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 bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
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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190 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
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 In the matrix dialog you can specify the number of columns and rows, the
5137 alignment and the decoration.
5138 The vertical alignment is hereby only of importance for matrices in inline
5142 \begin_layout Standard
5143 The first matrix is top
5144 \begin_inset Formula $\begin{array}[t]{cccc}
5152 \begin_inset Formula $\begin{array}{cccc}
5159 and the third bottom
5160 \begin_inset Formula $\begin{array}[b]{cccc}
5170 \begin_layout Standard
5171 The horizontal alignment specifies how the column entries should be aligned.
5172 It is set by entering a letter for every column.
5177 denotes left aligned,
5186 To create for example a 4
5191 \begin_inset space ~
5194 matrix where the first column is left aligned, the second and third are
5195 centered and the last one is right aligned, one enters for the horizontal
5201 Normally are in a matrix all columns centered, therefore the default is
5202 for every column is a
5209 \begin_layout Standard
5210 Horizontal alignment:
5213 \begin_layout Standard
5219 \begin_inset Formula $\begin{array}{lll}
5231 \begin_inset Formula $\begin{array}{ccc}
5243 \begin_inset Formula $\begin{array}{rrr}
5253 \begin_layout Standard
5254 To add or delete rows and columns subsequently, the math toolbar buttons
5256 \begin_inset Graphics
5257 filename ../images/tabular-feature_append-row.png
5263 \begin_inset Graphics
5264 filename ../images/tabular-feature_delete-row.png
5270 \begin_inset space \thinspace{}
5275 Edit\SpecialChar \menuseparator
5279 New rows can also be created with
5282 arg "newline-insert newline"
5288 \begin_layout Standard
5289 \begin_inset VSpace bigskip
5296 adds parentheses in the selected style around the matrix.
5297 Alternatively, parentheses can can either be created with the commands
5305 \begin_inset Index idx
5308 \begin_layout Plain Layout
5323 \begin_inset Index idx
5326 \begin_layout Plain Layout
5337 \begin_inset space ~
5343 \begin_inset CommandInset ref
5345 reference "sub:Automatic-Bracket-Size"
5349 , or by using the following commands:
5350 \begin_inset VSpace medskip
5356 \begin_layout Standard
5357 \begin_inset space \hfill{}
5361 \begin_inset Tabular
5362 <lyxtabular version="3" rows="4" columns="2">
5363 <features tabularvalignment="middle">
5364 <column alignment="center" valignment="top" width="0">
5365 <column alignment="center" valignment="top" width="0">
5367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5370 \begin_layout Plain Layout
5376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5379 \begin_layout Plain Layout
5381 \begin_inset Note Note
5384 \begin_layout Plain Layout
5391 is only used as spacer.
5403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5406 \begin_layout Plain Layout
5413 \begin_layout Plain Layout
5427 \begin_inset space \thinspace{}
5435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5438 \begin_layout Plain Layout
5439 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5440 0 & \textrm{-}\mathrm{i}\\
5442 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5455 \begin_layout Plain Layout
5462 \begin_layout Plain Layout
5476 \begin_inset space \thinspace{}
5484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5487 \begin_layout Plain Layout
5488 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5489 0 & \textrm{-}\mathrm{i}\\
5491 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5504 \begin_layout Plain Layout
5511 \begin_layout Plain Layout
5525 \begin_inset space \thinspace{}
5533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5536 \begin_layout Plain Layout
5537 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5538 0 & \textrm{-}\mathrm{i}\\
5540 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5554 \begin_inset space \hfill{}
5558 \begin_inset Tabular
5559 <lyxtabular version="3" rows="4" columns="2">
5560 <features tabularvalignment="middle">
5561 <column alignment="center" valignment="top" width="0">
5562 <column alignment="center" valignment="top" width="0">
5564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5567 \begin_layout Plain Layout
5573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5576 \begin_layout Plain Layout
5584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5587 \begin_layout Plain Layout
5594 \begin_layout Plain Layout
5608 \begin_inset space \thinspace{}
5616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5619 \begin_layout Plain Layout
5620 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5621 0 & \textrm{-}\mathrm{i}\\
5623 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5636 \begin_layout Plain Layout
5643 \begin_layout Plain Layout
5657 \begin_inset space \thinspace{}
5665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5668 \begin_layout Plain Layout
5669 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5670 0 & \textrm{-}\mathrm{i}\\
5672 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5685 \begin_layout Plain Layout
5692 \begin_layout Plain Layout
5706 \begin_inset space \thinspace{}
5714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5717 \begin_layout Plain Layout
5718 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5719 0 & \textrm{-}\mathrm{i}\\
5721 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5735 \begin_inset space \hfill{}
5741 \begin_layout Standard
5742 \begin_inset VSpace medskip
5746 \begin_inset space \thinspace{}
5750 \begin_inset space \space{}
5759 is inserted, a blue box appears between two vertical lines where the matrix
5761 \begin_inset Newline newline
5764 Note that decorated matrices ignore the vertical alignment.
5767 \begin_layout Standard
5768 \begin_inset VSpace bigskip
5771 As all multiline formulas are matrices, the length
5778 \begin_inset Index idx
5781 \begin_layout Plain Layout
5789 that is described in
5790 \begin_inset CommandInset ref
5792 reference "sub:Column-Separation"
5796 can also be used to change the column separation of matrices.
5799 \begin_layout Standard
5800 To change the row separation, the command
5807 \begin_inset Index idx
5810 \begin_layout Plain Layout
5819 It is used as follows:
5822 \begin_layout Standard
5829 arraystretch}{stretch factor}
5830 \begin_inset Index idx
5833 \begin_layout Plain Layout
5844 \begin_layout Standard
5851 assigns the stretch factor to the predefined command
5859 \begin_inset space \thinspace{}
5863 \begin_inset space \space{}
5866 the row separation, use the factor 2.
5867 This is then used for all following matrices.
5868 To go back to the original separation, assign the factor 1 to
5877 \begin_layout Standard
5878 To set matrices into a text line, the command
5885 \begin_inset Index idx
5888 \begin_layout Plain Layout
5897 When it is inserted a blue box with two dashed lines appears.
5898 In this box the matrix is inserted.
5901 \begin_layout Standard
5903 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5905 \end{smallmatrix}\right)$
5911 \begin_layout Section
5912 Brackets and Delimiters
5913 \begin_inset Index idx
5916 \begin_layout Plain Layout
5923 \begin_inset Index idx
5926 \begin_layout Plain Layout
5935 \begin_layout Subsection
5936 Vertical Brackets and Delimiters
5937 \begin_inset Index idx
5940 \begin_layout Plain Layout
5949 \begin_layout Standard
5950 \begin_inset space \hfill{}
5954 \begin_inset Tabular
5955 <lyxtabular version="3" rows="9" columns="2">
5956 <features tabularvalignment="middle">
5957 <column alignment="center" valignment="top" width="0pt">
5958 <column alignment="center" valignment="top" width="0pt">
5960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5963 \begin_layout Plain Layout
5969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5972 \begin_layout Plain Layout
5980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5983 \begin_layout Plain Layout
5989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5992 \begin_layout Plain Layout
5993 \begin_inset Formula $($
6003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6006 \begin_layout Plain Layout
6012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6015 \begin_layout Plain Layout
6016 \begin_inset Formula $\{$
6026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6029 \begin_layout Plain Layout
6035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6038 \begin_layout Plain Layout
6039 \begin_inset Formula $[$
6049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6052 \begin_layout Plain Layout
6060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6063 \begin_layout Plain Layout
6064 \begin_inset Formula $\langle$
6074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6077 \begin_layout Plain Layout
6085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6088 \begin_layout Plain Layout
6089 \begin_inset Formula $\lceil$
6099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6102 \begin_layout Plain Layout
6110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6113 \begin_layout Plain Layout
6114 \begin_inset Formula $\lfloor$
6124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6127 \begin_layout Plain Layout
6133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6136 \begin_layout Plain Layout
6137 \begin_inset Formula $/$
6147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6150 \begin_layout Plain Layout
6156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6159 \begin_layout Plain Layout
6160 \begin_inset Formula $|$
6174 \begin_inset space \hfill{}
6178 \begin_inset Tabular
6179 <lyxtabular version="3" rows="9" columns="2">
6180 <features tabularvalignment="middle">
6181 <column alignment="center" valignment="top" width="0pt">
6182 <column alignment="center" valignment="top" width="0pt">
6184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6187 \begin_layout Plain Layout
6193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6196 \begin_layout Plain Layout
6204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6207 \begin_layout Plain Layout
6213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6216 \begin_layout Plain Layout
6217 \begin_inset Formula $)$
6227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6230 \begin_layout Plain Layout
6236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6239 \begin_layout Plain Layout
6240 \begin_inset Formula $\}$
6250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6253 \begin_layout Plain Layout
6259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6262 \begin_layout Plain Layout
6263 \begin_inset Formula $]$
6273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6276 \begin_layout Plain Layout
6284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6287 \begin_layout Plain Layout
6288 \begin_inset Formula $\rangle$
6298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6301 \begin_layout Plain Layout
6309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6312 \begin_layout Plain Layout
6313 \begin_inset Formula $\rceil$
6323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6326 \begin_layout Plain Layout
6334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6337 \begin_layout Plain Layout
6338 \begin_inset Formula $\rfloor$
6348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6351 \begin_layout Plain Layout
6361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6364 \begin_layout Plain Layout
6365 \begin_inset Formula $\backslash$
6375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6378 \begin_layout Plain Layout
6386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6389 \begin_layout Plain Layout
6390 \begin_inset Formula $\|$
6404 \begin_inset space \hfill{}
6410 \begin_layout Standard
6413 \begin_inset Note Greyedout
6416 \begin_layout Plain Layout
6421 In TeX-mode the command
6428 \begin_inset Index idx
6431 \begin_layout Plain Layout
6439 must be used for the backslash, because the command
6447 produces there a line break.
6455 \begin_layout Standard
6456 For all characters listed above the size can be adjusted with the commands
6457 described in the following two subsections.
6458 When using these commands, the characters < and > can directly be used
6459 instead of the commands
6474 \begin_layout Subsubsection
6476 \begin_inset CommandInset label
6478 name "sub:Manual-Bracket-Size"
6483 \begin_inset Index idx
6486 \begin_layout Plain Layout
6487 Bracket size ! manual
6495 \begin_layout Standard
6496 The bracket size can be specified manually by the LaTeX-commands
6503 \begin_inset Index idx
6506 \begin_layout Plain Layout
6539 denotes the smallest and
6545 the largest bracket size.
6548 \begin_layout Standard
6549 These commands are used to emphasize levels of brackets:
6552 \begin_layout Standard
6554 \begin_inset Tabular
6555 <lyxtabular version="3" rows="2" columns="2">
6556 <features tabularvalignment="middle">
6557 <column alignment="center" valignment="top" width="0pt">
6558 <column alignment="center" valignment="top" width="0pt">
6560 <cell alignment="center" valignment="top" usebox="none">
6563 \begin_layout Plain Layout
6564 all brackets in the same size:
6569 <cell alignment="center" valignment="top" usebox="none">
6572 \begin_layout Plain Layout
6573 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6583 <cell alignment="center" valignment="top" usebox="none">
6586 \begin_layout Plain Layout
6592 <cell alignment="center" valignment="top" usebox="none">
6595 \begin_layout Plain Layout
6596 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6610 \begin_inset Note Note
6613 \begin_layout Plain Layout
6620 is only used as spacer.
6628 \begin_layout Standard
6629 For the second formula the command
6639 \begin_layout Plain Layout
6653 \begin_layout Standard
6654 Here is an overview about all bracket sizes:
6657 \begin_layout Standard
6677 \begin_layout Plain Layout
6694 \begin_layout Plain Layout
6707 \begin_layout Plain Layout
6723 \begin_layout Standard
6725 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6731 \begin_layout Standard
6738 -commands there is the variant
6745 \begin_inset Index idx
6748 \begin_layout Plain Layout
6756 that adds a bit more space between the bracket and its content, and the
6770 \begin_inset Index idx
6773 \begin_layout Plain Layout
6783 , that don't add additional space.
6788 at the end of the command
6794 is for a left bracket; for a right bracket this will be replaced by an
6800 A left or right bracket can each be an opening or closing bracket.
6803 \begin_layout Standard
6804 In the following table is a comparison of the variants:
6807 \begin_layout Standard
6809 \begin_inset Tabular
6810 <lyxtabular version="3" rows="5" columns="2">
6811 <features tabularvalignment="middle">
6812 <column alignment="center" valignment="middle" width="0">
6813 <column alignment="center" valignment="middle" width="0">
6815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6818 \begin_layout Plain Layout
6824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6827 \begin_layout Plain Layout
6829 \begin_inset Note Note
6832 \begin_layout Plain Layout
6839 is only used as spacer.
6851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6854 \begin_layout Plain Layout
6869 \begin_layout Plain Layout
6887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6890 \begin_layout Plain Layout
6891 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6904 \begin_layout Plain Layout
6919 \begin_layout Plain Layout
6937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6940 \begin_layout Plain Layout
6941 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6954 \begin_layout Plain Layout
6969 \begin_layout Plain Layout
6987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6990 \begin_layout Plain Layout
6991 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7004 \begin_layout Plain Layout
7016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7019 \begin_layout Plain Layout
7020 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7036 \begin_layout Subsubsection
7037 Automatic Bracket Size
7038 \begin_inset CommandInset label
7040 name "sub:Automatic-Bracket-Size"
7045 \begin_inset Index idx
7048 \begin_layout Plain Layout
7049 Bracket size ! automatic
7057 \begin_layout Standard
7058 Brackets with variable size can be inserted with the commands
7065 \begin_inset Index idx
7068 \begin_layout Plain Layout
7083 \begin_inset Index idx
7086 \begin_layout Plain Layout
7094 or via the math toolbar button
7095 \begin_inset Graphics
7096 filename ../images/dialog-show_mathdelimiter.png
7114 the wanted bracket must be inserted.
7115 The bracket size will then automatically be calculated for the output.
7118 \begin_layout Standard
7120 normal bracket: The command
7130 \begin_layout Plain Layout
7140 \begin_inset Formula $\downarrow$
7147 \begin_layout Plain Layout
7159 \begin_inset Formula \[
7167 \begin_layout Standard
7169 multiline bracket: The command
7181 \begin_layout Plain Layout
7191 \begin_inset Formula $\downarrow$
7198 \begin_layout Plain Layout
7212 \begin_inset Formula \[
7213 \ln\left(\frac{A}{C}\right)\]
7220 \begin_layout Standard
7236 \begin_inset space ~
7242 This has the advantage that you can see in LyX immediately the real bracket
7243 size and that the matching right bracket will be created too.
7244 \begin_inset Newline newline
7247 The command for the last example would then be:
7261 \begin_layout Plain Layout
7271 \begin_inset Formula $\downarrow$
7277 \begin_layout Standard
7278 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7279 For example the command
7289 \begin_layout Plain Layout
7299 \begin_inset Formula $\downarrow$
7306 \begin_layout Plain Layout
7322 \begin_inset Formula \[
7323 \left.\frac{A}{B}\right\} \]
7341 will be converted by LyX to brackets in the right size when the document
7342 is reloaded and an omitted bracket will appear as dashed line.
7345 \begin_layout Standard
7346 \begin_inset VSpace bigskip
7349 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7357 \begin_inset Index idx
7360 \begin_layout Plain Layout
7368 is additionally available for all brackets and limits.
7369 With this command the height of the following character is adapted to the
7370 one of the surrounding brackets, what is e.
7371 \begin_inset space \thinspace{}
7375 \begin_inset space \space{}
7378 needed for physical vectors:
7379 \begin_inset Formula \[
7380 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7384 For physical vectors there is a special LaTeX-package, described in
7385 \begin_inset CommandInset ref
7387 reference "sub:Physical-Vectors"
7394 \begin_layout Subsection
7396 \begin_inset Index idx
7399 \begin_layout Plain Layout
7400 Brackets ! horizontal
7408 \begin_layout Standard
7410 \begin_inset Tabular
7411 <lyxtabular version="3" rows="4" columns="2">
7412 <features tabularvalignment="middle">
7413 <column alignment="center" valignment="top" width="0pt">
7414 <column alignment="center" valignment="top" width="0pt">
7416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7419 \begin_layout Plain Layout
7421 \begin_inset Note Note
7424 \begin_layout Plain Layout
7431 is only used as spacer.
7441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7444 \begin_layout Plain Layout
7452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7455 \begin_layout Plain Layout
7459 \begin_layout Plain Layout
7474 \begin_layout Plain Layout
7487 \begin_layout Plain Layout
7500 \begin_layout Plain Layout
7513 \begin_layout Plain Layout
7521 \begin_inset Index idx
7524 \begin_layout Plain Layout
7537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7540 \begin_layout Plain Layout
7541 \begin_inset Formula $\overbrace{A+B}^{3}$
7551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7554 \begin_layout Plain Layout
7558 \begin_layout Plain Layout
7573 \begin_layout Plain Layout
7586 \begin_layout Plain Layout
7599 \begin_layout Plain Layout
7607 \begin_inset Index idx
7610 \begin_layout Plain Layout
7623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7626 \begin_layout Plain Layout
7627 \begin_inset Formula $\underbrace{A+B}_{5}$
7637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7640 \begin_layout Plain Layout
7647 \begin_layout Plain Layout
7662 \begin_layout Plain Layout
7675 \begin_layout Plain Layout
7688 \begin_layout Plain Layout
7701 \begin_layout Plain Layout
7714 \begin_layout Plain Layout
7727 \begin_layout Plain Layout
7741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7744 \begin_layout Plain Layout
7745 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7761 \begin_layout Standard
7762 In the last example it doesn't matter if
7774 is inserted at first.
7777 \begin_layout Standard
7778 \begin_inset VSpace bigskip
7781 When brackets are needed that overlap each other, multiline formulas, as
7783 \begin_inset CommandInset ref
7785 reference "sec:Multiline-Formulas"
7790 \begin_inset Formula \begin{eqnarray*}
7791 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7792 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7797 In the first row the formula is inserted together with the first brace.
7798 It is hereby important that the space command
7802 \begin_layout Plain Layout
7803 Space commands are explained in
7804 \begin_inset CommandInset ref
7806 reference "sub:Predefined-Space"
7821 is inserted before the first
7822 \begin_inset Formula $d$
7825 , because the brace that ends behind the
7826 \begin_inset Formula $q$
7829 prevents that the following
7830 \begin_inset Quotes eld
7834 \begin_inset Quotes erd
7837 is surrounded by space.
7841 \begin_layout Plain Layout
7842 because a bracket is not handled as character, see
7843 \begin_inset CommandInset ref
7845 reference "sub:Binary-Operators"
7854 In the second row the second brace is inserted.
7855 As it should begin before the
7856 \begin_inset Formula $b$
7871 \begin_layout Plain Layout
7879 \begin_inset CommandInset ref
7881 reference "sub:Placeholders"
7890 This space is needed because the
7891 \begin_inset Quotes eld
7895 \begin_inset Quotes erd
7898 is also surrounded by space in the formula.
7899 The brace is placed under the command
7908 \begin_layout Standard
7909 It gets more complicated when brackets overlap each other, like in the following
7914 \begin_layout Plain Layout
7926 \begin_inset Formula \begin{eqnarray*}
7927 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7928 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7937 \begin_layout Plain Layout
7948 The first formula row is the same as the second row of the previous example,
7949 with the difference that the brace is above.
7950 The second row contains the formula together with the second brace.
7951 To avoid that there is space between the upper brace in the first row and
7952 the formula, the row spacing need to be reduced.
7953 This is not easily possible due to a bug in LyX
7957 \begin_layout Plain Layout
7958 \begin_inset CommandInset href
7960 name "LyX-bug #1505"
7961 target "http://www.lyx.org/trac/ticket/1505"
7971 As solution for the problem, the global formula row separation
7978 \begin_inset Index idx
7981 \begin_layout Plain Layout
7989 must be changed to -6
7990 \begin_inset space \thinspace{}
7993 pt before the formula with the command
8008 is set back after the formula to the standard value of 3
8009 \begin_inset space \thinspace{}
8012 pt using the same command.
8013 More about the row separation in formulas is explained in
8014 \begin_inset CommandInset ref
8016 reference "sub:Line-Separation"
8023 \begin_layout Section
8025 \begin_inset Index idx
8028 \begin_layout Plain Layout
8037 \begin_layout Standard
8038 Arrows can be inserted via the math toolbar button
8039 \begin_inset Graphics
8040 filename ../images/math/leftarrow.png
8045 or the commands listed in the following subsections.
8048 \begin_layout Standard
8049 \begin_inset Newpage newpage
8055 \begin_layout Subsection
8057 \begin_inset Index idx
8060 \begin_layout Plain Layout
8069 \begin_layout Standard
8070 \begin_inset space \hfill{}
8074 \begin_inset Tabular
8075 <lyxtabular version="3" rows="8" columns="2">
8076 <features tabularvalignment="middle">
8077 <column alignment="center" valignment="top" width="0pt">
8078 <column alignment="center" valignment="top" width="0pt">
8080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8083 \begin_layout Plain Layout
8089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8092 \begin_layout Plain Layout
8100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8103 \begin_layout Plain Layout
8111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8114 \begin_layout Plain Layout
8115 \begin_inset Formula $\gets$
8125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8128 \begin_layout Plain Layout
8136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8139 \begin_layout Plain Layout
8140 \begin_inset Formula $\Leftarrow$
8150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8153 \begin_layout Plain Layout
8161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8164 \begin_layout Plain Layout
8165 \begin_inset Formula $\longleftarrow$
8175 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8178 \begin_layout Plain Layout
8186 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8189 \begin_layout Plain Layout
8190 \begin_inset Formula $\Longleftarrow$
8200 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8203 \begin_layout Plain Layout
8211 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8214 \begin_layout Plain Layout
8215 \begin_inset Formula $\leftharpoonup$
8225 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8228 \begin_layout Plain Layout
8236 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8239 \begin_layout Plain Layout
8240 \begin_inset Formula $\leftharpoondown$
8250 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8253 \begin_layout Plain Layout
8261 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8264 \begin_layout Plain Layout
8265 \begin_inset Formula $\hookleftarrow$
8279 \begin_inset space \hfill{}
8283 \begin_inset Tabular
8284 <lyxtabular version="3" rows="8" columns="2">
8285 <features tabularvalignment="middle">
8286 <column alignment="center" valignment="top" width="0pt">
8287 <column alignment="center" valignment="top" width="0pt">
8289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8292 \begin_layout Plain Layout
8298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8301 \begin_layout Plain Layout
8309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8312 \begin_layout Plain Layout
8320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8323 \begin_layout Plain Layout
8324 \begin_inset Formula $\to$
8334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8337 \begin_layout Plain Layout
8345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8348 \begin_layout Plain Layout
8349 \begin_inset Formula $\Rightarrow$
8359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8362 \begin_layout Plain Layout
8370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8373 \begin_layout Plain Layout
8374 \begin_inset Formula $\longrightarrow$
8384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8387 \begin_layout Plain Layout
8395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8398 \begin_layout Plain Layout
8399 \begin_inset Formula $\Longrightarrow$
8409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8412 \begin_layout Plain Layout
8420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8423 \begin_layout Plain Layout
8424 \begin_inset Formula $\rightharpoonup$
8434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8437 \begin_layout Plain Layout
8445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8448 \begin_layout Plain Layout
8449 \begin_inset Formula $\rightharpoondown$
8459 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8462 \begin_layout Plain Layout
8470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8473 \begin_layout Plain Layout
8474 \begin_inset Formula $\hookrightarrow$
8488 \begin_inset space \hfill{}
8494 \begin_layout Standard
8495 \begin_inset space \hfill{}
8499 \begin_inset Tabular
8500 <lyxtabular version="3" rows="6" columns="2">
8501 <features tabularvalignment="middle">
8502 <column alignment="center" valignment="top" width="0pt">
8503 <column alignment="center" valignment="top" width="0pt">
8505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8508 \begin_layout Plain Layout
8514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8517 \begin_layout Plain Layout
8525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8528 \begin_layout Plain Layout
8536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8539 \begin_layout Plain Layout
8540 \begin_inset Formula $\leftrightarrow$
8550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8553 \begin_layout Plain Layout
8561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8564 \begin_layout Plain Layout
8565 \begin_inset Formula $\Leftrightarrow$
8575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8578 \begin_layout Plain Layout
8586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8589 \begin_layout Plain Layout
8590 \begin_inset Formula $\longleftrightarrow$
8600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8603 \begin_layout Plain Layout
8611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8614 \begin_layout Plain Layout
8615 \begin_inset Formula $\Longleftrightarrow$
8625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8628 \begin_layout Plain Layout
8636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8639 \begin_layout Plain Layout
8640 \begin_inset Formula $\rightleftharpoons$
8654 \begin_inset space \hspace{}
8659 \begin_inset space \hfill{}
8663 \begin_inset Tabular
8664 <lyxtabular version="3" rows="5" columns="2">
8665 <features tabularvalignment="middle">
8666 <column alignment="center" valignment="top" width="0pt">
8667 <column alignment="center" valignment="top" width="0pt">
8669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8672 \begin_layout Plain Layout
8678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8681 \begin_layout Plain Layout
8689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8692 \begin_layout Plain Layout
8700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8703 \begin_layout Plain Layout
8704 \begin_inset Formula $\mapsto$
8714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8717 \begin_layout Plain Layout
8725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8728 \begin_layout Plain Layout
8729 \begin_inset Formula $\longmapsto$
8739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8742 \begin_layout Plain Layout
8750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8753 \begin_layout Plain Layout
8754 \begin_inset Formula $\leadsto$
8764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8767 \begin_layout Plain Layout
8775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8778 \begin_layout Plain Layout
8779 \begin_inset Formula $\dasharrow$
8793 \begin_inset space \hfill{}
8799 \begin_layout Standard
8800 \begin_inset VSpace medskip
8803 Arrows used as accent like e.
8804 \begin_inset space \thinspace{}
8808 \begin_inset space \space{}
8811 vector arrows are listed in
8812 \begin_inset CommandInset ref
8814 reference "sec:Accents"
8821 \begin_layout Standard
8822 \begin_inset VSpace bigskip
8825 Furthermore there are the labeled arrows
8826 \begin_inset Index idx
8829 \begin_layout Plain Layout
8842 \begin_inset Index idx
8845 \begin_layout Plain Layout
8860 \begin_inset Index idx
8863 \begin_layout Plain Layout
8870 \begin_layout Plain Layout
8885 When inserting one of these commands in a formula, an arrow with two blue
8886 boxes appear where the label can be inserted.
8887 The length of the arrow adapts to the label width.
8890 \begin_layout Standard
8892 \begin_inset Tabular
8893 <lyxtabular version="3" rows="3" columns="2">
8894 <features tabularvalignment="middle">
8895 <column alignment="center" valignment="top" width="0pt">
8896 <column alignment="center" valignment="top" width="0pt">
8898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8901 \begin_layout Plain Layout
8907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8910 \begin_layout Plain Layout
8912 \begin_inset Note Note
8915 \begin_layout Plain Layout
8922 is only used as spacer.
8934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8937 \begin_layout Plain Layout
8944 \begin_layout Plain Layout
8954 \begin_inset Formula $\downarrow$
8958 \begin_inset Formula $\to$
8966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8969 \begin_layout Plain Layout
8970 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8983 \begin_layout Plain Layout
8990 \begin_layout Plain Layout
9000 \begin_inset Formula $\downarrow$
9004 \begin_inset Formula $\to$
9012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9015 \begin_layout Plain Layout
9016 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9032 \begin_layout Subsection
9033 Vertical and diagonal Arrows
9034 \begin_inset Index idx
9037 \begin_layout Plain Layout
9044 \begin_inset Index idx
9047 \begin_layout Plain Layout
9056 \begin_layout Standard
9057 \begin_inset space \hfill{}
9061 \begin_inset Tabular
9062 <lyxtabular version="3" rows="7" columns="2">
9063 <features tabularvalignment="middle">
9064 <column alignment="center" valignment="top" width="0pt">
9065 <column alignment="center" valignment="top" width="0pt">
9067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9070 \begin_layout Plain Layout
9076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9079 \begin_layout Plain Layout
9087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9090 \begin_layout Plain Layout
9098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9101 \begin_layout Plain Layout
9102 \begin_inset Formula $\uparrow$
9112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9115 \begin_layout Plain Layout
9123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9126 \begin_layout Plain Layout
9127 \begin_inset Formula $\Uparrow$
9137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9140 \begin_layout Plain Layout
9148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9151 \begin_layout Plain Layout
9152 \begin_inset Formula $\updownarrow$
9162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9165 \begin_layout Plain Layout
9173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9176 \begin_layout Plain Layout
9177 \begin_inset Formula $\Updownarrow$
9187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9190 \begin_layout Plain Layout
9198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9201 \begin_layout Plain Layout
9202 \begin_inset Formula $\Downarrow$
9212 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9215 \begin_layout Plain Layout
9223 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9226 \begin_layout Plain Layout
9227 \begin_inset Formula $\downarrow$
9241 \begin_inset space \hfill{}
9245 \begin_inset Tabular
9246 <lyxtabular version="3" rows="5" columns="2">
9247 <features tabularvalignment="middle">
9248 <column alignment="center" valignment="top" width="0pt">
9249 <column alignment="center" valignment="top" width="0pt">
9251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9254 \begin_layout Plain Layout
9260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9263 \begin_layout Plain Layout
9271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9274 \begin_layout Plain Layout
9282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9285 \begin_layout Plain Layout
9286 \begin_inset Formula $\nearrow$
9296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9299 \begin_layout Plain Layout
9307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9310 \begin_layout Plain Layout
9311 \begin_inset Formula $\searrow$
9321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9324 \begin_layout Plain Layout
9332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9335 \begin_layout Plain Layout
9336 \begin_inset Formula $\swarrow$
9346 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9349 \begin_layout Plain Layout
9357 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9360 \begin_layout Plain Layout
9361 \begin_inset Formula $\nwarrow$
9375 \begin_inset space \hfill{}
9381 \begin_layout Standard
9382 \begin_inset VSpace medskip
9385 Vertical arrows can be used also as delimiter together with the commands
9387 \begin_inset CommandInset ref
9389 reference "sub:Manual-Bracket-Size"
9394 \begin_inset CommandInset ref
9396 reference "sub:Automatic-Bracket-Size"
9403 \begin_layout Standard
9404 \begin_inset Newpage newpage
9410 \begin_layout Section
9412 \begin_inset CommandInset label
9419 \begin_inset Index idx
9422 \begin_layout Plain Layout
9431 \begin_layout Standard
9432 Accents can be inserted via the math toolbar button
9433 \begin_inset Graphics
9434 filename ../images/math/hat.png
9439 or the commands listed in the following subsections.
