1 #LyX 2.0 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 % Folgendes Problem lösen:
27 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
28 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
29 % die Kapitelnummer geschrieben.
30 % Als Lösung wird mehr Platz zwischen Nummer und
31 % Überschrift eingefügt.
32 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
33 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
35 % To be able to enter the character ° and · directly in LyX,
37 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
38 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
40 % increase link area for cross-references and autoname them,
41 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
43 \settowidth{\abc}{\space}
45 \renewcommand{\equationautorefname}{\hspace{-\abc}}
46 \renewcommand{\sectionautorefname}{sec.\negthinspace}
47 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}
51 % don't load packages twice
52 % see first footnote in sec. 9.3
53 \@ifundefined{textcolor}{\usepackage{color}}{}
55 % the pages of the TOC are numbered roman
56 % and a PDF-bookmark for the TOC is added
58 \let\myTOC\tableofcontents
59 \renewcommand{\tableofcontents}{%
61 \pdfbookmark[1]{\contentsname}{}
64 \pagenumbering{arabic}}
66 % insert additional vertical space of 1.5 mm between footnotes,
68 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
70 % provides caption formatting
71 \setkomafont{captionlabel}{\bfseries}
74 \usepackage[samesize]{cancel}
76 % enables calculation of values
79 % for multiple columns used in sec. 24.7
85 % for the Fourier transformation symbol
88 % define a color, used in sec.9.3
89 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
91 % declare operators (see sec. 10.4 and sec. 15.2)
92 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
93 \DeclareMathOperator{\sgn}{sgn}
95 \newcommand{\spce}{\textvisiblespace}
97 % example definitions for sec. 20.1
98 \newcommand{\gr}{\Longrightarrow}
99 \newcommand{\us}[1]{\underline{#1}}
100 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
101 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
102 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
104 % example macro from sec. 19.4
105 %\def\tagform@#1{\maketag@@@{|#1|}}
107 % macro from sec. 10.2
108 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
109 \def\mathclap {\mathpalette \mathclapinternal}
110 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
113 % ------------------------------------
114 % used to check for needed LaTeX packages
117 % check for package eurosym
118 % used for the Euro symbol
120 \IfFileExists{eurosym.sty}
121 {\usepackage[gennarrow]{eurosym}
122 \setboolean{eurosym}{true}}
123 {\setboolean{eurosym}{false}}
125 % check for package braket
126 % used for physical vectors
128 \IfFileExists{braket.sty}
130 \setboolean{braket}{true}}
131 {\setboolean{braket}{false}}
133 % check for package cancel
135 \IfFileExists{cancel.sty}
137 \setboolean{cancel}{true}}
138 {\setboolean{cancel}{false}}
140 % check for package upgreek
142 \IfFileExists{upgreek.sty}
143 {\usepackage{upgreek}
144 \setboolean{upgreek}{true}}
145 {\setboolean{upgreek}{false}}
147 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
148 \use_default_options false
149 \maintain_unincluded_children false
151 \language_package default
156 \font_typewriter default
157 \font_default_family default
158 \use_non_tex_fonts false
165 \default_output_format default
167 \bibtex_command default
168 \index_command default
172 \pdf_title "LyX's Math Manual"
173 \pdf_author "LyX Team, Uwe Stöhr"
174 \pdf_subject "LyX-documentation about math"
175 \pdf_keywords "LyX, Mathed"
177 \pdf_bookmarksnumbered true
178 \pdf_bookmarksopen true
179 \pdf_bookmarksopenlevel 1
180 \pdf_breaklinks false
184 \pdf_pdfusetitle false
185 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
195 \paperorientation portrait
198 \notefontcolor #0000ff
205 \paragraph_separation skip
207 \quotes_language english
210 \paperpagestyle plain
214 \tracking_changes false
215 \output_changes false
218 \html_be_strict false
224 LyX's detailed Math manual
232 \begin_layout Plain Layout
234 If you have comments or error corrections, please send them to the LyX Documenta
238 \begin_inset CommandInset href
240 name "lyx-docs@lists.lyx.org"
241 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
252 \begin_inset Note Note
255 \begin_layout Plain Layout
262 \begin_inset Newline newline
266 \begin_inset Newline newline
274 \begin_layout Standard
275 \begin_inset CommandInset toc
276 LatexCommand tableofcontents
283 \begin_layout Standard
284 \begin_inset Note Note
287 \begin_layout Plain Layout
288 To export this document to PDF, PS or DVI the LaTeX-packages
290 braket, cancel, eurosym, mathdots, mhchem
297 If they are not installed the document can be export anyway but the sections
298 where the packages are required will not appear in the output.
303 ; if it is not installed, this file cannot be exported.
306 \begin_layout Plain Layout
307 The latest PDF-version of this document can be found here:
308 \begin_inset Newline newline
313 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
321 \begin_layout Standard
322 \begin_inset Newpage newpage
328 \begin_layout Section
332 \begin_layout Standard
333 This document explains LyX's math features and is furthermore a collection
334 of LaTeX-commands used for mathematical characters and constructs.
335 The explanations are designed for the usage of commands.
336 It is therefore required that you have read the section
347 \begin_layout Standard
348 Most of the characters and many constructs explained in this manual are
349 also accessible via the menu
353 \SpecialChar \menuseparator
369 But everybody who has to write lots of formulas will notice that it is
370 much faster to use commands instead of the math toolbar.
371 Therefore this manual is focused on commands but also mentions the correspondin
372 g toolbar buttons when available.
375 \begin_layout Standard
376 If not specially mentioned the commands are only available within formulas.
377 To be able to use all commands explained in this document, the option
381 must be used in the document settings (menu
383 Document\SpecialChar \menuseparator
384 Settings\SpecialChar \menuseparator
395 \begin_layout Plain Layout
398 Use AMS math package automatically
404 \begin_layout Plain Layout
413 -math when math constructs are found that are supported by LyX.
421 \begin_layout Standard
422 This document doesn't list all
426 \begin_layout Plain Layout
439 \begin_layout Plain Layout
444 \begin_layout Plain Layout
453 -math commands is in the file
456 \begin_inset CommandInset href
459 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
465 , which is part of every LaTeX standard installation.
470 for lucidity reasons.
473 \begin_layout Section
477 \begin_layout Standard
478 To create an inline formula
479 \begin_inset Index idx
482 \begin_layout Plain Layout
488 that is embedded into a text line, use one of the shortcuts
494 or the toolbar button
495 \begin_inset Graphics
496 filename ../images/math-mode.png
502 \begin_inset Newline newline
505 To create a display style formula
506 \begin_inset Index idx
509 \begin_layout Plain Layout
510 Formula ! display style
515 that will appear bigger and in an own paragraph, use one of these shortcuts:
525 \begin_layout Standard
526 To change a display style formula to an inline formula, set the cursor into
527 the formula and use one of the shortcuts
535 Edit\SpecialChar \menuseparator
536 Math\SpecialChar \menuseparator
540 The same way is used to change an inline formula to a display style formula.
543 \begin_layout Standard
544 To display parts of an inline formula in the size of a display style formula,
552 \begin_inset Index idx
555 \begin_layout Plain Layout
564 Then a new blue box appears in which the desired formula part is inserted.
567 \begin_layout Standard
568 Only inline formulas are allowed inside tables.
571 \begin_layout Standard
576 can be turned on in the menu
578 View\SpecialChar \menuseparator
582 When you click there on
583 \begin_inset Quotes eld
587 \begin_inset Quotes erd
590 the toolbar will be shown permanently at the bottom; this state is visualized
595 menu with a checkmark.
596 When you click in this state again on
597 \begin_inset Quotes eld
601 \begin_inset Quotes erd
612 is only shown when the cursor is within a formula; this state is visualized
613 by the renaming of the menu entry from
614 \begin_inset Quotes eld
618 \begin_inset Quotes erd
622 \begin_inset Quotes eld
630 \begin_inset Quotes erd
636 \begin_layout Standard
638 \begin_inset Index idx
641 \begin_layout Plain Layout
647 is invoked by pressing the toolbar button
648 \begin_inset Graphics
649 filename ../images/ert-insert.png
656 Insert\SpecialChar \menuseparator
661 \begin_layout Plain Layout
677 \begin_inset Note Note
680 \begin_layout Plain Layout
681 In LyX there are three
682 \begin_inset Quotes eld
686 \begin_inset Quotes erd
689 that appear in the output with sub- and superscript letters: TeX, LaTeX
693 \begin_layout Plain Layout
694 To avoid that these names are recognized as proper names, a TeX-brace pair
703 \begin_layout Standard
704 To change the LaTeX-preamble
705 \begin_inset Index idx
708 \begin_layout Plain Layout
716 Document\SpecialChar \menuseparator
717 Settings\SpecialChar \menuseparator
722 \begin_layout Plain Layout
738 \begin_layout Standard
739 To edit matrices, case differentiations and multiline formulas subsequently,
742 Edit\SpecialChar \menuseparator
747 Edit\SpecialChar \menuseparator
749 \begin_inset space \thinspace{}
753 \begin_inset space \thinspace{}
763 When lines and columns are swapped via the menu, the column or line where
764 the cursor is in is exchanged with the column to the right or the line
766 Is the cursor in the last column or row, the exchange is done with the
767 column to the left or the line above.
770 \begin_layout Standard
771 To write text in formulas
775 \begin_layout Plain Layout
776 For multiline formulas the command
783 \begin_inset CommandInset ref
785 reference "sub:Text-in-multiline"
799 \begin_inset Index idx
802 \begin_layout Plain Layout
809 \begin_inset Index idx
812 \begin_layout Plain Layout
819 This mode is invoked with the shortcut
825 or by the insertion of the command
832 \begin_inset Index idx
835 \begin_layout Plain Layout
844 The text appears black in LyX and can therefore be distinguished from the
845 other formula parts that appear blue.
846 In the output mathematical text is set upright, in contrary to other formula
850 \begin_layout Subsection*
854 \begin_layout Standard
855 Most of the LaTeX-commands for math constructs have the following scheme:
858 \begin_layout Standard
874 \begin_layout Standard
875 A command starts always with a backslash
876 \begin_inset Quotes gld
886 \begin_inset Quotes grd
890 To omit optional arguments, also omit the associated brackets.
891 The braces around the required arguments are named in this document as
893 \begin_inset Index idx
896 \begin_layout Plain Layout
903 If you add in a formula a left brace to a command name, LyX creates automatical
905 In all other cases TeX-braces are created in formulas with the command
913 TeX-braces appear red in LyX, in contrary to normal braces that appear
915 In TeX-mode no command is needed to get TeX-braces.
916 TeX-braces don't appear in the output.
919 \begin_layout Standard
920 When commands without arguments, like commands for symbols are entered in
921 TeX-mode, a space character must
925 be behind the command to end it.
926 This space doesn't appear in the output.
927 When the space should appear in the output, the space must be followed
928 by a protected space in normal text.
931 \begin_layout Standard
932 A protected space is inserted with
935 arg "space-insert protected"
941 \begin_layout Subsection*
942 \begin_inset Newpage newpage
948 \begin_layout Itemize
953 \begin_layout Plain Layout
954 This visible space character can be created with the command
961 \begin_inset Index idx
964 \begin_layout Plain Layout
972 , inserted in TeX-mode.
981 \begin_layout Plain Layout
994 denotes a space character to be input.
997 \begin_layout Itemize
999 \begin_inset Formula $\to$
1002 denotes the usage of the corresponding arrow key on the keyboard.
1005 \begin_layout Subsection*
1009 \begin_layout Standard
1011 \begin_inset Float table
1017 \begin_layout Plain Layout
1019 \begin_inset Caption
1021 \begin_layout Plain Layout
1022 \begin_inset CommandInset label
1024 name "tab:Available-units"
1036 \begin_layout Plain Layout
1038 \begin_inset Tabular
1039 <lyxtabular version="3" rows="13" columns="2">
1040 <features tabularvalignment="middle">
1041 <column alignment="center" valignment="top" width="0">
1042 <column alignment="center" valignment="top" width="0">
1044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1047 \begin_layout Plain Layout
1053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1056 \begin_layout Plain Layout
1064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1067 \begin_layout Plain Layout
1073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1076 \begin_layout Plain Layout
1084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1087 \begin_layout Plain Layout
1093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1096 \begin_layout Plain Layout
1104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1107 \begin_layout Plain Layout
1113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1116 \begin_layout Plain Layout
1118 \begin_inset space \thinspace{}
1122 \begin_inset space \thinspace{}
1132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1135 \begin_layout Plain Layout
1141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1144 \begin_layout Plain Layout
1146 \begin_inset space \thinspace{}
1150 \begin_inset space \thinspace{}
1160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1163 \begin_layout Plain Layout
1169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1172 \begin_layout Plain Layout
1174 \begin_inset space \thinspace{}
1178 \begin_inset space \thinspace{}
1188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1191 \begin_layout Plain Layout
1197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1200 \begin_layout Plain Layout
1202 \begin_inset space \thinspace{}
1206 \begin_inset space \thinspace{}
1216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1219 \begin_layout Plain Layout
1225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1228 \begin_layout Plain Layout
1230 \begin_inset space \thinspace{}
1234 \begin_inset space \thinspace{}
1244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1247 \begin_layout Plain Layout
1253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1256 \begin_layout Plain Layout
1258 \begin_inset space \thinspace{}
1262 \begin_inset Formula $\approx$
1266 \begin_inset space \thinspace{}
1276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1279 \begin_layout Plain Layout
1285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1288 \begin_layout Plain Layout
1290 \begin_inset space \thinspace{}
1294 \begin_inset space \thinspace{}
1304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1307 \begin_layout Plain Layout
1313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1316 \begin_layout Plain Layout
1320 \begin_inset Quotes eld
1326 \begin_inset Quotes erd
1336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1339 \begin_layout Plain Layout
1345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1348 \begin_layout Plain Layout
1350 \begin_inset Quotes eld
1358 \begin_inset Quotes erd
1368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1371 \begin_layout Plain Layout
1377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1380 \begin_layout Plain Layout
1382 \begin_inset space \thinspace{}
1386 \begin_inset Formula $\nicefrac{1}{18}$
1390 \begin_inset space \thinspace{}
1411 \begin_layout Standard
1412 \begin_inset Newpage newpage
1418 \begin_layout Section
1422 \begin_layout Subsection
1424 \begin_inset Index idx
1427 \begin_layout Plain Layout
1434 \begin_inset Index idx
1437 \begin_layout Plain Layout
1444 \begin_inset Index idx
1447 \begin_layout Plain Layout
1452 \begin_layout Plain Layout
1463 \begin_layout Plain Layout
1476 \begin_inset Index idx
1479 \begin_layout Plain Layout
1484 \begin_layout Plain Layout
1495 \begin_layout Plain Layout
1510 \begin_layout Standard
1511 Indices are created with an underscore
1512 \begin_inset Quotes eld
1516 \begin_inset Quotes erd
1519 or via the math toolbar button
1520 \begin_inset Graphics
1521 filename ../images/math-subscript.png
1526 , exponents with a caret
1527 \begin_inset Quotes eld
1531 \begin_inset Quotes erd
1534 or via the math toolbar button
1535 \begin_inset Graphics
1536 filename ../images/math-superscript.png
1544 \begin_layout Standard
1546 \begin_inset Tabular
1547 <lyxtabular version="3" rows="4" columns="2">
1548 <features tabularvalignment="middle">
1549 <column alignment="center" valignment="top" width="0pt">
1550 <column alignment="center" valignment="top" width="0pt">
1552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1555 \begin_layout Plain Layout
1561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1564 \begin_layout Plain Layout
1566 \begin_inset Note Note
1569 \begin_layout Plain Layout
1576 is only used as spacer.
1588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1591 \begin_layout Plain Layout
1597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1600 \begin_layout Plain Layout
1601 \begin_inset Formula $B_{V}$
1611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1614 \begin_layout Plain Layout
1620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1623 \begin_layout Plain Layout
1624 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1637 \begin_layout Plain Layout
1642 \begin_layout Plain Layout
1656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1659 \begin_layout Plain Layout
1660 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1676 \begin_layout Standard
1677 As the caret is in some languages an accent, vowels will be accentuated
1678 in this case and not set as exponents
1682 \begin_layout Plain Layout
1683 Depending on the used keyboard settings this can also happen for other character
1690 To get in this case exponents, press
1694 after the caret as in the last example.
1697 \begin_layout Subsection
1699 \begin_inset CommandInset label
1701 name "sub:Fractions"
1706 \begin_inset Index idx
1709 \begin_layout Plain Layout
1718 \begin_layout Standard
1719 Fractions are generated with the command
1726 \begin_inset Index idx
1729 \begin_layout Plain Layout
1737 or via the math toolbar button
1738 \begin_inset Graphics
1739 filename ../images/math/frac.png
1745 The font size is adjusted automatically, depending on whether the fraction
1746 is in an inline or display style formula.
1747 With the math toolbar button
1748 \begin_inset Graphics
1749 filename ../images/math/frac-square.png
1754 you can select different fraction types.
1757 \begin_layout Standard
1765 \begin_inset Index idx
1768 \begin_layout Plain Layout
1776 a fraction can be created that has in any case the size of a display style
1785 \begin_inset Index idx
1788 \begin_layout Plain Layout
1796 the fraction appears always with the size of an inline formula.
1800 \begin_layout Standard
1801 A line with the fraction
1802 \begin_inset Formula $\frac{1}{2}$
1805 that was created with the command
1814 \begin_layout Standard
1815 A line with the fraction
1816 \begin_inset Formula $\dfrac{1}{2}$
1819 that was created with the command
1828 \begin_layout Standard
1830 \begin_inset Tabular
1831 <lyxtabular version="3" rows="4" columns="2">
1832 <features tabularvalignment="middle">
1833 <column alignment="center" valignment="top" width="0pt">
1834 <column alignment="center" valignment="top" width="0pt">
1836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1839 \begin_layout Plain Layout
1845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1848 \begin_layout Plain Layout
1850 \begin_inset Note Note
1853 \begin_layout Plain Layout
1860 is only used as spacer.
1872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1875 \begin_layout Plain Layout
1882 \begin_layout Plain Layout
1892 \begin_inset Formula $\downarrow$
1900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1903 \begin_layout Plain Layout
1904 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1917 \begin_layout Plain Layout
1924 \begin_layout Plain Layout
1934 \begin_inset Formula $\downarrow$
1942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1945 \begin_layout Plain Layout
1946 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1959 \begin_layout Plain Layout
1966 \begin_layout Plain Layout
1979 \begin_layout Plain Layout
1994 \begin_layout Plain Layout
2004 \begin_inset Formula $\downarrow$
2008 \begin_inset Formula $\downarrow\downarrow$
2016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2019 \begin_layout Plain Layout
2020 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2036 \begin_layout Standard
2037 \begin_inset VSpace bigskip
2041 \begin_inset Newpage newpage
2044 For nested fractions the command
2051 \begin_inset Index idx
2054 \begin_layout Plain Layout
2064 \begin_inset VSpace -3mm
2070 \begin_layout Standard
2071 \begin_inset Formula
2073 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2074 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2082 \begin_layout Standard
2083 The command for the example above is:
2086 \begin_layout Standard
2095 \begin_layout Plain Layout
2105 \begin_inset Formula $\downarrow$
2114 \begin_layout Plain Layout
2129 \begin_layout Plain Layout
2139 \begin_inset Formula $\downarrow$
2143 \begin_inset Formula $\downarrow$
2149 \begin_layout Standard
2150 \begin_inset VSpace medskip
2156 \begin_layout Standard
2163 sets the fraction always in the size of a displayed formula, also when
2164 it is part of another fraction.
2167 \begin_layout Standard
2168 It is possible to specify the alignment of the numerator.
2175 is used to left align it, the command
2188 centers the numerator.
2189 These fractions demonstrate the different alignments:
2192 \begin_layout Standard
2193 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2197 \begin_inset Formula $\cfrac{A}{B+C}$
2201 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2207 \begin_layout Standard
2208 \begin_inset Note Greyedout
2211 \begin_layout Plain Layout
2228 are no real LaTeX commands but represent the command
2232 cfrac[alignment]{numerator}{denominator}
2235 Therefore you cannot use them in TeX code.
2243 \begin_layout Standard
2244 \begin_inset VSpace medskip
2247 It is often advantageous to combine
2260 \begin_inset Formula
2262 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2270 \begin_layout Standard
2271 For inline fractions with a sloped fraction stroke you can use the command
2279 \begin_inset Index idx
2282 \begin_layout Plain Layout
2291 \begin_inset Formula $\nicefrac{5}{31}$
2301 \begin_inset Index idx
2304 \begin_layout Plain Layout
2313 \begin_inset Formula $\unitfrac{5}{31}$
2316 There is furthermore the command
2322 that offers to write a fraction in combination with a number:
2323 \begin_inset Formula $\unitfrac[2]{1}{3}$
2329 \begin_layout Standard
2330 \begin_inset Note Greyedout
2333 \begin_layout Plain Layout
2344 is not a real LaTeX command but the command
2345 \begin_inset Newline newline
2352 unitfrac[number]{numerator}{denominator}
2355 Therefore you cannot use it in TeX code.
2363 \begin_layout Standard
2364 How to define own fractions where the fraction stroke can be changed, is
2366 \begin_inset CommandInset ref
2368 reference "sub:Self-defined-Fractions"
2375 \begin_layout Subsection
2377 \begin_inset Index idx
2380 \begin_layout Plain Layout
2389 \begin_layout Standard
2390 Square roots are created with
2397 \begin_inset Index idx
2400 \begin_layout Plain Layout
2408 or the math toolbar button
2409 \begin_inset Graphics
2410 filename ../images/math/sqrt.png
2415 , all other roots with the command
2422 \begin_inset Index idx
2425 \begin_layout Plain Layout
2433 or with the math toolbar button
2434 \begin_inset Graphics
2435 filename ../images/math/root.png
2443 \begin_layout Standard
2445 \begin_inset Tabular
2446 <lyxtabular version="3" rows="3" columns="2">
2447 <features tabularvalignment="middle">
2448 <column alignment="center" valignment="top" width="0pt">
2449 <column alignment="center" valignment="top" width="0pt">
2451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2454 \begin_layout Plain Layout
2460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2463 \begin_layout Plain Layout
2465 \begin_inset Note Note
2468 \begin_layout Plain Layout
2475 is only used as spacer.
2487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2490 \begin_layout Plain Layout
2497 \begin_layout Plain Layout
2511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2514 \begin_layout Plain Layout
2515 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2525 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2528 \begin_layout Plain Layout
2535 \begin_layout Plain Layout
2545 \begin_inset Formula $\downarrow$
2553 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2556 \begin_layout Plain Layout
2557 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2573 \begin_layout Standard
2574 A square root can also be created with
2580 when the root index field is left empty.
2583 \begin_layout Standard
2584 With certain indices the distance to the root is too small, like in this
2586 \begin_inset Formula $\sqrt[\beta]{B}$
2590 \begin_inset Newline newline
2594 \begin_inset Formula $\beta$
2598 To avoid this, the commands
2605 \begin_inset Index idx
2608 \begin_layout Plain Layout
2623 \begin_inset Index idx
2626 \begin_layout Plain Layout
2634 are used with the following scheme:
2637 \begin_layout Standard
2651 \begin_layout Standard
2652 Distance is the number of Big Points (unit bp;
2653 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2656 ), that the index should be moved to the left or top, resp..
2657 The commands are written to the index.
2658 This way the command
2659 \begin_inset Newline newline
2669 \begin_inset Formula $\to$
2675 \begin_inset Formula $\to$
2684 \begin_layout Plain Layout
2694 \begin_inset Formula $\to$
2698 \begin_inset Newline newline
2703 produces a correct typeset formula:
2704 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2710 \begin_layout Subsection
2711 Binomial Coefficients
2712 \begin_inset Index idx
2715 \begin_layout Plain Layout
2716 Binomial coefficients
2724 \begin_layout Standard
2725 Binomial coefficients are inserted with the command
2732 \begin_inset Index idx
2735 \begin_layout Plain Layout
2743 or with the submenu of the math toolbar button
2744 \begin_inset Graphics
2745 filename ../images/math/frac-square.png
2751 Analog to fractions (
2770 \begin_inset Index idx
2773 \begin_layout Plain Layout
2788 \begin_inset Index idx
2791 \begin_layout Plain Layout
2800 For other brackets around binomial coeficients there are the commands
2807 \begin_inset Index idx
2810 \begin_layout Plain Layout
2825 \begin_inset Index idx
2828 \begin_layout Plain Layout
2839 \begin_layout Standard
2841 \begin_inset Tabular
2842 <lyxtabular version="3" rows="6" columns="2">
2843 <features tabularvalignment="middle">
2844 <column alignment="center" valignment="top" width="0pt">
2845 <column alignment="center" valignment="top" width="0pt">
2847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2850 \begin_layout Plain Layout
2856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2859 \begin_layout Plain Layout
2861 \begin_inset Note Note
2864 \begin_layout Plain Layout
2871 is only used as spacer.
2883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2886 \begin_layout Plain Layout
2893 \begin_layout Plain Layout
2903 \begin_inset Formula $\downarrow$
2911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2914 \begin_layout Plain Layout
2915 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2928 \begin_layout Plain Layout
2935 \begin_layout Plain Layout
2945 \begin_inset Formula $\downarrow$
2953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2956 \begin_layout Plain Layout
2957 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2970 \begin_layout Plain Layout
2977 \begin_layout Plain Layout
2987 \begin_inset Formula $\downarrow$
2995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2998 \begin_layout Plain Layout
2999 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3012 \begin_layout Plain Layout
3019 \begin_layout Plain Layout
3029 \begin_inset Formula $\downarrow$
3037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3040 \begin_layout Plain Layout
3041 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3054 \begin_layout Plain Layout
3061 \begin_layout Plain Layout
3071 \begin_inset Formula $\downarrow$
3079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3082 \begin_layout Plain Layout
3083 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3099 \begin_layout Subsection
3100 Case Differentiations
3101 \begin_inset Index idx
3104 \begin_layout Plain Layout
3105 Case differentiations
3113 \begin_layout Standard
3115 \begin_inset Tabular
3116 <lyxtabular version="3" rows="3" columns="2">
3117 <features tabularvalignment="middle">
3118 <column alignment="center" valignment="top" width="0pt">
3119 <column alignment="center" valignment="top" width="0pt">
3121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3124 \begin_layout Plain Layout
3130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3133 \begin_layout Plain Layout
3141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3144 \begin_layout Plain Layout
3151 \begin_layout Plain Layout
3161 \begin_inset Formula $\to$
3165 \begin_inset Index idx
3168 \begin_layout Plain Layout
3181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3184 \begin_layout Plain Layout
3185 \begin_inset Formula $\begin{cases}
3196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3199 \begin_layout Plain Layout
3206 \begin_layout Plain Layout
3218 arg "newline-insert newline"
3226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3229 \begin_layout Plain Layout
3230 \begin_inset Formula $\begin{cases}
3231 A & \textrm{for }x>0\\
3232 B & \textrm{for }x=0
3249 \begin_layout Standard
3256 or the usage of the math toolbar button
3257 \begin_inset Graphics
3258 filename ../images/math/cases.png
3263 you can create new lines with the shortcut
3266 arg "newline-insert newline"
3269 or the table toolbar button
3270 \begin_inset Graphics
3271 filename ../images/tabular-feature_append-row.png
3279 \begin_layout Standard
3286 is also available via the menu
3288 Insert\SpecialChar \menuseparator
3289 Math\SpecialChar \menuseparator
3295 \begin_layout Subsection
3297 \begin_inset Index idx
3300 \begin_layout Plain Layout
3309 \begin_layout Standard
3317 \begin_inset Index idx
3320 \begin_layout Plain Layout
3328 every character can be displayed canceled.
3329 The characters are quasi accentuated by a slash.
3332 \begin_layout Standard
3334 \begin_inset Tabular
3335 <lyxtabular version="3" rows="4" columns="2">
3336 <features tabularvalignment="middle">
3337 <column alignment="center" valignment="top" width="0pt">
3338 <column alignment="center" valignment="top" width="0pt">
3340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3343 \begin_layout Plain Layout
3349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3352 \begin_layout Plain Layout
3360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3363 \begin_layout Plain Layout
3371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3374 \begin_layout Plain Layout
3375 \begin_inset Formula $\not=$
3385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3388 \begin_layout Plain Layout
3398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3401 \begin_layout Plain Layout
3402 \begin_inset Formula $\not\le$
3412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3415 \begin_layout Plain Layout
3425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3428 \begin_layout Plain Layout
3429 \begin_inset Formula $\not\parallel$
3445 \begin_layout Standard
3446 The last example shows, that not all negations look good.
3447 Therefore there are for some negations special commands (see
3448 \begin_inset CommandInset ref
3450 reference "sub:Mathematical-Symbols"
3455 \begin_inset CommandInset ref
3457 reference "sec:Relations"
3464 \begin_layout Subsection
3466 \begin_inset CommandInset label
3468 name "sub:Placeholders"
3473 \begin_inset Index idx
3476 \begin_layout Plain Layout
3483 \begin_inset Index idx
3486 \begin_layout Plain Layout
3487 Chemical characters ! Isotopes
3493 \begin_inset Index idx
3496 \begin_layout Plain Layout
3501 \begin_layout Plain Layout
3512 \begin_layout Plain Layout
3527 \begin_layout Standard
3529 \begin_inset space \thinspace{}
3533 \begin_inset space \space{}
3540 \begin_layout Plain Layout
3541 Typesetting isotopes and chemical symbols is described in
3542 \begin_inset CommandInset ref
3544 reference "sub:Chemical-Symbols-and"
3553 the following problem occurs:
3556 \begin_layout Standard
3558 \begin_inset Tabular
3559 <lyxtabular version="3" rows="2" columns="2">
3560 <features tabularvalignment="middle">
3561 <column alignment="center" valignment="top" width="0pt">
3562 <column alignment="center" valignment="top" width="0pt">
3564 <cell alignment="center" valignment="top" usebox="none">
3567 \begin_layout Plain Layout
3568 Indices created with sub- and superscripts:
3573 <cell alignment="center" valignment="top" usebox="none">
3576 \begin_layout Plain Layout
3577 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3587 <cell alignment="center" valignment="top" usebox="none">
3590 \begin_layout Plain Layout
3596 <cell alignment="center" valignment="top" usebox="none">
3599 \begin_layout Plain Layout
3600 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3614 \begin_inset Note Note
3617 \begin_layout Plain Layout
3624 is only used as spacer.
3632 \begin_layout Standard
3633 The shorter index is by default placed below or above the first character
3634 of the longer index.
3635 To avoid this there is the command
3642 \begin_inset Index idx
3645 \begin_layout Plain Layout
3653 or the math toolbar button
3654 \begin_inset space \thinspace{}
3661 \begin_layout Plain Layout
3662 can be found in the submenu of the toolbar button
3663 \begin_inset Graphics
3664 filename ../images/math/space.png
3675 \begin_inset Graphics
3676 filename ../images/math/phantom.png
3681 that creates one or more phantom characters.
3688 a small blue box appears that is superposed with two red arrows.
3689 The arrows indicate that the complete width and height of the box content
3690 will be created as placeholder.
3691 Phantom characters are accordingly placeholders with the size of the characters.
3694 \begin_layout Standard
3696 \begin_inset Tabular
3697 <lyxtabular version="3" rows="4" columns="2">
3698 <features tabularvalignment="middle">
3699 <column alignment="center" valignment="top" width="0">
3700 <column alignment="center" valignment="top" width="0">
3702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3705 \begin_layout Plain Layout
3711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3714 \begin_layout Plain Layout
3716 \begin_inset Note Note
3719 \begin_layout Plain Layout
3726 is only used as spacer.
3738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3741 \begin_layout Plain Layout
3746 \begin_layout Plain Layout
3761 \begin_layout Plain Layout
3771 \begin_inset Formula $\to$
3778 \begin_layout Plain Layout
3792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3795 \begin_layout Plain Layout
3796 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3809 \begin_layout Plain Layout
3814 \begin_layout Plain Layout
3829 \begin_layout Plain Layout
3839 \begin_inset Formula $\to$
3846 \begin_layout Plain Layout
3860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3863 \begin_layout Plain Layout
3864 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3877 \begin_layout Plain Layout
3884 \begin_layout Plain Layout
3899 \begin_layout Plain Layout
3909 \begin_inset Formula $\to$
3916 \begin_layout Plain Layout
3930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3933 \begin_layout Plain Layout
3934 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3950 \begin_layout Standard
3951 Furthermore there are the commands
3958 \begin_inset Index idx
3961 \begin_layout Plain Layout
3970 \begin_inset space ~
3974 \begin_inset Graphics
3975 filename ../images/math/vphantom.png
3987 \begin_inset Index idx
3990 \begin_layout Plain Layout
3999 \begin_inset space ~
4003 \begin_inset Graphics
4004 filename ../images/math/hphantom.png
4016 creates only space for the maximal height of the characters in the box
4017 but not for its width.
4024 creates only space for the width of the box content.
4025 Therefore the boxes of both commands have only one red arrow.
4028 \begin_layout Standard
4039 \begin_layout Plain Layout
4054 space for the height of the integral sign,
4058 \begin_layout Plain Layout
4065 creates an integral sign, see
4066 \begin_inset CommandInset ref
4068 reference "sub:Big-Operators"
4077 because this is the larger character.
4078 An example application is in
4079 \begin_inset CommandInset ref
4081 reference "sub:Multiline-Brackets"
4088 \begin_layout Standard
4089 Placeholders can also be used for text when it is inserted via the menu
4092 Insert\SpecialChar \menuseparator
4093 Formatting\SpecialChar \menuseparator
4099 \begin_layout Standard
4101 \begin_inset Newline newline
4105 \begin_inset Phantom Phantom
4108 \begin_layout Plain Layout
4117 \begin_layout Subsection
4119 \begin_inset Index idx
4122 \begin_layout Plain Layout
4129 \begin_inset Index idx
4132 \begin_layout Plain Layout
4133 Formula ! underlined
4141 \begin_layout Standard
4143 \begin_inset Tabular
4144 <lyxtabular version="3" rows="4" columns="2">
4145 <features tabularvalignment="middle">
4146 <column alignment="center" valignment="top" width="0pt">
4147 <column alignment="center" valignment="top" width="0pt">
4149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4152 \begin_layout Plain Layout
4158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4161 \begin_layout Plain Layout
4163 \begin_inset Note Note
4166 \begin_layout Plain Layout
4173 is only used as spacer.
4185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4188 \begin_layout Plain Layout
4195 \begin_layout Plain Layout
4205 \begin_inset Index idx
4208 \begin_layout Plain Layout
4221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4224 \begin_layout Plain Layout
4225 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4235 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4238 \begin_layout Plain Layout
4245 \begin_layout Plain Layout
4255 \begin_inset Index idx
4258 \begin_layout Plain Layout
4271 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4274 \begin_layout Plain Layout
4275 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4288 \begin_layout Plain Layout
4295 \begin_layout Plain Layout
4310 \begin_layout Plain Layout
4324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4327 \begin_layout Plain Layout
4328 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4344 \begin_layout Standard
4345 In the last example it doesn't matter if first
4360 \begin_layout Standard
4361 To double underline e.
4362 \begin_inset space \thinspace{}
4366 \begin_inset space \space{}
4378 \begin_layout Standard
4379 It is possible to place up to 6 lines above or below characters.
4382 \begin_layout Standard
4383 \begin_inset VSpace bigskip
4386 Custom lines can be created using the command
4393 \begin_inset Index idx
4396 \begin_layout Plain Layout
4404 which has the following scheme:
4407 \begin_layout Standard
4412 rule[vertical offset]{length}{thickness}
4415 \begin_layout Standard
4416 The optional vertical offset shifts the line upwards (or downwards, when
4417 the value is negative).
4419 \begin_inset CommandInset ref
4421 reference "tab:Available-units"
4425 can be used for the values.
4426 Here are two example lines created with the commands
4427 \begin_inset Newline newline
4434 rule[-2ex]{3cm}{2pt}
4445 \begin_layout Standard
4447 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4453 \begin_layout Standard
4460 can also be used for text when a line is inserted via the menu
4462 Insert\SpecialChar \menuseparator
4463 Formatting\SpecialChar \menuseparator
4465 \begin_inset space ~
4473 \begin_layout Standard
4475 \begin_inset CommandInset line
4486 \begin_layout Subsection
4488 \begin_inset CommandInset label
4495 \begin_inset Index idx
4498 \begin_layout Plain Layout
4507 \begin_layout Standard
4508 There are different types of ellipses available.
4512 \begin_layout Plain Layout
4513 In the math toolbar in the submenu of the button
4514 \begin_inset Graphics
4515 filename ../images/math/ldots.png
4525 For listings dots at the baseline are used (
4532 \begin_inset Index idx
4535 \begin_layout Plain Layout
4543 ), while for operations dots are needed that are on the same height as the
4551 \begin_inset Index idx
4554 \begin_layout Plain Layout
4563 When using the command
4570 \begin_inset Index idx
4573 \begin_layout Plain Layout
4581 , LaTeX decides on the basis of the next character what type is used.
