25590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25593 \begin_layout Plain Layout
25597 \begin_layout Plain Layout
25613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25616 \begin_layout Plain Layout
25620 \begin_inset space \textvisiblespace{}
25628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25631 \begin_layout Plain Layout
25635 \begin_layout Plain Layout
25651 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25654 \begin_layout Plain Layout
25658 \begin_inset space \textvisiblespace{}
25666 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25669 \begin_layout Plain Layout
25673 \begin_layout Plain Layout
25693 \begin_inset space \hfill{}
25697 \begin_inset Tabular
25698 <lyxtabular version="3" rows="8" columns="2">
25699 <features rotate="0" tabularvalignment="middle">
25700 <column alignment="block" valignment="top">
25701 <column alignment="center" valignment="top">
25703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25706 \begin_layout Plain Layout
25712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25715 \begin_layout Plain Layout
25723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25726 \begin_layout Plain Layout
25730 \begin_inset space \textvisiblespace{}
25738 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25741 \begin_layout Plain Layout
25745 \begin_layout Plain Layout
25761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25764 \begin_layout Plain Layout
25772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25775 \begin_layout Plain Layout
25779 \begin_layout Plain Layout
25795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25798 \begin_layout Plain Layout
25802 \begin_inset Index idx
25805 \begin_layout Plain Layout
25816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25819 \begin_layout Plain Layout
25823 \begin_layout Plain Layout
25839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25842 \begin_layout Plain Layout
25850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25853 \begin_layout Plain Layout
25857 \begin_layout Plain Layout
25873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25876 \begin_layout Plain Layout
25880 \begin_inset space \textvisiblespace{}
25888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25891 \begin_layout Plain Layout
25895 \begin_layout Plain Layout
25911 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25914 \begin_layout Plain Layout
25918 \begin_inset space \textvisiblespace{}
25926 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25929 \begin_layout Plain Layout
25933 \begin_layout Plain Layout
25949 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25952 \begin_layout Plain Layout
25956 \begin_inset space \textvisiblespace{}
25964 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25967 \begin_layout Plain Layout
25971 \begin_layout Plain Layout
25991 \begin_inset space \hfill{}
25997 \begin_layout Standard
25998 \begin_inset VSpace medskip
26007 also two different characters can be accented.
26013 \begin_inset space \textvisiblespace{}
26022 \begin_layout Plain Layout
26034 \begin_layout Standard
26047 can in combination with vowels directly be inserted with the keyboard without
26049 The same applies for the tilde
26053 \begin_layout Plain Layout
26054 This only applies for keyboards where the tilde is defined as accent.
26063 in combination with
26078 \begin_layout Standard
26121 and accents that are inserted directly with the keyboard are also available
26122 in mathematical text.
26123 For the other accents there are special math commands to be used in formulas,
26125 \begin_inset CommandInset ref
26127 reference "sub:Accents-for-one"
26134 \begin_layout Standard
26135 \begin_inset VSpace bigskip
26138 Furthermore, with the command
26145 \begin_inset Index idx
26148 \begin_layout Plain Layout
26156 all numbers and letters can be set into a circle, quasi accented with a
26157 circle, similar to the copyright symbol.
26160 \begin_layout Standard
26162 \begin_inset Tabular
26163 <lyxtabular version="3" rows="3" columns="2">
26164 <features rotate="0" tabularvalignment="middle">
26165 <column alignment="center" valignment="top">
26166 <column alignment="center" valignment="top">
26168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26171 \begin_layout Plain Layout
26177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26180 \begin_layout Plain Layout
26182 \begin_inset Note Note
26185 \begin_layout Plain Layout
26192 is only used as spacer.
26204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26207 \begin_layout Plain Layout
26215 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26218 \begin_layout Plain Layout
26222 \begin_layout Plain Layout
26238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26241 \begin_layout Plain Layout
26252 raisebox{-1.5pt}{W}}
26257 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26260 \begin_layout Plain Layout
26261 \begin_inset Formula $\raisebox{4.5mm}{}$
26268 \begin_layout Plain Layout
26286 \begin_inset Formula $\raisebox{-2mm}{}$
26302 \begin_layout Standard
26303 One has to take care that the character fits in the circle.
26314 \begin_layout Plain Layout
26316 \begin_inset CommandInset ref
26318 reference "sub:Font-Sizes"
26327 specifies thereby the size of the circle.
26338 \begin_layout Plain Layout
26340 \begin_inset CommandInset ref
26342 reference "sub:Boxes-without-Frame"
26351 the character can be centered.
26354 \begin_layout Subsection
26356 \begin_inset Index idx
26359 \begin_layout Plain Layout
26368 \begin_layout Standard
26369 Old-style figures (also known as old-style numerals) are created with the
26377 \begin_inset Index idx
26380 \begin_layout Plain Layout
26389 The command can be used in formulas and in TeX-mode.
26390 The command scheme is:
26393 \begin_layout Standard
26398 oldstylenums{number}
26401 \begin_layout Standard
26406 oldstylenums{0123456789
26409 \begin_inset Formula $\oldstylenums{0123456789}$
26415 \begin_layout Section
26417 \begin_inset CommandInset label
26419 name "sec:Formula-Styles"
26424 \begin_inset Index idx
26427 \begin_layout Plain Layout
26436 \begin_layout Itemize
26437 There are two different alignment styles:
26441 \begin_layout Description
26442 Centered is the predefined standard
26445 \begin_layout Description
26446 Indented for this the option
26450 must be inserted in the menu
26452 Document\SpecialChar \menuseparator
26458 \begin_inset space ~
26464 \begin_layout Standard
26469 is used, the indentation can be adjusted with the length
26476 \begin_inset Index idx
26479 \begin_layout Plain Layout
26488 Should the distance be 15
26489 \begin_inset space \thinspace{}
26492 mm, the following command line is inserted in the LaTeX-preamble
26495 \begin_layout Standard
26505 \begin_layout Standard
26506 When no length is specified, the predefined value of 30
26507 \begin_inset space \thinspace{}
26514 \begin_layout Itemize
26515 And two different numbering styles:
26519 \begin_layout Description
26520 Right is the predefined standard
26523 \begin_layout Description
26524 Left for this the option
26528 must be inserted in the menu
26530 Document\SpecialChar \menuseparator
26536 \begin_inset space ~
26543 \begin_layout Standard
26552 can also be used together.
26553 In this case both options are inserted, separated by a comma.
26556 \begin_layout Standard
26557 The chosen styles are used for all displayed formulas of the document.
26558 When both, centered and indented formulas should be created in a document,
26564 The indented formulas are then set in a flalign environment, see
26565 \begin_inset CommandInset ref
26567 reference "sub:Flalign-Environment"
26574 \begin_layout Section
26576 \begin_inset CommandInset label
26578 name "sec:Multiline-Formulas"
26583 \begin_inset Index idx
26586 \begin_layout Plain Layout
26587 Formula ! multiline
26595 \begin_layout Subsection
26599 \begin_layout Standard
26600 In LyX multiline formulas are created by pressing
26605 arg "newline-insert newline"
26611 This creates either an
26613 eqnarray environment
26615 that is described in
26616 \begin_inset CommandInset ref
26618 reference "sub:Eqnarray-Environment"
26622 or, when the option
26624 Use AMS math package
26626 in the document settings is selected, an
26630 that is described in
26631 \begin_inset CommandInset ref
26633 reference "sub:Standard-align-Environment"
26638 The align environment is recommended because it provides in any case a
26639 typographically correct output.
26642 \begin_layout Standard
26643 There are other multiline formula environments that can be created via the
26646 Insert\SpecialChar \menuseparator
26650 These environments are described in the following sections.
26653 \begin_layout Standard
26654 In all multiline formula environments a new line is created by pressing
26658 arg "newline-insert newline"
26662 To add or delete lines, the math toolbar buttons
26663 \begin_inset Graphics
26664 filename ../images/tabular-feature_append-row.png
26670 \begin_inset Graphics
26671 filename ../images/tabular-feature_delete-row.png
26676 , respectively, or the menu
26678 Edit\SpecialChar \menuseparator
26684 \begin_layout Subsubsection
26686 \begin_inset CommandInset label
26688 name "sub:Line-Separation"
26693 \begin_inset Index idx
26696 \begin_layout Plain Layout
26697 Formula ! multiline ! Line separation
26705 \begin_layout Standard
26706 There is sometimes not enough space in multiline formulas between the lines:
26707 \begin_inset Formula
26709 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}\\
26710 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
26718 \begin_layout Standard
26719 In LaTeX additional line space is specified as optional argument of the
26721 This is not yet possible in LyX
26725 \begin_layout Plain Layout
26727 \begin_inset CommandInset href
26729 name "LyX-bug #1505"
26730 target "http://www.lyx.org/trac/ticket/1505"
26739 , therefore the whole formula must be inserted in TeX-mode.
26740 To add in our example space, the command
26748 is inserted at the end of the first line.
26753 \begin_layout Plain Layout
26760 \begin_layout Plain Layout
26762 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
26765 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
26772 \begin_layout Plain Layout
26776 left(B^{2}+x_{0}^{2}
26784 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
26789 \begin_layout Plain Layout
26801 \begin_layout Standard
26802 \begin_inset VSpace bigskip
26805 To set the line separation for all lines in a formula, the length
26812 \begin_inset Index idx
26815 \begin_layout Plain Layout
26825 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
26836 \begin_inset space \thinspace{}
26841 \begin_inset space \thinspace{}
26844 mm additional line separation as in the previous example, the command
26847 \begin_layout Standard
26857 \begin_layout Standard
26858 is inserted in TeX-mode before the formula.
26859 This requires that the LaTeX-package
26867 \begin_layout Plain Layout
26872 is part of every LaTeX standard installation.
26878 \begin_inset Index idx
26881 \begin_layout Plain Layout
26887 was loaded in LaTeX-preamble with the line
26890 \begin_layout Standard
26898 \begin_layout Standard
26903 \begin_layout Plain Layout
26915 \begin_inset Formula
26917 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}\\
26918 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
26926 \begin_layout Standard
26930 \begin_layout Plain Layout
26941 To get back to the predefined distance,
26947 is set to the value 3
26948 \begin_inset space \thinspace{}
26954 \begin_layout Subsubsection
26956 \begin_inset CommandInset label
26958 name "sub:Column-Separation"
26963 \begin_inset Index idx
26966 \begin_layout Plain Layout
26967 Formula ! multiline ! Column separation
26975 \begin_layout Standard
26976 Multiline formulas form a matrix.
26977 A formula in the eqnarray environment is for example a matrix with three
26979 By changing the column separation in this environment, the space beside
26980 the relation sign can be changed.
26983 \begin_layout Standard
26984 The column separation is specified with the length
26991 \begin_inset Index idx
26994 \begin_layout Plain Layout
27003 \begin_inset Newline newline
27006 column separation = 2
27007 \begin_inset space \thinspace{}
27017 \begin_inset Newline newline
27023 \begin_layout Standard
27033 \begin_layout Standard
27034 inserted in TeX-mode, sets for all following formulas a column separation
27036 \begin_inset space \thinspace{}
27040 To get back to the predefined distance,
27047 \begin_inset space \thinspace{}
27053 \begin_layout Standard
27055 \begin_inset space \thinspace{}
27058 cm column separation:
27062 \begin_layout Plain Layout
27074 \begin_inset Formula
27082 A formula with the predefined column separation for matrices of 10
27083 \begin_inset space \thinspace{}
27090 \begin_layout Plain Layout
27102 \begin_inset Formula
27113 \begin_layout Subsubsection
27115 \begin_inset Index idx
27118 \begin_layout Plain Layout
27127 \begin_layout Standard
27128 Long formulas can be typeset using these methods:
27131 \begin_layout Itemize
27132 When one side of the equation is much shorter than the line width, this
27133 one is chosen for the left side and the right side is typeset over two
27135 \begin_inset Formula
27137 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 \\
27138 & & -\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}
27143 The minus sign at the beginning of the second line does normally not appear
27144 as an operator because it is the first character of the line.
27145 Thus it would not be surrounded by space and could not be distinguished
27146 from the fraction bar.