9442 \begin_layout Subsection
9443 Accents for one Character
9447 \begin_layout Plain Layout
9460 \begin_layout Plain Layout
9462 \begin_inset CommandInset ref
9464 reference "sub:Accents-in-Text"
9477 \begin_layout Plain Layout
9485 \begin_inset Note Note
9488 \begin_layout Plain Layout
9491 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9494 \begin_layout Plain Layout
9497 texorpdfstring is in section
9498 \begin_inset CommandInset ref
9500 reference "sub:Formulas-in-Section"
9510 \begin_inset CommandInset label
9512 name "sub:Accents-for-one"
9517 \begin_inset Index idx
9520 \begin_layout Plain Layout
9521 Accents ! for one character
9529 \begin_layout Standard
9530 \begin_inset space \hfill{}
9534 \begin_inset Tabular
9535 <lyxtabular version="3" rows="8" columns="2">
9536 <features tabularvalignment="middle">
9537 <column alignment="center" valignment="top" width="0pt">
9538 <column alignment="center" valignment="top" width="0pt">
9540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9543 \begin_layout Plain Layout
9549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9552 \begin_layout Plain Layout
9554 \begin_inset Note Note
9557 \begin_layout Plain Layout
9564 is only used as spacer.
9576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9579 \begin_layout Plain Layout
9586 \begin_layout Plain Layout
9600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9603 \begin_layout Plain Layout
9604 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9614 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9617 \begin_layout Plain Layout
9624 \begin_layout Plain Layout
9638 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9641 \begin_layout Plain Layout
9642 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9652 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9655 \begin_layout Plain Layout
9662 \begin_layout Plain Layout
9676 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9679 \begin_layout Plain Layout
9680 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9690 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9693 \begin_layout Plain Layout
9700 \begin_layout Plain Layout
9714 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9717 \begin_layout Plain Layout
9718 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9728 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9731 \begin_layout Plain Layout
9738 \begin_layout Plain Layout
9748 \begin_inset Index idx
9751 \begin_layout Plain Layout
9762 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9765 \begin_layout Plain Layout
9766 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9779 \begin_layout Plain Layout
9786 \begin_layout Plain Layout
9800 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9803 \begin_layout Plain Layout
9804 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9814 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9817 \begin_layout Plain Layout
9824 \begin_layout Plain Layout
9838 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9841 \begin_layout Plain Layout
9842 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9856 \begin_inset space \hfill{}
9860 \begin_inset Tabular
9861 <lyxtabular version="3" rows="7" columns="2">
9862 <features tabularvalignment="middle">
9863 <column alignment="center" valignment="top" width="0pt">
9864 <column alignment="center" valignment="top" width="0pt">
9866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9869 \begin_layout Plain Layout
9875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9878 \begin_layout Plain Layout
9886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9889 \begin_layout Plain Layout
9896 \begin_layout Plain Layout
9910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9913 \begin_layout Plain Layout
9914 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9924 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9927 \begin_layout Plain Layout
9934 \begin_layout Plain Layout
9948 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9951 \begin_layout Plain Layout
9952 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9962 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9965 \begin_layout Plain Layout
9972 \begin_layout Plain Layout
9986 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9989 \begin_layout Plain Layout
9990 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10000 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10003 \begin_layout Plain Layout
10010 \begin_layout Plain Layout
10024 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10027 \begin_layout Plain Layout
10028 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10038 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10041 \begin_layout Plain Layout
10048 \begin_layout Plain Layout
10062 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10065 \begin_layout Plain Layout
10066 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10076 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10079 \begin_layout Plain Layout
10086 \begin_layout Plain Layout
10100 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10103 \begin_layout Plain Layout
10104 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10118 \begin_inset space \hfill{}
10124 \begin_layout Standard
10125 \begin_inset VSpace bigskip
10131 \begin_layout Standard
10132 You can directly insert accents like é to formulas.
10133 LyX will transform them to the corresponding accent command.
10135 \begin_inset Index idx
10138 \begin_layout Plain Layout
10144 it is better to insert a quotation mark before the vowel.
10145 These two characters are then treated by LaTeX as
10149 character when the formula part with the umlaut is marked as German.
10157 \begin_inset Quotes eld
10161 \begin_inset Quotes erd
10164 umlauts are created as demonstrated in the following example:
10167 \begin_layout Standard
10168 \begin_inset VSpace -2mm
10174 \begin_layout Standard
10176 \begin_inset Tabular
10177 <lyxtabular version="3" rows="3" columns="2">
10178 <features tabularvalignment="middle">
10179 <column alignment="center" valignment="top" width="0">
10180 <column alignment="center" valignment="top" width="0">
10182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10185 \begin_layout Plain Layout
10191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10194 \begin_layout Plain Layout
10196 \begin_inset Note Note
10199 \begin_layout Plain Layout
10207 \begin_inset space \thinspace{}
10210 pt space are only used as spacer.
10222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10225 \begin_layout Plain Layout
10228 \begin_inset Quotes grd
10236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10239 \begin_layout Plain Layout
10240 \begin_inset space \hspace{}
10247 \begin_inset Formula $"i$
10257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10260 \begin_layout Plain Layout
10267 \begin_layout Plain Layout
10281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10284 \begin_layout Plain Layout
10285 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10301 \begin_layout Standard
10302 Another advantage to
10308 is that umlauts can directly be converted to mathematical text because
10309 the accent commands above are
10315 in mathematical text
10318 To convert an accented character to mathematical text, only the character
10319 under the accent may be converted.
10320 This applies also for all other conversions, e.
10321 \begin_inset space \thinspace{}
10325 \begin_inset space \space{}
10331 \begin_layout Standard
10332 In mathematical text, umlauts and other accented characters can directly
10336 \begin_layout Subsection
10337 Accents for Operators
10338 \begin_inset Index idx
10341 \begin_layout Plain Layout
10342 Accents ! for operators
10350 \begin_layout Standard
10358 \begin_inset Index idx
10361 \begin_layout Plain Layout
10376 \begin_inset Index idx
10379 \begin_layout Plain Layout
10387 characters can be placed above or below an operator, respectively, to accent
10396 \begin_inset Index idx
10399 \begin_layout Plain Layout
10407 characters can be set before and behind an operator.
10408 The command scheme is:
10411 \begin_layout Standard
10427 \begin_layout Standard
10434 must always be before the operator that should be accented.
10435 You can accent with several characters and even with other operators and
10443 for example only characters behind an operator, write nothing between the
10444 first braces but don't omit the braces.
10447 \begin_layout Standard
10448 For example the command
10453 \begin_inset Formula $\to$
10463 \begin_inset Formula $\to$
10472 \begin_layout Plain Layout
10488 \begin_inset Formula \[
10489 \sideset{}{'}\sum_{k=1}^{n}\]
10496 \begin_layout Standard
10505 \begin_layout Plain Layout
10520 \begin_layout Plain Layout
10532 \begin_inset Formula $\uparrow$
10540 \begin_inset Formula \[
10541 \overset{a}{\maltese}\]
10545 As seen in the last example, with
10557 also symbols and characters can be accented; with
10563 this is not possible.
10566 \begin_layout Subsection
10567 Accents for several Characters
10568 \begin_inset Index idx
10571 \begin_layout Plain Layout
10572 Accents ! for several characters
10580 \begin_layout Standard
10581 \begin_inset space \hfill{}
10585 \begin_inset Tabular
10586 <lyxtabular version="3" rows="5" columns="2">
10587 <features tabularvalignment="middle">
10588 <column alignment="center" valignment="top" width="0pt">
10589 <column alignment="center" valignment="top" width="0pt">
10591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10594 \begin_layout Plain Layout
10600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10603 \begin_layout Plain Layout
10605 \begin_inset Note Note
10608 \begin_layout Plain Layout
10615 is only used as spacer.
10627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10630 \begin_layout Plain Layout
10637 \begin_layout Plain Layout
10651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10654 \begin_layout Plain Layout
10655 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10665 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10668 \begin_layout Plain Layout
10675 \begin_layout Plain Layout
10689 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10692 \begin_layout Plain Layout
10693 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10703 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10706 \begin_layout Plain Layout
10713 \begin_layout Plain Layout
10727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10730 \begin_layout Plain Layout
10731 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10741 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10744 \begin_layout Plain Layout
10747 underleftrightarrow
10751 \begin_layout Plain Layout
10765 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10768 \begin_layout Plain Layout
10769 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10783 \begin_inset space \hfill{}
10787 \begin_inset Tabular
10788 <lyxtabular version="3" rows="5" columns="2">
10789 <features tabularvalignment="middle">
10790 <column alignment="center" valignment="top" width="0pt">
10791 <column alignment="center" valignment="top" width="0pt">
10793 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10796 \begin_layout Plain Layout
10802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10805 \begin_layout Plain Layout
10813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10816 \begin_layout Plain Layout
10823 \begin_layout Plain Layout
10837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10840 \begin_layout Plain Layout
10841 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10851 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10854 \begin_layout Plain Layout
10861 \begin_layout Plain Layout
10875 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10878 \begin_layout Plain Layout
10879 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10889 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10892 \begin_layout Plain Layout
10899 \begin_layout Plain Layout
10913 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10916 \begin_layout Plain Layout
10917 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10927 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10930 \begin_layout Plain Layout
10937 \begin_layout Plain Layout
10951 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10954 \begin_layout Plain Layout
10955 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10969 \begin_inset space \hfill{}
10975 \begin_layout Standard
10976 \begin_inset VSpace medskip
10979 With these commands as many characters as you like can be accented.
10992 will only be set in the output with a length of three characters, as shown
10993 in the following example:
10994 \begin_inset Formula \[
10995 \widetilde{A+B=C-D}\]
11002 \begin_layout Standard
11010 \begin_inset Index idx
11013 \begin_layout Plain Layout
11028 \begin_inset Index idx
11031 \begin_layout Plain Layout
11039 described in the previous subsection it is also possible to accent several
11049 \begin_layout Plain Layout
11059 \begin_inset Formula $\downarrow$
11065 \begin_inset Formula \[
11066 \underset{***}{A=B}\]
11073 \begin_layout Section
11075 \begin_inset CommandInset label
11082 \begin_inset Index idx
11085 \begin_layout Plain Layout
11094 \begin_layout Subsection
11096 \begin_inset CommandInset label
11098 name "sub:Predefined-Space"
11103 \begin_inset Index idx
11106 \begin_layout Plain Layout
11107 Space ! horizontal ! predefined
11115 \begin_layout Standard
11116 Sometimes it is necessary to insert horizontal space to a formula.
11117 This is done by inserting a protected space (shortcut
11120 arg "space-insert protected"
11125 \begin_inset Quotes eld
11134 \begin_layout Plain Layout
11146 \begin_inset Quotes erd
11149 appears and by pressing
11153 several times one can select one of eight different space sizes.
11154 The spaces can also be inserted using the math toolbar button
11155 \begin_inset Graphics
11156 filename ../images/math/space.png
11161 or special commands.
11162 Independent from the inserted command, one can select the size again by
11170 \begin_layout Standard
11173 \begin_inset VSpace -5mm
11177 \begin_inset Tabular
11178 <lyxtabular version="3" rows="3" columns="7">
11179 <features tabularvalignment="middle">
11180 <column alignment="center" valignment="middle" width="6.8cm">
11181 <column alignment="center" valignment="top" width="0">
11182 <column alignment="center" valignment="top" width="0">
11183 <column alignment="center" valignment="top" width="0">
11184 <column alignment="center" valignment="top" width="0">
11185 <column alignment="center" valignment="top" width="0">
11186 <column alignment="center" valignment="top" width="0">
11188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11191 \begin_layout Plain Layout
11197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11200 \begin_layout Plain Layout
11208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11211 \begin_layout Plain Layout
11219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11222 \begin_layout Plain Layout
11230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11233 \begin_layout Plain Layout
11241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11244 \begin_layout Plain Layout
11252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11255 \begin_layout Plain Layout
11265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11268 \begin_layout Plain Layout
11273 keystrokes after inserting the protected space
11278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11281 \begin_layout Plain Layout
11287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11290 \begin_layout Plain Layout
11296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11299 \begin_layout Plain Layout
11305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11308 \begin_layout Plain Layout
11314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11317 \begin_layout Plain Layout
11323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11326 \begin_layout Plain Layout
11334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11337 \begin_layout Plain Layout
11343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11346 \begin_layout Plain Layout
11347 \begin_inset Formula $A\, B$
11355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11358 \begin_layout Plain Layout
11359 \begin_inset Formula $A\: B$
11367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11370 \begin_layout Plain Layout
11371 \begin_inset Formula $A\; B$
11379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11382 \begin_layout Plain Layout
11383 \begin_inset Formula $A\quad B$
11391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11394 \begin_layout Plain Layout
11395 \begin_inset Formula $A\qquad B$
11403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11406 \begin_layout Plain Layout
11407 \begin_inset Formula $A\! B$
11423 \begin_layout Standard
11424 The last size seem to produce no space.
11425 It is displayed red in LyX contrary to the other sizes, because it is a
11427 There are two more negative spaces:
11430 \begin_layout Standard
11432 \begin_inset Tabular
11433 <lyxtabular version="3" rows="3" columns="3">
11434 <features tabularvalignment="middle">
11435 <column alignment="center" valignment="middle" width="6.8cm">
11436 <column alignment="center" valignment="top" width="0pt">
11437 <column alignment="center" valignment="top" width="0pt">
11439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11442 \begin_layout Plain Layout
11448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11451 \begin_layout Plain Layout
11459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11462 \begin_layout Plain Layout
11472 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11475 \begin_layout Plain Layout
11480 keystrokes after inserting the protected space
11485 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11488 \begin_layout Plain Layout
11494 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11497 \begin_layout Plain Layout
11505 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11508 \begin_layout Plain Layout
11514 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11517 \begin_layout Plain Layout
11518 \begin_inset Formula $A\negmedspace B$
11526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11529 \begin_layout Plain Layout
11530 \begin_inset Formula $A\negthickspace B$
11546 \begin_layout Standard
11547 Negative spaces can lead to characters overlapping each other.
11548 Thus they can be used to enforce ligatures, what is e.
11549 \begin_inset space \thinspace{}
11553 \begin_inset space \space{}
11556 useful for summation operators:
11559 \begin_layout Standard
11561 \begin_inset Tabular
11562 <lyxtabular version="3" rows="3" columns="2">
11563 <features tabularvalignment="middle">
11564 <column alignment="center" valignment="top" width="0">
11565 <column alignment="center" valignment="top" width="0">
11567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11570 \begin_layout Plain Layout
11576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11579 \begin_layout Plain Layout
11581 \begin_inset Note Note
11584 \begin_layout Plain Layout
11591 is only used as spacer.
11603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11606 \begin_layout Plain Layout
11615 \begin_layout Plain Layout
11629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11632 \begin_layout Plain Layout
11633 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11646 \begin_layout Plain Layout
11657 \begin_layout Plain Layout
11671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11674 \begin_layout Plain Layout
11675 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11691 \begin_layout Standard
11692 Relations like for example equal signs, are always surrounded by space.
11693 To suppress this, the equal sign is placed into a TeX-brace.
11694 The following example demonstrates this:
11697 \begin_layout Standard
11699 \begin_inset Tabular
11700 <lyxtabular version="3" rows="2" columns="2">
11701 <features tabularvalignment="middle">
11702 <column alignment="center" valignment="top" width="0pt">
11703 <column alignment="center" valignment="top" width="0pt">
11705 <cell alignment="center" valignment="top" usebox="none">
11708 \begin_layout Plain Layout
11714 <cell alignment="center" valignment="top" usebox="none">
11717 \begin_layout Plain Layout
11718 \begin_inset Formula $A=B$
11728 <cell alignment="center" valignment="top" usebox="none">
11731 \begin_layout Plain Layout
11732 \begin_inset Note Note
11735 \begin_layout Plain Layout
11742 is only used as spacer.
11748 \begin_inset Formula $\raisebox{5mm}{}$
11751 equation without space
11756 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11759 \begin_layout Plain Layout
11760 \begin_inset Formula $A{=}B$
11776 \begin_layout Standard
11778 The command for the last formula is:
11783 \begin_inset Formula $\to$
11789 \begin_layout Standard
11790 \begin_inset VSpace bigskip
11793 Spaces are needed for physical units, because the space between the value
11794 and the unit is the smallest one and not a normal space.
11795 For units in text, the smallest space is inserted via the menu
11797 Insert\SpecialChar \menuseparator
11798 Formatting\SpecialChar \menuseparator
11800 \begin_inset space ~
11808 arg "space-insert thin"
11814 \begin_layout Standard
11815 An example to visualize the difference:
11818 \begin_layout Standard
11819 \begin_inset Tabular
11820 <lyxtabular version="3" rows="2" columns="2">
11821 <features tabularvalignment="middle">
11822 <column alignment="left" valignment="top" width="0">
11823 <column alignment="left" valignment="top" width="0">
11825 <cell alignment="center" valignment="top" usebox="none">
11828 \begin_layout Plain Layout
11830 \begin_inset Formula $\cdot$
11838 <cell alignment="center" valignment="top" usebox="none">
11841 \begin_layout Plain Layout
11842 space between value and unit
11849 <cell alignment="center" valignment="top" usebox="none">
11852 \begin_layout Plain Layout
11854 \begin_inset space \thinspace{}
11858 \begin_inset Formula $\cdot$
11866 <cell alignment="center" valignment="top" usebox="none">
11869 \begin_layout Plain Layout
11870 smallest space between value and unit
11883 \begin_layout Subsection
11888 \begin_layout Plain Layout
11901 \begin_layout Plain Layout
11902 for vertical space in formulas see
11903 \begin_inset CommandInset ref
11905 reference "sub:Line-Separation"
11918 \begin_layout Plain Layout
11926 \begin_inset Note Note
11929 \begin_layout Plain Layout
11932 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11935 \begin_layout Plain Layout
11938 texorpdfstring is in section
11939 \begin_inset CommandInset ref
11941 reference "sub:Formulas-in-Section"
11951 \begin_inset CommandInset label
11953 name "sub:Variable-Space"
11958 \begin_inset Index idx
11961 \begin_layout Plain Layout
11962 Space ! horizontal ! variable
11970 \begin_layout Standard
11971 Space with a defined length can be inserted with the command
11978 \begin_inset Index idx
11981 \begin_layout Plain Layout
11991 \begin_inset Quotes eld
12000 \begin_layout Plain Layout
12012 \begin_inset Quotes erd
12016 The length can be specified by left-clicking on the
12017 \begin_inset Quotes eld
12026 \begin_layout Plain Layout
12038 \begin_inset Quotes erd
12042 The length may also be negative.
12043 To insert so many space that the formula uses all available space, the
12051 \begin_inset Index idx
12054 \begin_layout Plain Layout
12065 \begin_layout Standard
12066 \begin_inset VSpace -1mm
12072 \begin_layout Standard
12074 \begin_inset Tabular
12075 <lyxtabular version="3" rows="4" columns="2">
12076 <features tabularvalignment="middle">
12077 <column alignment="center" valignment="top" width="0">
12078 <column alignment="center" valignment="top" width="0">
12080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12083 \begin_layout Plain Layout
12091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12094 \begin_layout Plain Layout
12102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12105 \begin_layout Plain Layout
12112 \begin_layout Plain Layout
12122 \begin_inset Formula $\to$
12128 \begin_inset space \thinspace{}
12136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12139 \begin_layout Plain Layout
12140 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12153 \begin_layout Plain Layout
12160 \begin_layout Plain Layout
12170 \begin_inset Formula $\to$
12176 \begin_inset space \thinspace{}
12184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12187 \begin_layout Plain Layout
12188 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12201 \begin_layout Plain Layout
12208 \begin_layout Plain Layout
12222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12225 \begin_layout Plain Layout
12226 \begin_inset Formula $A=A\hfill B=B$
12242 \begin_layout Standard
12243 In the last example the available space is given by the longest column entry
12245 In an inline formula the space depends on the length of the line in which
12253 Thus, when the line uses the full width, no space will be created.
12260 only has an effect on displayed formulas when the formula style
12265 (Formula styles are explained in
12266 \begin_inset CommandInset ref
12268 reference "sec:Formula-Styles"
12275 \begin_layout Standard
12282 , there are the commands
12294 that fill the space with a pattern, see
12295 \begin_inset CommandInset ref
12297 reference "sub:Ellipses"
12304 \begin_layout Standard
12305 For text, variable space can be inserted via the menu
12307 Insert\SpecialChar \menuseparator
12308 Formatting\SpecialChar \menuseparator
12310 \begin_inset space ~
12318 \begin_layout Standard
12319 This is a line with
12320 \begin_inset space \hspace{}
12325 \begin_inset space \thinspace{}
12331 \begin_layout Standard
12332 This is a line with
12333 \begin_inset space \hfill{}
12339 \begin_layout Subsection
12340 Space besides inline Formulas
12341 \begin_inset Index idx
12344 \begin_layout Plain Layout
12345 Space ! besides inline formulas
12353 \begin_layout Standard
12354 The space that surrounds inline formulas can be adjusted with the length
12362 \begin_inset Index idx
12365 \begin_layout Plain Layout
12374 The value of a length is set with the command
12381 \begin_inset Index idx
12384 \begin_layout Plain Layout
12392 that has the following scheme:
12395 \begin_layout Standard
12400 setlength{length name}{value}
12403 \begin_layout Standard
12411 \begin_inset space \thinspace{}
12417 \begin_layout Standard
12427 \begin_layout Standard
12428 is inserted in TeX-mode.
12430 \begin_inset space \thinspace{}
12433 mm space will now be set around all inline formulas:
12437 \begin_layout Plain Layout
12451 \begin_layout Standard
12452 This is a line with an inline formula
12453 \begin_inset Formula $A=B$
12457 \begin_inset space \thinspace{}
12460 mm surrounding space.
12464 \begin_layout Plain Layout
12478 \begin_layout Standard
12479 To return to the predefined value,
12485 is set to the value 0
12486 \begin_inset space \thinspace{}
12492 \begin_layout Section
12494 \begin_inset Index idx
12497 \begin_layout Plain Layout
12504 \begin_inset Index idx
12507 \begin_layout Plain Layout
12512 \begin_layout Plain Layout
12523 \begin_layout Plain Layout
12538 \begin_layout Standard
12539 Boxes for text are described in chapter
12546 \begin_inset space ~
12554 \begin_layout Subsection
12556 \begin_inset CommandInset label
12558 name "sub:Boxes-with-Frame"
12563 \begin_inset Index idx
12566 \begin_layout Plain Layout
12575 \begin_layout Standard
12576 It is possible to frame formulas or parts of it with the commands
12583 \begin_inset Index idx
12586 \begin_layout Plain Layout
12601 \begin_inset Index idx
12604 \begin_layout Plain Layout
12615 \begin_layout Standard
12616 When one of these commands is inserted to a formula, a blue box appears
12617 within a frame to enter formula parts.
12624 an additional formula has to be created by
12628 within this box, because the box content will otherwise be treated as mathemati
12636 is used, a new formula is automatically created inside the frame.
12639 \begin_layout Standard
12646 is not suitable to frame displayed formulas because the formula will always
12647 be set in the size of the text.
12654 is in contrary not suitable to frame inline formulas, because the formula
12655 will always be set in the size of a displayed formula.
12658 \begin_layout Standard
12665 there is the command
12672 \begin_inset Index idx
12675 \begin_layout Plain Layout
12683 where additionally the frame width and the alignment can be specified.
12690 is used in the following scheme:
12693 \begin_layout Standard
12698 framebox[frame width][position]{box content}
12701 \begin_layout Standard
12702 The position can either be
12719 right aligns the formula in the box.
12720 When no position is given, the formula will be centered.
12721 \begin_inset Newline newline
12724 Is no width given, also no position can be given.
12725 In this case the frame width is adjusted to the box content like for
12734 \begin_layout Standard
12741 is inserted, a box appears containing three blue boxes.
12742 The first two boxes are surrounded by brackets and denote the two optional
12744 The third box is for formula parts like for
12753 \begin_layout Standard
12755 \begin_inset Tabular
12756 <lyxtabular version="3" rows="5" columns="2">
12757 <features tabularvalignment="middle">
12758 <column alignment="center" valignment="top" width="0">
12759 <column alignment="center" valignment="top" width="0">
12761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12764 \begin_layout Plain Layout
12770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12773 \begin_layout Plain Layout
12775 \begin_inset Note Note
12778 \begin_layout Plain Layout
12785 is only used as spacer.
12797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12800 \begin_layout Plain Layout
12807 \begin_layout Plain Layout
12826 \begin_layout Plain Layout
12840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12843 \begin_layout Plain Layout
12844 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12857 \begin_layout Plain Layout
12864 \begin_layout Plain Layout
12879 \begin_layout Plain Layout
12893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12896 \begin_layout Plain Layout
12897 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12910 \begin_layout Plain Layout
12917 \begin_layout Plain Layout
12931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12934 \begin_layout Plain Layout
12935 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12948 \begin_layout Plain Layout
12955 \begin_layout Plain Layout
12965 \begin_inset Formula $\to$
12969 \begin_inset Formula $\to$
12982 \begin_layout Plain Layout
12992 \begin_inset Formula $\downarrow$
13000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13003 \begin_layout Plain Layout
13004 \begin_inset Formula $\raisebox{6mm}{}$
13008 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13012 \begin_inset Formula $\raisebox{-4mm}{}$
13028 \begin_layout Standard
13029 The frame thickness can also be adjusted.
13030 To do this the following commands have to be inserted in TeX-mode before
13034 \begin_layout Standard
13044 \begin_inset Quotes eld
13048 \begin_inset Quotes erd
13062 \begin_inset Quotes eld
13066 \begin_inset Quotes erd
13072 \begin_layout Standard
13073 \begin_inset Quotes eld
13077 \begin_inset Quotes erd
13080 specifies the minimal distance between the frame and the first character
13082 An example for this is the following framed formula:
13086 \begin_layout Plain Layout
13098 \begin_inset Formula \[
13103 Before this formula the commands
13106 \begin_layout Standard
13128 \begin_layout Standard
13129 were inserted in TeX-mode.
13130 The given values are used for all following boxes.
13133 \begin_layout Standard
13134 To return to the standard frame size, the command
13137 \begin_layout Standard
13162 \begin_layout Plain Layout
13176 \begin_layout Standard
13177 is inserted in TeX-mode before the next formula.
13180 \begin_layout Subsection
13181 Boxes without Frame
13182 \begin_inset CommandInset label
13184 name "sub:Boxes-without-Frame"
13189 \begin_inset Index idx
13192 \begin_layout Plain Layout
13193 Boxes ! without frame
13201 \begin_layout Standard
13202 For boxes without a frame there are the following box commands:
13209 \begin_inset Index idx
13212 \begin_layout Plain Layout
13227 \begin_inset Index idx
13230 \begin_layout Plain Layout
13245 \begin_inset Index idx
13248 \begin_layout Plain Layout
13259 \begin_layout Standard
13266 a box can be super- or subscripted.
13267 But in contrary to normal super- and subscripting, the characters in the
13268 box keep their font size.
13275 is used in the following scheme:
13278 \begin_layout Standard
13283 raisebox{height}{box content}
13286 \begin_layout Standard
13287 When the box should contain a formula, an extra formula is needed like for
13298 \begin_inset Note Greyedout
13301 \begin_layout Plain Layout
13312 this extra formula is created by pressing
13316 twice instead of once because LyX doesn't yet support
13330 \begin_layout Standard
13332 \begin_inset Tabular
13333 <lyxtabular version="3" rows="4" columns="2">
13334 <features tabularvalignment="middle">
13335 <column alignment="center" valignment="top" width="0">
13336 <column alignment="center" valignment="top" width="0">
13338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13341 \begin_layout Plain Layout
13347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13350 \begin_layout Plain Layout
13358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13361 \begin_layout Plain Layout
13365 \begin_inset Formula $\to$
13371 \begin_inset Formula $\to$
13379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13382 \begin_layout Plain Layout
13383 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13396 \begin_layout Plain Layout
13400 \begin_inset Formula $\to$
13406 \begin_inset Formula $\to$
13414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13417 \begin_layout Plain Layout
13418 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13431 \begin_layout Plain Layout
13435 \begin_inset Formula $\to$
13454 \begin_layout Plain Layout
13468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13471 \begin_layout Plain Layout
13472 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13488 \begin_layout Standard
13513 , with the difference that there is no frame.
13516 \begin_layout Subsection
13518 \begin_inset CommandInset label
13520 name "sub:Colored-Boxes"
13525 \begin_inset Index idx
13528 \begin_layout Plain Layout
13537 \begin_layout Standard
13538 To be able to use all commands explained in this section, the LaTeX-package
13547 \begin_layout Plain Layout
13552 is part of every LaTeX standard installation.
13558 \begin_inset Index idx
13561 \begin_layout Plain Layout
13567 has to be loaded in the LaTeX-preamble with the line
13571 \begin_layout Plain Layout
13572 When text is colored somewhere in the document with a predefined color,
13573 LyX loads the LaTeX-package
13578 Thus it is possible that the package is loaded twice, but this doesn't
13585 \begin_inset Note Note
13588 \begin_layout Plain Layout
13589 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13598 \begin_layout Standard
13606 \begin_layout Standard
13607 \begin_inset VSpace medskip
13610 To color boxes, the command
13617 \begin_inset Index idx
13620 \begin_layout Plain Layout
13628 is used in the following scheme:
13631 \begin_layout Standard
13636 colorbox{color}{box content}
13639 \begin_layout Standard
13640 The box content can also be a box and a
13646 can also be part of another box (see the 2nd and 3rd example).
13647 When the box should contain a formula, an extra formula has to be created,
13648 the same way as for
13658 \begin_layout Plain Layout
13659 This also applies for the command
13673 \begin_layout Standard
13674 One of the following predefined colors can be chosen:
13677 \begin_layout Standard
13711 \begin_layout Standard
13713 \begin_inset Tabular
13714 <lyxtabular version="3" rows="4" columns="2">
13715 <features tabularvalignment="middle">
13716 <column alignment="center" valignment="top" width="0">
13717 <column alignment="center" valignment="top" width="0">
13719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13722 \begin_layout Plain Layout
13728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13731 \begin_layout Plain Layout
13733 \begin_inset Note Note
13736 \begin_layout Plain Layout
13743 is only used as spacer.
13755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13758 \begin_layout Plain Layout
13762 \begin_inset Formula $\to$
13772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13775 \begin_layout Plain Layout
13776 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13789 \begin_layout Plain Layout
13793 \begin_inset Formula $\to$
13804 \begin_layout Plain Layout
13818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13821 \begin_layout Plain Layout
13822 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13835 \begin_layout Plain Layout
13842 \begin_layout Plain Layout
13854 \begin_inset Formula $\to$
13873 \begin_layout Plain Layout
13887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13890 \begin_layout Plain Layout
13891 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13907 \begin_layout Standard
13914 only colors the box but not the characters in the box.
13915 To color all characters, the whole formula is highlighted and the wanted
13916 color is chosen in the
13919 \begin_inset space ~
13925 The dialog can be called with the toolbar button
13926 \begin_inset Graphics
13927 filename ../images/dialog-show_character.png
13934 Edit\SpecialChar \menuseparator
13936 \begin_inset space ~
13939 Style\SpecialChar \menuseparator
13943 The formula number has then the same color as the formula.
13944 When the formula number should get another color than the formula characters,
13945 the color must be changed within the formula.