4584 \begin_layout Standard
4586 \begin_inset Tabular
4587 <lyxtabular version="3" rows="9" columns="2">
4588 <features tabularvalignment="middle">
4589 <column alignment="center" valignment="top" width="0pt">
4590 <column alignment="center" valignment="top" width="0pt">
4592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4595 \begin_layout Plain Layout
4601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4604 \begin_layout Plain Layout
4612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4615 \begin_layout Plain Layout
4620 \begin_layout Plain Layout
4635 \begin_layout Plain Layout
4649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4652 \begin_layout Plain Layout
4653 \begin_inset Formula $A_{1},\dots,A_{n}$
4663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4666 \begin_layout Plain Layout
4671 \begin_layout Plain Layout
4686 \begin_layout Plain Layout
4700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4703 \begin_layout Plain Layout
4704 \begin_inset Formula $A_{1}+\dots+A_{n}$
4714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4717 \begin_layout Plain Layout
4722 \begin_layout Plain Layout
4737 \begin_layout Plain Layout
4751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4754 \begin_layout Plain Layout
4755 \begin_inset Formula $A_{1},\ldots,A_{n}$
4765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4768 \begin_layout Plain Layout
4773 \begin_layout Plain Layout
4788 \begin_layout Plain Layout
4802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4805 \begin_layout Plain Layout
4806 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4819 \begin_layout Plain Layout
4827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4830 \begin_layout Plain Layout
4831 \begin_inset Formula $\vdots$
4841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4844 \begin_layout Plain Layout
4852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4855 \begin_layout Plain Layout
4856 \begin_inset Formula $\ddots$
4866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4869 \begin_layout Plain Layout
4877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4880 \begin_layout Plain Layout
4881 \begin_inset Formula $\iddots$
4891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4894 \begin_layout Plain Layout
4896 \begin_inset space \thinspace{}
4899 matrix with the different dots
4904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4907 \begin_layout Plain Layout
4908 \begin_inset Formula $\begin{array}{ccc}
4909 A_{11} & \cdots & A_{1m}\\
4910 \vdots & \ddots & \vdots\\
4911 A_{n1} & \cdots & A_{nm}
4928 \begin_layout Standard
4929 The ellipses available in menu
4931 Insert\SpecialChar \menuseparator
4933 \begin_inset space ~
4947 \begin_layout Standard
4948 \begin_inset VSpace medskip
4957 , one of the options
4959 Use mathdots package (automatically)
4961 must be set in the document settings under
4964 \begin_inset space ~
4970 \begin_inset Newline newline
4975 Use mathdots package
4977 will improve the appearance of all dots in the documents if their font
4978 style or size is not the default.
4981 \begin_layout Standard
4982 \begin_inset VSpace medskip
4985 Specially for matrices there are ellipses that span over several columns.
4986 They are created with the command
4993 \begin_inset Index idx
4996 \begin_layout Plain Layout
5004 , that has the following scheme:
5007 \begin_layout Standard
5012 hdotsfor[distance]{number of columns}
5015 \begin_layout Standard
5016 The number of columns specifies how many columns should be spanned.
5017 Distance is a factor for the distance between the dots.
5020 \begin_layout Standard
5021 In the following matrix the command
5027 was inserted in the first box of the second line, to get an ellipsis with
5028 a dot distance twice as long as with the command
5035 \begin_inset Formula
5037 \left(\begin{array}{cccc}
5046 Note that the matrix fields that should be spanned must be empty, otherwise
5047 you get LaTeX-errors.
5050 \begin_layout Standard
5051 \begin_inset VSpace bigskip
5054 Furthermore you can fill with the command
5061 \begin_inset Index idx
5064 \begin_layout Plain Layout
5072 the rest of a line with dots.
5073 The effect of these commands is the same like with
5080 \begin_inset CommandInset ref
5082 reference "sub:Variable-Space"
5089 \begin_layout Standard
5090 For example the command
5098 \begin_layout Plain Layout
5112 \begin_layout Standard
5113 \begin_inset Formula $A\dotfill B$
5119 \begin_layout Standard
5126 there is for a line the command
5133 \begin_inset Index idx
5136 \begin_layout Plain Layout
5147 \begin_layout Standard
5148 \begin_inset Formula $A\hrulefill B$
5154 \begin_layout Standard
5155 To use the commands for text, they have to be inserted in TeX-mode.
5158 \begin_layout Section
5160 \begin_inset CommandInset label
5167 \begin_inset Index idx
5170 \begin_layout Plain Layout
5179 \begin_layout Standard
5180 Matrices can be inserted via the math toolbar button
5181 \begin_inset Graphics
5182 filename ../images/dialog-show_mathmatrix.png
5189 Insert\SpecialChar \menuseparator
5190 Math\SpecialChar \menuseparator
5194 In the matrix dialog you can specify the number of columns and rows, the
5195 alignment and the decoration.
5196 The vertical alignment is hereby only of importance for matrices in inline
5200 \begin_layout Standard
5201 The first matrix is top
5202 \begin_inset Formula $\begin{array}[t]{cccc}
5210 \begin_inset Formula $\begin{array}{cccc}
5217 and the third bottom
5218 \begin_inset Formula $\begin{array}[b]{cccc}
5228 \begin_layout Standard
5229 The horizontal alignment specifies how the column entries should be aligned.
5230 It is set by entering a letter for every column.
5235 denotes left aligned,
5244 To create for example a 4
5249 \begin_inset space ~
5252 matrix where the first column is left aligned, the second and third are
5253 centered and the last one is right aligned, one enters for the horizontal
5259 Normally are in a matrix all columns centered, therefore the default is
5260 for every column is a
5267 \begin_layout Standard
5268 Horizontal alignment:
5271 \begin_layout Standard
5277 \begin_inset Formula $\begin{array}{lll}
5289 \begin_inset Formula $\begin{array}{ccc}
5301 \begin_inset Formula $\begin{array}{rrr}
5311 \begin_layout Standard
5312 To add or delete rows and columns subsequently, the math toolbar buttons
5314 \begin_inset Graphics
5315 filename ../images/tabular-feature_append-row.png
5321 \begin_inset Graphics
5322 filename ../images/tabular-feature_delete-row.png
5328 \begin_inset space \thinspace{}
5333 Edit\SpecialChar \menuseparator
5337 New rows can also be created with
5340 arg "newline-insert newline"
5346 \begin_layout Standard
5347 \begin_inset VSpace bigskip
5354 adds parentheses in the selected style around the matrix.
5355 Alternatively, parentheses can can either be created with the commands
5363 \begin_inset Index idx
5366 \begin_layout Plain Layout
5381 \begin_inset Index idx
5384 \begin_layout Plain Layout
5395 \begin_inset space ~
5401 \begin_inset CommandInset ref
5403 reference "sub:Automatic-Bracket-Size"
5407 , or by using the following commands:
5408 \begin_inset VSpace medskip
5414 \begin_layout Standard
5415 \begin_inset space \hfill{}
5419 \begin_inset Tabular
5420 <lyxtabular version="3" rows="4" columns="2">
5421 <features tabularvalignment="middle">
5422 <column alignment="center" valignment="top" width="0">
5423 <column alignment="center" valignment="top" width="0">
5425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5428 \begin_layout Plain Layout
5434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5437 \begin_layout Plain Layout
5439 \begin_inset Note Note
5442 \begin_layout Plain Layout
5449 is only used as spacer.
5461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5464 \begin_layout Plain Layout
5471 \begin_layout Plain Layout
5485 \begin_inset space \thinspace{}
5493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5496 \begin_layout Plain Layout
5497 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5498 0 & \textrm{-}\mathrm{i}\\
5500 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5513 \begin_layout Plain Layout
5520 \begin_layout Plain Layout
5534 \begin_inset space \thinspace{}
5542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5545 \begin_layout Plain Layout
5546 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5547 0 & \textrm{-}\mathrm{i}\\
5549 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5562 \begin_layout Plain Layout
5569 \begin_layout Plain Layout
5583 \begin_inset space \thinspace{}
5591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5594 \begin_layout Plain Layout
5595 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5596 0 & \textrm{-}\mathrm{i}\\
5598 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5612 \begin_inset space \hfill{}
5616 \begin_inset Tabular
5617 <lyxtabular version="3" rows="4" columns="2">
5618 <features tabularvalignment="middle">
5619 <column alignment="center" valignment="top" width="0">
5620 <column alignment="center" valignment="top" width="0">
5622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5625 \begin_layout Plain Layout
5631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5634 \begin_layout Plain Layout
5642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5645 \begin_layout Plain Layout
5652 \begin_layout Plain Layout
5666 \begin_inset space \thinspace{}
5674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5677 \begin_layout Plain Layout
5678 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5679 0 & \textrm{-}\mathrm{i}\\
5681 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5694 \begin_layout Plain Layout
5701 \begin_layout Plain Layout
5715 \begin_inset space \thinspace{}
5723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5726 \begin_layout Plain Layout
5727 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5728 0 & \textrm{-}\mathrm{i}\\
5730 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5743 \begin_layout Plain Layout
5750 \begin_layout Plain Layout
5764 \begin_inset space \thinspace{}
5772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5775 \begin_layout Plain Layout
5776 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5777 0 & \textrm{-}\mathrm{i}\\
5779 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5793 \begin_inset space \hfill{}
5799 \begin_layout Standard
5800 \begin_inset VSpace medskip
5804 \begin_inset space \thinspace{}
5808 \begin_inset space \space{}
5817 is inserted, a blue box appears between two vertical lines where the matrix
5819 \begin_inset Newline newline
5822 Note that decorated matrices ignore the vertical alignment.
5825 \begin_layout Standard
5826 \begin_inset Note Greyedout
5829 \begin_layout Plain Layout
5834 LaTeX limits the number of matrix columns with decorations to 10.
5835 If you need more than 10
5836 \begin_inset space ~
5839 columns, you have to add this line to the document preamble:
5842 \begin_layout Plain Layout
5847 setcounter{MaxMatrixCols}{number}
5850 \begin_layout Plain Layout
5855 is the number of columns between 11 and 99.
5863 \begin_layout Standard
5864 \begin_inset VSpace bigskip
5867 As all multiline formulas are matrices, the length
5874 \begin_inset Index idx
5877 \begin_layout Plain Layout
5885 that is described in
5886 \begin_inset CommandInset ref
5888 reference "sub:Column-Separation"
5892 can also be used to change the column separation of matrices.
5895 \begin_layout Standard
5896 To change the row separation, the command
5903 \begin_inset Index idx
5906 \begin_layout Plain Layout
5915 It is used as follows:
5918 \begin_layout Standard
5925 arraystretch}{stretch factor}
5926 \begin_inset Index idx
5929 \begin_layout Plain Layout
5940 \begin_layout Standard
5947 assigns the stretch factor to the predefined command
5955 \begin_inset space \thinspace{}
5959 \begin_inset space \space{}
5962 the row separation, use the factor 2.
5963 This is then used for all following matrices.
5964 To go back to the original separation, assign the factor 1 to
5973 \begin_layout Standard
5974 To set matrices into a text line, the command
5981 \begin_inset Index idx
5984 \begin_layout Plain Layout
5993 When it is inserted a blue box with two dashed lines appears.
5994 In this box the matrix is inserted.
5997 \begin_layout Standard
5999 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
6001 \end{smallmatrix}\right)$
6007 \begin_layout Section
6008 Brackets and Delimiters
6009 \begin_inset Index idx
6012 \begin_layout Plain Layout
6019 \begin_inset Index idx
6022 \begin_layout Plain Layout
6031 \begin_layout Subsection
6032 Vertical Brackets and Delimiters
6033 \begin_inset Index idx
6036 \begin_layout Plain Layout
6045 \begin_layout Standard
6046 \begin_inset space \hfill{}
6050 \begin_inset Tabular
6051 <lyxtabular version="3" rows="9" columns="2">
6052 <features tabularvalignment="middle">
6053 <column alignment="center" valignment="top" width="0pt">
6054 <column alignment="center" valignment="top" width="0pt">
6056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6059 \begin_layout Plain Layout
6065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6068 \begin_layout Plain Layout
6076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6079 \begin_layout Plain Layout
6085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6088 \begin_layout Plain Layout
6089 \begin_inset Formula $($
6099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6102 \begin_layout Plain Layout
6108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6111 \begin_layout Plain Layout
6112 \begin_inset Formula $\{$
6122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6125 \begin_layout Plain Layout
6131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6134 \begin_layout Plain Layout
6135 \begin_inset Formula $[$
6145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6148 \begin_layout Plain Layout
6156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6159 \begin_layout Plain Layout
6160 \begin_inset Formula $\langle$
6170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6173 \begin_layout Plain Layout
6181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6184 \begin_layout Plain Layout
6185 \begin_inset Formula $\lceil$
6195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6198 \begin_layout Plain Layout
6206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6209 \begin_layout Plain Layout
6210 \begin_inset Formula $\lfloor$
6220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6223 \begin_layout Plain Layout
6229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6232 \begin_layout Plain Layout
6233 \begin_inset Formula $/$
6243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6246 \begin_layout Plain Layout
6252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6255 \begin_layout Plain Layout
6256 \begin_inset Formula $|$
6270 \begin_inset space \hfill{}
6274 \begin_inset Tabular
6275 <lyxtabular version="3" rows="9" columns="2">
6276 <features tabularvalignment="middle">
6277 <column alignment="center" valignment="top" width="0pt">
6278 <column alignment="center" valignment="top" width="0pt">
6280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6283 \begin_layout Plain Layout
6289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6292 \begin_layout Plain Layout
6300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6303 \begin_layout Plain Layout
6309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6312 \begin_layout Plain Layout
6313 \begin_inset Formula $)$
6323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6326 \begin_layout Plain Layout
6332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6335 \begin_layout Plain Layout
6336 \begin_inset Formula $\}$
6346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6349 \begin_layout Plain Layout
6355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6358 \begin_layout Plain Layout
6359 \begin_inset Formula $]$
6369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6372 \begin_layout Plain Layout
6380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6383 \begin_layout Plain Layout
6384 \begin_inset Formula $\rangle$
6394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6397 \begin_layout Plain Layout
6405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6408 \begin_layout Plain Layout
6409 \begin_inset Formula $\rceil$
6419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6422 \begin_layout Plain Layout
6430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6433 \begin_layout Plain Layout
6434 \begin_inset Formula $\rfloor$
6444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6447 \begin_layout Plain Layout
6457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6460 \begin_layout Plain Layout
6461 \begin_inset Formula $\backslash$
6471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6474 \begin_layout Plain Layout
6482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6485 \begin_layout Plain Layout
6486 \begin_inset Formula $\|$
6500 \begin_inset space \hfill{}
6506 \begin_layout Standard
6509 \begin_inset Note Greyedout
6512 \begin_layout Plain Layout
6517 In TeX-mode the command
6524 \begin_inset Index idx
6527 \begin_layout Plain Layout
6535 must be used for the backslash, because the command
6543 produces there a line break.
6551 \begin_layout Standard
6552 For all characters listed above the size can be adjusted with the commands
6553 described in the following two subsections.
6554 When using these commands, the characters < and > can directly be used
6555 instead of the commands
6570 \begin_layout Subsubsection
6572 \begin_inset CommandInset label
6574 name "sub:Manual-Bracket-Size"
6579 \begin_inset Index idx
6582 \begin_layout Plain Layout
6583 Bracket size ! manual
6591 \begin_layout Standard
6592 The bracket size can be specified manually by the LaTeX-commands
6599 \begin_inset Index idx
6602 \begin_layout Plain Layout
6635 denotes the smallest and
6641 the largest bracket size.
6644 \begin_layout Standard
6645 These commands are used to emphasize levels of brackets:
6648 \begin_layout Standard
6650 \begin_inset Tabular
6651 <lyxtabular version="3" rows="2" columns="2">
6652 <features tabularvalignment="middle">
6653 <column alignment="center" valignment="top" width="0pt">
6654 <column alignment="center" valignment="top" width="0pt">
6656 <cell alignment="center" valignment="top" usebox="none">
6659 \begin_layout Plain Layout
6660 all brackets in the same size:
6665 <cell alignment="center" valignment="top" usebox="none">
6668 \begin_layout Plain Layout
6669 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6679 <cell alignment="center" valignment="top" usebox="none">
6682 \begin_layout Plain Layout
6688 <cell alignment="center" valignment="top" usebox="none">
6691 \begin_layout Plain Layout
6692 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6706 \begin_inset Note Note
6709 \begin_layout Plain Layout
6716 is only used as spacer.
6724 \begin_layout Standard
6725 For the second formula the command
6735 \begin_layout Plain Layout
6749 \begin_layout Standard
6750 Here is an overview about all bracket sizes:
6753 \begin_layout Standard
6773 \begin_layout Plain Layout
6790 \begin_layout Plain Layout
6803 \begin_layout Plain Layout
6819 \begin_layout Standard
6821 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6827 \begin_layout Standard
6834 -commands there is the variant
6841 \begin_inset Index idx
6844 \begin_layout Plain Layout
6852 that adds a bit more space between the bracket and its content, and the
6866 \begin_inset Index idx
6869 \begin_layout Plain Layout
6879 , that don't add additional space.
6884 at the end of the command
6890 is for a left bracket; for a right bracket this will be replaced by an
6896 A left or right bracket can each be an opening or closing bracket.
6899 \begin_layout Standard
6900 In the following table is a comparison of the variants:
6903 \begin_layout Standard
6905 \begin_inset Tabular
6906 <lyxtabular version="3" rows="5" columns="2">
6907 <features tabularvalignment="middle">
6908 <column alignment="center" valignment="middle" width="0">
6909 <column alignment="center" valignment="middle" width="0">
6911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6914 \begin_layout Plain Layout
6920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6923 \begin_layout Plain Layout
6925 \begin_inset Note Note
6928 \begin_layout Plain Layout
6935 is only used as spacer.
6947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6950 \begin_layout Plain Layout
6965 \begin_layout Plain Layout
6983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6986 \begin_layout Plain Layout
6987 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7000 \begin_layout Plain Layout
7015 \begin_layout Plain Layout
7033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7036 \begin_layout Plain Layout
7037 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7050 \begin_layout Plain Layout
7065 \begin_layout Plain Layout
7083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7086 \begin_layout Plain Layout
7087 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7100 \begin_layout Plain Layout
7112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7115 \begin_layout Plain Layout
7116 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7132 \begin_layout Subsubsection
7133 Automatic Bracket Size
7134 \begin_inset CommandInset label
7136 name "sub:Automatic-Bracket-Size"
7141 \begin_inset Index idx
7144 \begin_layout Plain Layout
7145 Bracket size ! automatic
7153 \begin_layout Standard
7154 Brackets with variable size can be inserted with the commands
7161 \begin_inset Index idx
7164 \begin_layout Plain Layout
7179 \begin_inset Index idx
7182 \begin_layout Plain Layout
7190 or via the math toolbar button
7191 \begin_inset Graphics
7192 filename ../images/dialog-show_mathdelimiter.png
7210 the wanted bracket must be inserted.
7211 The bracket size will then automatically be calculated for the output.
7214 \begin_layout Standard
7216 normal bracket: The command
7226 \begin_layout Plain Layout
7236 \begin_inset Formula $\downarrow$
7243 \begin_layout Plain Layout
7255 \begin_inset Formula
7265 \begin_layout Standard
7267 multiline bracket: The command
7279 \begin_layout Plain Layout
7289 \begin_inset Formula $\downarrow$
7296 \begin_layout Plain Layout
7310 \begin_inset Formula
7312 \ln\left(\frac{A}{C}\right)
7320 \begin_layout Standard
7336 \begin_inset space ~
7342 This has the advantage that you can see in LyX immediately the real bracket
7343 size and that the matching right bracket will be created too.
7344 \begin_inset Newline newline
7347 The command for the last example would then be:
7361 \begin_layout Plain Layout
7371 \begin_inset Formula $\downarrow$
7377 \begin_layout Standard
7378 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7379 For example the command
7389 \begin_layout Plain Layout
7399 \begin_inset Formula $\downarrow$
7406 \begin_layout Plain Layout
7422 \begin_inset Formula
7424 \left.\frac{A}{B}\right\}
7443 will be converted by LyX to brackets in the right size when the document
7444 is reloaded and an omitted bracket will appear as dashed line.
7447 \begin_layout Standard
7448 \begin_inset VSpace bigskip
7451 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7459 \begin_inset Index idx
7462 \begin_layout Plain Layout
7470 is additionally available for all brackets and limits.
7471 With this command the height of the following character is adapted to the
7472 one of the surrounding brackets, what is e.
7473 \begin_inset space \thinspace{}
7477 \begin_inset space \space{}
7480 needed for physical vectors:
7481 \begin_inset Formula
7483 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
7488 For physical vectors there is a special LaTeX-package, described in
7489 \begin_inset CommandInset ref
7491 reference "sub:Physical-Vectors"
7498 \begin_layout Subsection
7500 \begin_inset Index idx
7503 \begin_layout Plain Layout
7504 Brackets ! horizontal
7512 \begin_layout Standard
7514 \begin_inset Tabular
7515 <lyxtabular version="3" rows="4" columns="2">
7516 <features tabularvalignment="middle">
7517 <column alignment="center" valignment="top" width="0pt">
7518 <column alignment="center" valignment="top" width="0pt">
7520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7523 \begin_layout Plain Layout
7525 \begin_inset Note Note
7528 \begin_layout Plain Layout
7535 is only used as spacer.
7545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7548 \begin_layout Plain Layout
7556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7559 \begin_layout Plain Layout
7563 \begin_layout Plain Layout
7578 \begin_layout Plain Layout
7591 \begin_layout Plain Layout
7604 \begin_layout Plain Layout
7617 \begin_layout Plain Layout
7625 \begin_inset Index idx
7628 \begin_layout Plain Layout
7641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7644 \begin_layout Plain Layout
7645 \begin_inset Formula $\overbrace{A+B}^{3}$
7655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7658 \begin_layout Plain Layout
7662 \begin_layout Plain Layout
7677 \begin_layout Plain Layout
7690 \begin_layout Plain Layout
7703 \begin_layout Plain Layout
7711 \begin_inset Index idx
7714 \begin_layout Plain Layout
7727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7730 \begin_layout Plain Layout
7731 \begin_inset Formula $\underbrace{A+B}_{5}$
7741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7744 \begin_layout Plain Layout
7751 \begin_layout Plain Layout
7766 \begin_layout Plain Layout
7779 \begin_layout Plain Layout
7792 \begin_layout Plain Layout
7805 \begin_layout Plain Layout
7818 \begin_layout Plain Layout
7831 \begin_layout Plain Layout
7845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7848 \begin_layout Plain Layout
7849 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7865 \begin_layout Standard
7866 In the last example it doesn't matter if
7878 is inserted at first.
7881 \begin_layout Standard
7882 \begin_inset VSpace bigskip
7885 When brackets are needed that overlap each other, multiline formulas, as
7887 \begin_inset CommandInset ref
7889 reference "sec:Multiline-Formulas"
7894 \begin_inset Formula
7896 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7897 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7902 In the first row the formula is inserted together with the first brace.
7903 It is hereby important that the space command
7907 \begin_layout Plain Layout
7908 Space commands are explained in
7909 \begin_inset CommandInset ref
7911 reference "sub:Predefined-Space"
7926 is inserted before the first
7927 \begin_inset Formula $d$
7930 , because the brace that ends behind the
7931 \begin_inset Formula $q$
7934 prevents that the following
7935 \begin_inset Quotes eld
7939 \begin_inset Quotes erd
7942 is surrounded by space.
7946 \begin_layout Plain Layout
7947 because a bracket is not handled as character, see
7948 \begin_inset CommandInset ref
7950 reference "sub:Binary-Operators"
7959 In the second row the second brace is inserted.
7960 As it should begin before the
7961 \begin_inset Formula $b$
7976 \begin_layout Plain Layout
7984 \begin_inset CommandInset ref
7986 reference "sub:Placeholders"
7995 This space is needed because the
7996 \begin_inset Quotes eld
8000 \begin_inset Quotes erd
8003 is also surrounded by space in the formula.
8004 The brace is placed under the command
8013 \begin_layout Standard
8014 It gets more complicated when brackets overlap each other, like in the following
8019 \begin_layout Plain Layout
8031 \begin_inset Formula
8033 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
8034 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
8043 \begin_layout Plain Layout
8054 The first formula row is the same as the second row of the previous example,
8055 with the difference that the brace is above.
8056 The second row contains the formula together with the second brace.
8057 To avoid that there is space between the upper brace in the first row and
8058 the formula, the row spacing need to be reduced.
8059 This is not easily possible due to a bug in LyX
8063 \begin_layout Plain Layout
8064 \begin_inset CommandInset href
8066 name "LyX-bug #1505"
8067 target "http://www.lyx.org/trac/ticket/1505"
8077 As solution for the problem, the global formula row separation
8084 \begin_inset Index idx
8087 \begin_layout Plain Layout
8095 must be changed to -6
8096 \begin_inset space \thinspace{}
8099 pt before the formula with the command
8114 is set back after the formula to the standard value of 3
8115 \begin_inset space \thinspace{}
8118 pt using the same command.
8119 More about the row separation in formulas is explained in
8120 \begin_inset CommandInset ref
8122 reference "sub:Line-Separation"
8129 \begin_layout Section
8131 \begin_inset Index idx
8134 \begin_layout Plain Layout
8143 \begin_layout Standard
8144 Arrows can be inserted via the math toolbar button
8145 \begin_inset Graphics
8146 filename ../images/math/leftarrow.png
8151 or the commands listed in the following subsections.
8154 \begin_layout Subsection
8156 \begin_inset Index idx
8159 \begin_layout Plain Layout
8168 \begin_layout Standard
8169 \begin_inset space \hfill{}
8173 \begin_inset Tabular
8174 <lyxtabular version="3" rows="8" columns="2">
8175 <features tabularvalignment="middle">
8176 <column alignment="center" valignment="top" width="0pt">
8177 <column alignment="center" valignment="top" width="0pt">
8179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8182 \begin_layout Plain Layout
8188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8191 \begin_layout Plain Layout
8199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8202 \begin_layout Plain Layout
8210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8213 \begin_layout Plain Layout
8214 \begin_inset Formula $\gets$
8224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8227 \begin_layout Plain Layout
8235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8238 \begin_layout Plain Layout
8239 \begin_inset Formula $\Leftarrow$
8249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8252 \begin_layout Plain Layout
8260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8263 \begin_layout Plain Layout
8264 \begin_inset Formula $\longleftarrow$
8274 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8277 \begin_layout Plain Layout
8285 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8288 \begin_layout Plain Layout
8289 \begin_inset Formula $\Longleftarrow$
8299 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8302 \begin_layout Plain Layout
8310 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8313 \begin_layout Plain Layout
8314 \begin_inset Formula $\leftharpoonup$
8324 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8327 \begin_layout Plain Layout
8335 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8338 \begin_layout Plain Layout
8339 \begin_inset Formula $\leftharpoondown$
8349 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8352 \begin_layout Plain Layout
8360 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8363 \begin_layout Plain Layout
8364 \begin_inset Formula $\hookleftarrow$
8378 \begin_inset space \hfill{}
8382 \begin_inset Tabular
8383 <lyxtabular version="3" rows="8" columns="2">
8384 <features tabularvalignment="middle">
8385 <column alignment="center" valignment="top" width="0pt">
8386 <column alignment="center" valignment="top" width="0pt">
8388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8391 \begin_layout Plain Layout
8397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8400 \begin_layout Plain Layout
8408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8411 \begin_layout Plain Layout
8419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8422 \begin_layout Plain Layout
8423 \begin_inset Formula $\to$
8433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8436 \begin_layout Plain Layout
8444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8447 \begin_layout Plain Layout
8448 \begin_inset Formula $\Rightarrow$
8458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8461 \begin_layout Plain Layout
8469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8472 \begin_layout Plain Layout
8473 \begin_inset Formula $\longrightarrow$
8483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8486 \begin_layout Plain Layout
8494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8497 \begin_layout Plain Layout
8498 \begin_inset Formula $\Longrightarrow$
8508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8511 \begin_layout Plain Layout
8519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8522 \begin_layout Plain Layout
8523 \begin_inset Formula $\rightharpoonup$
8533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8536 \begin_layout Plain Layout
8544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8547 \begin_layout Plain Layout
8548 \begin_inset Formula $\rightharpoondown$
8558 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8561 \begin_layout Plain Layout
8569 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8572 \begin_layout Plain Layout
8573 \begin_inset Formula $\hookrightarrow$
8587 \begin_inset space \hfill{}
8593 \begin_layout Standard
8594 \begin_inset space \hfill{}
8598 \begin_inset Tabular
8599 <lyxtabular version="3" rows="6" columns="2">
8600 <features tabularvalignment="middle">
8601 <column alignment="center" valignment="top" width="0pt">
8602 <column alignment="center" valignment="top" width="0pt">
8604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8607 \begin_layout Plain Layout
8613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8616 \begin_layout Plain Layout
8624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8627 \begin_layout Plain Layout
8635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8638 \begin_layout Plain Layout
8639 \begin_inset Formula $\leftrightarrow$
8649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8652 \begin_layout Plain Layout
8660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8663 \begin_layout Plain Layout
8664 \begin_inset Formula $\Leftrightarrow$
8674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8677 \begin_layout Plain Layout
8685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8688 \begin_layout Plain Layout
8689 \begin_inset Formula $\longleftrightarrow$
8699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8702 \begin_layout Plain Layout
8710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8713 \begin_layout Plain Layout
8714 \begin_inset Formula $\Longleftrightarrow$
8724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8727 \begin_layout Plain Layout
8735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8738 \begin_layout Plain Layout
8739 \begin_inset Formula $\rightleftharpoons$
8753 \begin_inset space \hspace{}
8758 \begin_inset space \hfill{}
8762 \begin_inset Tabular
8763 <lyxtabular version="3" rows="5" columns="2">
8764 <features tabularvalignment="middle">
8765 <column alignment="center" valignment="top" width="0pt">
8766 <column alignment="center" valignment="top" width="0pt">
8768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8771 \begin_layout Plain Layout
8777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8780 \begin_layout Plain Layout
8788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8791 \begin_layout Plain Layout
8799 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8802 \begin_layout Plain Layout
8803 \begin_inset Formula $\mapsto$
8813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8816 \begin_layout Plain Layout
8824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8827 \begin_layout Plain Layout
8828 \begin_inset Formula $\longmapsto$
8838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8841 \begin_layout Plain Layout
8849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8852 \begin_layout Plain Layout
8853 \begin_inset Formula $\leadsto$
8863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8866 \begin_layout Plain Layout
8874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8877 \begin_layout Plain Layout
8878 \begin_inset Formula $\dasharrow$
8892 \begin_inset space \hfill{}
8898 \begin_layout Standard
8899 \begin_inset VSpace medskip
8902 Arrows used as accent like e.
8903 \begin_inset space \thinspace{}
8907 \begin_inset space \space{}
8910 vector arrows are listed in
8911 \begin_inset CommandInset ref
8913 reference "sec:Accents"
8920 \begin_layout Standard
8921 \begin_inset VSpace bigskip
8924 Furthermore there are the labeled arrows
8925 \begin_inset Index idx
8928 \begin_layout Plain Layout
8941 \begin_inset Index idx
8944 \begin_layout Plain Layout
8959 \begin_inset Index idx
8962 \begin_layout Plain Layout
8969 \begin_layout Plain Layout
8984 When inserting one of these commands in a formula, an arrow with two blue
8985 boxes appear where the label can be inserted.
8986 The length of the arrow adapts to the label width.
8989 \begin_layout Standard
8991 \begin_inset Tabular
8992 <lyxtabular version="3" rows="3" columns="2">
8993 <features tabularvalignment="middle">
8994 <column alignment="center" valignment="top" width="0pt">
8995 <column alignment="center" valignment="top" width="0pt">
8997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9000 \begin_layout Plain Layout
9006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9009 \begin_layout Plain Layout
9011 \begin_inset Note Note
9014 \begin_layout Plain Layout
9021 is only used as spacer.
9033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9036 \begin_layout Plain Layout
9043 \begin_layout Plain Layout
9053 \begin_inset Formula $\downarrow$
9057 \begin_inset Formula $\to$
9065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9068 \begin_layout Plain Layout
9069 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9082 \begin_layout Plain Layout
9089 \begin_layout Plain Layout
9099 \begin_inset Formula $\downarrow$
9103 \begin_inset Formula $\to$
9111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9114 \begin_layout Plain Layout
9115 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9131 \begin_layout Subsection
9132 Vertical and diagonal Arrows
9133 \begin_inset Index idx
9136 \begin_layout Plain Layout
9143 \begin_inset Index idx
9146 \begin_layout Plain Layout
9155 \begin_layout Standard
9156 \begin_inset space \hfill{}
9160 \begin_inset Tabular
9161 <lyxtabular version="3" rows="7" columns="2">
9162 <features tabularvalignment="middle">
9163 <column alignment="center" valignment="top" width="0pt">
9164 <column alignment="center" valignment="top" width="0pt">
9166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9169 \begin_layout Plain Layout
9175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9178 \begin_layout Plain Layout
9186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9189 \begin_layout Plain Layout
9197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9200 \begin_layout Plain Layout
9201 \begin_inset Formula $\uparrow$
9211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9214 \begin_layout Plain Layout
9222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9225 \begin_layout Plain Layout
9226 \begin_inset Formula $\Uparrow$
9236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9239 \begin_layout Plain Layout
9247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9250 \begin_layout Plain Layout
9251 \begin_inset Formula $\updownarrow$
9261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9264 \begin_layout Plain Layout
9272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9275 \begin_layout Plain Layout
9276 \begin_inset Formula $\Updownarrow$
9286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9289 \begin_layout Plain Layout
9297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9300 \begin_layout Plain Layout
9301 \begin_inset Formula $\Downarrow$
9311 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9314 \begin_layout Plain Layout
9322 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9325 \begin_layout Plain Layout
9326 \begin_inset Formula $\downarrow$
9340 \begin_inset space \hfill{}
9344 \begin_inset Tabular
9345 <lyxtabular version="3" rows="5" columns="2">
9346 <features tabularvalignment="middle">
9347 <column alignment="center" valignment="top" width="0pt">
9348 <column alignment="center" valignment="top" width="0pt">
9350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9353 \begin_layout Plain Layout
9359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9362 \begin_layout Plain Layout
9370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9373 \begin_layout Plain Layout
9381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9384 \begin_layout Plain Layout
9385 \begin_inset Formula $\nearrow$
9395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9398 \begin_layout Plain Layout
9406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9409 \begin_layout Plain Layout
9410 \begin_inset Formula $\searrow$
9420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9423 \begin_layout Plain Layout
9431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9434 \begin_layout Plain Layout
9435 \begin_inset Formula $\swarrow$
9445 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9448 \begin_layout Plain Layout
9456 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9459 \begin_layout Plain Layout
9460 \begin_inset Formula $\nwarrow$
9474 \begin_inset space \hfill{}
9480 \begin_layout Standard
9481 \begin_inset VSpace medskip
9484 Vertical arrows can be used also as delimiter together with the commands
9486 \begin_inset CommandInset ref
9488 reference "sub:Manual-Bracket-Size"
9493 \begin_inset CommandInset ref
9495 reference "sub:Automatic-Bracket-Size"
9502 \begin_layout Section
9504 \begin_inset CommandInset label
9511 \begin_inset Index idx
9514 \begin_layout Plain Layout
9523 \begin_layout Standard
9524 Accents can be inserted via the math toolbar button
9525 \begin_inset Graphics
9526 filename ../images/math/hat.png
9531 or the commands listed in the following subsections.
9534 \begin_layout Subsection
9535 Accents for one Character
9539 \begin_layout Plain Layout
9552 \begin_layout Plain Layout
9554 \begin_inset CommandInset ref
9556 reference "sub:Accents-in-Text"
9569 \begin_layout Plain Layout
9577 \begin_inset Note Note
9580 \begin_layout Plain Layout
9587 is used to avoid that the footnote appears in the PDF-bookmark.
