1 #LyX 2.0.0svn 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}
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46 \renewcommand{\sectionautorefname}{sec.\negthinspace}
47 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
50 % don't load packages twice
51 % see first footnote in sec. 9.3
52 \@ifundefined{textcolor}{\usepackage{color}}{}
54 % the pages of the TOC are numbered roman
55 % and a PDF-bookmark for the TOC is added
57 \let\myTOC\tableofcontents
58 \renewcommand{\tableofcontents}{%
60 \pdfbookmark[1]{\contentsname}{}
63 \pagenumbering{arabic}}
65 % insert additional vertical space of 1.5 mm between footnotes,
67 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
69 % provides caption formatting
70 \setkomafont{captionlabel}{\bfseries}
73 \usepackage[samesize]{cancel}
75 % enables calculation of values,
78 % for multiple table row and column cells
85 % for the Fourier transformation symbol
88 % center multirows (e.g. in sec. 13.3)
89 \renewcommand{\multirowsetup}{\centering}
91 % define a color, used in sec.9.3
92 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
94 % declare operators (see sec. 10.4 and sec. 15.2)
95 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
96 \DeclareMathOperator{\sgn}{sgn}
98 \newcommand{\spce}{\textvisiblespace}
100 % example definitions for sec. 20.1
101 \newcommand{\gr}{\Longrightarrow}
102 \newcommand{\us}[1]{\underline{#1}}
103 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
104 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
105 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
107 % example macro from sec. 19.4
108 %\def\tagform@#1{\maketag@@@{|#1|}}
110 % macro from sec. 10.2
111 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
112 \def\mathclap {\mathpalette \mathclapinternal}
113 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
115 % redefine the greyed out note
116 \renewenvironment{lyxgreyedout}
117 {\textcolor{blue}\bgroup}{\egroup}
119 % ------------------------------------
120 % used to check for needed LaTeX packages
123 % check for package eurosym
124 % used for the Euro symbol
126 \IfFileExists{eurosym.sty}
127 {\usepackage[gennarrow]{eurosym}
128 \setboolean{eurosym}{true}}
129 {\setboolean{eurosym}{false}}
131 % check for package braket
132 % used for physical vectors
134 \IfFileExists{braket.sty}
136 \setboolean{braket}{true}}
137 {\setboolean{braket}{false}}
139 % check for package cancel
141 \IfFileExists{cancel.sty}
143 \setboolean{cancel}{true}}
144 {\setboolean{cancel}{false}}
146 % check for package upgreek
148 \IfFileExists{upgreek.sty}
149 {\usepackage{upgreek}
150 \setboolean{upgreek}{true}}
151 {\setboolean{upgreek}{false}}
153 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
154 \use_default_options false
155 \maintain_unincluded_children false
161 \font_typewriter default
162 \font_default_family default
170 \default_output_format default
172 \bibtex_command default
173 \index_command default
177 \pdf_title "LyX's Math Manual"
178 \pdf_author "LyX Team, Uwe Stöhr"
179 \pdf_subject "LyX-documentation about math"
180 \pdf_keywords "LyX, Mathed"
182 \pdf_bookmarksnumbered true
183 \pdf_bookmarksopen true
184 \pdf_bookmarksopenlevel 1
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200 \paperorientation portrait
208 \paragraph_separation skip
210 \quotes_language english
213 \paperpagestyle plain
217 \tracking_changes false
218 \output_changes false
220 \html_be_strict false
226 LyX's detailed Math manual
234 \begin_layout Plain Layout
236 If you have comments or error corrections, please send them to the LyX Documenta
240 \begin_inset CommandInset href
242 name "lyx-docs@lists.lyx.org"
243 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
254 \begin_inset Note Note
257 \begin_layout Plain Layout
264 \begin_inset Newline newline
268 \begin_inset Newline newline
276 \begin_layout Standard
277 \begin_inset CommandInset toc
278 LatexCommand tableofcontents
285 \begin_layout Standard
286 \begin_inset Note Note
289 \begin_layout Plain Layout
290 To export this document to PDF, PS or DVI the LaTeX-packages
292 braket, cancel, eurosym,
303 If they are not installed the document can be export anyway but the sections
304 where the packages are required will not appear in the output.
309 ; if it is not installed, this file cannot be exported.
312 \begin_layout Plain Layout
313 The latest PDF-version of this document can be found here:
314 \begin_inset Newline newline
319 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
327 \begin_layout Standard
328 \begin_inset Newpage newpage
334 \begin_layout Section
338 \begin_layout Standard
339 This document explains LyX's math features and is furthermore a collection
340 of LaTeX-commands used for mathematical characters and constructs.
341 The explanations are designed for the usage of commands.
342 It is therefore required that you have read the section
353 \begin_layout Standard
354 Most of the characters and many constructs explained in this manual are
355 also accessible via the menu
359 \SpecialChar \menuseparator
375 But everybody who has to write lots of formulas will notice that it is
376 much faster to use commands instead of the math toolbar.
377 Therefore this manual is focused on commands but also mentions the correspondin
378 g toolbar buttons when available.
381 \begin_layout Standard
382 If not specially mentioned the commands are only available within formulas.
383 To be able to use all commands explained in this document, the option
387 must be used in the document settings (menu
389 Document\SpecialChar \menuseparator
390 Settings\SpecialChar \menuseparator
401 \begin_layout Plain Layout
404 Use AMS math package automatically
410 \begin_layout Plain Layout
419 -math when math constructs are found that are supported by LyX.
427 \begin_layout Standard
428 This document doesn't list all
432 \begin_layout Plain Layout
445 \begin_layout Plain Layout
450 \begin_layout Plain Layout
459 -math commands is in the file
462 \begin_inset CommandInset href
465 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
471 , which is part of every LaTeX standard installation.
476 for lucidity reasons.
479 \begin_layout Section
483 \begin_layout Standard
484 To create an inline formula
485 \begin_inset Index idx
488 \begin_layout Plain Layout
494 that is embedded into a text line, use one of the shortcuts
500 or the toolbar button
501 \begin_inset Graphics
502 filename ../images/math-mode.png
508 \begin_inset Newline newline
511 To create a display style formula
512 \begin_inset Index idx
515 \begin_layout Plain Layout
516 Formula ! display style
521 that will appear bigger and in an own paragraph, use one of these shortcuts:
531 \begin_layout Standard
532 To change a display style formula to an inline formula, set the cursor into
533 the formula and use one of the shortcuts
541 Edit\SpecialChar \menuseparator
542 Math\SpecialChar \menuseparator
546 The same way is used to change an inline formula to a display style formula.
549 \begin_layout Standard
550 To display parts of an inline formula in the size of a display style formula,
558 \begin_inset Index idx
561 \begin_layout Plain Layout
570 Then a new blue box appears in which the desired formula part is inserted.
573 \begin_layout Standard
574 Only inline formulas are allowed inside tables.
577 \begin_layout Standard
582 can be turned on in the menu
584 View\SpecialChar \menuseparator
588 When you click there on
589 \begin_inset Quotes eld
593 \begin_inset Quotes erd
596 the toolbar will be shown permanently at the bottom; this state is visualized
601 menu with a checkmark.
602 When you click in this state again on
603 \begin_inset Quotes eld
607 \begin_inset Quotes erd
618 is only shown when the cursor is within a formula; this state is visualized
619 by the renaming of the menu entry from
620 \begin_inset Quotes eld
624 \begin_inset Quotes erd
628 \begin_inset Quotes eld
636 \begin_inset Quotes erd
642 \begin_layout Standard
644 \begin_inset Index idx
647 \begin_layout Plain Layout
653 is invoked by pressing the toolbar button
654 \begin_inset Graphics
655 filename ../images/ert-insert.png
662 Insert\SpecialChar \menuseparator
667 \begin_layout Plain Layout
683 \begin_inset Note Note
686 \begin_layout Plain Layout
687 In LyX there are three
688 \begin_inset Quotes eld
692 \begin_inset Quotes erd
695 that appear in the output with sub- and superscript letters: TeX, LaTeX
699 \begin_layout Plain Layout
700 To avoid that these names are recognized as proper names, a TeX-brace pair
709 \begin_layout Standard
710 To change the LaTeX-preamble
711 \begin_inset Index idx
714 \begin_layout Plain Layout
722 Document\SpecialChar \menuseparator
723 Settings\SpecialChar \menuseparator
728 \begin_layout Plain Layout
744 \begin_layout Standard
745 To edit matrices, case differentiations and multiline formulas subsequently,
748 Edit\SpecialChar \menuseparator
753 Edit\SpecialChar \menuseparator
755 \begin_inset space \thinspace{}
759 \begin_inset space \thinspace{}
769 When lines and columns are swapped via the menu, the column or line where
770 the cursor is in is exchanged with the column to the right or the line
772 Is the cursor in the last column or row, the exchange is done with the
773 column to the left or the line above.
776 \begin_layout Standard
777 To write text in formulas
781 \begin_layout Plain Layout
782 For multiline formulas the command
789 \begin_inset CommandInset ref
791 reference "sub:Text-in-multiline"
805 \begin_inset Index idx
808 \begin_layout Plain Layout
815 \begin_inset Index idx
818 \begin_layout Plain Layout
825 This mode is invoked with the shortcut
831 or by the insertion of the command
838 \begin_inset Index idx
841 \begin_layout Plain Layout
850 The text appears black in LyX and can therefore be distinguished from the
851 other formula parts that appear blue.
852 In the output mathematical text is set upright, in contrary to other formula
856 \begin_layout Subsection*
860 \begin_layout Standard
861 Most of the LaTeX-commands for math constructs have the following scheme:
864 \begin_layout Standard
880 \begin_layout Standard
881 A command starts always with a backslash
882 \begin_inset Quotes gld
892 \begin_inset Quotes grd
896 To omit optional arguments, also omit the associated brackets.
897 The braces around the required arguments are named in this document as
899 \begin_inset Index idx
902 \begin_layout Plain Layout
909 If you add in a formula a left brace to a command name, LyX creates automatical
911 In all other cases TeX-braces are created in formulas with the command
919 TeX-braces appear red in LyX, in contrary to normal braces that appear
921 In TeX-mode no command is needed to get TeX-braces.
922 TeX-braces don't appear in the output.
925 \begin_layout Standard
926 When commands without arguments, like commands for symbols are entered in
927 TeX-mode, a space character must
931 be behind the command to end it.
932 This space doesn't appear in the output.
933 When the space should appear in the output, the space must be followed
934 by a protected space in normal text.
937 \begin_layout Standard
938 A protected space is inserted with
941 arg "space-insert protected"
947 \begin_layout Subsection*
948 \begin_inset Newpage newpage
954 \begin_layout Itemize
959 \begin_layout Plain Layout
960 This visible space character can be created with the command
967 \begin_inset Index idx
970 \begin_layout Plain Layout
978 , inserted in TeX-mode.
987 \begin_layout Plain Layout
1000 denotes a space character to be input.
1003 \begin_layout Itemize
1005 \begin_inset Formula $\to$
1008 denotes the usage of the corresponding arrow key on the keyboard.
1011 \begin_layout Subsection*
1015 \begin_layout Standard
1017 \begin_inset Float table
1023 \begin_layout Plain Layout
1025 \begin_inset Caption
1027 \begin_layout Plain Layout
1028 \begin_inset CommandInset label
1030 name "tab:Available-units"
1042 \begin_layout Plain Layout
1044 \begin_inset Tabular
1045 <lyxtabular version="3" rows="13" columns="2">
1046 <features tabularvalignment="middle">
1047 <column alignment="center" valignment="top" width="0">
1048 <column alignment="center" valignment="top" width="0">
1050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1053 \begin_layout Plain Layout
1059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1062 \begin_layout Plain Layout
1070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1073 \begin_layout Plain Layout
1079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1082 \begin_layout Plain Layout
1090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1093 \begin_layout Plain Layout
1099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1102 \begin_layout Plain Layout
1110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1113 \begin_layout Plain Layout
1119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1122 \begin_layout Plain Layout
1124 \begin_inset space \thinspace{}
1128 \begin_inset space \thinspace{}
1138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1141 \begin_layout Plain Layout
1147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1150 \begin_layout Plain Layout
1152 \begin_inset space \thinspace{}
1156 \begin_inset space \thinspace{}
1166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1169 \begin_layout Plain Layout
1175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1178 \begin_layout Plain Layout
1180 \begin_inset space \thinspace{}
1184 \begin_inset space \thinspace{}
1194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1197 \begin_layout Plain Layout
1203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1206 \begin_layout Plain Layout
1208 \begin_inset space \thinspace{}
1212 \begin_inset space \thinspace{}
1222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1225 \begin_layout Plain Layout
1231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1234 \begin_layout Plain Layout
1236 \begin_inset space \thinspace{}
1240 \begin_inset space \thinspace{}
1250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1253 \begin_layout Plain Layout
1259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1262 \begin_layout Plain Layout
1264 \begin_inset space \thinspace{}
1268 \begin_inset Formula $\approx$
1272 \begin_inset space \thinspace{}
1282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1285 \begin_layout Plain Layout
1291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1294 \begin_layout Plain Layout
1296 \begin_inset space \thinspace{}
1300 \begin_inset space \thinspace{}
1310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1313 \begin_layout Plain Layout
1319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1322 \begin_layout Plain Layout
1326 \begin_inset Quotes eld
1332 \begin_inset Quotes erd
1342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1345 \begin_layout Plain Layout
1351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1354 \begin_layout Plain Layout
1356 \begin_inset Quotes eld
1364 \begin_inset Quotes erd
1374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1377 \begin_layout Plain Layout
1383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1386 \begin_layout Plain Layout
1388 \begin_inset space \thinspace{}
1392 \begin_inset Formula $\nicefrac{1}{18}$
1396 \begin_inset space \thinspace{}
1417 \begin_layout Standard
1418 \begin_inset Newpage newpage
1424 \begin_layout Section
1428 \begin_layout Subsection
1430 \begin_inset Index idx
1433 \begin_layout Plain Layout
1440 \begin_inset Index idx
1443 \begin_layout Plain Layout
1450 \begin_inset Index idx
1453 \begin_layout Plain Layout
1458 \begin_layout Plain Layout
1469 \begin_layout Plain Layout
1482 \begin_inset Index idx
1485 \begin_layout Plain Layout
1490 \begin_layout Plain Layout
1501 \begin_layout Plain Layout
1516 \begin_layout Standard
1517 Indices are created with an underscore
1518 \begin_inset Quotes eld
1522 \begin_inset Quotes erd
1525 or via the math toolbar button
1526 \begin_inset Graphics
1527 filename ../images/math-subscript.png
1532 , exponents with a caret
1533 \begin_inset Quotes eld
1537 \begin_inset Quotes erd
1540 or via the math toolbar button
1541 \begin_inset Graphics
1542 filename ../images/math-superscript.png
1550 \begin_layout Standard
1552 \begin_inset Tabular
1553 <lyxtabular version="3" rows="4" columns="2">
1554 <features tabularvalignment="middle">
1555 <column alignment="center" valignment="top" width="0pt">
1556 <column alignment="center" valignment="top" width="0pt">
1558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1561 \begin_layout Plain Layout
1567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1570 \begin_layout Plain Layout
1572 \begin_inset Note Note
1575 \begin_layout Plain Layout
1582 is only used as spacer.
1594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1597 \begin_layout Plain Layout
1603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1606 \begin_layout Plain Layout
1607 \begin_inset Formula $B_{V}$
1617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1620 \begin_layout Plain Layout
1626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1629 \begin_layout Plain Layout
1630 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1643 \begin_layout Plain Layout
1648 \begin_layout Plain Layout
1662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1665 \begin_layout Plain Layout
1666 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1682 \begin_layout Standard
1683 As the caret is in some languages an accent, vowels will be accentuated
1684 in this case and not set as exponents
1688 \begin_layout Plain Layout
1689 Depending on the used keyboard settings this can also happen for other character
1696 To get in this case exponents, press
1700 after the caret as in the last example.
1703 \begin_layout Subsection
1705 \begin_inset CommandInset label
1707 name "sub:Fractions"
1712 \begin_inset Index idx
1715 \begin_layout Plain Layout
1724 \begin_layout Standard
1725 Fractions are generated with the command
1732 \begin_inset Index idx
1735 \begin_layout Plain Layout
1743 or via the math toolbar button
1744 \begin_inset Graphics
1745 filename ../images/math/frac.png
1751 The font size is adjusted automatically, depending on whether the fraction
1752 is in an inline or display style formula.
1753 With the math toolbar button
1754 \begin_inset Graphics
1755 filename ../images/math/frac-square.png
1760 you can select different fraction types.
1763 \begin_layout Standard
1771 \begin_inset Index idx
1774 \begin_layout Plain Layout
1782 a fraction can be created that has in any case the size of a display style
1791 \begin_inset Index idx
1794 \begin_layout Plain Layout
1802 the fraction appears always with the size of an inline formula.
1806 \begin_layout Standard
1807 A line with the fraction
1808 \begin_inset Formula $\frac{1}{2}$
1811 that was created with the command
1820 \begin_layout Standard
1821 A line with the fraction
1822 \begin_inset Formula $\dfrac{1}{2}$
1825 that was created with the command
1834 \begin_layout Standard
1836 \begin_inset Tabular
1837 <lyxtabular version="3" rows="4" columns="2">
1838 <features tabularvalignment="middle">
1839 <column alignment="center" valignment="top" width="0pt">
1840 <column alignment="center" valignment="top" width="0pt">
1842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1845 \begin_layout Plain Layout
1851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1854 \begin_layout Plain Layout
1856 \begin_inset Note Note
1859 \begin_layout Plain Layout
1866 is only used as spacer.
1878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1881 \begin_layout Plain Layout
1888 \begin_layout Plain Layout
1898 \begin_inset Formula $\downarrow$
1906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1909 \begin_layout Plain Layout
1910 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1923 \begin_layout Plain Layout
1930 \begin_layout Plain Layout
1940 \begin_inset Formula $\downarrow$
1948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1951 \begin_layout Plain Layout
1952 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1965 \begin_layout Plain Layout
1972 \begin_layout Plain Layout
1985 \begin_layout Plain Layout
2000 \begin_layout Plain Layout
2010 \begin_inset Formula $\downarrow$
2014 \begin_inset Formula $\downarrow\downarrow$
2022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2025 \begin_layout Plain Layout
2026 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2042 \begin_layout Standard
2043 \begin_inset VSpace bigskip
2047 \begin_inset Newpage newpage
2050 For nested fractions the command
2057 \begin_inset Index idx
2060 \begin_layout Plain Layout
2070 \begin_inset VSpace -3mm
2076 \begin_layout Standard
2077 \begin_inset Formula \begin{align*}
2078 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2079 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2087 \begin_layout Standard
2088 The command for the example above is:
2091 \begin_layout Standard
2100 \begin_layout Plain Layout
2110 \begin_inset Formula $\downarrow$
2119 \begin_layout Plain Layout
2134 \begin_layout Plain Layout
2144 \begin_inset Formula $\downarrow$
2148 \begin_inset Formula $\downarrow$
2154 \begin_layout Standard
2155 \begin_inset VSpace medskip
2161 \begin_layout Standard
2168 sets the fraction always in the size of a displayed formula, also when
2169 it is part of another fraction.
2172 \begin_layout Standard
2173 It is possible to specify the alignment of the numerator.
2180 is used to left align it, the command
2193 centers the numerator.
2194 These fractions demonstrate the different alignments:
2197 \begin_layout Standard
2198 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2202 \begin_inset Formula $\cfrac{A}{B+C}$
2206 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2212 \begin_layout Standard
2213 \begin_inset Note Greyedout
2216 \begin_layout Plain Layout
2233 are no real LaTeX commands but represent the command
2237 cfrac[alignment]{numerator}{denominator}
2240 Therefore you cannot use them in TeX code.
2248 \begin_layout Standard
2249 \begin_inset VSpace medskip
2252 It is often advantageous to combine
2265 \begin_inset Formula \[
2266 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2273 \begin_layout Standard
2274 For inline fractions with a sloped fraction stroke you can use the command
2282 \begin_inset Index idx
2285 \begin_layout Plain Layout
2294 \begin_inset Formula $\nicefrac{5}{31}$
2304 \begin_inset Index idx
2307 \begin_layout Plain Layout
2316 \begin_inset Formula $\unitfrac{5}{31}$
2319 There is furthermore the command
2325 that offers to write a fraction in combination with a number:
2326 \begin_inset Formula $\unitfrac[2]{1}{3}$
2332 \begin_layout Standard
2333 \begin_inset Note Greyedout
2336 \begin_layout Plain Layout
2347 is not a real LaTeX command but the command
2348 \begin_inset Newline newline
2355 unitfrac[number]{numerator}{denominator}
2358 Therefore you cannot use it in TeX code.
2366 \begin_layout Standard
2367 How to define own fractions where the fraction stroke can be changed, is
2369 \begin_inset CommandInset ref
2371 reference "sub:Self-defined-Fractions"
2378 \begin_layout Subsection
2380 \begin_inset Index idx
2383 \begin_layout Plain Layout
2392 \begin_layout Standard
2393 Square roots are created with
2400 \begin_inset Index idx
2403 \begin_layout Plain Layout
2411 or the math toolbar button
2412 \begin_inset Graphics
2413 filename ../images/math/sqrt.png
2418 , all other roots with the command
2425 \begin_inset Index idx
2428 \begin_layout Plain Layout
2436 or with the math toolbar button
2437 \begin_inset Graphics
2438 filename ../images/math/root.png
2446 \begin_layout Standard
2448 \begin_inset Tabular
2449 <lyxtabular version="3" rows="3" columns="2">
2450 <features tabularvalignment="middle">
2451 <column alignment="center" valignment="top" width="0pt">
2452 <column alignment="center" valignment="top" width="0pt">
2454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2457 \begin_layout Plain Layout
2463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2466 \begin_layout Plain Layout
2468 \begin_inset Note Note
2471 \begin_layout Plain Layout
2478 is only used as spacer.
2490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2493 \begin_layout Plain Layout
2500 \begin_layout Plain Layout
2514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2517 \begin_layout Plain Layout
2518 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2531 \begin_layout Plain Layout
2538 \begin_layout Plain Layout
2548 \begin_inset Formula $\downarrow$
2556 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2559 \begin_layout Plain Layout
2560 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2576 \begin_layout Standard
2577 A square root can also be created with
2583 when the root index field is left empty.
2586 \begin_layout Standard
2587 With certain indices the distance to the root is too small, like in this
2589 \begin_inset Formula $\sqrt[\beta]{B}$
2593 \begin_inset Newline newline
2597 \begin_inset Formula $\beta$
2601 To avoid this, the commands
2608 \begin_inset Index idx
2611 \begin_layout Plain Layout
2626 \begin_inset Index idx
2629 \begin_layout Plain Layout
2637 are used with the following scheme:
2640 \begin_layout Standard
2654 \begin_layout Standard
2655 Distance is the number of Big Points (unit bp;
2656 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2659 ), that the index should be moved to the left or top, resp..
2660 The commands are written to the index.
2661 This way the command
2662 \begin_inset Newline newline
2672 \begin_inset Formula $\to$
2678 \begin_inset Formula $\to$
2687 \begin_layout Plain Layout
2697 \begin_inset Formula $\to$
2701 \begin_inset Newline newline
2706 produces a correct typeset formula:
2707 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2713 \begin_layout Subsection
2714 Binomial Coefficients
2715 \begin_inset Index idx
2718 \begin_layout Plain Layout
2719 Binomial coefficients
2727 \begin_layout Standard
2728 Binomial coefficients are inserted with the command
2735 \begin_inset Index idx
2738 \begin_layout Plain Layout
2746 or with the submenu of the math toolbar button
2747 \begin_inset Graphics
2748 filename ../images/math/frac-square.png
2754 Analog to fractions (
2773 \begin_inset Index idx
2776 \begin_layout Plain Layout
2791 \begin_inset Index idx
2794 \begin_layout Plain Layout
2803 For other brackets around binomial coeficients there are the commands
2810 \begin_inset Index idx
2813 \begin_layout Plain Layout
2828 \begin_inset Index idx
2831 \begin_layout Plain Layout
2842 \begin_layout Standard
2844 \begin_inset Tabular
2845 <lyxtabular version="3" rows="6" columns="2">
2846 <features tabularvalignment="middle">
2847 <column alignment="center" valignment="top" width="0pt">
2848 <column alignment="center" valignment="top" width="0pt">
2850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2853 \begin_layout Plain Layout
2859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2862 \begin_layout Plain Layout
2864 \begin_inset Note Note
2867 \begin_layout Plain Layout
2874 is only used as spacer.
2886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2889 \begin_layout Plain Layout
2896 \begin_layout Plain Layout
2906 \begin_inset Formula $\downarrow$
2914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2917 \begin_layout Plain Layout
2918 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2931 \begin_layout Plain Layout
2938 \begin_layout Plain Layout
2948 \begin_inset Formula $\downarrow$
2956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2959 \begin_layout Plain Layout
2960 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2973 \begin_layout Plain Layout
2980 \begin_layout Plain Layout
2990 \begin_inset Formula $\downarrow$
2998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3001 \begin_layout Plain Layout
3002 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3015 \begin_layout Plain Layout
3022 \begin_layout Plain Layout
3032 \begin_inset Formula $\downarrow$
3040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3043 \begin_layout Plain Layout
3044 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3057 \begin_layout Plain Layout
3064 \begin_layout Plain Layout
3074 \begin_inset Formula $\downarrow$
3082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3085 \begin_layout Plain Layout
3086 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3102 \begin_layout Subsection
3103 Case Differentiations
3104 \begin_inset Index idx
3107 \begin_layout Plain Layout
3108 Case differentiations
3116 \begin_layout Standard
3118 \begin_inset Tabular
3119 <lyxtabular version="3" rows="3" columns="2">
3120 <features tabularvalignment="middle">
3121 <column alignment="center" valignment="top" width="0pt">
3122 <column alignment="center" valignment="top" width="0pt">
3124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3127 \begin_layout Plain Layout
3133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3136 \begin_layout Plain Layout
3144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3147 \begin_layout Plain Layout
3154 \begin_layout Plain Layout
3164 \begin_inset Formula $\to$
3168 \begin_inset Index idx
3171 \begin_layout Plain Layout
3184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3187 \begin_layout Plain Layout
3188 \begin_inset Formula $\begin{cases}
3199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3202 \begin_layout Plain Layout
3209 \begin_layout Plain Layout
3221 arg "newline-insert newline"
3229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3232 \begin_layout Plain Layout
3233 \begin_inset Formula $\begin{cases}
3234 A & \textrm{for }x>0\\
3235 B & \textrm{for }x=0
3252 \begin_layout Standard
3259 or the usage of the math toolbar button
3260 \begin_inset Graphics
3261 filename ../images/math/cases.png
3266 you can create new lines with the shortcut
3269 arg "newline-insert newline"
3272 or the table toolbar button
3273 \begin_inset Graphics
3274 filename ../images/tabular-feature_append-row.png
3282 \begin_layout Standard
3289 is also available via the menu
3291 Insert\SpecialChar \menuseparator
3292 Math\SpecialChar \menuseparator
3298 \begin_layout Subsection
3300 \begin_inset Index idx
3303 \begin_layout Plain Layout
3312 \begin_layout Standard
3320 \begin_inset Index idx
3323 \begin_layout Plain Layout
3331 every character can be displayed canceled.
3332 The characters are quasi accentuated by a slash.
3335 \begin_layout Standard
3337 \begin_inset Tabular
3338 <lyxtabular version="3" rows="4" columns="2">
3339 <features tabularvalignment="middle">
3340 <column alignment="center" valignment="top" width="0pt">
3341 <column alignment="center" valignment="top" width="0pt">
3343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3346 \begin_layout Plain Layout
3352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3355 \begin_layout Plain Layout
3363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3366 \begin_layout Plain Layout
3374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3377 \begin_layout Plain Layout
3378 \begin_inset Formula $\not=$
3388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3391 \begin_layout Plain Layout
3401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3404 \begin_layout Plain Layout
3405 \begin_inset Formula $\not\le$
3415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3418 \begin_layout Plain Layout
3428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3431 \begin_layout Plain Layout
3432 \begin_inset Formula $\not\parallel$
3448 \begin_layout Standard
3449 The last example shows, that not all negations look good.
3450 Therefore there are for some negations special commands (see
3451 \begin_inset CommandInset ref
3453 reference "sub:Mathematical-Symbols"
3458 \begin_inset CommandInset ref
3460 reference "sec:Relations"
3467 \begin_layout Subsection
3469 \begin_inset CommandInset label
3471 name "sub:Placeholders"
3476 \begin_inset Index idx
3479 \begin_layout Plain Layout
3486 \begin_inset Index idx
3489 \begin_layout Plain Layout
3490 Chemical characters ! Isotopes
3496 \begin_inset Index idx
3499 \begin_layout Plain Layout
3504 \begin_layout Plain Layout
3515 \begin_layout Plain Layout
3530 \begin_layout Standard
3532 \begin_inset space \thinspace{}
3536 \begin_inset space \space{}
3543 \begin_layout Plain Layout
3544 Typesetting isotopes and chemical symbols is described in
3545 \begin_inset CommandInset ref
3547 reference "sub:Chemical-Symbols-and"
3556 the following problem occurs:
3559 \begin_layout Standard
3561 \begin_inset Tabular
3562 <lyxtabular version="3" rows="2" columns="2">
3563 <features tabularvalignment="middle">
3564 <column alignment="center" valignment="top" width="0pt">
3565 <column alignment="center" valignment="top" width="0pt">
3567 <cell alignment="center" valignment="top" usebox="none">
3570 \begin_layout Plain Layout
3571 Indices created with sub- and superscripts:
3576 <cell alignment="center" valignment="top" usebox="none">
3579 \begin_layout Plain Layout
3580 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3590 <cell alignment="center" valignment="top" usebox="none">
3593 \begin_layout Plain Layout
3599 <cell alignment="center" valignment="top" usebox="none">
3602 \begin_layout Plain Layout
3603 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3617 \begin_inset Note Note
3620 \begin_layout Plain Layout
3627 is only used as spacer.
3635 \begin_layout Standard
3636 The shorter index is by default placed below or above the first character
3637 of the longer index.
3638 To avoid this there is the command
3645 \begin_inset Index idx
3648 \begin_layout Plain Layout
3656 or the math toolbar button
3657 \begin_inset space \thinspace{}
3664 \begin_layout Plain Layout
3665 can be found in the submenu of the toolbar button
3666 \begin_inset Graphics
3667 filename ../images/math/space.png
3678 \begin_inset Graphics
3679 filename ../images/math/phantom.png
3684 that creates one or more phantom characters.
3691 a small blue box appears that is superposed with two red arrows.
3692 The arrows indicate that the complete width and height of the box content
3693 will be created as placeholder.
3694 Phantom characters are accordingly placeholders with the size of the characters.
3697 \begin_layout Standard
3699 \begin_inset Tabular
3700 <lyxtabular version="3" rows="4" columns="2">
3701 <features tabularvalignment="middle">
3702 <column alignment="center" valignment="top" width="0">
3703 <column alignment="center" valignment="top" width="0">
3705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3708 \begin_layout Plain Layout
3714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3717 \begin_layout Plain Layout
3719 \begin_inset Note Note
3722 \begin_layout Plain Layout
3729 is only used as spacer.
3741 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3744 \begin_layout Plain Layout
3749 \begin_layout Plain Layout
3764 \begin_layout Plain Layout
3774 \begin_inset Formula $\to$
3781 \begin_layout Plain Layout
3795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3798 \begin_layout Plain Layout
3799 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3812 \begin_layout Plain Layout
3817 \begin_layout Plain Layout
3832 \begin_layout Plain Layout
3842 \begin_inset Formula $\to$
3849 \begin_layout Plain Layout
3863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3866 \begin_layout Plain Layout
3867 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3880 \begin_layout Plain Layout
3887 \begin_layout Plain Layout
3902 \begin_layout Plain Layout
3912 \begin_inset Formula $\to$
3919 \begin_layout Plain Layout
3933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3936 \begin_layout Plain Layout
3937 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3953 \begin_layout Standard
3954 Furthermore there are the commands
3961 \begin_inset Index idx
3964 \begin_layout Plain Layout
3973 \begin_inset space ~
3977 \begin_inset Graphics
3978 filename ../images/math/vphantom.png
3990 \begin_inset Index idx
3993 \begin_layout Plain Layout
4002 \begin_inset space ~
4006 \begin_inset Graphics
4007 filename ../images/math/hphantom.png
4019 creates only space for the maximal height of the characters in the box
4020 but not for its width.
4027 creates only space for the width of the box content.
4028 Therefore the boxes of both commands have only one red arrow.
4031 \begin_layout Standard
4042 \begin_layout Plain Layout
4057 space for the height of the integral sign,
4061 \begin_layout Plain Layout
4068 creates an integral sign, see
4069 \begin_inset CommandInset ref
4071 reference "sub:Big-Operators"
4080 because this is the larger character.
4081 An example application is in
4082 \begin_inset CommandInset ref
4084 reference "sub:Multiline-Brackets"
4091 \begin_layout Standard
4092 Placeholders can also be used for text when it is inserted via the menu
4095 Insert\SpecialChar \menuseparator
4096 Formatting\SpecialChar \menuseparator
4102 \begin_layout Standard
4104 \begin_inset Newline newline
4108 \begin_inset Phantom Phantom
4111 \begin_layout Plain Layout
4120 \begin_layout Subsection
4122 \begin_inset Index idx
4125 \begin_layout Plain Layout
4132 \begin_inset Index idx
4135 \begin_layout Plain Layout
4136 Formula ! underlined
4144 \begin_layout Standard
4146 \begin_inset Tabular
4147 <lyxtabular version="3" rows="4" columns="2">
4148 <features tabularvalignment="middle">
4149 <column alignment="center" valignment="top" width="0pt">
4150 <column alignment="center" valignment="top" width="0pt">
4152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4155 \begin_layout Plain Layout
4161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4164 \begin_layout Plain Layout
4166 \begin_inset Note Note
4169 \begin_layout Plain Layout
4176 is only used as spacer.
4188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4191 \begin_layout Plain Layout
4198 \begin_layout Plain Layout
4208 \begin_inset Index idx
4211 \begin_layout Plain Layout
4224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4227 \begin_layout Plain Layout
4228 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4238 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4241 \begin_layout Plain Layout
4248 \begin_layout Plain Layout
4258 \begin_inset Index idx
4261 \begin_layout Plain Layout
4274 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4277 \begin_layout Plain Layout
4278 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4291 \begin_layout Plain Layout
4298 \begin_layout Plain Layout
4313 \begin_layout Plain Layout
4327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4330 \begin_layout Plain Layout
4331 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4347 \begin_layout Standard
4348 In the last example it doesn't matter if first
4363 \begin_layout Standard
4364 To double underline e.
4365 \begin_inset space \thinspace{}
4369 \begin_inset space \space{}
4381 \begin_layout Standard
4382 It is possible to place up to 6 lines above or below characters.
4385 \begin_layout Standard
4386 \begin_inset VSpace bigskip
4389 Custom lines can be created using the command
4396 \begin_inset Index idx
4399 \begin_layout Plain Layout
4407 which has the following scheme:
4410 \begin_layout Standard
4415 rule[vertical offset]{length}{thickness}
4418 \begin_layout Standard
4419 The optional vertical offset shifts the line upwards (or downwards, when
4420 the value is negative).
4422 \begin_inset CommandInset ref
4424 reference "tab:Available-units"
4428 can be used for the values.