13948 \begin_layout Standard
13952 \begin_layout Standard
13955 \begin_inset Formula \begin{equation}
13956 \int A=B\label{eq:red}\end{equation}
13963 \begin_inset Formula \begin{equation}
13964 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13971 \begin_layout Standard
13973 \begin_inset CommandInset ref
13979 is completely colored red.
13980 \begin_inset Newline newline
13984 \begin_inset CommandInset ref
13986 reference "eq:redgreen"
13990 was first completely colored green to set the color for the formula number.
13991 Subsequently the formula characters were colored red.
13994 \begin_layout Standard
13995 \begin_inset VSpace bigskip
13998 To color the frame different than the rest of the box, the command
14005 \begin_inset Index idx
14008 \begin_layout Plain Layout
14016 is used in the following scheme:
14019 \begin_layout Standard
14024 fcolorbox{frame color}{color}{box content}
14027 \begin_layout Standard
14034 is an extension of the command
14041 The frame width is set, like for
14064 \begin_layout Plain Layout
14076 \begin_inset Formula \[
14077 \fcolorbox{cyan}{magenta}{A=B}\]
14085 \begin_layout Plain Layout
14099 \begin_layout Standard
14100 This formula was created with the command
14101 \begin_inset Newline newline
14109 \begin_inset Formula $\to$
14115 \begin_inset Formula $\to$
14125 \begin_layout Standard
14126 \begin_inset VSpace bigskip
14129 To use other colors than the predefined ones, they have to be defined first.
14132 \begin_layout Standard
14133 One can for example define the color
14134 \begin_inset Quotes eld
14142 \begin_inset Quotes erd
14145 with the LaTeX-preamble line:
14148 \begin_layout Standard
14153 definecolor{darkgreen}{cmyk}{0.5,
14168 \begin_inset Index idx
14171 \begin_layout Plain Layout
14182 \begin_layout Standard
14187 is the color space that denotes the colors
14204 The four comma separated numbers are the portion factor for the corresponding
14205 colors of the color space.
14206 The factors can be in the range of 0
14207 \begin_inset space \thinspace{}
14211 \begin_inset space \thinspace{}
14219 also the color space
14223 can be used for definitions.
14240 , so that there are in this case three portion factors for the corresponding
14242 Furthermore there is the color space
14246 with one portion factor for the gray value.
14249 \begin_layout Standard
14250 As example a framed box with the new defined color
14254 where the characters have been colored
14259 \begin_inset Formula \begin{equation}
14260 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14267 \begin_layout Standard
14268 Self-defined colors can also be used for text with the help of the command
14276 \begin_inset Index idx
14279 \begin_layout Plain Layout
14288 \begin_layout Standard
14292 \begin_layout Plain Layout
14296 textcolor{darkgreen}{
14302 \begin_inset Quotes eld
14306 \begin_inset Quotes erd
14313 \begin_layout Plain Layout
14323 \begin_layout Standard
14331 \begin_inset Index idx
14334 \begin_layout Plain Layout
14342 is used in the scheme
14346 textcolor{color}{characters to color}
14351 \begin_layout Subsection
14353 \begin_inset CommandInset label
14355 name "sub:Paragraph-Boxes"
14360 \begin_inset Index idx
14363 \begin_layout Plain Layout
14364 Boxes ! as paragraph
14372 \begin_layout Standard
14373 A box that can contain several lines and paragraphs, a so called paragraph
14374 box (parbox), can be created with the menu
14376 Insert\SpecialChar \menuseparator
14379 or the toolbar button
14380 \begin_inset Graphics
14381 filename ../images/box-insert.png
14389 \begin_layout Standard
14390 The following example shows a framed parbox in a line:
14393 \begin_layout Standard
14394 \begin_inset VSpace medskip
14398 \begin_inset Box Boxed
14408 height_special "totalheight"
14411 \begin_layout Plain Layout
14412 This is a paragraph box.
14414 \begin_inset space \thinspace{}
14417 cm long and can also contain formulas:
14418 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14429 \begin_layout Standard
14430 \begin_inset VSpace medskip
14436 \begin_layout Standard
14437 Such a box is created by right-clicking on the gray box inset.
14438 A dialog pops up showing the box properties.
14452 \begin_inset space \thinspace{}
14457 Vertical Box Alignment
14462 \begin_layout Standard
14463 \begin_inset VSpace medskip
14466 In LaTeX a parbox is created with the command
14473 \begin_inset Index idx
14476 \begin_layout Plain Layout
14484 that has the following scheme:
14487 \begin_layout Standard
14492 parbox[position]{width}{box content}
14495 \begin_layout Standard
14509 for bottom means that the box is aligned within the surrounding text with
14515 for top this is done with the first line.
14516 When no position is given, the box will be vertically centered, see section
14524 \begin_inset space ~
14529 manual for examples.
14532 \begin_layout Standard
14533 \begin_inset VSpace bigskip
14536 To frame formulas completely, including the formula number, the formula
14537 must be set into a parbox.
14538 To do this, the command
14552 is inserted in TeX-mode before the formula.
14560 \begin_inset Index idx
14563 \begin_layout Plain Layout
14571 is hereby the line width set for the document.
14572 Because the frame is outside the parbox, 2
14573 \begin_inset space \thinspace{}
14576 times the frame separation and the frame thickness must be subtracted from
14578 As this is not automatically done by LyX due to a bug
14582 \begin_layout Plain Layout
14583 \begin_inset CommandInset href
14585 name "LyX-bug #4483"
14586 target "http://www.lyx.org/trac/ticket/4483"
14595 , TeX-mode has to be used.
14596 To be able to multiply and subtract in arguments, the LaTeX-package
14604 \begin_layout Plain Layout
14609 is part of every LaTeX standard installation.
14615 \begin_inset Index idx
14618 \begin_layout Plain Layout
14624 must be loaded in the LaTeX-preamble with the line
14627 \begin_layout Standard
14635 \begin_layout Standard
14636 Behind the formula both boxes are closed by entering
14641 Here is an example:
14645 \begin_layout Plain Layout
14659 \begin_layout Standard
14663 \begin_layout Plain Layout
14681 \begin_inset Formula \begin{equation}
14682 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14690 \begin_layout Plain Layout
14701 \begin_layout Plain Layout
14715 \begin_layout Standard
14716 \begin_inset VSpace medskip
14719 As a parbox is used as argument of
14725 , there is in this case no difference between
14740 \begin_layout Standard
14741 \begin_inset VSpace bigskip
14744 Paragraph boxes are very useful to comment formulas directly.
14751 is used in combination with the command
14765 \begin_inset CommandInset ref
14767 reference "sub:User-defined-Numbering"
14774 \begin_layout Standard
14775 An example of a formula commented with
14784 \begin_layout Standard
14788 \begin_layout Plain Layout
14801 This is a description.
14802 It is distinctly separated from the formula and multiline.
14806 \begin_layout Plain Layout
14818 \begin_layout Standard
14819 Such a formula must be inserted completely in TeX-mode because LyX does
14820 not yet support the command
14827 The formula is created with the following command sequence:
14830 \begin_layout Standard
14843 is inserted in TeX-mode.
14847 \begin_layout Plain Layout
14848 When the formula style
14860 can also be replaced by
14867 (formula styles see
14868 \begin_inset CommandInset ref
14870 reference "sec:Formula-Styles"
14879 Then the description follows as normal text and finally
14885 is inserted in TeX-mode.
14898 hereby create a displayed formula.
14901 \begin_layout Standard
14908 can be seen in this example that was
14909 \begin_inset Quotes eld
14913 \begin_inset Quotes erd
14916 using the mathematical textmode:
14917 \begin_inset Formula \[
14918 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14925 \begin_layout Section
14927 \begin_inset Index idx
14930 \begin_layout Plain Layout
14939 \begin_layout Subsection
14941 \begin_inset CommandInset label
14943 name "sub:Big-Operators"
14948 \begin_inset Index idx
14951 \begin_layout Plain Layout
14958 \begin_inset Index idx
14961 \begin_layout Plain Layout
14968 \begin_inset Index idx
14971 \begin_layout Plain Layout
14980 \begin_layout Standard
14981 To be able to use all integral operators listed here, the option
14983 Use esint package automatically
14985 must be set in the document settings under
14988 \begin_inset space ~
14996 \begin_layout Standard
14997 \begin_inset space \hfill{}
15001 \begin_inset Tabular
15002 <lyxtabular version="3" rows="11" columns="2">
15003 <features tabularvalignment="middle">
15004 <column alignment="center" valignment="top" width="0pt">
15005 <column alignment="center" valignment="top" width="0pt">
15007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15010 \begin_layout Plain Layout
15016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15019 \begin_layout Plain Layout
15027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15030 \begin_layout Plain Layout
15034 \begin_inset Index idx
15037 \begin_layout Plain Layout
15050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15053 \begin_layout Plain Layout
15054 \begin_inset Formula $\int$
15064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15067 \begin_layout Plain Layout
15075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15078 \begin_layout Plain Layout
15079 \begin_inset Formula $\oint$
15089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15092 \begin_layout Plain Layout
15100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15103 \begin_layout Plain Layout
15104 \begin_inset Formula $\ointctrclockwise$
15114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15117 \begin_layout Plain Layout
15125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15128 \begin_layout Plain Layout
15129 \begin_inset Formula $\ointclockwise$
15139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15142 \begin_layout Plain Layout
15150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15153 \begin_layout Plain Layout
15154 \begin_inset Formula $\sqint$
15164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15167 \begin_layout Plain Layout
15175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15178 \begin_layout Plain Layout
15180 \begin_inset Formula $\fint$
15190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15193 \begin_layout Plain Layout
15201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15204 \begin_layout Plain Layout
15206 \begin_inset Formula $\landupint$
15216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15219 \begin_layout Plain Layout
15227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15230 \begin_layout Plain Layout
15232 \begin_inset Formula $\landdownint$
15242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15245 \begin_layout Plain Layout
15253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15256 \begin_layout Plain Layout
15257 \begin_inset Formula $\bigcap$
15267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15270 \begin_layout Plain Layout
15278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15281 \begin_layout Plain Layout
15282 \begin_inset Formula $\bigcup$
15296 \begin_inset space \hfill{}
15300 \begin_inset Tabular
15301 <lyxtabular version="3" rows="11" columns="2">
15302 <features tabularvalignment="middle">
15303 <column alignment="center" valignment="top" width="0pt">
15304 <column alignment="center" valignment="top" width="0pt">
15306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15309 \begin_layout Plain Layout
15315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15318 \begin_layout Plain Layout
15326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15329 \begin_layout Plain Layout
15333 \begin_inset Index idx
15336 \begin_layout Plain Layout
15349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15352 \begin_layout Plain Layout
15353 \begin_inset Formula $\sum$
15363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15366 \begin_layout Plain Layout
15370 \begin_inset Index idx
15373 \begin_layout Plain Layout
15386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15389 \begin_layout Plain Layout
15390 \begin_inset Formula $\prod$
15400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15403 \begin_layout Plain Layout
15411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15414 \begin_layout Plain Layout
15415 \begin_inset Formula $\coprod$
15425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15428 \begin_layout Plain Layout
15436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15439 \begin_layout Plain Layout
15440 \begin_inset Formula $\bigodot$
15450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15453 \begin_layout Plain Layout
15461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15464 \begin_layout Plain Layout
15465 \begin_inset Formula $\bigotimes$
15475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15478 \begin_layout Plain Layout
15486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15489 \begin_layout Plain Layout
15490 \begin_inset Formula $\bigoplus$
15500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15503 \begin_layout Plain Layout
15511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15514 \begin_layout Plain Layout
15515 \begin_inset Formula $\bigwedge$
15525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15528 \begin_layout Plain Layout
15536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15539 \begin_layout Plain Layout
15540 \begin_inset Formula $\bigvee$
15550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15553 \begin_layout Plain Layout
15561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15564 \begin_layout Plain Layout
15565 \begin_inset Formula $\bigsqcup$
15575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15578 \begin_layout Plain Layout
15586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15589 \begin_layout Plain Layout
15590 \begin_inset Formula $\biguplus$
15604 \begin_inset space \hfill{}
15610 \begin_layout Standard
15611 All big operators can also be inserted via the math toolbar button
15612 \begin_inset Graphics
15613 filename ../images/math/intop.png
15621 \begin_layout Standard
15622 The operators are called big because they are bigger than the sometimes
15623 equal looking binary operators.
15624 All big operators can have limits as described in the next subsection.
15627 \begin_layout Standard
15628 For all integral operators there is a second version available, ending on
15646 These operators are different from
15653 \begin_inset space \space{}
15656 in the style the operator limits are displayed, see
15657 \begin_inset CommandInset ref
15659 reference "sub:Operator-Limits"
15667 \begin_layout Subsubsection*
15668 Advice for Integrals
15671 \begin_layout Standard
15676 in an integral is an operator, that therefore has to be set upright.
15677 This is done by highlighting the
15681 and using the keyboard shortcut
15691 \begin_layout Plain Layout
15697 \begin_inset CommandInset ref
15699 reference "sub:Font-Styles"
15709 Finally the smallest space is inserted before the
15713 , as this is usual for operators.
15717 \begin_layout Standard
15719 \begin_inset Formula $\int A(x)dx$
15723 \begin_inset Newline newline
15727 \begin_inset Phantom HPhantom
15730 \begin_layout Plain Layout
15737 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15743 \begin_layout Standard
15744 For multiple integrals there are the following commands:
15745 \begin_inset VSpace medskip
15751 \begin_layout Standard
15752 \begin_inset space \hfill{}
15756 \begin_inset Tabular
15757 <lyxtabular version="3" rows="4" columns="2">
15758 <features tabularvalignment="middle">
15759 <column alignment="center" valignment="top" width="0">
15760 <column alignment="center" valignment="top" width="0">
15762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15765 \begin_layout Plain Layout
15771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15774 \begin_layout Plain Layout
15776 \begin_inset Note Note
15779 \begin_layout Plain Layout
15786 is only used as spacer.
15798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15801 \begin_layout Plain Layout
15809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15812 \begin_layout Plain Layout
15813 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15826 \begin_layout Plain Layout
15834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15837 \begin_layout Plain Layout
15838 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15851 \begin_layout Plain Layout
15859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15862 \begin_layout Plain Layout
15863 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15877 \begin_inset space \hfill{}
15881 \begin_inset Tabular
15882 <lyxtabular version="3" rows="4" columns="2">
15883 <features tabularvalignment="middle">
15884 <column alignment="center" valignment="top" width="0">
15885 <column alignment="center" valignment="top" width="0">
15887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15890 \begin_layout Plain Layout
15896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15899 \begin_layout Plain Layout
15907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15910 \begin_layout Plain Layout
15918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15921 \begin_layout Plain Layout
15922 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15935 \begin_layout Plain Layout
15943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15946 \begin_layout Plain Layout
15947 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15960 \begin_layout Plain Layout
15968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15971 \begin_layout Plain Layout
15972 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15986 \begin_inset space \hfill{}
15992 \begin_layout Subsection
15994 \begin_inset CommandInset label
15996 name "sub:Operator-Limits"
16001 \begin_inset Index idx
16004 \begin_layout Plain Layout
16013 \begin_layout Standard
16014 Limits are created by super- and subscripts:
16017 \begin_layout Standard
16019 \begin_inset Tabular
16020 <lyxtabular version="3" rows="2" columns="2">
16021 <features tabularvalignment="middle">
16022 <column alignment="center" valignment="top" width="0pt">
16023 <column alignment="center" valignment="top" width="0pt">
16025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16028 \begin_layout Plain Layout
16034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16037 \begin_layout Plain Layout
16039 \begin_inset Note Note
16042 \begin_layout Plain Layout
16049 is only used as spacer.
16061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16064 \begin_layout Plain Layout
16073 \begin_layout Plain Layout
16083 \begin_inset Formula $\to$
16087 \begin_inset Formula $\to$
16095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16098 \begin_layout Plain Layout
16099 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16115 \begin_layout Standard
16116 Limits of inline formulas are set right beside the operator.
16117 Limits in displayed formulas are set above or below the operator, except
16118 for integral limits.
16121 \begin_layout Standard
16122 To force that the limits are set beside the operator, the cursor is set
16123 directly behind the operator and the limits type is changed with the menu
16126 Edit\SpecialChar \menuseparator
16127 Math\SpecialChar \menuseparator
16146 \begin_layout Standard
16147 The default limits type is this:
16148 \begin_inset Formula \[
16149 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16153 This is how it looks when the limits type was changed to
16160 \begin_inset Formula \[
16161 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16165 For integrals, except those ending with
16181 etc., the limits are by default set beside the operator.
16182 But for multiple integrals the limits are often set below the operator.
16183 In the following example the limits type was therefore set to
16187 and so set below the integrals:
16188 \begin_inset Formula \begin{equation}
16189 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16196 \begin_layout Standard
16197 \begin_inset VSpace medskip
16200 To specify conditions for limits, the commands
16207 \begin_inset Index idx
16210 \begin_layout Plain Layout
16225 \begin_inset Index idx
16228 \begin_layout Plain Layout
16237 To create for example this expression
16238 \begin_inset Formula \begin{equation}
16239 \sum_{\begin{subarray}{c}
16243 \end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16250 \begin_layout Standard
16251 the following has to be done:
16252 \begin_inset Newline newline
16267 \begin_layout Plain Layout
16279 One is now in a blue box under the summation operator and insert there
16288 \begin_layout Plain Layout
16300 The blue box is now within a purple box and now several lines can be written
16302 A new line is created by inserting a line break (
16305 arg "newline-insert newline"
16310 \begin_inset Newline newline
16315 0<k<1000 Ctrl+Return
16316 \begin_inset Newline newline
16321 is typed in, a new box appears below for the new line.
16324 \begin_layout Standard
16325 The alignment of the lines can be changed to left aligned with the
16335 Edit\SpecialChar \menuseparator
16339 To get right alignment,
16347 \begin_layout Plain Layout
16358 is inserted at the beginning of the line.
16361 \begin_layout Standard
16374 with the difference that the lines are always centered.
16377 \begin_layout Standard
16378 \begin_inset VSpace bigskip
16382 \begin_inset CommandInset ref
16384 reference "eq:substack"
16388 there can be too much space beside an operator, because the characters
16389 following the operator are set beside the limits.
16392 \begin_layout Standard
16393 To avoid this, the following macro can be used in the LaTeX-preamble:
16396 \begin_layout Standard
16410 \begin_inset Newline newline
16422 \begin_inset Newline newline
16429 mathclapinternal #1#2{
16433 mathsurround =0pt #1{#2}$}}
16436 \begin_layout Standard
16437 This defines the command
16444 \begin_inset Index idx
16447 \begin_layout Plain Layout
16455 that sets the width of the limit to 0
16456 \begin_inset space \thinspace{}
16460 The command scheme is
16463 \begin_layout Standard
16471 \begin_layout Standard
16472 where the limit can consist of several conditions.
16475 \begin_layout Standard
16477 \begin_inset CommandInset ref
16479 reference "eq:substack"
16483 , one uses the command
16486 \begin_layout Standard
16499 \begin_layout Plain Layout
16508 0<k<1000 Ctrl+Return
16511 \begin_layout Standard
16512 to create the lower limit.
16513 The summand is now directly behind the summation operator:
16514 \begin_inset Formula \[
16515 \sum_{\mathclap{\substack{0<k<1000\\
16526 \begin_layout Standard
16527 \begin_inset VSpace bigskip
16530 How to use one limit for several operators is described in
16531 \begin_inset CommandInset ref
16533 reference "sub:Self-defined-Operators"
16540 \begin_layout Subsection
16542 \begin_inset CommandInset label
16544 name "sub:Binary-Operators"
16549 \begin_inset Index idx
16552 \begin_layout Plain Layout
16561 \begin_layout Standard
16562 Binary operators are surrounded by space when there is a character before
16564 \begin_inset VSpace medskip
16570 \begin_layout Standard
16571 \begin_inset space \hfill{}
16575 \begin_inset Tabular
16576 <lyxtabular version="3" rows="13" columns="2">
16577 <features tabularvalignment="middle">
16578 <column alignment="center" valignment="top" width="0pt">
16579 <column alignment="center" valignment="top" width="0pt">
16581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16584 \begin_layout Plain Layout
16586 \begin_inset Note Note
16589 \begin_layout Plain Layout
16596 is only used as spacer.
16606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16609 \begin_layout Plain Layout
16617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16620 \begin_layout Plain Layout
16626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16629 \begin_layout Plain Layout
16630 \begin_inset Formula $+$
16640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16643 \begin_layout Plain Layout
16649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16652 \begin_layout Plain Layout
16653 \begin_inset Formula $-$
16663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16666 \begin_layout Plain Layout
16674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16677 \begin_layout Plain Layout
16678 \begin_inset Formula $\pm$
16688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16691 \begin_layout Plain Layout
16699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16702 \begin_layout Plain Layout
16703 \begin_inset Formula $\mp$
16713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16716 \begin_layout Plain Layout
16724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16727 \begin_layout Plain Layout
16728 \begin_inset Formula $\cdot$
16738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16741 \begin_layout Plain Layout
16749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16752 \begin_layout Plain Layout
16753 \begin_inset Formula $\times$
16763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16766 \begin_layout Plain Layout
16774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16777 \begin_layout Plain Layout
16778 \begin_inset Formula $\div$
16788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16791 \begin_layout Plain Layout
16795 \begin_layout Plain Layout
16808 \begin_layout Plain Layout
16820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16823 \begin_layout Plain Layout
16824 \begin_inset Formula $*$
16834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16837 \begin_layout Plain Layout
16845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16848 \begin_layout Plain Layout
16849 \begin_inset Formula $\star$
16859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16862 \begin_layout Plain Layout
16870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16873 \begin_layout Plain Layout
16874 \begin_inset Formula $\circ$
16884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16887 \begin_layout Plain Layout
16895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16898 \begin_layout Plain Layout
16899 \begin_inset Formula $\diamond$
16909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16912 \begin_layout Plain Layout
16920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16923 \begin_layout Plain Layout
16924 \begin_inset Formula $\bullet$
16938 \begin_inset space \hfill{}
16942 \begin_inset Tabular
16943 <lyxtabular version="3" rows="13" columns="2">
16944 <features tabularvalignment="middle">
16945 <column alignment="center" valignment="top" width="0pt">
16946 <column alignment="center" valignment="top" width="0pt">
16948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16951 \begin_layout Plain Layout
16957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16960 \begin_layout Plain Layout
16968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16971 \begin_layout Plain Layout
16979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16982 \begin_layout Plain Layout
16983 \begin_inset Formula $\nabla$
16993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16996 \begin_layout Plain Layout
17004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17007 \begin_layout Plain Layout
17008 \begin_inset Formula $\bigtriangledown$
17018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17021 \begin_layout Plain Layout
17029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17032 \begin_layout Plain Layout
17033 \begin_inset Formula $\bigtriangleup$
17043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17046 \begin_layout Plain Layout
17054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17057 \begin_layout Plain Layout
17058 \begin_inset Formula $\Box$
17068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17071 \begin_layout Plain Layout
17079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17082 \begin_layout Plain Layout
17083 \begin_inset Formula $\cap$
17093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17096 \begin_layout Plain Layout
17104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17107 \begin_layout Plain Layout
17108 \begin_inset Formula $\cup$
17118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17121 \begin_layout Plain Layout
17129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17132 \begin_layout Plain Layout
17133 \begin_inset Formula $\dagger$
17143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17146 \begin_layout Plain Layout
17154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17157 \begin_layout Plain Layout
17158 \begin_inset Formula $\ddagger$
17168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17171 \begin_layout Plain Layout
17179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17182 \begin_layout Plain Layout
17183 \begin_inset Formula $\wr$
17193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17196 \begin_layout Plain Layout
17204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17207 \begin_layout Plain Layout
17208 \begin_inset Formula $\bigcirc$
17218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17221 \begin_layout Plain Layout
17229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17232 \begin_layout Plain Layout
17233 \begin_inset Formula $\wedge$
17243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17246 \begin_layout Plain Layout
17254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17257 \begin_layout Plain Layout
17258 \begin_inset Formula $\vee$
17272 \begin_inset space \hfill{}
17276 \begin_inset Tabular
17277 <lyxtabular version="3" rows="13" columns="2">
17278 <features tabularvalignment="middle">
17279 <column alignment="center" valignment="top" width="0pt">
17280 <column alignment="center" valignment="top" width="0pt">
17282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17285 \begin_layout Plain Layout
17291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17294 \begin_layout Plain Layout
17302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17305 \begin_layout Plain Layout
17313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17316 \begin_layout Plain Layout
17317 \begin_inset Formula $\oplus$
17327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17330 \begin_layout Plain Layout
17338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17341 \begin_layout Plain Layout
17342 \begin_inset Formula $\ominus$
17352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17355 \begin_layout Plain Layout
17363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17366 \begin_layout Plain Layout
17367 \begin_inset Formula $\otimes$
17377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17380 \begin_layout Plain Layout
17388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17391 \begin_layout Plain Layout
17392 \begin_inset Formula $\oslash$
17402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17405 \begin_layout Plain Layout
17413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17416 \begin_layout Plain Layout
17417 \begin_inset Formula $\odot$
17427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17430 \begin_layout Plain Layout
17438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17441 \begin_layout Plain Layout
17442 \begin_inset Formula $\amalg$
17452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17455 \begin_layout Plain Layout
17463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17466 \begin_layout Plain Layout
17467 \begin_inset Formula $\uplus$
17477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17480 \begin_layout Plain Layout
17488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17491 \begin_layout Plain Layout
17492 \begin_inset Formula $\setminus$
17502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17505 \begin_layout Plain Layout
17513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17516 \begin_layout Plain Layout
17517 \begin_inset Formula $\sqcap$
17527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17530 \begin_layout Plain Layout
17538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17541 \begin_layout Plain Layout
17542 \begin_inset Formula $\sqcup$
17552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17555 \begin_layout Plain Layout
17563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17566 \begin_layout Plain Layout
17567 \begin_inset Formula $\triangleleft$
17577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17580 \begin_layout Plain Layout
17588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17591 \begin_layout Plain Layout
17592 \begin_inset Formula $\triangleright$
17606 \begin_inset space \hfill{}
17612 \begin_layout Standard
17613 All binary operators can also be inserted via the math toolbar button
17614 \begin_inset Graphics
17615 filename ../images/math/pm.png
17623 \begin_layout Standard
17624 To typeset the Laplace operator also
17641 \begin_inset Formula $\nabla^{2}$
17644 ) can be used instead of
17653 \begin_layout Standard
17660 Insert\SpecialChar \menuseparator
17672 \begin_layout Subsection
17673 Self-defined Operators
17674 \begin_inset CommandInset label
17676 name "sub:Self-defined-Operators"
17681 \begin_inset Index idx
17684 \begin_layout Plain Layout
17685 Operators ! self-defined
17693 \begin_layout Standard
17694 With the help of the command
17698 DeclareMathOperator
17701 \begin_inset Index idx
17704 \begin_layout Plain Layout
17709 DeclareMathOperator
17714 custom operators can be defined in the LaTeX-preamble.
17715 Its command scheme is:
17718 \begin_layout Standard
17723 DeclareMathOperator{new command}{display}
17726 \begin_layout Standard
17727 Display can be characters or symbols that define how the operator looks
17729 To define a big operator a * is set behind the command.
17730 All self-defined big operators can have limits as described in
17731 \begin_inset CommandInset ref
17733 reference "sub:Operator-Limits"
17740 \begin_layout Standard
17741 For example the LaTeX-preamble line
17744 \begin_layout Standard
17749 DeclareMathOperator*{
17756 \begin_layout Standard
17757 defines the command
17763 , that inserts a big operator consisting of the lozenge symbol from
17764 \begin_inset CommandInset ref
17766 reference "sub:Miscellaneous-Symbols"
17771 \begin_inset Formula \[
17772 \Lozenge_{n=1}^{\infty}\]
17776 The command for this formula is:
17787 \begin_inset Formula $\to$
17793 \begin_layout Standard
17794 \begin_inset VSpace bigskip
17797 When self-defined operators are not used several times in the document,
17798 they can also be defined with the commands
17805 \begin_inset Index idx
17808 \begin_layout Plain Layout
17823 \begin_inset Index idx
17826 \begin_layout Plain Layout
17834 , which have the following scheme:
17837 \begin_layout Standard
17851 \begin_layout Standard
17858 defines big operators,
17867 \begin_layout Standard
17875 \begin_inset space \thinspace{}
17879 \begin_inset space \space{}
17882 be used to use one limit for several operators:
17885 \begin_layout Standard
17886 \begin_inset Formula \[
17887 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17894 \begin_layout Standard
17895 The command for the formula above is:
17896 \begin_inset Newline newline
17915 \begin_layout Plain Layout
17927 \begin_inset Formula $\to$
17936 \begin_layout Plain Layout
17950 \begin_layout Section
17952 \begin_inset Index idx
17955 \begin_layout Plain Layout
17964 \begin_layout Subsection
17966 \begin_inset CommandInset label
17968 name "sub:Font-Styles"
17973 \begin_inset Index idx
17976 \begin_layout Plain Layout
17985 \begin_layout Standard
17986 Latin letters in formulas can be set in one of the following font styles:
17987 \begin_inset VSpace -2mm
17993 \begin_layout Standard
17995 \begin_inset Tabular
17996 <lyxtabular version="3" rows="7" columns="3">
17997 <features tabularvalignment="middle">
17998 <column alignment="center" valignment="top" width="0">
17999 <column alignment="center" valignment="top" width="0">
18000 <column alignment="center" valignment="top" width="0">
18002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18005 \begin_layout Plain Layout
18011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18014 \begin_layout Plain Layout
18020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18023 \begin_layout Plain Layout
18031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18034 \begin_layout Plain Layout
18043 \begin_layout Plain Layout
18059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18062 \begin_layout Plain Layout
18063 \begin_inset Formula $\mathbb{ABC}$
18071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18074 \begin_layout Plain Layout
18087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18090 \begin_layout Plain Layout
18099 \begin_layout Plain Layout
18115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18118 \begin_layout Plain Layout
18119 \begin_inset Formula $\mathbf{AbC}$
18127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18130 \begin_layout Plain Layout
18143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18146 \begin_layout Plain Layout
18155 \begin_layout Plain Layout
18171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18174 \begin_layout Plain Layout
18175 \begin_inset Formula $\boldsymbol{AbC}$
18183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18186 \begin_layout Plain Layout
18189 arg "font-boldsymbol"
18199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18202 \begin_layout Plain Layout
18211 \begin_layout Plain Layout
18227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18230 \begin_layout Plain Layout
18231 \begin_inset Formula $\mathcal{ABC}$
18239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18242 \begin_layout Plain Layout
18255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18258 \begin_layout Plain Layout
18267 \begin_layout Plain Layout
18283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18286 \begin_layout Plain Layout
18287 \begin_inset Formula $\mathfrak{AbC}$
18295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18298 \begin_layout Plain Layout
18306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18309 \begin_layout Plain Layout
18318 \begin_layout Plain Layout
18334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18337 \begin_layout Plain Layout
18338 \begin_inset Formula $\mathscr{AbC}$
18346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18349 \begin_layout Plain Layout
18363 \begin_layout Standard
18365 \begin_inset Tabular
18366 <lyxtabular version="3" rows="5" columns="3">
18367 <features tabularvalignment="middle">
18368 <column alignment="center" valignment="top" width="0">
18369 <column alignment="center" valignment="top" width="0">
18370 <column alignment="center" valignment="top" width="0">
18372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18375 \begin_layout Plain Layout
18381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18384 \begin_layout Plain Layout
18390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18393 \begin_layout Plain Layout
18401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18404 \begin_layout Plain Layout
18413 \begin_layout Plain Layout
18429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18432 \begin_layout Plain Layout
18433 \begin_inset Formula $\mathit{AbC}$
18441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18444 \begin_layout Plain Layout
18452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18455 \begin_layout Plain Layout
18464 \begin_layout Plain Layout
18480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18483 \begin_layout Plain Layout
18484 \begin_inset Formula $\mathrm{AbC}$
18492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18495 \begin_layout Plain Layout
18508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18511 \begin_layout Plain Layout
18520 \begin_layout Plain Layout
18536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18539 \begin_layout Plain Layout
18540 \begin_inset Formula $\mathsf{AbC}$
18548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18551 \begin_layout Plain Layout
18564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18567 \begin_layout Plain Layout
18576 \begin_layout Plain Layout
18592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18595 \begin_layout Plain Layout
18596 \begin_inset Formula $\mathtt{AbC}$
18604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18607 \begin_layout Plain Layout
18610 arg "font-typewriter"
18626 \begin_layout Standard
18627 \begin_inset Note Greyedout
18630 \begin_layout Plain Layout
18647 can only be used for big letters.