9590 \begin_layout Plain Layout
9598 \begin_inset CommandInset ref
9600 reference "sub:Formulas-in-Section"
9610 \begin_inset CommandInset label
9612 name "sub:Accents-for-one"
9617 \begin_inset Index idx
9620 \begin_layout Plain Layout
9621 Accents ! for one character
9629 \begin_layout Standard
9630 \begin_inset space \hfill{}
9634 \begin_inset Tabular
9635 <lyxtabular version="3" rows="8" columns="2">
9636 <features tabularvalignment="middle">
9637 <column alignment="center" valignment="top" width="0pt">
9638 <column alignment="center" valignment="top" width="0pt">
9640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9643 \begin_layout Plain Layout
9649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9652 \begin_layout Plain Layout
9654 \begin_inset Note Note
9657 \begin_layout Plain Layout
9664 is only used as spacer.
9676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9679 \begin_layout Plain Layout
9686 \begin_layout Plain Layout
9700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9703 \begin_layout Plain Layout
9704 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9714 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9717 \begin_layout Plain Layout
9724 \begin_layout Plain Layout
9738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9741 \begin_layout Plain Layout
9742 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9755 \begin_layout Plain Layout
9762 \begin_layout Plain Layout
9776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9779 \begin_layout Plain Layout
9780 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9790 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9793 \begin_layout Plain Layout
9800 \begin_layout Plain Layout
9814 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9817 \begin_layout Plain Layout
9818 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9831 \begin_layout Plain Layout
9838 \begin_layout Plain Layout
9848 \begin_inset Index idx
9851 \begin_layout Plain Layout
9862 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9865 \begin_layout Plain Layout
9866 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9876 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9879 \begin_layout Plain Layout
9886 \begin_layout Plain Layout
9900 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9903 \begin_layout Plain Layout
9904 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9914 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9917 \begin_layout Plain Layout
9924 \begin_layout Plain Layout
9938 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9941 \begin_layout Plain Layout
9942 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9956 \begin_inset space \hfill{}
9960 \begin_inset Tabular
9961 <lyxtabular version="3" rows="7" columns="2">
9962 <features tabularvalignment="middle">
9963 <column alignment="center" valignment="top" width="0pt">
9964 <column alignment="center" valignment="top" width="0pt">
9966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9969 \begin_layout Plain Layout
9975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9978 \begin_layout Plain Layout
9986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9989 \begin_layout Plain Layout
9996 \begin_layout Plain Layout
10010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10013 \begin_layout Plain Layout
10014 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
10024 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10027 \begin_layout Plain Layout
10034 \begin_layout Plain Layout
10048 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10051 \begin_layout Plain Layout
10052 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10062 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10065 \begin_layout Plain Layout
10072 \begin_layout Plain Layout
10086 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10089 \begin_layout Plain Layout
10090 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10100 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10103 \begin_layout Plain Layout
10110 \begin_layout Plain Layout
10124 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10127 \begin_layout Plain Layout
10128 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10138 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10141 \begin_layout Plain Layout
10148 \begin_layout Plain Layout
10162 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10165 \begin_layout Plain Layout
10166 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10176 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10179 \begin_layout Plain Layout
10186 \begin_layout Plain Layout
10200 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10203 \begin_layout Plain Layout
10204 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10218 \begin_inset space \hfill{}
10224 \begin_layout Standard
10225 \begin_inset VSpace bigskip
10231 \begin_layout Standard
10232 You can directly insert accents like é to formulas.
10233 LyX will transform them to the corresponding accent command.
10235 \begin_inset Index idx
10238 \begin_layout Plain Layout
10244 it is better to insert a quotation mark before the vowel.
10245 These two characters are then treated by LaTeX as
10249 character when the formula part with the umlaut is marked as German.
10257 \begin_inset Quotes eld
10261 \begin_inset Quotes erd
10264 umlauts are created as demonstrated in the following example:
10267 \begin_layout Standard
10268 \begin_inset VSpace -2mm
10274 \begin_layout Standard
10276 \begin_inset Tabular
10277 <lyxtabular version="3" rows="3" columns="2">
10278 <features tabularvalignment="middle">
10279 <column alignment="center" valignment="top" width="0">
10280 <column alignment="center" valignment="top" width="0">
10282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10285 \begin_layout Plain Layout
10291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10294 \begin_layout Plain Layout
10296 \begin_inset Note Note
10299 \begin_layout Plain Layout
10307 \begin_inset space \thinspace{}
10310 pt space are only used as spacer.
10322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10325 \begin_layout Plain Layout
10328 \begin_inset Quotes grd
10336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10339 \begin_layout Plain Layout
10340 \begin_inset space \hspace{}
10347 \begin_inset Formula $"i$
10357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10360 \begin_layout Plain Layout
10367 \begin_layout Plain Layout
10381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10384 \begin_layout Plain Layout
10385 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10401 \begin_layout Standard
10402 Another advantage to
10408 is that umlauts can directly be converted to mathematical text because
10409 the accent commands above are
10415 in mathematical text
10418 To convert an accented character to mathematical text, only the character
10419 under the accent may be converted.
10420 This applies also for all other conversions, e.
10421 \begin_inset space \thinspace{}
10425 \begin_inset space \space{}
10431 \begin_layout Standard
10432 In mathematical text, umlauts and other accented characters can directly
10436 \begin_layout Subsection
10437 Accents for Operators
10438 \begin_inset Index idx
10441 \begin_layout Plain Layout
10442 Accents ! for operators
10450 \begin_layout Standard
10458 \begin_inset Index idx
10461 \begin_layout Plain Layout
10476 \begin_inset Index idx
10479 \begin_layout Plain Layout
10487 characters can be placed above or below an operator, respectively, to accent
10496 \begin_inset Index idx
10499 \begin_layout Plain Layout
10507 characters can be set before and behind an operator.
10508 The command scheme is:
10511 \begin_layout Standard
10527 \begin_layout Standard
10534 must always be before the operator that should be accented.
10535 You can accent with several characters and even with other operators and
10543 for example only characters behind an operator, write nothing between the
10544 first braces but don't omit the braces.
10547 \begin_layout Standard
10548 For example the command
10553 \begin_inset Formula $\to$
10563 \begin_inset Formula $\to$
10572 \begin_layout Plain Layout
10588 \begin_inset Formula
10590 \sideset{}{'}\sum_{k=1}^{n}
10598 \begin_layout Standard
10607 \begin_layout Plain Layout
10622 \begin_layout Plain Layout
10634 \begin_inset Formula $\uparrow$
10642 \begin_inset Formula
10644 \overset{a}{\maltese}
10649 As seen in the last example, with
10661 also symbols and characters can be accented; with
10667 this is not possible.
10670 \begin_layout Subsection
10671 Accents for several Characters
10672 \begin_inset Index idx
10675 \begin_layout Plain Layout
10676 Accents ! for several characters
10684 \begin_layout Standard
10685 \begin_inset space \hfill{}
10689 \begin_inset Tabular
10690 <lyxtabular version="3" rows="5" columns="2">
10691 <features tabularvalignment="middle">
10692 <column alignment="center" valignment="top" width="0pt">
10693 <column alignment="center" valignment="top" width="0pt">
10695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10698 \begin_layout Plain Layout
10704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10707 \begin_layout Plain Layout
10709 \begin_inset Note Note
10712 \begin_layout Plain Layout
10719 is only used as spacer.
10731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10734 \begin_layout Plain Layout
10741 \begin_layout Plain Layout
10755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10758 \begin_layout Plain Layout
10759 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10769 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10772 \begin_layout Plain Layout
10779 \begin_layout Plain Layout
10793 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10796 \begin_layout Plain Layout
10797 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10810 \begin_layout Plain Layout
10817 \begin_layout Plain Layout
10831 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10834 \begin_layout Plain Layout
10835 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10845 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10848 \begin_layout Plain Layout
10851 underleftrightarrow
10855 \begin_layout Plain Layout
10869 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10872 \begin_layout Plain Layout
10873 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10887 \begin_inset space \hfill{}
10891 \begin_inset Tabular
10892 <lyxtabular version="3" rows="5" columns="2">
10893 <features tabularvalignment="middle">
10894 <column alignment="center" valignment="top" width="0pt">
10895 <column alignment="center" valignment="top" width="0pt">
10897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10900 \begin_layout Plain Layout
10906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10909 \begin_layout Plain Layout
10917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10920 \begin_layout Plain Layout
10927 \begin_layout Plain Layout
10941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10944 \begin_layout Plain Layout
10945 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10955 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10958 \begin_layout Plain Layout
10965 \begin_layout Plain Layout
10979 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10982 \begin_layout Plain Layout
10983 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10993 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10996 \begin_layout Plain Layout
11003 \begin_layout Plain Layout
11017 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11020 \begin_layout Plain Layout
11021 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
11031 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11034 \begin_layout Plain Layout
11041 \begin_layout Plain Layout
11055 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11058 \begin_layout Plain Layout
11059 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11073 \begin_inset space \hfill{}
11079 \begin_layout Standard
11080 \begin_inset VSpace medskip
11083 With these commands as many characters as you like can be accented.
11096 will only be set in the output with a length of three characters, as shown
11097 in the following example:
11098 \begin_inset Formula
11100 \widetilde{A+B=C-D}
11108 \begin_layout Standard
11116 \begin_inset Index idx
11119 \begin_layout Plain Layout
11134 \begin_inset Index idx
11137 \begin_layout Plain Layout
11145 described in the previous subsection it is also possible to accent several
11155 \begin_layout Plain Layout
11165 \begin_inset Formula $\downarrow$
11171 \begin_inset Formula
11173 \underset{***}{A=B}
11181 \begin_layout Section
11183 \begin_inset CommandInset label
11190 \begin_inset Index idx
11193 \begin_layout Plain Layout
11202 \begin_layout Subsection
11204 \begin_inset CommandInset label
11206 name "sub:Predefined-Space"
11211 \begin_inset Index idx
11214 \begin_layout Plain Layout
11215 Space ! horizontal ! predefined
11223 \begin_layout Standard
11224 Sometimes it is necessary to insert horizontal space to a formula.
11225 This is done by inserting a protected space (shortcut
11228 arg "space-insert protected"
11233 \begin_inset Quotes eld
11242 \begin_layout Plain Layout
11254 \begin_inset Quotes erd
11257 appears and by pressing
11261 several times one can select one of eight different space sizes.
11262 The spaces can also be inserted using the math toolbar button
11263 \begin_inset Graphics
11264 filename ../images/math/space.png
11269 or special commands.
11270 Independent from the inserted command, one can select the size again by
11278 \begin_layout Standard
11281 \begin_inset VSpace -5mm
11285 \begin_inset Tabular
11286 <lyxtabular version="3" rows="3" columns="7">
11287 <features tabularvalignment="middle">
11288 <column alignment="center" valignment="middle" width="6.8cm">
11289 <column alignment="center" valignment="top" width="0">
11290 <column alignment="center" valignment="top" width="0">
11291 <column alignment="center" valignment="top" width="0">
11292 <column alignment="center" valignment="top" width="0">
11293 <column alignment="center" valignment="top" width="0">
11294 <column alignment="center" valignment="top" width="0">
11296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11299 \begin_layout Plain Layout
11305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11308 \begin_layout Plain Layout
11316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11319 \begin_layout Plain Layout
11327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11330 \begin_layout Plain Layout
11338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11341 \begin_layout Plain Layout
11349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11352 \begin_layout Plain Layout
11360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11363 \begin_layout Plain Layout
11373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11376 \begin_layout Plain Layout
11381 keystrokes after inserting the protected space
11386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11389 \begin_layout Plain Layout
11395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11398 \begin_layout Plain Layout
11404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11407 \begin_layout Plain Layout
11413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11416 \begin_layout Plain Layout
11422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11425 \begin_layout Plain Layout
11431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11434 \begin_layout Plain Layout
11442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11445 \begin_layout Plain Layout
11451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11454 \begin_layout Plain Layout
11455 \begin_inset Formula $A\, B$
11463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11466 \begin_layout Plain Layout
11467 \begin_inset Formula $A\: B$
11475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11478 \begin_layout Plain Layout
11479 \begin_inset Formula $A\; B$
11487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11490 \begin_layout Plain Layout
11491 \begin_inset Formula $A\quad B$
11499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11502 \begin_layout Plain Layout
11503 \begin_inset Formula $A\qquad B$
11511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11514 \begin_layout Plain Layout
11515 \begin_inset Formula $A\! B$
11531 \begin_layout Standard
11532 The last size seem to produce no space.
11533 It is displayed red in LyX contrary to the other sizes, because it is a
11535 There are two more negative spaces:
11538 \begin_layout Standard
11540 \begin_inset Tabular
11541 <lyxtabular version="3" rows="3" columns="3">
11542 <features tabularvalignment="middle">
11543 <column alignment="center" valignment="middle" width="6.8cm">
11544 <column alignment="center" valignment="top" width="0pt">
11545 <column alignment="center" valignment="top" width="0pt">
11547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11550 \begin_layout Plain Layout
11556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11559 \begin_layout Plain Layout
11567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11570 \begin_layout Plain Layout
11580 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11583 \begin_layout Plain Layout
11588 keystrokes after inserting the protected space
11593 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11596 \begin_layout Plain Layout
11602 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11605 \begin_layout Plain Layout
11613 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11616 \begin_layout Plain Layout
11622 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11625 \begin_layout Plain Layout
11626 \begin_inset Formula $A\negmedspace B$
11634 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11637 \begin_layout Plain Layout
11638 \begin_inset Formula $A\negthickspace B$
11654 \begin_layout Standard
11655 Negative spaces can lead to characters overlapping each other.
11656 Thus they can be used to enforce ligatures, what is e.
11657 \begin_inset space \thinspace{}
11661 \begin_inset space \space{}
11664 useful for summation operators:
11667 \begin_layout Standard
11669 \begin_inset Tabular
11670 <lyxtabular version="3" rows="3" columns="2">
11671 <features tabularvalignment="middle">
11672 <column alignment="center" valignment="top" width="0">
11673 <column alignment="center" valignment="top" width="0">
11675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11678 \begin_layout Plain Layout
11684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11687 \begin_layout Plain Layout
11689 \begin_inset Note Note
11692 \begin_layout Plain Layout
11699 is only used as spacer.
11711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11714 \begin_layout Plain Layout
11723 \begin_layout Plain Layout
11737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11740 \begin_layout Plain Layout
11741 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11754 \begin_layout Plain Layout
11765 \begin_layout Plain Layout
11779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11782 \begin_layout Plain Layout
11783 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11799 \begin_layout Standard
11800 Relations like for example equal signs, are always surrounded by space.
11801 To suppress this, the equal sign is placed into a TeX-brace.
11802 The following example demonstrates this:
11805 \begin_layout Standard
11807 \begin_inset Tabular
11808 <lyxtabular version="3" rows="2" columns="2">
11809 <features tabularvalignment="middle">
11810 <column alignment="center" valignment="top" width="0pt">
11811 <column alignment="center" valignment="top" width="0pt">
11813 <cell alignment="center" valignment="top" usebox="none">
11816 \begin_layout Plain Layout
11822 <cell alignment="center" valignment="top" usebox="none">
11825 \begin_layout Plain Layout
11826 \begin_inset Formula $A=B$
11836 <cell alignment="center" valignment="top" usebox="none">
11839 \begin_layout Plain Layout
11840 \begin_inset Note Note
11843 \begin_layout Plain Layout
11850 is only used as spacer.
11856 \begin_inset Formula $\raisebox{5mm}{}$
11859 equation without space
11864 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11867 \begin_layout Plain Layout
11868 \begin_inset Formula $A{=}B$
11884 \begin_layout Standard
11886 The command for the last formula is:
11891 \begin_inset Formula $\to$
11897 \begin_layout Standard
11898 \begin_inset VSpace bigskip
11901 Spaces are needed for physical units, because the space between the value
11902 and the unit is the smallest one and not a normal space.
11903 For units in text, the smallest space is inserted via the menu
11905 Insert\SpecialChar \menuseparator
11906 Formatting\SpecialChar \menuseparator
11908 \begin_inset space ~
11916 arg "space-insert thin"
11922 \begin_layout Standard
11923 An example to visualize the difference:
11926 \begin_layout Standard
11927 \begin_inset Tabular
11928 <lyxtabular version="3" rows="2" columns="2">
11929 <features tabularvalignment="middle">
11930 <column alignment="left" valignment="top" width="0">
11931 <column alignment="left" valignment="top" width="0">
11933 <cell alignment="center" valignment="top" usebox="none">
11936 \begin_layout Plain Layout
11938 \begin_inset Formula $\cdot$
11946 <cell alignment="center" valignment="top" usebox="none">
11949 \begin_layout Plain Layout
11950 space between value and unit
11957 <cell alignment="center" valignment="top" usebox="none">
11960 \begin_layout Plain Layout
11962 \begin_inset space \thinspace{}
11966 \begin_inset Formula $\cdot$
11974 <cell alignment="center" valignment="top" usebox="none">
11977 \begin_layout Plain Layout
11978 smallest space between value and unit
11991 \begin_layout Subsection
11996 \begin_layout Plain Layout
12009 \begin_layout Plain Layout
12010 for vertical space in formulas see
12011 \begin_inset CommandInset ref
12013 reference "sub:Line-Separation"
12026 \begin_layout Plain Layout
12034 \begin_inset Note Note
12037 \begin_layout Plain Layout
12040 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12043 \begin_layout Plain Layout
12046 texorpdfstring is in section
12047 \begin_inset CommandInset ref
12049 reference "sub:Formulas-in-Section"
12059 \begin_inset CommandInset label
12061 name "sub:Variable-Space"
12066 \begin_inset Index idx
12069 \begin_layout Plain Layout
12070 Space ! horizontal ! variable
12078 \begin_layout Standard
12079 Space with a defined length can be inserted with the command
12086 \begin_inset Index idx
12089 \begin_layout Plain Layout
12099 \begin_inset Quotes eld
12108 \begin_layout Plain Layout
12120 \begin_inset Quotes erd
12124 The length can be specified by left-clicking on the
12125 \begin_inset Quotes eld
12134 \begin_layout Plain Layout
12146 \begin_inset Quotes erd
12150 The length may also be negative.
12151 To insert so many space that the formula uses all available space, the
12159 \begin_inset Index idx
12162 \begin_layout Plain Layout
12173 \begin_layout Standard
12174 \begin_inset VSpace -1mm
12180 \begin_layout Standard
12182 \begin_inset Tabular
12183 <lyxtabular version="3" rows="4" columns="2">
12184 <features tabularvalignment="middle">
12185 <column alignment="center" valignment="top" width="0">
12186 <column alignment="center" valignment="top" width="0">
12188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12191 \begin_layout Plain Layout
12199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12202 \begin_layout Plain Layout
12210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12213 \begin_layout Plain Layout
12220 \begin_layout Plain Layout
12230 \begin_inset Formula $\to$
12236 \begin_inset space \thinspace{}
12244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12247 \begin_layout Plain Layout
12248 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12261 \begin_layout Plain Layout
12268 \begin_layout Plain Layout
12278 \begin_inset Formula $\to$
12284 \begin_inset space \thinspace{}
12292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12295 \begin_layout Plain Layout
12296 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12309 \begin_layout Plain Layout
12316 \begin_layout Plain Layout
12330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12333 \begin_layout Plain Layout
12334 \begin_inset Formula $A=A\hfill B=B$
12350 \begin_layout Standard
12351 In the last example the available space is given by the longest column entry
12353 In an inline formula the space depends on the length of the line in which
12361 Thus, when the line uses the full width, no space will be created.
12368 only has an effect on displayed formulas when the formula style
12373 (Formula styles are explained in
12374 \begin_inset CommandInset ref
12376 reference "sec:Formula-Styles"
12383 \begin_layout Standard
12390 , there are the commands
12402 that fill the space with a pattern, see
12403 \begin_inset CommandInset ref
12405 reference "sub:Ellipses"
12412 \begin_layout Standard
12413 For text, variable space can be inserted via the menu
12415 Insert\SpecialChar \menuseparator
12416 Formatting\SpecialChar \menuseparator
12418 \begin_inset space ~
12426 \begin_layout Standard
12427 This is a line with
12428 \begin_inset space \hspace{}
12433 \begin_inset space \thinspace{}
12439 \begin_layout Standard
12440 This is a line with
12441 \begin_inset space \hfill{}
12447 \begin_layout Subsection
12448 Space besides inline Formulas
12449 \begin_inset Index idx
12452 \begin_layout Plain Layout
12453 Space ! besides inline formulas
12461 \begin_layout Standard
12462 The space that surrounds inline formulas can be adjusted with the length
12470 \begin_inset Index idx
12473 \begin_layout Plain Layout
12482 The value of a length is set with the command
12489 \begin_inset Index idx
12492 \begin_layout Plain Layout
12500 that has the following scheme:
12503 \begin_layout Standard
12508 setlength{length name}{value}
12511 \begin_layout Standard
12519 \begin_inset space \thinspace{}
12525 \begin_layout Standard
12535 \begin_layout Standard
12536 is inserted in TeX-mode.
12538 \begin_inset space \thinspace{}
12541 mm space will now be set around all inline formulas:
12545 \begin_layout Plain Layout
12559 \begin_layout Standard
12560 This is a line with an inline formula
12561 \begin_inset Formula $A=B$
12565 \begin_inset space \thinspace{}
12568 mm surrounding space.
12572 \begin_layout Plain Layout
12586 \begin_layout Standard
12587 To return to the predefined value,
12593 is set to the value 0
12594 \begin_inset space \thinspace{}
12600 \begin_layout Section
12602 \begin_inset Index idx
12605 \begin_layout Plain Layout
12612 \begin_inset Index idx
12615 \begin_layout Plain Layout
12620 \begin_layout Plain Layout
12631 \begin_layout Plain Layout
12646 \begin_layout Standard
12647 Boxes for text are described in chapter
12654 \begin_inset space ~
12662 \begin_layout Subsection
12664 \begin_inset CommandInset label
12666 name "sub:Boxes-with-Frame"
12671 \begin_inset Index idx
12674 \begin_layout Plain Layout
12683 \begin_layout Standard
12684 It is possible to frame formulas or parts of it with the commands
12691 \begin_inset Index idx
12694 \begin_layout Plain Layout
12709 \begin_inset Index idx
12712 \begin_layout Plain Layout
12723 \begin_layout Standard
12724 When one of these commands is inserted to a formula, a blue box appears
12725 within a frame to enter formula parts.
12732 an additional formula has to be created by
12736 within this box, because the box content will otherwise be treated as mathemati
12744 is used, a new formula is automatically created inside the frame.
12747 \begin_layout Standard
12754 is not suitable to frame displayed formulas because the formula will always
12755 be set in the size of the text.
12762 is in contrary not suitable to frame inline formulas, because the formula
12763 will always be set in the size of a displayed formula.
12766 \begin_layout Standard
12773 there is the command
12780 \begin_inset Index idx
12783 \begin_layout Plain Layout
12791 where additionally the frame width and the alignment can be specified.
12798 is used in the following scheme:
12801 \begin_layout Standard
12806 framebox[frame width][position]{box content}
12809 \begin_layout Standard
12810 The position can either be
12827 right aligns the formula in the box.
12828 When no position is given, the formula will be centered.
12829 \begin_inset Newline newline
12832 Is no width given, also no position can be given.
12833 In this case the frame width is adjusted to the box content like for
12842 \begin_layout Standard
12849 is inserted, a box appears containing three blue boxes.
12850 The first two boxes are surrounded by brackets and denote the two optional
12852 The third box is for formula parts like for
12861 \begin_layout Standard
12863 \begin_inset Tabular
12864 <lyxtabular version="3" rows="5" columns="2">
12865 <features tabularvalignment="middle">
12866 <column alignment="center" valignment="top" width="0">
12867 <column alignment="center" valignment="top" width="0">
12869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12872 \begin_layout Plain Layout
12878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12881 \begin_layout Plain Layout
12883 \begin_inset Note Note
12886 \begin_layout Plain Layout
12893 is only used as spacer.
12905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12908 \begin_layout Plain Layout
12915 \begin_layout Plain Layout
12934 \begin_layout Plain Layout
12948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12951 \begin_layout Plain Layout
12952 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12965 \begin_layout Plain Layout
12972 \begin_layout Plain Layout
12987 \begin_layout Plain Layout
13001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13004 \begin_layout Plain Layout
13005 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
13015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13018 \begin_layout Plain Layout
13025 \begin_layout Plain Layout
13039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13042 \begin_layout Plain Layout
13043 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13056 \begin_layout Plain Layout
13063 \begin_layout Plain Layout
13073 \begin_inset Formula $\to$
13077 \begin_inset Formula $\to$
13090 \begin_layout Plain Layout
13100 \begin_inset Formula $\downarrow$
13108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13111 \begin_layout Plain Layout
13112 \begin_inset Formula $\raisebox{6mm}{}$
13116 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13120 \begin_inset Formula $\raisebox{-4mm}{}$
13136 \begin_layout Standard
13137 The frame thickness can also be adjusted.
13138 To do this the following commands have to be inserted in TeX-mode before
13142 \begin_layout Standard
13152 \begin_inset Quotes eld
13156 \begin_inset Quotes erd
13170 \begin_inset Quotes eld
13174 \begin_inset Quotes erd
13180 \begin_layout Standard
13181 \begin_inset Quotes eld
13185 \begin_inset Quotes erd
13188 specifies the minimal distance between the frame and the first character
13190 An example for this is the following framed formula:
13194 \begin_layout Plain Layout
13206 \begin_inset Formula
13213 Before this formula the commands
13216 \begin_layout Standard
13238 \begin_layout Standard
13239 were inserted in TeX-mode.
13240 The given values are used for all following boxes.
13243 \begin_layout Standard
13244 To return to the standard frame size, the command
13247 \begin_layout Standard
13272 \begin_layout Plain Layout
13286 \begin_layout Standard
13287 is inserted in TeX-mode before the next formula.
13290 \begin_layout Subsection
13291 Boxes without Frame
13292 \begin_inset CommandInset label
13294 name "sub:Boxes-without-Frame"
13299 \begin_inset Index idx
13302 \begin_layout Plain Layout
13303 Boxes ! without frame
13311 \begin_layout Standard
13312 For boxes without a frame there are the following box commands:
13319 \begin_inset Index idx
13322 \begin_layout Plain Layout
13337 \begin_inset Index idx
13340 \begin_layout Plain Layout
13355 \begin_inset Index idx
13358 \begin_layout Plain Layout
13369 \begin_layout Standard
13376 a box can be super- or subscripted.
13377 But in contrary to normal super- and subscripting, the characters in the
13378 box keep their font size.
13385 is used in the following scheme:
13388 \begin_layout Standard
13393 raisebox{height}{box content}
13396 \begin_layout Standard
13397 When the box should contain a formula, an extra formula is needed like for
13408 \begin_inset Note Greyedout
13411 \begin_layout Plain Layout
13422 this extra formula is created by pressing
13426 twice instead of once because LyX doesn't yet support
13440 \begin_layout Standard
13442 \begin_inset Tabular
13443 <lyxtabular version="3" rows="4" columns="2">
13444 <features tabularvalignment="middle">
13445 <column alignment="center" valignment="top" width="0">
13446 <column alignment="center" valignment="top" width="0">
13448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13451 \begin_layout Plain Layout
13457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13460 \begin_layout Plain Layout
13468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13471 \begin_layout Plain Layout
13475 \begin_inset Formula $\to$
13481 \begin_inset Formula $\to$
13489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13492 \begin_layout Plain Layout
13493 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13506 \begin_layout Plain Layout
13510 \begin_inset Formula $\to$
13516 \begin_inset Formula $\to$
13524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13527 \begin_layout Plain Layout
13528 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13541 \begin_layout Plain Layout
13545 \begin_inset Formula $\to$
13564 \begin_layout Plain Layout
13578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13581 \begin_layout Plain Layout
13582 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13598 \begin_layout Standard
13623 , with the difference that there is no frame.
13626 \begin_layout Subsection
13628 \begin_inset CommandInset label
13630 name "sub:Colored-Boxes"
13635 \begin_inset Index idx
13638 \begin_layout Plain Layout
13647 \begin_layout Standard
13648 To be able to use all commands explained in this section, the LaTeX-package
13657 \begin_layout Plain Layout
13662 is part of every LaTeX standard installation.
13668 \begin_inset Index idx
13671 \begin_layout Plain Layout
13677 has to be loaded in the LaTeX-preamble with the line
13681 \begin_layout Plain Layout
13682 When text is colored somewhere in the document with a predefined color,
13683 LyX loads the LaTeX-package
13688 Thus it is possible that the package is loaded twice, but this doesn't
13695 \begin_inset Note Note
13698 \begin_layout Plain Layout
13699 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13708 \begin_layout Standard
13716 \begin_layout Standard
13717 \begin_inset VSpace medskip
13720 To color boxes, the command
13727 \begin_inset Index idx
13730 \begin_layout Plain Layout
13738 is used in the following scheme:
13741 \begin_layout Standard
13746 colorbox{color}{box content}
13749 \begin_layout Standard
13750 The box content can also be a box and a
13756 can also be part of another box (see the 2nd and 3rd example).
13757 When the box should contain a formula, an extra formula has to be created,
13758 the same way as for
13768 \begin_layout Plain Layout
13769 This also applies for the command
13783 \begin_layout Standard
13784 One of the following predefined colors can be chosen:
13787 \begin_layout Standard
13821 \begin_layout Standard
13823 \begin_inset Tabular
13824 <lyxtabular version="3" rows="4" columns="2">
13825 <features tabularvalignment="middle">
13826 <column alignment="center" valignment="top" width="0">
13827 <column alignment="center" valignment="top" width="0">
13829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13832 \begin_layout Plain Layout
13838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13841 \begin_layout Plain Layout
13843 \begin_inset Note Note
13846 \begin_layout Plain Layout
13853 is only used as spacer.
13865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13868 \begin_layout Plain Layout
13872 \begin_inset Formula $\to$
13882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13885 \begin_layout Plain Layout
13886 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13899 \begin_layout Plain Layout
13903 \begin_inset Formula $\to$
13914 \begin_layout Plain Layout
13928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13931 \begin_layout Plain Layout
13932 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13945 \begin_layout Plain Layout
13952 \begin_layout Plain Layout
13964 \begin_inset Formula $\to$
13983 \begin_layout Plain Layout
13997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14000 \begin_layout Plain Layout
14001 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
14017 \begin_layout Standard
14024 only colors the box but not the characters in the box.
14025 To color all characters, the whole formula is highlighted and the wanted
14026 color is chosen in the
14029 \begin_inset space ~
14035 The dialog can be called with the toolbar button
14036 \begin_inset Graphics
14037 filename ../images/dialog-show_character.png
14044 Edit\SpecialChar \menuseparator
14046 \begin_inset space ~
14049 Style\SpecialChar \menuseparator
14053 The formula number has then the same color as the formula.
14054 When the formula number should get another color than the formula characters,
14055 the color must be changed within the formula.
14058 \begin_layout Standard
14062 \begin_layout Standard
14065 \begin_inset Formula
14067 \int A=B\label{eq:red}
14075 \begin_inset Formula
14077 \textcolor{red}{\int A=B}\label{eq:redgreen}
14085 \begin_layout Standard
14087 \begin_inset CommandInset ref
14093 is completely colored red.
14094 \begin_inset Newline newline
14098 \begin_inset CommandInset ref
14100 reference "eq:redgreen"
14104 was first completely colored green to set the color for the formula number.
14105 Subsequently the formula characters were colored red.
14108 \begin_layout Standard
14109 \begin_inset VSpace bigskip
14112 To color the frame different than the rest of the box, the command
14119 \begin_inset Index idx
14122 \begin_layout Plain Layout
14130 is used in the following scheme:
14133 \begin_layout Standard
14138 fcolorbox{frame color}{color}{box content}
14141 \begin_layout Standard
14148 is an extension of the command
14155 The frame width is set, like for
14178 \begin_layout Plain Layout
14190 \begin_inset Formula
14192 \fcolorbox{cyan}{magenta}{A=B}
14201 \begin_layout Plain Layout
14215 \begin_layout Standard
14216 This formula was created with the command
14217 \begin_inset Newline newline
14225 \begin_inset Formula $\to$
14231 \begin_inset Formula $\to$
14241 \begin_layout Standard
14242 \begin_inset VSpace bigskip
14245 To use other colors than the predefined ones, they have to be defined first.
14248 \begin_layout Standard
14249 One can for example define the color
14250 \begin_inset Quotes eld
14258 \begin_inset Quotes erd
14261 with the LaTeX-preamble line:
14264 \begin_layout Standard
14269 definecolor{darkgreen}{cmyk}{0.5,
14284 \begin_inset Index idx
14287 \begin_layout Plain Layout
14298 \begin_layout Standard
14303 is the color space that denotes the colors
14320 The four comma separated numbers are the portion factor for the corresponding
14321 colors of the color space.
14322 The factors can be in the range of 0
14323 \begin_inset space \thinspace{}
14327 \begin_inset space \thinspace{}
14335 also the color space
14339 can be used for definitions.
14356 , so that there are in this case three portion factors for the corresponding
14358 Furthermore there is the color space
14362 with one portion factor for the gray value.
14365 \begin_layout Standard
14366 As example a framed box with the new defined color
14370 where the characters have been colored
14375 \begin_inset Formula
14377 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14385 \begin_layout Standard
14386 Self-defined colors can also be used for text with the help of the command
14394 \begin_inset Index idx
14397 \begin_layout Plain Layout
14406 \begin_layout Standard
14410 \begin_layout Plain Layout
14414 textcolor{darkgreen}{
14420 \begin_inset Quotes eld
14424 \begin_inset Quotes erd
14431 \begin_layout Plain Layout
14441 \begin_layout Standard
14449 \begin_inset Index idx
14452 \begin_layout Plain Layout
14460 is used in the scheme
14464 textcolor{color}{characters to color}
14469 \begin_layout Subsection
14471 \begin_inset CommandInset label
14473 name "sub:Paragraph-Boxes"
14478 \begin_inset Index idx
14481 \begin_layout Plain Layout
14482 Boxes ! as paragraph
14490 \begin_layout Standard
14491 A box that can contain several lines and paragraphs, a so called paragraph
14492 box (parbox), can be created with the menu
14494 Insert\SpecialChar \menuseparator
14497 or the toolbar button
14498 \begin_inset Graphics
14499 filename ../images/box-insert.png
14507 \begin_layout Standard
14508 The following example shows a framed parbox in a line:
14511 \begin_layout Standard
14512 \begin_inset VSpace medskip
14516 \begin_inset Box Boxed
14526 height_special "totalheight"
14529 \begin_layout Plain Layout
14530 This is a paragraph box.
14532 \begin_inset space \thinspace{}
14535 cm long and can also contain formulas:
14536 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14547 \begin_layout Standard
14548 \begin_inset VSpace medskip
14554 \begin_layout Standard
14555 Such a box is created by right-clicking on the gray box inset.
14556 A dialog pops up showing the box properties.
14570 \begin_inset space \thinspace{}
14575 Vertical Box Alignment
14580 \begin_layout Standard
14581 \begin_inset VSpace medskip
14584 In LaTeX a parbox is created with the command
14591 \begin_inset Index idx
14594 \begin_layout Plain Layout
14602 that has the following scheme:
14605 \begin_layout Standard
14610 parbox[position]{width}{box content}
14613 \begin_layout Standard
14627 for bottom means that the box is aligned within the surrounding text with
14633 for top this is done with the first line.
14634 When no position is given, the box will be vertically centered, see section
14642 \begin_inset space ~
14647 manual for examples.
14650 \begin_layout Standard
14651 \begin_inset VSpace bigskip
14654 To frame formulas completely, including the formula number, the formula
14655 must be set into a parbox.
14656 To do this, the command
14670 is inserted in TeX-mode before the formula.
14678 \begin_inset Index idx
14681 \begin_layout Plain Layout
14689 is hereby the line width set for the document.
14690 Because the frame is outside the parbox, 2
14691 \begin_inset space \thinspace{}
14694 times the frame separation and the frame thickness must be subtracted from
14696 As this is not automatically done by LyX due to a bug
14700 \begin_layout Plain Layout
14701 \begin_inset CommandInset href
14703 name "LyX-bug #4483"
14704 target "http://www.lyx.org/trac/ticket/4483"
14713 , TeX-mode has to be used.
14714 To be able to multiply and subtract in arguments, the LaTeX-package
14722 \begin_layout Plain Layout
14727 is part of every LaTeX standard installation.