4429 Here are two example lines created with the commands
4430 \begin_inset Newline newline
4437 rule[-2ex]{3cm}{2pt}
4448 \begin_layout Standard
4450 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4456 \begin_layout Standard
4463 can also be used for text when a line is inserted via the menu
4465 Insert\SpecialChar \menuseparator
4466 Formatting\SpecialChar \menuseparator
4468 \begin_inset space ~
4476 \begin_layout Standard
4478 \begin_inset CommandInset line
4489 \begin_layout Subsection
4491 \begin_inset CommandInset label
4498 \begin_inset Index idx
4501 \begin_layout Plain Layout
4510 \begin_layout Standard
4511 There are different types of ellipses available.
4515 \begin_layout Plain Layout
4516 In the math toolbar in the submenu of the button
4517 \begin_inset Graphics
4518 filename ../images/math/ldots.png
4528 For listings dots at the baseline are used (
4535 \begin_inset Index idx
4538 \begin_layout Plain Layout
4546 ), while for operations dots are needed that are on the same height as the
4554 \begin_inset Index idx
4557 \begin_layout Plain Layout
4566 When using the command
4573 \begin_inset Index idx
4576 \begin_layout Plain Layout
4584 , LaTeX decides on the basis of the next character what type is used.
4587 \begin_layout Standard
4589 \begin_inset Tabular
4590 <lyxtabular version="3" rows="8" columns="2">
4591 <features tabularvalignment="middle">
4592 <column alignment="center" valignment="top" width="0pt">
4593 <column alignment="center" valignment="top" width="0pt">
4595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4598 \begin_layout Plain Layout
4604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4607 \begin_layout Plain Layout
4615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4618 \begin_layout Plain Layout
4623 \begin_layout Plain Layout
4638 \begin_layout Plain Layout
4652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4655 \begin_layout Plain Layout
4656 \begin_inset Formula $A_{1},\dots,A_{n}$
4666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4669 \begin_layout Plain Layout
4674 \begin_layout Plain Layout
4689 \begin_layout Plain Layout
4703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4706 \begin_layout Plain Layout
4707 \begin_inset Formula $A_{1}+\dots+A_{n}$
4717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4720 \begin_layout Plain Layout
4725 \begin_layout Plain Layout
4740 \begin_layout Plain Layout
4754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4757 \begin_layout Plain Layout
4758 \begin_inset Formula $A_{1},\ldots,A_{n}$
4768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4771 \begin_layout Plain Layout
4776 \begin_layout Plain Layout
4791 \begin_layout Plain Layout
4805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4808 \begin_layout Plain Layout
4809 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4822 \begin_layout Plain Layout
4830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4833 \begin_layout Plain Layout
4834 \begin_inset Formula $\vdots$
4844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4847 \begin_layout Plain Layout
4855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4858 \begin_layout Plain Layout
4859 \begin_inset Formula $\ddots$
4869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4872 \begin_layout Plain Layout
4874 \begin_inset space \thinspace{}
4877 matrix with the different dots
4882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4885 \begin_layout Plain Layout
4886 \begin_inset Formula $\begin{array}{ccc}
4887 A_{11} & \cdots & A_{1m}\\
4888 \vdots & \ddots & \vdots\\
4889 A_{n1} & \cdots & A_{nm}
4906 \begin_layout Standard
4907 The ellipses available in menu
4909 Insert\SpecialChar \menuseparator
4911 \begin_inset space ~
4925 \begin_layout Standard
4926 \begin_inset VSpace medskip
4929 Specially for matrices there are ellipses that span over several columns.
4930 They are created with the command
4937 \begin_inset Index idx
4940 \begin_layout Plain Layout
4948 , that has the following scheme:
4951 \begin_layout Standard
4956 hdotsfor[distance]{number of columns}
4959 \begin_layout Standard
4960 The number of columns specifies how many columns should be spanned.
4961 Distance is a factor for the distance between the dots.
4964 \begin_layout Standard
4965 In the following matrix the command
4971 was inserted in the first box of the second line, to get an ellipsis with
4972 a dot distance twice as long as with the command
4979 \begin_inset Formula \[
4980 \left(\begin{array}{cccc}
4984 \end{array}\right)\]
4988 Note that the matrix fields that should be spanned must be empty, otherwise
4989 you get LaTeX-errors.
4992 \begin_layout Standard
4993 \begin_inset VSpace bigskip
4996 Furthermore you can fill with the command
5003 \begin_inset Index idx
5006 \begin_layout Plain Layout
5014 the rest of a line with dots.
5015 The effect of these commands is the same like with
5022 \begin_inset CommandInset ref
5024 reference "sub:Variable-Space"
5031 \begin_layout Standard
5032 For example the command
5040 \begin_layout Plain Layout
5054 \begin_layout Standard
5055 \begin_inset Formula $A\dotfill B$
5061 \begin_layout Standard
5068 there is for a line the command
5075 \begin_inset Index idx
5078 \begin_layout Plain Layout
5089 \begin_layout Standard
5090 \begin_inset Formula $A\hrulefill B$
5096 \begin_layout Standard
5097 To use the commands for text, they have to be inserted in TeX-mode.
5100 \begin_layout Section
5102 \begin_inset CommandInset label
5109 \begin_inset Index idx
5112 \begin_layout Plain Layout
5121 \begin_layout Standard
5122 Matrices can be inserted via the math toolbar button
5123 \begin_inset Graphics
5124 filename ../images/dialog-show_mathmatrix.png
5131 Insert\SpecialChar \menuseparator
5132 Math\SpecialChar \menuseparator
5136 You will be asked for the number of matrix columns and rows and the alignment.
5137 The vertical alignment is hereby only of importance for matrices in inline
5141 \begin_layout Standard
5142 The first matrix is top
5143 \begin_inset Formula $\begin{array}[t]{cccc}
5151 \begin_inset Formula $\begin{array}{cccc}
5158 and the third bottom
5159 \begin_inset Formula $\begin{array}[b]{cccc}
5169 \begin_layout Standard
5170 The horizontal alignment specifies how the column entries should be aligned.
5171 It is set by entering a letter for every column.
5176 denotes left aligned,
5185 To create for example a 4
5190 \begin_inset space ~
5193 matrix where the first column is left aligned, the second and third are
5194 centered and the last one is right aligned, one enters for the horizontal
5200 Normally are in a matrix all columns centered, therefore the default is
5201 for every column is a
5208 \begin_layout Standard
5209 Horizontal alignment:
5212 \begin_layout Standard
5218 \begin_inset Formula $\begin{array}{lll}
5230 \begin_inset Formula $\begin{array}{ccc}
5242 \begin_inset Formula $\begin{array}{rrr}
5252 \begin_layout Standard
5253 To add or delete rows and columns subsequently, the math toolbar buttons
5255 \begin_inset Graphics
5256 filename ../images/tabular-feature_append-row.png
5262 \begin_inset Graphics
5263 filename ../images/tabular-feature_delete-row.png
5269 \begin_inset space \thinspace{}
5274 Edit\SpecialChar \menuseparator
5278 New rows can also be created with
5281 arg "newline-insert newline"
5287 \begin_layout Standard
5288 \begin_inset VSpace bigskip
5291 Parentheses around a matrix can can either be created with the commands
5299 \begin_inset Index idx
5302 \begin_layout Plain Layout
5317 \begin_inset Index idx
5320 \begin_layout Plain Layout
5331 \begin_inset space ~
5337 \begin_inset CommandInset ref
5339 reference "sub:Automatic-Bracket-Size"
5343 , or by using the following commands:
5344 \begin_inset VSpace medskip
5350 \begin_layout Standard
5351 \begin_inset space \hfill{}
5355 \begin_inset Tabular
5356 <lyxtabular version="3" rows="4" columns="2">
5357 <features tabularvalignment="middle">
5358 <column alignment="center" valignment="top" width="0">
5359 <column alignment="center" valignment="top" width="0">
5361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5364 \begin_layout Plain Layout
5370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5373 \begin_layout Plain Layout
5375 \begin_inset Note Note
5378 \begin_layout Plain Layout
5385 is only used as spacer.
5397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5400 \begin_layout Plain Layout
5407 \begin_layout Plain Layout
5421 \begin_inset space \thinspace{}
5429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5432 \begin_layout Plain Layout
5433 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5434 0 & \textrm{-}\mathrm{i}\\
5436 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5449 \begin_layout Plain Layout
5456 \begin_layout Plain Layout
5470 \begin_inset space \thinspace{}
5478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5481 \begin_layout Plain Layout
5482 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5483 0 & \textrm{-}\mathrm{i}\\
5485 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5498 \begin_layout Plain Layout
5505 \begin_layout Plain Layout
5519 \begin_inset space \thinspace{}
5527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5530 \begin_layout Plain Layout
5531 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5532 0 & \textrm{-}\mathrm{i}\\
5534 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5548 \begin_inset space \hfill{}
5552 \begin_inset Tabular
5553 <lyxtabular version="3" rows="4" columns="2">
5554 <features tabularvalignment="middle">
5555 <column alignment="center" valignment="top" width="0">
5556 <column alignment="center" valignment="top" width="0">
5558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5561 \begin_layout Plain Layout
5567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5570 \begin_layout Plain Layout
5578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5581 \begin_layout Plain Layout
5588 \begin_layout Plain Layout
5602 \begin_inset space \thinspace{}
5610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5613 \begin_layout Plain Layout
5614 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5615 0 & \textrm{-}\mathrm{i}\\
5617 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5630 \begin_layout Plain Layout
5637 \begin_layout Plain Layout
5651 \begin_inset space \thinspace{}
5659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5662 \begin_layout Plain Layout
5663 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5664 0 & \textrm{-}\mathrm{i}\\
5666 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5679 \begin_layout Plain Layout
5686 \begin_layout Plain Layout
5700 \begin_inset space \thinspace{}
5708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5711 \begin_layout Plain Layout
5712 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5713 0 & \textrm{-}\mathrm{i}\\
5715 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5729 \begin_inset space \hfill{}
5735 \begin_layout Standard
5736 \begin_inset VSpace medskip
5740 \begin_inset space \thinspace{}
5744 \begin_inset space \space{}
5753 is inserted, a blue box appears between two vertical lines where the matrix
5757 \begin_layout Standard
5758 \begin_inset VSpace bigskip
5761 As all multiline formulas are matrices, the length
5768 \begin_inset Index idx
5771 \begin_layout Plain Layout
5779 that is described in
5780 \begin_inset CommandInset ref
5782 reference "sub:Column-Separation"
5786 can also be used to change the column separation of matrices.
5789 \begin_layout Standard
5790 To change the row separation, the command
5797 \begin_inset Index idx
5800 \begin_layout Plain Layout
5809 It is used as follows:
5812 \begin_layout Standard
5819 arraystretch}{stretch factor}
5820 \begin_inset Index idx
5823 \begin_layout Plain Layout
5834 \begin_layout Standard
5841 assigns the stretch factor to the predefined command
5849 \begin_inset space \thinspace{}
5853 \begin_inset space \space{}
5856 the row separation, use the factor 2.
5857 This is then used for all following matrices.
5858 To go back to the original separation, assign the factor 1 to
5867 \begin_layout Standard
5868 To set matrices into a text line, the command
5875 \begin_inset Index idx
5878 \begin_layout Plain Layout
5887 When it is inserted a blue box with two dashed lines appears.
5888 In this box the matrix is inserted.
5891 \begin_layout Standard
5893 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5895 \end{smallmatrix}\right)$
5901 \begin_layout Section
5902 Brackets and Delimiters
5903 \begin_inset Index idx
5906 \begin_layout Plain Layout
5913 \begin_inset Index idx
5916 \begin_layout Plain Layout
5925 \begin_layout Subsection
5926 Vertical Brackets and Delimiters
5927 \begin_inset Index idx
5930 \begin_layout Plain Layout
5939 \begin_layout Standard
5940 \begin_inset space \hfill{}
5944 \begin_inset Tabular
5945 <lyxtabular version="3" rows="9" columns="2">
5946 <features tabularvalignment="middle">
5947 <column alignment="center" valignment="top" width="0pt">
5948 <column alignment="center" valignment="top" width="0pt">
5950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5953 \begin_layout Plain Layout
5959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5962 \begin_layout Plain Layout
5970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5973 \begin_layout Plain Layout
5979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5982 \begin_layout Plain Layout
5983 \begin_inset Formula $($
5993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5996 \begin_layout Plain Layout
6002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6005 \begin_layout Plain Layout
6006 \begin_inset Formula $\{$
6016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6019 \begin_layout Plain Layout
6025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6028 \begin_layout Plain Layout
6029 \begin_inset Formula $[$
6039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6042 \begin_layout Plain Layout
6050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6053 \begin_layout Plain Layout
6054 \begin_inset Formula $\langle$
6064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6067 \begin_layout Plain Layout
6075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6078 \begin_layout Plain Layout
6079 \begin_inset Formula $\lceil$
6089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6092 \begin_layout Plain Layout
6100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6103 \begin_layout Plain Layout
6104 \begin_inset Formula $\lfloor$
6114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6117 \begin_layout Plain Layout
6123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6126 \begin_layout Plain Layout
6127 \begin_inset Formula $/$
6137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6140 \begin_layout Plain Layout
6146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6149 \begin_layout Plain Layout
6150 \begin_inset Formula $|$
6164 \begin_inset space \hfill{}
6168 \begin_inset Tabular
6169 <lyxtabular version="3" rows="9" columns="2">
6170 <features tabularvalignment="middle">
6171 <column alignment="center" valignment="top" width="0pt">
6172 <column alignment="center" valignment="top" width="0pt">
6174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6177 \begin_layout Plain Layout
6183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6186 \begin_layout Plain Layout
6194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6197 \begin_layout Plain Layout
6203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6206 \begin_layout Plain Layout
6207 \begin_inset Formula $)$
6217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6220 \begin_layout Plain Layout
6226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6229 \begin_layout Plain Layout
6230 \begin_inset Formula $\}$
6240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6243 \begin_layout Plain Layout
6249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6252 \begin_layout Plain Layout
6253 \begin_inset Formula $]$
6263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6266 \begin_layout Plain Layout
6274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6277 \begin_layout Plain Layout
6278 \begin_inset Formula $\rangle$
6288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6291 \begin_layout Plain Layout
6299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6302 \begin_layout Plain Layout
6303 \begin_inset Formula $\rceil$
6313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6316 \begin_layout Plain Layout
6324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6327 \begin_layout Plain Layout
6328 \begin_inset Formula $\rfloor$
6338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6341 \begin_layout Plain Layout
6351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6354 \begin_layout Plain Layout
6355 \begin_inset Formula $\backslash$
6365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6368 \begin_layout Plain Layout
6376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6379 \begin_layout Plain Layout
6380 \begin_inset Formula $\|$
6394 \begin_inset space \hfill{}
6400 \begin_layout Standard
6403 \begin_inset Note Greyedout
6406 \begin_layout Plain Layout
6411 In TeX-mode the command
6418 \begin_inset Index idx
6421 \begin_layout Plain Layout
6429 must be used for the backslash, because the command
6437 produces there a line break.
6445 \begin_layout Standard
6446 For all characters listed above the size can be adjusted with the commands
6447 described in the following two subsections.
6448 When using these commands, the characters < and > can directly be used
6449 instead of the commands
6464 \begin_layout Subsubsection
6466 \begin_inset CommandInset label
6468 name "sub:Manual-Bracket-Size"
6473 \begin_inset Index idx
6476 \begin_layout Plain Layout
6477 Bracket size ! manual
6485 \begin_layout Standard
6486 The bracket size can be specified manually by the LaTeX-commands
6493 \begin_inset Index idx
6496 \begin_layout Plain Layout
6529 denotes the smallest and
6535 the largest bracket size.
6538 \begin_layout Standard
6539 These commands are used to emphasize levels of brackets:
6542 \begin_layout Standard
6544 \begin_inset Tabular
6545 <lyxtabular version="3" rows="2" columns="2">
6546 <features tabularvalignment="middle">
6547 <column alignment="center" valignment="top" width="0pt">
6548 <column alignment="center" valignment="top" width="0pt">
6550 <cell alignment="center" valignment="top" usebox="none">
6553 \begin_layout Plain Layout
6554 all brackets in the same size:
6559 <cell alignment="center" valignment="top" usebox="none">
6562 \begin_layout Plain Layout
6563 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6573 <cell alignment="center" valignment="top" usebox="none">
6576 \begin_layout Plain Layout
6582 <cell alignment="center" valignment="top" usebox="none">
6585 \begin_layout Plain Layout
6586 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6600 \begin_inset Note Note
6603 \begin_layout Plain Layout
6610 is only used as spacer.
6618 \begin_layout Standard
6619 For the second formula the command
6629 \begin_layout Plain Layout
6643 \begin_layout Standard
6644 Here is an overview about all bracket sizes:
6647 \begin_layout Standard
6667 \begin_layout Plain Layout
6684 \begin_layout Plain Layout
6697 \begin_layout Plain Layout
6713 \begin_layout Standard
6715 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6721 \begin_layout Standard
6728 -commands there is the variant
6735 \begin_inset Index idx
6738 \begin_layout Plain Layout
6746 that adds a bit more space between the bracket and its content, and the
6760 \begin_inset Index idx
6763 \begin_layout Plain Layout
6773 , that don't add additional space.
6778 at the end of the command
6784 is for a left bracket; for a right bracket this will be replaced by an
6790 A left or right bracket can each be an opening or closing bracket.
6793 \begin_layout Standard
6794 In the following table is a comparison of the variants:
6797 \begin_layout Standard
6799 \begin_inset Tabular
6800 <lyxtabular version="3" rows="5" columns="2">
6801 <features tabularvalignment="middle">
6802 <column alignment="center" valignment="middle" width="0">
6803 <column alignment="center" valignment="middle" width="0">
6805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6808 \begin_layout Plain Layout
6814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6817 \begin_layout Plain Layout
6819 \begin_inset Note Note
6822 \begin_layout Plain Layout
6829 is only used as spacer.
6841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6844 \begin_layout Plain Layout
6859 \begin_layout Plain Layout
6877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6880 \begin_layout Plain Layout
6881 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6894 \begin_layout Plain Layout
6909 \begin_layout Plain Layout
6927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6930 \begin_layout Plain Layout
6931 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6944 \begin_layout Plain Layout
6959 \begin_layout Plain Layout
6977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6980 \begin_layout Plain Layout
6981 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6994 \begin_layout Plain Layout
7006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7009 \begin_layout Plain Layout
7010 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7026 \begin_layout Subsubsection
7027 Automatic Bracket Size
7028 \begin_inset CommandInset label
7030 name "sub:Automatic-Bracket-Size"
7035 \begin_inset Index idx
7038 \begin_layout Plain Layout
7039 Bracket size ! automatic
7047 \begin_layout Standard
7048 Brackets with variable size can be inserted with the commands
7055 \begin_inset Index idx
7058 \begin_layout Plain Layout
7073 \begin_inset Index idx
7076 \begin_layout Plain Layout
7084 or via the math toolbar button
7085 \begin_inset Graphics
7086 filename ../images/dialog-show_mathdelimiter.png
7104 the wanted bracket must be inserted.
7105 The bracket size will then automatically be calculated for the output.
7108 \begin_layout Standard
7110 normal bracket: The command
7120 \begin_layout Plain Layout
7130 \begin_inset Formula $\downarrow$
7137 \begin_layout Plain Layout
7149 \begin_inset Formula \[
7157 \begin_layout Standard
7159 multiline bracket: The command
7171 \begin_layout Plain Layout
7181 \begin_inset Formula $\downarrow$
7188 \begin_layout Plain Layout
7202 \begin_inset Formula \[
7203 \ln\left(\frac{A}{C}\right)\]
7210 \begin_layout Standard
7226 \begin_inset space ~
7232 This has the advantage that you can see in LyX immediately the real bracket
7233 size and that the matching right bracket will be created too.
7234 \begin_inset Newline newline
7237 The command for the last example would then be:
7251 \begin_layout Plain Layout
7261 \begin_inset Formula $\downarrow$
7267 \begin_layout Standard
7268 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7269 For example the command
7279 \begin_layout Plain Layout
7289 \begin_inset Formula $\downarrow$
7296 \begin_layout Plain Layout
7312 \begin_inset Formula \[
7313 \left.\frac{A}{B}\right\} \]
7331 will be converted by LyX to brackets in the right size when the document
7332 is reloaded and an omitted bracket will appear as dashed line.
7335 \begin_layout Standard
7336 \begin_inset VSpace bigskip
7339 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7347 \begin_inset Index idx
7350 \begin_layout Plain Layout
7358 is additionally available for all brackets and limits.
7359 With this command the height of the following character is adapted to the
7360 one of the surrounding brackets, what is e.
7361 \begin_inset space \thinspace{}
7365 \begin_inset space \space{}
7368 needed for physical vectors:
7369 \begin_inset Formula \[
7370 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7374 For physical vectors there is a special LaTeX-package, described in
7375 \begin_inset CommandInset ref
7377 reference "sub:Physical-Vectors"
7384 \begin_layout Subsection
7386 \begin_inset Index idx
7389 \begin_layout Plain Layout
7390 Brackets ! horizontal
7398 \begin_layout Standard
7400 \begin_inset Tabular
7401 <lyxtabular version="3" rows="4" columns="2">
7402 <features tabularvalignment="middle">
7403 <column alignment="center" valignment="top" width="0pt">
7404 <column alignment="center" valignment="top" width="0pt">
7406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7409 \begin_layout Plain Layout
7411 \begin_inset Note Note
7414 \begin_layout Plain Layout
7421 is only used as spacer.
7431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7434 \begin_layout Plain Layout
7442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7445 \begin_layout Plain Layout
7449 \begin_layout Plain Layout
7464 \begin_layout Plain Layout
7477 \begin_layout Plain Layout
7490 \begin_layout Plain Layout
7503 \begin_layout Plain Layout
7511 \begin_inset Index idx
7514 \begin_layout Plain Layout
7527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7530 \begin_layout Plain Layout
7531 \begin_inset Formula $\overbrace{A+B}^{3}$
7541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7544 \begin_layout Plain Layout
7548 \begin_layout Plain Layout
7563 \begin_layout Plain Layout
7576 \begin_layout Plain Layout
7589 \begin_layout Plain Layout
7597 \begin_inset Index idx
7600 \begin_layout Plain Layout
7613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7616 \begin_layout Plain Layout
7617 \begin_inset Formula $\underbrace{A+B}_{5}$
7627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7630 \begin_layout Plain Layout
7637 \begin_layout Plain Layout
7652 \begin_layout Plain Layout
7665 \begin_layout Plain Layout
7678 \begin_layout Plain Layout
7691 \begin_layout Plain Layout
7704 \begin_layout Plain Layout
7717 \begin_layout Plain Layout
7731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7734 \begin_layout Plain Layout
7735 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7751 \begin_layout Standard
7752 In the last example it doesn't matter if
7764 is inserted at first.
7767 \begin_layout Standard
7768 \begin_inset VSpace bigskip
7771 When brackets are needed that overlap each other, multiline formulas, as
7773 \begin_inset CommandInset ref
7775 reference "sec:Multiline-Formulas"
7780 \begin_inset Formula \begin{eqnarray*}
7781 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7782 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7787 In the first row the formula is inserted together with the first brace.
7788 It is hereby important that the space command
7792 \begin_layout Plain Layout
7793 Space commands are explained in
7794 \begin_inset CommandInset ref
7796 reference "sub:Predefined-Space"
7811 is inserted before the first
7812 \begin_inset Formula $d$
7815 , because the brace that ends behind the
7816 \begin_inset Formula $q$
7819 prevents that the following
7820 \begin_inset Quotes eld
7824 \begin_inset Quotes erd
7827 is surrounded by space.
7831 \begin_layout Plain Layout
7832 because a bracket is not handled as character, see
7833 \begin_inset CommandInset ref
7835 reference "sub:Binary-Operators"
7844 In the second row the second brace is inserted.
7845 As it should begin before the
7846 \begin_inset Formula $b$
7861 \begin_layout Plain Layout
7869 \begin_inset CommandInset ref
7871 reference "sub:Placeholders"
7880 This space is needed because the
7881 \begin_inset Quotes eld
7885 \begin_inset Quotes erd
7888 is also surrounded by space in the formula.
7889 The brace is placed under the command
7898 \begin_layout Standard
7899 It gets more complicated when brackets overlap each other, like in the following
7904 \begin_layout Plain Layout
7916 \begin_inset Formula \begin{eqnarray*}
7917 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7918 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7927 \begin_layout Plain Layout
7938 The first formula row is the same as the second row of the previous example,
7939 with the difference that the brace is above.
7940 The second row contains the formula together with the second brace.
7941 To avoid that there is space between the upper brace in the first row and
7942 the formula, the row spacing need to be reduced.
7943 This is not easily possible due to a bug in LyX
7947 \begin_layout Plain Layout
7948 \begin_inset CommandInset href
7950 name "LyX-bug #1505"
7951 target "http://www.lyx.org/trac/ticket/1505"
7961 As solution for the problem, the global formula row separation
7968 \begin_inset Index idx
7971 \begin_layout Plain Layout
7979 must be changed to -6
7980 \begin_inset space \thinspace{}
7983 pt before the formula with the command
7998 is set back after the formula to the standard value of 3
7999 \begin_inset space \thinspace{}
8002 pt using the same command.
8003 More about the row separation in formulas is explained in
8004 \begin_inset CommandInset ref
8006 reference "sub:Line-Separation"
8013 \begin_layout Section
8015 \begin_inset Index idx
8018 \begin_layout Plain Layout
8027 \begin_layout Standard
8028 Arrows can be inserted via the math toolbar button
8029 \begin_inset Graphics
8030 filename ../images/math/leftarrow.png
8035 or the commands listed in the following subsections.
8038 \begin_layout Standard
8039 \begin_inset Newpage newpage
8045 \begin_layout Subsection
8047 \begin_inset Index idx
8050 \begin_layout Plain Layout
8059 \begin_layout Standard
8060 \begin_inset space \hfill{}
8064 \begin_inset Tabular
8065 <lyxtabular version="3" rows="8" columns="2">
8066 <features tabularvalignment="middle">
8067 <column alignment="center" valignment="top" width="0pt">
8068 <column alignment="center" valignment="top" width="0pt">
8070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8073 \begin_layout Plain Layout
8079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8082 \begin_layout Plain Layout
8090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8093 \begin_layout Plain Layout
8101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8104 \begin_layout Plain Layout
8105 \begin_inset Formula $\gets$
8115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8118 \begin_layout Plain Layout
8126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8129 \begin_layout Plain Layout
8130 \begin_inset Formula $\Leftarrow$
8140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8143 \begin_layout Plain Layout
8151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8154 \begin_layout Plain Layout
8155 \begin_inset Formula $\longleftarrow$
8165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8168 \begin_layout Plain Layout
8176 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8179 \begin_layout Plain Layout
8180 \begin_inset Formula $\Longleftarrow$
8190 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8193 \begin_layout Plain Layout
8201 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8204 \begin_layout Plain Layout
8205 \begin_inset Formula $\leftharpoonup$
8215 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8218 \begin_layout Plain Layout
8226 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8229 \begin_layout Plain Layout
8230 \begin_inset Formula $\leftharpoondown$
8240 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8243 \begin_layout Plain Layout
8251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8254 \begin_layout Plain Layout
8255 \begin_inset Formula $\hookleftarrow$
8269 \begin_inset space \hfill{}
8273 \begin_inset Tabular
8274 <lyxtabular version="3" rows="8" columns="2">
8275 <features tabularvalignment="middle">
8276 <column alignment="center" valignment="top" width="0pt">
8277 <column alignment="center" valignment="top" width="0pt">
8279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8282 \begin_layout Plain Layout
8288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8291 \begin_layout Plain Layout
8299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8302 \begin_layout Plain Layout
8310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8313 \begin_layout Plain Layout
8314 \begin_inset Formula $\to$
8324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8327 \begin_layout Plain Layout
8335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8338 \begin_layout Plain Layout
8339 \begin_inset Formula $\Rightarrow$
8349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8352 \begin_layout Plain Layout
8360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8363 \begin_layout Plain Layout
8364 \begin_inset Formula $\longrightarrow$
8374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8377 \begin_layout Plain Layout
8385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8388 \begin_layout Plain Layout
8389 \begin_inset Formula $\Longrightarrow$
8399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8402 \begin_layout Plain Layout
8410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8413 \begin_layout Plain Layout
8414 \begin_inset Formula $\rightharpoonup$
8424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8427 \begin_layout Plain Layout
8435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8438 \begin_layout Plain Layout
8439 \begin_inset Formula $\rightharpoondown$
8449 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8452 \begin_layout Plain Layout
8460 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8463 \begin_layout Plain Layout
8464 \begin_inset Formula $\hookrightarrow$
8478 \begin_inset space \hfill{}
8484 \begin_layout Standard
8485 \begin_inset space \hfill{}
8489 \begin_inset Tabular
8490 <lyxtabular version="3" rows="6" columns="2">
8491 <features tabularvalignment="middle">
8492 <column alignment="center" valignment="top" width="0pt">
8493 <column alignment="center" valignment="top" width="0pt">
8495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8498 \begin_layout Plain Layout
8504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8507 \begin_layout Plain Layout
8515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8518 \begin_layout Plain Layout
8526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8529 \begin_layout Plain Layout
8530 \begin_inset Formula $\leftrightarrow$
8540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8543 \begin_layout Plain Layout
8551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8554 \begin_layout Plain Layout
8555 \begin_inset Formula $\Leftrightarrow$
8565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8568 \begin_layout Plain Layout
8576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8579 \begin_layout Plain Layout
8580 \begin_inset Formula $\longleftrightarrow$
8590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8593 \begin_layout Plain Layout
8601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8604 \begin_layout Plain Layout
8605 \begin_inset Formula $\Longleftrightarrow$
8615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8618 \begin_layout Plain Layout
8626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8629 \begin_layout Plain Layout
8630 \begin_inset Formula $\rightleftharpoons$
8644 \begin_inset space \hspace{}
8649 \begin_inset space \hfill{}
8653 \begin_inset Tabular
8654 <lyxtabular version="3" rows="5" columns="2">
8655 <features tabularvalignment="middle">
8656 <column alignment="center" valignment="top" width="0pt">
8657 <column alignment="center" valignment="top" width="0pt">
8659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8662 \begin_layout Plain Layout
8668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8671 \begin_layout Plain Layout
8679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8682 \begin_layout Plain Layout
8690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8693 \begin_layout Plain Layout
8694 \begin_inset Formula $\mapsto$
8704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8707 \begin_layout Plain Layout
8715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8718 \begin_layout Plain Layout
8719 \begin_inset Formula $\longmapsto$
8729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8732 \begin_layout Plain Layout
8740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8743 \begin_layout Plain Layout
8744 \begin_inset Formula $\leadsto$
8754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8757 \begin_layout Plain Layout
8765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8768 \begin_layout Plain Layout
8769 \begin_inset Formula $\dasharrow$
8783 \begin_inset space \hfill{}
8789 \begin_layout Standard
8790 \begin_inset VSpace medskip
8793 Arrows used as accent like e.
8794 \begin_inset space \thinspace{}
8798 \begin_inset space \space{}
8801 vector arrows are listed in
8802 \begin_inset CommandInset ref
8804 reference "sec:Accents"
8811 \begin_layout Standard
8812 \begin_inset VSpace bigskip
8815 Furthermore there are the labeled arrows
8816 \begin_inset Index idx
8819 \begin_layout Plain Layout
8832 \begin_inset Index idx
8835 \begin_layout Plain Layout
8850 \begin_inset Index idx
8853 \begin_layout Plain Layout
8860 \begin_layout Plain Layout
8875 When inserting one of these commands in a formula, an arrow with two blue
8876 boxes appear where the label can be inserted.
8877 The length of the arrow adapts to the label width.
8880 \begin_layout Standard
8882 \begin_inset Tabular
8883 <lyxtabular version="3" rows="3" columns="2">
8884 <features tabularvalignment="middle">
8885 <column alignment="center" valignment="top" width="0pt">
8886 <column alignment="center" valignment="top" width="0pt">
8888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8891 \begin_layout Plain Layout
8897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8900 \begin_layout Plain Layout
8902 \begin_inset Note Note
8905 \begin_layout Plain Layout
8912 is only used as spacer.
8924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8927 \begin_layout Plain Layout
8934 \begin_layout Plain Layout
8944 \begin_inset Formula $\downarrow$
8948 \begin_inset Formula $\to$
8956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8959 \begin_layout Plain Layout
8960 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8973 \begin_layout Plain Layout
8980 \begin_layout Plain Layout
8990 \begin_inset Formula $\downarrow$
8994 \begin_inset Formula $\to$
9002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9005 \begin_layout Plain Layout
9006 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9022 \begin_layout Subsection
9023 Vertical and diagonal Arrows
9024 \begin_inset Index idx
9027 \begin_layout Plain Layout
9034 \begin_inset Index idx
9037 \begin_layout Plain Layout
9046 \begin_layout Standard
9047 \begin_inset space \hfill{}
9051 \begin_inset Tabular
9052 <lyxtabular version="3" rows="7" columns="2">
9053 <features tabularvalignment="middle">
9054 <column alignment="center" valignment="top" width="0pt">
9055 <column alignment="center" valignment="top" width="0pt">
9057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9060 \begin_layout Plain Layout
9066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9069 \begin_layout Plain Layout
9077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9080 \begin_layout Plain Layout
9088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9091 \begin_layout Plain Layout
9092 \begin_inset Formula $\uparrow$
9102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9105 \begin_layout Plain Layout
9113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9116 \begin_layout Plain Layout
9117 \begin_inset Formula $\Uparrow$
9127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9130 \begin_layout Plain Layout
9138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9141 \begin_layout Plain Layout
9142 \begin_inset Formula $\updownarrow$
9152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9155 \begin_layout Plain Layout
9163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9166 \begin_layout Plain Layout
9167 \begin_inset Formula $\Updownarrow$
9177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9180 \begin_layout Plain Layout
9188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9191 \begin_layout Plain Layout
9192 \begin_inset Formula $\Downarrow$
9202 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9205 \begin_layout Plain Layout
9213 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9216 \begin_layout Plain Layout
9217 \begin_inset Formula $\downarrow$
9231 \begin_inset space \hfill{}
9235 \begin_inset Tabular
9236 <lyxtabular version="3" rows="5" columns="2">
9237 <features tabularvalignment="middle">
9238 <column alignment="center" valignment="top" width="0pt">
9239 <column alignment="center" valignment="top" width="0pt">
9241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9244 \begin_layout Plain Layout
9250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9253 \begin_layout Plain Layout
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 $\nearrow$
9286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9289 \begin_layout Plain Layout
9297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9300 \begin_layout Plain Layout
9301 \begin_inset Formula $\searrow$
9311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9314 \begin_layout Plain Layout
9322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9325 \begin_layout Plain Layout
9326 \begin_inset Formula $\swarrow$
9336 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9339 \begin_layout Plain Layout
9347 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9350 \begin_layout Plain Layout
9351 \begin_inset Formula $\nwarrow$
9365 \begin_inset space \hfill{}
9371 \begin_layout Standard
9372 \begin_inset VSpace medskip
9375 Vertical arrows can be used also as delimiter together with the commands
9377 \begin_inset CommandInset ref
9379 reference "sub:Manual-Bracket-Size"
9384 \begin_inset CommandInset ref
9386 reference "sub:Automatic-Bracket-Size"
9393 \begin_layout Standard
9394 \begin_inset Newpage newpage
9400 \begin_layout Section
9402 \begin_inset CommandInset label
9409 \begin_inset Index idx
9412 \begin_layout Plain Layout
9421 \begin_layout Standard
9422 Accents can be inserted via the math toolbar button
9423 \begin_inset Graphics
9424 filename ../images/math/hat.png
9429 or the commands listed in the following subsections.