18655 \begin_layout Standard
18656 Predefined is the style
18665 \begin_layout Standard
18666 The style commands work also for letters in mathematical constructs:
18667 \begin_inset Formula \[
18668 \mathfrak{A=\frac{b}{C}}\]
18675 \begin_layout Standard
18676 Characters in mathematical text don't appear in a math font style but in
18677 the text font style
18684 That their style can't be set correctly via the text style dialog is a
18689 \begin_layout Plain Layout
18690 \begin_inset CommandInset href
18692 name "LyX-bug #4629"
18693 target "http://www.lyx.org/trac/ticket/4629"
18705 \begin_layout Standard
18706 Instead of the style commands the dialog
18708 Edit\SpecialChar \menuseparator
18709 Math\SpecialChar \menuseparator
18712 or the toolbar button
18713 \begin_inset Graphics
18714 filename ../images/math/font.png
18722 \begin_layout Subsection
18724 \begin_inset CommandInset label
18726 name "sub:Bold-Formulas"
18731 \begin_inset Index idx
18734 \begin_layout Plain Layout
18743 \begin_layout Standard
18744 To make a complete formula bold, the command
18750 from the previous subsection cannot be used, because it doesn't work for
18751 small Greek letters.
18752 Furthermore it prints Latin letters always upright, like in the following
18756 \begin_layout Standard
18757 \begin_inset Formula \[
18758 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18765 \begin_layout Standard
18766 To display the formula correctly, the command
18773 \begin_inset Formula \[
18774 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18778 It is also possible to set the formula in a
18780 boldmath environment
18783 This environment is created by inserting the command
18790 \begin_inset Index idx
18793 \begin_layout Plain Layout
18802 To end the environment, the command
18809 \begin_inset Index idx
18812 \begin_layout Plain Layout
18820 is inserted in TeX-mode.
18824 \begin_layout Plain Layout
18834 \begin_inset Formula \[
18835 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18843 \begin_layout Plain Layout
18855 \begin_layout Subsection
18857 \begin_inset Index idx
18860 \begin_layout Plain Layout
18869 \begin_layout Standard
18870 Formulas can be colored like normal text: Highlight a formula or a formula
18876 Here is a formula in magenta:
18877 \begin_inset Formula \[
18878 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18885 \begin_layout Standard
18886 You can also define your own colors as described in
18887 \begin_inset CommandInset ref
18889 reference "sub:Colored-Boxes"
18894 They can be used with the TeX code command
18901 \begin_inset Index idx
18904 \begin_layout Plain Layout
18915 \begin_layout Standard
18920 textcolor{color}{characters or formula}
18923 \begin_layout Standard
18924 The following example was colored completely dark green and partly red:
18927 \begin_layout Standard
18931 \begin_layout Plain Layout
18935 textcolor{darkgreen}{
18941 \begin_inset Formula \[
18942 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18950 \begin_layout Plain Layout
18960 \begin_layout Standard
18961 Due to a bug in LyX only complete formulas can be colored with self-defined
18966 \begin_layout Plain Layout
18967 \begin_inset CommandInset href
18969 name "LyX-bug #5269"
18970 target "http://www.lyx.org/trac/ticket/5269"
18982 \begin_layout Subsection
18984 \begin_inset CommandInset label
18986 name "sub:Font-Sizes"
18991 \begin_inset Index idx
18994 \begin_layout Plain Layout
19003 \begin_layout Standard
19004 For characters in formulas there are, analog to characters in text, the
19005 following size commands:
19008 \begin_layout Standard
19052 \begin_inset Newline newline
19074 \begin_layout Standard
19075 The size produced by the commands depends on the document font size, that
19076 corresponds with the command
19083 The other commands produce smaller or larger sizes than
19090 The font size can however not exceed a certain value.
19091 Is for example the document font size 12
19092 \begin_inset space \thinspace{}
19101 switches to the same size as
19111 \begin_layout Standard
19112 A size command is inserted in TeX-mode before the formula and sets the size
19113 for all following formula and text characters.
19114 To switch back to the initial size, the command
19120 is inserted behind the formula in TeX-mode.
19123 \begin_layout Standard
19124 \begin_inset Newpage newpage
19130 \begin_layout Standard
19131 Within a formula the size can be changed using the following size commands:
19134 \begin_layout Standard
19137 \begin_inset Tabular
19138 <lyxtabular version="3" rows="5" columns="2">
19139 <features tabularvalignment="middle">
19140 <column alignment="center" valignment="top" width="0">
19141 <column alignment="center" valignment="top" width="0">
19143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19146 \begin_layout Plain Layout
19152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19155 \begin_layout Plain Layout
19157 \begin_inset Note Note
19160 \begin_layout Plain Layout
19167 is only used as spacer.
19179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19182 \begin_layout Plain Layout
19186 \begin_inset Index idx
19189 \begin_layout Plain Layout
19202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19205 \begin_layout Plain Layout
19206 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19219 \begin_layout Plain Layout
19227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19230 \begin_layout Plain Layout
19231 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19244 \begin_layout Plain Layout
19252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19255 \begin_layout Plain Layout
19256 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19269 \begin_layout Plain Layout
19277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19280 \begin_layout Plain Layout
19281 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19297 \begin_layout Standard
19298 After entering these commands, a blue box appears in which the formula parts
19302 \begin_layout Standard
19303 There is a further method to change the font size, that though only works
19304 for symbols or letters in mathematical text.
19305 To use it, one of the above text size commands is inserted in mathematical
19307 All following characters until the end of the mathematical text or until
19308 another size command will have the selected size.
19310 \begin_inset VSpace -2mm
19316 \begin_layout Standard
19320 \begin_layout Plain Layout
19330 \begin_inset Formula \[
19331 A=\frac{B}{c}\cdot\maltese\]
19336 \begin_inset Formula \[
19337 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
19345 \begin_layout Plain Layout
19357 \begin_layout Standard
19358 \begin_inset VSpace medskip
19361 Before both formulas the command
19368 The command for the second formula is:
19369 \begin_inset Newline newline
19380 \begin_layout Plain Layout
19395 \begin_layout Plain Layout
19410 \begin_layout Plain Layout
19425 \begin_layout Plain Layout
19435 \begin_inset Formula $\to$
19439 \begin_inset Formula $\to$
19443 \begin_inset Newline newline
19447 \begin_inset space \hspace*{}
19461 \begin_layout Plain Layout
19476 \begin_layout Plain Layout
19491 \begin_layout Plain Layout
19503 \begin_layout Standard
19504 If a symbol cannot be displayed in different sizes, it will always be displayed
19505 in the default size.
19508 \begin_layout Standard
19509 \begin_inset Newpage newpage
19515 \begin_layout Section
19517 \begin_inset Index idx
19520 \begin_layout Plain Layout
19529 \begin_layout Standard
19530 All Greek letters can also be inserted via the toolbar button
19531 \begin_inset Graphics
19532 filename ../images/math/alpha.png
19540 \begin_layout Subsection
19542 \begin_inset Index idx
19545 \begin_layout Plain Layout
19546 Greek letters ! small
19554 \begin_layout Standard
19555 \begin_inset space \hfill{}
19559 \begin_inset Tabular
19560 <lyxtabular version="3" rows="11" columns="2">
19561 <features tabularvalignment="middle">
19562 <column alignment="center" valignment="top" width="0pt">
19563 <column alignment="center" valignment="top" width="0pt">
19565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19568 \begin_layout Plain Layout
19574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19577 \begin_layout Plain Layout
19585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19588 \begin_layout Plain Layout
19596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19599 \begin_layout Plain Layout
19600 \begin_inset Formula $\alpha$
19610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19613 \begin_layout Plain Layout
19621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19624 \begin_layout Plain Layout
19625 \begin_inset Formula $\beta$
19635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19638 \begin_layout Plain Layout
19646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19649 \begin_layout Plain Layout
19650 \begin_inset Formula $\gamma$
19660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19663 \begin_layout Plain Layout
19671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19674 \begin_layout Plain Layout
19675 \begin_inset Formula $\delta$
19685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19688 \begin_layout Plain Layout
19696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19699 \begin_layout Plain Layout
19700 \begin_inset Formula $\epsilon$
19710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19713 \begin_layout Plain Layout
19721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19724 \begin_layout Plain Layout
19725 \begin_inset Formula $\varepsilon$
19735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19738 \begin_layout Plain Layout
19746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19749 \begin_layout Plain Layout
19750 \begin_inset Formula $\zeta$
19760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19763 \begin_layout Plain Layout
19771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19774 \begin_layout Plain Layout
19775 \begin_inset Formula $\eta$
19785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19788 \begin_layout Plain Layout
19796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19799 \begin_layout Plain Layout
19800 \begin_inset Formula $\theta$
19810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19813 \begin_layout Plain Layout
19821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19824 \begin_layout Plain Layout
19825 \begin_inset Formula $\vartheta$
19839 \begin_inset space \hfill{}
19843 \begin_inset Tabular
19844 <lyxtabular version="3" rows="12" columns="2">
19845 <features tabularvalignment="middle">
19846 <column alignment="center" valignment="top" width="0pt">
19847 <column alignment="center" valignment="top" width="0pt">
19849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19852 \begin_layout Plain Layout
19858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19861 \begin_layout Plain Layout
19869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19872 \begin_layout Plain Layout
19880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19883 \begin_layout Plain Layout
19884 \begin_inset Formula $\iota$
19894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19897 \begin_layout Plain Layout
19905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19908 \begin_layout Plain Layout
19909 \begin_inset Formula $\kappa$
19919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19922 \begin_layout Plain Layout
19930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19933 \begin_layout Plain Layout
19934 \begin_inset Formula $\varkappa$
19944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19947 \begin_layout Plain Layout
19955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19958 \begin_layout Plain Layout
19959 \begin_inset Formula $\lambda$
19969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19972 \begin_layout Plain Layout
19980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19983 \begin_layout Plain Layout
19984 \begin_inset Formula $\mu$
19994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19997 \begin_layout Plain Layout
20005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20008 \begin_layout Plain Layout
20009 \begin_inset Formula $\nu$
20019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20022 \begin_layout Plain Layout
20030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20033 \begin_layout Plain Layout
20034 \begin_inset Formula $\xi$
20044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20047 \begin_layout Plain Layout
20053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20056 \begin_layout Plain Layout
20057 \begin_inset Formula $o$
20067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20070 \begin_layout Plain Layout
20078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20081 \begin_layout Plain Layout
20082 \begin_inset Formula $\pi$
20092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20095 \begin_layout Plain Layout
20103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20106 \begin_layout Plain Layout
20107 \begin_inset Formula $\varpi$
20117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20120 \begin_layout Plain Layout
20128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20131 \begin_layout Plain Layout
20132 \begin_inset Formula $\rho$
20146 \begin_inset space \hfill{}
20150 \begin_inset Tabular
20151 <lyxtabular version="3" rows="11" columns="2">
20152 <features tabularvalignment="middle">
20153 <column alignment="center" valignment="top" width="0pt">
20154 <column alignment="center" valignment="top" width="0pt">
20156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20159 \begin_layout Plain Layout
20165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20168 \begin_layout Plain Layout
20176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20179 \begin_layout Plain Layout
20187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20190 \begin_layout Plain Layout
20191 \begin_inset Formula $\varrho$
20201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20204 \begin_layout Plain Layout
20212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20215 \begin_layout Plain Layout
20216 \begin_inset Formula $\sigma$
20226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20229 \begin_layout Plain Layout
20237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20240 \begin_layout Plain Layout
20241 \begin_inset Formula $\varsigma$
20251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20254 \begin_layout Plain Layout
20262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20265 \begin_layout Plain Layout
20266 \begin_inset Formula $\tau$
20276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20279 \begin_layout Plain Layout
20287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20290 \begin_layout Plain Layout
20291 \begin_inset Formula $\upsilon$
20301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20304 \begin_layout Plain Layout
20312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20315 \begin_layout Plain Layout
20316 \begin_inset Formula $\phi$
20326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20329 \begin_layout Plain Layout
20337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20340 \begin_layout Plain Layout
20341 \begin_inset Formula $\varphi$
20351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20354 \begin_layout Plain Layout
20362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20365 \begin_layout Plain Layout
20366 \begin_inset Formula $\chi$
20376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20379 \begin_layout Plain Layout
20387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20390 \begin_layout Plain Layout
20391 \begin_inset Formula $\psi$
20401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20404 \begin_layout Plain Layout
20412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20415 \begin_layout Plain Layout
20416 \begin_inset Formula $\omega$
20430 \begin_inset space \hfill{}
20436 \begin_layout Standard
20437 \begin_inset VSpace medskip
20443 \begin_layout Standard
20444 How to create upright Greek letters is explained in
20445 \begin_inset CommandInset ref
20447 reference "sub:Upright-small-Greek"
20454 \begin_layout Subsection
20456 \begin_inset Index idx
20459 \begin_layout Plain Layout
20460 Greek letters ! big
20468 \begin_layout Standard
20469 \begin_inset space \hfill{}
20473 \begin_inset Tabular
20474 <lyxtabular version="3" rows="7" columns="2">
20475 <features tabularvalignment="middle">
20476 <column alignment="center" valignment="top" width="0pt">
20477 <column alignment="center" valignment="top" width="0pt">
20479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20482 \begin_layout Plain Layout
20488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20491 \begin_layout Plain Layout
20499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20502 \begin_layout Plain Layout
20510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20513 \begin_layout Plain Layout
20514 \begin_inset Formula $\Gamma$
20524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20527 \begin_layout Plain Layout
20535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20538 \begin_layout Plain Layout
20539 \begin_inset Formula $\Delta$
20549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20552 \begin_layout Plain Layout
20560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20563 \begin_layout Plain Layout
20564 \begin_inset Formula $\Theta$
20574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20577 \begin_layout Plain Layout
20585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20588 \begin_layout Plain Layout
20589 \begin_inset Formula $\Lambda$
20599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20602 \begin_layout Plain Layout
20610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20613 \begin_layout Plain Layout
20614 \begin_inset Formula $\Xi$
20624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20627 \begin_layout Plain Layout
20635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20638 \begin_layout Plain Layout
20639 \begin_inset Formula $\Pi$
20653 \begin_inset space \hfill{}
20657 \begin_inset Tabular
20658 <lyxtabular version="3" rows="6" columns="2">
20659 <features tabularvalignment="middle">
20660 <column alignment="center" valignment="top" width="0pt">
20661 <column alignment="center" valignment="top" width="0pt">
20663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20666 \begin_layout Plain Layout
20672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20675 \begin_layout Plain Layout
20683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20686 \begin_layout Plain Layout
20694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20697 \begin_layout Plain Layout
20698 \begin_inset Formula $\Sigma$
20708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20711 \begin_layout Plain Layout
20719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20722 \begin_layout Plain Layout
20723 \begin_inset Formula $\Upsilon$
20733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20736 \begin_layout Plain Layout
20744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20747 \begin_layout Plain Layout
20748 \begin_inset Formula $\Phi$
20758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20761 \begin_layout Plain Layout
20769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20772 \begin_layout Plain Layout
20773 \begin_inset Formula $\Psi$
20783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20786 \begin_layout Plain Layout
20794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20797 \begin_layout Plain Layout
20798 \begin_inset Formula $\Omega$
20812 \begin_inset space \hfill{}
20818 \begin_layout Standard
20819 \begin_inset VSpace medskip
20822 That the big Greek letters appear upright is caused by a design bug when
20824 To get correct italic big letters, begin every command with
20829 For example the command
20836 \begin_inset Formula $\varGamma$
20842 \begin_layout Subsection
20844 \begin_inset Index idx
20847 \begin_layout Plain Layout
20848 Greek letters ! bold
20856 \begin_layout Standard
20857 Greek letters cannot be set with different font styles like Latin letters.
20858 They can only be made bold with the command
20865 \begin_inset Index idx
20868 \begin_layout Plain Layout
20879 \begin_layout Standard
20881 \begin_inset Tabular
20882 <lyxtabular version="3" rows="3" columns="2">
20883 <features tabularvalignment="middle">
20884 <column alignment="center" valignment="top" width="0">
20885 <column alignment="center" valignment="top" width="0">
20887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20890 \begin_layout Plain Layout
20896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20899 \begin_layout Plain Layout
20907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20910 \begin_layout Plain Layout
20922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20925 \begin_layout Plain Layout
20926 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20939 \begin_layout Plain Layout
20951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20954 \begin_layout Plain Layout
20955 \begin_inset Formula $\theta\boldsymbol{\theta}$
20971 \begin_layout Section
20976 \begin_layout Plain Layout
20989 \begin_layout Plain Layout
20990 A list with all symbols of most of the LaTeX-packages can be found in
20991 \begin_inset CommandInset citation
21006 \begin_layout Plain Layout
21014 \begin_inset Note Note
21017 \begin_layout Plain Layout
21020 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21023 \begin_layout Plain Layout
21026 texorpdfstring is in section
21027 \begin_inset CommandInset ref
21029 reference "sub:Formulas-in-Section"
21039 \begin_inset Index idx
21042 \begin_layout Plain Layout
21051 \begin_layout Standard
21052 Many of the symbols listed in this section can also be inserted via the
21054 \begin_inset Graphics
21055 filename ../images/math/nabla.png
21061 \begin_inset Graphics
21062 filename ../images/math/digamma.png
21070 \begin_layout Subsection
21071 Mathematical Symbols
21072 \begin_inset CommandInset label
21074 name "sub:Mathematical-Symbols"
21079 \begin_inset Index idx
21082 \begin_layout Plain Layout
21083 Symbols ! mathematical
21091 \begin_layout Standard
21092 \begin_inset space \hfill{}
21096 \begin_inset Tabular
21097 <lyxtabular version="3" rows="10" columns="2">
21098 <features tabularvalignment="middle">
21099 <column alignment="center" valignment="top" width="0pt">
21100 <column alignment="center" valignment="top" width="0pt">
21102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21105 \begin_layout Plain Layout
21111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21114 \begin_layout Plain Layout
21122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21125 \begin_layout Plain Layout
21133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21136 \begin_layout Plain Layout
21137 \begin_inset Formula $\neg$
21147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21150 \begin_layout Plain Layout
21158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21161 \begin_layout Plain Layout
21162 \begin_inset Formula $\Im$
21172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21175 \begin_layout Plain Layout
21183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21186 \begin_layout Plain Layout
21187 \begin_inset Formula $\Re$
21197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21200 \begin_layout Plain Layout
21208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21211 \begin_layout Plain Layout
21212 \begin_inset Formula $\aleph$
21222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21225 \begin_layout Plain Layout
21233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21236 \begin_layout Plain Layout
21237 \begin_inset Formula $\partial$
21247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21250 \begin_layout Plain Layout
21258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21261 \begin_layout Plain Layout
21262 \begin_inset Formula $\infty$
21272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21275 \begin_layout Plain Layout
21283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21286 \begin_layout Plain Layout
21287 \begin_inset Formula $\wp$
21297 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21300 \begin_layout Plain Layout
21308 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21311 \begin_layout Plain Layout
21312 \begin_inset Formula $\imath$
21322 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21325 \begin_layout Plain Layout
21333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21336 \begin_layout Plain Layout
21337 \begin_inset Formula $\jmath$
21351 \begin_inset space \hfill{}
21355 \begin_inset Tabular
21356 <lyxtabular version="3" rows="10" columns="2">
21357 <features tabularvalignment="middle">
21358 <column alignment="center" valignment="top" width="0pt">
21359 <column alignment="center" valignment="top" width="0pt">
21361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21364 \begin_layout Plain Layout
21370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21373 \begin_layout Plain Layout
21375 \begin_inset Note Note
21378 \begin_layout Plain Layout
21385 is only used as spacer.
21397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21400 \begin_layout Plain Layout
21408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21411 \begin_layout Plain Layout
21412 \begin_inset Formula $\forall$
21422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21425 \begin_layout Plain Layout
21433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21436 \begin_layout Plain Layout
21437 \begin_inset Formula $\exists$
21447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21450 \begin_layout Plain Layout
21458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21461 \begin_layout Plain Layout
21462 \begin_inset Formula $\nexists$
21472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21475 \begin_layout Plain Layout
21483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21486 \begin_layout Plain Layout
21487 \begin_inset Formula $\emptyset$
21497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21500 \begin_layout Plain Layout
21508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21511 \begin_layout Plain Layout
21512 \begin_inset Formula $\varnothing$
21522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21525 \begin_layout Plain Layout
21533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21536 \begin_layout Plain Layout
21537 \begin_inset Formula $\dag$
21547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21550 \begin_layout Plain Layout
21558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21561 \begin_layout Plain Layout
21562 \begin_inset Formula $\ddag$
21572 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21575 \begin_layout Plain Layout
21583 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21586 \begin_layout Plain Layout
21590 \begin_layout Plain Layout
21600 \begin_inset Formula $\complement$
21607 \begin_layout Plain Layout
21621 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21624 \begin_layout Plain Layout
21632 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21635 \begin_layout Plain Layout
21636 \begin_inset Formula $\Bbbk$
21650 \begin_inset space \hfill{}
21654 \begin_inset Tabular
21655 <lyxtabular version="3" rows="10" columns="2">
21656 <features tabularvalignment="middle">
21657 <column alignment="center" valignment="top" width="0pt">
21658 <column alignment="center" valignment="top" width="0pt">
21660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21663 \begin_layout Plain Layout
21669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21672 \begin_layout Plain Layout
21680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21683 \begin_layout Plain Layout
21691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21694 \begin_layout Plain Layout
21695 \begin_inset Formula $\prime$
21705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21708 \begin_layout Plain Layout
21716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21719 \begin_layout Plain Layout
21720 \begin_inset Formula $\backprime$
21730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21733 \begin_layout Plain Layout
21741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21744 \begin_layout Plain Layout
21745 \begin_inset Formula $\mho$
21755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21758 \begin_layout Plain Layout
21766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21769 \begin_layout Plain Layout
21770 \begin_inset Formula $\triangle$
21780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21783 \begin_layout Plain Layout
21791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21794 \begin_layout Plain Layout
21795 \begin_inset Formula $\angle$
21805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21808 \begin_layout Plain Layout
21816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21819 \begin_layout Plain Layout
21820 \begin_inset Formula $\measuredangle$
21830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21833 \begin_layout Plain Layout
21841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21844 \begin_layout Plain Layout
21845 \begin_inset Formula $\sphericalangle$
21855 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21858 \begin_layout Plain Layout
21866 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21869 \begin_layout Plain Layout
21870 \begin_inset Formula $\top$
21880 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21883 \begin_layout Plain Layout
21891 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21894 \begin_layout Plain Layout
21895 \begin_inset Formula $\bot$
21909 \begin_inset space \hfill{}
21915 \begin_layout Subsection
21916 Miscellaneous Symbols
21917 \begin_inset CommandInset label
21919 name "sub:Miscellaneous-Symbols"
21924 \begin_inset Index idx
21927 \begin_layout Plain Layout
21928 Symbols ! miscellaneous
21936 \begin_layout Standard
21939 \begin_inset Tabular
21940 <lyxtabular version="3" rows="10" columns="2">
21941 <features tabularvalignment="middle">
21942 <column alignment="center" valignment="top" width="0pt">
21943 <column alignment="center" valignment="top" width="0pt">
21945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21948 \begin_layout Plain Layout
21954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21957 \begin_layout Plain Layout
21965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21968 \begin_layout Plain Layout
21976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21979 \begin_layout Plain Layout
21980 \begin_inset Formula $\flat$
21990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21993 \begin_layout Plain Layout
22001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22004 \begin_layout Plain Layout
22005 \begin_inset Formula $\natural$
22015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22018 \begin_layout Plain Layout
22026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22029 \begin_layout Plain Layout
22030 \begin_inset Formula $\sharp$
22040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22043 \begin_layout Plain Layout
22051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22054 \begin_layout Plain Layout
22055 \begin_inset Formula $\surd$
22065 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22068 \begin_layout Plain Layout
22076 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22079 \begin_layout Plain Layout
22080 \begin_inset Formula $\checkmark$
22090 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22093 \begin_layout Plain Layout
22101 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22104 \begin_layout Plain Layout
22105 \begin_inset Formula $\yen$
22115 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22118 \begin_layout Plain Layout
22126 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22129 \begin_layout Plain Layout
22130 \begin_inset Formula $\pounds$
22140 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22143 \begin_layout Plain Layout
22149 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22152 \begin_layout Plain Layout
22153 \begin_inset Formula $\$$
22163 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22166 \begin_layout Plain Layout
22172 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22175 \begin_layout Plain Layout
22176 \begin_inset Formula $§$
22190 \begin_inset Tabular
22191 <lyxtabular version="3" rows="10" columns="2">
22192 <features tabularvalignment="middle">
22193 <column alignment="center" valignment="top" width="0">
22194 <column alignment="center" valignment="top" width="0">
22196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22199 \begin_layout Plain Layout
22205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22208 \begin_layout Plain Layout
22216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22219 \begin_layout Plain Layout
22227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22230 \begin_layout Plain Layout
22231 \begin_inset Formula $\hbar$
22241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22244 \begin_layout Plain Layout
22252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22255 \begin_layout Plain Layout
22256 \begin_inset Formula $\hslash$
22266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22269 \begin_layout Plain Layout
22277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22280 \begin_layout Plain Layout
22281 \begin_inset Formula $\clubsuit$
22291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22294 \begin_layout Plain Layout
22302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22305 \begin_layout Plain Layout
22306 \begin_inset Formula $\spadesuit$
22316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22319 \begin_layout Plain Layout
22327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22330 \begin_layout Plain Layout
22331 \begin_inset Formula $\bigstar$
22341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22344 \begin_layout Plain Layout
22352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22355 \begin_layout Plain Layout
22356 \begin_inset Formula $\blacklozenge$
22366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22369 \begin_layout Plain Layout
22377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22380 \begin_layout Plain Layout
22381 \begin_inset Formula $\blacktriangle$
22391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22394 \begin_layout Plain Layout
22402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22405 \begin_layout Plain Layout
22406 \begin_inset Formula $\blacktriangledown$
22416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22419 \begin_layout Plain Layout
22427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22430 \begin_layout Plain Layout
22431 \begin_inset Formula $\bullet$
22445 \begin_inset Tabular
22446 <lyxtabular version="3" rows="10" columns="2">
22447 <features tabularvalignment="middle">
22448 <column alignment="center" valignment="top" width="0pt">
22449 <column alignment="center" valignment="top" width="0pt">
22451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22454 \begin_layout Plain Layout
22460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22463 \begin_layout Plain Layout
22471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22474 \begin_layout Plain Layout
22482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22485 \begin_layout Plain Layout
22486 \begin_inset Formula $\diamondsuit$
22496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22499 \begin_layout Plain Layout
22507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22510 \begin_layout Plain Layout
22511 \begin_inset Formula $\Diamond$
22521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22524 \begin_layout Plain Layout
22532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22535 \begin_layout Plain Layout
22536 \begin_inset Formula $\heartsuit$
22546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22549 \begin_layout Plain Layout
22557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22560 \begin_layout Plain Layout
22561 \begin_inset Formula $\P$
22571 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22574 \begin_layout Plain Layout
22582 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22585 \begin_layout Plain Layout
22586 \begin_inset Formula $\copyright$
22596 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22599 \begin_layout Plain Layout
22607 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22610 \begin_layout Plain Layout
22611 \begin_inset Formula $\circledR$
22621 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22624 \begin_layout Plain Layout
22632 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22635 \begin_layout Plain Layout
22636 \begin_inset Formula $\maltese$
22646 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22649 \begin_layout Plain Layout
22657 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22660 \begin_layout Plain Layout
22661 \begin_inset Formula $\diagup$
22671 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22674 \begin_layout Plain Layout
22682 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22685 \begin_layout Plain Layout
22686 \begin_inset Formula $\diagdown$
22702 \begin_layout Standard
22703 \begin_inset VSpace medskip
22706 More symbols are listed in
22707 \begin_inset CommandInset ref
22709 reference "sub:Miscellaneous-special-Characters"
22716 \begin_layout Standard
22717 Some symbols can be displayed in different sizes, see
22718 \begin_inset CommandInset ref
22720 reference "sub:Font-Sizes"
22727 \begin_layout Subsection
22729 \begin_inset Index idx
22732 \begin_layout Plain Layout
22733 Symbols ! Euro-symbol
22739 \begin_inset Index idx
22742 \begin_layout Plain Layout
22749 \begin_layout Plain Layout
22766 \begin_layout Standard
22767 To use the Euro symbol in formulas, the LaTeX-package
22772 \begin_inset Index idx
22775 \begin_layout Plain Layout
22781 must be installed and loaded with the LaTeX-preamble line
22784 \begin_layout Standard
22789 usepackage[gennarrow]{eurosym}
22792 \begin_layout Standard
22793 The Euro symbol can now be inserted with the command
22800 \begin_inset Index idx
22803 \begin_layout Plain Layout
22814 \begin_layout Standard
22815 The Euro symbol can directly be inserted with the € key in mathematical
22816 text, without having
22831 can also be inserted in TeX-mode.
22832 The official currency symbol can then be inserted with the command
22839 \begin_inset Index idx
22842 \begin_layout Plain Layout
22850 , that is only available in TeX-mode.