27148 \begin_inset space \thinspace{}
27151 pt space was inserted behind the minus sign with the command
27161 \begin_layout Plain Layout
27169 \begin_inset CommandInset ref
27171 reference "sub:Variable-Space"
27181 \begin_inset Index idx
27184 \begin_layout Plain Layout
27195 \begin_layout Itemize
27196 When both sides of the equation are too long, the command
27203 \begin_inset Index idx
27206 \begin_layout Plain Layout
27215 It is inserted in the first column of the first line and causes all further
27216 insertions to overwrite the following columns:
27217 \begin_inset Formula
27219 \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 \\
27220 & & -\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 \\
27221 & & =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}
27226 After the insertion of
27232 , the cursor is in a purple box that is a bit shifted to the left from the
27234 In this the formula is inserted.
27235 \begin_inset Newline newline
27238 The content of the further lines is inserted to the second or another formula
27240 The greater the column number where it was inserted, the larger the indentation.
27241 \begin_inset VSpace medskip
27245 \begin_inset Newline newline
27249 \begin_inset Note Greyedout
27252 \begin_layout Plain Layout
27253 Note the following when using
27262 \begin_layout Itemize
27263 The formula doesn't use the full page width.
27265 \begin_inset space \thinspace{}
27269 \begin_inset space \space{}
27273 \begin_inset Formula $-B^{2}$
27276 is added to the first line in the above example, it would have been outside
27278 To better use the width, negative space can be inserted at the beginning
27282 \begin_layout Itemize
27283 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27288 \begin_layout Plain Layout
27289 \begin_inset CommandInset href
27291 name "LyX-bug #1429"
27292 target "http://www.lyx.org/trac/ticket/1429"
27301 One can only set the cursor at the beginning of the line and move it with
27310 \begin_layout Itemize
27311 Other methods to set long formulas are offered by the environments described
27313 \begin_inset CommandInset ref
27315 reference "sub:Multline-Environment"
27320 \begin_inset CommandInset ref
27322 reference "sub:Multiline-Formula-Parts"
27329 \begin_layout Subsubsection
27331 \begin_inset CommandInset label
27333 name "sub:Multiline-Brackets"
27338 \begin_inset Index idx
27341 \begin_layout Plain Layout
27342 Brackets ! for multiline expressions
27350 \begin_layout Standard
27351 For brackets spanning multiple lines the following problem occurs:
27352 \begin_inset Formula
27354 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27355 & & \left.\cdots+B-D\right]
27363 \begin_layout Standard
27364 The closing bracket is smaller than the opening bracket because brackets
27365 with variable size may not span multiple lines.
27368 \begin_layout Standard
27369 To set the bracket size for the second line correctly, the first line is
27377 \begin_inset Index idx
27380 \begin_layout Plain Layout
27388 and the second line with
27396 \begin_layout Plain Layout
27410 \begin_inset CommandInset ref
27412 reference "sub:Automatic-Bracket-Size"
27424 \begin_inset Index idx
27427 \begin_layout Plain Layout
27450 \begin_inset space \textvisiblespace{}
27460 \begin_inset space \textvisiblespace{}
27470 \begin_inset space \textvisiblespace{}
27476 \begin_inset Formula $\downarrow$
27482 \begin_inset Index idx
27485 \begin_layout Plain Layout
27493 is inserted, because the multiplication operator with its limits is the
27494 largest symbol in the first line and this should be the size for the bracket
27495 in the second line.
27498 \begin_layout Standard
27499 The result is this:
27500 \begin_inset Formula
27502 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27503 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
27511 \begin_layout Subsection
27515 \begin_layout Standard
27516 Align environments can be used for every kind of multiline formulas.
27517 They are especially useful to set several formulas side by side.
27520 \begin_layout Standard
27521 Align environments consist of columns.
27522 The odd columns are right aligned, the even ones left aligned.
27523 Every line in an Align environment can be numbered.
27526 \begin_layout Standard
27527 Align environments are created via the menu
27529 Insert\SpecialChar \menuseparator
27535 Edit\SpecialChar \menuseparator
27536 Math\SpecialChar \menuseparator
27537 Change Formula Type
27539 already existing formulas can be converted to Align environments.
27542 \begin_layout Standard
27543 To add or delete columns, the math toolbar buttons
27544 \begin_inset Graphics
27545 filename ../images/tabular-feature_append-column.png
27551 \begin_inset Graphics
27552 filename ../images/tabular-feature_delete-column.png
27557 , respectively, or the menu
27559 Edit\SpecialChar \menuseparator
27565 \begin_layout Subsubsection
27566 Standard align Environment
27567 \begin_inset CommandInset label
27569 name "sub:Standard-align-Environment"
27574 \begin_inset Index idx
27577 \begin_layout Plain Layout
27578 Formula ! multiline ! align environment
27586 \begin_layout Standard
27587 This Align environment is created by pressing
27590 arg "newline-insert newline"
27593 in a formula or by the menu
27595 Insert\SpecialChar \menuseparator
27596 Math\SpecialChar \menuseparator
27597 AMS align Environment
27602 \begin_layout Standard
27603 An example for two formulas set side by side, that are created with a four
27604 column align environment:
27605 \begin_inset Formula
27607 A & =\sin(B) & C & =D\\
27608 C & \ne A & B & \ne D
27613 As it can be seen, the formulas in this environment are placed so as if
27622 \begin_layout Plain Layout
27630 \begin_inset CommandInset ref
27632 reference "sub:Variable-Space"
27643 before the first and after every even column.
27644 When the formula style
27650 \begin_layout Plain Layout
27652 \begin_inset CommandInset ref
27654 reference "sec:Formula-Styles"
27665 is used, the formula is set without the
27671 before the first column.
27674 \begin_layout Subsubsection
27675 Alignat Environment
27676 \begin_inset Index idx
27679 \begin_layout Plain Layout
27680 Formula ! multiline ! alignat environment
27688 \begin_layout Standard
27689 The alignat environment has no predefined column separation.
27690 It can be inserted manually with the spaces that are described
27691 \begin_inset CommandInset ref
27693 reference "sub:Space"
27700 \begin_layout Standard
27701 The above example in the alignat environment where 1
27702 \begin_inset space \thinspace{}
27705 cm space was inserted at the beginning of the second formula:
27706 \begin_inset Formula
27707 \begin{alignat*}{2}
27708 A & =\sin(B) & \hspace{1cm}C & =D\\
27709 C & \ne A & B & \ne D
27714 Because the column separation can be set separately for every column, this
27715 environment is especially suitable to set three and more formulas side
27719 \begin_layout Subsubsection
27720 Flalign Environment
27721 \begin_inset CommandInset label
27723 name "sub:Flalign-Environment"
27728 \begin_inset Index idx
27731 \begin_layout Plain Layout
27732 Formula ! multiline ! flalign environment
27740 \begin_layout Standard
27741 In this environment the first two columns are always set as much as possible
27742 to the left and the last two ones to the right.
27744 \begin_inset Formula
27746 A & =1 & B & =2 & C & =3\\
27747 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
27755 \begin_layout Standard
27756 By creating a flalign environment with an odd number of columns where an
27757 empty TeX-brace is inserted to the last column, several formulas in a document
27758 can be set to the left, although the formula style
27763 As example the indented formula
27764 \begin_inset CommandInset ref
27766 reference "eq:VolInt"
27771 \begin_inset Formula
27773 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
27778 The first two columns contain the formula.
27779 To indent it as with the formula style
27784 \begin_inset space \thinspace{}
27787 pt space was inserted at the beginning of the first column.
27790 \begin_layout Subsection
27791 Eqnarray Environment
27792 \begin_inset CommandInset label
27794 name "sub:Eqnarray-Environment"
27799 \begin_inset Index idx
27802 \begin_layout Plain Layout
27803 Formula ! multiline ! eqnarray environment
27811 \begin_layout Standard
27812 When this environment has been created, three blue boxes appear.
27813 The content of the first box is right aligned, the content of the last
27815 The content of the middle box appears centered and a bit smaller, because
27816 it is designed to insert there only relation characters.
27817 \begin_inset Formula
27819 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
27829 \begin_layout Subsection
27831 \begin_inset Index idx
27834 \begin_layout Plain Layout
27835 Formula ! multiline ! gather environment
27843 \begin_layout Standard
27844 This environment consists of only one centered column.
27845 Every line can be numbered.
27846 \begin_inset Formula
27857 \begin_layout Subsection
27858 Multline Environment
27859 \begin_inset CommandInset label
27861 name "sub:Multline-Environment"
27866 \begin_inset Index idx
27869 \begin_layout Plain Layout
27870 Formula ! multiline ! multline environment
27878 \begin_layout Standard
27879 The multline environment consists, like the gather environment, of only
27881 But the first line is left aligned, the last one right aligned.
27882 All other lines are centered.
27883 Therefore this environment is suitable for long formulas.
27885 \begin_inset CommandInset ref
27887 reference "eq:lefteqn"
27891 in the multline environment:
27892 \begin_inset Formula
27894 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}\\
27895 -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}\\
27896 =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}}
27904 \begin_layout Standard
27905 In the output only the last (first) line of a multline environment appears
27906 numbered when the document numbering is right (left).
27910 \begin_layout Plain Layout
27911 numbering styles see
27912 \begin_inset CommandInset ref
27914 reference "sec:Formula-Styles"
27926 \begin_layout Standard
27934 \begin_inset Index idx
27937 \begin_layout Plain Layout
27952 \begin_inset Index idx
27955 \begin_layout Plain Layout
27963 a centered line can be right or left aligned, respectively.
27964 The commands are used as follows:
27967 \begin_layout Standard
27972 shoveright{line content}
27978 shoveleft{line content}
27981 \begin_layout Standard
27982 \begin_inset VSpace medskip
27992 \begin_inset Index idx
27995 \begin_layout Plain Layout
28003 specifies the distance of the first line from the left page margin.
28004 Predefined is the length 0
28005 \begin_inset space \thinspace{}
28011 \begin_layout Standard
28012 As example the above formula where the command
28015 \begin_layout Standard
28025 \begin_layout Standard
28026 was inserted in TeX-mode before:
28030 \begin_layout Plain Layout
28042 \begin_inset Formula
28044 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}\\
28045 \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}}\\
28046 =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}}
28055 \begin_layout Plain Layout
28066 The second line was left aligned using
28075 \begin_layout Subsection
28076 Multiline Formula Parts
28077 \begin_inset CommandInset label
28079 name "sub:Multiline-Formula-Parts"
28084 \begin_inset Index idx
28087 \begin_layout Plain Layout
28088 Formula ! multiline ! formula parts
28096 \begin_layout Standard
28097 To display only parts of a formula with multiple lines, one of the following
28098 environments is used:
28115 They can be inserted via the menu
28117 Insert\SpecialChar \menuseparator
28120 or by using the commands described in this section.
28123 \begin_layout Standard
28124 The first three have the same properties as the corresponding multiline
28125 formula environments, but it is possible to set further formula parts beside
28128 \begin_inset Formula
28130 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28131 \Delta E\Delta t & \ge\frac{\hbar}{2}
28133 \right\} \textrm{Uncertainty relations}
28141 \begin_layout Standard
28142 To get this formula, a displayed formula is created where the command
28149 \begin_inset Index idx
28152 \begin_layout Plain Layout
28161 A purple box appears around the blue formula box where now columns and
28162 lines can be added.
28163 Outside the multiline environment other formula parts can be set, like
28167 \begin_layout Standard
28168 The aligned environment is also suitable for long formulas whose lines are
28169 horizontally aligned.
28170 Using aligned in a displayed formula has the advantage that the formula
28171 number is vertically centered behind the lines.
28173 \begin_inset CommandInset ref
28175 reference "eq:shortlong"
28179 in the aligned environment:
28180 \begin_inset Formula
28182 \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}|}\\
28183 & -\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}|}
28192 \begin_layout Standard
28193 To use the environments
28212 \begin_inset Index idx
28215 \begin_layout Plain Layout
28230 \begin_inset Index idx
28233 \begin_layout Plain Layout
28248 \begin_inset Index idx
28251 \begin_layout Plain Layout
28259 are inserted, respectively.
28260 The split environment has the same properties as the aligned environment
28261 but it can only have two columns.