9432 \begin_layout Subsection
9433 Accents for one Character
9437 \begin_layout Plain Layout
9450 \begin_layout Plain Layout
9452 \begin_inset CommandInset ref
9454 reference "sub:Accents-in-Text"
9467 \begin_layout Plain Layout
9475 \begin_inset Note Note
9478 \begin_layout Plain Layout
9481 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9484 \begin_layout Plain Layout
9487 texorpdfstring is in section
9488 \begin_inset CommandInset ref
9490 reference "sub:Formulas-in-Section"
9500 \begin_inset CommandInset label
9502 name "sub:Accents-for-one"
9507 \begin_inset Index idx
9510 \begin_layout Plain Layout
9511 Accents ! for one character
9519 \begin_layout Standard
9520 \begin_inset space \hfill{}
9524 \begin_inset Tabular
9525 <lyxtabular version="3" rows="8" columns="2">
9526 <features tabularvalignment="middle">
9527 <column alignment="center" valignment="top" width="0pt">
9528 <column alignment="center" valignment="top" width="0pt">
9530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9533 \begin_layout Plain Layout
9539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9542 \begin_layout Plain Layout
9544 \begin_inset Note Note
9547 \begin_layout Plain Layout
9554 is only used as spacer.
9566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9569 \begin_layout Plain Layout
9576 \begin_layout Plain Layout
9590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9593 \begin_layout Plain Layout
9594 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9604 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9607 \begin_layout Plain Layout
9614 \begin_layout Plain Layout
9628 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9631 \begin_layout Plain Layout
9632 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9642 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9645 \begin_layout Plain Layout
9652 \begin_layout Plain Layout
9666 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9669 \begin_layout Plain Layout
9670 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9683 \begin_layout Plain Layout
9690 \begin_layout Plain Layout
9704 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9707 \begin_layout Plain Layout
9708 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9718 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9721 \begin_layout Plain Layout
9728 \begin_layout Plain Layout
9738 \begin_inset Index idx
9741 \begin_layout Plain Layout
9752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9755 \begin_layout Plain Layout
9756 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9766 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9769 \begin_layout Plain Layout
9776 \begin_layout Plain Layout
9790 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9793 \begin_layout Plain Layout
9794 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9804 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9807 \begin_layout Plain Layout
9814 \begin_layout Plain Layout
9828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9831 \begin_layout Plain Layout
9832 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9846 \begin_inset space \hfill{}
9850 \begin_inset Tabular
9851 <lyxtabular version="3" rows="7" columns="2">
9852 <features tabularvalignment="middle">
9853 <column alignment="center" valignment="top" width="0pt">
9854 <column alignment="center" valignment="top" width="0pt">
9856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9859 \begin_layout Plain Layout
9865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9868 \begin_layout Plain Layout
9876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9879 \begin_layout Plain Layout
9886 \begin_layout Plain Layout
9900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9903 \begin_layout Plain Layout
9904 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
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 $\raisebox{5mm}{}\hat{A}$
9952 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9955 \begin_layout Plain Layout
9962 \begin_layout Plain Layout
9976 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9979 \begin_layout Plain Layout
9980 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9990 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9993 \begin_layout Plain Layout
10000 \begin_layout Plain Layout
10014 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10017 \begin_layout Plain Layout
10018 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10028 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10031 \begin_layout Plain Layout
10038 \begin_layout Plain Layout
10052 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10055 \begin_layout Plain Layout
10056 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10066 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10069 \begin_layout Plain Layout
10076 \begin_layout Plain Layout
10090 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10093 \begin_layout Plain Layout
10094 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10108 \begin_inset space \hfill{}
10114 \begin_layout Standard
10115 \begin_inset VSpace bigskip
10121 \begin_layout Standard
10122 You can directly insert accents like é to formulas.
10123 LyX will transform them to the corresponding accent command.
10125 \begin_inset Index idx
10128 \begin_layout Plain Layout
10134 it is better to insert a quotation mark before the vowel.
10135 These two characters are then treated by LaTeX as
10139 character when the formula part with the umlaut is marked as German.
10147 \begin_inset Quotes eld
10151 \begin_inset Quotes erd
10154 umlauts are created as demonstrated in the following example:
10157 \begin_layout Standard
10158 \begin_inset VSpace -2mm
10164 \begin_layout Standard
10166 \begin_inset Tabular
10167 <lyxtabular version="3" rows="3" columns="2">
10168 <features tabularvalignment="middle">
10169 <column alignment="center" valignment="top" width="0">
10170 <column alignment="center" valignment="top" width="0">
10172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10175 \begin_layout Plain Layout
10181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10184 \begin_layout Plain Layout
10186 \begin_inset Note Note
10189 \begin_layout Plain Layout
10197 \begin_inset space \thinspace{}
10200 pt space are only used as spacer.
10212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10215 \begin_layout Plain Layout
10218 \begin_inset Quotes grd
10226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10229 \begin_layout Plain Layout
10230 \begin_inset space \hspace{}
10237 \begin_inset Formula $"i$
10247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10250 \begin_layout Plain Layout
10257 \begin_layout Plain Layout
10271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10274 \begin_layout Plain Layout
10275 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10291 \begin_layout Standard
10292 Another advantage to
10298 is that umlauts can directly be converted to mathematical text because
10299 the accent commands above are
10305 in mathematical text
10308 To convert an accented character to mathematical text, only the character
10309 under the accent may be converted.
10310 This applies also for all other conversions, e.
10311 \begin_inset space \thinspace{}
10315 \begin_inset space \space{}
10321 \begin_layout Standard
10322 In mathematical text, umlauts and other accented characters can directly
10326 \begin_layout Subsection
10327 Accents for Operators
10328 \begin_inset Index idx
10331 \begin_layout Plain Layout
10332 Accents ! for operators
10340 \begin_layout Standard
10348 \begin_inset Index idx
10351 \begin_layout Plain Layout
10366 \begin_inset Index idx
10369 \begin_layout Plain Layout
10377 characters can be placed above or below an operator, respectively, to accent
10386 \begin_inset Index idx
10389 \begin_layout Plain Layout
10397 characters can be set before and behind an operator.
10398 The command scheme is:
10401 \begin_layout Standard
10417 \begin_layout Standard
10424 must always be before the operator that should be accented.
10425 You can accent with several characters and even with other operators and
10433 for example only characters behind an operator, write nothing between the
10434 first braces but don't omit the braces.
10437 \begin_layout Standard
10438 For example the command
10443 \begin_inset Formula $\to$
10453 \begin_inset Formula $\to$
10462 \begin_layout Plain Layout
10478 \begin_inset Formula \[
10479 \sideset{}{'}\sum_{k=1}^{n}\]
10486 \begin_layout Standard
10495 \begin_layout Plain Layout
10510 \begin_layout Plain Layout
10522 \begin_inset Formula $\uparrow$
10530 \begin_inset Formula \[
10531 \overset{a}{\maltese}\]
10535 As seen in the last example, with
10547 also symbols and characters can be accented; with
10553 this is not possible.
10556 \begin_layout Subsection
10557 Accents for several Characters
10558 \begin_inset Index idx
10561 \begin_layout Plain Layout
10562 Accents ! for several characters
10570 \begin_layout Standard
10571 \begin_inset space \hfill{}
10575 \begin_inset Tabular
10576 <lyxtabular version="3" rows="5" columns="2">
10577 <features tabularvalignment="middle">
10578 <column alignment="center" valignment="top" width="0pt">
10579 <column alignment="center" valignment="top" width="0pt">
10581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10584 \begin_layout Plain Layout
10590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10593 \begin_layout Plain Layout
10595 \begin_inset Note Note
10598 \begin_layout Plain Layout
10605 is only used as spacer.
10617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10620 \begin_layout Plain Layout
10627 \begin_layout Plain Layout
10641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10644 \begin_layout Plain Layout
10645 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10655 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10658 \begin_layout Plain Layout
10665 \begin_layout Plain Layout
10679 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10682 \begin_layout Plain Layout
10683 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10693 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10696 \begin_layout Plain Layout
10703 \begin_layout Plain Layout
10717 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10720 \begin_layout Plain Layout
10721 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10731 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10734 \begin_layout Plain Layout
10737 underleftrightarrow
10741 \begin_layout Plain Layout
10755 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10758 \begin_layout Plain Layout
10759 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10773 \begin_inset space \hfill{}
10777 \begin_inset Tabular
10778 <lyxtabular version="3" rows="5" columns="2">
10779 <features tabularvalignment="middle">
10780 <column alignment="center" valignment="top" width="0pt">
10781 <column alignment="center" valignment="top" width="0pt">
10783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10786 \begin_layout Plain Layout
10792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10795 \begin_layout Plain Layout
10803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10806 \begin_layout Plain Layout
10813 \begin_layout Plain Layout
10827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10830 \begin_layout Plain Layout
10831 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10841 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10844 \begin_layout Plain Layout
10851 \begin_layout Plain Layout
10865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10868 \begin_layout Plain Layout
10869 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10879 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10882 \begin_layout Plain Layout
10889 \begin_layout Plain Layout
10903 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10906 \begin_layout Plain Layout
10907 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10917 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10920 \begin_layout Plain Layout
10927 \begin_layout Plain Layout
10941 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10944 \begin_layout Plain Layout
10945 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10959 \begin_inset space \hfill{}
10965 \begin_layout Standard
10966 \begin_inset VSpace medskip
10969 With these commands as many characters as you like can be accented.
10982 will only be set in the output with a length of three characters, as shown
10983 in the following example:
10984 \begin_inset Formula \[
10985 \widetilde{A+B=C-D}\]
10992 \begin_layout Standard
11000 \begin_inset Index idx
11003 \begin_layout Plain Layout
11018 \begin_inset Index idx
11021 \begin_layout Plain Layout
11029 described in the previous subsection it is also possible to accent several
11039 \begin_layout Plain Layout
11049 \begin_inset Formula $\downarrow$
11055 \begin_inset Formula \[
11056 \underset{***}{A=B}\]
11063 \begin_layout Section
11065 \begin_inset CommandInset label
11072 \begin_inset Index idx
11075 \begin_layout Plain Layout
11084 \begin_layout Subsection
11086 \begin_inset CommandInset label
11088 name "sub:Predefined-Space"
11093 \begin_inset Index idx
11096 \begin_layout Plain Layout
11097 Space ! horizontal ! predefined
11105 \begin_layout Standard
11106 Sometimes it is necessary to insert horizontal space to a formula.
11107 This is done by inserting a protected space (shortcut
11110 arg "space-insert protected"
11115 \begin_inset Quotes eld
11124 \begin_layout Plain Layout
11136 \begin_inset Quotes erd
11139 appears and by pressing
11143 several times one can select one of eight different space sizes.
11144 The spaces can also be inserted using the math toolbar button
11145 \begin_inset Graphics
11146 filename ../images/math/space.png
11151 or special commands.
11152 Independent from the inserted command, one can select the size again by
11160 \begin_layout Standard
11163 \begin_inset VSpace -5mm
11167 \begin_inset Tabular
11168 <lyxtabular version="3" rows="3" columns="7">
11169 <features tabularvalignment="middle">
11170 <column alignment="center" valignment="middle" width="6.8cm">
11171 <column alignment="center" valignment="top" width="0">
11172 <column alignment="center" valignment="top" width="0">
11173 <column alignment="center" valignment="top" width="0">
11174 <column alignment="center" valignment="top" width="0">
11175 <column alignment="center" valignment="top" width="0">
11176 <column alignment="center" valignment="top" width="0">
11178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11181 \begin_layout Plain Layout
11187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11190 \begin_layout Plain Layout
11198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11201 \begin_layout Plain Layout
11209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11212 \begin_layout Plain Layout
11220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11223 \begin_layout Plain Layout
11231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11234 \begin_layout Plain Layout
11242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11245 \begin_layout Plain Layout
11255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11258 \begin_layout Plain Layout
11263 keystrokes after inserting the protected space
11268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11271 \begin_layout Plain Layout
11277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11280 \begin_layout Plain Layout
11286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11289 \begin_layout Plain Layout
11295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11298 \begin_layout Plain Layout
11304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11307 \begin_layout Plain Layout
11313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11316 \begin_layout Plain Layout
11324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11327 \begin_layout Plain Layout
11333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11336 \begin_layout Plain Layout
11337 \begin_inset Formula $A\, B$
11345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11348 \begin_layout Plain Layout
11349 \begin_inset Formula $A\: B$
11357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11360 \begin_layout Plain Layout
11361 \begin_inset Formula $A\; B$
11369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11372 \begin_layout Plain Layout
11373 \begin_inset Formula $A\quad B$
11381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11384 \begin_layout Plain Layout
11385 \begin_inset Formula $A\qquad B$
11393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11396 \begin_layout Plain Layout
11397 \begin_inset Formula $A\! B$
11413 \begin_layout Standard
11414 The last size seem to produce no space.
11415 It is displayed red in LyX contrary to the other sizes, because it is a
11417 There are two more negative spaces:
11420 \begin_layout Standard
11422 \begin_inset Tabular
11423 <lyxtabular version="3" rows="3" columns="3">
11424 <features tabularvalignment="middle">
11425 <column alignment="center" valignment="middle" width="6.8cm">
11426 <column alignment="center" valignment="top" width="0pt">
11427 <column alignment="center" valignment="top" width="0pt">
11429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11432 \begin_layout Plain Layout
11438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11441 \begin_layout Plain Layout
11449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11452 \begin_layout Plain Layout
11462 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11465 \begin_layout Plain Layout
11470 keystrokes after inserting the protected space
11475 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11478 \begin_layout Plain Layout
11484 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11487 \begin_layout Plain Layout
11495 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11498 \begin_layout Plain Layout
11504 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11507 \begin_layout Plain Layout
11508 \begin_inset Formula $A\negmedspace B$
11516 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11519 \begin_layout Plain Layout
11520 \begin_inset Formula $A\negthickspace B$
11536 \begin_layout Standard
11537 Negative spaces can lead to characters overlapping each other.
11538 Thus they can be used to enforce ligatures, what is e.
11539 \begin_inset space \thinspace{}
11543 \begin_inset space \space{}
11546 useful for summation operators:
11549 \begin_layout Standard
11551 \begin_inset Tabular
11552 <lyxtabular version="3" rows="3" columns="2">
11553 <features tabularvalignment="middle">
11554 <column alignment="center" valignment="top" width="0">
11555 <column alignment="center" valignment="top" width="0">
11557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11560 \begin_layout Plain Layout
11566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11569 \begin_layout Plain Layout
11571 \begin_inset Note Note
11574 \begin_layout Plain Layout
11581 is only used as spacer.
11593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11596 \begin_layout Plain Layout
11605 \begin_layout Plain Layout
11619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11622 \begin_layout Plain Layout
11623 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11636 \begin_layout Plain Layout
11647 \begin_layout Plain Layout
11661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11664 \begin_layout Plain Layout
11665 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11681 \begin_layout Standard
11682 Relations like for example equal signs, are always surrounded by space.
11683 To suppress this, the equal sign is placed into a TeX-brace.
11684 The following example demonstrates this:
11687 \begin_layout Standard
11689 \begin_inset Tabular
11690 <lyxtabular version="3" rows="2" columns="2">
11691 <features tabularvalignment="middle">
11692 <column alignment="center" valignment="top" width="0pt">
11693 <column alignment="center" valignment="top" width="0pt">
11695 <cell alignment="center" valignment="top" usebox="none">
11698 \begin_layout Plain Layout
11704 <cell alignment="center" valignment="top" usebox="none">
11707 \begin_layout Plain Layout
11708 \begin_inset Formula $A=B$
11718 <cell alignment="center" valignment="top" usebox="none">
11721 \begin_layout Plain Layout
11722 \begin_inset Note Note
11725 \begin_layout Plain Layout
11732 is only used as spacer.
11738 \begin_inset Formula $\raisebox{5mm}{}$
11741 equation without space
11746 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11749 \begin_layout Plain Layout
11750 \begin_inset Formula $A{=}B$
11766 \begin_layout Standard
11768 The command for the last formula is:
11773 \begin_inset Formula $\to$
11779 \begin_layout Standard
11780 \begin_inset VSpace bigskip
11783 Spaces are needed for physical units, because the space between the value
11784 and the unit is the smallest one and not a normal space.
11785 For units in text, the smallest space is inserted via the menu
11787 Insert\SpecialChar \menuseparator
11788 Formatting\SpecialChar \menuseparator
11790 \begin_inset space ~
11798 arg "space-insert thin"
11804 \begin_layout Standard
11805 An example to visualize the difference:
11808 \begin_layout Standard
11809 \begin_inset Tabular
11810 <lyxtabular version="3" rows="2" columns="2">
11811 <features tabularvalignment="middle">
11812 <column alignment="left" valignment="top" width="0">
11813 <column alignment="left" valignment="top" width="0">
11815 <cell alignment="center" valignment="top" usebox="none">
11818 \begin_layout Plain Layout
11820 \begin_inset Formula $\cdot$
11828 <cell alignment="center" valignment="top" usebox="none">
11831 \begin_layout Plain Layout
11832 space between value and unit
11839 <cell alignment="center" valignment="top" usebox="none">
11842 \begin_layout Plain Layout
11844 \begin_inset space \thinspace{}
11848 \begin_inset Formula $\cdot$
11856 <cell alignment="center" valignment="top" usebox="none">
11859 \begin_layout Plain Layout
11860 smallest space between value and unit
11873 \begin_layout Subsection
11878 \begin_layout Plain Layout
11891 \begin_layout Plain Layout
11892 for vertical space in formulas see
11893 \begin_inset CommandInset ref
11895 reference "sub:Line-Separation"
11908 \begin_layout Plain Layout
11916 \begin_inset Note Note
11919 \begin_layout Plain Layout
11922 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11925 \begin_layout Plain Layout
11928 texorpdfstring is in section
11929 \begin_inset CommandInset ref
11931 reference "sub:Formulas-in-Section"
11941 \begin_inset CommandInset label
11943 name "sub:Variable-Space"
11948 \begin_inset Index idx
11951 \begin_layout Plain Layout
11952 Space ! horizontal ! variable
11960 \begin_layout Standard
11961 Space with a defined length can be inserted with the command
11968 \begin_inset Index idx
11971 \begin_layout Plain Layout
11981 \begin_inset Quotes eld
11990 \begin_layout Plain Layout
12002 \begin_inset Quotes erd
12006 The length can be specified by left-clicking on the
12007 \begin_inset Quotes eld
12016 \begin_layout Plain Layout
12028 \begin_inset Quotes erd
12032 The length may also be negative.
12033 To insert so many space that the formula uses all available space, the
12041 \begin_inset Index idx
12044 \begin_layout Plain Layout
12055 \begin_layout Standard
12056 \begin_inset VSpace -1mm
12062 \begin_layout Standard
12064 \begin_inset Tabular
12065 <lyxtabular version="3" rows="4" columns="2">
12066 <features tabularvalignment="middle">
12067 <column alignment="center" valignment="top" width="0">
12068 <column alignment="center" valignment="top" width="0">
12070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12073 \begin_layout Plain Layout
12081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12084 \begin_layout Plain Layout
12092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12095 \begin_layout Plain Layout
12102 \begin_layout Plain Layout
12112 \begin_inset Formula $\to$
12118 \begin_inset space \thinspace{}
12126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12129 \begin_layout Plain Layout
12130 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12143 \begin_layout Plain Layout
12150 \begin_layout Plain Layout
12160 \begin_inset Formula $\to$
12166 \begin_inset space \thinspace{}
12174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12177 \begin_layout Plain Layout
12178 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12191 \begin_layout Plain Layout
12198 \begin_layout Plain Layout
12212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12215 \begin_layout Plain Layout
12216 \begin_inset Formula $A=A\hfill B=B$
12232 \begin_layout Standard
12233 In the last example the available space is given by the longest column entry
12235 In an inline formula the space depends on the length of the line in which
12243 Thus, when the line uses the full width, no space will be created.
12250 only has an effect on displayed formulas when the formula style
12255 (Formula styles are explained in
12256 \begin_inset CommandInset ref
12258 reference "sec:Formula-Styles"
12265 \begin_layout Standard
12272 , there are the commands
12284 that fill the space with a pattern, see
12285 \begin_inset CommandInset ref
12287 reference "sub:Ellipses"
12294 \begin_layout Standard
12295 For text, variable space can be inserted via the menu
12297 Insert\SpecialChar \menuseparator
12298 Formatting\SpecialChar \menuseparator
12300 \begin_inset space ~
12308 \begin_layout Standard
12309 This is a line with
12310 \begin_inset space \hspace{}
12315 \begin_inset space \thinspace{}
12321 \begin_layout Standard
12322 This is a line with
12323 \begin_inset space \hfill{}
12329 \begin_layout Subsection
12330 Space besides inline Formulas
12331 \begin_inset Index idx
12334 \begin_layout Plain Layout
12335 Space ! besides inline formulas
12343 \begin_layout Standard
12344 The space that surrounds inline formulas can be adjusted with the length
12352 \begin_inset Index idx
12355 \begin_layout Plain Layout
12364 The value of a length is set with the command
12371 \begin_inset Index idx
12374 \begin_layout Plain Layout
12382 that has the following scheme:
12385 \begin_layout Standard
12390 setlength{length name}{value}
12393 \begin_layout Standard
12401 \begin_inset space \thinspace{}
12407 \begin_layout Standard
12417 \begin_layout Standard
12418 is inserted in TeX-mode.
12420 \begin_inset space \thinspace{}
12423 mm space will now be set around all inline formulas:
12427 \begin_layout Plain Layout
12441 \begin_layout Standard
12442 This is a line with an inline formula
12443 \begin_inset Formula $A=B$
12447 \begin_inset space \thinspace{}
12450 mm surrounding space.
12454 \begin_layout Plain Layout
12468 \begin_layout Standard
12469 To return to the predefined value,
12475 is set to the value 0
12476 \begin_inset space \thinspace{}
12482 \begin_layout Section
12484 \begin_inset Index idx
12487 \begin_layout Plain Layout
12494 \begin_inset Index idx
12497 \begin_layout Plain Layout
12502 \begin_layout Plain Layout
12513 \begin_layout Plain Layout
12528 \begin_layout Standard
12529 Boxes for text are described in chapter
12536 \begin_inset space ~
12544 \begin_layout Subsection
12546 \begin_inset CommandInset label
12548 name "sub:Boxes-with-Frame"
12553 \begin_inset Index idx
12556 \begin_layout Plain Layout
12565 \begin_layout Standard
12566 It is possible to frame formulas or parts of it with the commands
12573 \begin_inset Index idx
12576 \begin_layout Plain Layout
12591 \begin_inset Index idx
12594 \begin_layout Plain Layout
12605 \begin_layout Standard
12606 When one of these commands is inserted to a formula, a blue box appears
12607 within a frame to enter formula parts.
12614 an additional formula has to be created by
12618 within this box, because the box content will otherwise be treated as mathemati
12626 is used, a new formula is automatically created inside the frame.
12629 \begin_layout Standard
12636 is not suitable to frame displayed formulas because the formula will always
12637 be set in the size of the text.
12644 is in contrary not suitable to frame inline formulas, because the formula
12645 will always be set in the size of a displayed formula.
12648 \begin_layout Standard
12655 there is the command
12662 \begin_inset Index idx
12665 \begin_layout Plain Layout
12673 where additionally the frame width and the alignment can be specified.
12680 is used in the following scheme:
12683 \begin_layout Standard
12688 framebox[frame width][position]{box content}
12691 \begin_layout Standard
12692 The position can either be
12709 right aligns the formula in the box.
12710 When no position is given, the formula will be centered.
12711 \begin_inset Newline newline
12714 Is no width given, also no position can be given.
12715 In this case the frame width is adjusted to the box content like for
12724 \begin_layout Standard
12731 is inserted, a box appears containing three blue boxes.
12732 The first two boxes are surrounded by brackets and denote the two optional
12734 The third box is for formula parts like for
12743 \begin_layout Standard
12745 \begin_inset Tabular
12746 <lyxtabular version="3" rows="5" columns="2">
12747 <features tabularvalignment="middle">
12748 <column alignment="center" valignment="top" width="0">
12749 <column alignment="center" valignment="top" width="0">
12751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12754 \begin_layout Plain Layout
12760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12763 \begin_layout Plain Layout
12765 \begin_inset Note Note
12768 \begin_layout Plain Layout
12775 is only used as spacer.
12787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12790 \begin_layout Plain Layout
12797 \begin_layout Plain Layout
12816 \begin_layout Plain Layout
12830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12833 \begin_layout Plain Layout
12834 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12847 \begin_layout Plain Layout
12854 \begin_layout Plain Layout
12869 \begin_layout Plain Layout
12883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12886 \begin_layout Plain Layout
12887 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12900 \begin_layout Plain Layout
12907 \begin_layout Plain Layout
12921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12924 \begin_layout Plain Layout
12925 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12938 \begin_layout Plain Layout
12945 \begin_layout Plain Layout
12955 \begin_inset Formula $\to$
12959 \begin_inset Formula $\to$
12972 \begin_layout Plain Layout
12982 \begin_inset Formula $\downarrow$
12990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12993 \begin_layout Plain Layout
12994 \begin_inset Formula $\raisebox{6mm}{}$
12998 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13002 \begin_inset Formula $\raisebox{-4mm}{}$
13018 \begin_layout Standard
13019 The frame thickness can also be adjusted.
13020 To do this the following commands have to be inserted in TeX-mode before
13024 \begin_layout Standard
13034 \begin_inset Quotes eld
13038 \begin_inset Quotes erd
13052 \begin_inset Quotes eld
13056 \begin_inset Quotes erd
13062 \begin_layout Standard
13063 \begin_inset Quotes eld
13067 \begin_inset Quotes erd
13070 specifies the minimal distance between the frame and the first character
13072 An example for this is the following framed formula:
13076 \begin_layout Plain Layout
13088 \begin_inset Formula \[
13093 Before this formula the commands
13096 \begin_layout Standard
13118 \begin_layout Standard
13119 were inserted in TeX-mode.
13120 The given values are used for all following boxes.
13123 \begin_layout Standard
13124 To return to the standard frame size, the command
13127 \begin_layout Standard
13152 \begin_layout Plain Layout
13166 \begin_layout Standard
13167 is inserted in TeX-mode before the next formula.
13170 \begin_layout Subsection
13171 Boxes without Frame
13172 \begin_inset CommandInset label
13174 name "sub:Boxes-without-Frame"
13179 \begin_inset Index idx
13182 \begin_layout Plain Layout
13183 Boxes ! without frame
13191 \begin_layout Standard
13192 For boxes without a frame there are the following box commands:
13199 \begin_inset Index idx
13202 \begin_layout Plain Layout
13217 \begin_inset Index idx
13220 \begin_layout Plain Layout
13235 \begin_inset Index idx
13238 \begin_layout Plain Layout
13249 \begin_layout Standard
13256 a box can be super- or subscripted.
13257 But in contrary to normal super- and subscripting, the characters in the
13258 box keep their font size.
13265 is used in the following scheme:
13268 \begin_layout Standard
13273 raisebox{height}{box content}
13276 \begin_layout Standard
13277 When the box should contain a formula, an extra formula is needed like for
13288 \begin_inset Note Greyedout
13291 \begin_layout Plain Layout
13302 this extra formula is created by pressing
13306 twice instead of once because LyX doesn't yet support
13320 \begin_layout Standard
13322 \begin_inset Tabular
13323 <lyxtabular version="3" rows="4" columns="2">
13324 <features tabularvalignment="middle">
13325 <column alignment="center" valignment="top" width="0">
13326 <column alignment="center" valignment="top" width="0">
13328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13331 \begin_layout Plain Layout
13337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13340 \begin_layout Plain Layout
13348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13351 \begin_layout Plain Layout
13355 \begin_inset Formula $\to$
13361 \begin_inset Formula $\to$
13369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13372 \begin_layout Plain Layout
13373 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13386 \begin_layout Plain Layout
13390 \begin_inset Formula $\to$
13396 \begin_inset Formula $\to$
13404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13407 \begin_layout Plain Layout
13408 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13421 \begin_layout Plain Layout
13425 \begin_inset Formula $\to$
13444 \begin_layout Plain Layout
13458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13461 \begin_layout Plain Layout
13462 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13478 \begin_layout Standard
13503 , with the difference that there is no frame.
13506 \begin_layout Subsection
13508 \begin_inset CommandInset label
13510 name "sub:Colored-Boxes"
13515 \begin_inset Index idx
13518 \begin_layout Plain Layout
13527 \begin_layout Standard
13528 To be able to use all commands explained in this section, the LaTeX-package
13537 \begin_layout Plain Layout
13542 is part of every LaTeX standard installation.
13548 \begin_inset Index idx
13551 \begin_layout Plain Layout
13557 has to be loaded in the LaTeX-preamble with the line
13561 \begin_layout Plain Layout
13562 When text is colored somewhere in the document with a predefined color,
13563 LyX loads the LaTeX-package
13568 Thus it is possible that the package is loaded twice, but this doesn't
13575 \begin_inset Note Note
13578 \begin_layout Plain Layout
13579 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13588 \begin_layout Standard
13596 \begin_layout Standard
13597 \begin_inset VSpace medskip
13600 To color boxes, the command
13607 \begin_inset Index idx
13610 \begin_layout Plain Layout
13618 is used in the following scheme:
13621 \begin_layout Standard
13626 colorbox{color}{box content}
13629 \begin_layout Standard
13630 The box content can also be a box and a
13636 can also be part of another box (see the 2nd and 3rd example).
13637 When the box should contain a formula, an extra formula has to be created,
13638 the same way as for
13648 \begin_layout Plain Layout
13649 This also applies for the command
13663 \begin_layout Standard
13664 One of the following predefined colors can be chosen:
13667 \begin_layout Standard
13701 \begin_layout Standard
13703 \begin_inset Tabular
13704 <lyxtabular version="3" rows="4" columns="2">
13705 <features tabularvalignment="middle">
13706 <column alignment="center" valignment="top" width="0">
13707 <column alignment="center" valignment="top" width="0">
13709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13712 \begin_layout Plain Layout
13718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13721 \begin_layout Plain Layout
13723 \begin_inset Note Note
13726 \begin_layout Plain Layout
13733 is only used as spacer.
13745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13748 \begin_layout Plain Layout
13752 \begin_inset Formula $\to$
13762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13765 \begin_layout Plain Layout
13766 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13779 \begin_layout Plain Layout
13783 \begin_inset Formula $\to$
13794 \begin_layout Plain Layout
13808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13811 \begin_layout Plain Layout
13812 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13825 \begin_layout Plain Layout
13832 \begin_layout Plain Layout
13844 \begin_inset Formula $\to$
13863 \begin_layout Plain Layout
13877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13880 \begin_layout Plain Layout
13881 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13897 \begin_layout Standard
13904 only colors the box but not the characters in the box.
13905 To color all characters, the whole formula is highlighted and the wanted
13906 color is chosen in the
13909 \begin_inset space ~
13915 The dialog can be called with the toolbar button
13916 \begin_inset Graphics
13917 filename ../images/dialog-show_character.png
13924 Edit\SpecialChar \menuseparator
13926 \begin_inset space ~
13929 Style\SpecialChar \menuseparator
13933 The formula number has then the same color as the formula.
13934 When the formula number should get another color than the formula characters,
13935 the color must be changed within the formula.
13938 \begin_layout Standard
13942 \begin_layout Standard
13945 \begin_inset Formula \begin{equation}
13946 \int A=B\label{eq:red}\end{equation}
13953 \begin_inset Formula \begin{equation}
13954 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13961 \begin_layout Standard
13963 \begin_inset CommandInset ref
13969 is completely colored red.
13970 \begin_inset Newline newline
13974 \begin_inset CommandInset ref
13976 reference "eq:redgreen"
13980 was first completely colored green to set the color for the formula number.
13981 Subsequently the formula characters were colored red.
13984 \begin_layout Standard
13985 \begin_inset VSpace bigskip
13988 To color the frame different than the rest of the box, the command
13995 \begin_inset Index idx
13998 \begin_layout Plain Layout
14006 is used in the following scheme:
14009 \begin_layout Standard
14014 fcolorbox{frame color}{color}{box content}
14017 \begin_layout Standard
14024 is an extension of the command
14031 The frame width is set, like for
14054 \begin_layout Plain Layout
14066 \begin_inset Formula \[
14067 \fcolorbox{cyan}{magenta}{A=B}\]
14075 \begin_layout Plain Layout
14089 \begin_layout Standard
14090 This formula was created with the command
14091 \begin_inset Newline newline
14099 \begin_inset Formula $\to$
14105 \begin_inset Formula $\to$
14115 \begin_layout Standard
14116 \begin_inset VSpace bigskip
14119 To use other colors than the predefined ones, they have to be defined first.
14122 \begin_layout Standard
14123 One can for example define the color
14124 \begin_inset Quotes eld
14132 \begin_inset Quotes erd
14135 with the LaTeX-preamble line:
14138 \begin_layout Standard
14143 definecolor{darkgreen}{cmyk}{0.5,
14158 \begin_inset Index idx
14161 \begin_layout Plain Layout
14172 \begin_layout Standard
14177 is the color space that denotes the colors
14194 The four comma separated numbers are the portion factor for the corresponding
14195 colors of the color space.
14196 The factors can be in the range of 0
14197 \begin_inset space \thinspace{}
14201 \begin_inset space \thinspace{}
14209 also the color space
14213 can be used for definitions.
14230 , so that there are in this case three portion factors for the corresponding
14232 Furthermore there is the color space
14236 with one portion factor for the gray value.
14239 \begin_layout Standard
14240 As example a framed box with the new defined color
14244 where the characters have been colored
14249 \begin_inset Formula \begin{equation}
14250 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14257 \begin_layout Standard
14258 Self-defined colors can also be used for text with the help of the command
14266 \begin_inset Index idx
14269 \begin_layout Plain Layout
14278 \begin_layout Standard
14282 \begin_layout Plain Layout
14286 textcolor{darkgreen}{
14292 \begin_inset Quotes eld
14296 \begin_inset Quotes erd
14303 \begin_layout Plain Layout
14313 \begin_layout Standard
14321 \begin_inset Index idx
14324 \begin_layout Plain Layout
14332 is used in the scheme
14336 textcolor{color}{characters to color}
14341 \begin_layout Subsection
14343 \begin_inset CommandInset label
14345 name "sub:Paragraph-Boxes"
14350 \begin_inset Index idx
14353 \begin_layout Plain Layout
14354 Boxes ! as paragraph
14362 \begin_layout Standard
14363 A box that can contain several lines and paragraphs, a so called paragraph
14364 box (parbox), can be created with the menu
14366 Insert\SpecialChar \menuseparator
14369 or the toolbar button
14370 \begin_inset Graphics
14371 filename ../images/box-insert.png
14379 \begin_layout Standard
14380 The following example shows a framed parbox in a line:
14383 \begin_layout Standard
14384 \begin_inset VSpace medskip
14388 \begin_inset Box Boxed
14398 height_special "totalheight"
14401 \begin_layout Plain Layout
14402 This is a paragraph box.
14404 \begin_inset space \thinspace{}
14407 cm long and can also contain formulas:
14408 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14419 \begin_layout Standard
14420 \begin_inset VSpace medskip
14426 \begin_layout Standard
14427 Such a box is created by right-clicking on the gray box inset.
14428 A dialog pops up showing the box properties.
14442 \begin_inset space \thinspace{}
14447 Vertical Box Alignment
14452 \begin_layout Standard
14453 \begin_inset VSpace medskip
14456 In LaTeX a parbox is created with the command
14463 \begin_inset Index idx
14466 \begin_layout Plain Layout
14474 that has the following scheme:
14477 \begin_layout Standard
14482 parbox[position]{width}{box content}
14485 \begin_layout Standard
14499 for bottom means that the box is aligned within the surrounding text with
14505 for top this is done with the first line.
14506 When no position is given, the box will be vertically centered, see section
14514 \begin_inset space ~
14519 manual for examples.
14522 \begin_layout Standard
14523 \begin_inset VSpace bigskip
14526 To frame formulas completely, including the formula number, the formula
14527 must be set into a parbox.
14528 To do this, the command
14542 is inserted in TeX-mode before the formula.
14550 \begin_inset Index idx
14553 \begin_layout Plain Layout
14561 is hereby the line width set for the document.
14562 Because the frame is outside the parbox, 2
14563 \begin_inset space \thinspace{}
14566 times the frame separation and the frame thickness must be subtracted from
14568 As this is not automatically done by LyX due to a bug
14572 \begin_layout Plain Layout
14573 \begin_inset CommandInset href
14575 name "LyX-bug #4483"
14576 target "http://www.lyx.org/trac/ticket/4483"
14585 , TeX-mode has to be used.