22853 \begin_layout Standard
22857 \begin_layout Plain Layout
22867 \begin_inset Note Note
22870 \begin_layout Plain Layout
22871 The following table will only be displayed when the LaTeX-package
22883 \begin_layout Standard
22884 An overview about the different Euro symbols:
22887 \begin_layout Standard
22889 \begin_inset Tabular
22890 <lyxtabular version="3" rows="4" columns="3">
22891 <features tabularvalignment="middle">
22892 <column alignment="center" valignment="top" width="0pt">
22893 <column alignment="center" valignment="top" width="0pt">
22894 <column alignment="center" valignment="top" width="0pt">
22896 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22899 \begin_layout Plain Layout
22905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22908 \begin_layout Plain Layout
22914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22917 \begin_layout Plain Layout
22925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22928 \begin_layout Plain Layout
22934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22937 \begin_layout Plain Layout
22945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22948 \begin_layout Plain Layout
22949 \begin_inset Formula $\euro$
22959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22962 \begin_layout Plain Layout
22968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22971 \begin_layout Plain Layout
22977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22980 \begin_layout Plain Layout
22981 \begin_inset Formula $\mbox{€}$
22991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22994 \begin_layout Plain Layout
23000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23003 \begin_layout Plain Layout
23011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23014 \begin_layout Plain Layout
23018 \begin_layout Plain Layout
23040 \begin_layout Standard
23044 \begin_layout Plain Layout
23054 \begin_inset Note Note
23057 \begin_layout Plain Layout
23058 The following will be displayed when the LaTeX-package
23070 \begin_layout Standard
23071 You need to install the LaTeX-package
23075 to see the rest of this subsection in the output.
23078 \begin_layout Standard
23082 \begin_layout Plain Layout
23094 \begin_layout Section
23096 \begin_inset CommandInset label
23098 name "sec:Relations"
23103 \begin_inset Index idx
23106 \begin_layout Plain Layout
23113 \begin_inset Index idx
23116 \begin_layout Plain Layout
23121 \begin_layout Plain Layout
23132 \begin_layout Plain Layout
23147 \begin_layout Standard
23148 All relations can also be inserted via the toolbar button
23149 \begin_inset Graphics
23150 filename ../images/math/leq.png
23158 \begin_layout Standard
23159 \begin_inset space \hfill{}
23163 \begin_inset Tabular
23164 <lyxtabular version="3" rows="17" columns="2">
23165 <features tabularvalignment="middle">
23166 <column alignment="center" valignment="top" width="0pt">
23167 <column alignment="center" valignment="top" width="0pt">
23169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23172 \begin_layout Plain Layout
23178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23181 \begin_layout Plain Layout
23189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23192 \begin_layout Plain Layout
23198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23201 \begin_layout Plain Layout
23202 \begin_inset Formula $<$
23212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23215 \begin_layout Plain Layout
23223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23226 \begin_layout Plain Layout
23227 \begin_inset Formula $\le$
23237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23240 \begin_layout Plain Layout
23248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23251 \begin_layout Plain Layout
23252 \begin_inset Formula $\ll$
23262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23265 \begin_layout Plain Layout
23273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23276 \begin_layout Plain Layout
23277 \begin_inset Formula $\prec$
23287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23290 \begin_layout Plain Layout
23298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23301 \begin_layout Plain Layout
23302 \begin_inset Formula $\preceq$
23312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23315 \begin_layout Plain Layout
23323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23326 \begin_layout Plain Layout
23327 \begin_inset Formula $\subset$
23337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23340 \begin_layout Plain Layout
23348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23351 \begin_layout Plain Layout
23352 \begin_inset Formula $\subseteq$
23362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23365 \begin_layout Plain Layout
23373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23376 \begin_layout Plain Layout
23377 \begin_inset Formula $\sqsubseteq$
23387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23390 \begin_layout Plain Layout
23398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23401 \begin_layout Plain Layout
23402 \begin_inset Formula $\in$
23412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23415 \begin_layout Plain Layout
23423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23426 \begin_layout Plain Layout
23427 \begin_inset Formula $\vdash$
23437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23440 \begin_layout Plain Layout
23448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23451 \begin_layout Plain Layout
23452 \begin_inset Formula $\smile$
23462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23465 \begin_layout Plain Layout
23473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23476 \begin_layout Plain Layout
23477 \begin_inset Formula $\lhd$
23487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23490 \begin_layout Plain Layout
23498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23501 \begin_layout Plain Layout
23502 \begin_inset Formula $\unlhd$
23512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23515 \begin_layout Plain Layout
23523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23526 \begin_layout Plain Layout
23527 \begin_inset Formula $\gtrless$
23537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23540 \begin_layout Plain Layout
23548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23551 \begin_layout Plain Layout
23552 \begin_inset Formula $\mid$
23562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23565 \begin_layout Plain Layout
23573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23576 \begin_layout Plain Layout
23577 \begin_inset Formula $\nmid$
23591 \begin_inset space \hfill{}
23595 \begin_inset Tabular
23596 <lyxtabular version="3" rows="17" columns="2">
23597 <features tabularvalignment="middle">
23598 <column alignment="center" valignment="top" width="0pt">
23599 <column alignment="center" valignment="top" width="0pt">
23601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23604 \begin_layout Plain Layout
23610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23613 \begin_layout Plain Layout
23621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23624 \begin_layout Plain Layout
23630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23633 \begin_layout Plain Layout
23634 \begin_inset Formula $=$
23644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23647 \begin_layout Plain Layout
23655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23658 \begin_layout Plain Layout
23659 \begin_inset Formula $\not=$
23669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23672 \begin_layout Plain Layout
23680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23683 \begin_layout Plain Layout
23684 \begin_inset Formula $\equiv$
23694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23697 \begin_layout Plain Layout
23705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23708 \begin_layout Plain Layout
23709 \begin_inset Formula $\sim$
23719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23722 \begin_layout Plain Layout
23730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23733 \begin_layout Plain Layout
23734 \begin_inset Formula $\simeq$
23744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23747 \begin_layout Plain Layout
23755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23758 \begin_layout Plain Layout
23759 \begin_inset Formula $\approx$
23769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23772 \begin_layout Plain Layout
23780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23783 \begin_layout Plain Layout
23784 \begin_inset Formula $\cong$
23794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23797 \begin_layout Plain Layout
23805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23808 \begin_layout Plain Layout
23809 \begin_inset Formula $\bowtie$
23819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23822 \begin_layout Plain Layout
23830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23833 \begin_layout Plain Layout
23834 \begin_inset Formula $\notin$
23844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23847 \begin_layout Plain Layout
23855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23858 \begin_layout Plain Layout
23859 \begin_inset Formula $\perp$
23869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23872 \begin_layout Plain Layout
23880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23883 \begin_layout Plain Layout
23884 \begin_inset Formula $\propto$
23894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23897 \begin_layout Plain Layout
23905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23908 \begin_layout Plain Layout
23909 \begin_inset Formula $\asymp$
23919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23922 \begin_layout Plain Layout
23930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23933 \begin_layout Plain Layout
23934 \begin_inset Formula $\doteq$
23944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23947 \begin_layout Plain Layout
23955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23958 \begin_layout Plain Layout
23959 \begin_inset Formula $\circeq$
23969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23972 \begin_layout Plain Layout
23980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23983 \begin_layout Plain Layout
23984 \begin_inset Formula $\models$
23994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23997 \begin_layout Plain Layout
24005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24008 \begin_layout Plain Layout
24009 \begin_inset Formula $\widehat{=}$
24023 \begin_inset space \hfill{}
24027 \begin_inset Tabular
24028 <lyxtabular version="3" rows="17" columns="2">
24029 <features tabularvalignment="middle">
24030 <column alignment="center" valignment="top" width="0pt">
24031 <column alignment="center" valignment="top" width="0pt">
24033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24036 \begin_layout Plain Layout
24042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24045 \begin_layout Plain Layout
24053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24056 \begin_layout Plain Layout
24062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24065 \begin_layout Plain Layout
24066 \begin_inset Formula $>$
24076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24079 \begin_layout Plain Layout
24087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24090 \begin_layout Plain Layout
24091 \begin_inset Formula $\ge$
24101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24104 \begin_layout Plain Layout
24112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24115 \begin_layout Plain Layout
24116 \begin_inset Formula $\gg$
24126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24129 \begin_layout Plain Layout
24137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24140 \begin_layout Plain Layout
24141 \begin_inset Formula $\succ$
24151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24154 \begin_layout Plain Layout
24162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24165 \begin_layout Plain Layout
24166 \begin_inset Formula $\succeq$
24176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24179 \begin_layout Plain Layout
24187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24190 \begin_layout Plain Layout
24191 \begin_inset Formula $\supset$
24201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24204 \begin_layout Plain Layout
24212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24215 \begin_layout Plain Layout
24216 \begin_inset Formula $\supseteq$
24226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24229 \begin_layout Plain Layout
24237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24240 \begin_layout Plain Layout
24241 \begin_inset Formula $\sqsupseteq$
24251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24254 \begin_layout Plain Layout
24262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24265 \begin_layout Plain Layout
24266 \begin_inset Formula $\ni$
24276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24279 \begin_layout Plain Layout
24287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24290 \begin_layout Plain Layout
24291 \begin_inset Formula $\dashv$
24301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24304 \begin_layout Plain Layout
24312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24315 \begin_layout Plain Layout
24316 \begin_inset Formula $\frown$
24326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24329 \begin_layout Plain Layout
24337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24340 \begin_layout Plain Layout
24341 \begin_inset Formula $\rhd$
24351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24354 \begin_layout Plain Layout
24362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24365 \begin_layout Plain Layout
24366 \begin_inset Formula $\unrhd$
24376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24379 \begin_layout Plain Layout
24387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24390 \begin_layout Plain Layout
24391 \begin_inset Formula $\lessgtr$
24401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24404 \begin_layout Plain Layout
24412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24415 \begin_layout Plain Layout
24416 \begin_inset Formula $\parallel$
24426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24429 \begin_layout Plain Layout
24437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24440 \begin_layout Plain Layout
24441 \begin_inset Formula $\nparallel$
24455 \begin_inset space \hfill{}
24461 \begin_layout Standard
24462 \begin_inset VSpace medskip
24477 are bigger than the equal looking operators
24492 \begin_layout Standard
24493 Relations are, in contrary to symbols, always surrounded by space.
24496 \begin_layout Standard
24497 Relations with labels can be created with the command
24504 \begin_inset Index idx
24507 \begin_layout Plain Layout
24518 \begin_layout Standard
24520 \begin_inset Tabular
24521 <lyxtabular version="3" rows="2" columns="2">
24522 <features tabularvalignment="middle">
24523 <column alignment="center" valignment="top" width="0">
24524 <column alignment="center" valignment="top" width="0">
24526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24529 \begin_layout Plain Layout
24535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24538 \begin_layout Plain Layout
24540 \begin_inset Note Note
24543 \begin_layout Plain Layout
24550 is only used as spacer.
24562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24565 \begin_layout Plain Layout
24572 \begin_layout Plain Layout
24589 \begin_layout Plain Layout
24599 \begin_inset Formula $\downarrow$
24608 \begin_layout Plain Layout
24621 \begin_layout Plain Layout
24635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24638 \begin_layout Plain Layout
24639 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24655 \begin_layout Section
24659 \begin_layout Subsection
24660 Predefined Functions
24661 \begin_inset CommandInset label
24663 name "sub:Predefined-Functions"
24668 \begin_inset Index idx
24671 \begin_layout Plain Layout
24672 Functions ! predefined
24680 \begin_layout Standard
24681 In general, variables are set
24685 in mathematical expressions, but not function names, because
24686 \begin_inset Formula $sin$
24689 could be misunderstood as
24690 \begin_inset Formula $s\cdot i\cdot n$
24694 Therefore there are predefined functions, that are additionally a bit separated
24696 They are inserted as commands starting with a backslash before their name.
24699 \begin_layout Standard
24701 \begin_inset Tabular
24702 <lyxtabular version="3" rows="2" columns="4">
24703 <features tabularvalignment="middle">
24704 <column alignment="center" valignment="top" width="0pt">
24705 <column alignment="center" valignment="top" width="0pt">
24706 <column alignment="center" valignment="top" width="0pt">
24707 <column alignment="center" valignment="top" width="0pt">
24709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24712 \begin_layout Plain Layout
24718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24721 \begin_layout Plain Layout
24727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24730 \begin_layout Plain Layout
24736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24739 \begin_layout Plain Layout
24747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24750 \begin_layout Plain Layout
24756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24759 \begin_layout Plain Layout
24760 \begin_inset Formula $Asin(x)+B$
24768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24771 \begin_layout Plain Layout
24779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24782 \begin_layout Plain Layout
24783 \begin_inset Formula $A\sin(x)+B$
24799 \begin_layout Standard
24800 The following functions are predefined:
24803 \begin_layout Standard
24804 \begin_inset VSpace -2mm
24810 \begin_layout Standard
24812 \begin_inset Tabular
24813 <lyxtabular version="3" rows="9" columns="4">
24814 <features tabularvalignment="middle">
24815 <column alignment="center" valignment="top" width="0pt">
24816 <column alignment="center" valignment="top" width="0pt">
24817 <column alignment="center" valignment="top" width="0pt">
24818 <column alignment="center" valignment="top" width="0pt">
24820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24823 \begin_layout Plain Layout
24829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24832 \begin_layout Plain Layout
24838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24841 \begin_layout Plain Layout
24847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24850 \begin_layout Plain Layout
24858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24861 \begin_layout Plain Layout
24869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24872 \begin_layout Plain Layout
24880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24883 \begin_layout Plain Layout
24891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24894 \begin_layout Plain Layout
24904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24907 \begin_layout Plain Layout
24915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24918 \begin_layout Plain Layout
24926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24929 \begin_layout Plain Layout
24937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24940 \begin_layout Plain Layout
24950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24953 \begin_layout Plain Layout
24961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24964 \begin_layout Plain Layout
24972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24975 \begin_layout Plain Layout
24983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24986 \begin_layout Plain Layout
24996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24999 \begin_layout Plain Layout
25007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25010 \begin_layout Plain Layout
25018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25021 \begin_layout Plain Layout
25029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25032 \begin_layout Plain Layout
25042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25045 \begin_layout Plain Layout
25053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25056 \begin_layout Plain Layout
25064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25067 \begin_layout Plain Layout
25075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25078 \begin_layout Plain Layout
25088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25091 \begin_layout Plain Layout
25099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25102 \begin_layout Plain Layout
25110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25113 \begin_layout Plain Layout
25121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25124 \begin_layout Plain Layout
25134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25137 \begin_layout Plain Layout
25145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25148 \begin_layout Plain Layout
25156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25159 \begin_layout Plain Layout
25167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25170 \begin_layout Plain Layout
25180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25183 \begin_layout Plain Layout
25191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25194 \begin_layout Plain Layout
25202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25205 \begin_layout Plain Layout
25213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25216 \begin_layout Plain Layout
25232 \begin_layout Standard
25233 They can also be inserted with the math toolbar button
25234 \begin_inset Graphics
25235 filename ../images/math/functions.png
25243 \begin_layout Subsection
25244 Self-defined Functions
25245 \begin_inset Index idx
25248 \begin_layout Plain Layout
25249 Functions ! self-defined
25257 \begin_layout Standard
25258 To use a function that is not predefined, like for example the sign function
25259 sgn(x), there are two possibilities:
25262 \begin_layout Itemize
25263 Define the function by inserting the following line to the LaTeX-preamble
25267 \begin_layout Plain Layout
25272 DeclareMathOperator
25275 \begin_inset CommandInset ref
25277 reference "sub:Self-defined-Operators"
25287 \begin_inset Newline newline
25291 \begin_inset VSpace -3mm
25295 \begin_inset Newline newline
25302 DeclareMathOperator{
25307 \begin_inset Index idx
25310 \begin_layout Plain Layout
25315 DeclareMathOperator
25321 \begin_inset Newline newline
25325 \begin_inset VSpace -2mm
25329 \begin_inset Newline newline
25332 Now the new defined function can be called with the command
25341 \begin_layout Itemize
25342 Write the formula as usual, mark the formula name, in our example the letters
25347 , and change it to mathematical text.
25348 At last a space is inserted between prefactor and function.
25351 \begin_layout Standard
25352 The result is the same with both methods as with a predefined function
25356 \begin_layout Plain Layout
25357 In LyX self-defined functions are displayed red, predefined ones black.
25365 \begin_layout Standard
25367 \begin_inset Tabular
25368 <lyxtabular version="3" rows="3" columns="2">
25369 <features tabularvalignment="middle">
25370 <column alignment="center" valignment="top" width="0pt">
25371 <column alignment="center" valignment="top" width="0pt">
25373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25376 \begin_layout Plain Layout
25382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25385 \begin_layout Plain Layout
25393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25396 \begin_layout Plain Layout
25404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25407 \begin_layout Plain Layout
25408 \begin_inset Formula $A\sgn(x)+B$
25418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25421 \begin_layout Plain Layout
25425 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25436 \begin_layout Plain Layout
25437 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25453 \begin_layout Standard
25454 The first method is more suitable when the self-defined function should
25455 be used several times.
25458 \begin_layout Subsection
25460 \begin_inset Index idx
25463 \begin_layout Plain Layout
25472 \begin_layout Standard
25473 For limits there are defined besides
25480 \begin_inset Index idx
25483 \begin_layout Plain Layout
25503 furthermore the following functions:
25506 \begin_layout Standard
25508 \begin_inset Tabular
25509 <lyxtabular version="3" rows="5" columns="2">
25510 <features tabularvalignment="middle">
25511 <column alignment="center" valignment="top" width="0">
25512 <column alignment="center" valignment="top" width="0">
25514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25517 \begin_layout Plain Layout
25523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25526 \begin_layout Plain Layout
25528 \begin_inset Note Note
25531 \begin_layout Plain Layout
25538 is only used as spacer.
25550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25553 \begin_layout Plain Layout
25561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25564 \begin_layout Plain Layout
25565 \begin_inset Formula $\varliminf$
25575 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25578 \begin_layout Plain Layout
25586 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25589 \begin_layout Plain Layout
25590 \begin_inset Formula $\varlimsup$
25600 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25603 \begin_layout Plain Layout
25611 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25614 \begin_layout Plain Layout
25615 \begin_inset Formula $\varprojlim$
25625 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25628 \begin_layout Plain Layout
25636 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25639 \begin_layout Plain Layout
25640 \begin_inset Formula $\varinjlim$
25644 \begin_inset Formula $\raisebox{-2.5mm}{}$
25660 \begin_layout Standard
25661 \begin_inset VSpace medskip
25664 The limit is created by inserting a subscript.
25665 It is set right beside the function in an inline formula:
25668 \begin_layout Standard
25670 \begin_inset Tabular
25671 <lyxtabular version="3" rows="2" columns="2">
25672 <features tabularvalignment="middle">
25673 <column alignment="center" valignment="top" width="0pt">
25674 <column alignment="center" valignment="top" width="0pt">
25676 <cell alignment="center" valignment="top" usebox="none">
25679 \begin_layout Plain Layout
25685 <cell alignment="center" valignment="top" usebox="none">
25688 \begin_layout Plain Layout
25689 \begin_inset space \hspace{}
25694 \begin_inset Note Note
25697 \begin_layout Plain Layout
25704 are used here as spacer.
25716 <cell alignment="center" valignment="top" usebox="none">
25719 \begin_layout Plain Layout
25728 \begin_layout Plain Layout
25741 \begin_layout Plain Layout
25755 <cell alignment="center" valignment="top" usebox="none">
25758 \begin_layout Plain Layout
25759 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25775 \begin_layout Standard
25776 In a displayed formula the limit is set below the formula, as usual:
25777 \begin_inset Formula \[
25785 \begin_layout Subsection
25787 \begin_inset Index idx
25790 \begin_layout Plain Layout
25791 Functions ! modulo-
25799 \begin_layout Standard
25800 The modulo-function is special, because it exists in four variants.
25803 \begin_layout Standard
25804 The variants in a displayed formula:
25805 \begin_inset Formula \begin{align*}
25806 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25807 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25808 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25809 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25810 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
25818 \begin_layout Standard
25819 In an inline formula less space is set before the function names for all
25823 \begin_layout Section
25825 \begin_inset Index idx
25828 \begin_layout Plain Layout
25837 \begin_layout Subsection
25838 Special Characters in Mathematical Text
25841 \begin_layout Standard
25842 The following commands can only be used in mathematical text or in TeX-mode:
25845 \begin_layout Standard
25846 \begin_inset space \hfill{}
25850 \begin_inset Tabular
25851 <lyxtabular version="3" rows="8" columns="2">
25852 <features tabularvalignment="middle">
25853 <column alignment="block" valignment="top" width="0">
25854 <column alignment="block" valignment="top" width="0">
25856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25859 \begin_layout Plain Layout
25865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25868 \begin_layout Plain Layout
25876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25879 \begin_layout Plain Layout
25887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25890 \begin_layout Plain Layout
25891 \begin_inset Formula $\textrm{œ}$
25901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25904 \begin_layout Plain Layout
25912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25915 \begin_layout Plain Layout
25916 \begin_inset Formula $\textrm{Œ}$
25926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25929 \begin_layout Plain Layout
25937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25940 \begin_layout Plain Layout
25941 \begin_inset Formula $\textrm{æ}$
25951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25954 \begin_layout Plain Layout
25962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25965 \begin_layout Plain Layout
25966 \begin_inset Formula $\textrm{Æ}$
25976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25979 \begin_layout Plain Layout
25987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25990 \begin_layout Plain Layout
25991 \begin_inset Formula $\textrm{\aa}$
26001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26004 \begin_layout Plain Layout
26008 \begin_inset Index idx
26011 \begin_layout Plain Layout
26018 \begin_layout Plain Layout
26039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26042 \begin_layout Plain Layout
26043 \begin_inset Formula $\textrm{Å}$
26053 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26056 \begin_layout Plain Layout
26064 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26067 \begin_layout Plain Layout
26068 \begin_inset Formula $\textrm{ı}$
26082 \begin_inset space \hfill{}
26086 \begin_inset Tabular
26087 <lyxtabular version="3" rows="8" columns="2">
26088 <features tabularvalignment="middle">
26089 <column alignment="block" valignment="top" width="0">
26090 <column alignment="center" valignment="top" width="0">
26092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26095 \begin_layout Plain Layout
26097 \begin_inset Note Note
26100 \begin_layout Plain Layout
26102 \begin_inset space \thinspace{}
26105 mm is used for separation, because otherwise the output will be ¡ and ¿
26116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26119 \begin_layout Plain Layout
26127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26130 \begin_layout Plain Layout
26138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26141 \begin_layout Plain Layout
26142 \begin_inset Formula $\textrm{ø}$
26152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26155 \begin_layout Plain Layout
26163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26166 \begin_layout Plain Layout
26167 \begin_inset Formula $\textrm{Ø}$
26177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26180 \begin_layout Plain Layout
26188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26191 \begin_layout Plain Layout
26192 \begin_inset Formula $\textrm{ł}$
26202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26205 \begin_layout Plain Layout
26213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26216 \begin_layout Plain Layout
26217 \begin_inset Formula $\textrm{Ł}$
26227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26230 \begin_layout Plain Layout
26232 \begin_inset space \hspace{}
26240 \begin_layout Plain Layout
26254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26257 \begin_layout Plain Layout
26258 \begin_inset Formula $\textrm{!`}$
26268 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26271 \begin_layout Plain Layout
26273 \begin_inset space \hspace{}
26281 \begin_layout Plain Layout
26295 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26298 \begin_layout Plain Layout
26299 \begin_inset Formula $\textrm{?`}$
26309 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26312 \begin_layout Plain Layout
26320 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26323 \begin_layout Plain Layout
26324 \begin_inset Formula $\textrm{ȷ}$
26338 \begin_inset space \hfill{}
26344 \begin_layout Standard
26346 \begin_inset Formula $\textrm{\textrm{Å}}$
26350 \begin_inset Formula $\textrm{\textrm{Ø}}$
26353 can also be inserted via the math toolbar button
26354 \begin_inset Graphics
26355 filename ../images/math/digamma.png
26363 \begin_layout Standard
26364 An exception are the commands
26367 \begin_inset space \hspace{}
26376 \begin_inset space \hspace{}
26382 , because they can be inserted in LyX directly to text.
26385 \begin_layout Subsection
26387 \begin_inset CommandInset label
26389 name "sub:Accents-in-Text"
26394 \begin_inset Index idx
26397 \begin_layout Plain Layout
26406 \begin_layout Standard
26407 With the following commands all letters can be accented.
26408 The commands must be inserted in TeX-mode.
26411 \begin_layout Standard
26412 \begin_inset space \hfill{}
26416 \begin_inset Tabular
26417 <lyxtabular version="3" rows="8" columns="2">
26418 <features tabularvalignment="middle">
26419 <column alignment="block" valignment="top" width="0">
26420 <column alignment="block" valignment="top" width="0">
26422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26425 \begin_layout Plain Layout
26431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26434 \begin_layout Plain Layout
26442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26445 \begin_layout Plain Layout
26449 \begin_inset Quotes grd
26457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26460 \begin_layout Plain Layout
26464 \begin_layout Plain Layout
26480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26483 \begin_layout Plain Layout
26491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26494 \begin_layout Plain Layout
26498 \begin_layout Plain Layout
26514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26517 \begin_layout Plain Layout
26524 \begin_layout Plain Layout
26538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26541 \begin_layout Plain Layout
26545 \begin_layout Plain Layout
26561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26564 \begin_layout Plain Layout
26572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26575 \begin_layout Plain Layout
26579 \begin_layout Plain Layout
26595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26598 \begin_layout Plain Layout
26605 \begin_layout Plain Layout
26619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26622 \begin_layout Plain Layout
26626 \begin_layout Plain Layout
26642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26645 \begin_layout Plain Layout
26652 \begin_layout Plain Layout
26666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26669 \begin_layout Plain Layout
26673 \begin_layout Plain Layout
26689 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26692 \begin_layout Plain Layout
26699 \begin_layout Plain Layout
26713 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26716 \begin_layout Plain Layout
26720 \begin_layout Plain Layout
26740 \begin_inset space \hfill{}
26744 \begin_inset Tabular
26745 <lyxtabular version="3" rows="8" columns="2">
26746 <features tabularvalignment="middle">
26747 <column alignment="block" valignment="top" width="0">
26748 <column alignment="center" valignment="top" width="0">
26750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26753 \begin_layout Plain Layout
26759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26762 \begin_layout Plain Layout
26770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26773 \begin_layout Plain Layout
26780 \begin_layout Plain Layout
26794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26797 \begin_layout Plain Layout
26801 \begin_layout Plain Layout
26817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26820 \begin_layout Plain Layout
26828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26831 \begin_layout Plain Layout
26835 \begin_layout Plain Layout
26851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26854 \begin_layout Plain Layout
26858 \begin_inset Index idx
26861 \begin_layout Plain Layout
26872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26875 \begin_layout Plain Layout
26879 \begin_layout Plain Layout
26895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26898 \begin_layout Plain Layout
26906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26909 \begin_layout Plain Layout
26913 \begin_layout Plain Layout
26929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26932 \begin_layout Plain Layout
26939 \begin_layout Plain Layout
26953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26956 \begin_layout Plain Layout
26960 \begin_layout Plain Layout
26976 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26979 \begin_layout Plain Layout
26986 \begin_layout Plain Layout
27000 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27003 \begin_layout Plain Layout
27007 \begin_layout Plain Layout
27023 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27026 \begin_layout Plain Layout
27033 \begin_layout Plain Layout
27047 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27050 \begin_layout Plain Layout
27054 \begin_layout Plain Layout
27074 \begin_inset space \hfill{}
27080 \begin_layout Standard
27081 \begin_inset VSpace medskip
27090 also two different characters can be accented.
27099 \begin_layout Plain Layout
27114 \begin_layout Plain Layout
27126 \begin_layout Standard
27139 can in combination with vowels directly be inserted with the keyboard without
27141 The same applies for the tilde
27145 \begin_layout Plain Layout
27146 This only applies for keyboards where the tilde is defined as accent.
27155 in combination with
27170 \begin_layout Standard
27213 and accents that are inserted directly with the keyboard are also available
27214 in mathematical text.
27215 For the other accents there are special math commands to be used in formulas,
27217 \begin_inset CommandInset ref
27219 reference "sub:Accents-for-one"
27226 \begin_layout Standard
27227 \begin_inset VSpace bigskip
27230 Furthermore, with the command
27237 \begin_inset Index idx
27240 \begin_layout Plain Layout
27248 all numbers and letters can be set into a circle, quasi accented with a
27249 circle, similar to the copyright symbol.
27252 \begin_layout Standard
27254 \begin_inset Tabular
27255 <lyxtabular version="3" rows="3" columns="2">
27256 <features tabularvalignment="middle">
27257 <column alignment="center" valignment="top" width="0">
27258 <column alignment="center" valignment="top" width="0">
27260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27263 \begin_layout Plain Layout
27269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27272 \begin_layout Plain Layout
27274 \begin_inset Note Note
27277 \begin_layout Plain Layout
27284 is only used as spacer.
27296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27299 \begin_layout Plain Layout
27307 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27310 \begin_layout Plain Layout
27314 \begin_layout Plain Layout
27330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27333 \begin_layout Plain Layout
27344 raisebox{-1.5pt}{W}}
27349 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27352 \begin_layout Plain Layout
27353 \begin_inset Formula $\raisebox{4.5mm}{}$
27360 \begin_layout Plain Layout
27378 \begin_inset Formula $\raisebox{-2mm}{}$
27394 \begin_layout Standard
27395 One has to take care that the character fits in the circle.
27406 \begin_layout Plain Layout
27408 \begin_inset CommandInset ref
27410 reference "sub:Font-Sizes"
27419 specifies thereby the size of the circle.
27430 \begin_layout Plain Layout
27432 \begin_inset CommandInset ref
27434 reference "sub:Boxes-without-Frame"
27443 the character can be centered.