28264 \begin_layout Subsection
28265 Text in multiline Formulas
28266 \begin_inset CommandInset label
28268 name "sub:Text-in-multiline"
28273 \begin_inset Index idx
28276 \begin_layout Plain Layout
28283 \begin_inset Index idx
28286 \begin_layout Plain Layout
28287 Formula ! multiline ! text
28295 \begin_layout Standard
28296 In the Align environments, and the multline and gather environment, text
28297 can be inserted that will appear in a separate line and doesn't affect
28298 the column alignment.
28299 To do this, the command
28306 \begin_inset Index idx
28309 \begin_layout Plain Layout
28317 is used in the following scheme:
28320 \begin_layout Standard
28328 \begin_layout Standard
28329 The text should not be longer than a line because it cannot be hyphenated.
28330 As LyX doesn't yet support
28336 directly, the text is written as mathematical text.
28343 must hereby be at the beginning of a line and appears in the output above
28345 An example where the text was inserted at the beginning of the second line:
28346 \begin_inset Formula
28348 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
28349 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
28357 \begin_layout Section
28359 \begin_inset Index idx
28362 \begin_layout Plain Layout
28369 \begin_inset Index idx
28372 \begin_layout Plain Layout
28373 Formula ! numbering|see
28377 \begin_layout Plain Layout
28388 \begin_layout Plain Layout
28403 \begin_layout Subsection
28407 \begin_layout Standard
28408 Numbered formulas can be created with the menu
28410 Insert\SpecialChar \menuseparator
28411 Math\SpecialChar \menuseparator
28413 \begin_inset space ~
28421 \begin_inset space ~
28427 Existing formulas can be numbered with the menu
28429 Edit\SpecialChar \menuseparator
28430 Math\SpecialChar \menuseparator
28432 \begin_inset space ~
28440 arg "math-number-toggle"
28444 The formula number is displayed in LyX behind the formula as a number sign
28446 The number sign is replaced in the output by the formula number.
28449 \begin_layout Standard
28450 When numbering is turned on in multiline formulas, all lines will be numbered.
28451 But the numbering can be controlled with the menu
28453 Edit\SpecialChar \menuseparator
28454 Math\SpecialChar \menuseparator
28456 \begin_inset space ~
28460 \begin_inset space ~
28464 \begin_inset space ~
28472 arg "math-number-line-toggle"
28478 \begin_layout Standard
28479 Except for inline formulas, all formulas can be numbered with two different
28481 \begin_inset CommandInset ref
28483 reference "sec:Formula-Styles"
28490 \begin_layout Subsection
28492 \begin_inset Index idx
28495 \begin_layout Plain Layout
28496 Cross-references ! to formulas
28504 \begin_layout Standard
28505 All labeled formulas can be cross-referenced.
28506 A label is added by the menu
28508 Insert\SpecialChar \menuseparator
28511 or the toolbar button
28512 \begin_inset Graphics
28513 filename ../images/label-insert.png
28519 The cursor must hereby be inside a displayed formula.
28520 Alternatively you can right-click on the formula and choose
28525 A dialog pops up displaying the prefix
28530 The label is inserted there behind the prefix.
28531 The predefined prefix means
28532 \begin_inset Quotes eld
28536 \begin_inset Quotes erd
28539 and makes it easier to find labels in large documents because it marks
28540 it as formula label to divide it from e.
28541 \begin_inset space \thinspace{}
28545 \begin_inset space \space{}
28549 To change a label, the menu
28551 Insert\SpecialChar \menuseparator
28554 is used again or you right-click on a formula and then on
28561 \begin_layout Standard
28562 The name of the label is displayed in LyX within two parentheses behind
28564 A formula with a label is always numbered.
28567 \begin_layout Standard
28568 Cross-references are inserted via the menu
28570 Insert\SpecialChar \menuseparator
28573 or with the toolbar button
28574 \begin_inset Graphics
28575 filename ../images/dialog-show-new-inset_ref.png
28581 A formula cross-reference appears in the output as formula number.
28582 When in the cross-reference dialog window the format
28586 is chosen, the cross-reference appears in the output as formula number
28588 \begin_inset Newline newline
28591 By right-clicking on a cross-reference in LyX, one jumps to the formula
28592 that is referenced.
28595 \begin_layout Standard
28596 Here are as examples cross-references to formulas of the following subsections:
28597 \begin_inset Note Note
28600 \begin_layout Plain Layout
28601 Note the different cross-reference types.
28609 \begin_layout Standard
28611 \begin_inset CommandInset ref
28618 \begin_inset CommandInset ref
28626 \begin_inset CommandInset ref
28632 ) big Latin letters are used for the numbering in contrary to (
28633 \begin_inset CommandInset ref
28642 \begin_layout Standard
28643 \begin_inset VSpace medskip
28646 When the argument of
28654 \begin_layout Plain Layout
28662 \begin_inset CommandInset ref
28664 reference "sub:User-defined-Numbering"
28675 contains a box like in
28676 \begin_inset CommandInset ref
28678 reference "sub:Paragraph-Boxes"
28682 , the formula cannot be referenced.
28685 \begin_layout Subsection
28687 \begin_inset Index idx
28690 \begin_layout Plain Layout
28691 Formula numbering ! subnumbering
28699 \begin_layout Standard
28700 With the help of the commands
28704 begin{subequations}
28712 formulas can be subnumbered.
28713 Both commands are inserted in TeX-mode.
28716 \begin_layout Standard
28718 \begin_inset Formula
28729 \begin_layout Plain Layout
28733 addtocounter{equation}{-1}
28742 \begin_layout Plain Layout
28746 begin{subequations}
28752 \begin_inset VSpace -5mm
28756 \begin_inset Formula
28764 \begin_inset Formula
28774 \begin_layout Standard
28778 \begin_layout Plain Layout
28790 \begin_layout Standard
28791 To create the example, the following is done:
28794 \begin_layout Enumerate
28795 first formula is inserted
28798 \begin_layout Enumerate
28803 addtocounter{equation}{-1}
28805 begin{subequations}
28806 \begin_inset Index idx
28809 \begin_layout Plain Layout
28818 \begin_inset Newline newline
28823 is inserted after the first formula
28826 \begin_layout Enumerate
28827 second formula is inserted
28830 \begin_layout Enumerate
28831 third formula is inserted
28834 \begin_layout Enumerate
28841 is inserted after the third formula
28844 \begin_layout Standard
28845 Every formula between the commands
28857 is subnumbered as a, b,
28858 \begin_inset Newline linebreak
28861 c, \SpecialChar \ldots{}
28862 For multiline formulas every line will be subnumbered.
28863 All subnumbered formulas are treated as
28868 But as every numbered formula increases the counter
28872 by one, the command
28878 is needed to decrease it.
28879 Otherwise the formulas
28880 \begin_inset CommandInset ref
28887 \begin_inset CommandInset ref
28894 \begin_inset CommandInset ref
28900 would be numbered as
28901 \begin_inset CommandInset ref
28908 \begin_inset CommandInset ref
28915 \begin_inset CommandInset ref
28924 \begin_layout Standard
28925 By inserting the commands in TeX-mode, a space is created between the first
28928 \begin_inset space \thinspace{}
28931 mm vertical space is inserted after the command
28935 begin{subequations}
28938 When the formula style
28944 \begin_layout Plain Layout
28946 \begin_inset CommandInset ref
28948 reference "sec:Formula-Styles"
28960 \begin_inset space \thinspace{}
28963 mm space is inserted instead.
28966 \begin_layout Standard
28967 Here is an example for a multiline formula where the numbering was turned
28968 off for the second line:
28972 \begin_layout Plain Layout
28976 begin{subequations}
28982 \begin_inset Formula
28984 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
28985 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
28986 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
28995 \begin_layout Plain Layout
29007 \begin_layout Subsection
29008 User-defined Numbering
29009 \begin_inset CommandInset label
29011 name "sub:User-defined-Numbering"
29016 \begin_inset Index idx
29019 \begin_layout Plain Layout
29020 Formula numbering ! user-defined
29028 \begin_layout Standard
29029 \begin_inset Index idx
29032 \begin_layout Plain Layout
29033 Formula numbering ! self-defined delimiters
29038 With the standard numbering parentheses are set around the formula number.
29039 To replace the parentheses for example by vertical bars, the following
29040 line is added to the LaTeX-preamble:
29043 \begin_layout Standard
29055 \begin_inset Note Note
29058 \begin_layout Plain Layout
29059 This macro is already declared in the LaTeX-preamble for testing.
29060 To activate it, remove the percent sign at the beginning.
29068 \begin_layout Standard
29069 To use other characters, the vertical bars besides the
29073 are replaced by one ore more characters.
29074 To get only the formula number the vertical bars are omitted.
29077 \begin_layout Standard
29078 \begin_inset VSpace bigskip
29081 When there should be an expression of your choice instead of the consecutive
29082 formula number in parentheses behind the formula, the command
29089 \begin_inset Index idx
29092 \begin_layout Plain Layout
29101 \begin_inset Formula
29103 A+B=C\tag{something}\label{eq:tag}
29108 In this example the command
29113 \begin_inset space \textvisiblespace{}
29118 was inserted in the formula.
29121 \begin_layout Standard
29127 \begin_inset space \textvisiblespace{}
29132 is inserted instead, the star prevents the parentheses around the expression:
29133 \begin_inset Formula
29135 A+B=C\tag*{something}
29143 \begin_layout Standard
29144 \begin_inset VSpace bigskip
29147 To restart the formula numbering with new document parts or sections, the
29148 following command is used:
29151 \begin_layout Standard
29156 @addtoreset{equation}{part}
29159 \begin_inset Index idx
29162 \begin_layout Plain Layout
29167 \begin_layout Plain Layout
29178 \begin_layout Plain Layout
29191 \begin_layout Plain Layout
29202 \begin_layout Plain Layout
29215 \begin_inset Newline newline
29219 \begin_inset Newline newline
29226 @addtoreset{equation}{section}
29229 \begin_layout Standard
29230 To be able to use these commands in TeX-mode, the
29231 \begin_inset Quotes eld
29235 \begin_inset Quotes erd
29238 character has to be made
29239 \begin_inset Quotes eld
29243 \begin_inset Quotes erd
29246 for LaTeX using the command
29260 So the command sequence in TeX-mode is:
29263 \begin_layout Standard
29269 \begin_inset Newline newline
29274 @addtoreset{equation}{section}
29275 \begin_inset Newline newline
29283 \begin_layout Standard
29284 In the LaTeX-preamble
29296 can be omitted as they are automatically internally inserted by LyX.
29299 \begin_layout Standard
29314 \begin_layout Plain Layout
29319 is part of the LaTeX-package
29324 \begin_inset Index idx
29327 \begin_layout Plain Layout
29328 Packages ! carlisle
29333 that is part of every LaTeX standard installation.
29339 \begin_inset Index idx
29342 \begin_layout Plain Layout
29343 Packages ! remreset
29348 has to be loaded in the LaTeX-preamble with the line
29351 \begin_layout Standard
29356 usepackage{remreset}
29359 \begin_layout Standard
29367 \begin_inset Index idx
29370 \begin_layout Plain Layout
29375 \begin_layout Plain Layout
29386 \begin_layout Plain Layout
29399 \begin_layout Plain Layout
29410 \begin_layout Plain Layout
29422 can be used with the same scheme as
29431 \begin_layout Standard
29432 \begin_inset VSpace bigskip
29435 Sometimes formulas should be numbered in the following form:
29438 \begin_layout Standard
29441 (section number.formula number)
29444 \begin_layout Standard
29445 The formula number should start with every section with
29446 \begin_inset Quotes eld
29450 \begin_inset Quotes erd
29456 \begin_layout Standard
29457 For this case there is the command
29464 \begin_inset Index idx
29467 \begin_layout Plain Layout
29475 , which is used with the following scheme:
29478 \begin_layout Standard
29483 numberwithin{counter}{sectioning}
29486 \begin_layout Standard
29487 Counter denotes what kind of numbering is affected, sectioning denotes what
29488 number is before the dot.