14586 To be able to multiply and subtract in arguments, the LaTeX-package
14594 \begin_layout Plain Layout
14599 is part of every LaTeX standard installation.
14605 \begin_inset Index idx
14608 \begin_layout Plain Layout
14614 must be loaded in the LaTeX-preamble with the line
14617 \begin_layout Standard
14625 \begin_layout Standard
14626 Behind the formula both boxes are closed by entering
14631 Here is an example:
14635 \begin_layout Plain Layout
14649 \begin_layout Standard
14653 \begin_layout Plain Layout
14671 \begin_inset Formula \begin{equation}
14672 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14680 \begin_layout Plain Layout
14691 \begin_layout Plain Layout
14705 \begin_layout Standard
14706 \begin_inset VSpace medskip
14709 As a parbox is used as argument of
14715 , there is in this case no difference between
14730 \begin_layout Standard
14731 \begin_inset VSpace bigskip
14734 Paragraph boxes are very useful to comment formulas directly.
14741 is used in combination with the command
14755 \begin_inset CommandInset ref
14757 reference "sub:User-defined-Numbering"
14764 \begin_layout Standard
14765 An example of a formula commented with
14774 \begin_layout Standard
14778 \begin_layout Plain Layout
14791 This is a description.
14792 It is distinctly separated from the formula and multiline.
14796 \begin_layout Plain Layout
14808 \begin_layout Standard
14809 Such a formula must be inserted completely in TeX-mode because LyX does
14810 not yet support the command
14817 The formula is created with the following command sequence:
14820 \begin_layout Standard
14833 is inserted in TeX-mode.
14837 \begin_layout Plain Layout
14838 When the formula style
14850 can also be replaced by
14857 (formula styles see
14858 \begin_inset CommandInset ref
14860 reference "sec:Formula-Styles"
14869 Then the description follows as normal text and finally
14875 is inserted in TeX-mode.
14888 hereby create a displayed formula.
14891 \begin_layout Standard
14898 can be seen in this example that was
14899 \begin_inset Quotes eld
14903 \begin_inset Quotes erd
14906 using the mathematical textmode:
14907 \begin_inset Formula \[
14908 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14915 \begin_layout Section
14917 \begin_inset Index idx
14920 \begin_layout Plain Layout
14929 \begin_layout Subsection
14931 \begin_inset CommandInset label
14933 name "sub:Big-Operators"
14938 \begin_inset Index idx
14941 \begin_layout Plain Layout
14948 \begin_inset Index idx
14951 \begin_layout Plain Layout
14958 \begin_inset Index idx
14961 \begin_layout Plain Layout
14970 \begin_layout Standard
14971 To be able to use all integral operators listed here, the option
14973 Use esint package automatically
14975 must be set in the document settings under
14978 \begin_inset space ~
14986 \begin_layout Standard
14987 \begin_inset space \hfill{}
14991 \begin_inset Tabular
14992 <lyxtabular version="3" rows="11" columns="2">
14993 <features tabularvalignment="middle">
14994 <column alignment="center" valignment="top" width="0pt">
14995 <column alignment="center" valignment="top" width="0pt">
14997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15000 \begin_layout Plain Layout
15006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15009 \begin_layout Plain Layout
15017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15020 \begin_layout Plain Layout
15024 \begin_inset Index idx
15027 \begin_layout Plain Layout
15040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15043 \begin_layout Plain Layout
15044 \begin_inset Formula $\int$
15054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15057 \begin_layout Plain Layout
15065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15068 \begin_layout Plain Layout
15069 \begin_inset Formula $\oint$
15079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15082 \begin_layout Plain Layout
15090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15093 \begin_layout Plain Layout
15094 \begin_inset Formula $\ointctrclockwise$
15104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15107 \begin_layout Plain Layout
15115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15118 \begin_layout Plain Layout
15119 \begin_inset Formula $\ointclockwise$
15129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15132 \begin_layout Plain Layout
15140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15143 \begin_layout Plain Layout
15144 \begin_inset Formula $\sqint$
15154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15157 \begin_layout Plain Layout
15165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15168 \begin_layout Plain Layout
15170 \begin_inset Formula $\fint$
15180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15183 \begin_layout Plain Layout
15191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15194 \begin_layout Plain Layout
15196 \begin_inset Formula $\landupint$
15206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15209 \begin_layout Plain Layout
15217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15220 \begin_layout Plain Layout
15222 \begin_inset Formula $\landdownint$
15232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15235 \begin_layout Plain Layout
15243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15246 \begin_layout Plain Layout
15247 \begin_inset Formula $\bigcap$
15257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15260 \begin_layout Plain Layout
15268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15271 \begin_layout Plain Layout
15272 \begin_inset Formula $\bigcup$
15286 \begin_inset space \hfill{}
15290 \begin_inset Tabular
15291 <lyxtabular version="3" rows="11" columns="2">
15292 <features tabularvalignment="middle">
15293 <column alignment="center" valignment="top" width="0pt">
15294 <column alignment="center" valignment="top" width="0pt">
15296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15299 \begin_layout Plain Layout
15305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15308 \begin_layout Plain Layout
15316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15319 \begin_layout Plain Layout
15323 \begin_inset Index idx
15326 \begin_layout Plain Layout
15339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15342 \begin_layout Plain Layout
15343 \begin_inset Formula $\sum$
15353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15356 \begin_layout Plain Layout
15360 \begin_inset Index idx
15363 \begin_layout Plain Layout
15376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15379 \begin_layout Plain Layout
15380 \begin_inset Formula $\prod$
15390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15393 \begin_layout Plain Layout
15401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15404 \begin_layout Plain Layout
15405 \begin_inset Formula $\coprod$
15415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15418 \begin_layout Plain Layout
15426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15429 \begin_layout Plain Layout
15430 \begin_inset Formula $\bigodot$
15440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15443 \begin_layout Plain Layout
15451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15454 \begin_layout Plain Layout
15455 \begin_inset Formula $\bigotimes$
15465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15468 \begin_layout Plain Layout
15476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15479 \begin_layout Plain Layout
15480 \begin_inset Formula $\bigoplus$
15490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15493 \begin_layout Plain Layout
15501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15504 \begin_layout Plain Layout
15505 \begin_inset Formula $\bigwedge$
15515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15518 \begin_layout Plain Layout
15526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15529 \begin_layout Plain Layout
15530 \begin_inset Formula $\bigvee$
15540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15543 \begin_layout Plain Layout
15551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15554 \begin_layout Plain Layout
15555 \begin_inset Formula $\bigsqcup$
15565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15568 \begin_layout Plain Layout
15576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15579 \begin_layout Plain Layout
15580 \begin_inset Formula $\biguplus$
15594 \begin_inset space \hfill{}
15600 \begin_layout Standard
15601 All big operators can also be inserted via the math toolbar button
15602 \begin_inset Graphics
15603 filename ../images/math/intop.png
15611 \begin_layout Standard
15612 The operators are called big because they are bigger than the sometimes
15613 equal looking binary operators.
15614 All big operators can have limits as described in the next subsection.
15617 \begin_layout Standard
15618 For all integral operators there is a second version available, ending on
15636 These operators are different from
15643 \begin_inset space \space{}
15646 in the style the operator limits are displayed, see
15647 \begin_inset CommandInset ref
15649 reference "sub:Operator-Limits"
15657 \begin_layout Subsubsection*
15658 Advice for Integrals
15661 \begin_layout Standard
15666 in an integral is an operator, that therefore has to be set upright.
15667 This is done by highlighting the
15671 and using the keyboard shortcut
15681 \begin_layout Plain Layout
15687 \begin_inset CommandInset ref
15689 reference "sub:Font-Styles"
15699 Finally the smallest space is inserted before the
15703 , as this is usual for operators.
15707 \begin_layout Standard
15709 \begin_inset Formula $\int A(x)dx$
15713 \begin_inset Newline newline
15717 \begin_inset Phantom HPhantom
15720 \begin_layout Plain Layout
15727 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15733 \begin_layout Standard
15734 For multiple integrals there are the following commands:
15735 \begin_inset VSpace medskip
15741 \begin_layout Standard
15742 \begin_inset space \hfill{}
15746 \begin_inset Tabular
15747 <lyxtabular version="3" rows="4" columns="2">
15748 <features tabularvalignment="middle">
15749 <column alignment="center" valignment="top" width="0">
15750 <column alignment="center" valignment="top" width="0">
15752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15755 \begin_layout Plain Layout
15761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15764 \begin_layout Plain Layout
15766 \begin_inset Note Note
15769 \begin_layout Plain Layout
15776 is only used as spacer.
15788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15791 \begin_layout Plain Layout
15799 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15802 \begin_layout Plain Layout
15803 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15816 \begin_layout Plain Layout
15824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15827 \begin_layout Plain Layout
15828 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15841 \begin_layout Plain Layout
15849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15852 \begin_layout Plain Layout
15853 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15867 \begin_inset space \hfill{}
15871 \begin_inset Tabular
15872 <lyxtabular version="3" rows="4" columns="2">
15873 <features tabularvalignment="middle">
15874 <column alignment="center" valignment="top" width="0">
15875 <column alignment="center" valignment="top" width="0">
15877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15880 \begin_layout Plain Layout
15886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15889 \begin_layout Plain Layout
15897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15900 \begin_layout Plain Layout
15908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15911 \begin_layout Plain Layout
15912 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15925 \begin_layout Plain Layout
15933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15936 \begin_layout Plain Layout
15937 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15950 \begin_layout Plain Layout
15958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15961 \begin_layout Plain Layout
15962 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15976 \begin_inset space \hfill{}
15982 \begin_layout Subsection
15984 \begin_inset CommandInset label
15986 name "sub:Operator-Limits"
15991 \begin_inset Index idx
15994 \begin_layout Plain Layout
16003 \begin_layout Standard
16004 Limits are created by super- and subscripts:
16007 \begin_layout Standard
16009 \begin_inset Tabular
16010 <lyxtabular version="3" rows="2" columns="2">
16011 <features tabularvalignment="middle">
16012 <column alignment="center" valignment="top" width="0pt">
16013 <column alignment="center" valignment="top" width="0pt">
16015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16018 \begin_layout Plain Layout
16024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16027 \begin_layout Plain Layout
16029 \begin_inset Note Note
16032 \begin_layout Plain Layout
16039 is only used as spacer.
16051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16054 \begin_layout Plain Layout
16063 \begin_layout Plain Layout
16073 \begin_inset Formula $\to$
16077 \begin_inset Formula $\to$
16085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16088 \begin_layout Plain Layout
16089 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16105 \begin_layout Standard
16106 Limits of inline formulas are set right beside the operator.
16107 Limits in displayed formulas are set above or below the operator, except
16108 for integral limits.
16111 \begin_layout Standard
16112 To force that the limits are set beside the operator, the cursor is set
16113 directly behind the operator and the limits type is changed with the menu
16116 Edit\SpecialChar \menuseparator
16117 Math\SpecialChar \menuseparator
16136 \begin_layout Standard
16137 The default limits type is this:
16138 \begin_inset Formula \[
16139 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16143 This is how it looks when the limits type was changed to
16150 \begin_inset Formula \[
16151 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16155 For integrals, except those ending with
16171 etc., the limits are by default set beside the operator.
16172 But for multiple integrals the limits are often set below the operator.
16173 In the following example the limits type was therefore set to
16177 and so set below the integrals:
16178 \begin_inset Formula \begin{equation}
16179 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16186 \begin_layout Standard
16187 \begin_inset VSpace medskip
16190 To specify conditions for limits, the commands
16197 \begin_inset Index idx
16200 \begin_layout Plain Layout
16215 \begin_inset Index idx
16218 \begin_layout Plain Layout
16227 To create for example this expression
16228 \begin_inset Formula \begin{equation}
16229 \sum_{\begin{subarray}{c}
16233 \end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16240 \begin_layout Standard
16241 the following has to be done:
16242 \begin_inset Newline newline
16257 \begin_layout Plain Layout
16269 One is now in a blue box under the summation operator and insert there
16278 \begin_layout Plain Layout
16290 The blue box is now within a purple box and now several lines can be written
16292 A new line is created by inserting a line break (
16295 arg "newline-insert newline"
16300 \begin_inset Newline newline
16305 0<k<1000 Ctrl+Return
16306 \begin_inset Newline newline
16311 is typed in, a new box appears below for the new line.
16314 \begin_layout Standard
16315 The alignment of the lines can be changed to left aligned with the
16325 Edit\SpecialChar \menuseparator
16329 To get right alignment,
16337 \begin_layout Plain Layout
16348 is inserted at the beginning of the line.
16351 \begin_layout Standard
16364 with the difference that the lines are always centered.
16367 \begin_layout Standard
16368 \begin_inset VSpace bigskip
16372 \begin_inset CommandInset ref
16374 reference "eq:substack"
16378 there can be too much space beside an operator, because the characters
16379 following the operator are set beside the limits.
16382 \begin_layout Standard
16383 To avoid this, the following macro can be used in the LaTeX-preamble:
16386 \begin_layout Standard
16400 \begin_inset Newline newline
16412 \begin_inset Newline newline
16419 mathclapinternal #1#2{
16423 mathsurround =0pt #1{#2}$}}
16426 \begin_layout Standard
16427 This defines the command
16434 \begin_inset Index idx
16437 \begin_layout Plain Layout
16445 that sets the width of the limit to 0
16446 \begin_inset space \thinspace{}
16450 The command scheme is
16453 \begin_layout Standard
16461 \begin_layout Standard
16462 where the limit can consist of several conditions.
16465 \begin_layout Standard
16467 \begin_inset CommandInset ref
16469 reference "eq:substack"
16473 , one uses the command
16476 \begin_layout Standard
16489 \begin_layout Plain Layout
16498 0<k<1000 Ctrl+Return
16501 \begin_layout Standard
16502 to create the lower limit.
16503 The summand is now directly behind the summation operator:
16504 \begin_inset Formula \[
16505 \sum_{\mathclap{\substack{0<k<1000\\
16516 \begin_layout Standard
16517 \begin_inset VSpace bigskip
16520 How to use one limit for several operators is described in
16521 \begin_inset CommandInset ref
16523 reference "sub:Self-defined-Operators"
16530 \begin_layout Subsection
16532 \begin_inset CommandInset label
16534 name "sub:Binary-Operators"
16539 \begin_inset Index idx
16542 \begin_layout Plain Layout
16551 \begin_layout Standard
16552 Binary operators are surrounded by space when there is a character before
16554 \begin_inset VSpace medskip
16560 \begin_layout Standard
16561 \begin_inset space \hfill{}
16565 \begin_inset Tabular
16566 <lyxtabular version="3" rows="13" columns="2">
16567 <features tabularvalignment="middle">
16568 <column alignment="center" valignment="top" width="0pt">
16569 <column alignment="center" valignment="top" width="0pt">
16571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16574 \begin_layout Plain Layout
16576 \begin_inset Note Note
16579 \begin_layout Plain Layout
16586 is only used as spacer.
16596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16599 \begin_layout Plain Layout
16607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16610 \begin_layout Plain Layout
16616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16619 \begin_layout Plain Layout
16620 \begin_inset Formula $+$
16630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16633 \begin_layout Plain Layout
16639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16642 \begin_layout Plain Layout
16643 \begin_inset Formula $-$
16653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16656 \begin_layout Plain Layout
16664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16667 \begin_layout Plain Layout
16668 \begin_inset Formula $\pm$
16678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16681 \begin_layout Plain Layout
16689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16692 \begin_layout Plain Layout
16693 \begin_inset Formula $\mp$
16703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16706 \begin_layout Plain Layout
16714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16717 \begin_layout Plain Layout
16718 \begin_inset Formula $\cdot$
16728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16731 \begin_layout Plain Layout
16739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16742 \begin_layout Plain Layout
16743 \begin_inset Formula $\times$
16753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16756 \begin_layout Plain Layout
16764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16767 \begin_layout Plain Layout
16768 \begin_inset Formula $\div$
16778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16781 \begin_layout Plain Layout
16785 \begin_layout Plain Layout
16798 \begin_layout Plain Layout
16810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16813 \begin_layout Plain Layout
16814 \begin_inset Formula $*$
16824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16827 \begin_layout Plain Layout
16835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16838 \begin_layout Plain Layout
16839 \begin_inset Formula $\star$
16849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16852 \begin_layout Plain Layout
16860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16863 \begin_layout Plain Layout
16864 \begin_inset Formula $\circ$
16874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16877 \begin_layout Plain Layout
16885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16888 \begin_layout Plain Layout
16889 \begin_inset Formula $\diamond$
16899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16902 \begin_layout Plain Layout
16910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16913 \begin_layout Plain Layout
16914 \begin_inset Formula $\bullet$
16928 \begin_inset space \hfill{}
16932 \begin_inset Tabular
16933 <lyxtabular version="3" rows="13" columns="2">
16934 <features tabularvalignment="middle">
16935 <column alignment="center" valignment="top" width="0pt">
16936 <column alignment="center" valignment="top" width="0pt">
16938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16941 \begin_layout Plain Layout
16947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16950 \begin_layout Plain Layout
16958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16961 \begin_layout Plain Layout
16969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16972 \begin_layout Plain Layout
16973 \begin_inset Formula $\nabla$
16983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16986 \begin_layout Plain Layout
16994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16997 \begin_layout Plain Layout
16998 \begin_inset Formula $\bigtriangledown$
17008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17011 \begin_layout Plain Layout
17019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17022 \begin_layout Plain Layout
17023 \begin_inset Formula $\bigtriangleup$
17033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17036 \begin_layout Plain Layout
17044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17047 \begin_layout Plain Layout
17048 \begin_inset Formula $\Box$
17058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17061 \begin_layout Plain Layout
17069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17072 \begin_layout Plain Layout
17073 \begin_inset Formula $\cap$
17083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17086 \begin_layout Plain Layout
17094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17097 \begin_layout Plain Layout
17098 \begin_inset Formula $\cup$
17108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17111 \begin_layout Plain Layout
17119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17122 \begin_layout Plain Layout
17123 \begin_inset Formula $\dagger$
17133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17136 \begin_layout Plain Layout
17144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17147 \begin_layout Plain Layout
17148 \begin_inset Formula $\ddagger$
17158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17161 \begin_layout Plain Layout
17169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17172 \begin_layout Plain Layout
17173 \begin_inset Formula $\wr$
17183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17186 \begin_layout Plain Layout
17194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17197 \begin_layout Plain Layout
17198 \begin_inset Formula $\bigcirc$
17208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17211 \begin_layout Plain Layout
17219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17222 \begin_layout Plain Layout
17223 \begin_inset Formula $\wedge$
17233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17236 \begin_layout Plain Layout
17244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17247 \begin_layout Plain Layout
17248 \begin_inset Formula $\vee$
17262 \begin_inset space \hfill{}
17266 \begin_inset Tabular
17267 <lyxtabular version="3" rows="13" columns="2">
17268 <features tabularvalignment="middle">
17269 <column alignment="center" valignment="top" width="0pt">
17270 <column alignment="center" valignment="top" width="0pt">
17272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17275 \begin_layout Plain Layout
17281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17284 \begin_layout Plain Layout
17292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17295 \begin_layout Plain Layout
17303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17306 \begin_layout Plain Layout
17307 \begin_inset Formula $\oplus$
17317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17320 \begin_layout Plain Layout
17328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17331 \begin_layout Plain Layout
17332 \begin_inset Formula $\ominus$
17342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17345 \begin_layout Plain Layout
17353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17356 \begin_layout Plain Layout
17357 \begin_inset Formula $\otimes$
17367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17370 \begin_layout Plain Layout
17378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17381 \begin_layout Plain Layout
17382 \begin_inset Formula $\oslash$
17392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17395 \begin_layout Plain Layout
17403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17406 \begin_layout Plain Layout
17407 \begin_inset Formula $\odot$
17417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17420 \begin_layout Plain Layout
17428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17431 \begin_layout Plain Layout
17432 \begin_inset Formula $\amalg$
17442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17445 \begin_layout Plain Layout
17453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17456 \begin_layout Plain Layout
17457 \begin_inset Formula $\uplus$
17467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17470 \begin_layout Plain Layout
17478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17481 \begin_layout Plain Layout
17482 \begin_inset Formula $\setminus$
17492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17495 \begin_layout Plain Layout
17503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17506 \begin_layout Plain Layout
17507 \begin_inset Formula $\sqcap$
17517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17520 \begin_layout Plain Layout
17528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17531 \begin_layout Plain Layout
17532 \begin_inset Formula $\sqcup$
17542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17545 \begin_layout Plain Layout
17553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17556 \begin_layout Plain Layout
17557 \begin_inset Formula $\triangleleft$
17567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17570 \begin_layout Plain Layout
17578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17581 \begin_layout Plain Layout
17582 \begin_inset Formula $\triangleright$
17596 \begin_inset space \hfill{}
17602 \begin_layout Standard
17603 All binary operators can also be inserted via the math toolbar button
17604 \begin_inset Graphics
17605 filename ../images/math/pm.png
17613 \begin_layout Standard
17614 To typeset the Laplace operator also
17631 \begin_inset Formula $\nabla^{2}$
17634 ) can be used instead of
17643 \begin_layout Standard
17650 Insert\SpecialChar \menuseparator
17662 \begin_layout Subsection
17663 Self-defined Operators
17664 \begin_inset CommandInset label
17666 name "sub:Self-defined-Operators"
17671 \begin_inset Index idx
17674 \begin_layout Plain Layout
17675 Operators ! self-defined
17683 \begin_layout Standard
17684 With the help of the command
17688 DeclareMathOperator
17691 \begin_inset Index idx
17694 \begin_layout Plain Layout
17699 DeclareMathOperator
17704 custom operators can be defined in the LaTeX-preamble.
17705 Its command scheme is:
17708 \begin_layout Standard
17713 DeclareMathOperator{new command}{display}
17716 \begin_layout Standard
17717 Display can be characters or symbols that define how the operator looks
17719 To define a big operator a * is set behind the command.
17720 All self-defined big operators can have limits as described in
17721 \begin_inset CommandInset ref
17723 reference "sub:Operator-Limits"
17730 \begin_layout Standard
17731 For example the LaTeX-preamble line
17734 \begin_layout Standard
17739 DeclareMathOperator*{
17746 \begin_layout Standard
17747 defines the command
17753 , that inserts a big operator consisting of the lozenge symbol from
17754 \begin_inset CommandInset ref
17756 reference "sub:Miscellaneous-Symbols"
17761 \begin_inset Formula \[
17762 \Lozenge_{n=1}^{\infty}\]
17766 The command for this formula is:
17777 \begin_inset Formula $\to$
17783 \begin_layout Standard
17784 \begin_inset VSpace bigskip
17787 When self-defined operators are not used several times in the document,
17788 they can also be defined with the commands
17795 \begin_inset Index idx
17798 \begin_layout Plain Layout
17813 \begin_inset Index idx
17816 \begin_layout Plain Layout
17824 , which have the following scheme:
17827 \begin_layout Standard
17841 \begin_layout Standard
17848 defines big operators,
17857 \begin_layout Standard
17865 \begin_inset space \thinspace{}
17869 \begin_inset space \space{}
17872 be used to use one limit for several operators:
17875 \begin_layout Standard
17876 \begin_inset Formula \[
17877 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17884 \begin_layout Standard
17885 The command for the formula above is:
17886 \begin_inset Newline newline
17905 \begin_layout Plain Layout
17917 \begin_inset Formula $\to$
17926 \begin_layout Plain Layout
17940 \begin_layout Section
17942 \begin_inset Index idx
17945 \begin_layout Plain Layout
17954 \begin_layout Subsection
17956 \begin_inset CommandInset label
17958 name "sub:Font-Styles"
17963 \begin_inset Index idx
17966 \begin_layout Plain Layout
17975 \begin_layout Standard
17976 Latin letters in formulas can be set in one of the following font styles:
17977 \begin_inset VSpace -2mm
17983 \begin_layout Standard
17985 \begin_inset Tabular
17986 <lyxtabular version="3" rows="7" columns="3">
17987 <features tabularvalignment="middle">
17988 <column alignment="center" valignment="top" width="0">
17989 <column alignment="center" valignment="top" width="0">
17990 <column alignment="center" valignment="top" width="0">
17992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17995 \begin_layout Plain Layout
18001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18004 \begin_layout Plain Layout
18010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18013 \begin_layout Plain Layout
18021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18024 \begin_layout Plain Layout
18033 \begin_layout Plain Layout
18049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18052 \begin_layout Plain Layout
18053 \begin_inset Formula $\mathbb{ABC}$
18061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18064 \begin_layout Plain Layout
18077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18080 \begin_layout Plain Layout
18089 \begin_layout Plain Layout
18105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18108 \begin_layout Plain Layout
18109 \begin_inset Formula $\mathbf{AbC}$
18117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18120 \begin_layout Plain Layout
18133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18136 \begin_layout Plain Layout
18145 \begin_layout Plain Layout
18161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18164 \begin_layout Plain Layout
18165 \begin_inset Formula $\boldsymbol{AbC}$
18173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18176 \begin_layout Plain Layout
18179 arg "font-boldsymbol"
18189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18192 \begin_layout Plain Layout
18201 \begin_layout Plain Layout
18217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18220 \begin_layout Plain Layout
18221 \begin_inset Formula $\mathcal{ABC}$
18229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18232 \begin_layout Plain Layout
18245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18248 \begin_layout Plain Layout
18257 \begin_layout Plain Layout
18273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18276 \begin_layout Plain Layout
18277 \begin_inset Formula $\mathfrak{AbC}$
18285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18288 \begin_layout Plain Layout
18296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18299 \begin_layout Plain Layout
18308 \begin_layout Plain Layout
18324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18327 \begin_layout Plain Layout
18328 \begin_inset Formula $\mathscr{AbC}$
18336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18339 \begin_layout Plain Layout
18353 \begin_layout Standard
18355 \begin_inset Tabular
18356 <lyxtabular version="3" rows="5" columns="3">
18357 <features tabularvalignment="middle">
18358 <column alignment="center" valignment="top" width="0">
18359 <column alignment="center" valignment="top" width="0">
18360 <column alignment="center" valignment="top" width="0">
18362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18365 \begin_layout Plain Layout
18371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18374 \begin_layout Plain Layout
18380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18383 \begin_layout Plain Layout
18391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18394 \begin_layout Plain Layout
18403 \begin_layout Plain Layout
18419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18422 \begin_layout Plain Layout
18423 \begin_inset Formula $\mathit{AbC}$
18431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18434 \begin_layout Plain Layout
18442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18445 \begin_layout Plain Layout
18454 \begin_layout Plain Layout
18470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18473 \begin_layout Plain Layout
18474 \begin_inset Formula $\mathrm{AbC}$
18482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18485 \begin_layout Plain Layout
18498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18501 \begin_layout Plain Layout
18510 \begin_layout Plain Layout
18526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18529 \begin_layout Plain Layout
18530 \begin_inset Formula $\mathsf{AbC}$
18538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18541 \begin_layout Plain Layout
18554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18557 \begin_layout Plain Layout
18566 \begin_layout Plain Layout
18582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18585 \begin_layout Plain Layout
18586 \begin_inset Formula $\mathtt{AbC}$
18594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18597 \begin_layout Plain Layout
18600 arg "font-typewriter"
18616 \begin_layout Standard
18617 \begin_inset Note Greyedout
18620 \begin_layout Plain Layout
18637 can only be used for big letters.
18645 \begin_layout Standard
18646 Predefined is the style
18655 \begin_layout Standard
18656 The style commands work also for letters in mathematical constructs:
18657 \begin_inset Formula \[
18658 \mathfrak{A=\frac{b}{C}}\]
18665 \begin_layout Standard
18666 Characters in mathematical text don't appear in a math font style but in
18667 the text font style
18674 That their style can't be set correctly via the text style dialog is a
18679 \begin_layout Plain Layout
18680 \begin_inset CommandInset href
18682 name "LyX-bug #4629"
18683 target "http://www.lyx.org/trac/ticket/4629"
18695 \begin_layout Standard
18696 Instead of the style commands the dialog
18698 Edit\SpecialChar \menuseparator
18699 Math\SpecialChar \menuseparator
18702 or the toolbar button
18703 \begin_inset Graphics
18704 filename ../images/math/font.png
18712 \begin_layout Subsection
18714 \begin_inset CommandInset label
18716 name "sub:Bold-Formulas"
18721 \begin_inset Index idx
18724 \begin_layout Plain Layout
18733 \begin_layout Standard
18734 To make a complete formula bold, the command
18740 from the previous subsection cannot be used, because it doesn't work for
18741 small Greek letters.
18742 Furthermore it prints Latin letters always upright, like in the following
18746 \begin_layout Standard
18747 \begin_inset Formula \[
18748 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18755 \begin_layout Standard
18756 To display the formula correctly, the command
18763 \begin_inset Formula \[
18764 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18768 It is also possible to set the formula in a
18770 boldmath environment
18773 This environment is created by inserting the command
18780 \begin_inset Index idx
18783 \begin_layout Plain Layout
18792 To end the environment, the command
18799 \begin_inset Index idx
18802 \begin_layout Plain Layout
18810 is inserted in TeX-mode.
18814 \begin_layout Plain Layout
18824 \begin_inset Formula \[
18825 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18833 \begin_layout Plain Layout
18845 \begin_layout Subsection
18847 \begin_inset Index idx
18850 \begin_layout Plain Layout
18859 \begin_layout Standard
18860 Formulas can be colored like normal text: Highlight a formula or a formula
18866 Here is a formula in magenta:
18867 \begin_inset Formula \[
18868 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18875 \begin_layout Standard
18876 You can also define your own colors as described in
18877 \begin_inset CommandInset ref
18879 reference "sub:Colored-Boxes"
18884 They can be used with the TeX code command
18891 \begin_inset Index idx
18894 \begin_layout Plain Layout
18905 \begin_layout Standard
18910 textcolor{color}{characters or formula}
18913 \begin_layout Standard
18914 The following example was colored completely dark green and partly red:
18917 \begin_layout Standard
18921 \begin_layout Plain Layout
18925 textcolor{darkgreen}{
18931 \begin_inset Formula \[
18932 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18940 \begin_layout Plain Layout
18950 \begin_layout Standard
18951 Due to a bug in LyX only complete formulas can be colored with self-defined
18956 \begin_layout Plain Layout
18957 \begin_inset CommandInset href
18959 name "LyX-bug #5269"
18960 target "http://www.lyx.org/trac/ticket/5269"
18972 \begin_layout Subsection
18974 \begin_inset CommandInset label
18976 name "sub:Font-Sizes"
18981 \begin_inset Index idx
18984 \begin_layout Plain Layout
18993 \begin_layout Standard
18994 For characters in formulas there are, analog to characters in text, the
18995 following size commands:
18998 \begin_layout Standard
19042 \begin_inset Newline newline
19064 \begin_layout Standard
19065 The size produced by the commands depends on the document font size, that
19066 corresponds with the command
19073 The other commands produce smaller or larger sizes than
19080 The font size can however not exceed a certain value.
19081 Is for example the document font size 12
19082 \begin_inset space \thinspace{}
19091 switches to the same size as
19101 \begin_layout Standard
19102 A size command is inserted in TeX-mode before the formula and sets the size
19103 for all following formula and text characters.
19104 To switch back to the initial size, the command
19110 is inserted behind the formula in TeX-mode.
19113 \begin_layout Standard
19114 \begin_inset Newpage newpage
19120 \begin_layout Standard
19121 Within a formula the size can be changed using the following size commands:
19124 \begin_layout Standard
19127 \begin_inset Tabular
19128 <lyxtabular version="3" rows="5" columns="2">
19129 <features tabularvalignment="middle">
19130 <column alignment="center" valignment="top" width="0">
19131 <column alignment="center" valignment="top" width="0">
19133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19136 \begin_layout Plain Layout
19142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19145 \begin_layout Plain Layout
19147 \begin_inset Note Note
19150 \begin_layout Plain Layout
19157 is only used as spacer.
19169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19172 \begin_layout Plain Layout
19176 \begin_inset Index idx
19179 \begin_layout Plain Layout
19192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19195 \begin_layout Plain Layout
19196 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19209 \begin_layout Plain Layout
19217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19220 \begin_layout Plain Layout
19221 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19234 \begin_layout Plain Layout
19242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19245 \begin_layout Plain Layout
19246 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19259 \begin_layout Plain Layout
19267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19270 \begin_layout Plain Layout
19271 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19287 \begin_layout Standard
19288 After entering these commands, a blue box appears in which the formula parts
19292 \begin_layout Standard
19293 There is a further method to change the font size, that though only works
19294 for symbols or letters in mathematical text.
19295 To use it, one of the above text size commands is inserted in mathematical
19297 All following characters until the end of the mathematical text or until
19298 another size command will have the selected size.
19300 \begin_inset VSpace -2mm
19306 \begin_layout Standard
19310 \begin_layout Plain Layout
19320 \begin_inset Formula \[
19321 A=\frac{B}{c}\cdot\maltese\]
19326 \begin_inset Formula \[
19327 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
19335 \begin_layout Plain Layout
19347 \begin_layout Standard
19348 \begin_inset VSpace medskip
19351 Before both formulas the command
19358 The command for the second formula is:
19359 \begin_inset Newline newline
19370 \begin_layout Plain Layout
19385 \begin_layout Plain Layout
19400 \begin_layout Plain Layout
19415 \begin_layout Plain Layout
19425 \begin_inset Formula $\to$
19429 \begin_inset Formula $\to$
19433 \begin_inset Newline newline
19437 \begin_inset space \hspace*{}
19451 \begin_layout Plain Layout
19466 \begin_layout Plain Layout
19481 \begin_layout Plain Layout
19493 \begin_layout Standard
19494 If a symbol cannot be displayed in different sizes, it will always be displayed
19495 in the default size.