14733 \begin_inset Index idx
14736 \begin_layout Plain Layout
14742 must be loaded in the LaTeX-preamble with the line
14745 \begin_layout Standard
14753 \begin_layout Standard
14754 Behind the formula both boxes are closed by entering
14759 Here is an example:
14763 \begin_layout Plain Layout
14777 \begin_layout Standard
14781 \begin_layout Plain Layout
14799 \begin_inset Formula
14801 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14810 \begin_layout Plain Layout
14821 \begin_layout Plain Layout
14835 \begin_layout Standard
14836 \begin_inset VSpace medskip
14839 As a parbox is used as argument of
14845 , there is in this case no difference between
14860 \begin_layout Standard
14861 \begin_inset VSpace bigskip
14864 Paragraph boxes are very useful to comment formulas directly.
14871 is used in combination with the command
14885 \begin_inset CommandInset ref
14887 reference "sub:User-defined-Numbering"
14894 \begin_layout Standard
14895 An example of a formula commented with
14904 \begin_layout Standard
14908 \begin_layout Plain Layout
14921 This is a description.
14922 It is distinctly separated from the formula and multiline.
14926 \begin_layout Plain Layout
14938 \begin_layout Standard
14939 Such a formula must be inserted completely in TeX-mode because LyX does
14940 not yet support the command
14947 The formula is created with the following command sequence:
14950 \begin_layout Standard
14963 is inserted in TeX-mode.
14967 \begin_layout Plain Layout
14968 When the formula style
14980 can also be replaced by
14987 (formula styles see
14988 \begin_inset CommandInset ref
14990 reference "sec:Formula-Styles"
14999 Then the description follows as normal text and finally
15005 is inserted in TeX-mode.
15018 hereby create a displayed formula.
15021 \begin_layout Standard
15028 can be seen in this example that was
15029 \begin_inset Quotes eld
15033 \begin_inset Quotes erd
15036 using the mathematical textmode:
15037 \begin_inset Formula
15039 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15047 \begin_layout Section
15049 \begin_inset Index idx
15052 \begin_layout Plain Layout
15061 \begin_layout Subsection
15063 \begin_inset CommandInset label
15065 name "sub:Big-Operators"
15070 \begin_inset Index idx
15073 \begin_layout Plain Layout
15080 \begin_inset Index idx
15083 \begin_layout Plain Layout
15090 \begin_inset Index idx
15093 \begin_layout Plain Layout
15102 \begin_layout Standard
15103 To be able to use all integral operators listed here, the option
15105 Use esint package automatically
15107 must be set in the document settings under
15110 \begin_inset space ~
15118 \begin_layout Standard
15119 \begin_inset space \hfill{}
15123 \begin_inset Tabular
15124 <lyxtabular version="3" rows="11" columns="2">
15125 <features tabularvalignment="middle">
15126 <column alignment="center" valignment="top" width="0pt">
15127 <column alignment="center" valignment="top" width="0pt">
15129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15132 \begin_layout Plain Layout
15138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15141 \begin_layout Plain Layout
15149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15152 \begin_layout Plain Layout
15156 \begin_inset Index idx
15159 \begin_layout Plain Layout
15172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15175 \begin_layout Plain Layout
15176 \begin_inset Formula $\int$
15186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15189 \begin_layout Plain Layout
15197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15200 \begin_layout Plain Layout
15201 \begin_inset Formula $\oint$
15211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15214 \begin_layout Plain Layout
15222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15225 \begin_layout Plain Layout
15226 \begin_inset Formula $\ointctrclockwise$
15236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15239 \begin_layout Plain Layout
15247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15250 \begin_layout Plain Layout
15251 \begin_inset Formula $\ointclockwise$
15261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15264 \begin_layout Plain Layout
15272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15275 \begin_layout Plain Layout
15276 \begin_inset Formula $\sqint$
15286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15289 \begin_layout Plain Layout
15297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15300 \begin_layout Plain Layout
15302 \begin_inset Formula $\fint$
15312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15315 \begin_layout Plain Layout
15323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15326 \begin_layout Plain Layout
15328 \begin_inset Formula $\landupint$
15338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15341 \begin_layout Plain Layout
15349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15352 \begin_layout Plain Layout
15354 \begin_inset Formula $\landdownint$
15364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15367 \begin_layout Plain Layout
15375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15378 \begin_layout Plain Layout
15379 \begin_inset Formula $\bigcap$
15389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15392 \begin_layout Plain Layout
15400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15403 \begin_layout Plain Layout
15404 \begin_inset Formula $\bigcup$
15418 \begin_inset space \hfill{}
15422 \begin_inset Tabular
15423 <lyxtabular version="3" rows="11" columns="2">
15424 <features tabularvalignment="middle">
15425 <column alignment="center" valignment="top" width="0pt">
15426 <column alignment="center" valignment="top" width="0pt">
15428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15431 \begin_layout Plain Layout
15437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15440 \begin_layout Plain Layout
15448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15451 \begin_layout Plain Layout
15455 \begin_inset Index idx
15458 \begin_layout Plain Layout
15471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15474 \begin_layout Plain Layout
15475 \begin_inset Formula $\sum$
15485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15488 \begin_layout Plain Layout
15492 \begin_inset Index idx
15495 \begin_layout Plain Layout
15508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15511 \begin_layout Plain Layout
15512 \begin_inset Formula $\prod$
15522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15525 \begin_layout Plain Layout
15533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15536 \begin_layout Plain Layout
15537 \begin_inset Formula $\coprod$
15547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15550 \begin_layout Plain Layout
15558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15561 \begin_layout Plain Layout
15562 \begin_inset Formula $\bigodot$
15572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15575 \begin_layout Plain Layout
15583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15586 \begin_layout Plain Layout
15587 \begin_inset Formula $\bigotimes$
15597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15600 \begin_layout Plain Layout
15608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15611 \begin_layout Plain Layout
15612 \begin_inset Formula $\bigoplus$
15622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15625 \begin_layout Plain Layout
15633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15636 \begin_layout Plain Layout
15637 \begin_inset Formula $\bigwedge$
15647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15650 \begin_layout Plain Layout
15658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15661 \begin_layout Plain Layout
15662 \begin_inset Formula $\bigvee$
15672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15675 \begin_layout Plain Layout
15683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15686 \begin_layout Plain Layout
15687 \begin_inset Formula $\bigsqcup$
15697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15700 \begin_layout Plain Layout
15708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15711 \begin_layout Plain Layout
15712 \begin_inset Formula $\biguplus$
15726 \begin_inset space \hfill{}
15732 \begin_layout Standard
15733 All big operators can also be inserted via the math toolbar button
15734 \begin_inset Graphics
15735 filename ../images/math/intop.png
15743 \begin_layout Standard
15744 The operators are called big because they are bigger than the sometimes
15745 equal looking binary operators.
15746 All big operators can have limits as described in the next subsection.
15749 \begin_layout Standard
15750 For all integral operators there is a second version available, ending on
15768 These operators are different from
15775 \begin_inset space \space{}
15778 in the style the operator limits are displayed, see
15779 \begin_inset CommandInset ref
15781 reference "sub:Operator-Limits"
15789 \begin_layout Subsubsection*
15790 Advice for Integrals
15793 \begin_layout Standard
15798 in an integral is an operator, that therefore has to be set upright.
15799 This is done by highlighting the
15803 and using the keyboard shortcut
15813 \begin_layout Plain Layout
15819 \begin_inset CommandInset ref
15821 reference "sub:Font-Styles"
15831 Finally the smallest space is inserted before the
15835 , as this is usual for operators.
15839 \begin_layout Standard
15841 \begin_inset Formula $\int A(x)dx$
15845 \begin_inset Newline newline
15849 \begin_inset Phantom HPhantom
15852 \begin_layout Plain Layout
15859 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15865 \begin_layout Standard
15866 For multiple integrals there are the following commands:
15867 \begin_inset VSpace medskip
15873 \begin_layout Standard
15874 \begin_inset space \hfill{}
15878 \begin_inset Tabular
15879 <lyxtabular version="3" rows="4" columns="2">
15880 <features tabularvalignment="middle">
15881 <column alignment="center" valignment="top" width="0">
15882 <column alignment="center" valignment="top" width="0">
15884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15887 \begin_layout Plain Layout
15893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15896 \begin_layout Plain Layout
15898 \begin_inset Note Note
15901 \begin_layout Plain Layout
15908 is only used as spacer.
15920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15923 \begin_layout Plain Layout
15931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15934 \begin_layout Plain Layout
15935 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15948 \begin_layout Plain Layout
15956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15959 \begin_layout Plain Layout
15960 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15973 \begin_layout Plain Layout
15981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15984 \begin_layout Plain Layout
15985 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15999 \begin_inset space \hfill{}
16003 \begin_inset Tabular
16004 <lyxtabular version="3" rows="4" columns="2">
16005 <features tabularvalignment="middle">
16006 <column alignment="center" valignment="top" width="0">
16007 <column alignment="center" valignment="top" width="0">
16009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16012 \begin_layout Plain Layout
16018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16021 \begin_layout Plain Layout
16029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16032 \begin_layout Plain Layout
16040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16043 \begin_layout Plain Layout
16044 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16057 \begin_layout Plain Layout
16065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16068 \begin_layout Plain Layout
16069 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16082 \begin_layout Plain Layout
16090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16093 \begin_layout Plain Layout
16094 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16108 \begin_inset space \hfill{}
16114 \begin_layout Subsection
16116 \begin_inset CommandInset label
16118 name "sub:Operator-Limits"
16123 \begin_inset Index idx
16126 \begin_layout Plain Layout
16135 \begin_layout Standard
16136 Limits are created by super- and subscripts:
16139 \begin_layout Standard
16141 \begin_inset Tabular
16142 <lyxtabular version="3" rows="2" columns="2">
16143 <features tabularvalignment="middle">
16144 <column alignment="center" valignment="top" width="0pt">
16145 <column alignment="center" valignment="top" width="0pt">
16147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16150 \begin_layout Plain Layout
16156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16159 \begin_layout Plain Layout
16161 \begin_inset Note Note
16164 \begin_layout Plain Layout
16171 is only used as spacer.
16183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16186 \begin_layout Plain Layout
16195 \begin_layout Plain Layout
16205 \begin_inset Formula $\to$
16209 \begin_inset Formula $\to$
16217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16220 \begin_layout Plain Layout
16221 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16237 \begin_layout Standard
16238 Limits of inline formulas are set right beside the operator.
16239 Limits in displayed formulas are set above or below the operator, except
16240 for integral limits.
16243 \begin_layout Standard
16244 To force that the limits are set beside the operator, the cursor is set
16245 directly behind the operator and the limits type is changed with the menu
16248 Edit\SpecialChar \menuseparator
16249 Math\SpecialChar \menuseparator
16268 \begin_layout Standard
16269 The default limits type is this:
16270 \begin_inset Formula
16272 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16277 This is how it looks when the limits type was changed to
16284 \begin_inset Formula
16286 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16291 For integrals, except those ending with
16307 etc., the limits are by default set beside the operator.
16308 But for multiple integrals the limits are often set below the operator.
16309 In the following example the limits type was therefore set to
16313 and so set below the integrals:
16314 \begin_inset Formula
16316 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16324 \begin_layout Standard
16325 \begin_inset VSpace medskip
16328 To specify conditions for limits, the commands
16335 \begin_inset Index idx
16338 \begin_layout Plain Layout
16353 \begin_inset Index idx
16356 \begin_layout Plain Layout
16365 To create for example this expression
16366 \begin_inset Formula
16368 \sum_{\begin{subarray}{c}
16372 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16380 \begin_layout Standard
16381 the following has to be done:
16382 \begin_inset Newline newline
16397 \begin_layout Plain Layout
16409 One is now in a blue box under the summation operator and insert there
16418 \begin_layout Plain Layout
16430 The blue box is now within a purple box and now several lines can be written
16432 A new line is created by inserting a line break (
16435 arg "newline-insert newline"
16440 \begin_inset Newline newline
16445 0<k<1000 Ctrl+Return
16446 \begin_inset Newline newline
16451 is typed in, a new box appears below for the new line.
16454 \begin_layout Standard
16455 The alignment of the lines can be changed to left aligned with the
16465 Edit\SpecialChar \menuseparator
16469 To get right alignment,
16477 \begin_layout Plain Layout
16488 is inserted at the beginning of the line.
16491 \begin_layout Standard
16504 with the difference that the lines are always centered.
16507 \begin_layout Standard
16508 \begin_inset VSpace bigskip
16512 \begin_inset CommandInset ref
16514 reference "eq:substack"
16518 there can be too much space beside an operator, because the characters
16519 following the operator are set beside the limits.
16522 \begin_layout Standard
16523 To avoid this, the following macro can be used in the LaTeX-preamble:
16526 \begin_layout Standard
16540 \begin_inset Newline newline
16552 \begin_inset Newline newline
16559 mathclapinternal #1#2{
16563 mathsurround =0pt #1{#2}$}}
16566 \begin_layout Standard
16567 This defines the command
16574 \begin_inset Index idx
16577 \begin_layout Plain Layout
16585 that sets the width of the limit to 0
16586 \begin_inset space \thinspace{}
16590 The command scheme is
16593 \begin_layout Standard
16601 \begin_layout Standard
16602 where the limit can consist of several conditions.
16605 \begin_layout Standard
16607 \begin_inset CommandInset ref
16609 reference "eq:substack"
16613 , one uses the command
16616 \begin_layout Standard
16629 \begin_layout Plain Layout
16638 0<k<1000 Ctrl+Return
16641 \begin_layout Standard
16642 to create the lower limit.
16643 The summand is now directly behind the summation operator:
16644 \begin_inset Formula
16646 \sum_{\mathclap{\substack{0<k<1000\\
16658 \begin_layout Standard
16659 \begin_inset VSpace bigskip
16662 How to use one limit for several operators is described in
16663 \begin_inset CommandInset ref
16665 reference "sub:Self-defined-Operators"
16672 \begin_layout Standard
16673 \begin_inset Newpage newpage
16679 \begin_layout Subsection
16681 \begin_inset CommandInset label
16683 name "sub:Binary-Operators"
16688 \begin_inset Index idx
16691 \begin_layout Plain Layout
16700 \begin_layout Standard
16701 Binary operators are surrounded by space when there is a character before
16703 \begin_inset VSpace medskip
16709 \begin_layout Standard
16710 \begin_inset space \hfill{}
16714 \begin_inset Tabular
16715 <lyxtabular version="3" rows="13" columns="2">
16716 <features tabularvalignment="middle">
16717 <column alignment="center" valignment="top" width="0pt">
16718 <column alignment="center" valignment="top" width="0pt">
16720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16723 \begin_layout Plain Layout
16725 \begin_inset Note Note
16728 \begin_layout Plain Layout
16735 is only used as spacer.
16745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16748 \begin_layout Plain Layout
16756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16759 \begin_layout Plain Layout
16765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16768 \begin_layout Plain Layout
16769 \begin_inset Formula $+$
16779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16782 \begin_layout Plain Layout
16788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16791 \begin_layout Plain Layout
16792 \begin_inset Formula $-$
16802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16805 \begin_layout Plain Layout
16813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16816 \begin_layout Plain Layout
16817 \begin_inset Formula $\pm$
16827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16830 \begin_layout Plain Layout
16838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16841 \begin_layout Plain Layout
16842 \begin_inset Formula $\mp$
16852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16855 \begin_layout Plain Layout
16863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16866 \begin_layout Plain Layout
16867 \begin_inset Formula $\cdot$
16877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16880 \begin_layout Plain Layout
16888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16891 \begin_layout Plain Layout
16892 \begin_inset Formula $\times$
16902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16905 \begin_layout Plain Layout
16913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16916 \begin_layout Plain Layout
16917 \begin_inset Formula $\div$
16927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16930 \begin_layout Plain Layout
16934 \begin_layout Plain Layout
16947 \begin_layout Plain Layout
16959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16962 \begin_layout Plain Layout
16963 \begin_inset Formula $*$
16973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16976 \begin_layout Plain Layout
16984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16987 \begin_layout Plain Layout
16988 \begin_inset Formula $\star$
16998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17001 \begin_layout Plain Layout
17009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17012 \begin_layout Plain Layout
17013 \begin_inset Formula $\circ$
17023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17026 \begin_layout Plain Layout
17034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17037 \begin_layout Plain Layout
17038 \begin_inset Formula $\diamond$
17048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17051 \begin_layout Plain Layout
17059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17062 \begin_layout Plain Layout
17063 \begin_inset Formula $\bullet$
17077 \begin_inset space \hfill{}
17081 \begin_inset Tabular
17082 <lyxtabular version="3" rows="13" columns="2">
17083 <features tabularvalignment="middle">
17084 <column alignment="center" valignment="top" width="0pt">
17085 <column alignment="center" valignment="top" width="0pt">
17087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17090 \begin_layout Plain Layout
17096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17099 \begin_layout Plain Layout
17107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17110 \begin_layout Plain Layout
17118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17121 \begin_layout Plain Layout
17122 \begin_inset Formula $\nabla$
17132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17135 \begin_layout Plain Layout
17143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17146 \begin_layout Plain Layout
17147 \begin_inset Formula $\bigtriangledown$
17157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17160 \begin_layout Plain Layout
17168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17171 \begin_layout Plain Layout
17172 \begin_inset Formula $\bigtriangleup$
17182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17185 \begin_layout Plain Layout
17193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17196 \begin_layout Plain Layout
17197 \begin_inset Formula $\Box$
17207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17210 \begin_layout Plain Layout
17218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17221 \begin_layout Plain Layout
17222 \begin_inset Formula $\cap$
17232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17235 \begin_layout Plain Layout
17243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17246 \begin_layout Plain Layout
17247 \begin_inset Formula $\cup$
17257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17260 \begin_layout Plain Layout
17268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17271 \begin_layout Plain Layout
17272 \begin_inset Formula $\dagger$
17282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17285 \begin_layout Plain Layout
17293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17296 \begin_layout Plain Layout
17297 \begin_inset Formula $\ddagger$
17307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17310 \begin_layout Plain Layout
17318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17321 \begin_layout Plain Layout
17322 \begin_inset Formula $\wr$
17332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17335 \begin_layout Plain Layout
17343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17346 \begin_layout Plain Layout
17347 \begin_inset Formula $\bigcirc$
17357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17360 \begin_layout Plain Layout
17368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17371 \begin_layout Plain Layout
17372 \begin_inset Formula $\wedge$
17382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17385 \begin_layout Plain Layout
17393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17396 \begin_layout Plain Layout
17397 \begin_inset Formula $\vee$
17411 \begin_inset space \hfill{}
17415 \begin_inset Tabular
17416 <lyxtabular version="3" rows="13" columns="2">
17417 <features tabularvalignment="middle">
17418 <column alignment="center" valignment="top" width="0pt">
17419 <column alignment="center" valignment="top" width="0pt">
17421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17424 \begin_layout Plain Layout
17430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17433 \begin_layout Plain Layout
17441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17444 \begin_layout Plain Layout
17452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17455 \begin_layout Plain Layout
17456 \begin_inset Formula $\oplus$
17466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17469 \begin_layout Plain Layout
17477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17480 \begin_layout Plain Layout
17481 \begin_inset Formula $\ominus$
17491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17494 \begin_layout Plain Layout
17502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17505 \begin_layout Plain Layout
17506 \begin_inset Formula $\otimes$
17516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17519 \begin_layout Plain Layout
17527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17530 \begin_layout Plain Layout
17531 \begin_inset Formula $\oslash$
17541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17544 \begin_layout Plain Layout
17552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17555 \begin_layout Plain Layout
17556 \begin_inset Formula $\odot$
17566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17569 \begin_layout Plain Layout
17577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17580 \begin_layout Plain Layout
17581 \begin_inset Formula $\amalg$
17591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17594 \begin_layout Plain Layout
17602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17605 \begin_layout Plain Layout
17606 \begin_inset Formula $\uplus$
17616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17619 \begin_layout Plain Layout
17627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17630 \begin_layout Plain Layout
17631 \begin_inset Formula $\setminus$
17641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17644 \begin_layout Plain Layout
17652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17655 \begin_layout Plain Layout
17656 \begin_inset Formula $\sqcap$
17666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17669 \begin_layout Plain Layout
17677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17680 \begin_layout Plain Layout
17681 \begin_inset Formula $\sqcup$
17691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17694 \begin_layout Plain Layout
17702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17705 \begin_layout Plain Layout
17706 \begin_inset Formula $\triangleleft$
17716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17719 \begin_layout Plain Layout
17727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17730 \begin_layout Plain Layout
17731 \begin_inset Formula $\triangleright$
17745 \begin_inset space \hfill{}
17751 \begin_layout Standard
17752 All binary operators can also be inserted via the math toolbar button
17753 \begin_inset Graphics
17754 filename ../images/math/pm.png
17762 \begin_layout Standard
17763 To typeset the Laplace operator also
17780 \begin_inset Formula $\nabla^{2}$
17783 ) can be used instead of
17792 \begin_layout Standard
17799 Insert\SpecialChar \menuseparator
17811 \begin_layout Subsection
17812 Self-defined Operators
17813 \begin_inset CommandInset label
17815 name "sub:Self-defined-Operators"
17820 \begin_inset Index idx
17823 \begin_layout Plain Layout
17824 Operators ! self-defined
17832 \begin_layout Standard
17833 With the help of the command
17837 DeclareMathOperator
17840 \begin_inset Index idx
17843 \begin_layout Plain Layout
17848 DeclareMathOperator
17853 custom operators can be defined in the LaTeX-preamble.
17854 Its command scheme is:
17857 \begin_layout Standard
17862 DeclareMathOperator{new command}{display}
17865 \begin_layout Standard
17866 Display can be characters or symbols that define how the operator looks
17868 To define a big operator a * is set behind the command.
17869 All self-defined big operators can have limits as described in
17870 \begin_inset CommandInset ref
17872 reference "sub:Operator-Limits"
17879 \begin_layout Standard
17880 For example the LaTeX-preamble line
17883 \begin_layout Standard
17888 DeclareMathOperator*{
17895 \begin_layout Standard
17896 defines the command
17902 , that inserts a big operator consisting of the lozenge symbol from
17903 \begin_inset CommandInset ref
17905 reference "sub:Miscellaneous-Symbols"
17910 \begin_inset Formula
17912 \Lozenge_{n=1}^{\infty}
17917 The command for this formula is:
17928 \begin_inset Formula $\to$
17934 \begin_layout Standard
17935 \begin_inset VSpace bigskip
17938 When self-defined operators are not used several times in the document,
17939 they can also be defined with the commands
17946 \begin_inset Index idx
17949 \begin_layout Plain Layout
17964 \begin_inset Index idx
17967 \begin_layout Plain Layout
17975 , which have the following scheme:
17978 \begin_layout Standard
17992 \begin_layout Standard
17999 defines big operators,
18008 \begin_layout Standard
18016 \begin_inset space \thinspace{}
18020 \begin_inset space \space{}
18023 be used to use one limit for several operators:
18026 \begin_layout Standard
18027 \begin_inset Formula
18029 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18037 \begin_layout Standard
18038 The command for the formula above is:
18039 \begin_inset Newline newline
18058 \begin_layout Plain Layout
18070 \begin_inset Formula $\to$
18079 \begin_layout Plain Layout
18093 \begin_layout Section
18095 \begin_inset Index idx
18098 \begin_layout Plain Layout
18107 \begin_layout Subsection
18109 \begin_inset CommandInset label
18111 name "sub:Font-Styles"
18116 \begin_inset Index idx
18119 \begin_layout Plain Layout
18128 \begin_layout Standard
18129 Latin letters in formulas can be set in one of the following font styles:
18130 \begin_inset VSpace -2mm
18136 \begin_layout Standard
18138 \begin_inset Tabular
18139 <lyxtabular version="3" rows="7" columns="3">
18140 <features tabularvalignment="middle">
18141 <column alignment="center" valignment="top" width="0">
18142 <column alignment="center" valignment="top" width="0">
18143 <column alignment="center" valignment="top" width="0">
18145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18148 \begin_layout Plain Layout
18154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18157 \begin_layout Plain Layout
18163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18166 \begin_layout Plain Layout
18174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18177 \begin_layout Plain Layout
18186 \begin_layout Plain Layout
18202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18205 \begin_layout Plain Layout
18206 \begin_inset Formula $\mathbb{ABC}$
18214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18217 \begin_layout Plain Layout
18230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18233 \begin_layout Plain Layout
18242 \begin_layout Plain Layout
18258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18261 \begin_layout Plain Layout
18262 \begin_inset Formula $\mathbf{AbC}$
18270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18273 \begin_layout Plain Layout
18286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18289 \begin_layout Plain Layout
18298 \begin_layout Plain Layout
18314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18317 \begin_layout Plain Layout
18318 \begin_inset Formula $\boldsymbol{AbC}$
18326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18329 \begin_layout Plain Layout
18332 arg "font-boldsymbol"
18342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18345 \begin_layout Plain Layout
18354 \begin_layout Plain Layout
18370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18373 \begin_layout Plain Layout
18374 \begin_inset Formula $\mathcal{ABC}$
18382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18385 \begin_layout Plain Layout
18398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18401 \begin_layout Plain Layout
18410 \begin_layout Plain Layout
18426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18429 \begin_layout Plain Layout
18430 \begin_inset Formula $\mathfrak{AbC}$
18438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18441 \begin_layout Plain Layout
18449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18452 \begin_layout Plain Layout
18461 \begin_layout Plain Layout
18477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18480 \begin_layout Plain Layout
18481 \begin_inset Formula $\mathscr{AbC}$
18489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18492 \begin_layout Plain Layout
18506 \begin_layout Standard
18508 \begin_inset Tabular
18509 <lyxtabular version="3" rows="5" columns="3">
18510 <features tabularvalignment="middle">
18511 <column alignment="center" valignment="top" width="0">
18512 <column alignment="center" valignment="top" width="0">
18513 <column alignment="center" valignment="top" width="0">
18515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18518 \begin_layout Plain Layout
18524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18527 \begin_layout Plain Layout
18533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18536 \begin_layout Plain Layout
18544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18547 \begin_layout Plain Layout
18556 \begin_layout Plain Layout
18572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18575 \begin_layout Plain Layout
18576 \begin_inset Formula $\mathit{AbC}$
18584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18587 \begin_layout Plain Layout
18595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18598 \begin_layout Plain Layout
18607 \begin_layout Plain Layout
18623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18626 \begin_layout Plain Layout
18627 \begin_inset Formula $\mathrm{AbC}$
18635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18638 \begin_layout Plain Layout
18651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18654 \begin_layout Plain Layout
18663 \begin_layout Plain Layout
18679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18682 \begin_layout Plain Layout
18683 \begin_inset Formula $\mathsf{AbC}$
18691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18694 \begin_layout Plain Layout
18707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18710 \begin_layout Plain Layout
18719 \begin_layout Plain Layout
18735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18738 \begin_layout Plain Layout
18739 \begin_inset Formula $\mathtt{AbC}$
18747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18750 \begin_layout Plain Layout
18753 arg "font-typewriter"
18769 \begin_layout Standard
18770 \begin_inset Note Greyedout
18773 \begin_layout Plain Layout
18790 can only be used for big letters.
18798 \begin_layout Standard
18799 Predefined is the style
18808 \begin_layout Standard
18809 The style commands work also for letters in mathematical constructs:
18810 \begin_inset Formula
18812 \mathfrak{A=\frac{b}{C}}
18820 \begin_layout Standard
18821 Characters in mathematical text don't appear in a math font style but in
18822 the text font style
18829 That their style can't be set correctly via the text style dialog is a
18834 \begin_layout Plain Layout
18835 \begin_inset CommandInset href
18837 name "LyX-bug #4629"
18838 target "http://www.lyx.org/trac/ticket/4629"
18850 \begin_layout Standard
18851 Instead of the style commands the dialog
18853 Edit\SpecialChar \menuseparator
18854 Math\SpecialChar \menuseparator
18857 or the toolbar button
18858 \begin_inset Graphics
18859 filename ../images/math/font.png
18867 \begin_layout Subsection
18869 \begin_inset CommandInset label
18871 name "sub:Bold-Formulas"
18876 \begin_inset Index idx
18879 \begin_layout Plain Layout
18888 \begin_layout Standard
18889 To make a complete formula bold, the command
18895 from the previous subsection cannot be used, because it doesn't work for
18896 small Greek letters.
18897 Furthermore it prints Latin letters always upright, like in the following
18901 \begin_layout Standard
18902 \begin_inset Formula
18904 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18912 \begin_layout Standard
18913 To display the formula correctly, the command
18920 \begin_inset Formula
18922 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18927 It is also possible to set the formula in a
18929 boldmath environment
18932 This environment is created by inserting the command
18939 \begin_inset Index idx
18942 \begin_layout Plain Layout
18951 To end the environment, the command
18958 \begin_inset Index idx
18961 \begin_layout Plain Layout
18969 is inserted in TeX-mode.
18973 \begin_layout Plain Layout
18983 \begin_inset Formula
18985 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18994 \begin_layout Plain Layout
19006 \begin_layout Subsection
19008 \begin_inset Index idx
19011 \begin_layout Plain Layout
19020 \begin_layout Standard
19021 Formulas can be colored like normal text: Highlight a formula or a formula
19027 Here is a formula in magenta:
19028 \begin_inset Formula
19030 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19038 \begin_layout Standard
19039 You can also define your own colors as described in
19040 \begin_inset CommandInset ref
19042 reference "sub:Colored-Boxes"
19047 They can be used with the TeX code command
19054 \begin_inset Index idx
19057 \begin_layout Plain Layout
19068 \begin_layout Standard
19073 textcolor{color}{characters or formula}
19076 \begin_layout Standard
19077 The following example was colored completely dark green and partly red:
19080 \begin_layout Standard
19084 \begin_layout Plain Layout
19088 textcolor{darkgreen}{
19094 \begin_inset Formula
19096 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19105 \begin_layout Plain Layout
19115 \begin_layout Standard
19116 Due to a bug in LyX only complete formulas can be colored with self-defined
19121 \begin_layout Plain Layout
19122 \begin_inset CommandInset href
19124 name "LyX-bug #5269"
19125 target "http://www.lyx.org/trac/ticket/5269"
19137 \begin_layout Subsection
19139 \begin_inset CommandInset label
19141 name "sub:Font-Sizes"
19146 \begin_inset Index idx
19149 \begin_layout Plain Layout
19158 \begin_layout Standard
19159 For characters in formulas there are, analog to characters in text, the
19160 following size commands:
19163 \begin_layout Standard
19207 \begin_inset Newline newline
19229 \begin_layout Standard
19230 The size produced by the commands depends on the document font size, that
19231 corresponds with the command
19238 The other commands produce smaller or larger sizes than
19245 The font size can however not exceed a certain value.
19246 Is for example the document font size 12
19247 \begin_inset space \thinspace{}
19256 switches to the same size as
19266 \begin_layout Standard
19267 A size command is inserted in TeX-mode before the formula and sets the size
19268 for all following formula and text characters.
19269 To switch back to the initial size, the command
19275 is inserted behind the formula in TeX-mode.
19278 \begin_layout Standard
19279 Within a formula the size can be changed using the following size commands:
19282 \begin_layout Standard
19285 \begin_inset Tabular
19286 <lyxtabular version="3" rows="5" columns="2">
19287 <features tabularvalignment="middle">
19288 <column alignment="center" valignment="top" width="0">
19289 <column alignment="center" valignment="top" width="0">
19291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19294 \begin_layout Plain Layout
19300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19303 \begin_layout Plain Layout
19305 \begin_inset Note Note
19308 \begin_layout Plain Layout
19315 is only used as spacer.
19327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19330 \begin_layout Plain Layout
19334 \begin_inset Index idx
19337 \begin_layout Plain Layout
19350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19353 \begin_layout Plain Layout
19354 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19367 \begin_layout Plain Layout
19375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19378 \begin_layout Plain Layout
19379 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19392 \begin_layout Plain Layout
19400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19403 \begin_layout Plain Layout
19404 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19417 \begin_layout Plain Layout
19425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19428 \begin_layout Plain Layout
19429 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19445 \begin_layout Standard
19446 After entering these commands, a blue box appears in which the formula parts
19450 \begin_layout Standard
19451 There is a further method to change the font size, that though only works
19452 for symbols or letters in mathematical text.
19453 To use it, one of the above text size commands is inserted in mathematical
19455 All following characters until the end of the mathematical text or until
19456 another size command will have the selected size.
19458 \begin_inset VSpace -2mm
19464 \begin_layout Standard
19468 \begin_layout Plain Layout
19478 \begin_inset Formula
19480 A=\frac{B}{c}\cdot\maltese
19486 \begin_inset Formula
19488 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19497 \begin_layout Plain Layout
19509 \begin_layout Standard
19510 \begin_inset VSpace medskip
19513 Before both formulas the command
19520 The command for the second formula is:
19521 \begin_inset Newline newline
19532 \begin_layout Plain Layout
19547 \begin_layout Plain Layout
19562 \begin_layout Plain Layout
19577 \begin_layout Plain Layout
19587 \begin_inset Formula $\to$
19591 \begin_inset Formula $\to$
19595 \begin_inset Newline newline
19599 \begin_inset space \hspace*{}
19613 \begin_layout Plain Layout
19628 \begin_layout Plain Layout
19643 \begin_layout Plain Layout
19655 \begin_layout Standard
19656 If a symbol cannot be displayed in different sizes, it will always be displayed
19657 in the default size.
19660 \begin_layout Section
19662 \begin_inset Index idx
19665 \begin_layout Plain Layout
19674 \begin_layout Standard
19675 Greek letters can also be inserted via the toolbar button
19676 \begin_inset Graphics
19677 filename ../images/math/alpha.png
19683 All international typesetting norms purport that Greek letters in math
19684 have to be typeset italic/slanted.