29491 \begin_layout Standard
29492 Thus in our case the following LaTeX-preamble or TeX code line is used:
29495 \begin_layout Standard
29500 numberwithin{equation}{section}
29503 \begin_layout Standard
29504 This is the result:
29508 \begin_layout Plain Layout
29512 numberwithin{equation}{section}
29518 \begin_inset Formula
29528 \begin_layout Standard
29530 \begin_inset space \thinspace{}
29534 \begin_inset space \space{}
29537 tables so that the number of the part is the sectioning,
29538 \begin_inset Newline newline
29545 numberwithin{table}{part}
29550 \begin_layout Standard
29551 To go back to the standard numbering or to prevent this kind of numbering
29552 when it is defined by the document class, the following command is inserted
29553 as TeX code or to the LaTeX-preamble:
29556 \begin_layout Standard
29566 \begin_inset Index idx
29569 \begin_layout Plain Layout
29583 \begin_layout Plain Layout
29599 \begin_inset Newline newline
29607 \begin_inset Newline newline
29619 \begin_layout Standard
29626 uses internally the command
29632 , described above, that also needs to be reverted.
29636 \begin_layout Plain Layout
29643 \begin_layout Plain Layout
29647 @removefromreset{equation}{section}
29650 \begin_layout Plain Layout
29662 \begin_layout Subsection
29663 Numbering with Roman Numbers and Letters
29664 \begin_inset Index idx
29667 \begin_layout Plain Layout
29668 Formula numbering ! with letters
29674 \begin_inset Index idx
29677 \begin_layout Plain Layout
29678 Formula numbering ! with Roman numbers
29686 \begin_layout Standard
29687 Formulas can also be numbered with Roman numbers and Latin letters.
29688 To number for example with small Roman numbers, the command
29691 \begin_layout Standard
29703 \begin_layout Standard
29704 is inserted before the formula in TeX-mode.
29712 \begin_inset Index idx
29715 \begin_layout Plain Layout
29723 redefines the predefined command
29739 \begin_layout Plain Layout
29746 has the same scheme like the command
29752 that is described in
29753 \begin_inset CommandInset ref
29755 reference "sub:The-Command-newcommand"
29768 is the formula counter.
29775 is used as prefix for a counter, the value of the counter is output as
29777 When a formula is numbered, LaTeX sets internally the command
29783 behind the formula.
29789 \begin_inset Index idx
29792 \begin_layout Plain Layout
29802 outputs the counter as small Roman number.
29805 \begin_layout Standard
29806 All formulas behind the command
29816 are now numbered Roman.
29817 To switch to numbering with big Roman numbers, the command is inserted
29831 \begin_inset Index idx
29834 \begin_layout Plain Layout
29846 \begin_inset Quotes eld
29850 \begin_inset Quotes erd
29853 with small Latin letters there is the command
29860 \begin_inset Index idx
29863 \begin_layout Plain Layout
29871 , for big ones there is the command
29878 \begin_inset Index idx
29881 \begin_layout Plain Layout
29894 \begin_layout Standard
29895 \begin_inset Note Greyedout
29898 \begin_layout Plain Layout
29905 \begin_inset space ~
29908 formulas can be numbered with Latin letters in one document.
29916 \begin_layout Standard
29920 \begin_layout Plain Layout
29936 \begin_layout Standard
29937 \begin_inset Formula
29939 A=\textrm{small roman}
29948 \begin_layout Plain Layout
29962 \begin_inset Formula
29964 B=\textrm{big Roman}\label{eq:Rom}
29973 \begin_layout Plain Layout
29987 \begin_inset Formula
29989 C=\textrm{small Latin}
29998 \begin_layout Plain Layout
30012 \begin_inset Formula
30014 D=\textrm{big Latin}\label{eq:Lat}
30022 \begin_layout Standard
30023 To switch back to the default numbering, insert the command:
30026 \begin_layout Standard
30036 \begin_inset Index idx
30039 \begin_layout Plain Layout
30050 \begin_layout Standard
30054 \begin_layout Plain Layout
30068 \begin_inset Formula
30078 \begin_layout Standard
30079 \begin_inset VSpace medskip
30082 As you see, formulas are numbered serially independent from the numbering
30084 When then numbering should start with
30085 \begin_inset Quotes eld
30089 \begin_inset Quotes erd
30092 when the style is changed, new equation counters have to be defined.
30093 A description about this can be found in the file
30094 \begin_inset CommandInset href
30096 name "Formula-numbering.lyx"
30097 target "run:Formula-numbering.lyx"
30104 \begin_layout Standard
30105 \begin_inset Newpage newpage
30111 \begin_layout Section
30112 Chemical Symbols and Equations
30113 \begin_inset CommandInset label
30115 name "sub:Chemical-Symbols-and"
30120 \begin_inset Index idx
30123 \begin_layout Plain Layout
30124 Chemical characters ! Symbols
30130 \begin_inset Index idx
30133 \begin_layout Plain Layout
30140 \begin_inset Index idx
30143 \begin_layout Plain Layout
30152 \begin_layout Standard
30153 An example text from chemistry:
30156 \begin_layout Quote
30158 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30161 -ion reacts with two
30162 \begin_inset Formula $\mathrm{Na^{+}}$
30165 -ions to sodium sulfate
30166 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30170 The chemical equation for this is:
30171 \begin_inset Formula
30173 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
30181 \begin_layout Standard
30182 This chemical equation can directly be created as formula.
30183 To avoid that the symbols appear italic, everything is highlighted and
30184 changed by the shortcut
30190 to the upright font style.
30194 \begin_layout Plain Layout
30200 \begin_inset CommandInset ref
30202 reference "sub:Font-Styles"
30214 \begin_layout Standard
30215 A more convenient way to typeset chemical formulas is to use the command
30223 \begin_inset Index idx
30226 \begin_layout Plain Layout
30234 that is available when the LaTeX-package
30239 \begin_inset Index idx
30242 \begin_layout Plain Layout
30255 to a formula a new blue box appears where chemical formulas can be inserted
30256 in an intuitive way.
30259 \begin_layout Standard
30261 \begin_inset Tabular
30262 <lyxtabular version="3" rows="9" columns="2">
30263 <features rotate="0" tabularvalignment="middle">
30264 <column alignment="center" valignment="top">
30265 <column alignment="center" valignment="top">
30267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30270 \begin_layout Plain Layout
30276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30279 \begin_layout Plain Layout
30281 \begin_inset Note Note
30284 \begin_layout Plain Layout
30291 is only used as spacer.
30303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30306 \begin_layout Plain Layout
30310 \begin_inset space \textvisiblespace{}
30318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30321 \begin_layout Plain Layout
30322 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
30332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30335 \begin_layout Plain Layout
30339 \begin_inset space \textvisiblespace{}
30347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30350 \begin_layout Plain Layout
30351 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
30361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30364 \begin_layout Plain Layout
30368 \begin_inset space \textvisiblespace{}
30376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30379 \begin_layout Plain Layout
30380 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
30390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30393 \begin_layout Plain Layout
30397 \begin_inset space \textvisiblespace{}
30405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30408 \begin_layout Plain Layout
30409 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
30419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30422 \begin_layout Plain Layout
30426 \begin_inset space \textvisiblespace{}
30432 \begin_inset space \textvisiblespace{}
30438 \begin_inset space \textvisiblespace{}
30446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30449 \begin_layout Plain Layout
30450 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
30460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30463 \begin_layout Plain Layout
30467 \begin_inset space \textvisiblespace{}
30471 \begin_inset Formula $\downarrow$
30475 \begin_inset Formula $\to$
30483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30486 \begin_layout Plain Layout
30487 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
30497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30500 \begin_layout Plain Layout
30504 \begin_inset space \textvisiblespace{}
30508 \begin_inset space \textvisiblespace{}
30512 \begin_inset space \textvisiblespace{}
30516 \begin_inset space \textvisiblespace{}
30520 \begin_inset space \textvisiblespace{}
30528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30531 \begin_layout Plain Layout
30532 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
30542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30545 \begin_layout Plain Layout
30549 \begin_inset space \textvisiblespace{}
30553 \begin_inset space \textvisiblespace{}
30557 \begin_inset space \textvisiblespace{}
30561 \begin_inset space \textvisiblespace{}
30569 \begin_inset space \textvisiblespace{}
30577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30580 \begin_layout Plain Layout
30581 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
30597 \begin_layout Standard
30598 \begin_inset Note Greyedout
30601 \begin_layout Plain Layout
30607 Inserting a formula to a
30613 box will lead to LaTeX errors due to a LyX bug.
30619 \begin_layout Plain Layout
30620 \begin_inset CommandInset href
30622 name "LyX-bug #8566"
30623 target "http://www.lyx.org/trac/ticket/8566"
30634 In this case TeX code has to be used like for
30648 \begin_layout Plain Layout
30669 \begin_layout Standard
30670 \begin_inset Note Greyedout
30673 \begin_layout Plain Layout
30679 It is not possible in LyX to use the character ^ to get an up-arrow as
30685 One instead uses a negative thin space followed by the command
30692 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
30703 \begin_layout Standard
30710 the command for equation
30711 \begin_inset space ~
30715 \begin_inset CommandInset ref
30717 reference "eq:chem-reaction"
30722 \begin_inset Newline newline
30730 \begin_inset space \textvisiblespace{}
30734 \begin_inset space \textvisiblespace{}
30738 \begin_inset space \textvisiblespace{}
30742 \begin_inset space \textvisiblespace{}
30746 \begin_inset space \textvisiblespace{}
30750 \begin_inset space \textvisiblespace{}
30756 \begin_layout Standard
30757 To create multiline chemical equations first a multiline formula is created
30759 \begin_inset CommandInset ref
30761 reference "sec:Multiline-Formulas"
30766 Afterwards the command
30772 is used in every small blue box of the formula.
30774 \begin_inset CommandInset ref
30776 reference "eq:TEOS-reaction-1"
30781 \begin_inset CommandInset ref
30783 reference "eq:TEOS-reaction-2"
30787 are an example of a multi-stage chemical reaction where every equation
30788 has its own number.
30789 \begin_inset Formula
30791 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
30792 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
30800 \begin_layout Standard
30811 package provides the command
30818 \begin_inset Index idx
30821 \begin_layout Plain Layout
30829 that has to be used for special cases.
30830 For more information about
30836 and more examples have a look at the documentation of
30841 \begin_inset CommandInset citation
30850 \begin_layout Section
30854 \begin_layout Standard
30855 LyX supports two types of commutative diagrams:
30863 that are explained in the following.
30866 \begin_layout Subsection
30868 \begin_inset Index idx
30871 \begin_layout Plain Layout
30880 \begin_layout Standard
30881 Diagrams of this type visualize relations by vertical and horizontal lines
30883 \begin_inset Formula
30885 \begin{CD}A@>>>B@>>>C\\
30896 \begin_layout Standard
30897 To get them, the command
30902 \begin_inset Index idx
30905 \begin_layout Plain Layout
30915 is inserted to a formula.
30916 A blue box appears with two dashed lines where further commands can be
30921 arg "newline-insert newline"
30924 a new line is created.
30925 Horizontal relations are inserted in odd, vertical in even formula lines.
30928 \begin_layout Standard
30929 To create the relations there are the following commands:
30932 \begin_layout Itemize
30937 creates a left arrow,
30948 \begin_layout Itemize
30953 creates an up arrow,
30961 a vertical equal sign
30964 \begin_layout Itemize
30970 is a placeholder for non-existent relations
30973 \begin_layout Standard
30974 All arrows can be labeled as follows:
30977 \begin_layout Itemize
30978 If text inserted between the first and second < or >, resp., it is placed
30980 When it is inserted between the second and third one, it appears under
30984 \begin_layout Itemize
30985 When text for vertical arrows is inserted between the first and second A
30986 or V, resp., it is placed left beside the arrow.