19498 \begin_layout Standard
19499 \begin_inset Newpage newpage
19505 \begin_layout Section
19507 \begin_inset Index idx
19510 \begin_layout Plain Layout
19519 \begin_layout Standard
19520 All Greek letters can also be inserted via the toolbar button
19521 \begin_inset Graphics
19522 filename ../images/math/alpha.png
19530 \begin_layout Subsection
19532 \begin_inset Index idx
19535 \begin_layout Plain Layout
19536 Greek letters ! small
19544 \begin_layout Standard
19545 \begin_inset space \hfill{}
19549 \begin_inset Tabular
19550 <lyxtabular version="3" rows="11" columns="2">
19551 <features tabularvalignment="middle">
19552 <column alignment="center" valignment="top" width="0pt">
19553 <column alignment="center" valignment="top" width="0pt">
19555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19558 \begin_layout Plain Layout
19564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19567 \begin_layout Plain Layout
19575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19578 \begin_layout Plain Layout
19586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19589 \begin_layout Plain Layout
19590 \begin_inset Formula $\alpha$
19600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19603 \begin_layout Plain Layout
19611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19614 \begin_layout Plain Layout
19615 \begin_inset Formula $\beta$
19625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19628 \begin_layout Plain Layout
19636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19639 \begin_layout Plain Layout
19640 \begin_inset Formula $\gamma$
19650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19653 \begin_layout Plain Layout
19661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19664 \begin_layout Plain Layout
19665 \begin_inset Formula $\delta$
19675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19678 \begin_layout Plain Layout
19686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19689 \begin_layout Plain Layout
19690 \begin_inset Formula $\epsilon$
19700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19703 \begin_layout Plain Layout
19711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19714 \begin_layout Plain Layout
19715 \begin_inset Formula $\varepsilon$
19725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19728 \begin_layout Plain Layout
19736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19739 \begin_layout Plain Layout
19740 \begin_inset Formula $\zeta$
19750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19753 \begin_layout Plain Layout
19761 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19764 \begin_layout Plain Layout
19765 \begin_inset Formula $\eta$
19775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19778 \begin_layout Plain Layout
19786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19789 \begin_layout Plain Layout
19790 \begin_inset Formula $\theta$
19800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19803 \begin_layout Plain Layout
19811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19814 \begin_layout Plain Layout
19815 \begin_inset Formula $\vartheta$
19829 \begin_inset space \hfill{}
19833 \begin_inset Tabular
19834 <lyxtabular version="3" rows="12" columns="2">
19835 <features tabularvalignment="middle">
19836 <column alignment="center" valignment="top" width="0pt">
19837 <column alignment="center" valignment="top" width="0pt">
19839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19842 \begin_layout Plain Layout
19848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19851 \begin_layout Plain Layout
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 $\iota$
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 $\kappa$
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 $\varkappa$
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 $\lambda$
19959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19962 \begin_layout Plain Layout
19970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19973 \begin_layout Plain Layout
19974 \begin_inset Formula $\mu$
19984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19987 \begin_layout Plain Layout
19995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19998 \begin_layout Plain Layout
19999 \begin_inset Formula $\nu$
20009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20012 \begin_layout Plain Layout
20020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20023 \begin_layout Plain Layout
20024 \begin_inset Formula $\xi$
20034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20037 \begin_layout Plain Layout
20043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20046 \begin_layout Plain Layout
20047 \begin_inset Formula $o$
20057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20060 \begin_layout Plain Layout
20068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20071 \begin_layout Plain Layout
20072 \begin_inset Formula $\pi$
20082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20085 \begin_layout Plain Layout
20093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20096 \begin_layout Plain Layout
20097 \begin_inset Formula $\varpi$
20107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20110 \begin_layout Plain Layout
20118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20121 \begin_layout Plain Layout
20122 \begin_inset Formula $\rho$
20136 \begin_inset space \hfill{}
20140 \begin_inset Tabular
20141 <lyxtabular version="3" rows="11" columns="2">
20142 <features tabularvalignment="middle">
20143 <column alignment="center" valignment="top" width="0pt">
20144 <column alignment="center" valignment="top" width="0pt">
20146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20149 \begin_layout Plain Layout
20155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20158 \begin_layout Plain Layout
20166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20169 \begin_layout Plain Layout
20177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20180 \begin_layout Plain Layout
20181 \begin_inset Formula $\varrho$
20191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20194 \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 $\sigma$
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 $\varsigma$
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 $\tau$
20266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20269 \begin_layout Plain Layout
20277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20280 \begin_layout Plain Layout
20281 \begin_inset Formula $\upsilon$
20291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20294 \begin_layout Plain Layout
20302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20305 \begin_layout Plain Layout
20306 \begin_inset Formula $\phi$
20316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20319 \begin_layout Plain Layout
20327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20330 \begin_layout Plain Layout
20331 \begin_inset Formula $\varphi$
20341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20344 \begin_layout Plain Layout
20352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20355 \begin_layout Plain Layout
20356 \begin_inset Formula $\chi$
20366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20369 \begin_layout Plain Layout
20377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20380 \begin_layout Plain Layout
20381 \begin_inset Formula $\psi$
20391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20394 \begin_layout Plain Layout
20402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20405 \begin_layout Plain Layout
20406 \begin_inset Formula $\omega$
20420 \begin_inset space \hfill{}
20426 \begin_layout Standard
20427 \begin_inset VSpace medskip
20433 \begin_layout Standard
20434 How to create upright Greek letters is explained in
20435 \begin_inset CommandInset ref
20437 reference "sub:Upright-small-Greek"
20444 \begin_layout Subsection
20446 \begin_inset Index idx
20449 \begin_layout Plain Layout
20450 Greek letters ! big
20458 \begin_layout Standard
20459 \begin_inset space \hfill{}
20463 \begin_inset Tabular
20464 <lyxtabular version="3" rows="7" columns="2">
20465 <features tabularvalignment="middle">
20466 <column alignment="center" valignment="top" width="0pt">
20467 <column alignment="center" valignment="top" width="0pt">
20469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20472 \begin_layout Plain Layout
20478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20481 \begin_layout Plain Layout
20489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20492 \begin_layout Plain Layout
20500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20503 \begin_layout Plain Layout
20504 \begin_inset Formula $\Gamma$
20514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20517 \begin_layout Plain Layout
20525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20528 \begin_layout Plain Layout
20529 \begin_inset Formula $\Delta$
20539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20542 \begin_layout Plain Layout
20550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20553 \begin_layout Plain Layout
20554 \begin_inset Formula $\Theta$
20564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20567 \begin_layout Plain Layout
20575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20578 \begin_layout Plain Layout
20579 \begin_inset Formula $\Lambda$
20589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20592 \begin_layout Plain Layout
20600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20603 \begin_layout Plain Layout
20604 \begin_inset Formula $\Xi$
20614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20617 \begin_layout Plain Layout
20625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20628 \begin_layout Plain Layout
20629 \begin_inset Formula $\Pi$
20643 \begin_inset space \hfill{}
20647 \begin_inset Tabular
20648 <lyxtabular version="3" rows="6" columns="2">
20649 <features tabularvalignment="middle">
20650 <column alignment="center" valignment="top" width="0pt">
20651 <column alignment="center" valignment="top" width="0pt">
20653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20656 \begin_layout Plain Layout
20662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20665 \begin_layout Plain Layout
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 $\Sigma$
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 $\Upsilon$
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 $\Phi$
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 $\Psi$
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 $\Omega$
20802 \begin_inset space \hfill{}
20808 \begin_layout Standard
20809 \begin_inset VSpace medskip
20812 That the big Greek letters appear upright is caused by a design bug when
20814 To get correct italic big letters, begin every command with
20819 For example the command
20826 \begin_inset Formula $\varGamma$
20832 \begin_layout Subsection
20834 \begin_inset Index idx
20837 \begin_layout Plain Layout
20838 Greek letters ! bold
20846 \begin_layout Standard
20847 Greek letters cannot be set with different font styles like Latin letters.
20848 They can only be made bold with the command
20855 \begin_inset Index idx
20858 \begin_layout Plain Layout
20869 \begin_layout Standard
20871 \begin_inset Tabular
20872 <lyxtabular version="3" rows="3" columns="2">
20873 <features tabularvalignment="middle">
20874 <column alignment="center" valignment="top" width="0">
20875 <column alignment="center" valignment="top" width="0">
20877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20880 \begin_layout Plain Layout
20886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20889 \begin_layout Plain Layout
20897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20900 \begin_layout Plain Layout
20912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20915 \begin_layout Plain Layout
20916 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20929 \begin_layout Plain Layout
20941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20944 \begin_layout Plain Layout
20945 \begin_inset Formula $\theta\boldsymbol{\theta}$
20961 \begin_layout Section
20966 \begin_layout Plain Layout
20979 \begin_layout Plain Layout
20980 A list with all symbols of most of the LaTeX-packages can be found in
20981 \begin_inset CommandInset citation
20996 \begin_layout Plain Layout
21004 \begin_inset Note Note
21007 \begin_layout Plain Layout
21010 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21013 \begin_layout Plain Layout
21016 texorpdfstring is in section
21017 \begin_inset CommandInset ref
21019 reference "sub:Formulas-in-Section"
21029 \begin_inset Index idx
21032 \begin_layout Plain Layout
21041 \begin_layout Standard
21042 Many of the symbols listed in this section can also be inserted via the
21044 \begin_inset Graphics
21045 filename ../images/math/nabla.png
21051 \begin_inset Graphics
21052 filename ../images/math/digamma.png
21060 \begin_layout Subsection
21061 Mathematical Symbols
21062 \begin_inset CommandInset label
21064 name "sub:Mathematical-Symbols"
21069 \begin_inset Index idx
21072 \begin_layout Plain Layout
21073 Symbols ! mathematical
21081 \begin_layout Standard
21082 \begin_inset space \hfill{}
21086 \begin_inset Tabular
21087 <lyxtabular version="3" rows="10" columns="2">
21088 <features tabularvalignment="middle">
21089 <column alignment="center" valignment="top" width="0pt">
21090 <column alignment="center" valignment="top" width="0pt">
21092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21095 \begin_layout Plain Layout
21101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21104 \begin_layout Plain Layout
21112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21115 \begin_layout Plain Layout
21123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21126 \begin_layout Plain Layout
21127 \begin_inset Formula $\neg$
21137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21140 \begin_layout Plain Layout
21148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21151 \begin_layout Plain Layout
21152 \begin_inset Formula $\Im$
21162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21165 \begin_layout Plain Layout
21173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21176 \begin_layout Plain Layout
21177 \begin_inset Formula $\Re$
21187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21190 \begin_layout Plain Layout
21198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21201 \begin_layout Plain Layout
21202 \begin_inset Formula $\aleph$
21212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21215 \begin_layout Plain Layout
21223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21226 \begin_layout Plain Layout
21227 \begin_inset Formula $\partial$
21237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21240 \begin_layout Plain Layout
21248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21251 \begin_layout Plain Layout
21252 \begin_inset Formula $\infty$
21262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21265 \begin_layout Plain Layout
21273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21276 \begin_layout Plain Layout
21277 \begin_inset Formula $\wp$
21287 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21290 \begin_layout Plain Layout
21298 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21301 \begin_layout Plain Layout
21302 \begin_inset Formula $\imath$
21312 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21315 \begin_layout Plain Layout
21323 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21326 \begin_layout Plain Layout
21327 \begin_inset Formula $\jmath$
21341 \begin_inset space \hfill{}
21345 \begin_inset Tabular
21346 <lyxtabular version="3" rows="10" columns="2">
21347 <features tabularvalignment="middle">
21348 <column alignment="center" valignment="top" width="0pt">
21349 <column alignment="center" valignment="top" width="0pt">
21351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21354 \begin_layout Plain Layout
21360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21363 \begin_layout Plain Layout
21365 \begin_inset Note Note
21368 \begin_layout Plain Layout
21375 is only used as spacer.
21387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21390 \begin_layout Plain Layout
21398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21401 \begin_layout Plain Layout
21402 \begin_inset Formula $\forall$
21412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21415 \begin_layout Plain Layout
21423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21426 \begin_layout Plain Layout
21427 \begin_inset Formula $\exists$
21437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21440 \begin_layout Plain Layout
21448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21451 \begin_layout Plain Layout
21452 \begin_inset Formula $\nexists$
21462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21465 \begin_layout Plain Layout
21473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21476 \begin_layout Plain Layout
21477 \begin_inset Formula $\emptyset$
21487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21490 \begin_layout Plain Layout
21498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21501 \begin_layout Plain Layout
21502 \begin_inset Formula $\varnothing$
21512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21515 \begin_layout Plain Layout
21523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21526 \begin_layout Plain Layout
21527 \begin_inset Formula $\dag$
21537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21540 \begin_layout Plain Layout
21548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21551 \begin_layout Plain Layout
21552 \begin_inset Formula $\ddag$
21562 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21565 \begin_layout Plain Layout
21573 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21576 \begin_layout Plain Layout
21580 \begin_layout Plain Layout
21590 \begin_inset Formula $\complement$
21597 \begin_layout Plain Layout
21611 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21614 \begin_layout Plain Layout
21622 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21625 \begin_layout Plain Layout
21626 \begin_inset Formula $\Bbbk$
21640 \begin_inset space \hfill{}
21644 \begin_inset Tabular
21645 <lyxtabular version="3" rows="10" columns="2">
21646 <features tabularvalignment="middle">
21647 <column alignment="center" valignment="top" width="0pt">
21648 <column alignment="center" valignment="top" width="0pt">
21650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21653 \begin_layout Plain Layout
21659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21662 \begin_layout Plain Layout
21670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21673 \begin_layout Plain Layout
21681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21684 \begin_layout Plain Layout
21685 \begin_inset Formula $\prime$
21695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21698 \begin_layout Plain Layout
21706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21709 \begin_layout Plain Layout
21710 \begin_inset Formula $\backprime$
21720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21723 \begin_layout Plain Layout
21731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21734 \begin_layout Plain Layout
21735 \begin_inset Formula $\mho$
21745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21748 \begin_layout Plain Layout
21756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21759 \begin_layout Plain Layout
21760 \begin_inset Formula $\triangle$
21770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21773 \begin_layout Plain Layout
21781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21784 \begin_layout Plain Layout
21785 \begin_inset Formula $\angle$
21795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21798 \begin_layout Plain Layout
21806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21809 \begin_layout Plain Layout
21810 \begin_inset Formula $\measuredangle$
21820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21823 \begin_layout Plain Layout
21831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21834 \begin_layout Plain Layout
21835 \begin_inset Formula $\sphericalangle$
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 $\top$
21870 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21873 \begin_layout Plain Layout
21881 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21884 \begin_layout Plain Layout
21885 \begin_inset Formula $\bot$
21899 \begin_inset space \hfill{}
21905 \begin_layout Subsection
21906 Miscellaneous Symbols
21907 \begin_inset CommandInset label
21909 name "sub:Miscellaneous-Symbols"
21914 \begin_inset Index idx
21917 \begin_layout Plain Layout
21918 Symbols ! miscellaneous
21926 \begin_layout Standard
21929 \begin_inset Tabular
21930 <lyxtabular version="3" rows="10" columns="2">
21931 <features tabularvalignment="middle">
21932 <column alignment="center" valignment="top" width="0pt">
21933 <column alignment="center" valignment="top" width="0pt">
21935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21938 \begin_layout Plain Layout
21944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21947 \begin_layout Plain Layout
21955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21958 \begin_layout Plain Layout
21966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21969 \begin_layout Plain Layout
21970 \begin_inset Formula $\flat$
21980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21983 \begin_layout Plain Layout
21991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21994 \begin_layout Plain Layout
21995 \begin_inset Formula $\natural$
22005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22008 \begin_layout Plain Layout
22016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22019 \begin_layout Plain Layout
22020 \begin_inset Formula $\sharp$
22030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22033 \begin_layout Plain Layout
22041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22044 \begin_layout Plain Layout
22045 \begin_inset Formula $\surd$
22055 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22058 \begin_layout Plain Layout
22066 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22069 \begin_layout Plain Layout
22070 \begin_inset Formula $\checkmark$
22080 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22083 \begin_layout Plain Layout
22091 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22094 \begin_layout Plain Layout
22095 \begin_inset Formula $\yen$
22105 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22108 \begin_layout Plain Layout
22116 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22119 \begin_layout Plain Layout
22120 \begin_inset Formula $\pounds$
22130 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22133 \begin_layout Plain Layout
22139 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22142 \begin_layout Plain Layout
22143 \begin_inset Formula $\$$
22153 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22156 \begin_layout Plain Layout
22162 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22165 \begin_layout Plain Layout
22166 \begin_inset Formula $§$
22180 \begin_inset Tabular
22181 <lyxtabular version="3" rows="10" columns="2">
22182 <features tabularvalignment="middle">
22183 <column alignment="center" valignment="top" width="0">
22184 <column alignment="center" valignment="top" width="0">
22186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22189 \begin_layout Plain Layout
22195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22198 \begin_layout Plain Layout
22206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22209 \begin_layout Plain Layout
22217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22220 \begin_layout Plain Layout
22221 \begin_inset Formula $\hbar$
22231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22234 \begin_layout Plain Layout
22242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22245 \begin_layout Plain Layout
22246 \begin_inset Formula $\hslash$
22256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22259 \begin_layout Plain Layout
22267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22270 \begin_layout Plain Layout
22271 \begin_inset Formula $\clubsuit$
22281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22284 \begin_layout Plain Layout
22292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22295 \begin_layout Plain Layout
22296 \begin_inset Formula $\spadesuit$
22306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22309 \begin_layout Plain Layout
22317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22320 \begin_layout Plain Layout
22321 \begin_inset Formula $\bigstar$
22331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22334 \begin_layout Plain Layout
22342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22345 \begin_layout Plain Layout
22346 \begin_inset Formula $\blacklozenge$
22356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22359 \begin_layout Plain Layout
22367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22370 \begin_layout Plain Layout
22371 \begin_inset Formula $\blacktriangle$
22381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22384 \begin_layout Plain Layout
22392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22395 \begin_layout Plain Layout
22396 \begin_inset Formula $\blacktriangledown$
22406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22409 \begin_layout Plain Layout
22417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22420 \begin_layout Plain Layout
22421 \begin_inset Formula $\bullet$
22435 \begin_inset Tabular
22436 <lyxtabular version="3" rows="10" columns="2">
22437 <features tabularvalignment="middle">
22438 <column alignment="center" valignment="top" width="0pt">
22439 <column alignment="center" valignment="top" width="0pt">
22441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22444 \begin_layout Plain Layout
22450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22453 \begin_layout Plain Layout
22461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22464 \begin_layout Plain Layout
22472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22475 \begin_layout Plain Layout
22476 \begin_inset Formula $\diamondsuit$
22486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22489 \begin_layout Plain Layout
22497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22500 \begin_layout Plain Layout
22501 \begin_inset Formula $\Diamond$
22511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22514 \begin_layout Plain Layout
22522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22525 \begin_layout Plain Layout
22526 \begin_inset Formula $\heartsuit$
22536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22539 \begin_layout Plain Layout
22547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22550 \begin_layout Plain Layout
22551 \begin_inset Formula $\P$
22561 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22564 \begin_layout Plain Layout
22572 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22575 \begin_layout Plain Layout
22576 \begin_inset Formula $\copyright$
22586 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22589 \begin_layout Plain Layout
22597 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22600 \begin_layout Plain Layout
22601 \begin_inset Formula $\circledR$
22611 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22614 \begin_layout Plain Layout
22622 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22625 \begin_layout Plain Layout
22626 \begin_inset Formula $\maltese$
22636 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22639 \begin_layout Plain Layout
22647 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22650 \begin_layout Plain Layout
22651 \begin_inset Formula $\diagup$
22661 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22664 \begin_layout Plain Layout
22672 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22675 \begin_layout Plain Layout
22676 \begin_inset Formula $\diagdown$
22692 \begin_layout Standard
22693 \begin_inset VSpace medskip
22696 More symbols are listed in
22697 \begin_inset CommandInset ref
22699 reference "sub:Miscellaneous-special-Characters"
22706 \begin_layout Standard
22707 Some symbols can be displayed in different sizes, see
22708 \begin_inset CommandInset ref
22710 reference "sub:Font-Sizes"
22717 \begin_layout Subsection
22719 \begin_inset Index idx
22722 \begin_layout Plain Layout
22723 Symbols ! Euro-symbol
22729 \begin_inset Index idx
22732 \begin_layout Plain Layout
22739 \begin_layout Plain Layout
22756 \begin_layout Standard
22757 To use the Euro symbol in formulas, the LaTeX-package
22762 \begin_inset Index idx
22765 \begin_layout Plain Layout
22771 must be installed and loaded with the LaTeX-preamble line
22774 \begin_layout Standard
22779 usepackage[gennarrow]{eurosym}
22782 \begin_layout Standard
22783 The Euro symbol can now be inserted with the command
22790 \begin_inset Index idx
22793 \begin_layout Plain Layout
22804 \begin_layout Standard
22805 The Euro symbol can directly be inserted with the € key in mathematical
22806 text, without having
22821 can also be inserted in TeX-mode.
22822 The official currency symbol can then be inserted with the command
22829 \begin_inset Index idx
22832 \begin_layout Plain Layout
22840 , that is only available in TeX-mode.
22843 \begin_layout Standard
22847 \begin_layout Plain Layout
22857 \begin_inset Note Note
22860 \begin_layout Plain Layout
22861 The following table will only be displayed when the LaTeX-package
22873 \begin_layout Standard
22874 An overview about the different Euro symbols:
22877 \begin_layout Standard
22879 \begin_inset Tabular
22880 <lyxtabular version="3" rows="4" columns="3">
22881 <features tabularvalignment="middle">
22882 <column alignment="center" valignment="top" width="0pt">
22883 <column alignment="center" valignment="top" width="0pt">
22884 <column alignment="center" valignment="top" width="0pt">
22886 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22889 \begin_layout Plain Layout
22895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22898 \begin_layout Plain Layout
22904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22907 \begin_layout Plain Layout
22915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22918 \begin_layout Plain Layout
22924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22927 \begin_layout Plain Layout
22935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22938 \begin_layout Plain Layout
22939 \begin_inset Formula $\euro$
22949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22952 \begin_layout Plain Layout
22958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22961 \begin_layout Plain Layout
22967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22970 \begin_layout Plain Layout
22971 \begin_inset Formula $\mbox{€}$
22981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22984 \begin_layout Plain Layout
22990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22993 \begin_layout Plain Layout
23001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23004 \begin_layout Plain Layout
23008 \begin_layout Plain Layout
23030 \begin_layout Standard
23034 \begin_layout Plain Layout
23044 \begin_inset Note Note
23047 \begin_layout Plain Layout
23048 The following will be displayed when the LaTeX-package
23060 \begin_layout Standard
23061 You need to install the LaTeX-package
23065 to see the rest of this subsection in the output.
23068 \begin_layout Standard
23072 \begin_layout Plain Layout
23084 \begin_layout Section
23086 \begin_inset CommandInset label
23088 name "sec:Relations"
23093 \begin_inset Index idx
23096 \begin_layout Plain Layout
23103 \begin_inset Index idx
23106 \begin_layout Plain Layout
23111 \begin_layout Plain Layout
23122 \begin_layout Plain Layout
23137 \begin_layout Standard
23138 All relations can also be inserted via the toolbar button
23139 \begin_inset Graphics
23140 filename ../images/math/leq.png
23148 \begin_layout Standard
23149 \begin_inset space \hfill{}
23153 \begin_inset Tabular
23154 <lyxtabular version="3" rows="17" columns="2">
23155 <features tabularvalignment="middle">
23156 <column alignment="center" valignment="top" width="0pt">
23157 <column alignment="center" valignment="top" width="0pt">
23159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23162 \begin_layout Plain Layout
23168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23171 \begin_layout Plain Layout
23179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23182 \begin_layout Plain Layout
23188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23191 \begin_layout Plain Layout
23192 \begin_inset Formula $<$
23202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23205 \begin_layout Plain Layout
23213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23216 \begin_layout Plain Layout
23217 \begin_inset Formula $\le$
23227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23230 \begin_layout Plain Layout
23238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23241 \begin_layout Plain Layout
23242 \begin_inset Formula $\ll$
23252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23255 \begin_layout Plain Layout
23263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23266 \begin_layout Plain Layout
23267 \begin_inset Formula $\prec$
23277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23280 \begin_layout Plain Layout
23288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23291 \begin_layout Plain Layout
23292 \begin_inset Formula $\preceq$
23302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23305 \begin_layout Plain Layout
23313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23316 \begin_layout Plain Layout
23317 \begin_inset Formula $\subset$
23327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23330 \begin_layout Plain Layout
23338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23341 \begin_layout Plain Layout
23342 \begin_inset Formula $\subseteq$
23352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23355 \begin_layout Plain Layout
23363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23366 \begin_layout Plain Layout
23367 \begin_inset Formula $\sqsubseteq$
23377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23380 \begin_layout Plain Layout
23388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23391 \begin_layout Plain Layout
23392 \begin_inset Formula $\in$
23402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23405 \begin_layout Plain Layout
23413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23416 \begin_layout Plain Layout
23417 \begin_inset Formula $\vdash$
23427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23430 \begin_layout Plain Layout
23438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23441 \begin_layout Plain Layout
23442 \begin_inset Formula $\smile$
23452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23455 \begin_layout Plain Layout
23463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23466 \begin_layout Plain Layout
23467 \begin_inset Formula $\lhd$
23477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23480 \begin_layout Plain Layout
23488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23491 \begin_layout Plain Layout
23492 \begin_inset Formula $\unlhd$
23502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23505 \begin_layout Plain Layout
23513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23516 \begin_layout Plain Layout
23517 \begin_inset Formula $\gtrless$
23527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23530 \begin_layout Plain Layout
23538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23541 \begin_layout Plain Layout
23542 \begin_inset Formula $\mid$
23552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23555 \begin_layout Plain Layout
23563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23566 \begin_layout Plain Layout
23567 \begin_inset Formula $\nmid$
23581 \begin_inset space \hfill{}
23585 \begin_inset Tabular
23586 <lyxtabular version="3" rows="17" columns="2">
23587 <features tabularvalignment="middle">
23588 <column alignment="center" valignment="top" width="0pt">
23589 <column alignment="center" valignment="top" width="0pt">
23591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23594 \begin_layout Plain Layout
23600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23603 \begin_layout Plain Layout
23611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23614 \begin_layout Plain Layout
23620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23623 \begin_layout Plain Layout
23624 \begin_inset Formula $=$
23634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23637 \begin_layout Plain Layout
23645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23648 \begin_layout Plain Layout
23649 \begin_inset Formula $\not=$
23659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23662 \begin_layout Plain Layout
23670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23673 \begin_layout Plain Layout
23674 \begin_inset Formula $\equiv$
23684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23687 \begin_layout Plain Layout
23695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23698 \begin_layout Plain Layout
23699 \begin_inset Formula $\sim$
23709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23712 \begin_layout Plain Layout
23720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23723 \begin_layout Plain Layout
23724 \begin_inset Formula $\simeq$
23734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23737 \begin_layout Plain Layout
23745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23748 \begin_layout Plain Layout
23749 \begin_inset Formula $\approx$
23759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23762 \begin_layout Plain Layout
23770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23773 \begin_layout Plain Layout
23774 \begin_inset Formula $\cong$
23784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23787 \begin_layout Plain Layout
23795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23798 \begin_layout Plain Layout
23799 \begin_inset Formula $\bowtie$
23809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23812 \begin_layout Plain Layout
23820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23823 \begin_layout Plain Layout
23824 \begin_inset Formula $\notin$
23834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23837 \begin_layout Plain Layout
23845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23848 \begin_layout Plain Layout
23849 \begin_inset Formula $\perp$
23859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23862 \begin_layout Plain Layout
23870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23873 \begin_layout Plain Layout
23874 \begin_inset Formula $\propto$
23884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23887 \begin_layout Plain Layout
23895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23898 \begin_layout Plain Layout
23899 \begin_inset Formula $\asymp$
23909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23912 \begin_layout Plain Layout
23920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23923 \begin_layout Plain Layout
23924 \begin_inset Formula $\doteq$
23934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23937 \begin_layout Plain Layout
23945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23948 \begin_layout Plain Layout
23949 \begin_inset Formula $\circeq$
23959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23962 \begin_layout Plain Layout
23970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23973 \begin_layout Plain Layout
23974 \begin_inset Formula $\models$
23984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23987 \begin_layout Plain Layout
23995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23998 \begin_layout Plain Layout
23999 \begin_inset Formula $\widehat{=}$
24013 \begin_inset space \hfill{}
24017 \begin_inset Tabular
24018 <lyxtabular version="3" rows="17" columns="2">
24019 <features tabularvalignment="middle">
24020 <column alignment="center" valignment="top" width="0pt">
24021 <column alignment="center" valignment="top" width="0pt">
24023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24026 \begin_layout Plain Layout
24032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24035 \begin_layout Plain Layout
24043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24046 \begin_layout Plain Layout
24052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24055 \begin_layout Plain Layout
24056 \begin_inset Formula $>$
24066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24069 \begin_layout Plain Layout
24077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24080 \begin_layout Plain Layout
24081 \begin_inset Formula $\ge$
24091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24094 \begin_layout Plain Layout
24102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24105 \begin_layout Plain Layout
24106 \begin_inset Formula $\gg$
24116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24119 \begin_layout Plain Layout
24127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24130 \begin_layout Plain Layout
24131 \begin_inset Formula $\succ$
24141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24144 \begin_layout Plain Layout
24152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24155 \begin_layout Plain Layout
24156 \begin_inset Formula $\succeq$
24166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24169 \begin_layout Plain Layout
24177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24180 \begin_layout Plain Layout
24181 \begin_inset Formula $\supset$
24191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24194 \begin_layout Plain Layout
24202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24205 \begin_layout Plain Layout
24206 \begin_inset Formula $\supseteq$
24216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24219 \begin_layout Plain Layout
24227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24230 \begin_layout Plain Layout
24231 \begin_inset Formula $\sqsupseteq$
24241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24244 \begin_layout Plain Layout
24252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24255 \begin_layout Plain Layout
24256 \begin_inset Formula $\ni$
24266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24269 \begin_layout Plain Layout
24277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24280 \begin_layout Plain Layout
24281 \begin_inset Formula $\dashv$
24291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24294 \begin_layout Plain Layout
24302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24305 \begin_layout Plain Layout
24306 \begin_inset Formula $\frown$
24316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24319 \begin_layout Plain Layout
24327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24330 \begin_layout Plain Layout
24331 \begin_inset Formula $\rhd$
24341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24344 \begin_layout Plain Layout
24352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24355 \begin_layout Plain Layout
24356 \begin_inset Formula $\unrhd$
24366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24369 \begin_layout Plain Layout
24377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24380 \begin_layout Plain Layout
24381 \begin_inset Formula $\lessgtr$
24391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24394 \begin_layout Plain Layout
24402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24405 \begin_layout Plain Layout
24406 \begin_inset Formula $\parallel$
24416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24419 \begin_layout Plain Layout
24427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24430 \begin_layout Plain Layout
24431 \begin_inset Formula $\nparallel$
24445 \begin_inset space \hfill{}
24451 \begin_layout Standard
24452 \begin_inset VSpace medskip
24467 are bigger than the equal looking operators
24482 \begin_layout Standard
24483 Relations are, in contrary to symbols, always surrounded by space.
24486 \begin_layout Standard
24487 Relations with labels can be created with the command
24494 \begin_inset Index idx
24497 \begin_layout Plain Layout
24508 \begin_layout Standard
24510 \begin_inset Tabular
24511 <lyxtabular version="3" rows="2" columns="2">
24512 <features tabularvalignment="middle">
24513 <column alignment="center" valignment="top" width="0">
24514 <column alignment="center" valignment="top" width="0">
24516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24519 \begin_layout Plain Layout
24525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24528 \begin_layout Plain Layout
24530 \begin_inset Note Note
24533 \begin_layout Plain Layout
24540 is only used as spacer.
24552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24555 \begin_layout Plain Layout
24562 \begin_layout Plain Layout
24579 \begin_layout Plain Layout
24589 \begin_inset Formula $\downarrow$
24598 \begin_layout Plain Layout
24611 \begin_layout Plain Layout
24625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24628 \begin_layout Plain Layout
24629 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24645 \begin_layout Section
24649 \begin_layout Subsection
24650 Predefined Functions
24651 \begin_inset CommandInset label
24653 name "sub:Predefined-Functions"
24658 \begin_inset Index idx
24661 \begin_layout Plain Layout
24662 Functions ! predefined
24670 \begin_layout Standard
24671 In general, variables are set
24675 in mathematical expressions, but not function names, because
24676 \begin_inset Formula $sin$
24679 could be misunderstood as
24680 \begin_inset Formula $s\cdot i\cdot n$
24684 Therefore there are predefined functions, that are additionally a bit separated
24686 They are inserted as commands starting with a backslash before their name.
24689 \begin_layout Standard
24691 \begin_inset Tabular
24692 <lyxtabular version="3" rows="2" columns="4">
24693 <features tabularvalignment="middle">
24694 <column alignment="center" valignment="top" width="0pt">
24695 <column alignment="center" valignment="top" width="0pt">
24696 <column alignment="center" valignment="top" width="0pt">
24697 <column alignment="center" valignment="top" width="0pt">
24699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24702 \begin_layout Plain Layout
24708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24711 \begin_layout Plain Layout
24717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24720 \begin_layout Plain Layout
24726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24729 \begin_layout Plain Layout
24737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24740 \begin_layout Plain Layout
24746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24749 \begin_layout Plain Layout
24750 \begin_inset Formula $Asin(x)+B$
24758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24761 \begin_layout Plain Layout
24769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24772 \begin_layout Plain Layout
24773 \begin_inset Formula $A\sin(x)+B$
24789 \begin_layout Standard
24790 The following functions are predefined:
24793 \begin_layout Standard
24794 \begin_inset VSpace -2mm
24800 \begin_layout Standard
24802 \begin_inset Tabular
24803 <lyxtabular version="3" rows="9" columns="4">
24804 <features tabularvalignment="middle">
24805 <column alignment="center" valignment="top" width="0pt">
24806 <column alignment="center" valignment="top" width="0pt">
24807 <column alignment="center" valignment="top" width="0pt">
24808 <column alignment="center" valignment="top" width="0pt">
24810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24813 \begin_layout Plain Layout
24819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24822 \begin_layout Plain Layout
24828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24831 \begin_layout Plain Layout
24837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24840 \begin_layout Plain Layout
24848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24851 \begin_layout Plain Layout
24859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24862 \begin_layout Plain Layout
24870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24873 \begin_layout Plain Layout
24881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24884 \begin_layout Plain Layout
24894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24897 \begin_layout Plain Layout
24905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24908 \begin_layout Plain Layout
24916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24919 \begin_layout Plain Layout
24927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24930 \begin_layout Plain Layout
24940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24943 \begin_layout Plain Layout
24951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24954 \begin_layout Plain Layout
24962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24965 \begin_layout Plain Layout
24973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24976 \begin_layout Plain Layout
24986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24989 \begin_layout Plain Layout
24997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25000 \begin_layout Plain Layout
25008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25011 \begin_layout Plain Layout
25019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25022 \begin_layout Plain Layout
25032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25035 \begin_layout Plain Layout
25043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25046 \begin_layout Plain Layout
25054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25057 \begin_layout Plain Layout
25065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25068 \begin_layout Plain Layout
25078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25081 \begin_layout Plain Layout
25089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25092 \begin_layout Plain Layout
25100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25103 \begin_layout Plain Layout
25111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25114 \begin_layout Plain Layout
25124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25127 \begin_layout Plain Layout
25135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25138 \begin_layout Plain Layout
25146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25149 \begin_layout Plain Layout
25157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25160 \begin_layout Plain Layout
25170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25173 \begin_layout Plain Layout
25181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25184 \begin_layout Plain Layout
25192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25195 \begin_layout Plain Layout
25203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25206 \begin_layout Plain Layout
25222 \begin_layout Standard
25223 They can also be inserted with the math toolbar button
25224 \begin_inset Graphics
25225 filename ../images/math/functions.png
25233 \begin_layout Subsection
25234 Self-defined Functions
25235 \begin_inset Index idx
25238 \begin_layout Plain Layout
25239 Functions ! self-defined
25247 \begin_layout Standard
25248 To use a function that is not predefined, like for example the sign function
25249 sgn(x), there are two possibilities:
25252 \begin_layout Itemize
25253 Define the function by inserting the following line to the LaTeX-preamble
25257 \begin_layout Plain Layout
25262 DeclareMathOperator
25265 \begin_inset CommandInset ref
25267 reference "sub:Self-defined-Operators"
25277 \begin_inset Newline newline
25281 \begin_inset VSpace -3mm
25285 \begin_inset Newline newline
25292 DeclareMathOperator{
25297 \begin_inset Index idx
25300 \begin_layout Plain Layout
25305 DeclareMathOperator
25311 \begin_inset Newline newline
25315 \begin_inset VSpace -2mm
25319 \begin_inset Newline newline
25322 Now the new defined function can be called with the command
25331 \begin_layout Itemize
25332 Write the formula as usual, mark the formula name, in our example the letters
25337 , and change it to mathematical text.
25338 At last a space is inserted between prefactor and function.
25341 \begin_layout Standard
25342 The result is the same with both methods as with a predefined function
25346 \begin_layout Plain Layout
25347 In LyX self-defined functions are displayed red, predefined ones black.
25355 \begin_layout Standard
25357 \begin_inset Tabular
25358 <lyxtabular version="3" rows="3" columns="2">
25359 <features tabularvalignment="middle">
25360 <column alignment="center" valignment="top" width="0pt">
25361 <column alignment="center" valignment="top" width="0pt">
25363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25366 \begin_layout Plain Layout
25372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25375 \begin_layout Plain Layout
25383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25386 \begin_layout Plain Layout
25394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25397 \begin_layout Plain Layout
25398 \begin_inset Formula $A\sgn(x)+B$
25408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25411 \begin_layout Plain Layout
25415 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25426 \begin_layout Plain Layout
25427 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25443 \begin_layout Standard
25444 The first method is more suitable when the self-defined function should
25445 be used several times.