19685 In some languages, like French or Russian, they are nevertheless sometimes
19689 \begin_layout Subsection
19691 \begin_inset Index idx
19694 \begin_layout Plain Layout
19695 Greek letters ! small
19703 \begin_layout Standard
19704 \begin_inset space \hfill{}
19708 \begin_inset Tabular
19709 <lyxtabular version="3" rows="11" columns="2">
19710 <features tabularvalignment="middle">
19711 <column alignment="center" valignment="top" width="0pt">
19712 <column alignment="center" valignment="top" width="0pt">
19714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19717 \begin_layout Plain Layout
19723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19726 \begin_layout Plain Layout
19734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19737 \begin_layout Plain Layout
19745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19748 \begin_layout Plain Layout
19749 \begin_inset Formula $\alpha$
19759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19762 \begin_layout Plain Layout
19770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19773 \begin_layout Plain Layout
19774 \begin_inset Formula $\beta$
19784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19787 \begin_layout Plain Layout
19795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19798 \begin_layout Plain Layout
19799 \begin_inset Formula $\gamma$
19809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19812 \begin_layout Plain Layout
19820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19823 \begin_layout Plain Layout
19824 \begin_inset Formula $\delta$
19834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19837 \begin_layout Plain Layout
19845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19848 \begin_layout Plain Layout
19849 \begin_inset Formula $\epsilon$
19859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19862 \begin_layout Plain Layout
19870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19873 \begin_layout Plain Layout
19874 \begin_inset Formula $\varepsilon$
19884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19887 \begin_layout Plain Layout
19895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19898 \begin_layout Plain Layout
19899 \begin_inset Formula $\zeta$
19909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19912 \begin_layout Plain Layout
19920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19923 \begin_layout Plain Layout
19924 \begin_inset Formula $\eta$
19934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19937 \begin_layout Plain Layout
19945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19948 \begin_layout Plain Layout
19949 \begin_inset Formula $\theta$
19959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19962 \begin_layout Plain Layout
19970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19973 \begin_layout Plain Layout
19974 \begin_inset Formula $\vartheta$
19988 \begin_inset space \hfill{}
19992 \begin_inset Tabular
19993 <lyxtabular version="3" rows="12" columns="2">
19994 <features tabularvalignment="middle">
19995 <column alignment="center" valignment="top" width="0pt">
19996 <column alignment="center" valignment="top" width="0pt">
19998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20001 \begin_layout Plain Layout
20007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20010 \begin_layout Plain Layout
20018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20021 \begin_layout Plain Layout
20029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20032 \begin_layout Plain Layout
20033 \begin_inset Formula $\iota$
20043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20046 \begin_layout Plain Layout
20054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20057 \begin_layout Plain Layout
20058 \begin_inset Formula $\kappa$
20068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20071 \begin_layout Plain Layout
20079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20082 \begin_layout Plain Layout
20083 \begin_inset Formula $\varkappa$
20093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20096 \begin_layout Plain Layout
20104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20107 \begin_layout Plain Layout
20108 \begin_inset Formula $\lambda$
20118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20121 \begin_layout Plain Layout
20129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20132 \begin_layout Plain Layout
20133 \begin_inset Formula $\mu$
20143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20146 \begin_layout Plain Layout
20154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20157 \begin_layout Plain Layout
20158 \begin_inset Formula $\nu$
20168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20171 \begin_layout Plain Layout
20179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20182 \begin_layout Plain Layout
20183 \begin_inset Formula $\xi$
20193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20196 \begin_layout Plain Layout
20202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20205 \begin_layout Plain Layout
20206 \begin_inset Formula $o$
20216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20219 \begin_layout Plain Layout
20227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20230 \begin_layout Plain Layout
20231 \begin_inset Formula $\pi$
20241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20244 \begin_layout Plain Layout
20252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20255 \begin_layout Plain Layout
20256 \begin_inset Formula $\varpi$
20266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20269 \begin_layout Plain Layout
20277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20280 \begin_layout Plain Layout
20281 \begin_inset Formula $\rho$
20295 \begin_inset space \hfill{}
20299 \begin_inset Tabular
20300 <lyxtabular version="3" rows="11" columns="2">
20301 <features tabularvalignment="middle">
20302 <column alignment="center" valignment="top" width="0pt">
20303 <column alignment="center" valignment="top" width="0pt">
20305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20308 \begin_layout Plain Layout
20314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20317 \begin_layout Plain Layout
20325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20328 \begin_layout Plain Layout
20336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20339 \begin_layout Plain Layout
20340 \begin_inset Formula $\varrho$
20350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20353 \begin_layout Plain Layout
20361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20364 \begin_layout Plain Layout
20365 \begin_inset Formula $\sigma$
20375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20378 \begin_layout Plain Layout
20386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20389 \begin_layout Plain Layout
20390 \begin_inset Formula $\varsigma$
20400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20403 \begin_layout Plain Layout
20411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20414 \begin_layout Plain Layout
20415 \begin_inset Formula $\tau$
20425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20428 \begin_layout Plain Layout
20436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20439 \begin_layout Plain Layout
20440 \begin_inset Formula $\upsilon$
20450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20453 \begin_layout Plain Layout
20461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20464 \begin_layout Plain Layout
20465 \begin_inset Formula $\phi$
20475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20478 \begin_layout Plain Layout
20486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20489 \begin_layout Plain Layout
20490 \begin_inset Formula $\varphi$
20500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20503 \begin_layout Plain Layout
20511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20514 \begin_layout Plain Layout
20515 \begin_inset Formula $\chi$
20525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20528 \begin_layout Plain Layout
20536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20539 \begin_layout Plain Layout
20540 \begin_inset Formula $\psi$
20550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20553 \begin_layout Plain Layout
20561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20564 \begin_layout Plain Layout
20565 \begin_inset Formula $\omega$
20579 \begin_inset space \hfill{}
20585 \begin_layout Standard
20586 \begin_inset VSpace medskip
20592 \begin_layout Standard
20593 How to create special upright Greek letters is explained in
20594 \begin_inset CommandInset ref
20596 reference "sub:Upright-small-Greek"
20603 \begin_layout Subsection
20605 \begin_inset Index idx
20608 \begin_layout Plain Layout
20609 Greek letters ! big
20617 \begin_layout Standard
20618 \begin_inset space \hfill{}
20622 \begin_inset Tabular
20623 <lyxtabular version="3" rows="7" columns="2">
20624 <features tabularvalignment="middle">
20625 <column alignment="center" valignment="top" width="0pt">
20626 <column alignment="center" valignment="top" width="0pt">
20628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20631 \begin_layout Plain Layout
20637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20640 \begin_layout Plain Layout
20648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20651 \begin_layout Plain Layout
20659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20662 \begin_layout Plain Layout
20663 \begin_inset Formula $\Gamma$
20673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20676 \begin_layout Plain Layout
20684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20687 \begin_layout Plain Layout
20688 \begin_inset Formula $\Delta$
20698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20701 \begin_layout Plain Layout
20709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20712 \begin_layout Plain Layout
20713 \begin_inset Formula $\Theta$
20723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20726 \begin_layout Plain Layout
20734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20737 \begin_layout Plain Layout
20738 \begin_inset Formula $\Lambda$
20748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20751 \begin_layout Plain Layout
20759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20762 \begin_layout Plain Layout
20763 \begin_inset Formula $\Xi$
20773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20776 \begin_layout Plain Layout
20784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20787 \begin_layout Plain Layout
20788 \begin_inset Formula $\Pi$
20802 \begin_inset space \hfill{}
20806 \begin_inset Tabular
20807 <lyxtabular version="3" rows="6" columns="2">
20808 <features tabularvalignment="middle">
20809 <column alignment="center" valignment="top" width="0pt">
20810 <column alignment="center" valignment="top" width="0pt">
20812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20815 \begin_layout Plain Layout
20821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20824 \begin_layout Plain Layout
20832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20835 \begin_layout Plain Layout
20843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20846 \begin_layout Plain Layout
20847 \begin_inset Formula $\Sigma$
20857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20860 \begin_layout Plain Layout
20868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20871 \begin_layout Plain Layout
20872 \begin_inset Formula $\Upsilon$
20882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20885 \begin_layout Plain Layout
20893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20896 \begin_layout Plain Layout
20897 \begin_inset Formula $\Phi$
20907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20910 \begin_layout Plain Layout
20918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20921 \begin_layout Plain Layout
20922 \begin_inset Formula $\Psi$
20932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20935 \begin_layout Plain Layout
20943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20946 \begin_layout Plain Layout
20947 \begin_inset Formula $\Omega$
20961 \begin_inset space \hfill{}
20967 \begin_layout Standard
20968 \begin_inset VSpace medskip
20971 That the big Greek letters appear upright is caused by a design bug when
20973 To get correct italic big letters, begin every command with
20978 For example the command
20985 \begin_inset Formula $\varGamma$
20989 Another way is to load the package
20997 \begin_layout Plain Layout
21002 is part of the LaTeX-package
21007 \begin_inset Index idx
21010 \begin_layout Plain Layout
21015 \begin_layout Plain Layout
21035 \begin_inset Index idx
21038 \begin_layout Plain Layout
21044 with the LaTeX-preamble line
21047 \begin_layout Standard
21052 usepackage{fixmath}
21055 \begin_layout Standard
21056 Then all big Greek letters in a document will automatically be typeset italic.
21059 \begin_layout Subsection
21061 \begin_inset Index idx
21064 \begin_layout Plain Layout
21065 Greek letters ! bold
21073 \begin_layout Standard
21074 Greek letters cannot be set with different font styles like Latin letters.
21075 They can only be made bold with the command
21082 \begin_inset Index idx
21085 \begin_layout Plain Layout
21096 \begin_layout Standard
21098 \begin_inset Tabular
21099 <lyxtabular version="3" rows="3" columns="2">
21100 <features tabularvalignment="middle">
21101 <column alignment="center" valignment="top" width="0">
21102 <column alignment="center" valignment="top" width="0">
21104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21107 \begin_layout Plain Layout
21113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21116 \begin_layout Plain Layout
21124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21127 \begin_layout Plain Layout
21139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21142 \begin_layout Plain Layout
21143 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21156 \begin_layout Plain Layout
21168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21171 \begin_layout Plain Layout
21172 \begin_inset Formula $\theta\boldsymbol{\theta}$
21188 \begin_layout Standard
21189 \begin_inset Newpage newpage
21195 \begin_layout Section
21200 \begin_layout Plain Layout
21213 \begin_layout Plain Layout
21214 A list with all symbols of most of the LaTeX-packages can be found in
21215 \begin_inset CommandInset citation
21230 \begin_layout Plain Layout
21238 \begin_inset Note Note
21241 \begin_layout Plain Layout
21244 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21247 \begin_layout Plain Layout
21250 texorpdfstring is in section
21251 \begin_inset CommandInset ref
21253 reference "sub:Formulas-in-Section"
21263 \begin_inset Index idx
21266 \begin_layout Plain Layout
21275 \begin_layout Standard
21276 Many of the symbols listed in this section can also be inserted via the
21278 \begin_inset Graphics
21279 filename ../images/math/nabla.png
21285 \begin_inset Graphics
21286 filename ../images/math/digamma.png
21294 \begin_layout Subsection
21295 Mathematical Symbols
21296 \begin_inset CommandInset label
21298 name "sub:Mathematical-Symbols"
21303 \begin_inset Index idx
21306 \begin_layout Plain Layout
21307 Symbols ! mathematical
21315 \begin_layout Standard
21316 \begin_inset space \hfill{}
21320 \begin_inset Tabular
21321 <lyxtabular version="3" rows="10" columns="2">
21322 <features tabularvalignment="middle">
21323 <column alignment="center" valignment="top" width="0pt">
21324 <column alignment="center" valignment="top" width="0pt">
21326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21329 \begin_layout Plain Layout
21335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21338 \begin_layout Plain Layout
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 $\neg$
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 $\Im$
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 $\Re$
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 $\aleph$
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 $\partial$
21471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21474 \begin_layout Plain Layout
21482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21485 \begin_layout Plain Layout
21486 \begin_inset Formula $\infty$
21496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21499 \begin_layout Plain Layout
21507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21510 \begin_layout Plain Layout
21511 \begin_inset Formula $\wp$
21521 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21524 \begin_layout Plain Layout
21532 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21535 \begin_layout Plain Layout
21536 \begin_inset Formula $\imath$
21546 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21549 \begin_layout Plain Layout
21557 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21560 \begin_layout Plain Layout
21561 \begin_inset Formula $\jmath$
21575 \begin_inset space \hfill{}
21579 \begin_inset Tabular
21580 <lyxtabular version="3" rows="10" columns="2">
21581 <features tabularvalignment="middle">
21582 <column alignment="center" valignment="top" width="0pt">
21583 <column alignment="center" valignment="top" width="0pt">
21585 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21588 \begin_layout Plain Layout
21594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21597 \begin_layout Plain Layout
21599 \begin_inset Note Note
21602 \begin_layout Plain Layout
21609 is only used as spacer.
21621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21624 \begin_layout Plain Layout
21632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21635 \begin_layout Plain Layout
21636 \begin_inset Formula $\forall$
21646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21649 \begin_layout Plain Layout
21657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21660 \begin_layout Plain Layout
21661 \begin_inset Formula $\exists$
21671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21674 \begin_layout Plain Layout
21682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21685 \begin_layout Plain Layout
21686 \begin_inset Formula $\nexists$
21696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21699 \begin_layout Plain Layout
21707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21710 \begin_layout Plain Layout
21711 \begin_inset Formula $\emptyset$
21721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21724 \begin_layout Plain Layout
21732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21735 \begin_layout Plain Layout
21736 \begin_inset Formula $\varnothing$
21746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21749 \begin_layout Plain Layout
21757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21760 \begin_layout Plain Layout
21761 \begin_inset Formula $\dag$
21771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21774 \begin_layout Plain Layout
21782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21785 \begin_layout Plain Layout
21786 \begin_inset Formula $\ddag$
21796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21799 \begin_layout Plain Layout
21807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21810 \begin_layout Plain Layout
21814 \begin_layout Plain Layout
21824 \begin_inset Formula $\complement$
21831 \begin_layout Plain Layout
21845 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21848 \begin_layout Plain Layout
21856 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21859 \begin_layout Plain Layout
21860 \begin_inset Formula $\Bbbk$
21874 \begin_inset space \hfill{}
21878 \begin_inset Tabular
21879 <lyxtabular version="3" rows="10" columns="2">
21880 <features tabularvalignment="middle">
21881 <column alignment="center" valignment="top" width="0pt">
21882 <column alignment="center" valignment="top" width="0pt">
21884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21887 \begin_layout Plain Layout
21893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21896 \begin_layout Plain Layout
21904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21907 \begin_layout Plain Layout
21915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21918 \begin_layout Plain Layout
21919 \begin_inset Formula $\prime$
21929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21932 \begin_layout Plain Layout
21940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21943 \begin_layout Plain Layout
21944 \begin_inset Formula $\backprime$
21954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21957 \begin_layout Plain Layout
21965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21968 \begin_layout Plain Layout
21969 \begin_inset Formula $\mho$
21979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21982 \begin_layout Plain Layout
21990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21993 \begin_layout Plain Layout
21994 \begin_inset Formula $\triangle$
22004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22007 \begin_layout Plain Layout
22015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22018 \begin_layout Plain Layout
22019 \begin_inset Formula $\angle$
22029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22032 \begin_layout Plain Layout
22040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22043 \begin_layout Plain Layout
22044 \begin_inset Formula $\measuredangle$
22054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22057 \begin_layout Plain Layout
22065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22068 \begin_layout Plain Layout
22069 \begin_inset Formula $\sphericalangle$
22079 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22082 \begin_layout Plain Layout
22090 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22093 \begin_layout Plain Layout
22094 \begin_inset Formula $\top$
22104 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22107 \begin_layout Plain Layout
22115 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22118 \begin_layout Plain Layout
22119 \begin_inset Formula $\bot$
22133 \begin_inset space \hfill{}
22139 \begin_layout Subsection
22140 Miscellaneous Symbols
22141 \begin_inset CommandInset label
22143 name "sub:Miscellaneous-Symbols"
22148 \begin_inset Index idx
22151 \begin_layout Plain Layout
22152 Symbols ! miscellaneous
22160 \begin_layout Standard
22163 \begin_inset Tabular
22164 <lyxtabular version="3" rows="10" columns="2">
22165 <features tabularvalignment="middle">
22166 <column alignment="center" valignment="top" width="0pt">
22167 <column alignment="center" valignment="top" width="0pt">
22169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22172 \begin_layout Plain Layout
22178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22181 \begin_layout Plain Layout
22189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22192 \begin_layout Plain Layout
22200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22203 \begin_layout Plain Layout
22204 \begin_inset Formula $\flat$
22214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22217 \begin_layout Plain Layout
22225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22228 \begin_layout Plain Layout
22229 \begin_inset Formula $\natural$
22239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22242 \begin_layout Plain Layout
22250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22253 \begin_layout Plain Layout
22254 \begin_inset Formula $\sharp$
22264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22267 \begin_layout Plain Layout
22275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22278 \begin_layout Plain Layout
22279 \begin_inset Formula $\surd$
22289 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22292 \begin_layout Plain Layout
22300 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22303 \begin_layout Plain Layout
22304 \begin_inset Formula $\checkmark$
22314 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22317 \begin_layout Plain Layout
22325 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22328 \begin_layout Plain Layout
22329 \begin_inset Formula $\yen$
22339 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22342 \begin_layout Plain Layout
22350 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22353 \begin_layout Plain Layout
22354 \begin_inset Formula $\pounds$
22364 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22367 \begin_layout Plain Layout
22373 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22376 \begin_layout Plain Layout
22377 \begin_inset Formula $\$$
22387 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22390 \begin_layout Plain Layout
22396 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22399 \begin_layout Plain Layout
22400 \begin_inset Formula $§$
22414 \begin_inset Tabular
22415 <lyxtabular version="3" rows="10" columns="2">
22416 <features tabularvalignment="middle">
22417 <column alignment="center" valignment="top" width="0">
22418 <column alignment="center" valignment="top" width="0">
22420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22423 \begin_layout Plain Layout
22429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22432 \begin_layout Plain Layout
22440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22443 \begin_layout Plain Layout
22451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22454 \begin_layout Plain Layout
22455 \begin_inset Formula $\hbar$
22465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22468 \begin_layout Plain Layout
22476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22479 \begin_layout Plain Layout
22480 \begin_inset Formula $\hslash$
22490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22493 \begin_layout Plain Layout
22501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22504 \begin_layout Plain Layout
22505 \begin_inset Formula $\clubsuit$
22515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22518 \begin_layout Plain Layout
22526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22529 \begin_layout Plain Layout
22530 \begin_inset Formula $\spadesuit$
22540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22543 \begin_layout Plain Layout
22551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22554 \begin_layout Plain Layout
22555 \begin_inset Formula $\bigstar$
22565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22568 \begin_layout Plain Layout
22576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22579 \begin_layout Plain Layout
22580 \begin_inset Formula $\blacklozenge$
22590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22593 \begin_layout Plain Layout
22601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22604 \begin_layout Plain Layout
22605 \begin_inset Formula $\blacktriangle$
22615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22618 \begin_layout Plain Layout
22626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22629 \begin_layout Plain Layout
22630 \begin_inset Formula $\blacktriangledown$
22640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22643 \begin_layout Plain Layout
22651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22654 \begin_layout Plain Layout
22655 \begin_inset Formula $\bullet$
22669 \begin_inset Tabular
22670 <lyxtabular version="3" rows="10" columns="2">
22671 <features tabularvalignment="middle">
22672 <column alignment="center" valignment="top" width="0pt">
22673 <column alignment="center" valignment="top" width="0pt">
22675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22678 \begin_layout Plain Layout
22684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22687 \begin_layout Plain Layout
22695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22698 \begin_layout Plain Layout
22706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22709 \begin_layout Plain Layout
22710 \begin_inset Formula $\diamondsuit$
22720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22723 \begin_layout Plain Layout
22731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22734 \begin_layout Plain Layout
22735 \begin_inset Formula $\Diamond$
22745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22748 \begin_layout Plain Layout
22756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22759 \begin_layout Plain Layout
22760 \begin_inset Formula $\heartsuit$
22770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22773 \begin_layout Plain Layout
22781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22784 \begin_layout Plain Layout
22785 \begin_inset Formula $\P$
22795 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22798 \begin_layout Plain Layout
22806 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22809 \begin_layout Plain Layout
22810 \begin_inset Formula $\copyright$
22820 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22823 \begin_layout Plain Layout
22831 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22834 \begin_layout Plain Layout
22835 \begin_inset Formula $\circledR$
22845 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22848 \begin_layout Plain Layout
22856 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22859 \begin_layout Plain Layout
22860 \begin_inset Formula $\maltese$
22870 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22873 \begin_layout Plain Layout
22881 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22884 \begin_layout Plain Layout
22885 \begin_inset Formula $\diagup$
22895 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22898 \begin_layout Plain Layout
22906 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22909 \begin_layout Plain Layout
22910 \begin_inset Formula $\diagdown$
22926 \begin_layout Standard
22927 \begin_inset VSpace medskip
22930 More symbols are listed in
22931 \begin_inset CommandInset ref
22933 reference "sub:Miscellaneous-special-Characters"
22940 \begin_layout Standard
22941 Some symbols can be displayed in different sizes, see
22942 \begin_inset CommandInset ref
22944 reference "sub:Font-Sizes"
22951 \begin_layout Subsection
22953 \begin_inset Index idx
22956 \begin_layout Plain Layout
22957 Symbols ! Euro-symbol
22963 \begin_inset Index idx
22966 \begin_layout Plain Layout
22973 \begin_layout Plain Layout
22990 \begin_layout Standard
22991 To use the Euro symbol in formulas, the LaTeX-package
22996 \begin_inset Index idx
22999 \begin_layout Plain Layout
23005 must be installed and loaded with the LaTeX-preamble line
23008 \begin_layout Standard
23013 usepackage[gennarrow]{eurosym}
23016 \begin_layout Standard
23017 The Euro symbol can now be inserted with the command
23024 \begin_inset Index idx
23027 \begin_layout Plain Layout
23038 \begin_layout Standard
23039 The Euro symbol can directly be inserted with the € key in mathematical
23040 text, without having
23055 can also be inserted in TeX-mode.
23056 The official currency symbol can then be inserted with the command
23063 \begin_inset Index idx
23066 \begin_layout Plain Layout
23074 , that is only available in TeX-mode.
23077 \begin_layout Standard
23081 \begin_layout Plain Layout
23091 \begin_inset Note Note
23094 \begin_layout Plain Layout
23095 The following table will only be displayed when the LaTeX-package
23107 \begin_layout Standard
23108 An overview about the different Euro symbols:
23111 \begin_layout Standard
23113 \begin_inset Tabular
23114 <lyxtabular version="3" rows="4" columns="3">
23115 <features tabularvalignment="middle">
23116 <column alignment="center" valignment="top" width="0pt">
23117 <column alignment="center" valignment="top" width="0pt">
23118 <column alignment="center" valignment="top" width="0pt">
23120 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23123 \begin_layout Plain Layout
23129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23132 \begin_layout Plain Layout
23138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23141 \begin_layout Plain Layout
23149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23152 \begin_layout Plain Layout
23158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23161 \begin_layout Plain Layout
23169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23172 \begin_layout Plain Layout
23173 \begin_inset Formula $\euro$
23183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23186 \begin_layout Plain Layout
23192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23195 \begin_layout Plain Layout
23201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23204 \begin_layout Plain Layout
23205 \begin_inset Formula $\mbox{€}$
23215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23218 \begin_layout Plain Layout
23224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23227 \begin_layout Plain Layout
23235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23238 \begin_layout Plain Layout
23242 \begin_layout Plain Layout
23264 \begin_layout Standard
23268 \begin_layout Plain Layout
23278 \begin_inset Note Note
23281 \begin_layout Plain Layout
23282 The following will be displayed when the LaTeX-package
23294 \begin_layout Standard
23295 You need to install the LaTeX-package
23299 to see the rest of this subsection in the output.
23302 \begin_layout Standard
23306 \begin_layout Plain Layout
23318 \begin_layout Section
23320 \begin_inset CommandInset label
23322 name "sec:Relations"
23327 \begin_inset Index idx
23330 \begin_layout Plain Layout
23337 \begin_inset Index idx
23340 \begin_layout Plain Layout
23345 \begin_layout Plain Layout
23356 \begin_layout Plain Layout
23371 \begin_layout Standard
23372 All relations can also be inserted via the toolbar button
23373 \begin_inset Graphics
23374 filename ../images/math/leq.png
23382 \begin_layout Standard
23383 \begin_inset space \hfill{}
23387 \begin_inset Tabular
23388 <lyxtabular version="3" rows="17" columns="2">
23389 <features tabularvalignment="middle">
23390 <column alignment="center" valignment="top" width="0pt">
23391 <column alignment="center" valignment="top" width="0pt">
23393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23396 \begin_layout Plain Layout
23402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23405 \begin_layout Plain Layout
23413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23416 \begin_layout Plain Layout
23422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23425 \begin_layout Plain Layout
23426 \begin_inset Formula $<$
23436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23439 \begin_layout Plain Layout
23447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23450 \begin_layout Plain Layout
23451 \begin_inset Formula $\le$
23461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23464 \begin_layout Plain Layout
23472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23475 \begin_layout Plain Layout
23476 \begin_inset Formula $\ll$
23486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23489 \begin_layout Plain Layout
23497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23500 \begin_layout Plain Layout
23501 \begin_inset Formula $\prec$
23511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23514 \begin_layout Plain Layout
23522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23525 \begin_layout Plain Layout
23526 \begin_inset Formula $\preceq$
23536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23539 \begin_layout Plain Layout
23547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23550 \begin_layout Plain Layout
23551 \begin_inset Formula $\subset$
23561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23564 \begin_layout Plain Layout
23572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23575 \begin_layout Plain Layout
23576 \begin_inset Formula $\subseteq$
23586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23589 \begin_layout Plain Layout
23597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23600 \begin_layout Plain Layout
23601 \begin_inset Formula $\sqsubseteq$
23611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23614 \begin_layout Plain Layout
23622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23625 \begin_layout Plain Layout
23626 \begin_inset Formula $\in$
23636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23639 \begin_layout Plain Layout
23647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23650 \begin_layout Plain Layout
23651 \begin_inset Formula $\vdash$
23661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23664 \begin_layout Plain Layout
23672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23675 \begin_layout Plain Layout
23676 \begin_inset Formula $\smile$
23686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23689 \begin_layout Plain Layout
23697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23700 \begin_layout Plain Layout
23701 \begin_inset Formula $\lhd$
23711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23714 \begin_layout Plain Layout
23722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23725 \begin_layout Plain Layout
23726 \begin_inset Formula $\unlhd$
23736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23739 \begin_layout Plain Layout
23747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23750 \begin_layout Plain Layout
23751 \begin_inset Formula $\gtrless$
23761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23764 \begin_layout Plain Layout
23772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23775 \begin_layout Plain Layout
23776 \begin_inset Formula $\mid$
23786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23789 \begin_layout Plain Layout
23797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23800 \begin_layout Plain Layout
23801 \begin_inset Formula $\nmid$
23815 \begin_inset space \hfill{}
23819 \begin_inset Tabular
23820 <lyxtabular version="3" rows="17" columns="2">
23821 <features tabularvalignment="middle">
23822 <column alignment="center" valignment="top" width="0pt">
23823 <column alignment="center" valignment="top" width="0pt">
23825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23828 \begin_layout Plain Layout
23834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23837 \begin_layout Plain Layout
23845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23848 \begin_layout Plain Layout
23854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23857 \begin_layout Plain Layout
23858 \begin_inset Formula $=$
23868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23871 \begin_layout Plain Layout
23879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23882 \begin_layout Plain Layout
23883 \begin_inset Formula $\not=$
23893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23896 \begin_layout Plain Layout
23904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23907 \begin_layout Plain Layout
23908 \begin_inset Formula $\equiv$
23918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23921 \begin_layout Plain Layout
23929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23932 \begin_layout Plain Layout
23933 \begin_inset Formula $\sim$
23943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23946 \begin_layout Plain Layout
23954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23957 \begin_layout Plain Layout
23958 \begin_inset Formula $\simeq$
23968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23971 \begin_layout Plain Layout
23979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23982 \begin_layout Plain Layout
23983 \begin_inset Formula $\approx$
23993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23996 \begin_layout Plain Layout
24004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24007 \begin_layout Plain Layout
24008 \begin_inset Formula $\cong$
24018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24021 \begin_layout Plain Layout
24029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24032 \begin_layout Plain Layout
24033 \begin_inset Formula $\bowtie$
24043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24046 \begin_layout Plain Layout
24054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24057 \begin_layout Plain Layout
24058 \begin_inset Formula $\notin$
24068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24071 \begin_layout Plain Layout
24079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24082 \begin_layout Plain Layout
24083 \begin_inset Formula $\perp$
24093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24096 \begin_layout Plain Layout
24104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24107 \begin_layout Plain Layout
24108 \begin_inset Formula $\propto$
24118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24121 \begin_layout Plain Layout
24129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24132 \begin_layout Plain Layout
24133 \begin_inset Formula $\asymp$
24143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24146 \begin_layout Plain Layout
24154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24157 \begin_layout Plain Layout
24158 \begin_inset Formula $\doteq$
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
24183 \begin_inset Formula $\circeq$
24193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24196 \begin_layout Plain Layout
24204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24207 \begin_layout Plain Layout
24208 \begin_inset Formula $\models$
24218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24221 \begin_layout Plain Layout
24229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24232 \begin_layout Plain Layout
24233 \begin_inset Formula $\widehat{=}$
24247 \begin_inset space \hfill{}
24251 \begin_inset Tabular
24252 <lyxtabular version="3" rows="17" columns="2">
24253 <features tabularvalignment="middle">
24254 <column alignment="center" valignment="top" width="0pt">
24255 <column alignment="center" valignment="top" width="0pt">
24257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24260 \begin_layout Plain Layout
24266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24269 \begin_layout Plain Layout
24277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24280 \begin_layout Plain Layout
24286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24289 \begin_layout Plain Layout
24290 \begin_inset Formula $>$
24300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24303 \begin_layout Plain Layout
24311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24314 \begin_layout Plain Layout
24315 \begin_inset Formula $\ge$
24325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24328 \begin_layout Plain Layout
24336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24339 \begin_layout Plain Layout
24340 \begin_inset Formula $\gg$
24350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24353 \begin_layout Plain Layout
24361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24364 \begin_layout Plain Layout
24365 \begin_inset Formula $\succ$
24375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24378 \begin_layout Plain Layout
24386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24389 \begin_layout Plain Layout
24390 \begin_inset Formula $\succeq$
24400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24403 \begin_layout Plain Layout
24411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24414 \begin_layout Plain Layout
24415 \begin_inset Formula $\supset$
24425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24428 \begin_layout Plain Layout
24436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24439 \begin_layout Plain Layout
24440 \begin_inset Formula $\supseteq$
24450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24453 \begin_layout Plain Layout
24461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24464 \begin_layout Plain Layout
24465 \begin_inset Formula $\sqsupseteq$
24475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24478 \begin_layout Plain Layout
24486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24489 \begin_layout Plain Layout
24490 \begin_inset Formula $\ni$
24500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24503 \begin_layout Plain Layout
24511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24514 \begin_layout Plain Layout
24515 \begin_inset Formula $\dashv$
24525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24528 \begin_layout Plain Layout
24536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24539 \begin_layout Plain Layout
24540 \begin_inset Formula $\frown$
24550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24553 \begin_layout Plain Layout
24561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24564 \begin_layout Plain Layout
24565 \begin_inset Formula $\rhd$
24575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24578 \begin_layout Plain Layout
24586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24589 \begin_layout Plain Layout
24590 \begin_inset Formula $\unrhd$
24600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24603 \begin_layout Plain Layout
24611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24614 \begin_layout Plain Layout
24615 \begin_inset Formula $\lessgtr$
24625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24628 \begin_layout Plain Layout
24636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24639 \begin_layout Plain Layout
24640 \begin_inset Formula $\parallel$
24650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24653 \begin_layout Plain Layout
24661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24664 \begin_layout Plain Layout
24665 \begin_inset Formula $\nparallel$
24679 \begin_inset space \hfill{}
24685 \begin_layout Standard
24686 \begin_inset VSpace medskip
24701 are bigger than the equal looking operators
24716 \begin_layout Standard
24717 Relations are, in contrary to symbols, always surrounded by space.
24720 \begin_layout Standard
24721 Relations with labels can be created with the command
24728 \begin_inset Index idx
24731 \begin_layout Plain Layout
24742 \begin_layout Standard
24744 \begin_inset Tabular
24745 <lyxtabular version="3" rows="2" columns="2">
24746 <features tabularvalignment="middle">
24747 <column alignment="center" valignment="top" width="0">
24748 <column alignment="center" valignment="top" width="0">
24750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24753 \begin_layout Plain Layout
24759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24762 \begin_layout Plain Layout
24764 \begin_inset Note Note
24767 \begin_layout Plain Layout
24774 is only used as spacer.
24786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24789 \begin_layout Plain Layout
24796 \begin_layout Plain Layout
24813 \begin_layout Plain Layout
24823 \begin_inset Formula $\downarrow$
24832 \begin_layout Plain Layout
24845 \begin_layout Plain Layout
24859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24862 \begin_layout Plain Layout
24863 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24879 \begin_layout Section
24883 \begin_layout Subsection
24884 Predefined Functions
24885 \begin_inset CommandInset label
24887 name "sub:Predefined-Functions"
24892 \begin_inset Index idx
24895 \begin_layout Plain Layout
24896 Functions ! predefined
24904 \begin_layout Standard
24905 In general, variables are set
24909 in mathematical expressions, but not function names, because
24910 \begin_inset Formula $sin$
24913 could be misunderstood as
24914 \begin_inset Formula $s\cdot i\cdot n$
24918 Therefore there are predefined functions, that are additionally a bit separated
24920 They are inserted as commands starting with a backslash before their name.
24923 \begin_layout Standard
24925 \begin_inset Tabular
24926 <lyxtabular version="3" rows="2" columns="4">
24927 <features tabularvalignment="middle">
24928 <column alignment="center" valignment="top" width="0pt">
24929 <column alignment="center" valignment="top" width="0pt">
24930 <column alignment="center" valignment="top" width="0pt">
24931 <column alignment="center" valignment="top" width="0pt">
24933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24936 \begin_layout Plain Layout
24942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24945 \begin_layout Plain Layout
24951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24954 \begin_layout Plain Layout
24960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24963 \begin_layout Plain Layout
24971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24974 \begin_layout Plain Layout
24980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24983 \begin_layout Plain Layout
24984 \begin_inset Formula $Asin(x)+B$
24992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24995 \begin_layout Plain Layout
25003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25006 \begin_layout Plain Layout
25007 \begin_inset Formula $A\sin(x)+B$
25023 \begin_layout Standard
25024 The following functions are predefined:
25027 \begin_layout Standard
25028 \begin_inset VSpace -2mm
25034 \begin_layout Standard
25036 \begin_inset Tabular
25037 <lyxtabular version="3" rows="9" columns="4">
25038 <features tabularvalignment="middle">
25039 <column alignment="center" valignment="top" width="0pt">
25040 <column alignment="center" valignment="top" width="0pt">
25041 <column alignment="center" valignment="top" width="0pt">
25042 <column alignment="center" valignment="top" width="0pt">
25044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25047 \begin_layout Plain Layout
25053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25056 \begin_layout Plain Layout
25062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25065 \begin_layout Plain Layout
25071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25074 \begin_layout Plain Layout
25082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25085 \begin_layout Plain Layout
25093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25096 \begin_layout Plain Layout
25104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25107 \begin_layout Plain Layout
25115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25118 \begin_layout Plain Layout
25128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25131 \begin_layout Plain Layout
25139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25142 \begin_layout Plain Layout
25150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25153 \begin_layout Plain Layout
25161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25164 \begin_layout Plain Layout
25174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25177 \begin_layout Plain Layout
25185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25188 \begin_layout Plain Layout
25196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25199 \begin_layout Plain Layout
25207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25210 \begin_layout Plain Layout
25220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25223 \begin_layout Plain Layout
25231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25234 \begin_layout Plain Layout
25242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25245 \begin_layout Plain Layout
25253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25256 \begin_layout Plain Layout
25266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25269 \begin_layout Plain Layout
25277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25280 \begin_layout Plain Layout
25288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25291 \begin_layout Plain Layout
25299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25302 \begin_layout Plain Layout
25312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25315 \begin_layout Plain Layout
25323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25326 \begin_layout Plain Layout
25334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25337 \begin_layout Plain Layout
25345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25348 \begin_layout Plain Layout
25358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25361 \begin_layout Plain Layout
25369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25372 \begin_layout Plain Layout
25380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25383 \begin_layout Plain Layout
25391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25394 \begin_layout Plain Layout
25404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25407 \begin_layout Plain Layout
25415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25418 \begin_layout Plain Layout
25426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25429 \begin_layout Plain Layout
25437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25440 \begin_layout Plain Layout
25456 \begin_layout Standard
25457 They can also be inserted with the math toolbar button
25458 \begin_inset Graphics
25459 filename ../images/math/functions.png
25467 \begin_layout Subsection
25468 Self-defined Functions
25469 \begin_inset Index idx
25472 \begin_layout Plain Layout
25473 Functions ! self-defined
25481 \begin_layout Standard
25482 To use a function that is not predefined, like for example the sign function
25483 sgn(x), there are two possibilities:
25486 \begin_layout Itemize
25487 Define the function by inserting the following line to the LaTeX-preamble
25491 \begin_layout Plain Layout
25496 DeclareMathOperator
25499 \begin_inset CommandInset ref
25501 reference "sub:Self-defined-Operators"
25511 \begin_inset Newline newline
25515 \begin_inset VSpace -3mm
25519 \begin_inset Newline newline
25526 DeclareMathOperator{
25531 \begin_inset Index idx
25534 \begin_layout Plain Layout
25539 DeclareMathOperator
25545 \begin_inset Newline newline
25549 \begin_inset VSpace -2mm
25553 \begin_inset Newline newline
25556 Now the new defined function can be called with the command
25565 \begin_layout Itemize
25566 Write the formula as usual, mark the formula name, in our example the letters
25571 , and change it to mathematical text.
25572 At last a space is inserted between prefactor and function.
25575 \begin_layout Standard
25576 The result is the same with both methods as with a predefined function
25580 \begin_layout Plain Layout
25581 In LyX self-defined functions are displayed red, predefined ones black.
25589 \begin_layout Standard
25591 \begin_inset Tabular
25592 <lyxtabular version="3" rows="3" columns="2">
25593 <features tabularvalignment="middle">
25594 <column alignment="center" valignment="top" width="0pt">
25595 <column alignment="center" valignment="top" width="0pt">
25597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25600 \begin_layout Plain Layout
25606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25609 \begin_layout Plain Layout
25617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25620 \begin_layout Plain Layout
25628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25631 \begin_layout Plain Layout
25632 \begin_inset Formula $A\sgn(x)+B$
25642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25645 \begin_layout Plain Layout
25649 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25660 \begin_layout Plain Layout
25661 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25677 \begin_layout Standard
25678 The first method is more suitable when the self-defined function should
25679 be used several times.