27446 \begin_layout Subsection
27448 \begin_inset Index idx
27451 \begin_layout Plain Layout
27460 \begin_layout Standard
27461 Minuscule numbers are created with the command
27468 \begin_inset Index idx
27471 \begin_layout Plain Layout
27480 The command can be used in formulas and in TeX-mode.
27481 The command scheme is:
27484 \begin_layout Standard
27489 oldstylenums{number}
27492 \begin_layout Standard
27497 oldstylenums{0123456789
27500 \begin_inset Formula $\oldstylenums{0123456789}$
27506 \begin_layout Subsection
27507 Miscellaneous special Characters
27508 \begin_inset CommandInset label
27510 name "sub:Miscellaneous-special-Characters"
27515 \begin_inset Index idx
27518 \begin_layout Plain Layout
27519 Special characters ! miscellaneous
27527 \begin_layout Standard
27528 The following characters can only be inserted to formulas by using commands:
27531 \begin_layout Standard
27533 \begin_inset Tabular
27534 <lyxtabular version="3" rows="4" columns="2">
27535 <features tabularvalignment="middle">
27536 <column alignment="center" valignment="top" width="0">
27537 <column alignment="center" valignment="top" width="0">
27539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27542 \begin_layout Plain Layout
27548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27551 \begin_layout Plain Layout
27559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27562 \begin_layout Plain Layout
27569 \begin_layout Plain Layout
27583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27586 \begin_layout Plain Layout
27587 \begin_inset Formula $\mathcircumflex$
27597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27600 \begin_layout Plain Layout
27608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27611 \begin_layout Plain Layout
27612 \begin_inset Formula $\_$
27622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27625 \begin_layout Plain Layout
27630 \begin_layout Plain Layout
27642 \begin_inset Index idx
27645 \begin_layout Plain Layout
27658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27661 \begin_layout Plain Layout
27662 \begin_inset Formula $^{\circ}$
27678 \begin_layout Standard
27679 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27680 contains the following line
27684 \begin_layout Plain Layout
27685 More about this is described in
27686 \begin_inset CommandInset ref
27688 reference "sub:Text-Characters-in"
27700 \begin_layout Standard
27705 DeclareInputtext{176}{
27718 \begin_layout Section
27720 \begin_inset CommandInset label
27722 name "sec:Formula-Styles"
27727 \begin_inset Index idx
27730 \begin_layout Plain Layout
27739 \begin_layout Itemize
27740 There are two different alignment styles:
27744 \begin_layout Description
27745 Centered is the predefined standard
27748 \begin_layout Description
27749 Indented for this the option
27753 must be inserted in the menu
27755 Document\SpecialChar \menuseparator
27761 \begin_inset space ~
27767 \begin_layout Standard
27772 is used, the indentation can be adjusted with the length
27779 \begin_inset Index idx
27782 \begin_layout Plain Layout
27791 Should the distance be 15
27792 \begin_inset space \thinspace{}
27795 mm, the following command line is inserted in the LaTeX-preamble
27798 \begin_layout Standard
27808 \begin_layout Standard
27809 When no length is specified, the predefined value of 30
27810 \begin_inset space \thinspace{}
27817 \begin_layout Itemize
27818 And two different numbering styles:
27822 \begin_layout Description
27823 Right is the predefined standard
27826 \begin_layout Description
27827 Left for this the option
27831 must be inserted in the menu
27833 Document\SpecialChar \menuseparator
27839 \begin_inset space ~
27846 \begin_layout Standard
27855 can also be used together.
27856 In this case both options are inserted, separated by a comma.
27859 \begin_layout Standard
27860 The chosen styles are used for all displayed formulas of the document.
27861 When both, centered and indented formulas should be created in a document,
27867 The indented formulas are then set in a flalign environment, see
27868 \begin_inset CommandInset ref
27870 reference "sub:Flalign-Environment"
27877 \begin_layout Section
27879 \begin_inset CommandInset label
27881 name "sec:Multiline-Formulas"
27886 \begin_inset Index idx
27889 \begin_layout Plain Layout
27890 Formula ! multiline
27898 \begin_layout Subsection
27902 \begin_layout Standard
27903 In LyX multiline formulas are created by pressing
27908 arg "newline-insert newline"
27914 This creates either an
27916 eqnarray environment
27918 that is described in
27919 \begin_inset CommandInset ref
27921 reference "sub:Eqnarray-Environment"
27925 or, when the option
27927 Use AMS math package
27929 in the document settings is selected, an
27933 that is described in
27934 \begin_inset CommandInset ref
27936 reference "sub:Standard-align-Environment"
27943 \begin_layout Standard
27944 There are other multiline formula environments that can be created via the
27947 Insert\SpecialChar \menuseparator
27951 These environments are described in the following sections.
27954 \begin_layout Standard
27955 In all multiline formula environments a new line is created by pressing
27959 arg "newline-insert newline"
27963 To add or delete lines, the math toolbar buttons
27964 \begin_inset Graphics
27965 filename ../images/tabular-feature_append-row.png
27971 \begin_inset Graphics
27972 filename ../images/tabular-feature_delete-row.png
27977 , respectively, or the menu
27979 Edit\SpecialChar \menuseparator
27985 \begin_layout Subsubsection
27987 \begin_inset CommandInset label
27989 name "sub:Line-Separation"
27994 \begin_inset Index idx
27997 \begin_layout Plain Layout
27998 Formula ! multiline ! Line separation
28006 \begin_layout Standard
28007 There is sometimes not enough space in multiline formulas between the lines:
28008 \begin_inset Formula \begin{eqnarray*}
28009 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}\\
28010 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
28018 \begin_layout Standard
28019 In LaTeX additional line space is specified as optional argument of the
28021 This is not yet possible in LyX
28025 \begin_layout Plain Layout
28027 \begin_inset CommandInset href
28029 name "LyX-bug #1505"
28030 target "http://www.lyx.org/trac/ticket/1505"
28039 , therefore the whole formula must be inserted in TeX-mode.
28040 To add in our example space, the command
28048 is inserted at the end of the first line.
28053 \begin_layout Plain Layout
28060 \begin_layout Plain Layout
28062 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28065 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28072 \begin_layout Plain Layout
28076 left(B^{2}+x_{0}^{2}
28084 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28089 \begin_layout Plain Layout
28101 \begin_layout Standard
28102 \begin_inset VSpace bigskip
28105 To set the line separation for all lines in a formula, the length
28112 \begin_inset Index idx
28115 \begin_layout Plain Layout
28125 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28136 \begin_inset space \thinspace{}
28141 \begin_inset space \thinspace{}
28144 mm additional line separation as in the previous example, the command
28147 \begin_layout Standard
28157 \begin_layout Standard
28158 is inserted in TeX-mode before the formula.
28159 This requires that the LaTeX-package
28167 \begin_layout Plain Layout
28172 is part of every LaTeX standard installation.
28178 \begin_inset Index idx
28181 \begin_layout Plain Layout
28187 was loaded in LaTeX-preamble with the line
28190 \begin_layout Standard
28198 \begin_layout Standard
28203 \begin_layout Plain Layout
28215 \begin_inset Formula \begin{eqnarray*}
28216 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}\\
28217 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
28225 \begin_layout Standard
28229 \begin_layout Plain Layout
28240 To get back to the predefined distance,
28246 is set to the value 3
28247 \begin_inset space \thinspace{}
28253 \begin_layout Subsubsection
28255 \begin_inset CommandInset label
28257 name "sub:Column-Separation"
28262 \begin_inset Index idx
28265 \begin_layout Plain Layout
28266 Formula ! multiline ! Column separation
28274 \begin_layout Standard
28275 Multiline formulas form a matrix.
28276 A formula in the eqnarray environment is for example a matrix with three
28278 By changing the column separation in this environment, the space beside
28279 the relation sign can be changed.
28282 \begin_layout Standard
28283 The column separation is specified with the length
28290 \begin_inset Index idx
28293 \begin_layout Plain Layout
28302 \begin_inset Newline newline
28305 column separation = 2
28306 \begin_inset space \thinspace{}
28316 \begin_inset Newline newline
28322 \begin_layout Standard
28332 \begin_layout Standard
28333 inserted in TeX-mode, sets for all following formulas a column separation
28335 \begin_inset space \thinspace{}
28339 To get back to the predefined distance,
28346 \begin_inset space \thinspace{}
28352 \begin_layout Standard
28354 \begin_inset space \thinspace{}
28357 cm column separation:
28361 \begin_layout Plain Layout
28373 \begin_inset Formula \begin{eqnarray*}
28380 A formula with the predefined column separation for matrices of 10
28381 \begin_inset space \thinspace{}
28388 \begin_layout Plain Layout
28400 \begin_inset Formula \begin{eqnarray*}
28410 \begin_layout Subsubsection
28412 \begin_inset Index idx
28415 \begin_layout Plain Layout
28424 \begin_layout Standard
28425 Long formulas can be typeset using these methods:
28428 \begin_layout Itemize
28429 When one side of the equation is much shorther than the line width, this
28430 one is chosen for the left side and the right side is typeset over two
28432 \begin_inset Formula \begin{eqnarray}
28433 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 \\
28434 & & -\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}
28439 The minus sign at the beginning of the second line does normally not appear
28440 as operator because it is the first character of the line.
28441 Thus it would not be surrounded by space and could not be distinguished
28442 from the fraction bar.
28444 \begin_inset space \thinspace{}
28447 pt space was inserted behind the minus sign with the command
28457 \begin_layout Plain Layout
28465 \begin_inset CommandInset ref
28467 reference "sub:Variable-Space"
28477 \begin_inset Index idx
28480 \begin_layout Plain Layout
28491 \begin_layout Itemize
28492 When both sides of the equation are too long, the command
28499 \begin_inset Index idx
28502 \begin_layout Plain Layout
28511 It is inserted to the first column of the first line and effects that all
28512 further insertions overwrite the following columns:
28513 \begin_inset Formula \begin{eqnarray}
28514 \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 \\
28515 & & -\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 \\
28516 & & =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}
28521 After the insertion of
28527 , the cursor is in a purple box that is a bit shifted to the left from the
28529 In this the formula is inserted.
28530 \begin_inset Newline newline
28533 The content of the further lines is inserted to the second or another formula
28535 The greater the column number where it was inserted, the larger the indentation.
28536 \begin_inset VSpace medskip
28540 \begin_inset Newline newline
28544 \begin_inset Note Greyedout
28547 \begin_layout Plain Layout
28548 Note the following when using
28557 \begin_layout Itemize
28558 The formula doesn't use the full page width.
28560 \begin_inset space \thinspace{}
28564 \begin_inset space \space{}
28568 \begin_inset Formula $-B^{2}$
28571 is added to the first line in the above example, it would have been outside
28573 To better use the width, negative space can be inserted at the beginning
28577 \begin_layout Itemize
28578 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28583 \begin_layout Plain Layout
28584 \begin_inset CommandInset href
28586 name "LyX-bug #1429"
28587 target "http://www.lyx.org/trac/ticket/1429"
28596 One can only set the cursor at the beginning of the line and move it with
28605 \begin_layout Itemize
28606 Other methods to set long formulas are offered by the environments described
28608 \begin_inset CommandInset ref
28610 reference "sub:Multline-Environment"
28615 \begin_inset CommandInset ref
28617 reference "sub:Multiline-Formula-Parts"
28624 \begin_layout Subsubsection
28626 \begin_inset CommandInset label
28628 name "sub:Multiline-Brackets"
28633 \begin_inset Index idx
28636 \begin_layout Plain Layout
28637 Brackets ! for multiline expressions
28645 \begin_layout Standard
28646 For brackets spanning multiple lines the following problem occurs:
28647 \begin_inset Formula \begin{eqnarray*}
28648 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28649 & & \left.\cdots+B-D\right]
28657 \begin_layout Standard
28658 The closing bracket is smaller than the opening bracket because brackets
28659 with variable size may not span multiple lines.
28662 \begin_layout Standard
28663 To set the bracket size for the second line correctly, the first line is
28671 \begin_inset Index idx
28674 \begin_layout Plain Layout
28682 and the second line with
28690 \begin_layout Plain Layout
28704 \begin_inset CommandInset ref
28706 reference "sub:Automatic-Bracket-Size"
28718 \begin_inset Index idx
28721 \begin_layout Plain Layout
28747 \begin_layout Plain Layout
28766 \begin_layout Plain Layout
28785 \begin_layout Plain Layout
28797 \begin_inset Formula $\downarrow$
28803 \begin_inset Index idx
28806 \begin_layout Plain Layout
28814 is inserted, because the multiplication operator with its limits is the
28815 largest symbol in the first line and this should be the size for the bracket
28816 in the second line.
28819 \begin_layout Standard
28820 The result is this:
28821 \begin_inset Formula \begin{eqnarray*}
28822 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28823 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28831 \begin_layout Subsection
28835 \begin_layout Standard
28836 Align environments can be used for every kind of multiline formulas.
28837 They are specially useful to set several formulas side by side.
28840 \begin_layout Standard
28841 Align environments consist of columns.
28842 The odd columns are right aligned, the even ones left aligned.
28843 Every line in an Align environment can be numbered.
28846 \begin_layout Standard
28847 Align environments are created via the menu
28849 Insert\SpecialChar \menuseparator
28855 Edit\SpecialChar \menuseparator
28856 Math\SpecialChar \menuseparator
28857 Change Formula Type
28859 already existing formulas can be converted to Align environments.
28862 \begin_layout Standard
28863 To add or delete columns, the math toolbar buttons
28864 \begin_inset Graphics
28865 filename ../images/tabular-feature_append-column.png
28871 \begin_inset Graphics
28872 filename ../images/tabular-feature_delete-column.png
28877 , respectively, or the menu
28879 Edit\SpecialChar \menuseparator
28885 \begin_layout Subsubsection
28886 Standard align Environment
28887 \begin_inset CommandInset label
28889 name "sub:Standard-align-Environment"
28894 \begin_inset Index idx
28897 \begin_layout Plain Layout
28898 Formula ! multiline ! align environment
28906 \begin_layout Standard
28907 This Align environment is created by presssing
28910 arg "newline-insert newline"
28913 in a formula or by the menu
28915 Insert\SpecialChar \menuseparator
28916 Math\SpecialChar \menuseparator
28917 AMS align Environment
28922 \begin_layout Standard
28923 An example for two formulas set side by side, that are created with a four
28924 column align environment:
28925 \begin_inset Formula \begin{align*}
28926 A & =\sin(B) & C & =D\\
28927 C & \ne A & B & \ne D
28932 As it can be seen, the formulas in this environment are placed so as if
28941 \begin_layout Plain Layout
28949 \begin_inset CommandInset ref
28951 reference "sub:Variable-Space"
28962 before the first and after every even column.
28963 When the formula style
28969 \begin_layout Plain Layout
28971 \begin_inset CommandInset ref
28973 reference "sec:Formula-Styles"
28984 is used, the formula is set without the
28990 before the first column.
28993 \begin_layout Subsubsection
28994 Alignat Environment
28995 \begin_inset Index idx
28998 \begin_layout Plain Layout
28999 Formula ! multiline ! alignat environment
29007 \begin_layout Standard
29008 The alignat environment has no predefined column separation.
29009 It can be inserted manually with the spaces that are described
29010 \begin_inset CommandInset ref
29012 reference "sub:Space"
29019 \begin_layout Standard
29020 The above example in the alignat environment where 1
29021 \begin_inset space \thinspace{}
29024 cm space was inserted at the beginning of the second formula:
29025 \begin_inset Formula \begin{alignat*}{2}
29026 A & =\sin(B) & \hspace{1cm}C & =D\\
29027 C & \ne A & B & \ne D
29032 Because the column separation can be set separately for every column, this
29033 environment is especially suitable to set three and more formulas side
29037 \begin_layout Subsubsection
29038 Flalign Environment
29039 \begin_inset CommandInset label
29041 name "sub:Flalign-Environment"
29046 \begin_inset Index idx
29049 \begin_layout Plain Layout
29050 Formula ! multiline ! flalign environment
29058 \begin_layout Standard
29059 In this environment the first two columns are always set as much as possible
29060 to the left and the last two ones to the right.
29062 \begin_inset Formula \begin{flalign*}
29063 A & =1 & B & =2 & C & =3\\
29064 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29072 \begin_layout Standard
29073 By creating a flalign environment with an odd number of columns where an
29074 empty TeX-brace is inserted to the last column, several formulas in a document
29075 can be set to the left, although the formula style
29080 As example the indented formula
29081 \begin_inset CommandInset ref
29083 reference "eq:VolInt"
29088 \begin_inset Formula \begin{flalign}
29089 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
29093 The first two columns contain the formula.
29094 To indent it as with the formula style
29099 \begin_inset space \thinspace{}
29102 pt space was inserted at the beginning of the first column.
29105 \begin_layout Subsection
29106 Eqnarray Environment
29107 \begin_inset CommandInset label
29109 name "sub:Eqnarray-Environment"
29114 \begin_inset Index idx
29117 \begin_layout Plain Layout
29118 Formula ! multiline ! eqnarray environment
29126 \begin_layout Standard
29127 When this environment has been created, three blue boxes appear.
29128 The content of the first box is right aligned, the content of the last
29130 The content of the middle box appears centered and a bit smaller, because
29131 it is designed to insert there only relation characters.
29132 \begin_inset Formula \begin{eqnarray*}
29133 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29143 \begin_layout Subsection
29145 \begin_inset Index idx
29148 \begin_layout Plain Layout
29149 Formula ! multiline ! gather environment
29157 \begin_layout Standard
29158 This environment consists of only one centered column.
29159 Every line can be numbered.
29160 \begin_inset Formula \begin{gather}
29170 \begin_layout Subsection
29171 Multline Environment
29172 \begin_inset CommandInset label
29174 name "sub:Multline-Environment"
29179 \begin_inset Index idx
29182 \begin_layout Plain Layout
29183 Formula ! multiline ! multline environment
29191 \begin_layout Standard
29192 The multline environment consists, like the gather environment, of only
29194 But the first line is left aligned, the last one right aligned.
29195 All other lines are centered.
29196 Therefore this environment is suitable for long formulas.
29198 \begin_inset CommandInset ref
29200 reference "eq:lefteqn"
29204 in the multline environment:
29205 \begin_inset Formula \begin{multline}
29206 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}\\
29207 -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}\\
29208 =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}}
29216 \begin_layout Standard
29217 In the output only the last (first) line of a multline environment appears
29218 numbered when the document numbering is right (left).
29222 \begin_layout Plain Layout
29223 numbering styles see
29224 \begin_inset CommandInset ref
29226 reference "sec:Formula-Styles"
29238 \begin_layout Standard
29246 \begin_inset Index idx
29249 \begin_layout Plain Layout
29264 \begin_inset Index idx
29267 \begin_layout Plain Layout
29275 a centered line can be right or left aligned, respectively.
29276 The commands are used as follows:
29279 \begin_layout Standard
29284 shoveright{line content}
29290 shoveleft{line content}
29293 \begin_layout Standard
29294 \begin_inset VSpace medskip
29304 \begin_inset Index idx
29307 \begin_layout Plain Layout
29315 specifies the distance of the first line from the left page margin.
29316 Predefined is the length 0
29317 \begin_inset space \thinspace{}
29323 \begin_layout Standard
29324 As example the above formula where the command
29327 \begin_layout Standard
29337 \begin_layout Standard
29338 was inserted in TeX-mode before:
29342 \begin_layout Plain Layout
29354 \begin_inset Formula \begin{multline}
29355 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}\\
29356 \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}}\\
29357 =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}}
29366 \begin_layout Plain Layout
29377 The second line was left aligned using
29386 \begin_layout Subsection
29387 Multiline Formula Parts
29388 \begin_inset CommandInset label
29390 name "sub:Multiline-Formula-Parts"
29395 \begin_inset Index idx
29398 \begin_layout Plain Layout
29399 Formula ! multiline ! formula parts
29407 \begin_layout Standard
29408 To display only parts of a formula with multiple lines, one of the following
29409 environments are used:
29426 They can be inserted via the menu
29428 Insert\SpecialChar \menuseparator
29431 or by using the commands described in this section.
29434 \begin_layout Standard
29435 The first three have the same properties as the corresponding multiline
29436 formula environments, but it is possible to set further formula parts beside
29439 \begin_inset Formula \[
29440 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29441 \Delta E\Delta t & \ge\frac{\hbar}{2}
29443 \right\} \textrm{Uncertainty relations}\]
29450 \begin_layout Standard
29451 To get this formula, a displayed formula is created where the command
29458 \begin_inset Index idx
29461 \begin_layout Plain Layout
29470 A purple box appears around the blue formula box where now columns and
29471 lines can be added.
29472 Outside the multiline environment other formula parts can be set, like
29476 \begin_layout Standard
29477 The aligned environment is also suitable for long formulas whose lines are
29478 horizontally aligned.
29479 Using aligned in a displayed formula has the advantage that the formula
29480 number is vertically centered behind the lines.
29482 \begin_inset CommandInset ref
29484 reference "eq:shortlong"
29488 in the aligned environment:
29489 \begin_inset Formula \begin{equation}
29490 \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}|}\\
29491 & -\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}|}
29500 \begin_layout Standard
29501 To use the environments
29520 \begin_inset Index idx
29523 \begin_layout Plain Layout
29538 \begin_inset Index idx
29541 \begin_layout Plain Layout
29556 \begin_inset Index idx
29559 \begin_layout Plain Layout
29567 are inserted, respectively.
29568 The split environment has the same properties as the aligned environment
29569 but it can only have two columns.
29572 \begin_layout Subsection
29573 Text in multiline Formulas
29574 \begin_inset CommandInset label
29576 name "sub:Text-in-multiline"
29581 \begin_inset Index idx
29584 \begin_layout Plain Layout
29591 \begin_inset Index idx
29594 \begin_layout Plain Layout
29595 Formula ! multiline ! text
29603 \begin_layout Standard
29604 In the Align environments, and the multline and gather environment, text
29605 can be inserted that will appear in a separate line and doesn't affect
29606 the column alignment.
29607 To do this, the command
29614 \begin_inset Index idx
29617 \begin_layout Plain Layout
29625 is used in the following scheme:
29628 \begin_layout Standard
29636 \begin_layout Standard
29637 The text should not be longer than a line because it cannot be hyphenated.
29638 As LyX doesn't yet support
29644 directly, the text is written as mathematical text.
29651 must hereby be at the beginning of a line and appears in the output above
29653 An example where the text was inserted at the beginning of the second line:
29654 \begin_inset Formula \begin{align}
29655 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29656 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29664 \begin_layout Section
29666 \begin_inset Index idx
29669 \begin_layout Plain Layout
29676 \begin_inset Index idx
29679 \begin_layout Plain Layout
29680 Formula ! numbering|see
29684 \begin_layout Plain Layout
29695 \begin_layout Plain Layout
29710 \begin_layout Subsection
29714 \begin_layout Standard
29715 Numbered formulas can be created with the menu
29717 Insert\SpecialChar \menuseparator
29718 Math\SpecialChar \menuseparator
29720 \begin_inset space ~
29728 \begin_inset space ~
29734 Existing formulas can be numbered with the menu
29736 Edit\SpecialChar \menuseparator
29737 Math\SpecialChar \menuseparator
29739 \begin_inset space ~
29747 arg "math-number-toggle"
29751 The formula number is displayed in LyX behind the formula as number sign
29753 The number sign is replaced in the output by the formula number.
29756 \begin_layout Standard
29757 When numbering is turned on in multiline formulas, all lines will be numbered.
29758 But the numbering can be controlled with the menu
29760 Edit\SpecialChar \menuseparator
29761 Math\SpecialChar \menuseparator
29763 \begin_inset space ~
29767 \begin_inset space ~
29771 \begin_inset space ~
29779 arg "math-number-line-toggle"
29785 \begin_layout Standard
29786 Except for inline formulas, all formulas can be numbered with two different
29788 \begin_inset CommandInset ref
29790 reference "sec:Formula-Styles"
29797 \begin_layout Subsection
29799 \begin_inset Index idx
29802 \begin_layout Plain Layout
29803 Cross-references ! to formulas
29811 \begin_layout Standard
29812 All labeled formulas can be cross-referenced.
29813 A label is added by the menu
29815 Insert\SpecialChar \menuseparator
29818 or the toolbar button
29819 \begin_inset Graphics
29820 filename ../images/label-insert.png
29826 The cursor must hereby be inside a displayed formula.
29827 A dialog pops up displaying the prefix
29832 The label is inserted there behind the prefix.
29833 The predefined prefix means
29834 \begin_inset Quotes eld
29838 \begin_inset Quotes erd
29841 and makes it easier to find labels in large documents because it marks
29842 it as formula label to divide it from e.
29843 \begin_inset space \thinspace{}
29847 \begin_inset space \space{}
29851 To change a label, the menu
29853 Insert\SpecialChar \menuseparator
29859 \begin_layout Standard
29860 The name of the label is displayed in LyX within two parentheses behind
29862 A formula with a label is always numbered.
29865 \begin_layout Standard
29866 Cross-references are inserted via the menu
29868 Insert\SpecialChar \menuseparator
29871 or with the toolbar button
29872 \begin_inset Graphics
29873 filename ../images/dialog-show-new-inset_ref.png
29879 A formula cross-reference appears in the output as formula number.
29880 When in the cross-reference dialog window the format
29884 is chosen, the cross-reference appears in the output as formula number
29886 \begin_inset Newline newline
29889 By right-clicking on a cross-reference in LyX, one jumps to the formula
29890 that is referenced.
29893 \begin_layout Standard
29894 Here are as examples cross-references to formulas of the following subsections:
29895 \begin_inset Note Note
29898 \begin_layout Plain Layout
29899 Note the different cross-reference types.
29907 \begin_layout Standard
29909 \begin_inset CommandInset ref
29916 \begin_inset CommandInset ref
29924 \begin_inset CommandInset ref
29930 ) big Latin letters are used for the numbering in contrary to (
29931 \begin_inset CommandInset ref
29940 \begin_layout Standard
29941 \begin_inset VSpace medskip
29944 When the argument of
29952 \begin_layout Plain Layout
29960 \begin_inset CommandInset ref
29962 reference "sub:User-defined-Numbering"
29973 contains a box like in
29974 \begin_inset CommandInset ref
29976 reference "sub:Paragraph-Boxes"
29980 , the formula cannot be referenced.
29983 \begin_layout Subsection
29985 \begin_inset Index idx
29988 \begin_layout Plain Layout
29989 Formula numbering ! subnumbering
29997 \begin_layout Standard
29998 With the help of the commands
30002 begin{subequations}
30010 formulas can be subnumbered.
30011 Both commands are inserted in TeX-mode.
30014 \begin_layout Standard
30016 \begin_inset Formula \begin{equation}
30017 A=C-B\label{eq:a}\end{equation}
30025 \begin_layout Plain Layout
30029 addtocounter{equation}{-1}
30038 \begin_layout Plain Layout
30042 begin{subequations}
30048 \begin_inset VSpace -5mm
30052 \begin_inset Formula \begin{equation}
30053 B=C-A\label{eq:b}\end{equation}
30058 \begin_inset Formula \begin{equation}
30059 C=A+B\label{eq:c}\end{equation}
30066 \begin_layout Standard
30070 \begin_layout Plain Layout
30082 \begin_layout Standard
30083 To create the example, the following is done:
30086 \begin_layout Enumerate
30087 first formula is inserted
30090 \begin_layout Enumerate
30095 addtocounter{equation}{-1}
30097 begin{subequations}
30098 \begin_inset Index idx
30101 \begin_layout Plain Layout
30110 \begin_inset Newline newline
30115 is inserted after the first formula
30118 \begin_layout Enumerate
30119 second formula is inserted
30122 \begin_layout Enumerate
30123 third formula is inserted
30126 \begin_layout Enumerate
30133 is inserted after the third formula
30136 \begin_layout Standard
30137 Every formula between the commands
30149 is subnumbered as a, b,
30150 \begin_inset Newline linebreak
30153 c, \SpecialChar \ldots{}
30154 For multiline formulas every line will be subnumbered.
30155 All subnumbered formulas are treated as
30160 But as every numbered formula increases the counter
30164 by one, the command
30170 is needed to decrease it.
30171 Otherwise the formulas
30172 \begin_inset CommandInset ref
30179 \begin_inset CommandInset ref
30186 \begin_inset CommandInset ref
30192 would be numbered as
30193 \begin_inset CommandInset ref
30200 \begin_inset CommandInset ref
30207 \begin_inset CommandInset ref
30216 \begin_layout Standard
30217 By inserting the commands in TeX-mode, a space is created between the first
30220 \begin_inset space \thinspace{}
30223 mm vertical space is inserted after the command
30227 begin{subequations}
30230 When the formula style
30236 \begin_layout Plain Layout
30238 \begin_inset CommandInset ref
30240 reference "sec:Formula-Styles"
30252 \begin_inset space \thinspace{}
30255 mm space is inserted instead.
30258 \begin_layout Standard
30259 Here is an example for a multiline formula where the numbering was turned
30260 off for the second line:
30264 \begin_layout Plain Layout
30268 begin{subequations}
30274 \begin_inset Formula \begin{eqnarray}
30275 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30276 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30277 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30286 \begin_layout Plain Layout
30298 \begin_layout Subsection
30299 User-defined Numbering
30300 \begin_inset CommandInset label
30302 name "sub:User-defined-Numbering"
30307 \begin_inset Index idx
30310 \begin_layout Plain Layout
30311 Formula numbering ! user-defined
30319 \begin_layout Standard
30320 \begin_inset Index idx
30323 \begin_layout Plain Layout
30324 Formula numbering ! self-defined delimiters
30329 With the standard numbering parentheses are set around the formula number.
30330 To replace the parentheses for example by vertical bars, the following
30331 line is added to the LaTeX-preamble:
30334 \begin_layout Standard
30346 \begin_inset Note Note
30349 \begin_layout Plain Layout
30350 This macro is already declared in the LaTeX-preamble for testing.
30351 To activate it, remove the percent sign at the beginning.
30359 \begin_layout Standard
30360 To use other characters, the vertical bars besides the
30364 are replaced by one ore more characters.
30365 To get only the formula number the vertical bars are omitted.
30368 \begin_layout Standard
30369 \begin_inset VSpace bigskip
30372 When there should be an expression of your choice instead of the consecutive
30373 formula number in parentheses behind the formula, the command
30380 \begin_inset Index idx
30383 \begin_layout Plain Layout
30392 \begin_inset Formula \begin{equation}
30393 A+B=C\tag{something}\label{eq:tag}\end{equation}
30397 In this example the command
30405 \begin_layout Plain Layout
30416 was inserted to the formula.
30419 \begin_layout Standard
30428 \begin_layout Plain Layout
30439 is inserted instead, the star prevents the parentheses around the expression:
30440 \begin_inset Formula \[
30441 A+B=C\tag*{something}\]
30448 \begin_layout Standard
30449 \begin_inset VSpace bigskip
30452 To restart the formula numbering with new document parts or sections, the
30453 following command is used:
30456 \begin_layout Standard
30461 @addtoreset{equation}{part}
30464 \begin_inset Index idx
30467 \begin_layout Plain Layout
30472 \begin_layout Plain Layout
30483 \begin_layout Plain Layout
30496 \begin_layout Plain Layout
30507 \begin_layout Plain Layout
30520 \begin_inset Newline newline
30524 \begin_inset Newline newline
30531 @addtoreset{equation}{section}
30534 \begin_layout Standard
30535 To be able to use these commands in TeX-mode, the
30536 \begin_inset Quotes eld
30540 \begin_inset Quotes erd
30543 character has to be made
30544 \begin_inset Quotes eld
30548 \begin_inset Quotes erd
30551 for LaTeX using the command
30565 So the command sequence in TeX-mode is:
30568 \begin_layout Standard
30574 \begin_inset Newline newline
30579 @addtoreset{equation}{section}
30580 \begin_inset Newline newline
30588 \begin_layout Standard
30589 In the LaTeX-preamble
30601 can be omitted as they are automatically internally inserted by LyX.
30604 \begin_layout Standard
30619 \begin_layout Plain Layout
30624 is part of the LaTeX-package
30629 \begin_inset Index idx
30632 \begin_layout Plain Layout
30633 Packages ! carlisle
30638 that is part of every LaTeX standard installation.