25448 \begin_layout Subsection
25450 \begin_inset Index idx
25453 \begin_layout Plain Layout
25462 \begin_layout Standard
25463 For limits there are defined besides
25470 \begin_inset Index idx
25473 \begin_layout Plain Layout
25493 furthermore the following functions:
25496 \begin_layout Standard
25498 \begin_inset Tabular
25499 <lyxtabular version="3" rows="5" columns="2">
25500 <features tabularvalignment="middle">
25501 <column alignment="center" valignment="top" width="0">
25502 <column alignment="center" valignment="top" width="0">
25504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25507 \begin_layout Plain Layout
25513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25516 \begin_layout Plain Layout
25518 \begin_inset Note Note
25521 \begin_layout Plain Layout
25528 is only used as spacer.
25540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25543 \begin_layout Plain Layout
25551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25554 \begin_layout Plain Layout
25555 \begin_inset Formula $\varliminf$
25565 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25568 \begin_layout Plain Layout
25576 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25579 \begin_layout Plain Layout
25580 \begin_inset Formula $\varlimsup$
25590 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25593 \begin_layout Plain Layout
25601 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25604 \begin_layout Plain Layout
25605 \begin_inset Formula $\varprojlim$
25615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25618 \begin_layout Plain Layout
25626 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25629 \begin_layout Plain Layout
25630 \begin_inset Formula $\varinjlim$
25634 \begin_inset Formula $\raisebox{-2.5mm}{}$
25650 \begin_layout Standard
25651 \begin_inset VSpace medskip
25654 The limit is created by inserting a subscript.
25655 It is set right beside the function in an inline formula:
25658 \begin_layout Standard
25660 \begin_inset Tabular
25661 <lyxtabular version="3" rows="2" columns="2">
25662 <features tabularvalignment="middle">
25663 <column alignment="center" valignment="top" width="0pt">
25664 <column alignment="center" valignment="top" width="0pt">
25666 <cell alignment="center" valignment="top" usebox="none">
25669 \begin_layout Plain Layout
25675 <cell alignment="center" valignment="top" usebox="none">
25678 \begin_layout Plain Layout
25679 \begin_inset space \hspace{}
25684 \begin_inset Note Note
25687 \begin_layout Plain Layout
25694 are used here as spacer.
25706 <cell alignment="center" valignment="top" usebox="none">
25709 \begin_layout Plain Layout
25718 \begin_layout Plain Layout
25731 \begin_layout Plain Layout
25745 <cell alignment="center" valignment="top" usebox="none">
25748 \begin_layout Plain Layout
25749 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25765 \begin_layout Standard
25766 In a displayed formula the limit is set below the formula, as usual:
25767 \begin_inset Formula \[
25775 \begin_layout Subsection
25777 \begin_inset Index idx
25780 \begin_layout Plain Layout
25781 Functions ! modulo-
25789 \begin_layout Standard
25790 The modulo-function is special, because it exists in four variants.
25793 \begin_layout Standard
25794 The variants in a displayed formula:
25795 \begin_inset Formula \begin{align*}
25796 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25797 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25798 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25799 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25800 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
25808 \begin_layout Standard
25809 In an inline formula less space is set before the function names for all
25813 \begin_layout Section
25815 \begin_inset Index idx
25818 \begin_layout Plain Layout
25827 \begin_layout Subsection
25828 Special Characters in Mathematical Text
25831 \begin_layout Standard
25832 The following commands can only be used in mathematical text or in TeX-mode:
25835 \begin_layout Standard
25836 \begin_inset space \hfill{}
25840 \begin_inset Tabular
25841 <lyxtabular version="3" rows="8" columns="2">
25842 <features tabularvalignment="middle">
25843 <column alignment="block" valignment="top" width="0">
25844 <column alignment="block" valignment="top" width="0">
25846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25849 \begin_layout Plain Layout
25855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25858 \begin_layout Plain Layout
25866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25869 \begin_layout Plain Layout
25877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25880 \begin_layout Plain Layout
25881 \begin_inset Formula $\textrm{œ}$
25891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25894 \begin_layout Plain Layout
25902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25905 \begin_layout Plain Layout
25906 \begin_inset Formula $\textrm{Œ}$
25916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25919 \begin_layout Plain Layout
25927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25930 \begin_layout Plain Layout
25931 \begin_inset Formula $\textrm{æ}$
25941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25944 \begin_layout Plain Layout
25952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25955 \begin_layout Plain Layout
25956 \begin_inset Formula $\textrm{Æ}$
25966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25969 \begin_layout Plain Layout
25977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25980 \begin_layout Plain Layout
25981 \begin_inset Formula $\textrm{\aa}$
25991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25994 \begin_layout Plain Layout
25998 \begin_inset Index idx
26001 \begin_layout Plain Layout
26008 \begin_layout Plain Layout
26029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26032 \begin_layout Plain Layout
26033 \begin_inset Formula $\textrm{Å}$
26043 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26046 \begin_layout Plain Layout
26054 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26057 \begin_layout Plain Layout
26058 \begin_inset Formula $\textrm{ı}$
26072 \begin_inset space \hfill{}
26076 \begin_inset Tabular
26077 <lyxtabular version="3" rows="8" columns="2">
26078 <features tabularvalignment="middle">
26079 <column alignment="block" valignment="top" width="0">
26080 <column alignment="center" valignment="top" width="0">
26082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26085 \begin_layout Plain Layout
26087 \begin_inset Note Note
26090 \begin_layout Plain Layout
26092 \begin_inset space \thinspace{}
26095 mm is used for separation, because otherwise the output will be ¡ and ¿
26106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26109 \begin_layout Plain Layout
26117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26120 \begin_layout Plain Layout
26128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26131 \begin_layout Plain Layout
26132 \begin_inset Formula $\textrm{ø}$
26142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26145 \begin_layout Plain Layout
26153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26156 \begin_layout Plain Layout
26157 \begin_inset Formula $\textrm{Ø}$
26167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26170 \begin_layout Plain Layout
26178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26181 \begin_layout Plain Layout
26182 \begin_inset Formula $\textrm{ł}$
26192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26195 \begin_layout Plain Layout
26203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26206 \begin_layout Plain Layout
26207 \begin_inset Formula $\textrm{Ł}$
26217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26220 \begin_layout Plain Layout
26222 \begin_inset space \hspace{}
26230 \begin_layout Plain Layout
26244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26247 \begin_layout Plain Layout
26248 \begin_inset Formula $\textrm{!`}$
26258 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26261 \begin_layout Plain Layout
26263 \begin_inset space \hspace{}
26271 \begin_layout Plain Layout
26285 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26288 \begin_layout Plain Layout
26289 \begin_inset Formula $\textrm{?`}$
26299 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26302 \begin_layout Plain Layout
26310 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26313 \begin_layout Plain Layout
26314 \begin_inset Formula $\textrm{ȷ}$
26328 \begin_inset space \hfill{}
26334 \begin_layout Standard
26336 \begin_inset Formula $\textrm{\textrm{Å}}$
26340 \begin_inset Formula $\textrm{\textrm{Ø}}$
26343 can also be inserted via the math toolbar button
26344 \begin_inset Graphics
26345 filename ../images/math/digamma.png
26353 \begin_layout Standard
26354 An exception are the commands
26357 \begin_inset space \hspace{}
26366 \begin_inset space \hspace{}
26372 , because they can be inserted in LyX directly to text.
26375 \begin_layout Subsection
26377 \begin_inset CommandInset label
26379 name "sub:Accents-in-Text"
26384 \begin_inset Index idx
26387 \begin_layout Plain Layout
26396 \begin_layout Standard
26397 With the following commands all letters can be accented.
26398 The commands must be inserted in TeX-mode.
26401 \begin_layout Standard
26402 \begin_inset space \hfill{}
26406 \begin_inset Tabular
26407 <lyxtabular version="3" rows="8" columns="2">
26408 <features tabularvalignment="middle">
26409 <column alignment="block" valignment="top" width="0">
26410 <column alignment="block" valignment="top" width="0">
26412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26415 \begin_layout Plain Layout
26421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26424 \begin_layout Plain Layout
26432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26435 \begin_layout Plain Layout
26439 \begin_inset Quotes grd
26447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26450 \begin_layout Plain Layout
26454 \begin_layout Plain Layout
26470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26473 \begin_layout Plain Layout
26481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26484 \begin_layout Plain Layout
26488 \begin_layout Plain Layout
26504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26507 \begin_layout Plain Layout
26514 \begin_layout Plain Layout
26528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26531 \begin_layout Plain Layout
26535 \begin_layout Plain Layout
26551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26554 \begin_layout Plain Layout
26562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26565 \begin_layout Plain Layout
26569 \begin_layout Plain Layout
26585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26588 \begin_layout Plain Layout
26595 \begin_layout Plain Layout
26609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26612 \begin_layout Plain Layout
26616 \begin_layout Plain Layout
26632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26635 \begin_layout Plain Layout
26642 \begin_layout Plain Layout
26656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26659 \begin_layout Plain Layout
26663 \begin_layout Plain Layout
26679 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26682 \begin_layout Plain Layout
26689 \begin_layout Plain Layout
26703 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26706 \begin_layout Plain Layout
26710 \begin_layout Plain Layout
26730 \begin_inset space \hfill{}
26734 \begin_inset Tabular
26735 <lyxtabular version="3" rows="8" columns="2">
26736 <features tabularvalignment="middle">
26737 <column alignment="block" valignment="top" width="0">
26738 <column alignment="center" valignment="top" width="0">
26740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26743 \begin_layout Plain Layout
26749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26752 \begin_layout Plain Layout
26760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26763 \begin_layout Plain Layout
26770 \begin_layout Plain Layout
26784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26787 \begin_layout Plain Layout
26791 \begin_layout Plain Layout
26807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26810 \begin_layout Plain Layout
26818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26821 \begin_layout Plain Layout
26825 \begin_layout Plain Layout
26841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26844 \begin_layout Plain Layout
26848 \begin_inset Index idx
26851 \begin_layout Plain Layout
26862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26865 \begin_layout Plain Layout
26869 \begin_layout Plain Layout
26885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26888 \begin_layout Plain Layout
26896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26899 \begin_layout Plain Layout
26903 \begin_layout Plain Layout
26919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26922 \begin_layout Plain Layout
26929 \begin_layout Plain Layout
26943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26946 \begin_layout Plain Layout
26950 \begin_layout Plain Layout
26966 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26969 \begin_layout Plain Layout
26976 \begin_layout Plain Layout
26990 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26993 \begin_layout Plain Layout
26997 \begin_layout Plain Layout
27013 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27016 \begin_layout Plain Layout
27023 \begin_layout Plain Layout
27037 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27040 \begin_layout Plain Layout
27044 \begin_layout Plain Layout
27064 \begin_inset space \hfill{}
27070 \begin_layout Standard
27071 \begin_inset VSpace medskip
27080 also two different characters can be accented.
27089 \begin_layout Plain Layout
27104 \begin_layout Plain Layout
27116 \begin_layout Standard
27129 can in combination with vowels directly be inserted with the keyboard without
27131 The same applies for the tilde
27135 \begin_layout Plain Layout
27136 This only applies for keyboards where the tilde is defined as accent.
27145 in combination with
27160 \begin_layout Standard
27203 and accents that are inserted directly with the keyboard are also available
27204 in mathematical text.
27205 For the other accents there are special math commands to be used in formulas,
27207 \begin_inset CommandInset ref
27209 reference "sub:Accents-for-one"
27216 \begin_layout Standard
27217 \begin_inset VSpace bigskip
27220 Furthermore, with the command
27227 \begin_inset Index idx
27230 \begin_layout Plain Layout
27238 all numbers and letters can be set into a circle, quasi accented with a
27239 circle, similar to the copyright symbol.
27242 \begin_layout Standard
27244 \begin_inset Tabular
27245 <lyxtabular version="3" rows="3" columns="2">
27246 <features tabularvalignment="middle">
27247 <column alignment="center" valignment="top" width="0">
27248 <column alignment="center" valignment="top" width="0">
27250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27253 \begin_layout Plain Layout
27259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27262 \begin_layout Plain Layout
27264 \begin_inset Note Note
27267 \begin_layout Plain Layout
27274 is only used as spacer.
27286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27289 \begin_layout Plain Layout
27297 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27300 \begin_layout Plain Layout
27304 \begin_layout Plain Layout
27320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27323 \begin_layout Plain Layout
27334 raisebox{-1.5pt}{W}}
27339 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27342 \begin_layout Plain Layout
27343 \begin_inset Formula $\raisebox{4.5mm}{}$
27350 \begin_layout Plain Layout
27368 \begin_inset Formula $\raisebox{-2mm}{}$
27384 \begin_layout Standard
27385 One has to take care that the character fits in the circle.
27396 \begin_layout Plain Layout
27398 \begin_inset CommandInset ref
27400 reference "sub:Font-Sizes"
27409 specifies thereby the size of the circle.
27420 \begin_layout Plain Layout
27422 \begin_inset CommandInset ref
27424 reference "sub:Boxes-without-Frame"
27433 the character can be centered.
27436 \begin_layout Subsection
27438 \begin_inset Index idx
27441 \begin_layout Plain Layout
27450 \begin_layout Standard
27451 Minuscule numbers are created with the command
27458 \begin_inset Index idx
27461 \begin_layout Plain Layout
27470 The command can be used in formulas and in TeX-mode.
27471 The command scheme is:
27474 \begin_layout Standard
27479 oldstylenums{number}
27482 \begin_layout Standard
27487 oldstylenums{0123456789
27490 \begin_inset Formula $\oldstylenums{0123456789}$
27496 \begin_layout Subsection
27497 Miscellaneous special Characters
27498 \begin_inset CommandInset label
27500 name "sub:Miscellaneous-special-Characters"
27505 \begin_inset Index idx
27508 \begin_layout Plain Layout
27509 Special characters ! miscellaneous
27517 \begin_layout Standard
27518 The following characters can only be inserted to formulas by using commands:
27521 \begin_layout Standard
27523 \begin_inset Tabular
27524 <lyxtabular version="3" rows="4" columns="2">
27525 <features tabularvalignment="middle">
27526 <column alignment="center" valignment="top" width="0">
27527 <column alignment="center" valignment="top" width="0">
27529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27532 \begin_layout Plain Layout
27538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27541 \begin_layout Plain Layout
27549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27552 \begin_layout Plain Layout
27559 \begin_layout Plain Layout
27573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27576 \begin_layout Plain Layout
27577 \begin_inset Formula $\mathcircumflex$
27587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27590 \begin_layout Plain Layout
27598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27601 \begin_layout Plain Layout
27602 \begin_inset Formula $\_$
27612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27615 \begin_layout Plain Layout
27620 \begin_layout Plain Layout
27632 \begin_inset Index idx
27635 \begin_layout Plain Layout
27648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27651 \begin_layout Plain Layout
27652 \begin_inset Formula $^{\circ}$
27668 \begin_layout Standard
27669 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27670 contains the following line
27674 \begin_layout Plain Layout
27675 More about this is described in
27676 \begin_inset CommandInset ref
27678 reference "sub:Text-Characters-in"
27690 \begin_layout Standard
27695 DeclareInputtext{176}{
27708 \begin_layout Section
27710 \begin_inset CommandInset label
27712 name "sec:Formula-Styles"
27717 \begin_inset Index idx
27720 \begin_layout Plain Layout
27729 \begin_layout Itemize
27730 There are two different alignment styles:
27734 \begin_layout Description
27735 Centered is the predefined standard
27738 \begin_layout Description
27739 Indented for this the option
27743 must be inserted in the menu
27745 Document\SpecialChar \menuseparator
27751 \begin_inset space ~
27757 \begin_layout Standard
27762 is used, the indentation can be adjusted with the length
27769 \begin_inset Index idx
27772 \begin_layout Plain Layout
27781 Should the distance be 15
27782 \begin_inset space \thinspace{}
27785 mm, the following command line is inserted in the LaTeX-preamble
27788 \begin_layout Standard
27798 \begin_layout Standard
27799 When no length is specified, the predefined value of 30
27800 \begin_inset space \thinspace{}
27807 \begin_layout Itemize
27808 And two different numbering styles:
27812 \begin_layout Description
27813 Right is the predefined standard
27816 \begin_layout Description
27817 Left for this the option
27821 must be inserted in the menu
27823 Document\SpecialChar \menuseparator
27829 \begin_inset space ~
27836 \begin_layout Standard
27845 can also be used together.
27846 In this case both options are inserted, separated by a comma.
27849 \begin_layout Standard
27850 The chosen styles are used for all displayed formulas of the document.
27851 When both, centered and indented formulas should be created in a document,
27857 The indented formulas are then set in a flalign environment, see
27858 \begin_inset CommandInset ref
27860 reference "sub:Flalign-Environment"
27867 \begin_layout Section
27869 \begin_inset CommandInset label
27871 name "sec:Multiline-Formulas"
27876 \begin_inset Index idx
27879 \begin_layout Plain Layout
27880 Formula ! multiline
27888 \begin_layout Subsection
27892 \begin_layout Standard
27893 In LyX multiline formulas are created by pressing
27898 arg "newline-insert newline"
27904 This creates either an
27906 eqnarray environment
27908 that is described in
27909 \begin_inset CommandInset ref
27911 reference "sub:Eqnarray-Environment"
27915 or, when the option
27917 Use AMS math package
27919 in the document settings is selected, an
27923 that is described in
27924 \begin_inset CommandInset ref
27926 reference "sub:Standard-align-Environment"
27933 \begin_layout Standard
27934 There are other multiline formula environments that can be created via the
27937 Insert\SpecialChar \menuseparator
27941 These environments are described in the following sections.
27944 \begin_layout Standard
27945 In all multiline formula environments a new line is created by pressing
27949 arg "newline-insert newline"
27953 To add or delete lines, the math toolbar buttons
27954 \begin_inset Graphics
27955 filename ../images/tabular-feature_append-row.png
27961 \begin_inset Graphics
27962 filename ../images/tabular-feature_delete-row.png
27967 , respectively, or the menu
27969 Edit\SpecialChar \menuseparator
27975 \begin_layout Subsubsection
27977 \begin_inset CommandInset label
27979 name "sub:Line-Separation"
27984 \begin_inset Index idx
27987 \begin_layout Plain Layout
27988 Formula ! multiline ! Line separation
27996 \begin_layout Standard
27997 There is sometimes not enough space in multiline formulas between the lines:
27998 \begin_inset Formula \begin{eqnarray*}
27999 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}\\
28000 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
28008 \begin_layout Standard
28009 In LaTeX additional line space is specified as optional argument of the
28011 This is not yet possible in LyX
28015 \begin_layout Plain Layout
28017 \begin_inset CommandInset href
28019 name "LyX-bug #1505"
28020 target "http://www.lyx.org/trac/ticket/1505"
28029 , therefore the whole formula must be inserted in TeX-mode.
28030 To add in our example space, the command
28038 is inserted at the end of the first line.
28043 \begin_layout Plain Layout
28050 \begin_layout Plain Layout
28052 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28055 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28062 \begin_layout Plain Layout
28066 left(B^{2}+x_{0}^{2}
28074 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28079 \begin_layout Plain Layout
28091 \begin_layout Standard
28092 \begin_inset VSpace bigskip
28095 To set the line separation for all lines in a formula, the length
28102 \begin_inset Index idx
28105 \begin_layout Plain Layout
28115 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28126 \begin_inset space \thinspace{}
28131 \begin_inset space \thinspace{}
28134 mm additional line separation as in the previous example, the command
28137 \begin_layout Standard
28147 \begin_layout Standard
28148 is inserted in TeX-mode before the formula.
28149 This requires that the LaTeX-package
28157 \begin_layout Plain Layout
28162 is part of every LaTeX standard installation.
28168 \begin_inset Index idx
28171 \begin_layout Plain Layout
28177 was loaded in LaTeX-preamble with the line
28180 \begin_layout Standard
28188 \begin_layout Standard
28193 \begin_layout Plain Layout
28205 \begin_inset Formula \begin{eqnarray*}
28206 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}\\
28207 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
28215 \begin_layout Standard
28219 \begin_layout Plain Layout
28230 To get back to the predefined distance,
28236 is set to the value 3
28237 \begin_inset space \thinspace{}
28243 \begin_layout Subsubsection
28245 \begin_inset CommandInset label
28247 name "sub:Column-Separation"
28252 \begin_inset Index idx
28255 \begin_layout Plain Layout
28256 Formula ! multiline ! Column separation
28264 \begin_layout Standard
28265 Multiline formulas form a matrix.
28266 A formula in the eqnarray environment is for example a matrix with three
28268 By changing the column separation in this environment, the space beside
28269 the relation sign can be changed.
28272 \begin_layout Standard
28273 The column separation is specified with the length
28280 \begin_inset Index idx
28283 \begin_layout Plain Layout
28292 \begin_inset Newline newline
28295 column separation = 2
28296 \begin_inset space \thinspace{}
28306 \begin_inset Newline newline
28312 \begin_layout Standard
28322 \begin_layout Standard
28323 inserted in TeX-mode, sets for all following formulas a column separation
28325 \begin_inset space \thinspace{}
28329 To get back to the predefined distance,
28336 \begin_inset space \thinspace{}
28342 \begin_layout Standard
28344 \begin_inset space \thinspace{}
28347 cm column separation:
28351 \begin_layout Plain Layout
28363 \begin_inset Formula \begin{eqnarray*}
28370 A formula with the predefined column separation for matrices of 10
28371 \begin_inset space \thinspace{}
28378 \begin_layout Plain Layout
28390 \begin_inset Formula \begin{eqnarray*}
28400 \begin_layout Subsubsection
28402 \begin_inset Index idx
28405 \begin_layout Plain Layout
28414 \begin_layout Standard
28415 Long formulas can be typeset using these methods:
28418 \begin_layout Itemize
28419 When one side of the equation is much shorther than the line width, this
28420 one is chosen for the left side and the right side is typeset over two
28422 \begin_inset Formula \begin{eqnarray}
28423 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 \\
28424 & & -\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}
28429 The minus sign at the beginning of the second line does normally not appear
28430 as operator because it is the first character of the line.
28431 Thus it would not be surrounded by space and could not be distinguished
28432 from the fraction bar.
28434 \begin_inset space \thinspace{}
28437 pt space was inserted behind the minus sign with the command
28447 \begin_layout Plain Layout
28455 \begin_inset CommandInset ref
28457 reference "sub:Variable-Space"
28467 \begin_inset Index idx
28470 \begin_layout Plain Layout
28481 \begin_layout Itemize
28482 When both sides of the equation are too long, the command
28489 \begin_inset Index idx
28492 \begin_layout Plain Layout
28501 It is inserted to the first column of the first line and effects that all
28502 further insertions overwrite the following columns:
28503 \begin_inset Formula \begin{eqnarray}
28504 \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 \\
28505 & & -\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 \\
28506 & & =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}
28511 After the insertion of
28517 , the cursor is in a purple box that is a bit shifted to the left from the
28519 In this the formula is inserted.
28520 \begin_inset Newline newline
28523 The content of the further lines is inserted to the second or another formula
28525 The greater the column number where it was inserted, the larger the indentation.
28526 \begin_inset VSpace medskip
28530 \begin_inset Newline newline
28534 \begin_inset Note Greyedout
28537 \begin_layout Plain Layout
28538 Note the following when using
28547 \begin_layout Itemize
28548 The formula doesn't use the full page width.
28550 \begin_inset space \thinspace{}
28554 \begin_inset space \space{}
28558 \begin_inset Formula $-B^{2}$
28561 is added to the first line in the above example, it would have been outside
28563 To better use the width, negative space can be inserted at the beginning
28567 \begin_layout Itemize
28568 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28573 \begin_layout Plain Layout
28574 \begin_inset CommandInset href
28576 name "LyX-bug #1429"
28577 target "http://www.lyx.org/trac/ticket/1429"
28586 One can only set the cursor at the beginning of the line and move it with
28595 \begin_layout Itemize
28596 Other methods to set long formulas are offered by the environments described
28598 \begin_inset CommandInset ref
28600 reference "sub:Multline-Environment"
28605 \begin_inset CommandInset ref
28607 reference "sub:Multiline-Formula-Parts"
28614 \begin_layout Subsubsection
28616 \begin_inset CommandInset label
28618 name "sub:Multiline-Brackets"
28623 \begin_inset Index idx
28626 \begin_layout Plain Layout
28627 Brackets ! for multiline expressions
28635 \begin_layout Standard
28636 For brackets spanning multiple lines the following problem occurs:
28637 \begin_inset Formula \begin{eqnarray*}
28638 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28639 & & \left.\cdots+B-D\right]
28647 \begin_layout Standard
28648 The closing bracket is smaller than the opening bracket because brackets
28649 with variable size may not span multiple lines.
28652 \begin_layout Standard
28653 To set the bracket size for the second line correctly, the first line is
28661 \begin_inset Index idx
28664 \begin_layout Plain Layout
28672 and the second line with
28680 \begin_layout Plain Layout
28694 \begin_inset CommandInset ref
28696 reference "sub:Automatic-Bracket-Size"
28708 \begin_inset Index idx
28711 \begin_layout Plain Layout
28737 \begin_layout Plain Layout
28756 \begin_layout Plain Layout
28775 \begin_layout Plain Layout
28787 \begin_inset Formula $\downarrow$
28793 \begin_inset Index idx
28796 \begin_layout Plain Layout
28804 is inserted, because the multiplication operator with its limits is the
28805 largest symbol in the first line and this should be the size for the bracket
28806 in the second line.
28809 \begin_layout Standard
28810 The result is this:
28811 \begin_inset Formula \begin{eqnarray*}
28812 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28813 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28821 \begin_layout Subsection
28825 \begin_layout Standard
28826 Align environments can be used for every kind of multiline formulas.
28827 They are specially useful to set several formulas side by side.
28830 \begin_layout Standard
28831 Align environments consist of columns.
28832 The odd columns are right aligned, the even ones left aligned.
28833 Every line in an Align environment can be numbered.
28836 \begin_layout Standard
28837 Align environments are created via the menu
28839 Insert\SpecialChar \menuseparator
28845 Edit\SpecialChar \menuseparator
28846 Math\SpecialChar \menuseparator
28847 Change Formula Type
28849 already existing formulas can be converted to Align environments.
28852 \begin_layout Standard
28853 To add or delete columns, the math toolbar buttons
28854 \begin_inset Graphics
28855 filename ../images/tabular-feature_append-column.png
28861 \begin_inset Graphics
28862 filename ../images/tabular-feature_delete-column.png
28867 , respectively, or the menu
28869 Edit\SpecialChar \menuseparator
28875 \begin_layout Subsubsection
28876 Standard align Environment
28877 \begin_inset CommandInset label
28879 name "sub:Standard-align-Environment"
28884 \begin_inset Index idx
28887 \begin_layout Plain Layout
28888 Formula ! multiline ! align environment
28896 \begin_layout Standard
28897 This Align environment is created by presssing
28900 arg "newline-insert newline"
28903 in a formula or by the menu
28905 Insert\SpecialChar \menuseparator
28906 Math\SpecialChar \menuseparator
28907 AMS align Environment
28912 \begin_layout Standard
28913 An example for two formulas set side by side, that are created with a four
28914 column align environment:
28915 \begin_inset Formula \begin{align*}
28916 A & =\sin(B) & C & =D\\
28917 C & \ne A & B & \ne D
28922 As it can be seen, the formulas in this environment are placed so as if
28931 \begin_layout Plain Layout
28939 \begin_inset CommandInset ref
28941 reference "sub:Variable-Space"
28952 before the first and after every even column.
28953 When the formula style
28959 \begin_layout Plain Layout
28961 \begin_inset CommandInset ref
28963 reference "sec:Formula-Styles"
28974 is used, the formula is set without the
28980 before the first column.
28983 \begin_layout Subsubsection
28984 Alignat Environment
28985 \begin_inset Index idx
28988 \begin_layout Plain Layout
28989 Formula ! multiline ! alignat environment
28997 \begin_layout Standard
28998 The alignat environment has no predefined column separation.
28999 It can be inserted manually with the spaces that are described
29000 \begin_inset CommandInset ref
29002 reference "sub:Space"
29009 \begin_layout Standard
29010 The above example in the alignat environment where 1
29011 \begin_inset space \thinspace{}
29014 cm space was inserted at the beginning of the second formula:
29015 \begin_inset Formula \begin{alignat*}{2}
29016 A & =\sin(B) & \hspace{1cm}C & =D\\
29017 C & \ne A & B & \ne D
29022 Because the column separation can be set separately for every column, this
29023 environment is especially suitable to set three and more formulas side
29027 \begin_layout Subsubsection
29028 Flalign Environment
29029 \begin_inset CommandInset label
29031 name "sub:Flalign-Environment"
29036 \begin_inset Index idx
29039 \begin_layout Plain Layout
29040 Formula ! multiline ! flalign environment
29048 \begin_layout Standard
29049 In this environment the first two columns are always set as much as possible
29050 to the left and the last two ones to the right.
29052 \begin_inset Formula \begin{flalign*}
29053 A & =1 & B & =2 & C & =3\\
29054 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29062 \begin_layout Standard
29063 By creating a flalign environment with an odd number of columns where an
29064 empty TeX-brace is inserted to the last column, several formulas in a document
29065 can be set to the left, although the formula style
29070 As example the indented formula
29071 \begin_inset CommandInset ref
29073 reference "eq:VolInt"
29078 \begin_inset Formula \begin{flalign}
29079 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
29083 The first two columns contain the formula.
29084 To indent it as with the formula style
29089 \begin_inset space \thinspace{}
29092 pt space was inserted at the beginning of the first column.
29095 \begin_layout Subsection
29096 Eqnarray Environment
29097 \begin_inset CommandInset label
29099 name "sub:Eqnarray-Environment"
29104 \begin_inset Index idx
29107 \begin_layout Plain Layout
29108 Formula ! multiline ! eqnarray environment
29116 \begin_layout Standard
29117 When this environment has been created, three blue boxes appear.
29118 The content of the first box is right aligned, the content of the last
29120 The content of the middle box appears centered and a bit smaller, because
29121 it is designed to insert there only relation characters.
29122 \begin_inset Formula \begin{eqnarray*}
29123 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29133 \begin_layout Subsection
29135 \begin_inset Index idx
29138 \begin_layout Plain Layout
29139 Formula ! multiline ! gather environment
29147 \begin_layout Standard
29148 This environment consists of only one centered column.
29149 Every line can be numbered.
29150 \begin_inset Formula \begin{gather}
29160 \begin_layout Subsection
29161 Multline Environment
29162 \begin_inset CommandInset label
29164 name "sub:Multline-Environment"
29169 \begin_inset Index idx
29172 \begin_layout Plain Layout
29173 Formula ! multiline ! multline environment
29181 \begin_layout Standard
29182 The multline environment consists, like the gather environment, of only
29184 But the first line is left aligned, the last one right aligned.
29185 All other lines are centered.
29186 Therefore this environment is suitable for long formulas.
29188 \begin_inset CommandInset ref
29190 reference "eq:lefteqn"
29194 in the multline environment:
29195 \begin_inset Formula \begin{multline}
29196 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}\\
29197 -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}\\
29198 =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}}
29206 \begin_layout Standard
29207 In the output only the last (first) line of a multline environment appears
29208 numbered when the document numbering is right (left).
29212 \begin_layout Plain Layout
29213 numbering styles see
29214 \begin_inset CommandInset ref
29216 reference "sec:Formula-Styles"
29228 \begin_layout Standard
29236 \begin_inset Index idx
29239 \begin_layout Plain Layout
29254 \begin_inset Index idx
29257 \begin_layout Plain Layout
29265 a centered line can be right or left aligned, respectively.
29266 The commands are used as follows:
29269 \begin_layout Standard
29274 shoveright{line content}
29280 shoveleft{line content}
29283 \begin_layout Standard
29284 \begin_inset VSpace medskip
29294 \begin_inset Index idx
29297 \begin_layout Plain Layout
29305 specifies the distance of the first line from the left page margin.
29306 Predefined is the length 0
29307 \begin_inset space \thinspace{}
29313 \begin_layout Standard
29314 As example the above formula where the command
29317 \begin_layout Standard
29327 \begin_layout Standard
29328 was inserted in TeX-mode before:
29332 \begin_layout Plain Layout
29344 \begin_inset Formula \begin{multline}
29345 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}\\
29346 \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}}\\
29347 =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}}
29356 \begin_layout Plain Layout
29367 The second line was left aligned using
29376 \begin_layout Subsection
29377 Multiline Formula Parts
29378 \begin_inset CommandInset label
29380 name "sub:Multiline-Formula-Parts"
29385 \begin_inset Index idx
29388 \begin_layout Plain Layout
29389 Formula ! multiline ! formula parts
29397 \begin_layout Standard
29398 To display only parts of a formula with multiple lines, one of the following
29399 environments are used:
29416 They can be inserted via the menu
29418 Insert\SpecialChar \menuseparator
29421 or by using the commands described in this section.
29424 \begin_layout Standard
29425 The first three have the same properties as the corresponding multiline
29426 formula environments, but it is possible to set further formula parts beside
29429 \begin_inset Formula \[
29430 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29431 \Delta E\Delta t & \ge\frac{\hbar}{2}
29433 \right\} \textrm{Uncertainty relations}\]
29440 \begin_layout Standard
29441 To get this formula, a displayed formula is created where the command
29448 \begin_inset Index idx
29451 \begin_layout Plain Layout
29460 A purple box appears around the blue formula box where now columns and
29461 lines can be added.
29462 Outside the multiline environment other formula parts can be set, like
29466 \begin_layout Standard
29467 The aligned environment is also suitable for long formulas whose lines are
29468 horizontally aligned.
29469 Using aligned in a displayed formula has the advantage that the formula
29470 number is vertically centered behind the lines.
29472 \begin_inset CommandInset ref
29474 reference "eq:shortlong"
29478 in the aligned environment:
29479 \begin_inset Formula \begin{equation}
29480 \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}|}\\
29481 & -\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}|}
29490 \begin_layout Standard
29491 To use the environments
29510 \begin_inset Index idx
29513 \begin_layout Plain Layout
29528 \begin_inset Index idx
29531 \begin_layout Plain Layout
29546 \begin_inset Index idx
29549 \begin_layout Plain Layout
29557 are inserted, respectively.
29558 The split environment has the same properties as the aligned environment
29559 but it can only have two columns.
29562 \begin_layout Subsection
29563 Text in multiline Formulas
29564 \begin_inset CommandInset label
29566 name "sub:Text-in-multiline"
29571 \begin_inset Index idx
29574 \begin_layout Plain Layout
29581 \begin_inset Index idx
29584 \begin_layout Plain Layout
29585 Formula ! multiline ! text
29593 \begin_layout Standard
29594 In the Align environments, and the multline and gather environment, text
29595 can be inserted that will appear in a separate line and doesn't affect
29596 the column alignment.
29597 To do this, the command
29604 \begin_inset Index idx
29607 \begin_layout Plain Layout
29615 is used in the following scheme:
29618 \begin_layout Standard
29626 \begin_layout Standard
29627 The text should not be longer than a line because it cannot be hyphenated.
29628 As LyX doesn't yet support
29634 directly, the text is written as mathematical text.