30987 When it is inserted between the second and third one, it appears right
30989 If the text contains an A or V, these letters must be set into a TeX-brace.
30992 \begin_layout Standard
30993 As example a diagram with all possible relations:
30996 \begin_layout Standard
30997 \begin_inset Formula
30999 \begin{CD}A@>j>>B@>>k>C@=F\\
31010 \begin_layout Standard
31011 The command for this is:
31012 \begin_inset Newline newline
31020 \begin_inset space \textvisiblespace{}
31023 A@>j>>B@>>k>C@=F Ctrl+Return
31024 \begin_inset Newline newline
31028 \begin_inset Phantom HPhantom
31031 \begin_layout Plain Layout
31037 \begin_inset space \textvisiblespace{}
31050 \begin_inset Formula $\to$
31056 \begin_inset Newline newline
31060 \begin_inset Phantom HPhantom
31063 \begin_layout Plain Layout
31069 \begin_inset space \textvisiblespace{}
31080 \begin_layout Subsection
31082 \begin_inset Index idx
31085 \begin_layout Plain Layout
31086 Diagrams ! xymatrix
31094 \begin_layout Standard
31095 To be able to use xymatrices, the LaTeX-package
31100 A xymatrix is created by inserting the command
31107 Then you are able to add new matrix columns and rows like for normal matrices,
31109 \begin_inset CommandInset ref
31111 reference "sec:Matrices"
31118 \begin_layout Standard
31119 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31121 All possibilities to create commutative diagrams and decorations are explained
31126 that you find in the menu
31128 Help\SpecialChar \menuseparator
31130 \begin_inset space ~
31138 \begin_layout Subsection
31144 \begin_inset Index idx
31147 \begin_layout Plain Layout
31156 \begin_layout Standard
31161 -diagrams, the LaTeX-package
31170 -diagram is created by inserting the command
31177 Then you are able to add new matrix columns and rows like for normal matrices,
31179 \begin_inset CommandInset ref
31181 reference "sec:Matrices"
31188 \begin_layout Standard
31189 Examples how to create
31193 diagrams in LyX is given in the
31195 Feynman-diagram manual
31197 that you find in the menu
31199 Help\SpecialChar \menuseparator
31201 \begin_inset space ~
31209 \begin_layout Standard
31210 \begin_inset Newpage newpage
31216 \begin_layout Section
31217 User-defined Commands
31218 \begin_inset Index idx
31221 \begin_layout Plain Layout
31222 User-defined commands
31230 \begin_layout Standard
31231 \begin_inset Note Greyedout
31234 \begin_layout Plain Layout
31239 The names of user-defined commands and macros may only consist of Latin
31248 \begin_layout Subsection
31252 \begin_inset CommandInset label
31254 name "sub:The-Command-newcommand"
31259 \begin_inset Index idx
31262 \begin_layout Plain Layout
31263 User-defined commands !
31271 \begin_inset Index idx
31274 \begin_layout Plain Layout
31285 \begin_layout Standard
31286 Many LaTeX-commands are too long to be used frequently.
31287 But it is possible to define with the command
31293 new shorter commands.
31296 \begin_layout Standard
31297 The command scheme of
31306 \begin_layout Standard
31311 newcommand{new command name}[number of arguments][optional
31316 \begin_inset Newline newline
31320 \begin_inset Phantom HPhantom
31323 \begin_layout Plain Layout
31333 {command definition}
31336 \begin_layout Standard
31337 \begin_inset Note Greyedout
31340 \begin_layout Plain Layout
31345 Assure that the name of the new command is not already used in your document
31346 or by LaTeX-packages that you use.
31347 When you for example define the command
31359 , you get an error message because
31365 is already defined as command for
31366 \begin_inset Quotes eld
31370 \begin_inset Formula $\le$
31374 \begin_inset Quotes erd
31385 \begin_layout Standard
31386 The number of arguments is an integer in the range 0
31387 \begin_inset space \thinspace{}
31391 \begin_inset space \thinspace{}
31394 9 and specifies how many arguments the new command should have.
31395 With the optional value a value for an optional argument can be predefined.
31396 When this is done, the
31404 rgument of the new command is automatically an optional one.
31407 \begin_layout Standard
31408 Here are some examples:
31411 \begin_layout Itemize
31412 To define the command
31424 , the LaTeX-preamble line is:
31425 \begin_inset VSpace medskip
31429 \begin_inset Newline newline
31443 \begin_layout Itemize
31444 To define the command
31456 , the argument (that should be underlined) must be taken into account.
31457 For this the preamble line is:
31458 \begin_inset VSpace medskip
31462 \begin_inset Newline newline
31476 \begin_inset VSpace medskip
31480 \begin_inset Newline newline
31487 acts as argument placeholder, the
31491 behind it denotes that it is the placeholder for the first argument.
31494 \begin_layout Itemize
31502 \begin_inset space \thinspace{}
31506 \begin_inset space \space{}
31516 \begin_inset VSpace medskip
31520 \begin_inset Newline newline
31531 framebox#1#2{$#3$}}
31534 \begin_inset VSpace medskip
31538 \begin_inset Newline newline
31541 The two Dollar signs creates the extra formula needed for
31548 \begin_inset CommandInset ref
31550 reference "sub:Boxes-with-Frame"
31557 \begin_layout Itemize
31558 To create a new command for
31564 where the color for the box need not be specified, the argument for the
31565 color is defined optional:
31566 \begin_inset VSpace medskip
31570 \begin_inset Newline newline
31581 fcolorbox{#2}{#1}{$#3$}}
31584 \begin_inset VSpace medskip
31588 \begin_inset Newline newline
31591 When the color is not specified when using
31597 , the predefined color
31604 \begin_layout Standard
31605 A test of the new defined commands:
31608 \begin_layout Standard
31610 \begin_inset Tabular
31611 <lyxtabular version="3" rows="6" columns="2">
31612 <features rotate="0" tabularvalignment="middle">
31613 <column alignment="center" valignment="top">
31614 <column alignment="center" valignment="top">
31616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31619 \begin_layout Plain Layout
31625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31628 \begin_layout Plain Layout
31630 \begin_inset Note Note
31633 \begin_layout Plain Layout
31640 is only used as spacer.
31652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31655 \begin_layout Plain Layout
31659 \begin_inset space \textvisiblespace{}
31667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31670 \begin_layout Plain Layout
31671 \begin_inset Formula $A\gr B$
31681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31684 \begin_layout Plain Layout
31692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31695 \begin_layout Plain Layout
31696 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31709 \begin_layout Plain Layout
31713 \begin_inset Formula $\to$
31719 \begin_inset Formula $\to$
31727 \begin_inset space \textvisiblespace{}
31735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31738 \begin_layout Plain Layout
31739 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31752 \begin_layout Plain Layout
31756 \begin_inset Formula $\to$
31764 \begin_inset space \textvisiblespace{}
31772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31775 \begin_layout Plain Layout
31776 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31789 \begin_layout Plain Layout
31795 \begin_inset Formula $\to$
31803 \begin_inset space \textvisiblespace{}
31811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31814 \begin_layout Plain Layout
31815 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31831 \begin_layout Subsection
31833 \begin_inset Index idx
31836 \begin_layout Plain Layout
31837 User-defined commands! Math macros
31843 \begin_inset Index idx
31846 \begin_layout Plain Layout
31855 \begin_layout Standard
31856 User-defined commands are especially convenient for complex expressions.
31857 When you are for example dealing with a document that has quadratic equations,
31858 the same solution type occurs several times.
31859 The general form of a quadratic equation is
31860 \begin_inset Formula
31862 0=\lambda^{2}+p\lambda+q
31867 The general form of the solution is
31868 \begin_inset Formula
31870 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
31878 \begin_layout Standard
31879 To define a command for the solution formula where only the three parameters
31881 \begin_inset Formula $\lambda$
31885 \begin_inset Formula $p$
31889 \begin_inset Formula $q$
31892 need to be specified and the index of
31893 \begin_inset Formula $\lambda$
31896 can be given optionally, the LaTeX-preamble line is
31897 \begin_inset Newline newline
31913 \begin_inset Newline newline
31917 \begin_inset Phantom HPhantom
31920 \begin_layout Plain Layout
31934 frac{#3^{2}}{4}-#4}}
31937 \begin_layout Standard
31938 To create with this the solution formula, the command
31939 \begin_inset Newline newline
31949 \begin_inset Formula $\to$
31955 \begin_inset Formula $\to$
31962 is inserted to a formula
31967 \begin_layout Standard
31968 The definition of the new command is unintuitive because one has to know
31969 the schemes of all used LaTeX commands, e.
31970 \begin_inset space \thinspace{}
31974 \begin_inset space \space{}
31977 that a fraction is inserted in LaTeX as
31981 frac{numerator}{denominator}
31984 Furthermore one can easily forget a brace in the definition and cannot
31985 see in LyX what the new command is doing.
31986 To avoid these problems LyX offers the possibility to use math macros instead
31996 \begin_layout Standard
31997 A math macro is created by using the menu
31999 Insert\SpecialChar \menuseparator
32000 Math\SpecialChar \menuseparator
32003 or the toolbar button
32004 \begin_inset Graphics
32005 filename ../images/math-macro_newmacroname_newcommand.png
32011 The math macro toolbar appears together with the following box where the
32013 \begin_inset Newline newline
32017 \begin_inset space \hspace*{\fill}
32021 \begin_inset Graphics
32022 filename clipart/macrobox.png
32027 \begin_inset space \hspace*{\fill}
32031 \begin_inset Newline newline
32035 \begin_inset FormulaMacro
32036 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
32041 newmacroname is the default name of the macro that should be changed to
32042 something sensible.
32043 The wanted formula is inserted in the first blue box.
32044 An argument placeholder is inserted with the command
32051 \begin_inset space \thinspace{}
32055 \begin_inset space \space{}
32064 or by using the macro toolbar button
32065 \begin_inset Graphics
32066 filename ../images/math-macro-add-param.png
32072 Argument placeholders are displayed red.
32074 \begin_inset space ~
32077 arguments are possible.
32078 Optional arguments are created with the toolbar button
32079 \begin_inset Graphics
32080 filename ../images/math-macro-add-optional-param.png
32086 The first non-optional argument can be transformed to an optional one with
32088 \begin_inset Graphics
32089 filename ../images/math-macro-make-optional.png
32095 In the second blue box the appearance of the macro in LyX can be defined.
32096 Normally you want to see it as it is defined, so the box is kept empty.
32097 But when you have created a macro that needs lot of space on the screen,
32098 you can insert in the box for example
32099 \begin_inset Newline newline
32129 \begin_inset Newline newline
32134 For the macro only the arguments with the macro name in front of them will
32135 then be displayed in LyX, leading to a better overview.
32136 The formula appears in the output as defined in the first box.
32137 \begin_inset Newline newline
32140 The appearance of macros in formulas can furthermore be changed for single
32141 macros by setting the cursor in the macro and using the menu
32143 View\SpecialChar \menuseparator
32145 \begin_inset space ~
32149 \begin_inset space ~
32157 \begin_layout Standard
32158 To use a macro, the macro name is inserted as command to a formula, in our
32166 Our macro looks in LyX like this:
32167 \begin_inset Newline newline
32171 \begin_inset space \hspace*{\fill}
32175 \begin_inset Graphics
32176 filename clipart/macrouse.png
32181 \begin_inset space \hspace*{\fill}
32185 \begin_inset Newline newline
32188 Here is our macro example with the arguments
32189 \begin_inset Formula $x$
32193 \begin_inset Formula $\ln(x)$
32197 \begin_inset Formula $B$
32203 \begin_layout Standard
32204 \begin_inset Formula
32214 \begin_layout Standard
32215 LyX offers in the menu
32217 Tools\SpecialChar \menuseparator
32218 Preferences\SpecialChar \menuseparator
32219 Editing\SpecialChar \menuseparator
32222 different styles to edit macros.
32223 To find the style that suits you the most, choose a style and set the cursor
32224 in a macro formula to see the difference.
32227 \begin_layout Standard
32228 A math macro is transformed internally to a
32234 command when exporting the document.
32241 command is not placed in the LaTeX-preamble, therefore macros can only
32242 be used in formulas that are in the document below the macro definition
32246 \begin_layout Standard
32247 Math macros can also be directly created from a
32254 When writing for example the command
32257 \begin_inset Newline newline
32266 xleftarrow[#2]{#1}}
32267 \begin_inset Newline newline
32272 in LyX as normal text, highlighting it completely and using then the shortcut
32277 , the command will be transformed to a math macro.
32278 Using this method you need to be careful that the
32284 command is typed correctly, otherwise you get a faulty macro leading to
32288 \begin_layout Standard
32289 Math macros currently have the problem that further formulas in macro definition
32290 s are handled wrongly.
32291 Therefore the example
32298 \begin_inset CommandInset ref
32300 reference "sub:The-Command-newcommand"
32304 cannot be created as macro.