30644 \begin_inset Index idx
30647 \begin_layout Plain Layout
30648 Packages ! remreset
30653 has to be loaded in the LaTeX-preamble with the line
30656 \begin_layout Standard
30661 usepackage{remreset}
30664 \begin_layout Standard
30672 \begin_inset Index idx
30675 \begin_layout Plain Layout
30680 \begin_layout Plain Layout
30691 \begin_layout Plain Layout
30704 \begin_layout Plain Layout
30715 \begin_layout Plain Layout
30727 can be used with the same scheme as
30736 \begin_layout Standard
30737 \begin_inset VSpace bigskip
30740 Sometimes formulas should be numbered in the following form:
30743 \begin_layout Standard
30746 (section number.formula number)
30749 \begin_layout Standard
30750 The formula number should start with every section with
30751 \begin_inset Quotes eld
30755 \begin_inset Quotes erd
30761 \begin_layout Standard
30762 For this case there is the command
30769 \begin_inset Index idx
30772 \begin_layout Plain Layout
30780 , which is used with the following scheme:
30783 \begin_layout Standard
30788 numberwithin{counter}{sectioning}
30791 \begin_layout Standard
30792 Counter denotes what kind of numbering is affected, sectioning denotes what
30793 number is before the dot.
30796 \begin_layout Standard
30797 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30800 \begin_layout Standard
30805 numberwithin{equation}{section}
30808 \begin_layout Standard
30809 This is the result:
30813 \begin_layout Plain Layout
30817 numberwithin{equation}{section}
30823 \begin_inset Formula \begin{equation}
30824 A+B=C\end{equation}
30831 \begin_layout Standard
30833 \begin_inset space \thinspace{}
30837 \begin_inset space \space{}
30840 tables so that the number of the part is the sectioning,
30841 \begin_inset Newline newline
30848 numberwithin{table}{part}
30853 \begin_layout Standard
30854 To go back to the standard numbering or to prevent this kind of numbering
30855 when it is defined by the document class, the following command is inserted
30856 as TeX-Code or to the LaTeX-preamble:
30859 \begin_layout Standard
30869 \begin_inset Index idx
30872 \begin_layout Plain Layout
30886 \begin_layout Plain Layout
30902 \begin_inset Newline newline
30910 \begin_inset Newline newline
30922 \begin_layout Standard
30929 uses internally the command
30935 , described above, that also needs to be reverted.
30939 \begin_layout Plain Layout
30946 \begin_layout Plain Layout
30950 @removefromreset{equation}{section}
30953 \begin_layout Plain Layout
30965 \begin_layout Subsection
30966 Numbering with Roman Numbers and Letters
30967 \begin_inset Index idx
30970 \begin_layout Plain Layout
30971 Formula numbering ! with letters
30977 \begin_inset Index idx
30980 \begin_layout Plain Layout
30981 Formula numbering ! with Roman numbers
30989 \begin_layout Standard
30990 Formulas can also be numbered with Roman numbers and Latin letters.
30991 To number for example with small Roman numbers, the command
30994 \begin_layout Standard
31006 \begin_layout Standard
31007 is inserted before the formula in TeX-mode.
31015 \begin_inset Index idx
31018 \begin_layout Plain Layout
31026 redefines the predefined command
31042 \begin_layout Plain Layout
31049 has the same scheme like the command
31055 that is described in
31056 \begin_inset CommandInset ref
31058 reference "sub:The-Command-newcommand"
31071 is the formula counter.
31078 is used as prefix for a counter, the value of the counter is output as
31080 When a formula is numbered, LaTeX sets internally the command
31086 behind the formula.
31092 \begin_inset Index idx
31095 \begin_layout Plain Layout
31105 outputs the counter as small Roman number.
31108 \begin_layout Standard
31109 All formulas behind the command
31119 are now numbered Roman.
31120 To switch to numbering with big Roman numbers, the command is inserted
31134 \begin_inset Index idx
31137 \begin_layout Plain Layout
31149 \begin_inset Quotes eld
31153 \begin_inset Quotes erd
31156 with small Latin letters there is the command
31163 \begin_inset Index idx
31166 \begin_layout Plain Layout
31174 , for big ones there is the command
31181 \begin_inset Index idx
31184 \begin_layout Plain Layout
31197 \begin_layout Standard
31198 \begin_inset Note Greyedout
31201 \begin_layout Plain Layout
31206 Only maximal 26 formulas can be numbered with Latin letters in one document.
31214 \begin_layout Standard
31218 \begin_layout Plain Layout
31234 \begin_layout Standard
31235 \begin_inset Formula \begin{equation}
31236 A=\textrm{small roman}\end{equation}
31244 \begin_layout Plain Layout
31258 \begin_inset Formula \begin{equation}
31259 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
31267 \begin_layout Plain Layout
31281 \begin_inset Formula \begin{equation}
31282 C=\textrm{small Latin}\end{equation}
31290 \begin_layout Plain Layout
31304 \begin_inset Formula \begin{equation}
31305 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
31312 \begin_layout Standard
31313 To switch back to the default numbering, insert the command:
31316 \begin_layout Standard
31326 \begin_inset Index idx
31329 \begin_layout Plain Layout
31340 \begin_layout Standard
31344 \begin_layout Plain Layout
31358 \begin_inset Formula \begin{equation}
31359 E=\textrm{Arabic}\end{equation}
31366 \begin_layout Standard
31367 \begin_inset VSpace medskip
31370 As you see, formulas are numbered serially independent from the numbering
31372 When then numbering should start with
31373 \begin_inset Quotes eld
31377 \begin_inset Quotes erd
31380 when the style is changed, new equation counters have to be defined.
31381 A description about this can be found in the file
31382 \begin_inset CommandInset href
31384 name "Formula-numbering.lyx"
31385 target "run:Formula-numbering.lyx"
31392 \begin_layout Section
31393 Chemical Symbols and Equations
31394 \begin_inset CommandInset label
31396 name "sub:Chemical-Symbols-and"
31401 \begin_inset Index idx
31404 \begin_layout Plain Layout
31405 Chemical characters ! Symbols
31411 \begin_inset Index idx
31414 \begin_layout Plain Layout
31421 \begin_inset Index idx
31424 \begin_layout Plain Layout
31433 \begin_layout Standard
31434 An example text from chemistry:
31437 \begin_layout Quote
31439 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31442 -ion reacts with two
31443 \begin_inset Formula $\mathrm{Na^{+}}$
31446 -ions to sodium sulfate
31447 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31451 The chemical equation for this is:
31452 \begin_inset Formula \begin{equation}
31453 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
31460 \begin_layout Standard
31461 This chemical equation can directly be created as formula.
31462 To avoid that the symbols appear italic, everything is highlighted and
31463 changed by the shortcut
31469 to the upright font style.
31473 \begin_layout Plain Layout
31479 \begin_inset CommandInset ref
31481 reference "sub:Font-Styles"
31493 \begin_layout Standard
31494 A more convenient way to typeset chemical formulas is to use the command
31502 \begin_inset Index idx
31505 \begin_layout Plain Layout
31513 that is available when the LaTeX-package
31518 \begin_inset Index idx
31521 \begin_layout Plain Layout
31534 to a formula a new blue box appears where chemical formulas can be inserted
31535 in an intuitive way.
31538 \begin_layout Standard
31540 \begin_inset Tabular
31541 <lyxtabular version="3" rows="9" columns="2">
31542 <features tabularvalignment="middle">
31543 <column alignment="center" valignment="top" width="0">
31544 <column alignment="center" valignment="top" width="0">
31546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31549 \begin_layout Plain Layout
31555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31558 \begin_layout Plain Layout
31560 \begin_inset Note Note
31563 \begin_layout Plain Layout
31570 is only used as spacer.
31582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31585 \begin_layout Plain Layout
31592 \begin_layout Plain Layout
31606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31609 \begin_layout Plain Layout
31610 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31623 \begin_layout Plain Layout
31630 \begin_layout Plain Layout
31644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31647 \begin_layout Plain Layout
31648 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31661 \begin_layout Plain Layout
31668 \begin_layout Plain Layout
31682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31685 \begin_layout Plain Layout
31686 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31699 \begin_layout Plain Layout
31706 \begin_layout Plain Layout
31720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31723 \begin_layout Plain Layout
31724 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31737 \begin_layout Plain Layout
31744 \begin_layout Plain Layout
31759 \begin_layout Plain Layout
31774 \begin_layout Plain Layout
31788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31791 \begin_layout Plain Layout
31792 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31805 \begin_layout Plain Layout
31812 \begin_layout Plain Layout
31822 \begin_inset Formula $\downarrow$
31826 \begin_inset Formula $\to$
31834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31837 \begin_layout Plain Layout
31838 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31851 \begin_layout Plain Layout
31858 \begin_layout Plain Layout
31871 \begin_layout Plain Layout
31884 \begin_layout Plain Layout
31897 \begin_layout Plain Layout
31910 \begin_layout Plain Layout
31924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31927 \begin_layout Plain Layout
31928 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
31938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31941 \begin_layout Plain Layout
31948 \begin_layout Plain Layout
31961 \begin_layout Plain Layout
31974 \begin_layout Plain Layout
31987 \begin_layout Plain Layout
32004 \begin_layout Plain Layout
32018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32021 \begin_layout Plain Layout
32022 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32038 \begin_layout Standard
32039 \begin_inset Note Greyedout
32042 \begin_layout Plain Layout
32047 Inserting a formula to a
32053 box will lead to LaTeX errors.
32054 In this case TeX code has to be used like for
32068 \begin_layout Plain Layout
32089 \begin_layout Standard
32096 the command for equation
32097 \begin_inset space ~
32101 \begin_inset CommandInset ref
32103 reference "eq:chem-reaction"
32108 \begin_inset Newline newline
32119 \begin_layout Plain Layout
32132 \begin_layout Plain Layout
32145 \begin_layout Plain Layout
32158 \begin_layout Plain Layout
32171 \begin_layout Plain Layout
32184 \begin_layout Plain Layout
32196 \begin_layout Standard
32197 To create multiline chemical equations first a multiline formula is created
32199 \begin_inset CommandInset ref
32201 reference "sec:Multiline-Formulas"
32206 Afterwards the command
32212 is used in every small blue box of the formula.
32214 \begin_inset CommandInset ref
32216 reference "eq:TEOS-reaction-1"
32221 \begin_inset CommandInset ref
32223 reference "eq:TEOS-reaction-2"
32227 are an example of a multi-stage chemical reaction where every equation
32228 has its own number.
32229 \begin_inset Formula \begin{eqnarray}
32230 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32231 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32239 \begin_layout Standard
32250 package provides the command
32257 \begin_inset Index idx
32260 \begin_layout Plain Layout
32268 that has to be used for special cases.
32269 For more information about
32275 and more examples have a look at the documentation of
32280 \begin_inset CommandInset citation
32289 \begin_layout Standard
32290 \begin_inset Newpage newpage
32296 \begin_layout Section
32300 \begin_layout Standard
32301 LyX supports two types of commutative diagrams:
32309 that are explained in the following.
32312 \begin_layout Subsection
32314 \begin_inset Index idx
32317 \begin_layout Plain Layout
32326 \begin_layout Standard
32327 Diagrams of this type visualize relations by vertical and horizontal lines
32329 \begin_inset Formula \[
32330 \begin{CD}A@>>>B@>>>C\\
32340 \begin_layout Standard
32341 To get them, the command
32346 \begin_inset Index idx
32349 \begin_layout Plain Layout
32359 is inserted to a formula.
32360 A blue box appears with two dashed lines where further commands can be
32365 arg "newline-insert newline"
32368 a new line is created.
32369 Horizontal relations are inserted in odd, vertical in even formula lines.
32372 \begin_layout Standard
32373 To create the relations there are the following commands:
32376 \begin_layout Itemize
32381 creates a left arrow,
32392 \begin_layout Itemize
32397 creates an up arrow,
32405 a vertical equal sign
32408 \begin_layout Itemize
32414 is a placeholder for non-existent relations
32417 \begin_layout Standard
32418 All arrows can be labeled as follows:
32421 \begin_layout Itemize
32422 Is text inserted between the first and second < or >, resp., it is placed
32424 When it is inserted between the second and third one, it appears under
32428 \begin_layout Itemize
32429 When text for vertical arrows is inserted between the first and second A
32430 or V, resp., it is placed left beside the arrow.
32431 When it is inserted between the second and third one, it appears right
32433 If the text contains an A or V, these letters must be set into a TeX-brace.
32436 \begin_layout Standard
32437 As example a diagram with all possible relations:
32440 \begin_layout Standard
32441 \begin_inset Formula \[
32442 \begin{CD}A@>j>>B@>>k>C@=F\\
32452 \begin_layout Standard
32453 The command for this is:
32454 \begin_inset Newline newline
32465 \begin_layout Plain Layout
32474 A@>j>>B@>>k>C@=F Ctrl+Return
32475 \begin_inset Newline newline
32479 \begin_inset Phantom HPhantom
32482 \begin_layout Plain Layout
32491 \begin_layout Plain Layout
32510 \begin_inset Formula $\to$
32516 \begin_inset Newline newline
32520 \begin_inset Phantom HPhantom
32523 \begin_layout Plain Layout
32532 \begin_layout Plain Layout
32549 \begin_layout Subsection
32551 \begin_inset Index idx
32554 \begin_layout Plain Layout
32555 Diagrams ! xymatrix
32563 \begin_layout Standard
32564 To be able to use xymatrices, the LaTeX-package
32569 A xymatrix is created by inserting the command
32576 Then you are able to add new matrix columns and rows like for normal matrices,
32578 \begin_inset CommandInset ref
32580 reference "sec:Matrices"
32587 \begin_layout Standard
32588 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32590 All possibilities to create commutative diagrams and decorations are explained
32595 that you find in the menu
32597 Help\SpecialChar \menuseparator
32599 \begin_inset space ~
32607 \begin_layout Subsection
32613 \begin_inset Index idx
32616 \begin_layout Plain Layout
32625 \begin_layout Standard
32630 -diagrams, the LaTeX-package
32639 -diagram is created by inserting the command
32646 Then you are able to add new matrix columns and rows like for normal matrices,
32648 \begin_inset CommandInset ref
32650 reference "sec:Matrices"
32657 \begin_layout Standard
32658 Examples how to create
32662 diagrams in LyX is given in the
32664 Feynman-diagram manual
32666 that you find in the menu
32668 Help\SpecialChar \menuseparator
32670 \begin_inset space ~
32678 \begin_layout Section
32679 User-defined Commands
32680 \begin_inset Index idx
32683 \begin_layout Plain Layout
32684 User-defined commands
32692 \begin_layout Standard
32693 \begin_inset Note Greyedout
32696 \begin_layout Plain Layout
32701 The names of user-defined commands and macros may only consist of Latin
32710 \begin_layout Subsection
32714 \begin_inset CommandInset label
32716 name "sub:The-Command-newcommand"
32721 \begin_inset Index idx
32724 \begin_layout Plain Layout
32725 User-defined commands !
32733 \begin_inset Index idx
32736 \begin_layout Plain Layout
32747 \begin_layout Standard
32748 Many LaTeX-commands are too long to be used frequently.
32749 But it is possible to define with the command
32755 new shorter commands.
32758 \begin_layout Standard
32759 The command scheme of
32768 \begin_layout Standard
32773 newcommand{new command name}[number of arguments][optional
32778 \begin_inset Newline newline
32782 \begin_inset Phantom HPhantom
32785 \begin_layout Plain Layout
32795 {command definition}
32798 \begin_layout Standard
32799 \begin_inset Note Greyedout
32802 \begin_layout Plain Layout
32807 Assure that the name of the new command is not already used in your document
32808 or by LaTeX-packages that you use.
32809 When you for example define the command
32821 , you get an error message because
32827 is already defined as command for
32828 \begin_inset Quotes eld
32832 \begin_inset Formula $\le$
32836 \begin_inset Quotes erd
32847 \begin_layout Standard
32848 The number of arguments is an integer in the range 0
32849 \begin_inset space \thinspace{}
32853 \begin_inset space \thinspace{}
32856 9 and specifies how many arguments the new command should have.
32857 With the optional value a value for an optional argument can be predefined.
32858 When this is done, the
32866 rgument of the new command is automatically an optional one.
32869 \begin_layout Standard
32870 Here are some examples:
32873 \begin_layout Itemize
32874 To define the command
32886 , the LaTeX-preamble line is:
32887 \begin_inset VSpace medskip
32891 \begin_inset Newline newline
32905 \begin_layout Itemize
32906 To define the command
32918 , the argument (that should be underlined) must be taken into account.
32919 For this the preamble line is:
32920 \begin_inset VSpace medskip
32924 \begin_inset Newline newline
32938 \begin_inset VSpace medskip
32942 \begin_inset Newline newline
32949 acts as argument placeholder, the
32953 behind it denotes that it is the placeholder for the first argument.
32956 \begin_layout Itemize
32964 \begin_inset space \thinspace{}
32968 \begin_inset space \space{}
32978 \begin_inset VSpace medskip
32982 \begin_inset Newline newline
32993 framebox#1#2{$#3$}}
32996 \begin_inset VSpace medskip
33000 \begin_inset Newline newline
33003 The two Dollar signs creates the extra formula needed for
33010 \begin_inset CommandInset ref
33012 reference "sub:Boxes-with-Frame"
33019 \begin_layout Itemize
33020 To create a new command for
33026 where the color for the box needn't to be specified, the argument for the
33027 color is defined optional:
33028 \begin_inset VSpace medskip
33032 \begin_inset Newline newline
33043 fcolorbox{#2}{#1}{$#3$}}
33046 \begin_inset VSpace medskip
33050 \begin_inset Newline newline
33053 When the color is not specified when using
33059 , the predefined color
33066 \begin_layout Standard
33067 A test of the new defined commands:
33070 \begin_layout Standard
33072 \begin_inset Tabular
33073 <lyxtabular version="3" rows="6" columns="2">
33074 <features tabularvalignment="middle">
33075 <column alignment="center" valignment="top" width="0">
33076 <column alignment="center" valignment="top" width="0">
33078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33081 \begin_layout Plain Layout
33087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33090 \begin_layout Plain Layout
33092 \begin_inset Note Note
33095 \begin_layout Plain Layout
33102 is only used as spacer.
33114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33117 \begin_layout Plain Layout
33124 \begin_layout Plain Layout
33138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33141 \begin_layout Plain Layout
33142 \begin_inset Formula $A\gr B$
33152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33155 \begin_layout Plain Layout
33163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33166 \begin_layout Plain Layout
33167 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33180 \begin_layout Plain Layout
33184 \begin_inset Formula $\to$
33190 \begin_inset Formula $\to$
33201 \begin_layout Plain Layout
33215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33218 \begin_layout Plain Layout
33219 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33232 \begin_layout Plain Layout
33236 \begin_inset Formula $\to$
33247 \begin_layout Plain Layout
33261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33264 \begin_layout Plain Layout
33265 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33278 \begin_layout Plain Layout
33284 \begin_inset Formula $\to$
33295 \begin_layout Plain Layout
33309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33312 \begin_layout Plain Layout
33313 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33329 \begin_layout Subsection
33331 \begin_inset Index idx
33334 \begin_layout Plain Layout
33335 User-defined commands! Math macros
33341 \begin_inset Index idx
33344 \begin_layout Plain Layout
33353 \begin_layout Standard
33354 User-defined commands are especially convenient for complex expressions.
33355 When you are for example dealing in a document with quadratic equations,
33356 the same solution type occurs several times.
33357 The general form of a quadratic equation is
33358 \begin_inset Formula \[
33359 0=\lambda^{2}+p\lambda+q\]
33363 The general form of the solution is
33364 \begin_inset Formula \[
33365 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
33372 \begin_layout Standard
33373 To define a command for the solution formula where only the three parameters
33375 \begin_inset Formula $\lambda$
33379 \begin_inset Formula $p$
33383 \begin_inset Formula $q$
33386 need to be specified and the index of
33387 \begin_inset Formula $\lambda$
33390 can be given optionally, the LaTeX-preamble line is
33391 \begin_inset Newline newline
33407 \begin_inset Newline newline
33411 \begin_inset Phantom HPhantom
33414 \begin_layout Plain Layout
33428 frac{#3^{2}}{4}-#4}}
33431 \begin_layout Standard
33432 To create with this the solution formula, the command
33433 \begin_inset Newline newline
33443 \begin_inset Formula $\to$
33449 \begin_inset Formula $\to$
33456 is inserted to a formula
33461 \begin_layout Standard
33462 The definition of the new command is unintuitive because one has to know
33463 the schemes of all used LaTeX commands, e.
33464 \begin_inset space \thinspace{}
33468 \begin_inset space \space{}
33471 that a fraction is inserted in LaTeX as
33475 frac{numerator}{denominator}
33478 Furthermore one can easily forget a brace in the definition and cannot
33479 see in LyX what the new command is doing.
33480 To avoid these problems LyX offers the possibility to use math macros instead
33490 \begin_layout Standard
33491 A math macro is created by using the menu
33493 Insert\SpecialChar \menuseparator
33494 Math\SpecialChar \menuseparator
33497 or the toolbar button
33498 \begin_inset Graphics
33499 filename ../images/math-macro_newmacroname_newcommand.png
33505 The math macro toolbar appears together with the following box where the
33507 \begin_inset Newline newline
33511 \begin_inset space \hspace*{\fill}
33515 \begin_inset Graphics
33516 filename clipart/macrobox.png
33521 \begin_inset space \hspace*{\fill}
33525 \begin_inset Newline newline
33529 \begin_inset FormulaMacro
33530 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33535 newmacroname is the default name of the macro that should be changed to
33536 something sensible.
33537 The wanted formula is inserted in the first blue box.
33538 An argument placeholder is inserted with the command
33545 \begin_inset space \thinspace{}
33549 \begin_inset space \space{}
33558 or by using the macro toolbar button
33559 \begin_inset Graphics
33560 filename ../images/math-macro-add-param.png
33566 Argument placeholders are displayed red.
33567 Maximum 9 arguments are possible.
33568 Optional arguments are created with the toolbar button
33569 \begin_inset Graphics
33570 filename ../images/math-macro-add-optional-param.png
33576 The first non-optional argument can be transformed to an optional one with
33578 \begin_inset Graphics
33579 filename ../images/math-macro-make-optional.png
33585 In the second blue box the appearance of the macro in LyX can be defined.
33586 Normally you want to see it as it is defined, so the box is kept empty.
33587 But when you have created a macro that needs lot of space on the screen,
33588 you can insert in the box for example
33589 \begin_inset Newline newline
33619 \begin_inset Newline newline
33624 For the macro only the arguments with the macro name in front of them will
33625 then be displayed in LyX, leading to a better overview.
33626 The formula appears in the output as defined in the first box.
33627 \begin_inset Newline newline
33630 The appearance of macros in formulas can furthermore be changed for single
33631 macros by setting the cursor in the macro and using the menu
33633 View\SpecialChar \menuseparator
33635 \begin_inset space ~
33639 \begin_inset space ~
33647 \begin_layout Standard
33648 To use a macro, the macro name is inserted as command to a formula, in our
33656 Our macro looks in LyX like this:
33657 \begin_inset Newline newline
33661 \begin_inset space \hspace*{\fill}
33665 \begin_inset Graphics
33666 filename clipart/macrouse.png
33671 \begin_inset space \hspace*{\fill}
33675 \begin_inset Newline newline
33678 Here is our macro example with the arguments
33679 \begin_inset Formula $x$
33683 \begin_inset Formula $\ln(x)$
33687 \begin_inset Formula $B$
33693 \begin_layout Standard
33694 \begin_inset Formula \[
33702 \begin_layout Standard
33703 LyX offers in the menu
33705 Tools\SpecialChar \menuseparator
33706 Preferences\SpecialChar \menuseparator
33707 Editing\SpecialChar \menuseparator
33710 different styles to edit macros.
33711 To find the style that suits you the most, choose a style and set the cursor
33712 in a macro formula to see the difference.
33715 \begin_layout Standard
33716 A math macro is transformed internally to a
33722 command when exporting the document.
33729 command is not placed in the LaTeX-preamble, therefore macros can only
33730 be used in formulas that are in the document below the macro definition
33734 \begin_layout Standard
33735 Math macros can also be directly be created from a
33742 When writing for example the command
33745 \begin_inset Newline newline
33754 xleftarrow[#2]{#1}}
33755 \begin_inset Newline newline
33760 in LyX as normal text, highlighting it completely and using then the shortcut
33765 , the command will be transformed to a math macro.
33766 Using this method you need to be careful that the
33772 command is typed correctly, otherwise you get a faulty macro leading to
33776 \begin_layout Standard
33777 Math macros currently yet have the problem that further formulas in macro
33778 definitions are handled wrongly.
33779 Therefore the example
33786 \begin_inset CommandInset ref
33788 reference "sub:The-Command-newcommand"
33792 cannot be created as macro.
33795 \begin_layout Standard
33796 When the cursor is in a macro definition box, you will see the macro toolbar
33800 \begin_layout Standard
33801 \begin_inset VSpace defskip
33807 \begin_layout Standard
33808 \begin_inset Graphics
33809 filename clipart/MacroToolbar.png
33814 \begin_inset Index idx
33817 \begin_layout Plain Layout
33826 \begin_layout Standard
33827 \begin_inset VSpace defskip
33833 \begin_layout Standard
33834 The macro toolbar contains from left to right the following buttons:
33837 \begin_layout Standard
33838 \begin_inset VSpace defskip
33844 \begin_layout Standard
33845 \begin_inset Tabular
33846 <lyxtabular version="3" rows="9" columns="2">
33847 <features islongtable="true" longtabularalignment="center">
33848 <column alignment="left" valignment="top" width="0">
33849 <column alignment="left" valignment="top" width="85col%">
33850 <row interlinespace="2.5mm">
33851 <cell alignment="center" valignment="top" usebox="none">
33854 \begin_layout Plain Layout
33855 \begin_inset Graphics
33856 filename ../images/math-macro-remove-param.png
33857 BoundingBox 0bp 5bp 20bp 25bp
33858 rotateOrigin center
33867 <cell alignment="center" valignment="top" usebox="none">
33870 \begin_layout Plain Layout
33873 Edit\SpecialChar \menuseparator
33874 Math\SpecialChar \menuseparator
33876 \begin_inset space ~
33879 Definition\SpecialChar \menuseparator
33880 Remove Last Argument
33886 <row interlinespace="2.5mm">
33887 <cell alignment="center" valignment="top" usebox="none">
33890 \begin_layout Plain Layout
33891 \begin_inset Graphics
33892 filename ../images/math-macro-add-param.png
33893 BoundingBox 0bp 5bp 20bp 25bp
33894 rotateOrigin center
33903 <cell alignment="center" valignment="top" usebox="none">
33906 \begin_layout Plain Layout
33909 Edit\SpecialChar \menuseparator
33910 Math\SpecialChar \menuseparator
33912 \begin_inset space ~
33915 Definition\SpecialChar \menuseparator
33922 <row interlinespace="2.5mm">
33923 <cell alignment="center" valignment="top" usebox="none">
33926 \begin_layout Plain Layout
33927 \begin_inset Graphics
33928 filename ../images/math-macro-make-optional.png
33929 BoundingBox 0bp 5bp 20bp 25bp
33930 rotateOrigin center
33939 <cell alignment="center" valignment="top" usebox="none">
33942 \begin_layout Plain Layout
33945 Edit\SpecialChar \menuseparator
33946 Math\SpecialChar \menuseparator
33948 \begin_inset space ~
33951 Definition\SpecialChar \menuseparator
33952 Make First Non-Optional into
33953 \begin_inset Newline newline
33957 \begin_inset Phantom HPhantom
33960 \begin_layout Plain Layout
33963 Edit\SpecialChar \menuseparator
33964 Math\SpecialChar \menuseparator
33966 \begin_inset space ~
33969 Definition\SpecialChar \menuseparator
33981 <row interlinespace="2.5mm">
33982 <cell alignment="center" valignment="top" usebox="none">
33985 \begin_layout Plain Layout
33986 \begin_inset Graphics
33987 filename ../images/math-macro-make-nonoptional.png
33988 BoundingBox 0bp 5bp 20bp 25bp
33989 rotateOrigin center
33998 <cell alignment="center" valignment="top" usebox="none">
34001 \begin_layout Plain Layout
34004 Edit\SpecialChar \menuseparator
34005 Math\SpecialChar \menuseparator
34007 \begin_inset space ~
34010 Definition\SpecialChar \menuseparator
34011 Make Last Optional into
34012 \begin_inset Newline newline
34016 \begin_inset Phantom HPhantom
34019 \begin_layout Plain Layout
34022 Edit\SpecialChar \menuseparator
34023 Math\SpecialChar \menuseparator
34025 \begin_inset space ~
34028 Definition\SpecialChar \menuseparator
34034 Non-Optional Argument
34040 <row interlinespace="2.5mm">
34041 <cell alignment="center" valignment="top" usebox="none">
34044 \begin_layout Plain Layout
34045 \begin_inset Graphics
34046 filename ../images/math-macro-remove-optional-param.png
34047 BoundingBox 0bp 5bp 20bp 25bp
34048 rotateOrigin center
34057 <cell alignment="center" valignment="top" usebox="none">
34060 \begin_layout Plain Layout
34063 Edit\SpecialChar \menuseparator
34064 Math\SpecialChar \menuseparator
34066 \begin_inset space ~
34069 Definition\SpecialChar \menuseparator
34070 Remove Optional Argument
34076 <row interlinespace="2.5mm">
34077 <cell alignment="center" valignment="top" usebox="none">
34080 \begin_layout Plain Layout
34081 \begin_inset Graphics
34082 filename ../images/math-macro-add-optional-param.png
34083 BoundingBox 0bp 5bp 20bp 25bp
34084 rotateOrigin center
34093 <cell alignment="center" valignment="top" usebox="none">
34096 \begin_layout Plain Layout
34099 Edit\SpecialChar \menuseparator
34100 Math\SpecialChar \menuseparator
34102 \begin_inset space ~
34105 Definition\SpecialChar \menuseparator
34106 Insert Optional Argument
34112 <row interlinespace="2.5mm">
34113 <cell alignment="center" valignment="top" usebox="none">
34116 \begin_layout Plain Layout
34117 \begin_inset Graphics
34118 filename ../images/math-macro-remove-greedy-param.png
34119 BoundingBox 0bp 5bp 20bp 25bp
34120 rotateOrigin center
34129 <cell alignment="center" valignment="top" usebox="none">
34132 \begin_layout Plain Layout
34135 Edit\SpecialChar \menuseparator
34136 Math\SpecialChar \menuseparator
34138 \begin_inset space ~
34141 Definition\SpecialChar \menuseparator
34142 Remove Last Argument
34143 \begin_inset Newline newline
34147 \begin_inset Phantom HPhantom
34150 \begin_layout Plain Layout
34153 Edit\SpecialChar \menuseparator
34154 Math\SpecialChar \menuseparator
34156 \begin_inset space ~
34159 Definition\SpecialChar \menuseparator
34165 Spitting Out To The Right
34171 <row interlinespace="2.5mm">
34172 <cell alignment="center" valignment="top" usebox="none">
34175 \begin_layout Plain Layout
34176 \begin_inset Graphics
34177 filename ../images/math-macro-append-greedy-param.png
34178 BoundingBox 0bp 5bp 20bp 25bp
34179 rotateOrigin center
34188 <cell alignment="center" valignment="top" usebox="none">
34191 \begin_layout Plain Layout
34194 Edit\SpecialChar \menuseparator
34195 Math\SpecialChar \menuseparator
34197 \begin_inset space ~
34200 Definition\SpecialChar \menuseparator
34202 \begin_inset Newline newline
34206 \begin_inset Phantom HPhantom
34209 \begin_layout Plain Layout
34212 Edit\SpecialChar \menuseparator
34213 Math\SpecialChar \menuseparator
34215 \begin_inset space ~
34218 Definition\SpecialChar \menuseparator
34224 Eating From The Right
34230 <row interlinespace="2.5mm">
34231 <cell alignment="center" valignment="top" usebox="none">
34234 \begin_layout Plain Layout
34235 \begin_inset Graphics
34236 filename ../images/math-macro-add-greedy-optional-param.png
34237 BoundingBox 0bp 5bp 20bp 25bp
34238 rotateOrigin center
34247 <cell alignment="center" valignment="top" usebox="none">
34250 \begin_layout Plain Layout
34253 Edit\SpecialChar \menuseparator
34254 Math\SpecialChar \menuseparator
34256 \begin_inset space ~
34259 Definition\SpecialChar \menuseparator
34260 Append Optional Argument
34261 \begin_inset Newline newline
34265 \begin_inset Phantom HPhantom
34268 \begin_layout Plain Layout
34271 Edit\SpecialChar \menuseparator
34272 Math\SpecialChar \menuseparator
34274 \begin_inset space ~
34277 Definition\SpecialChar \menuseparator
34283 Eating From The Right
34296 \begin_layout Standard
34297 \begin_inset Newpage newpage
34303 \begin_layout Section
34305 \begin_inset Index idx
34308 \begin_layout Plain Layout
34317 \begin_layout Subsection
34319 \begin_inset Index idx
34322 \begin_layout Plain Layout
34331 \begin_layout Standard
34332 Negative numbers often look ugly in formulas because the minus sign before
34333 the number is set with the same length as the minus operator sign.