29641 must hereby be at the beginning of a line and appears in the output above
29643 An example where the text was inserted at the beginning of the second line:
29644 \begin_inset Formula \begin{align}
29645 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29646 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29654 \begin_layout Section
29656 \begin_inset Index idx
29659 \begin_layout Plain Layout
29666 \begin_inset Index idx
29669 \begin_layout Plain Layout
29670 Formula ! numbering|see
29674 \begin_layout Plain Layout
29685 \begin_layout Plain Layout
29700 \begin_layout Subsection
29704 \begin_layout Standard
29705 Numbered formulas can be created with the menu
29707 Insert\SpecialChar \menuseparator
29708 Math\SpecialChar \menuseparator
29710 \begin_inset space ~
29718 \begin_inset space ~
29724 Existing formulas can be numbered with the menu
29726 Edit\SpecialChar \menuseparator
29727 Math\SpecialChar \menuseparator
29729 \begin_inset space ~
29737 arg "math-number-toggle"
29741 The formula number is displayed in LyX behind the formula as number sign
29743 The number sign is replaced in the output by the formula number.
29746 \begin_layout Standard
29747 When numbering is turned on in multiline formulas, all lines will be numbered.
29748 But the numbering can be controlled with the menu
29750 Edit\SpecialChar \menuseparator
29751 Math\SpecialChar \menuseparator
29753 \begin_inset space ~
29757 \begin_inset space ~
29761 \begin_inset space ~
29769 arg "math-number-line-toggle"
29775 \begin_layout Standard
29776 Except for inline formulas, all formulas can be numbered with two different
29778 \begin_inset CommandInset ref
29780 reference "sec:Formula-Styles"
29787 \begin_layout Subsection
29789 \begin_inset Index idx
29792 \begin_layout Plain Layout
29793 Cross-references ! to formulas
29801 \begin_layout Standard
29802 All labeled formulas can be cross-referenced.
29803 A label is added by the menu
29805 Insert\SpecialChar \menuseparator
29808 or the toolbar button
29809 \begin_inset Graphics
29810 filename ../images/label-insert.png
29816 The cursor must hereby be inside a displayed formula.
29817 A dialog pops up displaying the prefix
29822 The label is inserted there behind the prefix.
29823 The predefined prefix means
29824 \begin_inset Quotes eld
29828 \begin_inset Quotes erd
29831 and makes it easier to find labels in large documents because it marks
29832 it as formula label to divide it from e.
29833 \begin_inset space \thinspace{}
29837 \begin_inset space \space{}
29841 To change a label, the menu
29843 Insert\SpecialChar \menuseparator
29849 \begin_layout Standard
29850 The name of the label is displayed in LyX within two parentheses behind
29852 A formula with a label is always numbered.
29855 \begin_layout Standard
29856 Cross-references are inserted via the menu
29858 Insert\SpecialChar \menuseparator
29861 or with the toolbar button
29862 \begin_inset Graphics
29863 filename ../images/dialog-show-new-inset_ref.png
29869 A formula cross-reference appears in the output as formula number.
29870 When in the cross-reference dialog window the format
29874 is chosen, the cross-reference appears in the output as formula number
29876 \begin_inset Newline newline
29879 By right-clicking on a cross-reference in LyX, one jumps to the formula
29880 that is referenced.
29883 \begin_layout Standard
29884 Here are as examples cross-references to formulas of the following subsections:
29885 \begin_inset Note Note
29888 \begin_layout Plain Layout
29889 Note the different cross-reference types.
29897 \begin_layout Standard
29899 \begin_inset CommandInset ref
29906 \begin_inset CommandInset ref
29914 \begin_inset CommandInset ref
29920 ) big Latin letters are used for the numbering in contrary to (
29921 \begin_inset CommandInset ref
29930 \begin_layout Standard
29931 \begin_inset VSpace medskip
29934 When the argument of
29942 \begin_layout Plain Layout
29950 \begin_inset CommandInset ref
29952 reference "sub:User-defined-Numbering"
29963 contains a box like in
29964 \begin_inset CommandInset ref
29966 reference "sub:Paragraph-Boxes"
29970 , the formula cannot be referenced.
29973 \begin_layout Subsection
29975 \begin_inset Index idx
29978 \begin_layout Plain Layout
29979 Formula numbering ! subnumbering
29987 \begin_layout Standard
29988 With the help of the commands
29992 begin{subequations}
30000 formulas can be subnumbered.
30001 Both commands are inserted in TeX-mode.
30004 \begin_layout Standard
30006 \begin_inset Formula \begin{equation}
30007 A=C-B\label{eq:a}\end{equation}
30015 \begin_layout Plain Layout
30019 addtocounter{equation}{-1}
30028 \begin_layout Plain Layout
30032 begin{subequations}
30038 \begin_inset VSpace -5mm
30042 \begin_inset Formula \begin{equation}
30043 B=C-A\label{eq:b}\end{equation}
30048 \begin_inset Formula \begin{equation}
30049 C=A+B\label{eq:c}\end{equation}
30056 \begin_layout Standard
30060 \begin_layout Plain Layout
30072 \begin_layout Standard
30073 To create the example, the following is done:
30076 \begin_layout Enumerate
30077 first formula is inserted
30080 \begin_layout Enumerate
30085 addtocounter{equation}{-1}
30087 begin{subequations}
30088 \begin_inset Index idx
30091 \begin_layout Plain Layout
30100 \begin_inset Newline newline
30105 is inserted after the first formula
30108 \begin_layout Enumerate
30109 second formula is inserted
30112 \begin_layout Enumerate
30113 third formula is inserted
30116 \begin_layout Enumerate
30123 is inserted after the third formula
30126 \begin_layout Standard
30127 Every formula between the commands
30139 is subnumbered as a, b,
30140 \begin_inset Newline linebreak
30143 c, \SpecialChar \ldots{}
30144 For multiline formulas every line will be subnumbered.
30145 All subnumbered formulas are treated as
30150 But as every numbered formula increases the counter
30154 by one, the command
30160 is needed to decrease it.
30161 Otherwise the formulas
30162 \begin_inset CommandInset ref
30169 \begin_inset CommandInset ref
30176 \begin_inset CommandInset ref
30182 would be numbered as
30183 \begin_inset CommandInset ref
30190 \begin_inset CommandInset ref
30197 \begin_inset CommandInset ref
30206 \begin_layout Standard
30207 By inserting the commands in TeX-mode, a space is created between the first
30210 \begin_inset space \thinspace{}
30213 mm vertical space is inserted after the command
30217 begin{subequations}
30220 When the formula style
30226 \begin_layout Plain Layout
30228 \begin_inset CommandInset ref
30230 reference "sec:Formula-Styles"
30242 \begin_inset space \thinspace{}
30245 mm space is inserted instead.
30248 \begin_layout Standard
30249 Here is an example for a multiline formula where the numbering was turned
30250 off for the second line:
30254 \begin_layout Plain Layout
30258 begin{subequations}
30264 \begin_inset Formula \begin{eqnarray}
30265 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30266 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30267 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30276 \begin_layout Plain Layout
30288 \begin_layout Subsection
30289 User-defined Numbering
30290 \begin_inset CommandInset label
30292 name "sub:User-defined-Numbering"
30297 \begin_inset Index idx
30300 \begin_layout Plain Layout
30301 Formula numbering ! user-defined
30309 \begin_layout Standard
30310 \begin_inset Index idx
30313 \begin_layout Plain Layout
30314 Formula numbering ! self-defined delimiters
30319 With the standard numbering parentheses are set around the formula number.
30320 To replace the parentheses for example by vertical bars, the following
30321 line is added to the LaTeX-preamble:
30324 \begin_layout Standard
30336 \begin_inset Note Note
30339 \begin_layout Plain Layout
30340 This macro is already declared in the LaTeX-preamble for testing.
30341 To activate it, remove the percent sign at the beginning.
30349 \begin_layout Standard
30350 To use other characters, the vertical bars besides the
30354 are replaced by one ore more characters.
30355 To get only the formula number the vertical bars are omitted.
30358 \begin_layout Standard
30359 \begin_inset VSpace bigskip
30362 When there should be an expression of your choice instead of the consecutive
30363 formula number in parentheses behind the formula, the command
30370 \begin_inset Index idx
30373 \begin_layout Plain Layout
30382 \begin_inset Formula \begin{equation}
30383 A+B=C\tag{something}\label{eq:tag}\end{equation}
30387 In this example the command
30395 \begin_layout Plain Layout
30406 was inserted to the formula.
30409 \begin_layout Standard
30418 \begin_layout Plain Layout
30429 is inserted instead, the star prevents the parentheses around the expression:
30430 \begin_inset Formula \[
30431 A+B=C\tag*{something}\]
30438 \begin_layout Standard
30439 \begin_inset VSpace bigskip
30442 To restart the formula numbering with new document parts or sections, the
30443 following command is used:
30446 \begin_layout Standard
30451 @addtoreset{equation}{part}
30454 \begin_inset Index idx
30457 \begin_layout Plain Layout
30462 \begin_layout Plain Layout
30473 \begin_layout Plain Layout
30486 \begin_layout Plain Layout
30497 \begin_layout Plain Layout
30510 \begin_inset Newline newline
30514 \begin_inset Newline newline
30521 @addtoreset{equation}{section}
30524 \begin_layout Standard
30525 To be able to use these commands in TeX-mode, the
30526 \begin_inset Quotes eld
30530 \begin_inset Quotes erd
30533 character has to be made
30534 \begin_inset Quotes eld
30538 \begin_inset Quotes erd
30541 for LaTeX using the command
30555 So the command sequence in TeX-mode is:
30558 \begin_layout Standard
30564 \begin_inset Newline newline
30569 @addtoreset{equation}{section}
30570 \begin_inset Newline newline
30578 \begin_layout Standard
30579 In the LaTeX-preamble
30591 can be omitted as they are automatically internally inserted by LyX.
30594 \begin_layout Standard
30609 \begin_layout Plain Layout
30614 is part of the LaTeX-package
30619 \begin_inset Index idx
30622 \begin_layout Plain Layout
30623 Packages ! carlisle
30628 that is part of every LaTeX standard installation.
30634 \begin_inset Index idx
30637 \begin_layout Plain Layout
30638 Packages ! remreset
30643 has to be loaded in the LaTeX-preamble with the line
30646 \begin_layout Standard
30651 usepackage{remreset}
30654 \begin_layout Standard
30662 \begin_inset Index idx
30665 \begin_layout Plain Layout
30670 \begin_layout Plain Layout
30681 \begin_layout Plain Layout
30694 \begin_layout Plain Layout
30705 \begin_layout Plain Layout
30717 can be used with the same scheme as
30726 \begin_layout Standard
30727 \begin_inset VSpace bigskip
30730 Sometimes formulas should be numbered in the following form:
30733 \begin_layout Standard
30736 (section number.formula number)
30739 \begin_layout Standard
30740 The formula number should start with every section with
30741 \begin_inset Quotes eld
30745 \begin_inset Quotes erd
30751 \begin_layout Standard
30752 For this case there is the command
30759 \begin_inset Index idx
30762 \begin_layout Plain Layout
30770 , which is used with the following scheme:
30773 \begin_layout Standard
30778 numberwithin{counter}{sectioning}
30781 \begin_layout Standard
30782 Counter denotes what kind of numbering is affected, sectioning denotes what
30783 number is before the dot.
30786 \begin_layout Standard
30787 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30790 \begin_layout Standard
30795 numberwithin{equation}{section}
30798 \begin_layout Standard
30799 This is the result:
30803 \begin_layout Plain Layout
30807 numberwithin{equation}{section}
30813 \begin_inset Formula \begin{equation}
30814 A+B=C\end{equation}
30821 \begin_layout Standard
30823 \begin_inset space \thinspace{}
30827 \begin_inset space \space{}
30830 tables so that the number of the part is the sectioning,
30831 \begin_inset Newline newline
30838 numberwithin{table}{part}
30843 \begin_layout Standard
30844 To go back to the standard numbering or to prevent this kind of numbering
30845 when it is defined by the document class, the following command is inserted
30846 as TeX-Code or to the LaTeX-preamble:
30849 \begin_layout Standard
30859 \begin_inset Index idx
30862 \begin_layout Plain Layout
30876 \begin_layout Plain Layout
30892 \begin_inset Newline newline
30900 \begin_inset Newline newline
30912 \begin_layout Standard
30919 uses internally the command
30925 , described above, that also needs to be reverted.
30929 \begin_layout Plain Layout
30936 \begin_layout Plain Layout
30940 @removefromreset{equation}{section}
30943 \begin_layout Plain Layout
30955 \begin_layout Subsection
30956 Numbering with Roman Numbers and Letters
30957 \begin_inset Index idx
30960 \begin_layout Plain Layout
30961 Formula numbering ! with letters
30967 \begin_inset Index idx
30970 \begin_layout Plain Layout
30971 Formula numbering ! with Roman numbers
30979 \begin_layout Standard
30980 Formulas can also be numbered with Roman numbers and Latin letters.
30981 To number for example with small Roman numbers, the command
30984 \begin_layout Standard
30996 \begin_layout Standard
30997 is inserted before the formula in TeX-mode.
31005 \begin_inset Index idx
31008 \begin_layout Plain Layout
31016 redefines the predefined command
31032 \begin_layout Plain Layout
31039 has the same scheme like the command
31045 that is described in
31046 \begin_inset CommandInset ref
31048 reference "sub:The-Command-newcommand"
31061 is the formula counter.
31068 is used as prefix for a counter, the value of the counter is output as
31070 When a formula is numbered, LaTeX sets internally the command
31076 behind the formula.
31082 \begin_inset Index idx
31085 \begin_layout Plain Layout
31095 outputs the counter as small Roman number.
31098 \begin_layout Standard
31099 All formulas behind the command
31109 are now numbered Roman.
31110 To switch to numbering with big Roman numbers, the command is inserted
31124 \begin_inset Index idx
31127 \begin_layout Plain Layout
31139 \begin_inset Quotes eld
31143 \begin_inset Quotes erd
31146 with small Latin letters there is the command
31153 \begin_inset Index idx
31156 \begin_layout Plain Layout
31164 , for big ones there is the command
31171 \begin_inset Index idx
31174 \begin_layout Plain Layout
31187 \begin_layout Standard
31188 \begin_inset Note Greyedout
31191 \begin_layout Plain Layout
31196 Only maximal 26 formulas can be numbered with Latin letters in one document.
31204 \begin_layout Standard
31208 \begin_layout Plain Layout
31224 \begin_layout Standard
31225 \begin_inset Formula \begin{equation}
31226 A=\textrm{small roman}\end{equation}
31234 \begin_layout Plain Layout
31248 \begin_inset Formula \begin{equation}
31249 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
31257 \begin_layout Plain Layout
31271 \begin_inset Formula \begin{equation}
31272 C=\textrm{small Latin}\end{equation}
31280 \begin_layout Plain Layout
31294 \begin_inset Formula \begin{equation}
31295 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
31302 \begin_layout Standard
31303 To switch back to the default numbering, insert the command:
31306 \begin_layout Standard
31316 \begin_inset Index idx
31319 \begin_layout Plain Layout
31330 \begin_layout Standard
31334 \begin_layout Plain Layout
31348 \begin_inset Formula \begin{equation}
31349 E=\textrm{Arabic}\end{equation}
31356 \begin_layout Standard
31357 \begin_inset VSpace medskip
31360 As you see, formulas are numbered serially independent from the numbering
31362 When then numbering should start with
31363 \begin_inset Quotes eld
31367 \begin_inset Quotes erd
31370 when the style is changed, new equation counters have to be defined.
31371 A description about this can be found in the file
31372 \begin_inset CommandInset href
31374 name "Formula-numbering.lyx"
31375 target "run:Formula-numbering.lyx"
31382 \begin_layout Section
31383 Chemical Symbols and Equations
31384 \begin_inset CommandInset label
31386 name "sub:Chemical-Symbols-and"
31391 \begin_inset Index idx
31394 \begin_layout Plain Layout
31395 Chemical characters ! Symbols
31401 \begin_inset Index idx
31404 \begin_layout Plain Layout
31411 \begin_inset Index idx
31414 \begin_layout Plain Layout
31423 \begin_layout Standard
31424 An example text from chemistry:
31427 \begin_layout Quote
31429 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31432 -ion reacts with two
31433 \begin_inset Formula $\mathrm{Na^{+}}$
31436 -ions to sodium sulfate
31437 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31441 The chemical equation for this is:
31442 \begin_inset Formula \begin{equation}
31443 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
31450 \begin_layout Standard
31451 This chemical equation can directly be created as formula.
31452 To avoid that the symbols appear italic, everything is highlighted and
31453 changed by the shortcut
31459 to the upright font style.
31463 \begin_layout Plain Layout
31469 \begin_inset CommandInset ref
31471 reference "sub:Font-Styles"
31483 \begin_layout Standard
31484 A more convenient way to typeset chemical formulas is to use the command
31492 \begin_inset Index idx
31495 \begin_layout Plain Layout
31503 that is available when the LaTeX-package
31508 \begin_inset Index idx
31511 \begin_layout Plain Layout
31524 to a formula a new blue box appears where chemical formulas can be inserted
31525 in an intuitive way.
31528 \begin_layout Standard
31530 \begin_inset Tabular
31531 <lyxtabular version="3" rows="9" columns="2">
31532 <features tabularvalignment="middle">
31533 <column alignment="center" valignment="top" width="0">
31534 <column alignment="center" valignment="top" width="0">
31536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31539 \begin_layout Plain Layout
31545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31548 \begin_layout Plain Layout
31550 \begin_inset Note Note
31553 \begin_layout Plain Layout
31560 is only used as spacer.
31572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31575 \begin_layout Plain Layout
31582 \begin_layout Plain Layout
31596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31599 \begin_layout Plain Layout
31600 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31613 \begin_layout Plain Layout
31620 \begin_layout Plain Layout
31634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31637 \begin_layout Plain Layout
31638 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31651 \begin_layout Plain Layout
31658 \begin_layout Plain Layout
31672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31675 \begin_layout Plain Layout
31676 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31689 \begin_layout Plain Layout
31696 \begin_layout Plain Layout
31710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31713 \begin_layout Plain Layout
31714 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31727 \begin_layout Plain Layout
31734 \begin_layout Plain Layout
31749 \begin_layout Plain Layout
31764 \begin_layout Plain Layout
31778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31781 \begin_layout Plain Layout
31782 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31795 \begin_layout Plain Layout
31802 \begin_layout Plain Layout
31812 \begin_inset Formula $\downarrow$
31816 \begin_inset Formula $\to$
31824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31827 \begin_layout Plain Layout
31828 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31841 \begin_layout Plain Layout
31848 \begin_layout Plain Layout
31861 \begin_layout Plain Layout
31874 \begin_layout Plain Layout
31887 \begin_layout Plain Layout
31900 \begin_layout Plain Layout
31914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31917 \begin_layout Plain Layout
31918 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
31928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31931 \begin_layout Plain Layout
31938 \begin_layout Plain Layout
31951 \begin_layout Plain Layout
31964 \begin_layout Plain Layout
31977 \begin_layout Plain Layout
31994 \begin_layout Plain Layout
32008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32011 \begin_layout Plain Layout
32012 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32028 \begin_layout Standard
32029 \begin_inset Note Greyedout
32032 \begin_layout Plain Layout
32037 Inserting a formula to a
32043 box will lead to LaTeX errors.
32044 In this case TeX code has to be used like for
32058 \begin_layout Plain Layout
32079 \begin_layout Standard
32086 the command for equation
32087 \begin_inset space ~
32091 \begin_inset CommandInset ref
32093 reference "eq:chem-reaction"
32098 \begin_inset Newline newline
32109 \begin_layout Plain Layout
32122 \begin_layout Plain Layout
32135 \begin_layout Plain Layout
32148 \begin_layout Plain Layout
32161 \begin_layout Plain Layout
32174 \begin_layout Plain Layout
32186 \begin_layout Standard
32187 To create multiline chemical equations first a multiline formula is created
32189 \begin_inset CommandInset ref
32191 reference "sec:Multiline-Formulas"
32196 Afterwards the command
32202 is used in every small blue box of the formula.
32204 \begin_inset CommandInset ref
32206 reference "eq:TEOS-reaction-1"
32211 \begin_inset CommandInset ref
32213 reference "eq:TEOS-reaction-2"
32217 are an example of a multi-stage chemical reaction where every equation
32218 has its own number.
32219 \begin_inset Formula \begin{eqnarray}
32220 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32221 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32229 \begin_layout Standard
32240 package provides the command
32247 \begin_inset Index idx
32250 \begin_layout Plain Layout
32258 that has to be used for special cases.
32259 For more information about
32265 and more examples have a look at the documentation of
32270 \begin_inset CommandInset citation
32279 \begin_layout Standard
32280 \begin_inset Newpage newpage
32286 \begin_layout Section
32290 \begin_layout Standard
32291 LyX supports two types of commutative diagrams:
32299 that are explained in the following.
32302 \begin_layout Subsection
32304 \begin_inset Index idx
32307 \begin_layout Plain Layout
32316 \begin_layout Standard
32317 Diagrams of this type visualize relations by vertical and horizontal lines
32319 \begin_inset Formula \[
32320 \begin{CD}A@>>>B@>>>C\\
32330 \begin_layout Standard
32331 To get them, the command
32336 \begin_inset Index idx
32339 \begin_layout Plain Layout
32349 is inserted to a formula.
32350 A blue box appears with two dashed lines where further commands can be
32355 arg "newline-insert newline"
32358 a new line is created.
32359 Horizontal relations are inserted in odd, vertical in even formula lines.
32362 \begin_layout Standard
32363 To create the relations there are the following commands:
32366 \begin_layout Itemize
32371 creates a left arrow,
32382 \begin_layout Itemize
32387 creates an up arrow,
32395 a vertical equal sign
32398 \begin_layout Itemize
32404 is a placeholder for non-existent relations
32407 \begin_layout Standard
32408 All arrows can be labeled as follows:
32411 \begin_layout Itemize
32412 Is text inserted between the first and second < or >, resp., it is placed
32414 When it is inserted between the second and third one, it appears under
32418 \begin_layout Itemize
32419 When text for vertical arrows is inserted between the first and second A
32420 or V, resp., it is placed left beside the arrow.
32421 When it is inserted between the second and third one, it appears right
32423 If the text contains an A or V, these letters must be set into a TeX-brace.
32426 \begin_layout Standard
32427 As example a diagram with all possible relations:
32430 \begin_layout Standard
32431 \begin_inset Formula \[
32432 \begin{CD}A@>j>>B@>>k>C@=F\\
32442 \begin_layout Standard
32443 The command for this is:
32444 \begin_inset Newline newline
32455 \begin_layout Plain Layout
32464 A@>j>>B@>>k>C@=F Ctrl+Return
32465 \begin_inset Newline newline
32469 \begin_inset Phantom HPhantom
32472 \begin_layout Plain Layout
32481 \begin_layout Plain Layout
32500 \begin_inset Formula $\to$
32506 \begin_inset Newline newline
32510 \begin_inset Phantom HPhantom
32513 \begin_layout Plain Layout
32522 \begin_layout Plain Layout
32539 \begin_layout Subsection
32541 \begin_inset Index idx
32544 \begin_layout Plain Layout
32545 Diagrams ! xymatrix
32553 \begin_layout Standard
32554 To be able to use xymatrices, the LaTeX-package
32559 A xymatrix is created by inserting the command
32566 Then you are able to add new matrix columns and rows like for normal matrices,
32568 \begin_inset CommandInset ref
32570 reference "sec:Matrices"
32577 \begin_layout Standard
32578 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32580 All possibilities to create commutative diagrams and decorations are explained
32585 that you find in the menu
32587 Help\SpecialChar \menuseparator
32589 \begin_inset space ~
32597 \begin_layout Subsection
32603 \begin_inset Index idx
32606 \begin_layout Plain Layout
32615 \begin_layout Standard
32620 -diagrams, the LaTeX-package
32629 -diagram is created by inserting the command
32636 Then you are able to add new matrix columns and rows like for normal matrices,
32638 \begin_inset CommandInset ref
32640 reference "sec:Matrices"
32647 \begin_layout Standard
32648 Examples how to create
32652 diagrams in LyX is given in the
32654 Feynman-diagram manual
32656 that you find in the menu
32658 Help\SpecialChar \menuseparator
32660 \begin_inset space ~
32668 \begin_layout Section
32669 User-defined Commands
32670 \begin_inset Index idx
32673 \begin_layout Plain Layout
32674 User-defined commands
32682 \begin_layout Standard
32683 \begin_inset Note Greyedout
32686 \begin_layout Plain Layout
32691 The names of user-defined commands and macros may only consist of Latin
32700 \begin_layout Subsection
32704 \begin_inset CommandInset label
32706 name "sub:The-Command-newcommand"
32711 \begin_inset Index idx
32714 \begin_layout Plain Layout
32715 User-defined commands !
32723 \begin_inset Index idx
32726 \begin_layout Plain Layout
32737 \begin_layout Standard
32738 Many LaTeX-commands are too long to be used frequently.
32739 But it is possible to define with the command
32745 new shorter commands.
32748 \begin_layout Standard
32749 The command scheme of
32758 \begin_layout Standard
32763 newcommand{new command name}[number of arguments][optional
32768 \begin_inset Newline newline
32772 \begin_inset Phantom HPhantom
32775 \begin_layout Plain Layout
32785 {command definition}
32788 \begin_layout Standard
32789 \begin_inset Note Greyedout
32792 \begin_layout Plain Layout
32797 Assure that the name of the new command is not already used in your document
32798 or by LaTeX-packages that you use.
32799 When you for example define the command
32811 , you get an error message because
32817 is already defined as command for
32818 \begin_inset Quotes eld
32822 \begin_inset Formula $\le$
32826 \begin_inset Quotes erd
32837 \begin_layout Standard
32838 The number of arguments is an integer in the range 0
32839 \begin_inset space \thinspace{}
32843 \begin_inset space \thinspace{}
32846 9 and specifies how many arguments the new command should have.
32847 With the optional value a value for an optional argument can be predefined.
32848 When this is done, the
32856 rgument of the new command is automatically an optional one.
32859 \begin_layout Standard
32860 Here are some examples:
32863 \begin_layout Itemize
32864 To define the command
32876 , the LaTeX-preamble line is:
32877 \begin_inset VSpace medskip
32881 \begin_inset Newline newline
32895 \begin_layout Itemize
32896 To define the command
32908 , the argument (that should be underlined) must be taken into account.
32909 For this the preamble line is:
32910 \begin_inset VSpace medskip
32914 \begin_inset Newline newline
32928 \begin_inset VSpace medskip
32932 \begin_inset Newline newline
32939 acts as argument placeholder, the
32943 behind it denotes that it is the placeholder for the first argument.
32946 \begin_layout Itemize
32954 \begin_inset space \thinspace{}
32958 \begin_inset space \space{}
32968 \begin_inset VSpace medskip
32972 \begin_inset Newline newline
32983 framebox#1#2{$#3$}}
32986 \begin_inset VSpace medskip
32990 \begin_inset Newline newline
32993 The two Dollar signs creates the extra formula needed for
33000 \begin_inset CommandInset ref
33002 reference "sub:Boxes-with-Frame"
33009 \begin_layout Itemize
33010 To create a new command for
33016 where the color for the box needn't to be specified, the argument for the
33017 color is defined optional:
33018 \begin_inset VSpace medskip
33022 \begin_inset Newline newline
33033 fcolorbox{#2}{#1}{$#3$}}
33036 \begin_inset VSpace medskip
33040 \begin_inset Newline newline
33043 When the color is not specified when using
33049 , the predefined color
33056 \begin_layout Standard
33057 A test of the new defined commands:
33060 \begin_layout Standard
33062 \begin_inset Tabular
33063 <lyxtabular version="3" rows="6" columns="2">
33064 <features tabularvalignment="middle">
33065 <column alignment="center" valignment="top" width="0">
33066 <column alignment="center" valignment="top" width="0">
33068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33071 \begin_layout Plain Layout
33077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33080 \begin_layout Plain Layout
33082 \begin_inset Note Note
33085 \begin_layout Plain Layout
33092 is only used as spacer.
33104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33107 \begin_layout Plain Layout
33114 \begin_layout Plain Layout
33128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33131 \begin_layout Plain Layout
33132 \begin_inset Formula $A\gr B$
33142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33145 \begin_layout Plain Layout
33153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33156 \begin_layout Plain Layout
33157 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33170 \begin_layout Plain Layout
33174 \begin_inset Formula $\to$
33180 \begin_inset Formula $\to$
33191 \begin_layout Plain Layout
33205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33208 \begin_layout Plain Layout
33209 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33222 \begin_layout Plain Layout
33226 \begin_inset Formula $\to$
33237 \begin_layout Plain Layout
33251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33254 \begin_layout Plain Layout
33255 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33268 \begin_layout Plain Layout
33274 \begin_inset Formula $\to$
33285 \begin_layout Plain Layout
33299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33302 \begin_layout Plain Layout
33303 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33319 \begin_layout Subsection
33321 \begin_inset Index idx
33324 \begin_layout Plain Layout
33325 User-defined commands! Math macros
33331 \begin_inset Index idx
33334 \begin_layout Plain Layout
33343 \begin_layout Standard
33344 User-defined commands are especially convenient for complex expressions.
33345 When you are for example dealing in a document with quadratic equations,
33346 the same solution type occurs several times.
33347 The general form of a quadratic equation is
33348 \begin_inset Formula \[
33349 0=\lambda^{2}+p\lambda+q\]
33353 The general form of the solution is
33354 \begin_inset Formula \[
33355 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
33362 \begin_layout Standard
33363 To define a command for the solution formula where only the three parameters
33365 \begin_inset Formula $\lambda$
33369 \begin_inset Formula $p$
33373 \begin_inset Formula $q$
33376 need to be specified and the index of
33377 \begin_inset Formula $\lambda$
33380 can be given optionally, the LaTeX-preamble line is
33381 \begin_inset Newline newline
33397 \begin_inset Newline newline
33401 \begin_inset Phantom HPhantom
33404 \begin_layout Plain Layout
33418 frac{#3^{2}}{4}-#4}}
33421 \begin_layout Standard
33422 To create with this the solution formula, the command
33423 \begin_inset Newline newline
33433 \begin_inset Formula $\to$
33439 \begin_inset Formula $\to$
33446 is inserted to a formula
33451 \begin_layout Standard
33452 The definition of the new command is unintuitive because one has to know
33453 the schemes of all used LaTeX commands, e.
33454 \begin_inset space \thinspace{}
33458 \begin_inset space \space{}
33461 that a fraction is inserted in LaTeX as
33465 frac{numerator}{denominator}
33468 Furthermore one can easily forget a brace in the definition and cannot
33469 see in LyX what the new command is doing.
33470 To avoid these problems LyX offers the possibility to use math macros instead
33480 \begin_layout Standard
33481 A math macro is created by using the menu
33483 Insert\SpecialChar \menuseparator
33484 Math\SpecialChar \menuseparator
33487 or the toolbar button
33488 \begin_inset Graphics
33489 filename ../images/math-macro_newmacroname_newcommand.png
33495 The math macro toolbar appears together with the following box where the
33497 \begin_inset Newline newline
33501 \begin_inset space \hspace*{\fill}
33505 \begin_inset Graphics
33506 filename clipart/macrobox.png
33511 \begin_inset space \hspace*{\fill}
33515 \begin_inset Newline newline
33519 \begin_inset FormulaMacro
33520 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33525 newmacroname is the default name of the macro that should be changed to
33526 something sensible.
33527 The wanted formula is inserted in the first blue box.
33528 An argument placeholder is inserted with the command
33535 \begin_inset space \thinspace{}
33539 \begin_inset space \space{}
33548 or by using the macro toolbar button
33549 \begin_inset Graphics
33550 filename ../images/math-macro-add-param.png
33556 Argument placeholders are displayed red.
33557 Maximum 9 arguments are possible.
33558 Optional arguments are created with the toolbar button
33559 \begin_inset Graphics
33560 filename ../images/math-macro-add-optional-param.png
33566 The first non-optional argument can be transformed to an optional one with
33568 \begin_inset Graphics
33569 filename ../images/math-macro-make-optional.png
33575 In the second blue box the appearance of the macro in LyX can be defined.
33576 Normally you want to see it as it is defined, so the box is kept empty.
33577 But when you have created a macro that needs lot of space on the screen,
33578 you can insert in the box for example
33579 \begin_inset Newline newline
33609 \begin_inset Newline newline
33614 For the macro only the arguments with the macro name in front of them will
33615 then be displayed in LyX, leading to a better overview.
33616 The formula appears in the output as defined in the first box.
33617 \begin_inset Newline newline
33620 The appearance of macros in formulas can furthermore be changed for single
33621 macros by setting the cursor in the macro and using the menu
33623 View\SpecialChar \menuseparator
33625 \begin_inset space ~
33629 \begin_inset space ~
33637 \begin_layout Standard
33638 To use a macro, the macro name is inserted as command to a formula, in our
33646 Our macro looks in LyX like this:
33647 \begin_inset Newline newline
33651 \begin_inset space \hspace*{\fill}
33655 \begin_inset Graphics
33656 filename clipart/macrouse.png
33661 \begin_inset space \hspace*{\fill}
33665 \begin_inset Newline newline
33668 Here is our macro example with the arguments
33669 \begin_inset Formula $x$
33673 \begin_inset Formula $\ln(x)$
33677 \begin_inset Formula $B$
33683 \begin_layout Standard
33684 \begin_inset Formula \[
33692 \begin_layout Standard
33693 LyX offers in the menu
33695 Tools\SpecialChar \menuseparator
33696 Preferences\SpecialChar \menuseparator
33697 Editing\SpecialChar \menuseparator
33700 different styles to edit macros.
33701 To find the style that suits you the most, choose a style and set the cursor
33702 in a macro formula to see the difference.
33705 \begin_layout Standard
33706 A math macro is transformed internally to a
33712 command when exporting the document.
33719 command is not placed in the LaTeX-preamble, therefore macros can only
33720 be used in formulas that are in the document below the macro definition
33724 \begin_layout Standard
33725 Math macros can also be directly be created from a
33732 When writing for example the command
33735 \begin_inset Newline newline
33744 xleftarrow[#2]{#1}}
33745 \begin_inset Newline newline
33750 in LyX as normal text, highlighting it completely and using then the shortcut
33755 , the command will be transformed to a math macro.
33756 Using this method you need to be careful that the
33762 command is typed correctly, otherwise you get a faulty macro leading to
33766 \begin_layout Standard
33767 Math macros currently yet have the problem that further formulas in macro
33768 definitions are handled wrongly.
33769 Therefore the example
33776 \begin_inset CommandInset ref
33778 reference "sub:The-Command-newcommand"
33782 cannot be created as macro.