25682 \begin_layout Subsection
25684 \begin_inset Index idx
25687 \begin_layout Plain Layout
25696 \begin_layout Standard
25697 For limits there are defined besides
25704 \begin_inset Index idx
25707 \begin_layout Plain Layout
25727 furthermore the following functions:
25730 \begin_layout Standard
25732 \begin_inset Tabular
25733 <lyxtabular version="3" rows="5" columns="2">
25734 <features tabularvalignment="middle">
25735 <column alignment="center" valignment="top" width="0">
25736 <column alignment="center" valignment="top" width="0">
25738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25741 \begin_layout Plain Layout
25747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25750 \begin_layout Plain Layout
25752 \begin_inset Note Note
25755 \begin_layout Plain Layout
25762 is only used as spacer.
25774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25777 \begin_layout Plain Layout
25785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25788 \begin_layout Plain Layout
25789 \begin_inset Formula $\varliminf$
25799 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25802 \begin_layout Plain Layout
25810 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25813 \begin_layout Plain Layout
25814 \begin_inset Formula $\varlimsup$
25824 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25827 \begin_layout Plain Layout
25835 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25838 \begin_layout Plain Layout
25839 \begin_inset Formula $\varprojlim$
25849 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25852 \begin_layout Plain Layout
25860 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25863 \begin_layout Plain Layout
25864 \begin_inset Formula $\varinjlim$
25868 \begin_inset Formula $\raisebox{-2.5mm}{}$
25884 \begin_layout Standard
25885 \begin_inset VSpace medskip
25888 The limit is created by inserting a subscript.
25889 It is set right beside the function in an inline formula:
25892 \begin_layout Standard
25894 \begin_inset Tabular
25895 <lyxtabular version="3" rows="2" columns="2">
25896 <features tabularvalignment="middle">
25897 <column alignment="center" valignment="top" width="0pt">
25898 <column alignment="center" valignment="top" width="0pt">
25900 <cell alignment="center" valignment="top" usebox="none">
25903 \begin_layout Plain Layout
25909 <cell alignment="center" valignment="top" usebox="none">
25912 \begin_layout Plain Layout
25913 \begin_inset space \hspace{}
25918 \begin_inset Note Note
25921 \begin_layout Plain Layout
25928 are used here as spacer.
25940 <cell alignment="center" valignment="top" usebox="none">
25943 \begin_layout Plain Layout
25952 \begin_layout Plain Layout
25965 \begin_layout Plain Layout
25979 <cell alignment="center" valignment="top" usebox="none">
25982 \begin_layout Plain Layout
25983 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25999 \begin_layout Standard
26000 In a displayed formula the limit is set below the formula, as usual:
26001 \begin_inset Formula
26011 \begin_layout Subsection
26013 \begin_inset Index idx
26016 \begin_layout Plain Layout
26017 Functions ! modulo-
26025 \begin_layout Standard
26026 The modulo-function is special, because it exists in four variants.
26027 The variants in a displayed formula are:
26028 \begin_inset Formula
26030 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26031 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
26032 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
26033 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
26034 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
26042 \begin_layout Standard
26043 In an inline formula less space is set before the function names for all
26045 By default the modulo-functions take only the first following character
26047 To use more than one character, one has to put them into TeX-braces:
26048 \begin_inset Formula
26050 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26051 \mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\
26052 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26060 \begin_layout Section
26062 \begin_inset Index idx
26065 \begin_layout Plain Layout
26074 \begin_layout Subsection
26075 Special Characters in Mathematical Text
26078 \begin_layout Standard
26079 The following commands can only be used in mathematical text or in TeX-mode:
26082 \begin_layout Standard
26083 \begin_inset space \hfill{}
26087 \begin_inset Tabular
26088 <lyxtabular version="3" rows="8" columns="2">
26089 <features tabularvalignment="middle">
26090 <column alignment="block" valignment="top" width="0">
26091 <column alignment="block" valignment="top" width="0">
26093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26096 \begin_layout Plain Layout
26102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26105 \begin_layout Plain Layout
26113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26116 \begin_layout Plain Layout
26124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26127 \begin_layout Plain Layout
26128 \begin_inset Formula $\textrm{œ}$
26138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26141 \begin_layout Plain Layout
26149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26152 \begin_layout Plain Layout
26153 \begin_inset Formula $\textrm{Œ}$
26163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26166 \begin_layout Plain Layout
26174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26177 \begin_layout Plain Layout
26178 \begin_inset Formula $\textrm{æ}$
26188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26191 \begin_layout Plain Layout
26199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26202 \begin_layout Plain Layout
26203 \begin_inset Formula $\textrm{Æ}$
26213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26216 \begin_layout Plain Layout
26224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26227 \begin_layout Plain Layout
26228 \begin_inset Formula $\textrm{\aa}$
26238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26241 \begin_layout Plain Layout
26245 \begin_inset Index idx
26248 \begin_layout Plain Layout
26255 \begin_layout Plain Layout
26276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26279 \begin_layout Plain Layout
26280 \begin_inset Formula $\textrm{Å}$
26290 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26293 \begin_layout Plain Layout
26301 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26304 \begin_layout Plain Layout
26305 \begin_inset Formula $\textrm{ı}$
26319 \begin_inset space \hfill{}
26323 \begin_inset Tabular
26324 <lyxtabular version="3" rows="8" columns="2">
26325 <features tabularvalignment="middle">
26326 <column alignment="block" valignment="top" width="0">
26327 <column alignment="center" valignment="top" width="0">
26329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26332 \begin_layout Plain Layout
26334 \begin_inset Note Note
26337 \begin_layout Plain Layout
26339 \begin_inset space \thinspace{}
26342 mm is used for separation, because otherwise the output will be ¡ and ¿
26353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26356 \begin_layout Plain Layout
26364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26367 \begin_layout Plain Layout
26375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26378 \begin_layout Plain Layout
26379 \begin_inset Formula $\textrm{ø}$
26389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26392 \begin_layout Plain Layout
26400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26403 \begin_layout Plain Layout
26404 \begin_inset Formula $\textrm{Ø}$
26414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26417 \begin_layout Plain Layout
26425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26428 \begin_layout Plain Layout
26429 \begin_inset Formula $\textrm{ł}$
26439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26442 \begin_layout Plain Layout
26450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26453 \begin_layout Plain Layout
26454 \begin_inset Formula $\textrm{Ł}$
26464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26467 \begin_layout Plain Layout
26469 \begin_inset space \hspace{}
26477 \begin_layout Plain Layout
26491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26494 \begin_layout Plain Layout
26495 \begin_inset Formula $\textrm{!`}$
26505 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26508 \begin_layout Plain Layout
26510 \begin_inset space \hspace{}
26518 \begin_layout Plain Layout
26532 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26535 \begin_layout Plain Layout
26536 \begin_inset Formula $\textrm{?`}$
26546 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26549 \begin_layout Plain Layout
26557 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26560 \begin_layout Plain Layout
26561 \begin_inset Formula $\textrm{ȷ}$
26575 \begin_inset space \hfill{}
26581 \begin_layout Standard
26583 \begin_inset Formula $\textrm{\textrm{Å}}$
26587 \begin_inset Formula $\textrm{\textrm{Ø}}$
26590 can also be inserted via the math toolbar button
26591 \begin_inset Graphics
26592 filename ../images/math/digamma.png
26600 \begin_layout Standard
26601 An exception are the commands
26604 \begin_inset space \hspace{}
26613 \begin_inset space \hspace{}
26619 , because they can be inserted in LyX directly to text.
26622 \begin_layout Subsection
26624 \begin_inset CommandInset label
26626 name "sub:Accents-in-Text"
26631 \begin_inset Index idx
26634 \begin_layout Plain Layout
26643 \begin_layout Standard
26644 With the following commands all letters can be accented.
26645 The commands must be inserted in TeX-mode.
26648 \begin_layout Standard
26649 \begin_inset space \hfill{}
26653 \begin_inset Tabular
26654 <lyxtabular version="3" rows="8" columns="2">
26655 <features tabularvalignment="middle">
26656 <column alignment="block" valignment="top" width="0">
26657 <column alignment="block" valignment="top" width="0">
26659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26662 \begin_layout Plain Layout
26668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26671 \begin_layout Plain Layout
26679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26682 \begin_layout Plain Layout
26686 \begin_inset Quotes grd
26694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26697 \begin_layout Plain Layout
26701 \begin_layout Plain Layout
26717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26720 \begin_layout Plain Layout
26728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26731 \begin_layout Plain Layout
26735 \begin_layout Plain Layout
26751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26754 \begin_layout Plain Layout
26761 \begin_layout Plain Layout
26775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26778 \begin_layout Plain Layout
26782 \begin_layout Plain Layout
26798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26801 \begin_layout Plain Layout
26809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26812 \begin_layout Plain Layout
26816 \begin_layout Plain Layout
26832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26835 \begin_layout Plain Layout
26842 \begin_layout Plain Layout
26856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26859 \begin_layout Plain Layout
26863 \begin_layout Plain Layout
26879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26882 \begin_layout Plain Layout
26889 \begin_layout Plain Layout
26903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26906 \begin_layout Plain Layout
26910 \begin_layout Plain Layout
26926 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26929 \begin_layout Plain Layout
26936 \begin_layout Plain Layout
26950 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26953 \begin_layout Plain Layout
26957 \begin_layout Plain Layout
26977 \begin_inset space \hfill{}
26981 \begin_inset Tabular
26982 <lyxtabular version="3" rows="8" columns="2">
26983 <features tabularvalignment="middle">
26984 <column alignment="block" valignment="top" width="0">
26985 <column alignment="center" valignment="top" width="0">
26987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26990 \begin_layout Plain Layout
26996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26999 \begin_layout Plain Layout
27007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27010 \begin_layout Plain Layout
27017 \begin_layout Plain Layout
27031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27034 \begin_layout Plain Layout
27038 \begin_layout Plain Layout
27054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27057 \begin_layout Plain Layout
27065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27068 \begin_layout Plain Layout
27072 \begin_layout Plain Layout
27088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27091 \begin_layout Plain Layout
27095 \begin_inset Index idx
27098 \begin_layout Plain Layout
27109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27112 \begin_layout Plain Layout
27116 \begin_layout Plain Layout
27132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27135 \begin_layout Plain Layout
27143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27146 \begin_layout Plain Layout
27150 \begin_layout Plain Layout
27166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27169 \begin_layout Plain Layout
27176 \begin_layout Plain Layout
27190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27193 \begin_layout Plain Layout
27197 \begin_layout Plain Layout
27213 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27216 \begin_layout Plain Layout
27223 \begin_layout Plain Layout
27237 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27240 \begin_layout Plain Layout
27244 \begin_layout Plain Layout
27260 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27263 \begin_layout Plain Layout
27270 \begin_layout Plain Layout
27284 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27287 \begin_layout Plain Layout
27291 \begin_layout Plain Layout
27311 \begin_inset space \hfill{}
27317 \begin_layout Standard
27318 \begin_inset VSpace medskip
27327 also two different characters can be accented.
27336 \begin_layout Plain Layout
27351 \begin_layout Plain Layout
27363 \begin_layout Standard
27376 can in combination with vowels directly be inserted with the keyboard without
27378 The same applies for the tilde
27382 \begin_layout Plain Layout
27383 This only applies for keyboards where the tilde is defined as accent.
27392 in combination with
27407 \begin_layout Standard
27450 and accents that are inserted directly with the keyboard are also available
27451 in mathematical text.
27452 For the other accents there are special math commands to be used in formulas,
27454 \begin_inset CommandInset ref
27456 reference "sub:Accents-for-one"
27463 \begin_layout Standard
27464 \begin_inset VSpace bigskip
27467 Furthermore, with the command
27474 \begin_inset Index idx
27477 \begin_layout Plain Layout
27485 all numbers and letters can be set into a circle, quasi accented with a
27486 circle, similar to the copyright symbol.
27489 \begin_layout Standard
27491 \begin_inset Tabular
27492 <lyxtabular version="3" rows="3" columns="2">
27493 <features tabularvalignment="middle">
27494 <column alignment="center" valignment="top" width="0">
27495 <column alignment="center" valignment="top" width="0">
27497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27500 \begin_layout Plain Layout
27506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27509 \begin_layout Plain Layout
27511 \begin_inset Note Note
27514 \begin_layout Plain Layout
27521 is only used as spacer.
27533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27536 \begin_layout Plain Layout
27544 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27547 \begin_layout Plain Layout
27551 \begin_layout Plain Layout
27567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27570 \begin_layout Plain Layout
27581 raisebox{-1.5pt}{W}}
27586 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27589 \begin_layout Plain Layout
27590 \begin_inset Formula $\raisebox{4.5mm}{}$
27597 \begin_layout Plain Layout
27615 \begin_inset Formula $\raisebox{-2mm}{}$
27631 \begin_layout Standard
27632 One has to take care that the character fits in the circle.
27643 \begin_layout Plain Layout
27645 \begin_inset CommandInset ref
27647 reference "sub:Font-Sizes"
27656 specifies thereby the size of the circle.
27667 \begin_layout Plain Layout
27669 \begin_inset CommandInset ref
27671 reference "sub:Boxes-without-Frame"
27680 the character can be centered.
27683 \begin_layout Subsection
27685 \begin_inset Index idx
27688 \begin_layout Plain Layout
27697 \begin_layout Standard
27698 Old-style figures (also known as old-style numerals) are created with the
27706 \begin_inset Index idx
27709 \begin_layout Plain Layout
27718 The command can be used in formulas and in TeX-mode.
27719 The command scheme is:
27722 \begin_layout Standard
27727 oldstylenums{number}
27730 \begin_layout Standard
27735 oldstylenums{0123456789
27738 \begin_inset Formula $\oldstylenums{0123456789}$
27744 \begin_layout Subsection
27745 Miscellaneous special Characters
27746 \begin_inset CommandInset label
27748 name "sub:Miscellaneous-special-Characters"
27753 \begin_inset Index idx
27756 \begin_layout Plain Layout
27757 Special characters ! miscellaneous
27765 \begin_layout Standard
27766 The following characters can only be inserted to formulas by using commands:
27769 \begin_layout Standard
27771 \begin_inset Tabular
27772 <lyxtabular version="3" rows="4" columns="2">
27773 <features tabularvalignment="middle">
27774 <column alignment="center" valignment="top" width="0">
27775 <column alignment="center" valignment="top" width="0">
27777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27780 \begin_layout Plain Layout
27786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27789 \begin_layout Plain Layout
27797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27800 \begin_layout Plain Layout
27807 \begin_layout Plain Layout
27821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27824 \begin_layout Plain Layout
27825 \begin_inset Formula $\mathcircumflex$
27835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27838 \begin_layout Plain Layout
27846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27849 \begin_layout Plain Layout
27850 \begin_inset Formula $\_$
27860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27863 \begin_layout Plain Layout
27868 \begin_layout Plain Layout
27880 \begin_inset Index idx
27883 \begin_layout Plain Layout
27896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27899 \begin_layout Plain Layout
27900 \begin_inset Formula $^{\circ}$
27916 \begin_layout Standard
27917 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27918 contains the following line
27922 \begin_layout Plain Layout
27923 More about this is described in
27924 \begin_inset CommandInset ref
27926 reference "sub:Text-Characters-in"
27938 \begin_layout Standard
27943 DeclareInputtext{176}{
27956 \begin_layout Standard
27957 \begin_inset Newpage newpage
27963 \begin_layout Section
27965 \begin_inset CommandInset label
27967 name "sec:Formula-Styles"
27972 \begin_inset Index idx
27975 \begin_layout Plain Layout
27984 \begin_layout Itemize
27985 There are two different alignment styles:
27989 \begin_layout Description
27990 Centered is the predefined standard
27993 \begin_layout Description
27994 Indented for this the option
27998 must be inserted in the menu
28000 Document\SpecialChar \menuseparator
28006 \begin_inset space ~
28012 \begin_layout Standard
28017 is used, the indentation can be adjusted with the length
28024 \begin_inset Index idx
28027 \begin_layout Plain Layout
28036 Should the distance be 15
28037 \begin_inset space \thinspace{}
28040 mm, the following command line is inserted in the LaTeX-preamble
28043 \begin_layout Standard
28053 \begin_layout Standard
28054 When no length is specified, the predefined value of 30
28055 \begin_inset space \thinspace{}
28062 \begin_layout Itemize
28063 And two different numbering styles:
28067 \begin_layout Description
28068 Right is the predefined standard
28071 \begin_layout Description
28072 Left for this the option
28076 must be inserted in the menu
28078 Document\SpecialChar \menuseparator
28084 \begin_inset space ~
28091 \begin_layout Standard
28100 can also be used together.
28101 In this case both options are inserted, separated by a comma.
28104 \begin_layout Standard
28105 The chosen styles are used for all displayed formulas of the document.
28106 When both, centered and indented formulas should be created in a document,
28112 The indented formulas are then set in a flalign environment, see
28113 \begin_inset CommandInset ref
28115 reference "sub:Flalign-Environment"
28122 \begin_layout Section
28124 \begin_inset CommandInset label
28126 name "sec:Multiline-Formulas"
28131 \begin_inset Index idx
28134 \begin_layout Plain Layout
28135 Formula ! multiline
28143 \begin_layout Subsection
28147 \begin_layout Standard
28148 In LyX multiline formulas are created by pressing
28153 arg "newline-insert newline"
28159 This creates either an
28161 eqnarray environment
28163 that is described in
28164 \begin_inset CommandInset ref
28166 reference "sub:Eqnarray-Environment"
28170 or, when the option
28172 Use AMS math package
28174 in the document settings is selected, an
28178 that is described in
28179 \begin_inset CommandInset ref
28181 reference "sub:Standard-align-Environment"
28188 \begin_layout Standard
28189 There are other multiline formula environments that can be created via the
28192 Insert\SpecialChar \menuseparator
28196 These environments are described in the following sections.
28199 \begin_layout Standard
28200 In all multiline formula environments a new line is created by pressing
28204 arg "newline-insert newline"
28208 To add or delete lines, the math toolbar buttons
28209 \begin_inset Graphics
28210 filename ../images/tabular-feature_append-row.png
28216 \begin_inset Graphics
28217 filename ../images/tabular-feature_delete-row.png
28222 , respectively, or the menu
28224 Edit\SpecialChar \menuseparator
28230 \begin_layout Subsubsection
28232 \begin_inset CommandInset label
28234 name "sub:Line-Separation"
28239 \begin_inset Index idx
28242 \begin_layout Plain Layout
28243 Formula ! multiline ! Line separation
28251 \begin_layout Standard
28252 There is sometimes not enough space in multiline formulas between the lines:
28253 \begin_inset Formula
28255 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}\\
28256 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
28264 \begin_layout Standard
28265 In LaTeX additional line space is specified as optional argument of the
28267 This is not yet possible in LyX
28271 \begin_layout Plain Layout
28273 \begin_inset CommandInset href
28275 name "LyX-bug #1505"
28276 target "http://www.lyx.org/trac/ticket/1505"
28285 , therefore the whole formula must be inserted in TeX-mode.
28286 To add in our example space, the command
28294 is inserted at the end of the first line.
28299 \begin_layout Plain Layout
28306 \begin_layout Plain Layout
28308 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28311 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28318 \begin_layout Plain Layout
28322 left(B^{2}+x_{0}^{2}
28330 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28335 \begin_layout Plain Layout
28347 \begin_layout Standard
28348 \begin_inset VSpace bigskip
28351 To set the line separation for all lines in a formula, the length
28358 \begin_inset Index idx
28361 \begin_layout Plain Layout
28371 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28382 \begin_inset space \thinspace{}
28387 \begin_inset space \thinspace{}
28390 mm additional line separation as in the previous example, the command
28393 \begin_layout Standard
28403 \begin_layout Standard
28404 is inserted in TeX-mode before the formula.
28405 This requires that the LaTeX-package
28413 \begin_layout Plain Layout
28418 is part of every LaTeX standard installation.
28424 \begin_inset Index idx
28427 \begin_layout Plain Layout
28433 was loaded in LaTeX-preamble with the line
28436 \begin_layout Standard
28444 \begin_layout Standard
28449 \begin_layout Plain Layout
28461 \begin_inset Formula
28463 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}\\
28464 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
28472 \begin_layout Standard
28476 \begin_layout Plain Layout
28487 To get back to the predefined distance,
28493 is set to the value 3
28494 \begin_inset space \thinspace{}
28500 \begin_layout Subsubsection
28502 \begin_inset CommandInset label
28504 name "sub:Column-Separation"
28509 \begin_inset Index idx
28512 \begin_layout Plain Layout
28513 Formula ! multiline ! Column separation
28521 \begin_layout Standard
28522 Multiline formulas form a matrix.
28523 A formula in the eqnarray environment is for example a matrix with three
28525 By changing the column separation in this environment, the space beside
28526 the relation sign can be changed.
28529 \begin_layout Standard
28530 The column separation is specified with the length
28537 \begin_inset Index idx
28540 \begin_layout Plain Layout
28549 \begin_inset Newline newline
28552 column separation = 2
28553 \begin_inset space \thinspace{}
28563 \begin_inset Newline newline
28569 \begin_layout Standard
28579 \begin_layout Standard
28580 inserted in TeX-mode, sets for all following formulas a column separation
28582 \begin_inset space \thinspace{}
28586 To get back to the predefined distance,
28593 \begin_inset space \thinspace{}
28599 \begin_layout Standard
28601 \begin_inset space \thinspace{}
28604 cm column separation:
28608 \begin_layout Plain Layout
28620 \begin_inset Formula
28628 A formula with the predefined column separation for matrices of 10
28629 \begin_inset space \thinspace{}
28636 \begin_layout Plain Layout
28648 \begin_inset Formula
28659 \begin_layout Subsubsection
28661 \begin_inset Index idx
28664 \begin_layout Plain Layout
28673 \begin_layout Standard
28674 Long formulas can be typeset using these methods:
28677 \begin_layout Itemize
28678 When one side of the equation is much shorther than the line width, this
28679 one is chosen for the left side and the right side is typeset over two
28681 \begin_inset Formula
28683 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 \\
28684 & & -\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}
28689 The minus sign at the beginning of the second line does normally not appear
28690 as operator because it is the first character of the line.
28691 Thus it would not be surrounded by space and could not be distinguished
28692 from the fraction bar.
28694 \begin_inset space \thinspace{}
28697 pt space was inserted behind the minus sign with the command
28707 \begin_layout Plain Layout
28715 \begin_inset CommandInset ref
28717 reference "sub:Variable-Space"
28727 \begin_inset Index idx
28730 \begin_layout Plain Layout
28741 \begin_layout Itemize
28742 When both sides of the equation are too long, the command
28749 \begin_inset Index idx
28752 \begin_layout Plain Layout
28761 It is inserted to the first column of the first line and effects that all
28762 further insertions overwrite the following columns:
28763 \begin_inset Formula
28765 \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 \\
28766 & & -\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 \\
28767 & & =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}
28772 After the insertion of
28778 , the cursor is in a purple box that is a bit shifted to the left from the
28780 In this the formula is inserted.
28781 \begin_inset Newline newline
28784 The content of the further lines is inserted to the second or another formula
28786 The greater the column number where it was inserted, the larger the indentation.
28787 \begin_inset VSpace medskip
28791 \begin_inset Newline newline
28795 \begin_inset Note Greyedout
28798 \begin_layout Plain Layout
28799 Note the following when using
28808 \begin_layout Itemize
28809 The formula doesn't use the full page width.
28811 \begin_inset space \thinspace{}
28815 \begin_inset space \space{}
28819 \begin_inset Formula $-B^{2}$
28822 is added to the first line in the above example, it would have been outside
28824 To better use the width, negative space can be inserted at the beginning
28828 \begin_layout Itemize
28829 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28834 \begin_layout Plain Layout
28835 \begin_inset CommandInset href
28837 name "LyX-bug #1429"
28838 target "http://www.lyx.org/trac/ticket/1429"
28847 One can only set the cursor at the beginning of the line and move it with
28856 \begin_layout Itemize
28857 Other methods to set long formulas are offered by the environments described
28859 \begin_inset CommandInset ref
28861 reference "sub:Multline-Environment"
28866 \begin_inset CommandInset ref
28868 reference "sub:Multiline-Formula-Parts"
28875 \begin_layout Subsubsection
28877 \begin_inset CommandInset label
28879 name "sub:Multiline-Brackets"
28884 \begin_inset Index idx
28887 \begin_layout Plain Layout
28888 Brackets ! for multiline expressions
28896 \begin_layout Standard
28897 For brackets spanning multiple lines the following problem occurs:
28898 \begin_inset Formula
28900 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28901 & & \left.\cdots+B-D\right]
28909 \begin_layout Standard
28910 The closing bracket is smaller than the opening bracket because brackets
28911 with variable size may not span multiple lines.
28914 \begin_layout Standard
28915 To set the bracket size for the second line correctly, the first line is
28923 \begin_inset Index idx
28926 \begin_layout Plain Layout
28934 and the second line with
28942 \begin_layout Plain Layout
28956 \begin_inset CommandInset ref
28958 reference "sub:Automatic-Bracket-Size"
28970 \begin_inset Index idx
28973 \begin_layout Plain Layout
28999 \begin_layout Plain Layout
29018 \begin_layout Plain Layout
29037 \begin_layout Plain Layout
29049 \begin_inset Formula $\downarrow$
29055 \begin_inset Index idx
29058 \begin_layout Plain Layout
29066 is inserted, because the multiplication operator with its limits is the
29067 largest symbol in the first line and this should be the size for the bracket
29068 in the second line.
29071 \begin_layout Standard
29072 The result is this:
29073 \begin_inset Formula
29075 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29076 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29084 \begin_layout Subsection
29088 \begin_layout Standard
29089 Align environments can be used for every kind of multiline formulas.
29090 They are specially useful to set several formulas side by side.
29093 \begin_layout Standard
29094 Align environments consist of columns.
29095 The odd columns are right aligned, the even ones left aligned.
29096 Every line in an Align environment can be numbered.
29099 \begin_layout Standard
29100 Align environments are created via the menu
29102 Insert\SpecialChar \menuseparator
29108 Edit\SpecialChar \menuseparator
29109 Math\SpecialChar \menuseparator
29110 Change Formula Type
29112 already existing formulas can be converted to Align environments.
29115 \begin_layout Standard
29116 To add or delete columns, the math toolbar buttons
29117 \begin_inset Graphics
29118 filename ../images/tabular-feature_append-column.png
29124 \begin_inset Graphics
29125 filename ../images/tabular-feature_delete-column.png
29130 , respectively, or the menu
29132 Edit\SpecialChar \menuseparator
29138 \begin_layout Subsubsection
29139 Standard align Environment
29140 \begin_inset CommandInset label
29142 name "sub:Standard-align-Environment"
29147 \begin_inset Index idx
29150 \begin_layout Plain Layout
29151 Formula ! multiline ! align environment
29159 \begin_layout Standard
29160 This Align environment is created by presssing
29163 arg "newline-insert newline"
29166 in a formula or by the menu
29168 Insert\SpecialChar \menuseparator
29169 Math\SpecialChar \menuseparator
29170 AMS align Environment
29175 \begin_layout Standard
29176 An example for two formulas set side by side, that are created with a four
29177 column align environment:
29178 \begin_inset Formula
29180 A & =\sin(B) & C & =D\\
29181 C & \ne A & B & \ne D
29186 As it can be seen, the formulas in this environment are placed so as if
29195 \begin_layout Plain Layout
29203 \begin_inset CommandInset ref
29205 reference "sub:Variable-Space"
29216 before the first and after every even column.
29217 When the formula style
29223 \begin_layout Plain Layout
29225 \begin_inset CommandInset ref
29227 reference "sec:Formula-Styles"
29238 is used, the formula is set without the
29244 before the first column.
29247 \begin_layout Subsubsection
29248 Alignat Environment
29249 \begin_inset Index idx
29252 \begin_layout Plain Layout
29253 Formula ! multiline ! alignat environment
29261 \begin_layout Standard
29262 The alignat environment has no predefined column separation.
29263 It can be inserted manually with the spaces that are described
29264 \begin_inset CommandInset ref
29266 reference "sub:Space"
29273 \begin_layout Standard
29274 The above example in the alignat environment where 1
29275 \begin_inset space \thinspace{}
29278 cm space was inserted at the beginning of the second formula:
29279 \begin_inset Formula
29280 \begin{alignat*}{2}
29281 A & =\sin(B) & \hspace{1cm}C & =D\\
29282 C & \ne A & B & \ne D
29287 Because the column separation can be set separately for every column, this
29288 environment is especially suitable to set three and more formulas side
29292 \begin_layout Subsubsection
29293 Flalign Environment
29294 \begin_inset CommandInset label
29296 name "sub:Flalign-Environment"
29301 \begin_inset Index idx
29304 \begin_layout Plain Layout
29305 Formula ! multiline ! flalign environment
29313 \begin_layout Standard
29314 In this environment the first two columns are always set as much as possible
29315 to the left and the last two ones to the right.
29317 \begin_inset Formula
29319 A & =1 & B & =2 & C & =3\\
29320 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29328 \begin_layout Standard
29329 By creating a flalign environment with an odd number of columns where an
29330 empty TeX-brace is inserted to the last column, several formulas in a document
29331 can be set to the left, although the formula style
29336 As example the indented formula
29337 \begin_inset CommandInset ref
29339 reference "eq:VolInt"
29344 \begin_inset Formula
29346 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29351 The first two columns contain the formula.
29352 To indent it as with the formula style
29357 \begin_inset space \thinspace{}
29360 pt space was inserted at the beginning of the first column.
29363 \begin_layout Subsection
29364 Eqnarray Environment
29365 \begin_inset CommandInset label
29367 name "sub:Eqnarray-Environment"
29372 \begin_inset Index idx
29375 \begin_layout Plain Layout
29376 Formula ! multiline ! eqnarray environment
29384 \begin_layout Standard
29385 When this environment has been created, three blue boxes appear.
29386 The content of the first box is right aligned, the content of the last
29388 The content of the middle box appears centered and a bit smaller, because
29389 it is designed to insert there only relation characters.
29390 \begin_inset Formula
29392 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29402 \begin_layout Subsection
29404 \begin_inset Index idx
29407 \begin_layout Plain Layout
29408 Formula ! multiline ! gather environment
29416 \begin_layout Standard
29417 This environment consists of only one centered column.
29418 Every line can be numbered.
29419 \begin_inset Formula
29430 \begin_layout Subsection
29431 Multline Environment
29432 \begin_inset CommandInset label
29434 name "sub:Multline-Environment"
29439 \begin_inset Index idx
29442 \begin_layout Plain Layout
29443 Formula ! multiline ! multline environment
29451 \begin_layout Standard
29452 The multline environment consists, like the gather environment, of only
29454 But the first line is left aligned, the last one right aligned.
29455 All other lines are centered.
29456 Therefore this environment is suitable for long formulas.
29458 \begin_inset CommandInset ref
29460 reference "eq:lefteqn"
29464 in the multline environment:
29465 \begin_inset Formula
29467 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}\\
29468 -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}\\
29469 =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}}
29477 \begin_layout Standard
29478 In the output only the last (first) line of a multline environment appears
29479 numbered when the document numbering is right (left).
29483 \begin_layout Plain Layout
29484 numbering styles see
29485 \begin_inset CommandInset ref
29487 reference "sec:Formula-Styles"
29499 \begin_layout Standard
29507 \begin_inset Index idx
29510 \begin_layout Plain Layout
29525 \begin_inset Index idx
29528 \begin_layout Plain Layout
29536 a centered line can be right or left aligned, respectively.
29537 The commands are used as follows:
29540 \begin_layout Standard
29545 shoveright{line content}
29551 shoveleft{line content}
29554 \begin_layout Standard
29555 \begin_inset VSpace medskip
29565 \begin_inset Index idx
29568 \begin_layout Plain Layout
29576 specifies the distance of the first line from the left page margin.
29577 Predefined is the length 0
29578 \begin_inset space \thinspace{}
29584 \begin_layout Standard
29585 As example the above formula where the command
29588 \begin_layout Standard
29598 \begin_layout Standard
29599 was inserted in TeX-mode before:
29603 \begin_layout Plain Layout
29615 \begin_inset Formula
29617 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}\\
29618 \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}}\\
29619 =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}}
29628 \begin_layout Plain Layout
29639 The second line was left aligned using
29648 \begin_layout Subsection
29649 Multiline Formula Parts
29650 \begin_inset CommandInset label
29652 name "sub:Multiline-Formula-Parts"
29657 \begin_inset Index idx
29660 \begin_layout Plain Layout
29661 Formula ! multiline ! formula parts
29669 \begin_layout Standard
29670 To display only parts of a formula with multiple lines, one of the following
29671 environments are used:
29688 They can be inserted via the menu
29690 Insert\SpecialChar \menuseparator
29693 or by using the commands described in this section.
29696 \begin_layout Standard
29697 The first three have the same properties as the corresponding multiline
29698 formula environments, but it is possible to set further formula parts beside
29701 \begin_inset Formula
29703 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29704 \Delta E\Delta t & \ge\frac{\hbar}{2}
29706 \right\} \textrm{Uncertainty relations}
29714 \begin_layout Standard
29715 To get this formula, a displayed formula is created where the command
29722 \begin_inset Index idx
29725 \begin_layout Plain Layout
29734 A purple box appears around the blue formula box where now columns and
29735 lines can be added.
29736 Outside the multiline environment other formula parts can be set, like
29740 \begin_layout Standard
29741 The aligned environment is also suitable for long formulas whose lines are
29742 horizontally aligned.
29743 Using aligned in a displayed formula has the advantage that the formula
29744 number is vertically centered behind the lines.
29746 \begin_inset CommandInset ref
29748 reference "eq:shortlong"
29752 in the aligned environment:
29753 \begin_inset Formula
29755 \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}|}\\
29756 & -\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}|}
29765 \begin_layout Standard
29766 To use the environments
29785 \begin_inset Index idx
29788 \begin_layout Plain Layout
29803 \begin_inset Index idx
29806 \begin_layout Plain Layout
29821 \begin_inset Index idx
29824 \begin_layout Plain Layout
29832 are inserted, respectively.
29833 The split environment has the same properties as the aligned environment
29834 but it can only have two columns.
29837 \begin_layout Subsection
29838 Text in multiline Formulas
29839 \begin_inset CommandInset label
29841 name "sub:Text-in-multiline"
29846 \begin_inset Index idx
29849 \begin_layout Plain Layout
29856 \begin_inset Index idx
29859 \begin_layout Plain Layout
29860 Formula ! multiline ! text
29868 \begin_layout Standard
29869 In the Align environments, and the multline and gather environment, text
29870 can be inserted that will appear in a separate line and doesn't affect
29871 the column alignment.
29872 To do this, the command
29879 \begin_inset Index idx
29882 \begin_layout Plain Layout
29890 is used in the following scheme:
29893 \begin_layout Standard
29901 \begin_layout Standard
29902 The text should not be longer than a line because it cannot be hyphenated.
29903 As LyX doesn't yet support
29909 directly, the text is written as mathematical text.
29916 must hereby be at the beginning of a line and appears in the output above
29918 An example where the text was inserted at the beginning of the second line:
29919 \begin_inset Formula
29921 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29922 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29930 \begin_layout Standard
29931 \begin_inset Newpage newpage
29937 \begin_layout Section
29939 \begin_inset Index idx
29942 \begin_layout Plain Layout
29949 \begin_inset Index idx
29952 \begin_layout Plain Layout
29953 Formula ! numbering|see
29957 \begin_layout Plain Layout
29968 \begin_layout Plain Layout
29983 \begin_layout Subsection
29987 \begin_layout Standard
29988 Numbered formulas can be created with the menu
29990 Insert\SpecialChar \menuseparator
29991 Math\SpecialChar \menuseparator
29993 \begin_inset space ~
30001 \begin_inset space ~
30007 Existing formulas can be numbered with the menu
30009 Edit\SpecialChar \menuseparator
30010 Math\SpecialChar \menuseparator
30012 \begin_inset space ~
30020 arg "math-number-toggle"
30024 The formula number is displayed in LyX behind the formula as number sign
30026 The number sign is replaced in the output by the formula number.
30029 \begin_layout Standard
30030 When numbering is turned on in multiline formulas, all lines will be numbered.
30031 But the numbering can be controlled with the menu
30033 Edit\SpecialChar \menuseparator
30034 Math\SpecialChar \menuseparator
30036 \begin_inset space ~
30040 \begin_inset space ~
30044 \begin_inset space ~
30052 arg "math-number-line-toggle"
30058 \begin_layout Standard
30059 Except for inline formulas, all formulas can be numbered with two different
30061 \begin_inset CommandInset ref
30063 reference "sec:Formula-Styles"
30070 \begin_layout Subsection
30072 \begin_inset Index idx
30075 \begin_layout Plain Layout
30076 Cross-references ! to formulas
30084 \begin_layout Standard
30085 All labeled formulas can be cross-referenced.
30086 A label is added by the menu
30088 Insert\SpecialChar \menuseparator
30091 or the toolbar button
30092 \begin_inset Graphics
30093 filename ../images/label-insert.png
30099 The cursor must hereby be inside a displayed formula.
30100 A dialog pops up displaying the prefix
30105 The label is inserted there behind the prefix.
30106 The predefined prefix means
30107 \begin_inset Quotes eld
30111 \begin_inset Quotes erd
30114 and makes it easier to find labels in large documents because it marks
30115 it as formula label to divide it from e.