32307 \begin_layout Standard
32308 When the cursor is in a macro definition box, you will see the macro toolbar
32312 \begin_layout Standard
32313 \begin_inset VSpace defskip
32319 \begin_layout Standard
32320 \begin_inset Graphics
32321 filename clipart/MacroToolbar.png
32326 \begin_inset Index idx
32329 \begin_layout Plain Layout
32338 \begin_layout Standard
32339 \begin_inset VSpace defskip
32345 \begin_layout Standard
32346 The macro toolbar contains from left to right the following buttons:
32349 \begin_layout Standard
32350 \begin_inset VSpace defskip
32356 \begin_layout Standard
32357 \begin_inset Tabular
32358 <lyxtabular version="3" rows="9" columns="2">
32359 <features rotate="0" islongtable="true" longtabularalignment="center">
32360 <column alignment="left" valignment="top">
32361 <column alignment="left" valignment="top" width="85col%">
32362 <row interlinespace="2.5mm">
32363 <cell alignment="center" valignment="top" usebox="none">
32366 \begin_layout Plain Layout
32367 \begin_inset Graphics
32368 filename ../images/math-macro-remove-param.png
32369 rotateOrigin center
32378 <cell alignment="center" valignment="top" usebox="none">
32381 \begin_layout Plain Layout
32384 Edit\SpecialChar \menuseparator
32385 Math\SpecialChar \menuseparator
32387 \begin_inset space ~
32390 Definition\SpecialChar \menuseparator
32391 Remove Last Argument
32397 <row interlinespace="2.5mm">
32398 <cell alignment="center" valignment="top" usebox="none">
32401 \begin_layout Plain Layout
32402 \begin_inset Graphics
32403 filename ../images/math-macro-add-param.png
32404 rotateOrigin center
32413 <cell alignment="center" valignment="top" usebox="none">
32416 \begin_layout Plain Layout
32419 Edit\SpecialChar \menuseparator
32420 Math\SpecialChar \menuseparator
32422 \begin_inset space ~
32425 Definition\SpecialChar \menuseparator
32432 <row interlinespace="2.5mm">
32433 <cell alignment="center" valignment="top" usebox="none">
32436 \begin_layout Plain Layout
32437 \begin_inset Graphics
32438 filename ../images/math-macro-make-optional.png
32439 rotateOrigin center
32448 <cell alignment="center" valignment="top" usebox="none">
32451 \begin_layout Plain Layout
32454 Edit\SpecialChar \menuseparator
32455 Math\SpecialChar \menuseparator
32457 \begin_inset space ~
32460 Definition\SpecialChar \menuseparator
32461 Make First Non-Optional into
32462 \begin_inset Newline newline
32466 \begin_inset Phantom HPhantom
32469 \begin_layout Plain Layout
32472 Edit\SpecialChar \menuseparator
32473 Math\SpecialChar \menuseparator
32475 \begin_inset space ~
32478 Definition\SpecialChar \menuseparator
32490 <row interlinespace="2.5mm">
32491 <cell alignment="center" valignment="top" usebox="none">
32494 \begin_layout Plain Layout
32495 \begin_inset Graphics
32496 filename ../images/math-macro-make-nonoptional.png
32497 rotateOrigin center
32506 <cell alignment="center" valignment="top" usebox="none">
32509 \begin_layout Plain Layout
32512 Edit\SpecialChar \menuseparator
32513 Math\SpecialChar \menuseparator
32515 \begin_inset space ~
32518 Definition\SpecialChar \menuseparator
32519 Make Last Optional into
32520 \begin_inset Newline newline
32524 \begin_inset Phantom HPhantom
32527 \begin_layout Plain Layout
32530 Edit\SpecialChar \menuseparator
32531 Math\SpecialChar \menuseparator
32533 \begin_inset space ~
32536 Definition\SpecialChar \menuseparator
32542 Non-Optional Argument
32548 <row interlinespace="2.5mm">
32549 <cell alignment="center" valignment="top" usebox="none">
32552 \begin_layout Plain Layout
32553 \begin_inset Graphics
32554 filename ../images/math-macro-remove-optional-param.png
32555 rotateOrigin center
32564 <cell alignment="center" valignment="top" usebox="none">
32567 \begin_layout Plain Layout
32570 Edit\SpecialChar \menuseparator
32571 Math\SpecialChar \menuseparator
32573 \begin_inset space ~
32576 Definition\SpecialChar \menuseparator
32577 Remove Optional Argument
32583 <row interlinespace="2.5mm">
32584 <cell alignment="center" valignment="top" usebox="none">
32587 \begin_layout Plain Layout
32588 \begin_inset Graphics
32589 filename ../images/math-macro-add-optional-param.png
32590 rotateOrigin center
32599 <cell alignment="center" valignment="top" usebox="none">
32602 \begin_layout Plain Layout
32605 Edit\SpecialChar \menuseparator
32606 Math\SpecialChar \menuseparator
32608 \begin_inset space ~
32611 Definition\SpecialChar \menuseparator
32612 Insert Optional Argument
32618 <row interlinespace="2.5mm">
32619 <cell alignment="center" valignment="top" usebox="none">
32622 \begin_layout Plain Layout
32623 \begin_inset Graphics
32624 filename ../images/math-macro-remove-greedy-param.png
32625 rotateOrigin center
32634 <cell alignment="center" valignment="top" usebox="none">
32637 \begin_layout Plain Layout
32640 Edit\SpecialChar \menuseparator
32641 Math\SpecialChar \menuseparator
32643 \begin_inset space ~
32646 Definition\SpecialChar \menuseparator
32647 Remove Last Argument
32648 \begin_inset Newline newline
32652 \begin_inset Phantom HPhantom
32655 \begin_layout Plain Layout
32658 Edit\SpecialChar \menuseparator
32659 Math\SpecialChar \menuseparator
32661 \begin_inset space ~
32664 Definition\SpecialChar \menuseparator
32670 Spitting Out To The Right
32676 <row interlinespace="2.5mm">
32677 <cell alignment="center" valignment="top" usebox="none">
32680 \begin_layout Plain Layout
32681 \begin_inset Graphics
32682 filename ../images/math-macro-append-greedy-param.png
32683 rotateOrigin center
32692 <cell alignment="center" valignment="top" usebox="none">
32695 \begin_layout Plain Layout
32698 Edit\SpecialChar \menuseparator
32699 Math\SpecialChar \menuseparator
32701 \begin_inset space ~
32704 Definition\SpecialChar \menuseparator
32706 \begin_inset Newline newline
32710 \begin_inset Phantom HPhantom
32713 \begin_layout Plain Layout
32716 Edit\SpecialChar \menuseparator
32717 Math\SpecialChar \menuseparator
32719 \begin_inset space ~
32722 Definition\SpecialChar \menuseparator
32728 Eating From The Right
32734 <row interlinespace="2.5mm">
32735 <cell alignment="center" valignment="top" usebox="none">
32738 \begin_layout Plain Layout
32739 \begin_inset Graphics
32740 filename ../images/math-macro-add-greedy-optional-param.png
32741 rotateOrigin center
32750 <cell alignment="center" valignment="top" usebox="none">
32753 \begin_layout Plain Layout
32756 Edit\SpecialChar \menuseparator
32757 Math\SpecialChar \menuseparator
32759 \begin_inset space ~
32762 Definition\SpecialChar \menuseparator
32763 Append Optional Argument
32764 \begin_inset Newline newline
32768 \begin_inset Phantom HPhantom
32771 \begin_layout Plain Layout
32774 Edit\SpecialChar \menuseparator
32775 Math\SpecialChar \menuseparator
32777 \begin_inset space ~
32780 Definition\SpecialChar \menuseparator
32786 Eating From The Right
32799 \begin_layout Section
32800 Computer Algebra Systems
32803 \begin_layout Standard
32804 LyX offers the exchange between mathematical expressions written in LyX's
32805 math editor and external applications or user defined scripts.
32806 Currently supported applications are
32823 Note that the set of supported mathematical constructs is limited only
32824 to very simple cases.
32827 \begin_layout Subsection
32831 \begin_layout Standard
32832 Write some expression in a formula, go to the
32834 Edit\SpecialChar \menuseparator
32835 Math\SpecialChar \menuseparator
32836 Use Computer Algebra System
32838 menu and choose the application you have installed on the computer.
32839 After that the result of computation should show on the right side of the
32840 expression together with the
32841 \begin_inset Quotes eld
32845 \begin_inset Quotes erd
32851 \begin_layout Standard
32852 Here are few simple examples (with results from
32856 ) to show what kind of computations can be performed:
32859 \begin_layout Itemize
32860 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
32866 \begin_layout Itemize
32867 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
32873 \begin_layout Itemize
32874 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
32880 \begin_layout Itemize
32881 \begin_inset Formula $\det\left[\begin{array}{ccc}
32885 \end{array}\right]=-56$
32891 \begin_layout Itemize
32892 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
32898 \begin_layout Subsection
32902 \begin_layout Standard
32903 Currently there is no keyboard shortcut for calling the algebra applications.
32904 One can easily bind a shortcut to the
32908 LyX function (see the
32916 \begin_inset space \thinspace{}
32920 \begin_inset space \space{}
32927 key inside the math editor.
32932 one would use this shortcut definition command:
32935 \begin_layout Standard
32938 command-alternatives break-paragraph;math-extern maxima
32941 \begin_layout Section
32943 \begin_inset Index idx
32946 \begin_layout Plain Layout
32955 \begin_layout Subsection
32957 \begin_inset Index idx
32960 \begin_layout Plain Layout
32969 \begin_layout Standard
32970 Negative numbers often look ugly in formulas because the minus sign before
32971 the number is set with the same length as the minus operator sign.
32972 When writing the negative number in normal text, the minus sign appears
32976 \begin_layout Standard
32977 Thus, the problem disappears when converting the minus sign to mathematical
32981 \begin_layout Standard
32982 An example to visualize the problem:
32985 \begin_layout Standard
32987 \begin_inset Tabular
32988 <lyxtabular version="3" rows="3" columns="2">
32989 <features rotate="0" tabularvalignment="middle">
32990 <column alignment="right" valignment="top">
32991 <column alignment="left" valignment="top">
32993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32996 \begin_layout Plain Layout
33002 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33005 \begin_layout Plain Layout
33013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33016 \begin_layout Plain Layout
33022 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33025 \begin_layout Plain Layout
33026 \begin_inset Formula $x=-2$
33036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33039 \begin_layout Plain Layout
33045 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33048 \begin_layout Plain Layout
33049 \begin_inset Formula $x=\textrm{-}2$
33065 \begin_layout Subsection
33066 Comma as decimal Separator
33067 \begin_inset Index idx
33070 \begin_layout Plain Layout
33079 \begin_layout Standard
33080 In LaTeX a comma inside a formula is used, according to the English convention,
33081 as number group separator.
33082 So there will be space added behind all commas in formulas.
33085 \begin_layout Standard
33086 To avoid this, the comma is highlighted and changed to mathematical text
33096 \begin_layout Standard
33097 To use all formula commas in the document as decimal separator, the file
33106 \begin_layout Plain Layout
33111 is part of the LaTeX-package
33116 \begin_inset Index idx
33119 \begin_layout Plain Layout
33124 \begin_layout Plain Layout
33144 \begin_inset Index idx
33147 \begin_layout Plain Layout
33153 is loaded with the LaTeX-preamble line
33156 \begin_layout Standard
33164 \begin_layout Subsection
33166 \begin_inset CommandInset label
33168 name "sub:Physical-Vectors"
33173 \begin_inset Index idx
33176 \begin_layout Plain Layout
33185 \begin_layout Standard
33186 Predefined vectors are offered by the LaTeX-package
33191 \begin_inset Index idx
33194 \begin_layout Plain Layout
33200 that is loaded with the LaTeX-preamble line
33203 \begin_layout Standard
33211 \begin_layout Standard
33215 \begin_layout Plain Layout
33225 \begin_inset Note Note
33228 \begin_layout Plain Layout
33229 The following table will only be displayed when the LaTeX-package
33241 \begin_layout Standard
33242 The following commands are defined:
33245 \begin_layout Standard
33247 \begin_inset Tabular
33248 <lyxtabular version="3" rows="4" columns="2">
33249 <features rotate="0" tabularvalignment="middle">
33250 <column alignment="center" valignment="top">
33251 <column alignment="center" valignment="top">
33253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33256 \begin_layout Plain Layout
33262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33265 \begin_layout Plain Layout
33273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33276 \begin_layout Plain Layout
33286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33289 \begin_layout Plain Layout
33290 \begin_inset Formula $\Bra{\psi}$
33300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33303 \begin_layout Plain Layout
33313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33316 \begin_layout Plain Layout
33317 \begin_inset Formula $\Ket{\psi}$
33327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33330 \begin_layout Plain Layout
33342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33345 \begin_layout Plain Layout
33346 \begin_inset Formula $\Braket{\psi|\phi}$
33362 \begin_layout Standard
33369 assures that all vertical bars are set in the size of the surrounding brackets:
33370 \begin_inset Formula
33372 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
33381 \begin_layout Plain Layout
33391 \begin_inset Note Note
33394 \begin_layout Plain Layout
33395 The following will be displayed when the LaTeX-package
33407 \begin_layout Standard
33408 You need to install the LaTeX-package
33412 to see the rest of this subsection in the output.