34334 When writing the negative number in normal text, the minus sign appears
34338 \begin_layout Standard
34339 Thus, the problem disappears when converting the minus sign to mathematical
34343 \begin_layout Standard
34344 An example to visualize the problem:
34347 \begin_layout Standard
34349 \begin_inset Tabular
34350 <lyxtabular version="3" rows="3" columns="2">
34351 <features tabularvalignment="middle">
34352 <column alignment="right" valignment="top" width="0">
34353 <column alignment="left" valignment="top" width="0">
34355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34358 \begin_layout Plain Layout
34364 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34367 \begin_layout Plain Layout
34375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34378 \begin_layout Plain Layout
34384 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34387 \begin_layout Plain Layout
34388 \begin_inset Formula $x=-2$
34398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34401 \begin_layout Plain Layout
34407 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34410 \begin_layout Plain Layout
34411 \begin_inset Formula $x=\textrm{-}2$
34427 \begin_layout Subsection
34428 Comma as decimal Separator
34429 \begin_inset Index idx
34432 \begin_layout Plain Layout
34441 \begin_layout Standard
34442 In LaTeX a comma inside a formula is used, according to the English convention,
34443 as number group separator.
34444 So there will be space added behind all commas in formulas.
34447 \begin_layout Standard
34448 To avoid this, the comma is highlighted and changed to mathematical text
34458 \begin_layout Standard
34459 To use all formula commas in the document as decimal separator, the file
34468 \begin_layout Plain Layout
34473 is part of the LaTeX-package
34478 \begin_inset Index idx
34481 \begin_layout Plain Layout
34486 \begin_layout Plain Layout
34506 \begin_inset Index idx
34509 \begin_layout Plain Layout
34515 is loaded with the LaTeX-preamble line
34518 \begin_layout Standard
34526 \begin_layout Subsection
34528 \begin_inset CommandInset label
34530 name "sub:Physical-Vectors"
34535 \begin_inset Index idx
34538 \begin_layout Plain Layout
34547 \begin_layout Standard
34548 Predefined vectors are offered by the LaTeX-package
34553 \begin_inset Index idx
34556 \begin_layout Plain Layout
34562 that is loaded with the LaTeX-preamble line
34565 \begin_layout Standard
34573 \begin_layout Standard
34577 \begin_layout Plain Layout
34587 \begin_inset Note Note
34590 \begin_layout Plain Layout
34591 The following table will only be displayed when the LaTeX-package
34603 \begin_layout Standard
34604 The following commands are defined:
34607 \begin_layout Standard
34609 \begin_inset Tabular
34610 <lyxtabular version="3" rows="4" columns="2">
34611 <features tabularvalignment="middle">
34612 <column alignment="center" valignment="top" width="0">
34613 <column alignment="center" valignment="top" width="0">
34615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34618 \begin_layout Plain Layout
34624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34627 \begin_layout Plain Layout
34635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34638 \begin_layout Plain Layout
34648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34651 \begin_layout Plain Layout
34652 \begin_inset Formula $\Bra{\psi}$
34662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34665 \begin_layout Plain Layout
34675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34678 \begin_layout Plain Layout
34679 \begin_inset Formula $\Ket{\psi}$
34689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34692 \begin_layout Plain Layout
34704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34707 \begin_layout Plain Layout
34708 \begin_inset Formula $\Braket{\psi|\phi}$
34724 \begin_layout Standard
34731 assures that all vertical bars are set in the size of the surrounding brackets:
34732 \begin_inset Formula \[
34733 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
34741 \begin_layout Plain Layout
34751 \begin_inset Note Note
34754 \begin_layout Plain Layout
34755 The following will be displayed when the LaTeX-package
34767 \begin_layout Standard
34768 You need to install the LaTeX-package
34772 to see the rest of this subsection in the output.
34775 \begin_layout Standard
34779 \begin_layout Plain Layout
34791 \begin_layout Standard
34798 can also be achieved using the command
34804 , that is described in
34805 \begin_inset CommandInset ref
34807 reference "sub:Automatic-Bracket-Size"
34814 \begin_layout Subsection
34815 Self-defined Fractions
34816 \begin_inset CommandInset label
34818 name "sub:Self-defined-Fractions"
34823 \begin_inset Index idx
34826 \begin_layout Plain Layout
34827 Fractions ! self-defined
34835 \begin_layout Standard
34836 To define custom commands for fractions, the command
34843 \begin_inset Index idx
34846 \begin_layout Plain Layout
34854 is used in the following scheme:
34857 \begin_layout Standard
34870 bracket}{fraction bar thickness}{style}
34871 \begin_inset Newline newline
34875 \begin_inset Phantom HPhantom
34878 \begin_layout Plain Layout
34888 {numerator}{denominator}
34891 \begin_layout Standard
34892 The style is a number in the range of 0
34893 \begin_inset space \thinspace{}
34897 \begin_inset space \thinspace{}
34903 \begin_layout Standard
34905 \begin_inset Tabular
34906 <lyxtabular version="3" rows="5" columns="2">
34907 <features tabularvalignment="middle">
34908 <column alignment="center" valignment="top" width="0">
34909 <column alignment="center" valignment="top" width="0">
34911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34914 \begin_layout Plain Layout
34920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34923 \begin_layout Plain Layout
34931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34934 \begin_layout Plain Layout
34940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34943 \begin_layout Plain Layout
34944 display style formula
34951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34954 \begin_layout Plain Layout
34960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34963 \begin_layout Plain Layout
34971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34974 \begin_layout Plain Layout
34980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34983 \begin_layout Plain Layout
34991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34994 \begin_layout Plain Layout
35000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35003 \begin_layout Plain Layout
35017 \begin_layout Standard
35018 When no style is given, the size is adjusted to the surrounding environment
35019 like for the command
35028 \begin_layout Standard
35029 When no fraction bar thickness is given, the predefined value of 0.4
35030 \begin_inset space \thinspace{}
35036 \begin_layout Standard
35037 \begin_inset VSpace medskip
35040 For example, the commands
35053 \begin_inset CommandInset ref
35055 reference "sub:Fractions"
35059 are defined with the commands
35062 \begin_layout Standard
35071 genfrac{}{}{}{0}{#1}{#2}}
35074 \begin_layout Standard
35078 \begin_layout Standard
35087 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35090 \begin_layout Standard
35091 \begin_inset VSpace medskip
35094 To define a fraction where the fraction bar thickness can be given as optional
35095 argument, the following line is inserted to the LaTeX-preamble:
35098 \begin_layout Standard
35107 genfrac{}{}{#1}{}{#2}{#3}}
35110 \begin_layout Standard
35112 \begin_inset Formula \begin{align*}
35113 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35114 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35119 As one can see, the distance of the numerator and the denominator to the
35120 fraction bar is round about three times the bar thickness.
35123 \begin_layout Subsection
35125 \begin_inset Index idx
35128 \begin_layout Plain Layout
35137 \begin_layout Standard
35138 To cancel formulas or formula parts, the LaTeX-package
35143 \begin_inset Index idx
35146 \begin_layout Plain Layout
35152 has to be loaded with the LaTeX-preamble line
35155 \begin_layout Standard
35160 usepackage[samesize]{cancel}
35163 \begin_layout Standard
35167 \begin_layout Plain Layout
35177 \begin_inset Note Note
35180 \begin_layout Plain Layout
35181 The following table will only be displayed when the LaTeX-package
35193 \begin_layout Standard
35194 There are four ways to cancel formulas:
35197 \begin_layout Standard
35199 \begin_inset Tabular
35200 <lyxtabular version="3" rows="5" columns="2">
35201 <features tabularvalignment="middle">
35202 <column alignment="center" valignment="top" width="0">
35203 <column alignment="center" valignment="top" width="0">
35205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35208 \begin_layout Plain Layout
35214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35217 \begin_layout Plain Layout
35219 \begin_inset Note Note
35222 \begin_layout Plain Layout
35229 are used here as spacer.
35241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35244 \begin_layout Plain Layout
35253 \begin_layout Plain Layout
35267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35270 \begin_layout Plain Layout
35271 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35284 \begin_layout Plain Layout
35293 \begin_layout Plain Layout
35307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35310 \begin_layout Plain Layout
35311 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35324 \begin_layout Plain Layout
35333 \begin_layout Plain Layout
35347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35350 \begin_layout Plain Layout
35351 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35364 \begin_layout Plain Layout
35368 \begin_inset Formula $\to$
35379 \begin_layout Plain Layout
35393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35396 \begin_layout Plain Layout
35397 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35413 \begin_layout Standard
35420 is especially suitable to visualize the reduction of fractions within formulas:
35421 \begin_inset Formula \[
35422 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
35429 \begin_layout Standard
35433 \begin_layout Plain Layout
35443 \begin_inset Note Note
35446 \begin_layout Plain Layout
35447 The following will be displayed when the LaTeX-package
35459 \begin_layout Standard
35460 You need to install the LaTeX-package
35464 to see the rest of this subsection in the output.
35467 \begin_layout Standard
35471 \begin_layout Plain Layout
35483 \begin_layout Subsection
35484 Formulas in Section Headings
35485 \begin_inset CommandInset label
35487 name "sub:Formulas-in-Section"
35492 \begin_inset Index idx
35495 \begin_layout Plain Layout
35496 Formula ! in section headings
35504 \begin_layout Standard
35505 When formulas are used in section headings, the following has to be taken
35509 \begin_layout Standard
35510 \begin_inset Note Greyedout
35513 \begin_layout Plain Layout
35519 \begin_inset Index idx
35522 \begin_layout Plain Layout
35523 Packages ! hyperref
35528 support is enabled in the document settings dialog under
35531 \begin_inset space ~
35536 , PDF-bookmarks are created for every section heading in the table of contents.
35537 If a section heading contains formulas, they are incorrectly displayed
35538 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35547 \begin_layout Standard
35548 Both problems can be solved by inserting at the end of the section heading
35549 a short title with the menu
35551 Insert\SpecialChar \menuseparator
35553 \begin_inset space ~
35559 Short titles are used as alternative for multiline section headings to
35560 keep the table of contents clearly arranged.
35561 Only the short title appears in the table of contents and therefore also
35562 in the PDF-bookmark.
35565 \begin_layout Standard
35566 When formulas should be used in the table of contents but
35570 is used, one can use the following command in TeX-mode:
35573 \begin_layout Standard
35578 texorpdfstring{part}{alternative}
35579 \begin_inset Index idx
35582 \begin_layout Plain Layout
35593 \begin_layout Standard
35594 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35595 This can be characters, formulas, footnotes, but also cross-references.
35596 The alternative is used instead of the part for the bookmark.
35599 \begin_layout Standard
35600 Here are two example headings:
35601 \begin_inset VSpace -3mm
35608 \begin_layout Plain Layout
35620 \begin_layout Subsubsection
35621 Heading without formula in table of contents
35622 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35626 \begin_inset Argument
35629 \begin_layout Plain Layout
35630 Heading without formula in table of contents
35638 \begin_layout Subsubsection
35639 Heading with formula in table of contents
35643 \begin_layout Plain Layout
35653 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35660 \begin_layout Plain Layout
35670 \begin_layout Standard
35674 \begin_layout Plain Layout
35683 In the first heading a short title was used, in the second one
35692 \begin_layout Standard
35693 To get the same formatting as for the other headings, the complete heading
35702 \begin_layout Plain Layout
35704 \begin_inset CommandInset ref
35706 reference "sub:Bold-Formulas"
35718 \begin_layout Subsection
35719 Formulas in multi-column Text
35720 \begin_inset Index idx
35723 \begin_layout Plain Layout
35724 Formula ! in multi-column text
35732 \begin_layout Standard
35733 Formulas in multi-column text are often too wide to fit into a column and
35734 thus need to be set over the whole page width.
35735 This is done by using the LaTeX-package
35743 \begin_layout Plain Layout
35748 is part of every LaTeX standard installation.
35754 \begin_inset Index idx
35757 \begin_layout Plain Layout
35758 Packages ! multicol
35763 , that is loaded with the LaTeX-preamble line
35766 \begin_layout Standard
35771 usepackage{multicol}
35774 \begin_layout Standard
35775 \begin_inset Note Greyedout
35778 \begin_layout Plain Layout
35779 Note herby that the setting
35782 \begin_inset space ~
35789 Document\SpecialChar \menuseparator
35795 \begin_inset space ~
35815 \begin_layout Standard
35816 Before the multi-column text the command
35819 \begin_layout Standard
35824 begin{multicols}{column number}
35827 \begin_layout Standard
35828 is written in TeX-mode.
35829 The column number is a number in the range of 2
35830 \begin_inset space \thinspace{}
35834 \begin_inset space \thinspace{}
35838 Before the formula the multi-column text is ended by inserting the command
35841 \begin_layout Standard
35849 \begin_layout Standard
35853 \begin_layout Standard
35854 Due to the command some space is automatically added before the formula.
35856 \begin_inset space \thinspace{}
35859 mm vertical space is inserted before the formula.
35860 When the formula style
35866 \begin_layout Plain Layout
35868 \begin_inset CommandInset ref
35870 reference "sec:Formula-Styles"
35882 \begin_inset space \thinspace{}
35885 mm space is inserted instead.
35888 \begin_layout Standard
35889 As example a multi-column text with a displayed formula:
35892 \begin_layout Standard
35898 \begin_layout Plain Layout
35902 begin{multicols}{2}
35907 Das Spektrum wird fouriertransformiert.
35908 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35909 , Lösungsmittel) zu trennen.
35910 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35911 nun das Aussehen des Ausgangssignals.
35912 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35913 über alle Phasen integrieren muss.
35915 \begin_inset Formula $S$
35918 unser normiertes Ausgangssignal und
35919 \begin_inset Formula $P$
35922 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35926 \begin_layout Plain Layout
35936 \begin_inset VSpace -6mm
35940 \begin_inset Formula \begin{equation}
35941 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
35949 \begin_layout Plain Layout
35953 begin{multicols}{2}
35959 \begin_inset Formula $S_{0}$
35962 das Signal ohne Gradient ist und die Normierungsbedingung
35963 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35967 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35969 \begin_inset Formula $\nicefrac{\pi}{2}$
35973 \begin_inset space \thinspace{}
35976 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35977 das Signal zusätzlich abschwächt.
35978 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35980 \begin_inset Formula $T_{2}$
35986 \begin_layout Standard
35992 \begin_layout Plain Layout
36004 \begin_layout Subsection
36005 Formulas with Description of Variables
36006 \begin_inset Index idx
36009 \begin_layout Plain Layout
36010 Formula ! with description of variables
36018 \begin_layout Standard
36019 To describe variables within a formula, like in formula
36020 \begin_inset CommandInset ref
36022 reference "eq:within"
36031 \begin_inset Formula $n$
36035 \begin_inset space ~
36038 matrix is used with left aligned columns for the
36039 \begin_inset Formula $n$
36046 \begin_layout Plain Layout
36048 \begin_inset CommandInset ref
36050 reference "sec:Matrices"
36059 To set the description in a smaller size, before the matrix e.
36060 \begin_inset space \thinspace{}
36064 \begin_inset space \space{}
36077 \begin_layout Plain Layout
36079 \begin_inset CommandInset ref
36081 reference "sub:Font-Sizes"
36093 \begin_layout Standard
36094 When the formula style
36100 \begin_layout Plain Layout
36102 \begin_inset CommandInset ref
36104 reference "sec:Formula-Styles"
36125 \begin_layout Plain Layout
36132 only works in formulas with the style
36137 \begin_inset CommandInset ref
36139 reference "sub:Variable-Space"
36148 is inserted before and after the matrix to have the same separation of
36149 the matrix from the equation and the side margin.
36152 \begin_layout Standard
36153 When the formula style
36157 is used, the method described in
36158 \begin_inset CommandInset ref
36160 reference "sub:Flalign-Environment"
36164 is used to indent formulas.
36166 \begin_inset CommandInset ref
36168 reference "eq:within"
36172 consists of five columns whereas in the first two columns contain the equation,
36173 the third the matrix and the last one an empty TeX-brace.
36174 \begin_inset Formula \begin{flalign}
36175 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36176 \rho & \textrm{density}\\
36177 V & \textrm{volume}\\
36178 g & \textrm{gravitational acceleration}
36179 \end{array} & & {}\label{eq:within}\end{flalign}
36186 \begin_layout Subsection
36187 Upright small Greek Letters
36188 \begin_inset CommandInset label
36190 name "sub:Upright-small-Greek"
36195 \begin_inset Index idx
36198 \begin_layout Plain Layout
36199 Greek letters ! upright
36207 \begin_layout Standard
36208 Most of the math fonts only provide italic small Greek letters.
36209 But for symbols of elementary particles like pions and neutrinos, upright
36210 Greek letters are needed.
36219 \begin_layout Plain Layout
36224 is part of the LaTeX-package
36229 \begin_inset Index idx
36232 \begin_layout Plain Layout
36237 \begin_layout Plain Layout
36257 \begin_inset Index idx
36260 \begin_layout Plain Layout
36266 that is loaded with the LaTeX-preamble line
36269 \begin_layout Standard
36274 usepackage{upgreek}
36277 \begin_layout Standard
36283 \begin_layout Plain Layout
36293 \begin_inset Note Note
36296 \begin_layout Plain Layout
36297 The following table will only be displayed when the LaTeX-package
36306 They are created when the command for a small Greek letters is started
36312 For example the command
36319 \begin_inset Formula $\uptau$
36325 \begin_layout Standard
36326 With these commands reactions of elementary particles can be typeset:
36327 \begin_inset Formula \[
36328 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
36335 \begin_layout Standard
36336 The upright letters are more bold and wider than the italic ones.
36337 They should therefore not be used for units like
36338 \begin_inset Quotes eld
36342 \begin_inset Quotes erd
36348 \begin_layout Standard
36352 \begin_layout Plain Layout
36362 \begin_inset Note Note
36365 \begin_layout Plain Layout
36366 The following will be displayed when the LaTeX-package
36378 \begin_layout Standard
36379 You need to install the LaTeX-package
36383 to see the rest of this subsection in the output.
36386 \begin_layout Standard
36390 \begin_layout Plain Layout
36402 \begin_layout Subsection
36403 Text Characters in Formulas
36404 \begin_inset CommandInset label
36406 name "sub:Text-Characters-in"
36411 \begin_inset Index idx
36414 \begin_layout Plain Layout
36423 \begin_layout Standard
36424 In some cases you might want to insert text characters directly into formulas.
36425 When for example the centered dot · is often used in formulas like
36426 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36429 , one would have to insert the command
36439 \begin_layout Plain Layout
36441 \begin_inset CommandInset ref
36443 reference "sub:Binary-Operators"
36452 all the time, because this character is defined in all encodings as text
36454 But the encoding can be changed by this LaTeX-preamble line:
36457 \begin_layout Standard
36462 Declare Inputtext{183}{
36472 f\SpecialChar \textcompwordmark{}
36476 \begin_layout Standard
36477 The character encoding (menu
36479 Document\SpecialChar \menuseparator
36480 Settings\SpecialChar \menuseparator
36483 ) specifies what character appears when a keyboard key is pressed.
36484 When the key for the character '·' is pressed, internally the command
36491 But this command is not available in a formula so that you would get LaTeX-erro
36493 With the changed encoding the right command is chosen automatically, depending
36494 on if the character was inserted into a formula or not.
36497 \begin_layout Standard
36498 The encoding of several characters is saved in definition files.
36499 Fore example the encoding
36503 is defined in the file
36507 that is in the installation folder of LaTeX.
36508 Encodings should only be changed via the LaTeX-preamble and not in the
36510 Otherwise own documents could not be edited by other LyX users working
36511 on other computers.
36514 \begin_layout Standard
36515 \begin_inset VSpace medskip
36518 Besides the centered dot, in this document the degree sign ° is defined
36519 with the following LaTeX-preamble line so that it can directly be inserted
36523 \begin_layout Standard
36528 DeclareInputtext{176}{
36538 f\SpecialChar \textcompwordmark{}
36542 \begin_layout Standard
36543 \begin_inset Newpage newpage
36549 \begin_layout Section
36552 \begin_inset Index idx
36555 \begin_layout Plain Layout
36564 \begin_layout Standard
36565 This section is a summary of the most important typographic rules, listed
36570 \begin_layout Plain Layout
36571 This collection was partly taken from the German semi-official dictionary
36573 \begin_inset Quotes eld
36577 \begin_inset Quotes erd
36581 \begin_inset CommandInset citation
36587 that lists some of the ISO rules.
36588 More rules are listed in
36589 \begin_inset CommandInset citation
36603 \begin_layout Itemize
36612 \begin_layout Plain Layout
36613 done with font styles, see
36614 \begin_inset CommandInset ref
36616 reference "sub:Font-Styles"
36625 , no matter if they appear in italic text: 30
36626 \begin_inset space \thinspace{}
36630 \begin_inset Newline newline
36633 Between the value and the unit is the smallest space, see
36634 \begin_inset CommandInset ref
36636 reference "sub:Predefined-Space"
36641 \begin_inset Newline newline
36644 This convention is automatically fulfilled when the command
36651 When it is entered to a formula, two boxes appear.
36652 In the first one the value is inserted, in the second one the unit, and
36654 \begin_inset Formula $\unit[30]{km/h}$
36658 \begin_inset space \thinspace{}
36668 is not a real LaTeX command but the command
36674 , therefore you cannot use it in TeX code.
36677 \begin_layout Itemize
36678 Percent and perthousand signs are set like physical units:
36679 \begin_inset Newline newline
36683 \begin_inset space \thinspace{}
36689 \begin_layout Itemize
36690 The degree sign follows directly on the value: 15°, but not when it is used
36692 \begin_inset space \thinspace{}
36698 \begin_layout Itemize
36699 In numbers with more than four digits the smallest space is inserted before
36700 every third digit to group them:
36710 \begin_inset space \thinspace{}
36714 \begin_inset space \thinspace{}
36720 \begin_layout Itemize
36721 For dimensions like 120×90×40
36722 \begin_inset space \thinspace{}
36725 cm the multiplication sign
36726 \begin_inset Quotes eld
36730 \begin_inset Quotes erd
36734 It is available either via the command
36742 Insert\SpecialChar \menuseparator
36743 Special Character\SpecialChar \menuseparator
36749 \begin_layout Itemize
36750 Functions with names consisting of several letters are set upright to avoid
36752 \begin_inset CommandInset ref
36754 reference "sub:Predefined-Functions"
36761 \begin_layout Itemize
36762 Indices consisting of several letters, are set upright:
36763 \begin_inset Formula $E_{\mathrm{kin}}$
36767 \begin_inset Newline newline
36770 Components of matrices are set italic:
36771 \begin_inset Formula $\hat{H}_{kl}$
36777 \begin_layout Itemize
36778 The differentiation/integration operator 'd', the Euler's number 'e' and
36779 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36783 \begin_layout Itemize
36784 The character that denotes a
36788 transformation is inserted either by the command
36796 \begin_layout Plain Layout
36809 Insert\SpecialChar \menuseparator
36810 Special Character\SpecialChar \menuseparator
36811 Symbols\SpecialChar \menuseparator
36813 \begin_inset space ~
36819 \begin_inset Formula $\mathscr{F}$
36825 \begin_layout Standard
36826 \begin_inset Newpage newpage
36832 \begin_layout Section
36834 \begin_inset Index idx
36837 \begin_layout Plain Layout
36846 \begin_layout Standard
36847 Some characters and symbols can be created with several commands.
36848 Here is a list of the synonym commands:
36851 \begin_layout Standard
36852 \begin_inset VSpace bigskip
36856 \begin_inset space \hfill{}
36860 \begin_inset Tabular
36861 <lyxtabular version="3" rows="12" columns="2">
36862 <features tabularvalignment="middle">
36863 <column alignment="center" valignment="top" width="0pt">
36864 <column alignment="center" valignment="top" width="0pt">
36866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36869 \begin_layout Plain Layout
36875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36878 \begin_layout Plain Layout
36880 \begin_inset Note Note
36883 \begin_layout Plain Layout
36890 is only used as spacer.
36902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36905 \begin_layout Plain Layout
36913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36916 \begin_layout Plain Layout
36920 \begin_layout Plain Layout
36933 \begin_layout Plain Layout
36947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36950 \begin_layout Plain Layout
36958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36961 \begin_layout Plain Layout
36971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36974 \begin_layout Plain Layout
36982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36985 \begin_layout Plain Layout
36995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36998 \begin_layout Plain Layout
37006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37009 \begin_layout Plain Layout
37017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37020 \begin_layout Plain Layout
37028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37031 \begin_layout Plain Layout
37039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37042 \begin_layout Plain Layout
37050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37053 \begin_layout Plain Layout
37063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37066 \begin_layout Plain Layout
37074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37077 \begin_layout Plain Layout
37087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37090 \begin_layout Plain Layout
37098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37101 \begin_layout Plain Layout
37111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37114 \begin_layout Plain Layout
37122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37125 \begin_layout Plain Layout
37135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37138 \begin_layout Plain Layout
37146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37149 \begin_layout Plain Layout
37157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37160 \begin_layout Plain Layout
37168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37171 \begin_layout Plain Layout
37183 \begin_inset space \hfill{}
37187 \begin_inset Tabular
37188 <lyxtabular version="3" rows="12" columns="2">
37189 <features tabularvalignment="middle">
37190 <column alignment="center" valignment="top" width="0pt">
37191 <column alignment="center" valignment="top" width="0pt">
37193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37196 \begin_layout Plain Layout
37202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37205 \begin_layout Plain Layout
37213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37216 \begin_layout Plain Layout
37224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37227 \begin_layout Plain Layout
37239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37242 \begin_layout Plain Layout
37250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37253 \begin_layout Plain Layout
37263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37266 \begin_layout Plain Layout
37274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37277 \begin_layout Plain Layout
37287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37290 \begin_layout Plain Layout
37298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37301 \begin_layout Plain Layout
37309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37312 \begin_layout Plain Layout
37320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37323 \begin_layout Plain Layout
37331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37334 \begin_layout Plain Layout
37342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37345 \begin_layout Plain Layout
37355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37358 \begin_layout Plain Layout
37366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37369 \begin_layout Plain Layout
37379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37382 \begin_layout Plain Layout
37390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37393 \begin_layout Plain Layout
37403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37406 \begin_layout Plain Layout
37414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37417 \begin_layout Plain Layout
37427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37430 \begin_layout Plain Layout
37438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37441 \begin_layout Plain Layout
37451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37454 \begin_layout Plain Layout
37462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37465 \begin_layout Plain Layout
37479 \begin_inset space \hfill{}
37485 \begin_layout Standard
37486 \begin_inset Newpage newpage
37492 \begin_layout Bibliography
37493 \labelwidthstring References
37494 \begin_inset CommandInset bibitem
37495 LatexCommand bibitem
37507 The LaTeX Companion
37510 Addison Wesley, 2004
37513 \begin_layout Bibliography
37514 \labelwidthstring References
37515 \begin_inset CommandInset bibitem
37516 LatexCommand bibitem
37522 \begin_inset CommandInset href
37525 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37529 of LaTeX's math abilities
37532 \begin_layout Bibliography
37533 \labelwidthstring References
37534 \begin_inset CommandInset bibitem
37535 LatexCommand bibitem
37541 \begin_inset CommandInset href
37544 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37552 \begin_layout Plain Layout
37564 \begin_layout Bibliography
37565 \labelwidthstring References
37566 \begin_inset CommandInset bibitem
37567 LatexCommand bibitem
37573 \begin_inset CommandInset href
37576 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37580 of all symbols available with LaTeX-packages
37583 \begin_layout Bibliography
37584 \labelwidthstring References
37585 \begin_inset CommandInset bibitem
37586 LatexCommand bibitem
37592 \begin_inset CommandInset href
37594 name "Documentation"
37595 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37599 of the LaTeX-package
37604 \begin_inset Index idx
37607 \begin_layout Plain Layout
37608 Packages ! hyperref
37616 \begin_layout Bibliography
37617 \labelwidthstring References
37618 \begin_inset CommandInset bibitem
37619 LatexCommand bibitem
37625 \begin_inset CommandInset href
37627 name "Documentation"
37628 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37632 of the LaTeX-package
37637 \begin_inset Index idx
37640 \begin_layout Plain Layout
37649 \begin_layout Bibliography
37650 \labelwidthstring References
37651 \begin_inset CommandInset bibitem
37652 LatexCommand bibitem
37658 \begin_inset CommandInset href
37661 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
37672 \begin_inset CommandInset ref
37674 reference "sub:Operator-Limits"
37679 \begin_inset Index idx
37682 \begin_layout Plain Layout
37693 \begin_layout Bibliography
37694 \labelwidthstring References
37695 \begin_inset CommandInset bibitem
37696 LatexCommand bibitem
37707 Auflage, Duden 2001
37710 \begin_layout Bibliography
37711 \labelwidthstring References
37712 \begin_inset CommandInset bibitem
37713 LatexCommand bibitem
37719 \begin_inset CommandInset href
37722 target "http://physics.nist.gov/Document/checklist.pdf"
37726 for reviewing manuscripts
37729 \begin_layout Standard
37730 \begin_inset CommandInset index_print
37731 LatexCommand printindex