30116 \begin_inset space \thinspace{}
30120 \begin_inset space \space{}
30124 To change a label, the menu
30126 Insert\SpecialChar \menuseparator
30132 \begin_layout Standard
30133 The name of the label is displayed in LyX within two parentheses behind
30135 A formula with a label is always numbered.
30138 \begin_layout Standard
30139 Cross-references are inserted via the menu
30141 Insert\SpecialChar \menuseparator
30144 or with the toolbar button
30145 \begin_inset Graphics
30146 filename ../images/dialog-show-new-inset_ref.png
30152 A formula cross-reference appears in the output as formula number.
30153 When in the cross-reference dialog window the format
30157 is chosen, the cross-reference appears in the output as formula number
30159 \begin_inset Newline newline
30162 By right-clicking on a cross-reference in LyX, one jumps to the formula
30163 that is referenced.
30166 \begin_layout Standard
30167 Here are as examples cross-references to formulas of the following subsections:
30168 \begin_inset Note Note
30171 \begin_layout Plain Layout
30172 Note the different cross-reference types.
30180 \begin_layout Standard
30182 \begin_inset CommandInset ref
30189 \begin_inset CommandInset ref
30197 \begin_inset CommandInset ref
30203 ) big Latin letters are used for the numbering in contrary to (
30204 \begin_inset CommandInset ref
30213 \begin_layout Standard
30214 \begin_inset VSpace medskip
30217 When the argument of
30225 \begin_layout Plain Layout
30233 \begin_inset CommandInset ref
30235 reference "sub:User-defined-Numbering"
30246 contains a box like in
30247 \begin_inset CommandInset ref
30249 reference "sub:Paragraph-Boxes"
30253 , the formula cannot be referenced.
30256 \begin_layout Subsection
30258 \begin_inset Index idx
30261 \begin_layout Plain Layout
30262 Formula numbering ! subnumbering
30270 \begin_layout Standard
30271 With the help of the commands
30275 begin{subequations}
30283 formulas can be subnumbered.
30284 Both commands are inserted in TeX-mode.
30287 \begin_layout Standard
30289 \begin_inset Formula
30300 \begin_layout Plain Layout
30304 addtocounter{equation}{-1}
30313 \begin_layout Plain Layout
30317 begin{subequations}
30323 \begin_inset VSpace -5mm
30327 \begin_inset Formula
30335 \begin_inset Formula
30345 \begin_layout Standard
30349 \begin_layout Plain Layout
30361 \begin_layout Standard
30362 To create the example, the following is done:
30365 \begin_layout Enumerate
30366 first formula is inserted
30369 \begin_layout Enumerate
30374 addtocounter{equation}{-1}
30376 begin{subequations}
30377 \begin_inset Index idx
30380 \begin_layout Plain Layout
30389 \begin_inset Newline newline
30394 is inserted after the first formula
30397 \begin_layout Enumerate
30398 second formula is inserted
30401 \begin_layout Enumerate
30402 third formula is inserted
30405 \begin_layout Enumerate
30412 is inserted after the third formula
30415 \begin_layout Standard
30416 Every formula between the commands
30428 is subnumbered as a, b,
30429 \begin_inset Newline linebreak
30432 c, \SpecialChar \ldots{}
30433 For multiline formulas every line will be subnumbered.
30434 All subnumbered formulas are treated as
30439 But as every numbered formula increases the counter
30443 by one, the command
30449 is needed to decrease it.
30450 Otherwise the formulas
30451 \begin_inset CommandInset ref
30458 \begin_inset CommandInset ref
30465 \begin_inset CommandInset ref
30471 would be numbered as
30472 \begin_inset CommandInset ref
30479 \begin_inset CommandInset ref
30486 \begin_inset CommandInset ref
30495 \begin_layout Standard
30496 By inserting the commands in TeX-mode, a space is created between the first
30499 \begin_inset space \thinspace{}
30502 mm vertical space is inserted after the command
30506 begin{subequations}
30509 When the formula style
30515 \begin_layout Plain Layout
30517 \begin_inset CommandInset ref
30519 reference "sec:Formula-Styles"
30531 \begin_inset space \thinspace{}
30534 mm space is inserted instead.
30537 \begin_layout Standard
30538 Here is an example for a multiline formula where the numbering was turned
30539 off for the second line:
30543 \begin_layout Plain Layout
30547 begin{subequations}
30553 \begin_inset Formula
30555 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30556 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30557 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30566 \begin_layout Plain Layout
30578 \begin_layout Subsection
30579 User-defined Numbering
30580 \begin_inset CommandInset label
30582 name "sub:User-defined-Numbering"
30587 \begin_inset Index idx
30590 \begin_layout Plain Layout
30591 Formula numbering ! user-defined
30599 \begin_layout Standard
30600 \begin_inset Index idx
30603 \begin_layout Plain Layout
30604 Formula numbering ! self-defined delimiters
30609 With the standard numbering parentheses are set around the formula number.
30610 To replace the parentheses for example by vertical bars, the following
30611 line is added to the LaTeX-preamble:
30614 \begin_layout Standard
30626 \begin_inset Note Note
30629 \begin_layout Plain Layout
30630 This macro is already declared in the LaTeX-preamble for testing.
30631 To activate it, remove the percent sign at the beginning.
30639 \begin_layout Standard
30640 To use other characters, the vertical bars besides the
30644 are replaced by one ore more characters.
30645 To get only the formula number the vertical bars are omitted.
30648 \begin_layout Standard
30649 \begin_inset VSpace bigskip
30652 When there should be an expression of your choice instead of the consecutive
30653 formula number in parentheses behind the formula, the command
30660 \begin_inset Index idx
30663 \begin_layout Plain Layout
30672 \begin_inset Formula
30674 A+B=C\tag{something}\label{eq:tag}
30679 In this example the command
30687 \begin_layout Plain Layout
30698 was inserted to the formula.
30701 \begin_layout Standard
30710 \begin_layout Plain Layout
30721 is inserted instead, the star prevents the parentheses around the expression:
30722 \begin_inset Formula
30724 A+B=C\tag*{something}
30732 \begin_layout Standard
30733 \begin_inset VSpace bigskip
30736 To restart the formula numbering with new document parts or sections, the
30737 following command is used:
30740 \begin_layout Standard
30745 @addtoreset{equation}{part}
30748 \begin_inset Index idx
30751 \begin_layout Plain Layout
30756 \begin_layout Plain Layout
30767 \begin_layout Plain Layout
30780 \begin_layout Plain Layout
30791 \begin_layout Plain Layout
30804 \begin_inset Newline newline
30808 \begin_inset Newline newline
30815 @addtoreset{equation}{section}
30818 \begin_layout Standard
30819 To be able to use these commands in TeX-mode, the
30820 \begin_inset Quotes eld
30824 \begin_inset Quotes erd
30827 character has to be made
30828 \begin_inset Quotes eld
30832 \begin_inset Quotes erd
30835 for LaTeX using the command
30849 So the command sequence in TeX-mode is:
30852 \begin_layout Standard
30858 \begin_inset Newline newline
30863 @addtoreset{equation}{section}
30864 \begin_inset Newline newline
30872 \begin_layout Standard
30873 In the LaTeX-preamble
30885 can be omitted as they are automatically internally inserted by LyX.
30888 \begin_layout Standard
30903 \begin_layout Plain Layout
30908 is part of the LaTeX-package
30913 \begin_inset Index idx
30916 \begin_layout Plain Layout
30917 Packages ! carlisle
30922 that is part of every LaTeX standard installation.
30928 \begin_inset Index idx
30931 \begin_layout Plain Layout
30932 Packages ! remreset
30937 has to be loaded in the LaTeX-preamble with the line
30940 \begin_layout Standard
30945 usepackage{remreset}
30948 \begin_layout Standard
30956 \begin_inset Index idx
30959 \begin_layout Plain Layout
30964 \begin_layout Plain Layout
30975 \begin_layout Plain Layout
30988 \begin_layout Plain Layout
30999 \begin_layout Plain Layout
31011 can be used with the same scheme as
31020 \begin_layout Standard
31021 \begin_inset VSpace bigskip
31024 Sometimes formulas should be numbered in the following form:
31027 \begin_layout Standard
31030 (section number.formula number)
31033 \begin_layout Standard
31034 The formula number should start with every section with
31035 \begin_inset Quotes eld
31039 \begin_inset Quotes erd
31045 \begin_layout Standard
31046 For this case there is the command
31053 \begin_inset Index idx
31056 \begin_layout Plain Layout
31064 , which is used with the following scheme:
31067 \begin_layout Standard
31072 numberwithin{counter}{sectioning}
31075 \begin_layout Standard
31076 Counter denotes what kind of numbering is affected, sectioning denotes what
31077 number is before the dot.
31080 \begin_layout Standard
31081 Thus in our case the following LaTeX-preamble or TeX code line is used:
31084 \begin_layout Standard
31089 numberwithin{equation}{section}
31092 \begin_layout Standard
31093 This is the result:
31097 \begin_layout Plain Layout
31101 numberwithin{equation}{section}
31107 \begin_inset Formula
31117 \begin_layout Standard
31119 \begin_inset space \thinspace{}
31123 \begin_inset space \space{}
31126 tables so that the number of the part is the sectioning,
31127 \begin_inset Newline newline
31134 numberwithin{table}{part}
31139 \begin_layout Standard
31140 To go back to the standard numbering or to prevent this kind of numbering
31141 when it is defined by the document class, the following command is inserted
31142 as TeX code or to the LaTeX-preamble:
31145 \begin_layout Standard
31155 \begin_inset Index idx
31158 \begin_layout Plain Layout
31172 \begin_layout Plain Layout
31188 \begin_inset Newline newline
31196 \begin_inset Newline newline
31208 \begin_layout Standard
31215 uses internally the command
31221 , described above, that also needs to be reverted.
31225 \begin_layout Plain Layout
31232 \begin_layout Plain Layout
31236 @removefromreset{equation}{section}
31239 \begin_layout Plain Layout
31251 \begin_layout Subsection
31252 Numbering with Roman Numbers and Letters
31253 \begin_inset Index idx
31256 \begin_layout Plain Layout
31257 Formula numbering ! with letters
31263 \begin_inset Index idx
31266 \begin_layout Plain Layout
31267 Formula numbering ! with Roman numbers
31275 \begin_layout Standard
31276 Formulas can also be numbered with Roman numbers and Latin letters.
31277 To number for example with small Roman numbers, the command
31280 \begin_layout Standard
31292 \begin_layout Standard
31293 is inserted before the formula in TeX-mode.
31301 \begin_inset Index idx
31304 \begin_layout Plain Layout
31312 redefines the predefined command
31328 \begin_layout Plain Layout
31335 has the same scheme like the command
31341 that is described in
31342 \begin_inset CommandInset ref
31344 reference "sub:The-Command-newcommand"
31357 is the formula counter.
31364 is used as prefix for a counter, the value of the counter is output as
31366 When a formula is numbered, LaTeX sets internally the command
31372 behind the formula.
31378 \begin_inset Index idx
31381 \begin_layout Plain Layout
31391 outputs the counter as small Roman number.
31394 \begin_layout Standard
31395 All formulas behind the command
31405 are now numbered Roman.
31406 To switch to numbering with big Roman numbers, the command is inserted
31420 \begin_inset Index idx
31423 \begin_layout Plain Layout
31435 \begin_inset Quotes eld
31439 \begin_inset Quotes erd
31442 with small Latin letters there is the command
31449 \begin_inset Index idx
31452 \begin_layout Plain Layout
31460 , for big ones there is the command
31467 \begin_inset Index idx
31470 \begin_layout Plain Layout
31483 \begin_layout Standard
31484 \begin_inset Note Greyedout
31487 \begin_layout Plain Layout
31492 Only maximal 26 formulas can be numbered with Latin letters in one document.
31500 \begin_layout Standard
31504 \begin_layout Plain Layout
31520 \begin_layout Standard
31521 \begin_inset Formula
31523 A=\textrm{small roman}
31532 \begin_layout Plain Layout
31546 \begin_inset Formula
31548 B=\textrm{big Roman}\label{eq:Rom}
31557 \begin_layout Plain Layout
31571 \begin_inset Formula
31573 C=\textrm{small Latin}
31582 \begin_layout Plain Layout
31596 \begin_inset Formula
31598 D=\textrm{big Latin}\label{eq:Lat}
31606 \begin_layout Standard
31607 To switch back to the default numbering, insert the command:
31610 \begin_layout Standard
31620 \begin_inset Index idx
31623 \begin_layout Plain Layout
31634 \begin_layout Standard
31638 \begin_layout Plain Layout
31652 \begin_inset Formula
31662 \begin_layout Standard
31663 \begin_inset VSpace medskip
31666 As you see, formulas are numbered serially independent from the numbering
31668 When then numbering should start with
31669 \begin_inset Quotes eld
31673 \begin_inset Quotes erd
31676 when the style is changed, new equation counters have to be defined.
31677 A description about this can be found in the file
31678 \begin_inset CommandInset href
31680 name "Formula-numbering.lyx"
31681 target "run:Formula-numbering.lyx"
31688 \begin_layout Section
31689 Chemical Symbols and Equations
31690 \begin_inset CommandInset label
31692 name "sub:Chemical-Symbols-and"
31697 \begin_inset Index idx
31700 \begin_layout Plain Layout
31701 Chemical characters ! Symbols
31707 \begin_inset Index idx
31710 \begin_layout Plain Layout
31717 \begin_inset Index idx
31720 \begin_layout Plain Layout
31729 \begin_layout Standard
31730 An example text from chemistry:
31733 \begin_layout Quote
31735 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31738 -ion reacts with two
31739 \begin_inset Formula $\mathrm{Na^{+}}$
31742 -ions to sodium sulfate
31743 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31747 The chemical equation for this is:
31748 \begin_inset Formula
31750 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31758 \begin_layout Standard
31759 This chemical equation can directly be created as formula.
31760 To avoid that the symbols appear italic, everything is highlighted and
31761 changed by the shortcut
31767 to the upright font style.
31771 \begin_layout Plain Layout
31777 \begin_inset CommandInset ref
31779 reference "sub:Font-Styles"
31791 \begin_layout Standard
31792 A more convenient way to typeset chemical formulas is to use the command
31800 \begin_inset Index idx
31803 \begin_layout Plain Layout
31811 that is available when the LaTeX-package
31816 \begin_inset Index idx
31819 \begin_layout Plain Layout
31832 to a formula a new blue box appears where chemical formulas can be inserted
31833 in an intuitive way.
31836 \begin_layout Standard
31838 \begin_inset Tabular
31839 <lyxtabular version="3" rows="9" columns="2">
31840 <features tabularvalignment="middle">
31841 <column alignment="center" valignment="top" width="0">
31842 <column alignment="center" valignment="top" width="0">
31844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31847 \begin_layout Plain Layout
31853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31856 \begin_layout Plain Layout
31858 \begin_inset Note Note
31861 \begin_layout Plain Layout
31868 is only used as spacer.
31880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31883 \begin_layout Plain Layout
31890 \begin_layout Plain Layout
31904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31907 \begin_layout Plain Layout
31908 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31921 \begin_layout Plain Layout
31928 \begin_layout Plain Layout
31942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31945 \begin_layout Plain Layout
31946 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31959 \begin_layout Plain Layout
31966 \begin_layout Plain Layout
31980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31983 \begin_layout Plain Layout
31984 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31997 \begin_layout Plain Layout
32004 \begin_layout Plain Layout
32018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32021 \begin_layout Plain Layout
32022 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32035 \begin_layout Plain Layout
32042 \begin_layout Plain Layout
32057 \begin_layout Plain Layout
32072 \begin_layout Plain Layout
32086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32089 \begin_layout Plain Layout
32090 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32103 \begin_layout Plain Layout
32110 \begin_layout Plain Layout
32120 \begin_inset Formula $\downarrow$
32124 \begin_inset Formula $\to$
32132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32135 \begin_layout Plain Layout
32136 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32149 \begin_layout Plain Layout
32156 \begin_layout Plain Layout
32169 \begin_layout Plain Layout
32182 \begin_layout Plain Layout
32195 \begin_layout Plain Layout
32208 \begin_layout Plain Layout
32222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32225 \begin_layout Plain Layout
32226 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32239 \begin_layout Plain Layout
32246 \begin_layout Plain Layout
32259 \begin_layout Plain Layout
32272 \begin_layout Plain Layout
32285 \begin_layout Plain Layout
32302 \begin_layout Plain Layout
32316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32319 \begin_layout Plain Layout
32320 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32336 \begin_layout Standard
32337 \begin_inset Note Greyedout
32340 \begin_layout Plain Layout
32345 Inserting a formula to a
32351 box will lead to LaTeX errors.
32352 In this case TeX code has to be used like for
32366 \begin_layout Plain Layout
32387 \begin_layout Standard
32394 the command for equation
32395 \begin_inset space ~
32399 \begin_inset CommandInset ref
32401 reference "eq:chem-reaction"
32406 \begin_inset Newline newline
32417 \begin_layout Plain Layout
32430 \begin_layout Plain Layout
32443 \begin_layout Plain Layout
32456 \begin_layout Plain Layout
32469 \begin_layout Plain Layout
32482 \begin_layout Plain Layout
32494 \begin_layout Standard
32495 To create multiline chemical equations first a multiline formula is created
32497 \begin_inset CommandInset ref
32499 reference "sec:Multiline-Formulas"
32504 Afterwards the command
32510 is used in every small blue box of the formula.
32512 \begin_inset CommandInset ref
32514 reference "eq:TEOS-reaction-1"
32519 \begin_inset CommandInset ref
32521 reference "eq:TEOS-reaction-2"
32525 are an example of a multi-stage chemical reaction where every equation
32526 has its own number.
32527 \begin_inset Formula
32529 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32530 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32538 \begin_layout Standard
32549 package provides the command
32556 \begin_inset Index idx
32559 \begin_layout Plain Layout
32567 that has to be used for special cases.
32568 For more information about
32574 and more examples have a look at the documentation of
32579 \begin_inset CommandInset citation
32588 \begin_layout Section
32592 \begin_layout Standard
32593 LyX supports two types of commutative diagrams:
32601 that are explained in the following.
32604 \begin_layout Subsection
32606 \begin_inset Index idx
32609 \begin_layout Plain Layout
32618 \begin_layout Standard
32619 Diagrams of this type visualize relations by vertical and horizontal lines
32621 \begin_inset Formula
32623 \begin{CD}A@>>>B@>>>C\\
32634 \begin_layout Standard
32635 To get them, the command
32640 \begin_inset Index idx
32643 \begin_layout Plain Layout
32653 is inserted to a formula.
32654 A blue box appears with two dashed lines where further commands can be
32659 arg "newline-insert newline"
32662 a new line is created.
32663 Horizontal relations are inserted in odd, vertical in even formula lines.
32666 \begin_layout Standard
32667 To create the relations there are the following commands:
32670 \begin_layout Itemize
32675 creates a left arrow,
32686 \begin_layout Itemize
32691 creates an up arrow,
32699 a vertical equal sign
32702 \begin_layout Itemize
32708 is a placeholder for non-existent relations
32711 \begin_layout Standard
32712 All arrows can be labeled as follows:
32715 \begin_layout Itemize
32716 Is text inserted between the first and second < or >, resp., it is placed
32718 When it is inserted between the second and third one, it appears under
32722 \begin_layout Itemize
32723 When text for vertical arrows is inserted between the first and second A
32724 or V, resp., it is placed left beside the arrow.
32725 When it is inserted between the second and third one, it appears right
32727 If the text contains an A or V, these letters must be set into a TeX-brace.
32730 \begin_layout Standard
32731 As example a diagram with all possible relations:
32734 \begin_layout Standard
32735 \begin_inset Formula
32737 \begin{CD}A@>j>>B@>>k>C@=F\\
32748 \begin_layout Standard
32749 The command for this is:
32750 \begin_inset Newline newline
32761 \begin_layout Plain Layout
32770 A@>j>>B@>>k>C@=F Ctrl+Return
32771 \begin_inset Newline newline
32775 \begin_inset Phantom HPhantom
32778 \begin_layout Plain Layout
32787 \begin_layout Plain Layout
32806 \begin_inset Formula $\to$
32812 \begin_inset Newline newline
32816 \begin_inset Phantom HPhantom
32819 \begin_layout Plain Layout
32828 \begin_layout Plain Layout
32845 \begin_layout Subsection
32847 \begin_inset Index idx
32850 \begin_layout Plain Layout
32851 Diagrams ! xymatrix
32859 \begin_layout Standard
32860 To be able to use xymatrices, the LaTeX-package
32865 A xymatrix is created by inserting the command
32872 Then you are able to add new matrix columns and rows like for normal matrices,
32874 \begin_inset CommandInset ref
32876 reference "sec:Matrices"
32883 \begin_layout Standard
32884 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32886 All possibilities to create commutative diagrams and decorations are explained
32891 that you find in the menu
32893 Help\SpecialChar \menuseparator
32895 \begin_inset space ~
32903 \begin_layout Subsection
32909 \begin_inset Index idx
32912 \begin_layout Plain Layout
32921 \begin_layout Standard
32926 -diagrams, the LaTeX-package
32935 -diagram is created by inserting the command
32942 Then you are able to add new matrix columns and rows like for normal matrices,
32944 \begin_inset CommandInset ref
32946 reference "sec:Matrices"
32953 \begin_layout Standard
32954 Examples how to create
32958 diagrams in LyX is given in the
32960 Feynman-diagram manual
32962 that you find in the menu
32964 Help\SpecialChar \menuseparator
32966 \begin_inset space ~
32974 \begin_layout Section
32975 User-defined Commands
32976 \begin_inset Index idx
32979 \begin_layout Plain Layout
32980 User-defined commands
32988 \begin_layout Standard
32989 \begin_inset Note Greyedout
32992 \begin_layout Plain Layout
32997 The names of user-defined commands and macros may only consist of Latin
33006 \begin_layout Subsection
33010 \begin_inset CommandInset label
33012 name "sub:The-Command-newcommand"
33017 \begin_inset Index idx
33020 \begin_layout Plain Layout
33021 User-defined commands !
33029 \begin_inset Index idx
33032 \begin_layout Plain Layout
33043 \begin_layout Standard
33044 Many LaTeX-commands are too long to be used frequently.
33045 But it is possible to define with the command
33051 new shorter commands.
33054 \begin_layout Standard
33055 The command scheme of
33064 \begin_layout Standard
33069 newcommand{new command name}[number of arguments][optional
33074 \begin_inset Newline newline
33078 \begin_inset Phantom HPhantom
33081 \begin_layout Plain Layout
33091 {command definition}
33094 \begin_layout Standard
33095 \begin_inset Note Greyedout
33098 \begin_layout Plain Layout
33103 Assure that the name of the new command is not already used in your document
33104 or by LaTeX-packages that you use.
33105 When you for example define the command
33117 , you get an error message because
33123 is already defined as command for
33124 \begin_inset Quotes eld
33128 \begin_inset Formula $\le$
33132 \begin_inset Quotes erd
33143 \begin_layout Standard
33144 The number of arguments is an integer in the range 0
33145 \begin_inset space \thinspace{}
33149 \begin_inset space \thinspace{}
33152 9 and specifies how many arguments the new command should have.
33153 With the optional value a value for an optional argument can be predefined.
33154 When this is done, the
33162 rgument of the new command is automatically an optional one.
33165 \begin_layout Standard
33166 Here are some examples:
33169 \begin_layout Itemize
33170 To define the command
33182 , the LaTeX-preamble line is:
33183 \begin_inset VSpace medskip
33187 \begin_inset Newline newline
33201 \begin_layout Itemize
33202 To define the command
33214 , the argument (that should be underlined) must be taken into account.
33215 For this the preamble line is:
33216 \begin_inset VSpace medskip
33220 \begin_inset Newline newline
33234 \begin_inset VSpace medskip
33238 \begin_inset Newline newline
33245 acts as argument placeholder, the
33249 behind it denotes that it is the placeholder for the first argument.
33252 \begin_layout Itemize
33260 \begin_inset space \thinspace{}
33264 \begin_inset space \space{}
33274 \begin_inset VSpace medskip
33278 \begin_inset Newline newline
33289 framebox#1#2{$#3$}}
33292 \begin_inset VSpace medskip
33296 \begin_inset Newline newline
33299 The two Dollar signs creates the extra formula needed for
33306 \begin_inset CommandInset ref
33308 reference "sub:Boxes-with-Frame"
33315 \begin_layout Itemize
33316 To create a new command for
33322 where the color for the box needn't to be specified, the argument for the
33323 color is defined optional:
33324 \begin_inset VSpace medskip
33328 \begin_inset Newline newline
33339 fcolorbox{#2}{#1}{$#3$}}
33342 \begin_inset VSpace medskip
33346 \begin_inset Newline newline
33349 When the color is not specified when using
33355 , the predefined color
33362 \begin_layout Standard
33363 A test of the new defined commands:
33366 \begin_layout Standard
33368 \begin_inset Tabular
33369 <lyxtabular version="3" rows="6" columns="2">
33370 <features tabularvalignment="middle">
33371 <column alignment="center" valignment="top" width="0">
33372 <column alignment="center" valignment="top" width="0">
33374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33377 \begin_layout Plain Layout
33383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33386 \begin_layout Plain Layout
33388 \begin_inset Note Note
33391 \begin_layout Plain Layout
33398 is only used as spacer.
33410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33413 \begin_layout Plain Layout
33420 \begin_layout Plain Layout
33434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33437 \begin_layout Plain Layout
33438 \begin_inset Formula $A\gr B$
33448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33451 \begin_layout Plain Layout
33459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33462 \begin_layout Plain Layout
33463 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33476 \begin_layout Plain Layout
33480 \begin_inset Formula $\to$
33486 \begin_inset Formula $\to$
33497 \begin_layout Plain Layout
33511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33514 \begin_layout Plain Layout
33515 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33528 \begin_layout Plain Layout
33532 \begin_inset Formula $\to$
33543 \begin_layout Plain Layout
33557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33560 \begin_layout Plain Layout
33561 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33574 \begin_layout Plain Layout
33580 \begin_inset Formula $\to$
33591 \begin_layout Plain Layout
33605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33608 \begin_layout Plain Layout
33609 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33625 \begin_layout Subsection
33627 \begin_inset Index idx
33630 \begin_layout Plain Layout
33631 User-defined commands! Math macros
33637 \begin_inset Index idx
33640 \begin_layout Plain Layout
33649 \begin_layout Standard
33650 User-defined commands are especially convenient for complex expressions.
33651 When you are for example dealing in a document with quadratic equations,
33652 the same solution type occurs several times.
33653 The general form of a quadratic equation is
33654 \begin_inset Formula
33656 0=\lambda^{2}+p\lambda+q
33661 The general form of the solution is
33662 \begin_inset Formula
33664 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33672 \begin_layout Standard
33673 To define a command for the solution formula where only the three parameters
33675 \begin_inset Formula $\lambda$
33679 \begin_inset Formula $p$
33683 \begin_inset Formula $q$
33686 need to be specified and the index of
33687 \begin_inset Formula $\lambda$
33690 can be given optionally, the LaTeX-preamble line is
33691 \begin_inset Newline newline
33707 \begin_inset Newline newline
33711 \begin_inset Phantom HPhantom
33714 \begin_layout Plain Layout
33728 frac{#3^{2}}{4}-#4}}
33731 \begin_layout Standard
33732 To create with this the solution formula, the command
33733 \begin_inset Newline newline
33743 \begin_inset Formula $\to$
33749 \begin_inset Formula $\to$
33756 is inserted to a formula
33761 \begin_layout Standard
33762 The definition of the new command is unintuitive because one has to know
33763 the schemes of all used LaTeX commands, e.
33764 \begin_inset space \thinspace{}
33768 \begin_inset space \space{}
33771 that a fraction is inserted in LaTeX as
33775 frac{numerator}{denominator}
33778 Furthermore one can easily forget a brace in the definition and cannot
33779 see in LyX what the new command is doing.
33780 To avoid these problems LyX offers the possibility to use math macros instead
33790 \begin_layout Standard
33791 A math macro is created by using the menu
33793 Insert\SpecialChar \menuseparator
33794 Math\SpecialChar \menuseparator
33797 or the toolbar button
33798 \begin_inset Graphics
33799 filename ../images/math-macro_newmacroname_newcommand.png
33805 The math macro toolbar appears together with the following box where the
33807 \begin_inset Newline newline
33811 \begin_inset space \hspace*{\fill}
33815 \begin_inset Graphics
33816 filename clipart/macrobox.png
33821 \begin_inset space \hspace*{\fill}
33825 \begin_inset Newline newline
33829 \begin_inset FormulaMacro
33830 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33835 newmacroname is the default name of the macro that should be changed to
33836 something sensible.
33837 The wanted formula is inserted in the first blue box.
33838 An argument placeholder is inserted with the command
33845 \begin_inset space \thinspace{}
33849 \begin_inset space \space{}
33858 or by using the macro toolbar button
33859 \begin_inset Graphics
33860 filename ../images/math-macro-add-param.png
33866 Argument placeholders are displayed red.
33867 Maximum 9 arguments are possible.
33868 Optional arguments are created with the toolbar button
33869 \begin_inset Graphics
33870 filename ../images/math-macro-add-optional-param.png
33876 The first non-optional argument can be transformed to an optional one with
33878 \begin_inset Graphics
33879 filename ../images/math-macro-make-optional.png
33885 In the second blue box the appearance of the macro in LyX can be defined.
33886 Normally you want to see it as it is defined, so the box is kept empty.
33887 But when you have created a macro that needs lot of space on the screen,
33888 you can insert in the box for example
33889 \begin_inset Newline newline
33919 \begin_inset Newline newline
33924 For the macro only the arguments with the macro name in front of them will
33925 then be displayed in LyX, leading to a better overview.
33926 The formula appears in the output as defined in the first box.
33927 \begin_inset Newline newline
33930 The appearance of macros in formulas can furthermore be changed for single
33931 macros by setting the cursor in the macro and using the menu
33933 View\SpecialChar \menuseparator
33935 \begin_inset space ~
33939 \begin_inset space ~
33947 \begin_layout Standard
33948 To use a macro, the macro name is inserted as command to a formula, in our
33956 Our macro looks in LyX like this:
33957 \begin_inset Newline newline
33961 \begin_inset space \hspace*{\fill}
33965 \begin_inset Graphics
33966 filename clipart/macrouse.png
33971 \begin_inset space \hspace*{\fill}
33975 \begin_inset Newline newline
33978 Here is our macro example with the arguments
33979 \begin_inset Formula $x$
33983 \begin_inset Formula $\ln(x)$
33987 \begin_inset Formula $B$
33993 \begin_layout Standard
33994 \begin_inset Formula
34004 \begin_layout Standard
34005 LyX offers in the menu
34007 Tools\SpecialChar \menuseparator
34008 Preferences\SpecialChar \menuseparator
34009 Editing\SpecialChar \menuseparator
34012 different styles to edit macros.
34013 To find the style that suits you the most, choose a style and set the cursor
34014 in a macro formula to see the difference.
34017 \begin_layout Standard
34018 A math macro is transformed internally to a
34024 command when exporting the document.
34031 command is not placed in the LaTeX-preamble, therefore macros can only
34032 be used in formulas that are in the document below the macro definition
34036 \begin_layout Standard
34037 Math macros can also be directly be created from a
34044 When writing for example the command
34047 \begin_inset Newline newline
34056 xleftarrow[#2]{#1}}
34057 \begin_inset Newline newline
34062 in LyX as normal text, highlighting it completely and using then the shortcut
34067 , the command will be transformed to a math macro.
34068 Using this method you need to be careful that the
34074 command is typed correctly, otherwise you get a faulty macro leading to
34078 \begin_layout Standard
34079 Math macros currently yet have the problem that further formulas in macro
34080 definitions are handled wrongly.
34081 Therefore the example
34088 \begin_inset CommandInset ref
34090 reference "sub:The-Command-newcommand"
34094 cannot be created as macro.