33415 \begin_layout Standard
33419 \begin_layout Plain Layout
33431 \begin_layout Standard
33438 can also be achieved using the command
33444 , that is described in
33445 \begin_inset CommandInset ref
33447 reference "sub:Automatic-Bracket-Size"
33454 \begin_layout Subsection
33455 Self-defined Fractions
33456 \begin_inset CommandInset label
33458 name "sub:Self-defined-Fractions"
33463 \begin_inset Index idx
33466 \begin_layout Plain Layout
33467 Fractions ! self-defined
33475 \begin_layout Standard
33476 To define custom commands for fractions, the command
33483 \begin_inset Index idx
33486 \begin_layout Plain Layout
33493 \begin_layout Plain Layout
33507 is used in the following scheme:
33510 \begin_layout Standard
33523 bracket}{fraction bar thickness}{style}
33524 \begin_inset Newline newline
33528 \begin_inset Phantom HPhantom
33531 \begin_layout Plain Layout
33541 {numerator}{denominator}
33544 \begin_layout Standard
33545 The style is a number in the range of 0
33546 \begin_inset space \thinspace{}
33550 \begin_inset space \thinspace{}
33556 \begin_layout Standard
33558 \begin_inset Tabular
33559 <lyxtabular version="3" rows="5" columns="2">
33560 <features rotate="0" tabularvalignment="middle">
33561 <column alignment="center" valignment="top">
33562 <column alignment="center" valignment="top">
33564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33567 \begin_layout Plain Layout
33573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33576 \begin_layout Plain Layout
33584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33587 \begin_layout Plain Layout
33593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33596 \begin_layout Plain Layout
33597 display style formula
33604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33607 \begin_layout Plain Layout
33613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33616 \begin_layout Plain Layout
33624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33627 \begin_layout Plain Layout
33633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33636 \begin_layout Plain Layout
33644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33647 \begin_layout Plain Layout
33653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33656 \begin_layout Plain Layout
33670 \begin_layout Standard
33671 When no style is given, the size is adjusted to the surrounding environment
33672 like for the command
33681 \begin_layout Standard
33682 When no fraction bar thickness is given, the predefined value of 0.4
33683 \begin_inset space \thinspace{}
33689 \begin_layout Standard
33690 \begin_inset VSpace medskip
33693 For example, the commands
33706 \begin_inset CommandInset ref
33708 reference "sub:Fractions"
33712 are defined with the commands
33715 \begin_layout Standard
33724 genfrac{}{}{}{0}{#1}{#2}}
33727 \begin_layout Standard
33731 \begin_layout Standard
33740 genfrac{(}{)}{0pt}{1}{#1}{#2}}
33743 \begin_layout Standard
33744 \begin_inset VSpace medskip
33747 To define a fraction where the fraction bar thickness can be given as optional
33748 argument, the following line is inserted to the LaTeX-preamble:
33751 \begin_layout Standard
33760 genfrac{}{}{#1}{}{#2}{#3}}
33763 \begin_layout Standard
33765 \begin_inset Formula
33767 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
33768 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
33773 As one can see, the distance of the numerator and the denominator to the
33774 fraction bar is round about three times the bar thickness.
33777 \begin_layout Subsection
33779 \begin_inset Index idx
33782 \begin_layout Plain Layout
33791 \begin_layout Standard
33792 There are four ways to cancel formulas or parts of formulas:
33795 \begin_layout Standard
33799 \begin_layout Plain Layout
33809 \begin_inset Note Note
33812 \begin_layout Plain Layout
33813 The following table will only be displayed when the LaTeX-package
33825 \begin_layout Standard
33827 \begin_inset Tabular
33828 <lyxtabular version="3" rows="5" columns="2">
33829 <features rotate="0" tabularvalignment="middle">
33830 <column alignment="center" valignment="top">
33831 <column alignment="center" valignment="top">
33833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33836 \begin_layout Plain Layout
33842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33845 \begin_layout Plain Layout
33847 \begin_inset Note Note
33850 \begin_layout Plain Layout
33857 are used here as spacer.
33869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33872 \begin_layout Plain Layout
33876 \begin_inset space \textvisiblespace{}
33882 \begin_inset space \textvisiblespace{}
33890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33893 \begin_layout Plain Layout
33894 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33907 \begin_layout Plain Layout
33911 \begin_inset space \textvisiblespace{}
33917 \begin_inset space \textvisiblespace{}
33925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33928 \begin_layout Plain Layout
33929 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33942 \begin_layout Plain Layout
33946 \begin_inset space \textvisiblespace{}
33952 \begin_inset space \textvisiblespace{}
33960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33963 \begin_layout Plain Layout
33964 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33977 \begin_layout Plain Layout
33981 \begin_inset space \textvisiblespace{}
33987 \begin_inset space \textvisiblespace{}
33991 \begin_inset Formula $\to$
33999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34002 \begin_layout Plain Layout
34003 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34019 \begin_layout Standard
34026 is especially suitable to visualize the reduction of fractions within formulas:
34027 \begin_inset Formula
34029 \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}}}
34037 \begin_layout Standard
34038 To change the size of
34045 \begin_inset Quotes eld
34049 \begin_inset Quotes erd
34052 value one can add the LaTeX-preamble line
34055 \begin_layout Standard
34060 PassOptionsToPackage{option}{cancel}
34063 \begin_layout Standard
34072 which leads to the same size as for the canceled value, or
34076 which makes is it a bit smaller than normal.
34079 \begin_layout Standard
34080 To color the cancellation bar one adds this command as TeX code:
34083 \begin_layout Standard
34095 \begin_layout Standard
34100 can be replaced by a color of your choice.
34103 \begin_layout Standard
34107 \begin_layout Plain Layout
34123 \begin_layout Standard
34124 \begin_inset Formula
34126 \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}}}
34134 \begin_layout Standard
34138 \begin_layout Plain Layout
34152 \begin_inset Note Note
34155 \begin_layout Plain Layout
34164 \begin_layout Standard
34165 For further customizations, see the documentation of the package
34170 \begin_inset CommandInset citation
34177 \begin_inset Index idx
34180 \begin_layout Plain Layout
34189 \begin_layout Standard
34193 \begin_layout Plain Layout
34203 \begin_inset Note Note
34206 \begin_layout Plain Layout
34207 The following will be displayed when the LaTeX-package
34219 \begin_layout Standard
34220 You need to install the LaTeX-package
34224 to see the rest of this subsection in the output.
34227 \begin_layout Standard
34231 \begin_layout Plain Layout
34243 \begin_layout Standard
34244 \begin_inset Newpage newpage
34250 \begin_layout Subsection
34251 Formulas in Section Headings
34252 \begin_inset CommandInset label
34254 name "sub:Formulas-in-Section"
34259 \begin_inset Index idx
34262 \begin_layout Plain Layout
34263 Formula ! in section headings
34271 \begin_layout Standard
34272 When formulas are used in section headings, the following has to be taken
34276 \begin_layout Standard
34277 \begin_inset Note Greyedout
34280 \begin_layout Plain Layout
34286 \begin_inset Index idx
34289 \begin_layout Plain Layout
34290 Packages ! hyperref
34295 support is enabled in the document settings dialog under
34298 \begin_inset space ~
34303 , PDF-bookmarks are created for every section heading in the table of contents.
34304 If a section heading contains formulas, they are incorrectly displayed
34305 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34314 \begin_layout Standard
34315 Both problems can be solved by inserting at the end of the section heading
34316 a short title with the menu
34318 Insert\SpecialChar \menuseparator
34320 \begin_inset space ~
34326 Short titles are used as alternative for multiline section headings to
34327 keep the table of contents clearly arranged.
34328 Only the short title appears in the table of contents and therefore also
34329 in the PDF-bookmark.
34332 \begin_layout Standard
34333 When formulas should be used in the table of contents but
34337 is used, one can use the following command in TeX-mode:
34340 \begin_layout Standard
34345 texorpdfstring{part}{alternative}
34346 \begin_inset Index idx
34349 \begin_layout Plain Layout
34360 \begin_layout Standard
34361 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34362 This can be characters, formulas, footnotes, but also cross-references.
34363 The alternative is used instead of the part for the bookmark.
34366 \begin_layout Standard
34367 Here are two example headings:
34368 \begin_inset VSpace -3mm
34375 \begin_layout Plain Layout
34387 \begin_layout Subsubsection
34388 Heading without formula in table of contents
34389 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34393 \begin_inset Argument 1
34396 \begin_layout Plain Layout
34397 Heading without formula in table of contents
34405 \begin_layout Subsubsection
34406 Heading with formula in table of contents
34410 \begin_layout Plain Layout
34420 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34427 \begin_layout Plain Layout
34437 \begin_layout Standard
34441 \begin_layout Plain Layout
34450 In the first heading a short title was used, in the second one
34459 \begin_layout Standard
34460 To get the same formatting as for the other headings, the complete heading
34469 \begin_layout Plain Layout
34471 \begin_inset CommandInset ref
34473 reference "sub:Bold-Formulas"
34485 \begin_layout Subsection
34486 Formulas in multi-column Text
34487 \begin_inset Index idx
34490 \begin_layout Plain Layout
34491 Formula ! in multi-column text
34499 \begin_layout Standard
34500 Formulas in multi-column text are often too wide to fit into a column and
34501 thus need to be set over the whole page width.
34502 This is done by using the LaTeX-package
34510 \begin_layout Plain Layout
34515 is part of every LaTeX standard installation.
34521 \begin_inset Index idx
34524 \begin_layout Plain Layout
34525 Packages ! multicol
34530 , that is loaded with the LaTeX-preamble line
34533 \begin_layout Standard
34538 usepackage{multicol}
34541 \begin_layout Standard
34542 \begin_inset Note Greyedout
34545 \begin_layout Plain Layout
34546 Note that in this case the setting
34549 \begin_inset space ~
34556 Document\SpecialChar \menuseparator
34562 \begin_inset space ~
34582 \begin_layout Standard
34583 Before the multi-column text the command
34586 \begin_layout Standard
34591 begin{multicols}{column number}
34594 \begin_layout Standard
34595 is written in TeX-mode.
34596 The column number is a number in the range of 2
34597 \begin_inset space \thinspace{}
34601 \begin_inset space \thinspace{}
34605 Before the formula the multi-column text is ended by inserting the command
34608 \begin_layout Standard
34616 \begin_layout Standard
34620 \begin_layout Standard
34621 Due to the command some space is automatically added before the formula.
34623 \begin_inset space \thinspace{}
34626 mm vertical space is inserted before the formula.
34627 When the formula style
34633 \begin_layout Plain Layout
34635 \begin_inset CommandInset ref
34637 reference "sec:Formula-Styles"
34649 \begin_inset space \thinspace{}
34652 mm space is inserted instead.
34655 \begin_layout Standard
34656 As example a multi-column text with a displayed formula:
34659 \begin_layout Standard
34665 \begin_layout Plain Layout
34669 begin{multicols}{2}
34674 Das Spektrum wird fouriertransformiert.
34675 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
34676 , Lösungsmittel) zu trennen.
34677 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
34678 nun das Aussehen des Ausgangssignals.
34679 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
34680 über alle Phasen integrieren muss.