33785 \begin_layout Standard
33786 When the cursor is in a macro definition box, you will see the macro toolbar
33790 \begin_layout Standard
33791 \begin_inset VSpace defskip
33797 \begin_layout Standard
33798 \begin_inset Graphics
33799 filename clipart/MacroToolbar.png
33804 \begin_inset Index idx
33807 \begin_layout Plain Layout
33816 \begin_layout Standard
33817 \begin_inset VSpace defskip
33823 \begin_layout Standard
33824 The macro toolbar contains from left to right the following buttons:
33827 \begin_layout Standard
33828 \begin_inset VSpace defskip
33834 \begin_layout Standard
33835 \begin_inset Tabular
33836 <lyxtabular version="3" rows="9" columns="2">
33837 <features islongtable="true" longtabularalignment="center">
33838 <column alignment="left" valignment="top" width="0">
33839 <column alignment="left" valignment="top" width="85col%">
33840 <row interlinespace="2.5mm">
33841 <cell alignment="center" valignment="top" usebox="none">
33844 \begin_layout Plain Layout
33845 \begin_inset Graphics
33846 filename ../images/math-macro-remove-param.png
33847 BoundingBox 0bp 5bp 20bp 25bp
33848 rotateOrigin center
33857 <cell alignment="center" valignment="top" usebox="none">
33860 \begin_layout Plain Layout
33863 Edit\SpecialChar \menuseparator
33864 Math\SpecialChar \menuseparator
33866 \begin_inset space ~
33869 Definition\SpecialChar \menuseparator
33870 Remove Last Argument
33876 <row interlinespace="2.5mm">
33877 <cell alignment="center" valignment="top" usebox="none">
33880 \begin_layout Plain Layout
33881 \begin_inset Graphics
33882 filename ../images/math-macro-add-param.png
33883 BoundingBox 0bp 5bp 20bp 25bp
33884 rotateOrigin center
33893 <cell alignment="center" valignment="top" usebox="none">
33896 \begin_layout Plain Layout
33899 Edit\SpecialChar \menuseparator
33900 Math\SpecialChar \menuseparator
33902 \begin_inset space ~
33905 Definition\SpecialChar \menuseparator
33912 <row interlinespace="2.5mm">
33913 <cell alignment="center" valignment="top" usebox="none">
33916 \begin_layout Plain Layout
33917 \begin_inset Graphics
33918 filename ../images/math-macro-make-optional.png
33919 BoundingBox 0bp 5bp 20bp 25bp
33920 rotateOrigin center
33929 <cell alignment="center" valignment="top" usebox="none">
33932 \begin_layout Plain Layout
33935 Edit\SpecialChar \menuseparator
33936 Math\SpecialChar \menuseparator
33938 \begin_inset space ~
33941 Definition\SpecialChar \menuseparator
33942 Make First Non-Optional into
33943 \begin_inset Newline newline
33947 \begin_inset Phantom HPhantom
33950 \begin_layout Plain Layout
33953 Edit\SpecialChar \menuseparator
33954 Math\SpecialChar \menuseparator
33956 \begin_inset space ~
33959 Definition\SpecialChar \menuseparator
33971 <row interlinespace="2.5mm">
33972 <cell alignment="center" valignment="top" usebox="none">
33975 \begin_layout Plain Layout
33976 \begin_inset Graphics
33977 filename ../images/math-macro-make-nonoptional.png
33978 BoundingBox 0bp 5bp 20bp 25bp
33979 rotateOrigin center
33988 <cell alignment="center" valignment="top" usebox="none">
33991 \begin_layout Plain Layout
33994 Edit\SpecialChar \menuseparator
33995 Math\SpecialChar \menuseparator
33997 \begin_inset space ~
34000 Definition\SpecialChar \menuseparator
34001 Make Last Optional into
34002 \begin_inset Newline newline
34006 \begin_inset Phantom HPhantom
34009 \begin_layout Plain Layout
34012 Edit\SpecialChar \menuseparator
34013 Math\SpecialChar \menuseparator
34015 \begin_inset space ~
34018 Definition\SpecialChar \menuseparator
34024 Non-Optional Argument
34030 <row interlinespace="2.5mm">
34031 <cell alignment="center" valignment="top" usebox="none">
34034 \begin_layout Plain Layout
34035 \begin_inset Graphics
34036 filename ../images/math-macro-remove-optional-param.png
34037 BoundingBox 0bp 5bp 20bp 25bp
34038 rotateOrigin center
34047 <cell alignment="center" valignment="top" usebox="none">
34050 \begin_layout Plain Layout
34053 Edit\SpecialChar \menuseparator
34054 Math\SpecialChar \menuseparator
34056 \begin_inset space ~
34059 Definition\SpecialChar \menuseparator
34060 Remove Optional Argument
34066 <row interlinespace="2.5mm">
34067 <cell alignment="center" valignment="top" usebox="none">
34070 \begin_layout Plain Layout
34071 \begin_inset Graphics
34072 filename ../images/math-macro-add-optional-param.png
34073 BoundingBox 0bp 5bp 20bp 25bp
34074 rotateOrigin center
34083 <cell alignment="center" valignment="top" usebox="none">
34086 \begin_layout Plain Layout
34089 Edit\SpecialChar \menuseparator
34090 Math\SpecialChar \menuseparator
34092 \begin_inset space ~
34095 Definition\SpecialChar \menuseparator
34096 Insert Optional Argument
34102 <row interlinespace="2.5mm">
34103 <cell alignment="center" valignment="top" usebox="none">
34106 \begin_layout Plain Layout
34107 \begin_inset Graphics
34108 filename ../images/math-macro-remove-greedy-param.png
34109 BoundingBox 0bp 5bp 20bp 25bp
34110 rotateOrigin center
34119 <cell alignment="center" valignment="top" usebox="none">
34122 \begin_layout Plain Layout
34125 Edit\SpecialChar \menuseparator
34126 Math\SpecialChar \menuseparator
34128 \begin_inset space ~
34131 Definition\SpecialChar \menuseparator
34132 Remove Last Argument
34133 \begin_inset Newline newline
34137 \begin_inset Phantom HPhantom
34140 \begin_layout Plain Layout
34143 Edit\SpecialChar \menuseparator
34144 Math\SpecialChar \menuseparator
34146 \begin_inset space ~
34149 Definition\SpecialChar \menuseparator
34155 Spitting Out To The Right
34161 <row interlinespace="2.5mm">
34162 <cell alignment="center" valignment="top" usebox="none">
34165 \begin_layout Plain Layout
34166 \begin_inset Graphics
34167 filename ../images/math-macro-append-greedy-param.png
34168 BoundingBox 0bp 5bp 20bp 25bp
34169 rotateOrigin center
34178 <cell alignment="center" valignment="top" usebox="none">
34181 \begin_layout Plain Layout
34184 Edit\SpecialChar \menuseparator
34185 Math\SpecialChar \menuseparator
34187 \begin_inset space ~
34190 Definition\SpecialChar \menuseparator
34192 \begin_inset Newline newline
34196 \begin_inset Phantom HPhantom
34199 \begin_layout Plain Layout
34202 Edit\SpecialChar \menuseparator
34203 Math\SpecialChar \menuseparator
34205 \begin_inset space ~
34208 Definition\SpecialChar \menuseparator
34214 Eating From The Right
34220 <row interlinespace="2.5mm">
34221 <cell alignment="center" valignment="top" usebox="none">
34224 \begin_layout Plain Layout
34225 \begin_inset Graphics
34226 filename ../images/math-macro-add-greedy-optional-param.png
34227 BoundingBox 0bp 5bp 20bp 25bp
34228 rotateOrigin center
34237 <cell alignment="center" valignment="top" usebox="none">
34240 \begin_layout Plain Layout
34243 Edit\SpecialChar \menuseparator
34244 Math\SpecialChar \menuseparator
34246 \begin_inset space ~
34249 Definition\SpecialChar \menuseparator
34250 Append Optional Argument
34251 \begin_inset Newline newline
34255 \begin_inset Phantom HPhantom
34258 \begin_layout Plain Layout
34261 Edit\SpecialChar \menuseparator
34262 Math\SpecialChar \menuseparator
34264 \begin_inset space ~
34267 Definition\SpecialChar \menuseparator
34273 Eating From The Right
34286 \begin_layout Standard
34287 \begin_inset Newpage newpage
34293 \begin_layout Section
34295 \begin_inset Index idx
34298 \begin_layout Plain Layout
34307 \begin_layout Subsection
34309 \begin_inset Index idx
34312 \begin_layout Plain Layout
34321 \begin_layout Standard
34322 Negative numbers often look ugly in formulas because the minus sign before
34323 the number is set with the same length as the minus operator sign.
34324 When writing the negative number in normal text, the minus sign appears
34328 \begin_layout Standard
34329 Thus, the problem disappears when converting the minus sign to mathematical
34333 \begin_layout Standard
34334 An example to visualize the problem:
34337 \begin_layout Standard
34339 \begin_inset Tabular
34340 <lyxtabular version="3" rows="3" columns="2">
34341 <features tabularvalignment="middle">
34342 <column alignment="right" valignment="top" width="0">
34343 <column alignment="left" valignment="top" width="0">
34345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34348 \begin_layout Plain Layout
34354 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34357 \begin_layout Plain Layout
34365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34368 \begin_layout Plain Layout
34374 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34377 \begin_layout Plain Layout
34378 \begin_inset Formula $x=-2$
34388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34391 \begin_layout Plain Layout
34397 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34400 \begin_layout Plain Layout
34401 \begin_inset Formula $x=\textrm{-}2$
34417 \begin_layout Subsection
34418 Comma as decimal Separator
34419 \begin_inset Index idx
34422 \begin_layout Plain Layout
34431 \begin_layout Standard
34432 In LaTeX a comma inside a formula is used, according to the English convention,
34433 as number group separator.
34434 So there will be space added behind all commas in formulas.
34437 \begin_layout Standard
34438 To avoid this, the comma is highlighted and changed to mathematical text
34448 \begin_layout Standard
34449 To use all formula commas in the document as decimal separator, the file
34458 \begin_layout Plain Layout
34463 is part of the LaTeX-package
34468 \begin_inset Index idx
34471 \begin_layout Plain Layout
34476 \begin_layout Plain Layout
34496 \begin_inset Index idx
34499 \begin_layout Plain Layout
34505 is loaded with the LaTeX-preamble line
34508 \begin_layout Standard
34516 \begin_layout Subsection
34518 \begin_inset CommandInset label
34520 name "sub:Physical-Vectors"
34525 \begin_inset Index idx
34528 \begin_layout Plain Layout
34537 \begin_layout Standard
34538 Predefined vectors are offered by the LaTeX-package
34543 \begin_inset Index idx
34546 \begin_layout Plain Layout
34552 that is loaded with the LaTeX-preamble line
34555 \begin_layout Standard
34563 \begin_layout Standard
34567 \begin_layout Plain Layout
34577 \begin_inset Note Note
34580 \begin_layout Plain Layout
34581 The following table will only be displayed when the LaTeX-package
34593 \begin_layout Standard
34594 The following commands are defined:
34597 \begin_layout Standard
34599 \begin_inset Tabular
34600 <lyxtabular version="3" rows="4" columns="2">
34601 <features tabularvalignment="middle">
34602 <column alignment="center" valignment="top" width="0">
34603 <column alignment="center" valignment="top" width="0">
34605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34608 \begin_layout Plain Layout
34614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34617 \begin_layout Plain Layout
34625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34628 \begin_layout Plain Layout
34638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34641 \begin_layout Plain Layout
34642 \begin_inset Formula $\Bra{\psi}$
34652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34655 \begin_layout Plain Layout
34665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34668 \begin_layout Plain Layout
34669 \begin_inset Formula $\Ket{\psi}$
34679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34682 \begin_layout Plain Layout
34694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34697 \begin_layout Plain Layout
34698 \begin_inset Formula $\Braket{\psi|\phi}$
34714 \begin_layout Standard
34721 assures that all vertical bars are set in the size of the surrounding brackets:
34722 \begin_inset Formula \[
34723 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
34731 \begin_layout Plain Layout
34741 \begin_inset Note Note
34744 \begin_layout Plain Layout
34745 The following will be displayed when the LaTeX-package
34757 \begin_layout Standard
34758 You need to install the LaTeX-package
34762 to see the rest of this subsection in the output.
34765 \begin_layout Standard
34769 \begin_layout Plain Layout
34781 \begin_layout Standard
34788 can also be achieved using the command
34794 , that is described in
34795 \begin_inset CommandInset ref
34797 reference "sub:Automatic-Bracket-Size"
34804 \begin_layout Subsection
34805 Self-defined Fractions
34806 \begin_inset CommandInset label
34808 name "sub:Self-defined-Fractions"
34813 \begin_inset Index idx
34816 \begin_layout Plain Layout
34817 Fractions ! self-defined
34825 \begin_layout Standard
34826 To define custom commands for fractions, the command
34833 \begin_inset Index idx
34836 \begin_layout Plain Layout
34844 is used in the following scheme:
34847 \begin_layout Standard
34860 bracket}{fraction bar thickness}{style}
34861 \begin_inset Newline newline
34865 \begin_inset Phantom HPhantom
34868 \begin_layout Plain Layout
34878 {numerator}{denominator}
34881 \begin_layout Standard
34882 The style is a number in the range of 0
34883 \begin_inset space \thinspace{}
34887 \begin_inset space \thinspace{}
34893 \begin_layout Standard
34895 \begin_inset Tabular
34896 <lyxtabular version="3" rows="5" columns="2">
34897 <features tabularvalignment="middle">
34898 <column alignment="center" valignment="top" width="0">
34899 <column alignment="center" valignment="top" width="0">
34901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34904 \begin_layout Plain Layout
34910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34913 \begin_layout Plain Layout
34921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34924 \begin_layout Plain Layout
34930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34933 \begin_layout Plain Layout
34934 display style formula
34941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34944 \begin_layout Plain Layout
34950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34953 \begin_layout Plain Layout
34961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34964 \begin_layout Plain Layout
34970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34973 \begin_layout Plain Layout
34981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34984 \begin_layout Plain Layout
34990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34993 \begin_layout Plain Layout
35007 \begin_layout Standard
35008 When no style is given, the size is adjusted to the surrounding environment
35009 like for the command
35018 \begin_layout Standard
35019 When no fraction bar thickness is given, the predefined value of 0.4
35020 \begin_inset space \thinspace{}
35026 \begin_layout Standard
35027 \begin_inset VSpace medskip
35030 For example, the commands
35043 \begin_inset CommandInset ref
35045 reference "sub:Fractions"
35049 are defined with the commands
35052 \begin_layout Standard
35061 genfrac{}{}{}{0}{#1}{#2}}
35064 \begin_layout Standard
35068 \begin_layout Standard
35077 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35080 \begin_layout Standard
35081 \begin_inset VSpace medskip
35084 To define a fraction where the fraction bar thickness can be given as optional
35085 argument, the following line is inserted to the LaTeX-preamble:
35088 \begin_layout Standard
35097 genfrac{}{}{#1}{}{#2}{#3}}
35100 \begin_layout Standard
35102 \begin_inset Formula \begin{align*}
35103 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35104 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35109 As one can see, the distance of the numerator and the denominator to the
35110 fraction bar is round about three times the bar thickness.
35113 \begin_layout Subsection
35115 \begin_inset Index idx
35118 \begin_layout Plain Layout
35127 \begin_layout Standard
35128 To cancel formulas or formula parts, the LaTeX-package
35133 \begin_inset Index idx
35136 \begin_layout Plain Layout
35142 has to be loaded with the LaTeX-preamble line
35145 \begin_layout Standard
35150 usepackage[samesize]{cancel}
35153 \begin_layout Standard
35157 \begin_layout Plain Layout
35167 \begin_inset Note Note
35170 \begin_layout Plain Layout
35171 The following table will only be displayed when the LaTeX-package
35183 \begin_layout Standard
35184 There are four ways to cancel formulas:
35187 \begin_layout Standard
35189 \begin_inset Tabular
35190 <lyxtabular version="3" rows="5" columns="2">
35191 <features tabularvalignment="middle">
35192 <column alignment="center" valignment="top" width="0">
35193 <column alignment="center" valignment="top" width="0">
35195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35198 \begin_layout Plain Layout
35204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35207 \begin_layout Plain Layout
35209 \begin_inset Note Note
35212 \begin_layout Plain Layout
35219 are used here as spacer.
35231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35234 \begin_layout Plain Layout
35243 \begin_layout Plain Layout
35257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35260 \begin_layout Plain Layout
35261 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35274 \begin_layout Plain Layout
35283 \begin_layout Plain Layout
35297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35300 \begin_layout Plain Layout
35301 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35314 \begin_layout Plain Layout
35323 \begin_layout Plain Layout
35337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35340 \begin_layout Plain Layout
35341 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35354 \begin_layout Plain Layout
35358 \begin_inset Formula $\to$
35369 \begin_layout Plain Layout
35383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35386 \begin_layout Plain Layout
35387 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35403 \begin_layout Standard
35410 is especially suitable to visualize the reduction of fractions within formulas:
35411 \begin_inset Formula \[
35412 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
35419 \begin_layout Standard
35423 \begin_layout Plain Layout
35433 \begin_inset Note Note
35436 \begin_layout Plain Layout
35437 The following will be displayed when the LaTeX-package
35449 \begin_layout Standard
35450 You need to install the LaTeX-package
35454 to see the rest of this subsection in the output.
35457 \begin_layout Standard
35461 \begin_layout Plain Layout
35473 \begin_layout Subsection
35474 Formulas in Section Headings
35475 \begin_inset CommandInset label
35477 name "sub:Formulas-in-Section"
35482 \begin_inset Index idx
35485 \begin_layout Plain Layout
35486 Formula ! in section headings
35494 \begin_layout Standard
35495 When formulas are used in section headings, the following has to be taken
35499 \begin_layout Standard
35500 \begin_inset Note Greyedout
35503 \begin_layout Plain Layout
35509 \begin_inset Index idx
35512 \begin_layout Plain Layout
35513 Packages ! hyperref
35518 support is enabled in the document settings dialog under
35521 \begin_inset space ~
35526 , PDF-bookmarks are created for every section heading in the table of contents.
35527 If a section heading contains formulas, they are incorrectly displayed
35528 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35537 \begin_layout Standard
35538 Both problems can be solved by inserting at the end of the section heading
35539 a short title with the menu
35541 Insert\SpecialChar \menuseparator
35543 \begin_inset space ~
35549 Short titles are used as alternative for multiline section headings to
35550 keep the table of contents clearly arranged.
35551 Only the short title appears in the table of contents and therefore also
35552 in the PDF-bookmark.
35555 \begin_layout Standard
35556 When formulas should be used in the table of contents but
35560 is used, one can use the following command in TeX-mode:
35563 \begin_layout Standard
35568 texorpdfstring{part}{alternative}
35569 \begin_inset Index idx
35572 \begin_layout Plain Layout
35583 \begin_layout Standard
35584 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35585 This can be characters, formulas, footnotes, but also cross-references.
35586 The alternative is used instead of the part for the bookmark.
35589 \begin_layout Standard
35590 Here are two example headings:
35591 \begin_inset VSpace -3mm
35598 \begin_layout Plain Layout
35610 \begin_layout Subsubsection
35611 Heading without formula in table of contents
35612 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35616 \begin_inset Argument
35619 \begin_layout Plain Layout
35620 Heading without formula in table of contents
35628 \begin_layout Subsubsection
35629 Heading with formula in table of contents
35633 \begin_layout Plain Layout
35643 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35650 \begin_layout Plain Layout
35660 \begin_layout Standard
35664 \begin_layout Plain Layout
35673 In the first heading a short title was used, in the second one
35682 \begin_layout Standard
35683 To get the same formatting as for the other headings, the complete heading
35692 \begin_layout Plain Layout
35694 \begin_inset CommandInset ref
35696 reference "sub:Bold-Formulas"
35708 \begin_layout Subsection
35709 Formulas in multi-column Text
35710 \begin_inset Index idx
35713 \begin_layout Plain Layout
35714 Formula ! in multi-column text
35722 \begin_layout Standard
35723 Formulas in multi-column text are often too wide to fit into a column and
35724 thus need to be set over the whole page width.
35725 This is done by using the LaTeX-package
35733 \begin_layout Plain Layout
35738 is part of every LaTeX standard installation.
35744 \begin_inset Index idx
35747 \begin_layout Plain Layout
35748 Packages ! multicol
35753 , that is loaded with the LaTeX-preamble line
35756 \begin_layout Standard
35761 usepackage{multicol}
35764 \begin_layout Standard
35765 \begin_inset Note Greyedout
35768 \begin_layout Plain Layout
35769 Note herby that the setting
35772 \begin_inset space ~
35779 Document\SpecialChar \menuseparator
35785 \begin_inset space ~
35805 \begin_layout Standard
35806 Before the multi-column text the command
35809 \begin_layout Standard
35814 begin{multicols}{column number}
35817 \begin_layout Standard
35818 is written in TeX-mode.
35819 The column number is a number in the range of 2
35820 \begin_inset space \thinspace{}
35824 \begin_inset space \thinspace{}
35828 Before the formula the multi-column text is ended by inserting the command
35831 \begin_layout Standard
35839 \begin_layout Standard
35843 \begin_layout Standard
35844 Due to the command some space is automatically added before the formula.
35846 \begin_inset space \thinspace{}
35849 mm vertical space is inserted before the formula.
35850 When the formula style
35856 \begin_layout Plain Layout
35858 \begin_inset CommandInset ref
35860 reference "sec:Formula-Styles"
35872 \begin_inset space \thinspace{}
35875 mm space is inserted instead.
35878 \begin_layout Standard
35879 As example a multi-column text with a displayed formula:
35882 \begin_layout Standard
35888 \begin_layout Plain Layout
35892 begin{multicols}{2}
35897 Das Spektrum wird fouriertransformiert.
35898 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35899 , Lösungsmittel) zu trennen.
35900 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35901 nun das Aussehen des Ausgangssignals.
35902 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35903 über alle Phasen integrieren muss.
35905 \begin_inset Formula $S$
35908 unser normiertes Ausgangssignal und
35909 \begin_inset Formula $P$
35912 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35916 \begin_layout Plain Layout
35926 \begin_inset VSpace -6mm
35930 \begin_inset Formula \begin{equation}
35931 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
35939 \begin_layout Plain Layout
35943 begin{multicols}{2}
35949 \begin_inset Formula $S_{0}$
35952 das Signal ohne Gradient ist und die Normierungsbedingung
35953 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35957 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35959 \begin_inset Formula $\nicefrac{\pi}{2}$
35963 \begin_inset space \thinspace{}
35966 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35967 das Signal zusätzlich abschwächt.
35968 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35970 \begin_inset Formula $T_{2}$
35976 \begin_layout Standard
35982 \begin_layout Plain Layout
35994 \begin_layout Subsection
35995 Formulas with Description of Variables
35996 \begin_inset Index idx
35999 \begin_layout Plain Layout
36000 Formula ! with description of variables
36008 \begin_layout Standard
36009 To describe variables within a formula, like in formula
36010 \begin_inset CommandInset ref
36012 reference "eq:within"
36021 \begin_inset Formula $n$
36025 \begin_inset space ~
36028 matrix is used with left aligned columns for the
36029 \begin_inset Formula $n$
36036 \begin_layout Plain Layout
36038 \begin_inset CommandInset ref
36040 reference "sec:Matrices"
36049 To set the description in a smaller size, before the matrix e.
36050 \begin_inset space \thinspace{}
36054 \begin_inset space \space{}
36067 \begin_layout Plain Layout
36069 \begin_inset CommandInset ref
36071 reference "sub:Font-Sizes"
36083 \begin_layout Standard
36084 When the formula style
36090 \begin_layout Plain Layout
36092 \begin_inset CommandInset ref
36094 reference "sec:Formula-Styles"
36115 \begin_layout Plain Layout
36122 only works in formulas with the style
36127 \begin_inset CommandInset ref
36129 reference "sub:Variable-Space"
36138 is inserted before and after the matrix to have the same separation of
36139 the matrix from the equation and the side margin.
36142 \begin_layout Standard
36143 When the formula style
36147 is used, the method described in
36148 \begin_inset CommandInset ref
36150 reference "sub:Flalign-Environment"
36154 is used to indent formulas.
36156 \begin_inset CommandInset ref
36158 reference "eq:within"
36162 consists of five columns whereas in the first two columns contain the equation,
36163 the third the matrix and the last one an empty TeX-brace.
36164 \begin_inset Formula \begin{flalign}
36165 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36166 \rho & \textrm{density}\\
36167 V & \textrm{volume}\\
36168 g & \textrm{gravitational acceleration}
36169 \end{array} & & {}\label{eq:within}\end{flalign}
36176 \begin_layout Subsection
36177 Upright small Greek Letters
36178 \begin_inset CommandInset label
36180 name "sub:Upright-small-Greek"
36185 \begin_inset Index idx
36188 \begin_layout Plain Layout
36189 Greek letters ! upright
36197 \begin_layout Standard
36198 Most of the math fonts only provide italic small Greek letters.
36199 But for symbols of elementary particles like pions and neutrinos, upright
36200 Greek letters are needed.
36209 \begin_layout Plain Layout
36214 is part of the LaTeX-package
36219 \begin_inset Index idx
36222 \begin_layout Plain Layout
36227 \begin_layout Plain Layout
36247 \begin_inset Index idx
36250 \begin_layout Plain Layout
36256 that is loaded with the LaTeX-preamble line
36259 \begin_layout Standard
36264 usepackage{upgreek}
36267 \begin_layout Standard
36273 \begin_layout Plain Layout
36283 \begin_inset Note Note
36286 \begin_layout Plain Layout
36287 The following table will only be displayed when the LaTeX-package
36296 They are created when the command for a small Greek letters is started
36302 For example the command
36309 \begin_inset Formula $\uptau$
36315 \begin_layout Standard
36316 With these commands reactions of elementary particles can be typeset:
36317 \begin_inset Formula \[
36318 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
36325 \begin_layout Standard
36326 The upright letters are more bold and wider than the italic ones.
36327 They should therefore not be used for units like
36328 \begin_inset Quotes eld
36332 \begin_inset Quotes erd
36338 \begin_layout Standard
36342 \begin_layout Plain Layout
36352 \begin_inset Note Note
36355 \begin_layout Plain Layout
36356 The following will be displayed when the LaTeX-package
36368 \begin_layout Standard
36369 You need to install the LaTeX-package
36373 to see the rest of this subsection in the output.
36376 \begin_layout Standard
36380 \begin_layout Plain Layout
36392 \begin_layout Subsection
36393 Text Characters in Formulas
36394 \begin_inset CommandInset label
36396 name "sub:Text-Characters-in"
36401 \begin_inset Index idx
36404 \begin_layout Plain Layout
36413 \begin_layout Standard
36414 In some cases you might want to insert text characters directly into formulas.
36415 When for example the centered dot · is often used in formulas like
36416 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36419 , one would have to insert the command
36429 \begin_layout Plain Layout
36431 \begin_inset CommandInset ref
36433 reference "sub:Binary-Operators"
36442 all the time, because this character is defined in all encodings as text
36444 But the encoding can be changed by this LaTeX-preamble line:
36447 \begin_layout Standard
36452 Declare Inputtext{183}{
36462 f\SpecialChar \textcompwordmark{}
36466 \begin_layout Standard
36467 The character encoding (menu
36469 Document\SpecialChar \menuseparator
36470 Settings\SpecialChar \menuseparator
36473 ) specifies what character appears when a keyboard key is pressed.
36474 When the key for the character '·' is pressed, internally the command
36481 But this command is not available in a formula so that you would get LaTeX-erro
36483 With the changed encoding the right command is chosen automatically, depending
36484 on if the character was inserted into a formula or not.
36487 \begin_layout Standard
36488 The encoding of several characters is saved in definition files.
36489 Fore example the encoding
36493 is defined in the file
36497 that is in the installation folder of LaTeX.
36498 Encodings should only be changed via the LaTeX-preamble and not in the
36500 Otherwise own documents could not be edited by other LyX users working
36501 on other computers.
36504 \begin_layout Standard
36505 \begin_inset VSpace medskip
36508 Besides the centered dot, in this document the degree sign ° is defined
36509 with the following LaTeX-preamble line so that it can directly be inserted
36513 \begin_layout Standard
36518 DeclareInputtext{176}{
36528 f\SpecialChar \textcompwordmark{}
36532 \begin_layout Standard
36533 \begin_inset Newpage newpage
36539 \begin_layout Section
36542 \begin_inset Index idx
36545 \begin_layout Plain Layout
36554 \begin_layout Standard
36555 This section is a summary of the most important typographic rules, listed
36560 \begin_layout Plain Layout
36561 This collection was partly taken from the German semi-official dictionary
36563 \begin_inset Quotes eld
36567 \begin_inset Quotes erd
36571 \begin_inset CommandInset citation
36577 that lists some of the ISO rules.
36578 More rules are listed in
36579 \begin_inset CommandInset citation
36593 \begin_layout Itemize
36602 \begin_layout Plain Layout
36603 done with font styles, see
36604 \begin_inset CommandInset ref
36606 reference "sub:Font-Styles"
36615 , no matter if they appear in italic text: 30
36616 \begin_inset space \thinspace{}
36620 \begin_inset Newline newline
36623 Between the value and the unit is the smallest space, see
36624 \begin_inset CommandInset ref
36626 reference "sub:Predefined-Space"
36631 \begin_inset Newline newline
36634 This convention is automatically fulfilled when the command
36641 When it is entered to a formula, two boxes appear.
36642 In the first one the value is inserted, in the second one the unit, and
36644 \begin_inset Formula $\unit[30]{km/h}$
36648 \begin_inset space \thinspace{}
36658 is not a real LaTeX command but the command
36664 , therefore you cannot use it in TeX code.
36667 \begin_layout Itemize
36668 Percent and perthousand signs are set like physical units:
36669 \begin_inset Newline newline
36673 \begin_inset space \thinspace{}
36679 \begin_layout Itemize
36680 The degree sign follows directly on the value: 15°, but not when it is used
36682 \begin_inset space \thinspace{}
36688 \begin_layout Itemize
36689 In numbers with more than four digits the smallest space is inserted before
36690 every third digit to group them:
36700 \begin_inset space \thinspace{}
36704 \begin_inset space \thinspace{}
36710 \begin_layout Itemize
36711 For dimensions like 120×90×40
36712 \begin_inset space \thinspace{}
36715 cm the multiplication sign
36716 \begin_inset Quotes eld
36720 \begin_inset Quotes erd
36724 It is available either via the command
36732 Insert\SpecialChar \menuseparator
36733 Special Character\SpecialChar \menuseparator
36739 \begin_layout Itemize
36740 Functions with names consisting of several letters are set upright to avoid
36742 \begin_inset CommandInset ref
36744 reference "sub:Predefined-Functions"
36751 \begin_layout Itemize
36752 Indices consisting of several letters, are set upright:
36753 \begin_inset Formula $E_{\mathrm{kin}}$
36757 \begin_inset Newline newline
36760 Components of matrices are set italic:
36761 \begin_inset Formula $\hat{H}_{kl}$
36767 \begin_layout Itemize
36768 The differentiation/integration operator 'd', the Euler's number 'e' and
36769 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36773 \begin_layout Itemize
36774 The character that denotes a
36778 transformation is inserted either by the command
36786 \begin_layout Plain Layout
36799 Insert\SpecialChar \menuseparator
36800 Special Character\SpecialChar \menuseparator
36801 Symbols\SpecialChar \menuseparator
36803 \begin_inset space ~
36809 \begin_inset Formula $\mathscr{F}$
36815 \begin_layout Standard
36816 \begin_inset Newpage newpage
36822 \begin_layout Section
36824 \begin_inset Index idx
36827 \begin_layout Plain Layout
36836 \begin_layout Standard
36837 Some characters and symbols can be created with several commands.
36838 Here is a list of the synonym commands:
36841 \begin_layout Standard
36842 \begin_inset VSpace bigskip
36846 \begin_inset space \hfill{}
36850 \begin_inset Tabular
36851 <lyxtabular version="3" rows="12" columns="2">
36852 <features tabularvalignment="middle">
36853 <column alignment="center" valignment="top" width="0pt">
36854 <column alignment="center" valignment="top" width="0pt">
36856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36859 \begin_layout Plain Layout
36865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36868 \begin_layout Plain Layout
36870 \begin_inset Note Note
36873 \begin_layout Plain Layout
36880 is only used as spacer.
36892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36895 \begin_layout Plain Layout
36903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36906 \begin_layout Plain Layout
36910 \begin_layout Plain Layout
36923 \begin_layout Plain Layout
36937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36940 \begin_layout Plain Layout
36948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36951 \begin_layout Plain Layout
36961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36964 \begin_layout Plain Layout
36972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36975 \begin_layout Plain Layout
36985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36988 \begin_layout Plain Layout
36996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36999 \begin_layout Plain Layout
37007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37010 \begin_layout Plain Layout
37018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37021 \begin_layout Plain Layout
37029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37032 \begin_layout Plain Layout
37040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37043 \begin_layout Plain Layout
37053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37056 \begin_layout Plain Layout
37064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37067 \begin_layout Plain Layout
37077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37080 \begin_layout Plain Layout
37088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37091 \begin_layout Plain Layout
37101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37104 \begin_layout Plain Layout
37112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37115 \begin_layout Plain Layout
37125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37128 \begin_layout Plain Layout
37136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37139 \begin_layout Plain Layout
37147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37150 \begin_layout Plain Layout
37158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37161 \begin_layout Plain Layout
37173 \begin_inset space \hfill{}
37177 \begin_inset Tabular
37178 <lyxtabular version="3" rows="12" columns="2">
37179 <features tabularvalignment="middle">
37180 <column alignment="center" valignment="top" width="0pt">
37181 <column alignment="center" valignment="top" width="0pt">
37183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37186 \begin_layout Plain Layout
37192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37195 \begin_layout Plain Layout
37203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37206 \begin_layout Plain Layout
37214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37217 \begin_layout Plain Layout
37229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37232 \begin_layout Plain Layout
37240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37243 \begin_layout Plain Layout
37253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37256 \begin_layout Plain Layout
37264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37267 \begin_layout Plain Layout
37277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37280 \begin_layout Plain Layout
37288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37291 \begin_layout Plain Layout
37299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37302 \begin_layout Plain Layout
37310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37313 \begin_layout Plain Layout
37321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37324 \begin_layout Plain Layout
37332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37335 \begin_layout Plain Layout
37345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37348 \begin_layout Plain Layout
37356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37359 \begin_layout Plain Layout
37369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37372 \begin_layout Plain Layout
37380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37383 \begin_layout Plain Layout
37393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37396 \begin_layout Plain Layout
37404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37407 \begin_layout Plain Layout
37417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37420 \begin_layout Plain Layout
37428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37431 \begin_layout Plain Layout
37441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37444 \begin_layout Plain Layout
37452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37455 \begin_layout Plain Layout
37469 \begin_inset space \hfill{}
37475 \begin_layout Standard
37476 \begin_inset Newpage newpage
37482 \begin_layout Bibliography
37483 \labelwidthstring References
37484 \begin_inset CommandInset bibitem
37485 LatexCommand bibitem
37497 The LaTeX Companion
37500 Addison Wesley, 2004
37503 \begin_layout Bibliography
37504 \labelwidthstring References
37505 \begin_inset CommandInset bibitem
37506 LatexCommand bibitem
37512 \begin_inset CommandInset href
37515 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37519 of LaTeX's math abilities
37522 \begin_layout Bibliography
37523 \labelwidthstring References
37524 \begin_inset CommandInset bibitem
37525 LatexCommand bibitem
37531 \begin_inset CommandInset href
37534 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37542 \begin_layout Plain Layout
37554 \begin_layout Bibliography
37555 \labelwidthstring References
37556 \begin_inset CommandInset bibitem
37557 LatexCommand bibitem
37563 \begin_inset CommandInset href
37566 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37570 of all symbols available with LaTeX-packages
37573 \begin_layout Bibliography
37574 \labelwidthstring References
37575 \begin_inset CommandInset bibitem
37576 LatexCommand bibitem
37582 \begin_inset CommandInset href
37584 name "Documentation"
37585 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37589 of the LaTeX-package
37594 \begin_inset Index idx
37597 \begin_layout Plain Layout
37598 Packages ! hyperref
37606 \begin_layout Bibliography
37607 \labelwidthstring References
37608 \begin_inset CommandInset bibitem
37609 LatexCommand bibitem
37615 \begin_inset CommandInset href
37617 name "Documentation"
37618 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37622 of the LaTeX-package
37627 \begin_inset Index idx
37630 \begin_layout Plain Layout
37639 \begin_layout Bibliography
37640 \labelwidthstring References
37641 \begin_inset CommandInset bibitem
37642 LatexCommand bibitem
37648 \begin_inset CommandInset href
37651 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
37662 \begin_inset CommandInset ref
37664 reference "sub:Operator-Limits"
37669 \begin_inset Index idx
37672 \begin_layout Plain Layout
37683 \begin_layout Bibliography
37684 \labelwidthstring References
37685 \begin_inset CommandInset bibitem
37686 LatexCommand bibitem
37697 Auflage, Duden 2001
37700 \begin_layout Bibliography
37701 \labelwidthstring References
37702 \begin_inset CommandInset bibitem
37703 LatexCommand bibitem
37709 \begin_inset CommandInset href
37712 target "http://physics.nist.gov/Document/checklist.pdf"
37716 for reviewing manuscripts
37719 \begin_layout Standard
37720 \begin_inset CommandInset index_print
37721 LatexCommand printindex