34097 \begin_layout Standard
34098 When the cursor is in a macro definition box, you will see the macro toolbar
34102 \begin_layout Standard
34103 \begin_inset VSpace defskip
34109 \begin_layout Standard
34110 \begin_inset Graphics
34111 filename clipart/MacroToolbar.png
34116 \begin_inset Index idx
34119 \begin_layout Plain Layout
34128 \begin_layout Standard
34129 \begin_inset VSpace defskip
34135 \begin_layout Standard
34136 The macro toolbar contains from left to right the following buttons:
34139 \begin_layout Standard
34140 \begin_inset VSpace defskip
34146 \begin_layout Standard
34147 \begin_inset Tabular
34148 <lyxtabular version="3" rows="9" columns="2">
34149 <features islongtable="true" longtabularalignment="center">
34150 <column alignment="left" valignment="top" width="0">
34151 <column alignment="left" valignment="top" width="85col%">
34152 <row interlinespace="2.5mm">
34153 <cell alignment="center" valignment="top" usebox="none">
34156 \begin_layout Plain Layout
34157 \begin_inset Graphics
34158 filename ../images/math-macro-remove-param.png
34159 rotateOrigin center
34168 <cell alignment="center" valignment="top" usebox="none">
34171 \begin_layout Plain Layout
34174 Edit\SpecialChar \menuseparator
34175 Math\SpecialChar \menuseparator
34177 \begin_inset space ~
34180 Definition\SpecialChar \menuseparator
34181 Remove Last Argument
34187 <row interlinespace="2.5mm">
34188 <cell alignment="center" valignment="top" usebox="none">
34191 \begin_layout Plain Layout
34192 \begin_inset Graphics
34193 filename ../images/math-macro-add-param.png
34194 rotateOrigin center
34203 <cell alignment="center" valignment="top" usebox="none">
34206 \begin_layout Plain Layout
34209 Edit\SpecialChar \menuseparator
34210 Math\SpecialChar \menuseparator
34212 \begin_inset space ~
34215 Definition\SpecialChar \menuseparator
34222 <row interlinespace="2.5mm">
34223 <cell alignment="center" valignment="top" usebox="none">
34226 \begin_layout Plain Layout
34227 \begin_inset Graphics
34228 filename ../images/math-macro-make-optional.png
34229 rotateOrigin center
34238 <cell alignment="center" valignment="top" usebox="none">
34241 \begin_layout Plain Layout
34244 Edit\SpecialChar \menuseparator
34245 Math\SpecialChar \menuseparator
34247 \begin_inset space ~
34250 Definition\SpecialChar \menuseparator
34251 Make First Non-Optional into
34252 \begin_inset Newline newline
34256 \begin_inset Phantom HPhantom
34259 \begin_layout Plain Layout
34262 Edit\SpecialChar \menuseparator
34263 Math\SpecialChar \menuseparator
34265 \begin_inset space ~
34268 Definition\SpecialChar \menuseparator
34280 <row interlinespace="2.5mm">
34281 <cell alignment="center" valignment="top" usebox="none">
34284 \begin_layout Plain Layout
34285 \begin_inset Graphics
34286 filename ../images/math-macro-make-nonoptional.png
34287 rotateOrigin center
34296 <cell alignment="center" valignment="top" usebox="none">
34299 \begin_layout Plain Layout
34302 Edit\SpecialChar \menuseparator
34303 Math\SpecialChar \menuseparator
34305 \begin_inset space ~
34308 Definition\SpecialChar \menuseparator
34309 Make Last Optional into
34310 \begin_inset Newline newline
34314 \begin_inset Phantom HPhantom
34317 \begin_layout Plain Layout
34320 Edit\SpecialChar \menuseparator
34321 Math\SpecialChar \menuseparator
34323 \begin_inset space ~
34326 Definition\SpecialChar \menuseparator
34332 Non-Optional Argument
34338 <row interlinespace="2.5mm">
34339 <cell alignment="center" valignment="top" usebox="none">
34342 \begin_layout Plain Layout
34343 \begin_inset Graphics
34344 filename ../images/math-macro-remove-optional-param.png
34345 rotateOrigin center
34354 <cell alignment="center" valignment="top" usebox="none">
34357 \begin_layout Plain Layout
34360 Edit\SpecialChar \menuseparator
34361 Math\SpecialChar \menuseparator
34363 \begin_inset space ~
34366 Definition\SpecialChar \menuseparator
34367 Remove Optional Argument
34373 <row interlinespace="2.5mm">
34374 <cell alignment="center" valignment="top" usebox="none">
34377 \begin_layout Plain Layout
34378 \begin_inset Graphics
34379 filename ../images/math-macro-add-optional-param.png
34380 rotateOrigin center
34389 <cell alignment="center" valignment="top" usebox="none">
34392 \begin_layout Plain Layout
34395 Edit\SpecialChar \menuseparator
34396 Math\SpecialChar \menuseparator
34398 \begin_inset space ~
34401 Definition\SpecialChar \menuseparator
34402 Insert Optional Argument
34408 <row interlinespace="2.5mm">
34409 <cell alignment="center" valignment="top" usebox="none">
34412 \begin_layout Plain Layout
34413 \begin_inset Graphics
34414 filename ../images/math-macro-remove-greedy-param.png
34415 rotateOrigin center
34424 <cell alignment="center" valignment="top" usebox="none">
34427 \begin_layout Plain Layout
34430 Edit\SpecialChar \menuseparator
34431 Math\SpecialChar \menuseparator
34433 \begin_inset space ~
34436 Definition\SpecialChar \menuseparator
34437 Remove Last Argument
34438 \begin_inset Newline newline
34442 \begin_inset Phantom HPhantom
34445 \begin_layout Plain Layout
34448 Edit\SpecialChar \menuseparator
34449 Math\SpecialChar \menuseparator
34451 \begin_inset space ~
34454 Definition\SpecialChar \menuseparator
34460 Spitting Out To The Right
34466 <row interlinespace="2.5mm">
34467 <cell alignment="center" valignment="top" usebox="none">
34470 \begin_layout Plain Layout
34471 \begin_inset Graphics
34472 filename ../images/math-macro-append-greedy-param.png
34473 rotateOrigin center
34482 <cell alignment="center" valignment="top" usebox="none">
34485 \begin_layout Plain Layout
34488 Edit\SpecialChar \menuseparator
34489 Math\SpecialChar \menuseparator
34491 \begin_inset space ~
34494 Definition\SpecialChar \menuseparator
34496 \begin_inset Newline newline
34500 \begin_inset Phantom HPhantom
34503 \begin_layout Plain Layout
34506 Edit\SpecialChar \menuseparator
34507 Math\SpecialChar \menuseparator
34509 \begin_inset space ~
34512 Definition\SpecialChar \menuseparator
34518 Eating From The Right
34524 <row interlinespace="2.5mm">
34525 <cell alignment="center" valignment="top" usebox="none">
34528 \begin_layout Plain Layout
34529 \begin_inset Graphics
34530 filename ../images/math-macro-add-greedy-optional-param.png
34531 rotateOrigin center
34540 <cell alignment="center" valignment="top" usebox="none">
34543 \begin_layout Plain Layout
34546 Edit\SpecialChar \menuseparator
34547 Math\SpecialChar \menuseparator
34549 \begin_inset space ~
34552 Definition\SpecialChar \menuseparator
34553 Append Optional Argument
34554 \begin_inset Newline newline
34558 \begin_inset Phantom HPhantom
34561 \begin_layout Plain Layout
34564 Edit\SpecialChar \menuseparator
34565 Math\SpecialChar \menuseparator
34567 \begin_inset space ~
34570 Definition\SpecialChar \menuseparator
34576 Eating From The Right
34589 \begin_layout Section
34590 Computer Algebra Systems
34593 \begin_layout Standard
34594 LyX offers the exchange between mathematical expressions written in LyX's
34595 math editor and external applications or user defined scripts.
34596 Currently supported applications are
34613 Note that the set of supported mathematical constructs is limited only
34614 to very simple cases.
34617 \begin_layout Subsection
34621 \begin_layout Standard
34622 Write some expression in a formula, go to the
34624 Edit\SpecialChar \menuseparator
34625 Math\SpecialChar \menuseparator
34626 Use Computer Algebra System
34628 menu and choose the application you have installed on the computer.
34629 After that the result of computation should show on the right side of the
34630 expression together with the
34631 \begin_inset Quotes eld
34635 \begin_inset Quotes erd
34641 \begin_layout Standard
34642 Here are few simple examples (with results from
34646 ) to show what kind of computations can be performed:
34649 \begin_layout Itemize
34650 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34656 \begin_layout Itemize
34657 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34663 \begin_layout Itemize
34664 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34670 \begin_layout Itemize
34671 \begin_inset Formula $\det\left[\begin{array}{ccc}
34675 \end{array}\right]=-56$
34681 \begin_layout Itemize
34682 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34688 \begin_layout Subsection
34692 \begin_layout Standard
34693 Currently there is no keyboard shortcut for calling the algebra applications.
34694 One can easily bind a shortcut to the
34698 LyX function (see the
34706 \begin_inset space \thinspace{}
34710 \begin_inset space ~
34717 key inside the math editor.
34722 one would use this shortcut definition command:
34725 \begin_layout Standard
34728 command-alternatives break-paragraph;math-extern maxima
34731 \begin_layout Standard
34732 \begin_inset Newpage newpage
34738 \begin_layout Section
34740 \begin_inset Index idx
34743 \begin_layout Plain Layout
34752 \begin_layout Subsection
34754 \begin_inset Index idx
34757 \begin_layout Plain Layout
34766 \begin_layout Standard
34767 Negative numbers often look ugly in formulas because the minus sign before
34768 the number is set with the same length as the minus operator sign.
34769 When writing the negative number in normal text, the minus sign appears
34773 \begin_layout Standard
34774 Thus, the problem disappears when converting the minus sign to mathematical
34778 \begin_layout Standard
34779 An example to visualize the problem:
34782 \begin_layout Standard
34784 \begin_inset Tabular
34785 <lyxtabular version="3" rows="3" columns="2">
34786 <features tabularvalignment="middle">
34787 <column alignment="right" valignment="top" width="0">
34788 <column alignment="left" valignment="top" width="0">
34790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34793 \begin_layout Plain Layout
34799 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34802 \begin_layout Plain Layout
34810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34813 \begin_layout Plain Layout
34819 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34822 \begin_layout Plain Layout
34823 \begin_inset Formula $x=-2$
34833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34836 \begin_layout Plain Layout
34842 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34845 \begin_layout Plain Layout
34846 \begin_inset Formula $x=\textrm{-}2$
34862 \begin_layout Subsection
34863 Comma as decimal Separator
34864 \begin_inset Index idx
34867 \begin_layout Plain Layout
34876 \begin_layout Standard
34877 In LaTeX a comma inside a formula is used, according to the English convention,
34878 as number group separator.
34879 So there will be space added behind all commas in formulas.
34882 \begin_layout Standard
34883 To avoid this, the comma is highlighted and changed to mathematical text
34893 \begin_layout Standard
34894 To use all formula commas in the document as decimal separator, the file
34903 \begin_layout Plain Layout
34908 is part of the LaTeX-package
34913 \begin_inset Index idx
34916 \begin_layout Plain Layout
34921 \begin_layout Plain Layout
34941 \begin_inset Index idx
34944 \begin_layout Plain Layout
34950 is loaded with the LaTeX-preamble line
34953 \begin_layout Standard
34961 \begin_layout Subsection
34963 \begin_inset CommandInset label
34965 name "sub:Physical-Vectors"
34970 \begin_inset Index idx
34973 \begin_layout Plain Layout
34982 \begin_layout Standard
34983 Predefined vectors are offered by the LaTeX-package
34988 \begin_inset Index idx
34991 \begin_layout Plain Layout
34997 that is loaded with the LaTeX-preamble line
35000 \begin_layout Standard
35008 \begin_layout Standard
35012 \begin_layout Plain Layout
35022 \begin_inset Note Note
35025 \begin_layout Plain Layout
35026 The following table will only be displayed when the LaTeX-package
35038 \begin_layout Standard
35039 The following commands are defined:
35042 \begin_layout Standard
35044 \begin_inset Tabular
35045 <lyxtabular version="3" rows="4" columns="2">
35046 <features tabularvalignment="middle">
35047 <column alignment="center" valignment="top" width="0">
35048 <column alignment="center" valignment="top" width="0">
35050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35053 \begin_layout Plain Layout
35059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35062 \begin_layout Plain Layout
35070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35073 \begin_layout Plain Layout
35083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35086 \begin_layout Plain Layout
35087 \begin_inset Formula $\Bra{\psi}$
35097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35100 \begin_layout Plain Layout
35110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35113 \begin_layout Plain Layout
35114 \begin_inset Formula $\Ket{\psi}$
35124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35127 \begin_layout Plain Layout
35139 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35142 \begin_layout Plain Layout
35143 \begin_inset Formula $\Braket{\psi|\phi}$
35159 \begin_layout Standard
35166 assures that all vertical bars are set in the size of the surrounding brackets:
35167 \begin_inset Formula
35169 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
35178 \begin_layout Plain Layout
35188 \begin_inset Note Note
35191 \begin_layout Plain Layout
35192 The following will be displayed when the LaTeX-package
35204 \begin_layout Standard
35205 You need to install the LaTeX-package
35209 to see the rest of this subsection in the output.
35212 \begin_layout Standard
35216 \begin_layout Plain Layout
35228 \begin_layout Standard
35235 can also be achieved using the command
35241 , that is described in
35242 \begin_inset CommandInset ref
35244 reference "sub:Automatic-Bracket-Size"
35251 \begin_layout Subsection
35252 Self-defined Fractions
35253 \begin_inset CommandInset label
35255 name "sub:Self-defined-Fractions"
35260 \begin_inset Index idx
35263 \begin_layout Plain Layout
35264 Fractions ! self-defined
35272 \begin_layout Standard
35273 To define custom commands for fractions, the command
35280 \begin_inset Index idx
35283 \begin_layout Plain Layout
35291 is used in the following scheme:
35294 \begin_layout Standard
35307 bracket}{fraction bar thickness}{style}
35308 \begin_inset Newline newline
35312 \begin_inset Phantom HPhantom
35315 \begin_layout Plain Layout
35325 {numerator}{denominator}
35328 \begin_layout Standard
35329 The style is a number in the range of 0
35330 \begin_inset space \thinspace{}
35334 \begin_inset space \thinspace{}
35340 \begin_layout Standard
35342 \begin_inset Tabular
35343 <lyxtabular version="3" rows="5" columns="2">
35344 <features tabularvalignment="middle">
35345 <column alignment="center" valignment="top" width="0">
35346 <column alignment="center" valignment="top" width="0">
35348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35351 \begin_layout Plain Layout
35357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35360 \begin_layout Plain Layout
35368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35371 \begin_layout Plain Layout
35377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35380 \begin_layout Plain Layout
35381 display style formula
35388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35391 \begin_layout Plain Layout
35397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35400 \begin_layout Plain Layout
35408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35411 \begin_layout Plain Layout
35417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35420 \begin_layout Plain Layout
35428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35431 \begin_layout Plain Layout
35437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35440 \begin_layout Plain Layout
35454 \begin_layout Standard
35455 When no style is given, the size is adjusted to the surrounding environment
35456 like for the command
35465 \begin_layout Standard
35466 When no fraction bar thickness is given, the predefined value of 0.4
35467 \begin_inset space \thinspace{}
35473 \begin_layout Standard
35474 \begin_inset VSpace medskip
35477 For example, the commands
35490 \begin_inset CommandInset ref
35492 reference "sub:Fractions"
35496 are defined with the commands
35499 \begin_layout Standard
35508 genfrac{}{}{}{0}{#1}{#2}}
35511 \begin_layout Standard
35515 \begin_layout Standard
35524 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35527 \begin_layout Standard
35528 \begin_inset VSpace medskip
35531 To define a fraction where the fraction bar thickness can be given as optional
35532 argument, the following line is inserted to the LaTeX-preamble:
35535 \begin_layout Standard
35544 genfrac{}{}{#1}{}{#2}{#3}}
35547 \begin_layout Standard
35548 \begin_inset Newpage newpage
35554 \begin_layout Standard
35556 \begin_inset Formula
35558 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35559 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35564 As one can see, the distance of the numerator and the denominator to the
35565 fraction bar is round about three times the bar thickness.
35568 \begin_layout Subsection
35570 \begin_inset Index idx
35573 \begin_layout Plain Layout
35582 \begin_layout Standard
35583 To cancel formulas or formula parts, the LaTeX-package
35588 \begin_inset Index idx
35591 \begin_layout Plain Layout
35597 has to be loaded with the LaTeX-preamble line
35600 \begin_layout Standard
35608 \begin_layout Standard
35612 \begin_layout Plain Layout
35622 \begin_inset Note Note
35625 \begin_layout Plain Layout
35626 The following table will only be displayed when the LaTeX-package
35638 \begin_layout Standard
35639 There are four ways to cancel formulas:
35642 \begin_layout Standard
35644 \begin_inset Tabular
35645 <lyxtabular version="3" rows="5" columns="2">
35646 <features tabularvalignment="middle">
35647 <column alignment="center" valignment="top" width="0">
35648 <column alignment="center" valignment="top" width="0">
35650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35653 \begin_layout Plain Layout
35659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35662 \begin_layout Plain Layout
35664 \begin_inset Note Note
35667 \begin_layout Plain Layout
35674 are used here as spacer.
35686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35689 \begin_layout Plain Layout
35698 \begin_layout Plain Layout
35712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35715 \begin_layout Plain Layout
35716 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35729 \begin_layout Plain Layout
35738 \begin_layout Plain Layout
35752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35755 \begin_layout Plain Layout
35756 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35769 \begin_layout Plain Layout
35778 \begin_layout Plain Layout
35792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35795 \begin_layout Plain Layout
35796 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35809 \begin_layout Plain Layout
35813 \begin_inset Formula $\to$
35824 \begin_layout Plain Layout
35838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35841 \begin_layout Plain Layout
35842 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35858 \begin_layout Standard
35865 is especially suitable to visualize the reduction of fractions within formulas:
35866 \begin_inset Formula
35868 \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}}}
35876 \begin_layout Standard
35877 To change the size of
35884 \begin_inset Quotes eld
35888 \begin_inset Quotes erd
35891 value one can load the package
35895 with either the option
35899 which leads to the same size as for the canceled value or with the option
35904 which makes is it a bit smaller than the size one gets without using a
35910 was loaded with this line:
35913 \begin_layout Standard
35918 usepackage[samesize]{cancel}
35921 \begin_layout Standard
35922 To color the cancellation bar one adds this command as TeX code:
35925 \begin_layout Standard
35937 \begin_layout Standard
35942 can be replaced by a color of your choice.
35945 \begin_layout Standard
35949 \begin_layout Plain Layout
35965 \begin_layout Standard
35966 \begin_inset Formula
35968 \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}}}
35976 \begin_layout Standard
35980 \begin_layout Plain Layout
35994 \begin_inset Note Note
35997 \begin_layout Plain Layout
36006 \begin_layout Standard
36007 For further customizations, see the documentation of the package
36012 \begin_inset CommandInset citation
36021 \begin_layout Standard
36025 \begin_layout Plain Layout
36035 \begin_inset Note Note
36038 \begin_layout Plain Layout
36039 The following will be displayed when the LaTeX-package
36051 \begin_layout Standard
36052 You need to install the LaTeX-package
36056 to see the rest of this subsection in the output.
36059 \begin_layout Standard
36063 \begin_layout Plain Layout
36075 \begin_layout Subsection
36076 Formulas in Section Headings
36077 \begin_inset CommandInset label
36079 name "sub:Formulas-in-Section"
36084 \begin_inset Index idx
36087 \begin_layout Plain Layout
36088 Formula ! in section headings
36096 \begin_layout Standard
36097 When formulas are used in section headings, the following has to be taken
36101 \begin_layout Standard
36102 \begin_inset Note Greyedout
36105 \begin_layout Plain Layout
36111 \begin_inset Index idx
36114 \begin_layout Plain Layout
36115 Packages ! hyperref
36120 support is enabled in the document settings dialog under
36123 \begin_inset space ~
36128 , PDF-bookmarks are created for every section heading in the table of contents.
36129 If a section heading contains formulas, they are incorrectly displayed
36130 in the bookmark text, because formulas in bookmarks infringe the PDF convention
36139 \begin_layout Standard
36140 Both problems can be solved by inserting at the end of the section heading
36141 a short title with the menu
36143 Insert\SpecialChar \menuseparator
36145 \begin_inset space ~
36151 Short titles are used as alternative for multiline section headings to
36152 keep the table of contents clearly arranged.
36153 Only the short title appears in the table of contents and therefore also
36154 in the PDF-bookmark.
36157 \begin_layout Standard
36158 When formulas should be used in the table of contents but
36162 is used, one can use the following command in TeX-mode:
36165 \begin_layout Standard
36170 texorpdfstring{part}{alternative}
36171 \begin_inset Index idx
36174 \begin_layout Plain Layout
36185 \begin_layout Standard
36186 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36187 This can be characters, formulas, footnotes, but also cross-references.
36188 The alternative is used instead of the part for the bookmark.
36191 \begin_layout Standard
36192 Here are two example headings:
36193 \begin_inset VSpace -3mm
36200 \begin_layout Plain Layout
36212 \begin_layout Subsubsection
36213 Heading without formula in table of contents
36214 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36218 \begin_inset Argument
36221 \begin_layout Plain Layout
36222 Heading without formula in table of contents
36230 \begin_layout Subsubsection
36231 Heading with formula in table of contents
36235 \begin_layout Plain Layout
36245 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36252 \begin_layout Plain Layout
36262 \begin_layout Standard
36266 \begin_layout Plain Layout
36275 In the first heading a short title was used, in the second one
36284 \begin_layout Standard
36285 To get the same formatting as for the other headings, the complete heading
36294 \begin_layout Plain Layout
36296 \begin_inset CommandInset ref
36298 reference "sub:Bold-Formulas"
36310 \begin_layout Subsection
36311 Formulas in multi-column Text
36312 \begin_inset Index idx
36315 \begin_layout Plain Layout
36316 Formula ! in multi-column text
36324 \begin_layout Standard
36325 Formulas in multi-column text are often too wide to fit into a column and
36326 thus need to be set over the whole page width.
36327 This is done by using the LaTeX-package
36335 \begin_layout Plain Layout
36340 is part of every LaTeX standard installation.
36346 \begin_inset Index idx
36349 \begin_layout Plain Layout
36350 Packages ! multicol
36355 , that is loaded with the LaTeX-preamble line
36358 \begin_layout Standard
36363 usepackage{multicol}
36366 \begin_layout Standard
36367 \begin_inset Note Greyedout
36370 \begin_layout Plain Layout
36371 Note herby that the setting
36374 \begin_inset space ~
36381 Document\SpecialChar \menuseparator
36387 \begin_inset space ~
36407 \begin_layout Standard
36408 Before the multi-column text the command
36411 \begin_layout Standard
36416 begin{multicols}{column number}
36419 \begin_layout Standard
36420 is written in TeX-mode.
36421 The column number is a number in the range of 2
36422 \begin_inset space \thinspace{}
36426 \begin_inset space \thinspace{}
36430 Before the formula the multi-column text is ended by inserting the command
36433 \begin_layout Standard
36441 \begin_layout Standard
36445 \begin_layout Standard
36446 Due to the command some space is automatically added before the formula.
36448 \begin_inset space \thinspace{}
36451 mm vertical space is inserted before the formula.
36452 When the formula style
36458 \begin_layout Plain Layout
36460 \begin_inset CommandInset ref
36462 reference "sec:Formula-Styles"
36474 \begin_inset space \thinspace{}
36477 mm space is inserted instead.
36480 \begin_layout Standard
36481 As example a multi-column text with a displayed formula:
36484 \begin_layout Standard
36490 \begin_layout Plain Layout
36494 begin{multicols}{2}
36499 Das Spektrum wird fouriertransformiert.
36500 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36501 , Lösungsmittel) zu trennen.
36502 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36503 nun das Aussehen des Ausgangssignals.
36504 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36505 über alle Phasen integrieren muss.
36507 \begin_inset Formula $S$
36510 unser normiertes Ausgangssignal und
36511 \begin_inset Formula $P$
36514 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36518 \begin_layout Plain Layout
36528 \begin_inset VSpace -6mm
36532 \begin_inset Formula
36534 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36543 \begin_layout Plain Layout
36547 begin{multicols}{2}
36553 \begin_inset Formula $S_{0}$
36556 das Signal ohne Gradient ist und die Normierungsbedingung
36557 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36561 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36563 \begin_inset Formula $\nicefrac{\pi}{2}$
36567 \begin_inset space \thinspace{}
36570 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36571 das Signal zusätzlich abschwächt.
36572 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36574 \begin_inset Formula $T_{2}$
36580 \begin_layout Standard
36586 \begin_layout Plain Layout
36598 \begin_layout Subsection
36599 Formulas with Description of Variables
36600 \begin_inset Index idx
36603 \begin_layout Plain Layout
36604 Formula ! with description of variables
36612 \begin_layout Standard
36613 To describe variables within a formula, like in formula
36614 \begin_inset CommandInset ref
36616 reference "eq:within"
36625 \begin_inset Formula $n$
36629 \begin_inset space ~
36632 matrix is used with left aligned columns for the
36633 \begin_inset Formula $n$
36640 \begin_layout Plain Layout
36642 \begin_inset CommandInset ref
36644 reference "sec:Matrices"
36653 To set the description in a smaller size, before the matrix e.
36654 \begin_inset space \thinspace{}
36658 \begin_inset space \space{}
36671 \begin_layout Plain Layout
36673 \begin_inset CommandInset ref
36675 reference "sub:Font-Sizes"
36687 \begin_layout Standard
36688 When the formula style
36694 \begin_layout Plain Layout
36696 \begin_inset CommandInset ref
36698 reference "sec:Formula-Styles"
36719 \begin_layout Plain Layout
36726 only works in formulas with the style
36731 \begin_inset CommandInset ref
36733 reference "sub:Variable-Space"
36742 is inserted before and after the matrix to have the same separation of
36743 the matrix from the equation and the side margin.
36746 \begin_layout Standard
36747 When the formula style
36751 is used, the method described in
36752 \begin_inset CommandInset ref
36754 reference "sub:Flalign-Environment"
36758 is used to indent formulas.
36760 \begin_inset CommandInset ref
36762 reference "eq:within"
36766 consists of five columns whereas in the first two columns contain the equation,
36767 the third the matrix and the last one an empty TeX-brace.
36768 \begin_inset Formula
36770 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36771 \rho & \textrm{density}\\
36772 V & \textrm{volume}\\
36773 g & \textrm{gravitational acceleration}
36774 \end{array} & & {}\label{eq:within}
36782 \begin_layout Subsection
36783 Upright small Greek Letters
36784 \begin_inset CommandInset label
36786 name "sub:Upright-small-Greek"
36791 \begin_inset Index idx
36794 \begin_layout Plain Layout
36795 Greek letters ! upright
36803 \begin_layout Standard
36804 Most of the math fonts only provide italic small Greek letters.
36805 But for symbols of elementary particles like pions and neutrinos, upright
36806 Greek letters are needed.
36815 \begin_layout Plain Layout
36820 is part of the LaTeX-package
36825 \begin_inset Index idx
36828 \begin_layout Plain Layout
36833 \begin_layout Plain Layout
36853 \begin_inset Index idx
36856 \begin_layout Plain Layout
36862 that is loaded with the LaTeX-preamble line
36865 \begin_layout Standard
36870 usepackage{upgreek}
36873 \begin_layout Standard
36879 \begin_layout Plain Layout
36889 \begin_inset Note Note
36892 \begin_layout Plain Layout
36893 The following table will only be displayed when the LaTeX-package
36902 They are created when the command for a small Greek letters is started
36908 For example the command
36915 \begin_inset Formula $\uptau$
36921 \begin_layout Standard
36922 With these commands reactions of elementary particles can be typeset:
36923 \begin_inset Formula
36925 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36933 \begin_layout Standard
36934 The upright letters are more bold and wider than the italic ones.
36935 They should therefore not be used for units like
36936 \begin_inset Quotes eld
36940 \begin_inset Quotes erd
36946 \begin_layout Standard
36950 \begin_layout Plain Layout
36960 \begin_inset Note Note
36963 \begin_layout Plain Layout
36964 The following will be displayed when the LaTeX-package
36976 \begin_layout Standard
36977 You need to install the LaTeX-package
36981 to see the rest of this subsection in the output.
36984 \begin_layout Standard
36988 \begin_layout Plain Layout
37000 \begin_layout Standard
37001 \begin_inset Newpage newpage
37007 \begin_layout Subsection
37008 Text Characters in Formulas
37009 \begin_inset CommandInset label
37011 name "sub:Text-Characters-in"
37016 \begin_inset Index idx
37019 \begin_layout Plain Layout
37028 \begin_layout Standard
37029 In some cases you might want to insert text characters directly into formulas.
37030 When for example the centered dot · is often used in formulas like
37031 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
37034 , one would have to insert the command
37044 \begin_layout Plain Layout
37046 \begin_inset CommandInset ref
37048 reference "sub:Binary-Operators"
37057 all the time, because this character is defined in all encodings as text
37059 But the encoding can be changed by this LaTeX-preamble line:
37062 \begin_layout Standard
37067 Declare Inputtext{183}{
37077 f\SpecialChar \textcompwordmark{}
37081 \begin_layout Standard
37082 The character encoding (menu
37084 Document\SpecialChar \menuseparator
37085 Settings\SpecialChar \menuseparator
37088 ) specifies what character appears when a keyboard key is pressed.
37089 When the key for the character '·' is pressed, internally the command
37096 But this command is not available in a formula so that you would get LaTeX-erro
37098 With the changed encoding the right command is chosen automatically, depending
37099 on if the character was inserted into a formula or not.
37102 \begin_layout Standard
37103 The encoding of several characters is saved in definition files.
37104 Fore example the encoding
37108 is defined in the file
37112 that is in the installation folder of LaTeX.
37113 Encodings should only be changed via the LaTeX-preamble and not in the
37115 Otherwise own documents could not be edited by other LyX users working
37116 on other computers.
37119 \begin_layout Standard
37120 \begin_inset VSpace medskip
37123 Besides the centered dot, in this document the degree sign ° is defined
37124 with the following LaTeX-preamble line so that it can directly be inserted
37128 \begin_layout Standard
37133 DeclareInputtext{176}{
37143 f\SpecialChar \textcompwordmark{}
37147 \begin_layout Standard
37148 \begin_inset Newpage newpage
37154 \begin_layout Section
37157 \begin_inset Index idx
37160 \begin_layout Plain Layout
37169 \begin_layout Standard
37170 This section is a summary of the most important typographic rules, listed
37175 \begin_layout Plain Layout
37176 This collection was partly taken from the German semi-official dictionary
37178 \begin_inset Quotes eld
37182 \begin_inset Quotes erd
37186 \begin_inset CommandInset citation
37192 that lists some of the ISO rules.
37193 More rules are listed in
37194 \begin_inset CommandInset citation
37208 \begin_layout Itemize
37217 \begin_layout Plain Layout
37218 done with font styles, see
37219 \begin_inset CommandInset ref
37221 reference "sub:Font-Styles"
37230 , no matter if they appear in italic text: 30
37231 \begin_inset space \thinspace{}
37235 \begin_inset Newline newline
37238 Between the value and the unit is the smallest space, see
37239 \begin_inset CommandInset ref
37241 reference "sub:Predefined-Space"
37246 \begin_inset Newline newline
37249 This convention is automatically fulfilled when the command
37256 When it is entered to a formula, two boxes appear.
37257 In the first one the value is inserted, in the second one the unit, and
37259 \begin_inset Formula $\unit[30]{km/h}$
37263 \begin_inset space \thinspace{}
37273 is not a real LaTeX command but the command
37279 , therefore you cannot use it in TeX code.
37282 \begin_layout Itemize
37283 Percent and perthousand signs are set like physical units:
37284 \begin_inset Newline newline
37288 \begin_inset space \thinspace{}
37294 \begin_layout Itemize
37295 The degree sign follows directly on the value: 15°, but not when it is used
37297 \begin_inset space \thinspace{}
37303 \begin_layout Itemize
37304 In numbers with more than four digits the smallest space is inserted before
37305 every third digit to group them:
37315 \begin_inset space \thinspace{}
37319 \begin_inset space \thinspace{}
37325 \begin_layout Itemize
37326 For dimensions like 120×90×40
37327 \begin_inset space \thinspace{}
37330 cm the multiplication sign
37331 \begin_inset Quotes eld
37335 \begin_inset Quotes erd
37339 It is available either via the command
37347 Insert\SpecialChar \menuseparator
37348 Special Character\SpecialChar \menuseparator
37354 \begin_layout Itemize
37355 Functions with names consisting of several letters are set upright to avoid
37357 \begin_inset CommandInset ref
37359 reference "sub:Predefined-Functions"
37366 \begin_layout Itemize
37367 Indices consisting of several letters, are set upright:
37368 \begin_inset Formula $E_{\mathrm{kin}}$
37372 \begin_inset Newline newline
37375 Components of matrices are set italic:
37376 \begin_inset Formula $\hat{H}_{kl}$
37382 \begin_layout Itemize
37383 The differentiation/integration operator 'd', the Euler's number 'e' and
37384 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37388 \begin_layout Itemize
37389 The character that denotes a
37393 transformation is inserted either by the command
37401 \begin_layout Plain Layout
37414 Insert\SpecialChar \menuseparator
37415 Special Character\SpecialChar \menuseparator
37416 Symbols\SpecialChar \menuseparator
37418 \begin_inset space ~
37424 \begin_inset Formula $\mathscr{F}$
37430 \begin_layout Standard
37431 \begin_inset Newpage newpage
37437 \begin_layout Section
37439 \begin_inset Index idx
37442 \begin_layout Plain Layout
37451 \begin_layout Standard
37452 Some characters and symbols can be created with several commands.
37453 Here is a list of the synonym commands:
37456 \begin_layout Standard
37457 \begin_inset VSpace bigskip
37461 \begin_inset space \hfill{}
37465 \begin_inset Tabular
37466 <lyxtabular version="3" rows="12" columns="2">
37467 <features tabularvalignment="middle">
37468 <column alignment="center" valignment="top" width="0pt">
37469 <column alignment="center" valignment="top" width="0pt">
37471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37474 \begin_layout Plain Layout
37480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37483 \begin_layout Plain Layout
37485 \begin_inset Note Note
37488 \begin_layout Plain Layout
37495 is only used as spacer.
37507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37510 \begin_layout Plain Layout
37518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37521 \begin_layout Plain Layout
37525 \begin_layout Plain Layout
37538 \begin_layout Plain Layout
37552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37555 \begin_layout Plain Layout
37563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37566 \begin_layout Plain Layout
37576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37579 \begin_layout Plain Layout
37587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37590 \begin_layout Plain Layout
37600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37603 \begin_layout Plain Layout
37611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37614 \begin_layout Plain Layout
37622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37625 \begin_layout Plain Layout
37633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37636 \begin_layout Plain Layout
37644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37647 \begin_layout Plain Layout
37655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37658 \begin_layout Plain Layout
37668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37671 \begin_layout Plain Layout
37679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37682 \begin_layout Plain Layout
37692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37695 \begin_layout Plain Layout
37703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37706 \begin_layout Plain Layout
37716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37719 \begin_layout Plain Layout
37727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37730 \begin_layout Plain Layout
37740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37743 \begin_layout Plain Layout
37751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37754 \begin_layout Plain Layout
37762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37765 \begin_layout Plain Layout
37773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37776 \begin_layout Plain Layout
37788 \begin_inset space \hfill{}
37792 \begin_inset Tabular
37793 <lyxtabular version="3" rows="12" columns="2">
37794 <features tabularvalignment="middle">
37795 <column alignment="center" valignment="top" width="0pt">
37796 <column alignment="center" valignment="top" width="0pt">
37798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37801 \begin_layout Plain Layout
37807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37810 \begin_layout Plain Layout
37818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37821 \begin_layout Plain Layout
37829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37832 \begin_layout Plain Layout
37844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37847 \begin_layout Plain Layout
37855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37858 \begin_layout Plain Layout
37868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37871 \begin_layout Plain Layout
37879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37882 \begin_layout Plain Layout
37892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37895 \begin_layout Plain Layout
37903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37906 \begin_layout Plain Layout
37914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37917 \begin_layout Plain Layout
37925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37928 \begin_layout Plain Layout
37936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37939 \begin_layout Plain Layout
37947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37950 \begin_layout Plain Layout
37960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37963 \begin_layout Plain Layout
37971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37974 \begin_layout Plain Layout
37984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37987 \begin_layout Plain Layout
37995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37998 \begin_layout Plain Layout
38008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38011 \begin_layout Plain Layout
38019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38022 \begin_layout Plain Layout
38032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38035 \begin_layout Plain Layout
38043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38046 \begin_layout Plain Layout
38056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
38059 \begin_layout Plain Layout
38067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
38070 \begin_layout Plain Layout
38084 \begin_inset space \hfill{}
38090 \begin_layout Standard
38091 \begin_inset Newpage newpage
38097 \begin_layout Bibliography
38098 \labelwidthstring References
38099 \begin_inset CommandInset bibitem
38100 LatexCommand bibitem
38112 The LaTeX Companion
38115 Addison Wesley, 2004
38118 \begin_layout Bibliography
38119 \labelwidthstring References
38120 \begin_inset CommandInset bibitem
38121 LatexCommand bibitem
38127 \begin_inset CommandInset href
38130 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
38134 of LaTeX's math abilities
38137 \begin_layout Bibliography
38138 \labelwidthstring References
38139 \begin_inset CommandInset bibitem
38140 LatexCommand bibitem
38146 \begin_inset CommandInset href
38149 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
38157 \begin_layout Plain Layout
38169 \begin_layout Bibliography
38170 \labelwidthstring References
38171 \begin_inset CommandInset bibitem
38172 LatexCommand bibitem
38178 \begin_inset CommandInset href
38181 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38185 of all symbols available with LaTeX-packages
38188 \begin_layout Bibliography
38189 \labelwidthstring References
38190 \begin_inset CommandInset bibitem
38191 LatexCommand bibitem
38197 \begin_inset CommandInset href
38199 name "Documentation"
38200 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
38204 of the LaTeX-package
38209 \begin_inset Index idx
38212 \begin_layout Plain Layout
38221 \begin_layout Bibliography
38222 \labelwidthstring References
38223 \begin_inset CommandInset bibitem
38224 LatexCommand bibitem
38230 \begin_inset CommandInset href
38232 name "Documentation"
38233 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38237 of the LaTeX-package
38242 \begin_inset Index idx
38245 \begin_layout Plain Layout
38246 Packages ! hyperref
38254 \begin_layout Bibliography
38255 \labelwidthstring References
38256 \begin_inset CommandInset bibitem
38257 LatexCommand bibitem
38263 \begin_inset CommandInset href
38265 name "Documentation"
38266 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38270 of the LaTeX-package
38275 \begin_inset Index idx
38278 \begin_layout Plain Layout
38287 \begin_layout Bibliography
38288 \labelwidthstring References
38289 \begin_inset CommandInset bibitem
38290 LatexCommand bibitem
38296 \begin_inset CommandInset href
38299 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
38310 \begin_inset CommandInset ref
38312 reference "sub:Operator-Limits"
38317 \begin_inset Index idx
38320 \begin_layout Plain Layout
38331 \begin_layout Bibliography
38332 \labelwidthstring References
38333 \begin_inset CommandInset bibitem
38334 LatexCommand bibitem
38345 Auflage, Duden 2001
38348 \begin_layout Bibliography
38349 \labelwidthstring References
38350 \begin_inset CommandInset bibitem
38351 LatexCommand bibitem
38357 \begin_inset CommandInset href
38360 target "http://physics.nist.gov/Document/checklist.pdf"
38364 for reviewing manuscripts
38367 \begin_layout Standard
38368 \begin_inset CommandInset index_print
38369 LatexCommand printindex