34682 \begin_inset Formula $S$
34685 unser normiertes Ausgangssignal und
34686 \begin_inset Formula $P$
34689 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
34693 \begin_layout Plain Layout
34703 \begin_inset VSpace -6mm
34707 \begin_inset Formula
34709 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
34718 \begin_layout Plain Layout
34722 begin{multicols}{2}
34728 \begin_inset Formula $S_{0}$
34731 das Signal ohne Gradient ist und die Normierungsbedingung
34732 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
34736 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
34738 \begin_inset Formula $\nicefrac{\pi}{2}$
34742 \begin_inset space \thinspace{}
34745 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
34746 das Signal zusätzlich abschwächt.
34747 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
34749 \begin_inset Formula $T_{2}$
34755 \begin_layout Standard
34761 \begin_layout Plain Layout
34773 \begin_layout Subsection
34774 Formulas with Description of Variables
34775 \begin_inset Index idx
34778 \begin_layout Plain Layout
34779 Formula ! with description of variables
34787 \begin_layout Standard
34788 To describe variables within a formula, like in formula
34789 \begin_inset CommandInset ref
34791 reference "eq:within"
34800 \begin_inset Formula $n$
34804 \begin_inset space ~
34807 matrix is used with left aligned columns for the
34808 \begin_inset Formula $n$
34815 \begin_layout Plain Layout
34817 \begin_inset CommandInset ref
34819 reference "sec:Matrices"
34828 To set the description in a smaller size, before the matrix e.
34829 \begin_inset space \thinspace{}
34833 \begin_inset space \space{}
34846 \begin_layout Plain Layout
34848 \begin_inset CommandInset ref
34850 reference "sub:Font-Sizes"
34862 \begin_layout Standard
34863 When the formula style
34869 \begin_layout Plain Layout
34871 \begin_inset CommandInset ref
34873 reference "sec:Formula-Styles"
34894 \begin_layout Plain Layout
34901 only works in formulas with the style
34906 \begin_inset CommandInset ref
34908 reference "sub:Variable-Space"
34917 is inserted before and after the matrix to have the same separation of
34918 the matrix from the equation and the side margin.
34921 \begin_layout Standard
34922 When the formula style
34926 is used, the method described in
34927 \begin_inset CommandInset ref
34929 reference "sub:Flalign-Environment"
34933 is used to indent formulas.
34935 \begin_inset CommandInset ref
34937 reference "eq:within"
34941 consists of five columns where in the first two columns contain the equation,
34942 the third the matrix and the last one an empty TeX-brace.
34943 \begin_inset Formula
34945 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
34946 \rho & \textrm{density}\\
34947 V & \textrm{volume}\\
34948 g & \textrm{gravitational acceleration}
34949 \end{array} & & {}\label{eq:within}
34957 \begin_layout Subsection
34958 Upright small Greek Letters
34959 \begin_inset CommandInset label
34961 name "sub:Upright-small-Greek"
34966 \begin_inset Index idx
34969 \begin_layout Plain Layout
34970 Greek letters ! upright
34978 \begin_layout Standard
34979 Most of the math fonts only provide italic small Greek letters.
34980 But for symbols of elementary particles like pions and neutrinos, upright
34981 Greek letters are needed.
34990 \begin_layout Plain Layout
34995 is part of the LaTeX-package
35000 \begin_inset Index idx
35003 \begin_layout Plain Layout
35008 \begin_layout Plain Layout
35028 \begin_inset Index idx
35031 \begin_layout Plain Layout
35037 that is loaded with the LaTeX-preamble line
35040 \begin_layout Standard
35045 usepackage{upgreek}
35048 \begin_layout Standard
35054 \begin_layout Plain Layout
35064 \begin_inset Note Note
35067 \begin_layout Plain Layout
35068 The following table will only be displayed when the LaTeX-package
35077 They are created when the command for a small Greek letter is started with
35083 For example the command
35090 \begin_inset Formula $\uptau$
35096 \begin_layout Standard
35097 With these commands reactions of elementary particles can be typeset:
35098 \begin_inset Formula
35100 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
35108 \begin_layout Standard
35109 The upright letters are more bold and wider than the italic ones.
35110 They should therefore not be used for units like
35111 \begin_inset Quotes eld
35115 \begin_inset Quotes erd
35121 \begin_layout Standard
35125 \begin_layout Plain Layout
35135 \begin_inset Note Note
35138 \begin_layout Plain Layout
35139 The following will be displayed when the LaTeX-package
35151 \begin_layout Standard
35152 You need to install the LaTeX-package
35156 to see the rest of this subsection in the output.
35159 \begin_layout Standard
35163 \begin_layout Plain Layout
35175 \begin_layout Subsection
35176 Text Characters in Formulas
35177 \begin_inset CommandInset label
35179 name "sub:Text-Characters-in"
35184 \begin_inset Index idx
35187 \begin_layout Plain Layout
35196 \begin_layout Standard
35197 In some cases you might want to insert text characters directly into formulas.
35198 When for example the centered dot · is often used in formulas like
35199 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35202 , one would have to insert the command
35212 \begin_layout Plain Layout
35214 \begin_inset CommandInset ref
35216 reference "sub:Binary-Operators"
35225 all the time, because this character is defined in all encodings as text
35227 But the encoding can be changed by this LaTeX-preamble line:
35230 \begin_layout Standard
35235 Declare Inputtext{183}{
35245 f\SpecialChar \textcompwordmark{}
35249 \begin_layout Standard
35250 The character encoding (menu
35252 Document\SpecialChar \menuseparator
35253 Settings\SpecialChar \menuseparator
35256 ) specifies what character appears when a keyboard key is pressed.
35257 When the key for the character '·' is pressed, internally the command
35264 But this command is not available in a formula so that you would get LaTeX-erro
35266 With the changed encoding the right command is chosen automatically, depending
35267 on if the character was inserted into a formula or not.
35270 \begin_layout Standard
35271 The encoding of several characters is saved in definition files.
35272 For example the encoding
35276 is defined in the file
35280 which is in the installation folder of LaTeX.
35281 Encodings should only be changed via the LaTeX-preamble and not in the
35283 Otherwise documents could not be edited by other LyX users working on other
35287 \begin_layout Standard
35288 \begin_inset VSpace medskip
35291 Besides the centered dot, in this document the degree sign ° is defined
35292 with the following LaTeX-preamble line so that it can be directly inserted
35296 \begin_layout Standard
35301 DeclareInputtext{176}{
35311 f\SpecialChar \textcompwordmark{}
35315 \begin_layout Standard
35316 \begin_inset Newpage newpage
35322 \begin_layout Section
35325 \begin_inset Index idx
35328 \begin_layout Plain Layout
35337 \begin_layout Standard
35338 This section is a summary of the most important typographic rules, listed
35343 \begin_layout Plain Layout
35344 This collection was partly taken from the German semi-official dictionary
35346 \begin_inset Quotes eld
35350 \begin_inset Quotes erd
35354 \begin_inset CommandInset citation
35360 that lists some of the ISO rules.
35361 More rules are listed in
35362 \begin_inset CommandInset citation
35376 \begin_layout Itemize
35385 \begin_layout Plain Layout
35386 done with font styles, see
35387 \begin_inset CommandInset ref
35389 reference "sub:Font-Styles"
35398 , no matter if they appear in italic text: 30
35399 \begin_inset space \thinspace{}
35403 \begin_inset Newline newline
35406 Between the value and the unit is the smallest space, see
35407 \begin_inset CommandInset ref
35409 reference "sub:Predefined-Space"
35414 \begin_inset Newline newline
35417 This convention is automatically fulfilled when the command
35424 When it is entered to a formula, two boxes appear.
35425 In the first one the value is inserted, in the second one the unit, and
35427 \begin_inset Formula $\unit[30]{km/h}$
35431 \begin_inset space \thinspace{}
35441 is not a real LaTeX command but the command
35447 , therefore you cannot use it in TeX code.
35450 \begin_layout Itemize
35451 Percent and perthousand signs are set like physical units:
35452 \begin_inset Newline newline
35456 \begin_inset space \thinspace{}
35462 \begin_layout Itemize
35463 The degree sign follows directly on the value: 15°, but not when it is used
35465 \begin_inset space \thinspace{}
35471 \begin_layout Itemize
35472 In numbers with more than four digits the smallest space is inserted before
35473 every third digit to group them:
35483 \begin_inset space \thinspace{}
35487 \begin_inset space \thinspace{}
35493 \begin_layout Itemize
35494 For dimensions like 120×90×40
35495 \begin_inset space \thinspace{}
35498 cm the multiplication sign
35499 \begin_inset Quotes eld
35503 \begin_inset Quotes erd
35507 It is available either via the command
35515 Insert\SpecialChar \menuseparator
35516 Special Character\SpecialChar \menuseparator
35522 \begin_layout Itemize
35523 Functions with names consisting of several letters are set upright to avoid
35525 \begin_inset CommandInset ref
35527 reference "sub:Predefined-Functions"
35534 \begin_layout Itemize
35535 Indices consisting of several letters, are set upright:
35536 \begin_inset Formula $E_{\mathrm{kin}}$
35540 \begin_inset Newline newline
35543 Components of matrices are set italic:
35544 \begin_inset Formula $\hat{H}_{kl}$
35550 \begin_layout Itemize
35551 The differentiation/integration operator 'd', the Euler's number 'e' and
35552 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35556 \begin_layout Itemize
35557 The character that denotes a
35561 transformation is inserted either by the command
35566 \begin_inset space \textvisiblespace{}
35573 Insert\SpecialChar \menuseparator
35574 Special Character\SpecialChar \menuseparator
35575 Symbols\SpecialChar \menuseparator
35577 \begin_inset space ~
35583 \begin_inset Formula $\mathscr{F}$
35589 \begin_layout Standard
35590 \begin_inset Newpage newpage
35596 \begin_layout Section
35598 \begin_inset Index idx
35601 \begin_layout Plain Layout
35610 \begin_layout Standard
35611 Some characters and symbols can be created with several commands.
35612 Here is a list of the synonym commands:
35615 \begin_layout Standard
35616 \begin_inset VSpace bigskip
35620 \begin_inset space \hfill{}
35624 \begin_inset Tabular
35625 <lyxtabular version="3" rows="12" columns="2">
35626 <features rotate="0" tabularvalignment="middle">
35627 <column alignment="center" valignment="top" width="0pt">
35628 <column alignment="center" valignment="top" width="0pt">
35630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35633 \begin_layout Plain Layout
35639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35642 \begin_layout Plain Layout
35644 \begin_inset Note Note
35647 \begin_layout Plain Layout
35654 is only used as spacer.
35666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35669 \begin_layout Plain Layout
35677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35680 \begin_layout Plain Layout
35684 \begin_layout Plain Layout
35697 \begin_layout Plain Layout
35711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35714 \begin_layout Plain Layout
35722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35725 \begin_layout Plain Layout
35735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35738 \begin_layout Plain Layout
35746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35749 \begin_layout Plain Layout
35759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35762 \begin_layout Plain Layout
35770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35773 \begin_layout Plain Layout
35781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35784 \begin_layout Plain Layout
35792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35795 \begin_layout Plain Layout
35803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35806 \begin_layout Plain Layout
35814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35817 \begin_layout Plain Layout
35827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35830 \begin_layout Plain Layout
35838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35841 \begin_layout Plain Layout
35851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35854 \begin_layout Plain Layout
35862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35865 \begin_layout Plain Layout
35875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35878 \begin_layout Plain Layout
35886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35889 \begin_layout Plain Layout
35899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35902 \begin_layout Plain Layout
35910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35913 \begin_layout Plain Layout
35921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35924 \begin_layout Plain Layout
35932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35935 \begin_layout Plain Layout
35947 \begin_inset space \hfill{}
35951 \begin_inset Tabular
35952 <lyxtabular version="3" rows="12" columns="2">
35953 <features rotate="0" tabularvalignment="middle">
35954 <column alignment="center" valignment="top" width="0pt">
35955 <column alignment="center" valignment="top" width="0pt">
35957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35960 \begin_layout Plain Layout
35966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35969 \begin_layout Plain Layout
35977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35980 \begin_layout Plain Layout
35988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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36273 Addison Wesley, 2004
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36287 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
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36495 Auflage, Duden 2001
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