1 #LyX 2.0.0svn created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % Folgendes Problem lösen:
27 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
28 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
29 % die Kapitelnummer geschrieben.
30 % Als Lösung wird mehr Platz zwischen Nummer und
31 % Überschrift eingefügt.
32 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
33 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
35 % To be able to enter the character ° and · directly in LyX,
37 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
38 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
40 % increase link area for cross-references and autoname them,
41 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
43 \settowidth{\abc}{\space}
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46 \renewcommand{\sectionautorefname}{sec.\negthinspace}
47 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
50 % don't load packages twice
51 % see first footnote in sec. 9.3
52 \@ifundefined{textcolor}{\usepackage{color}}{}
54 % the pages of the TOC are numbered roman
55 % and a PDF-bookmark for the TOC is added
57 \let\myTOC\tableofcontents
58 \renewcommand{\tableofcontents}{%
60 \pdfbookmark[1]{\contentsname}{}
63 \pagenumbering{arabic}}
65 % insert additional vertical space of 1.5 mm between footnotes,
67 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
69 % provides caption formatting
70 \setkomafont{captionlabel}{\bfseries}
73 \usepackage[samesize]{cancel}
75 % enables calculation of values,
78 % for multiple table row and column cells
85 % for the Fourier transformation symbol
88 % center multirows (e.g. in sec. 13.3)
89 \renewcommand{\multirowsetup}{\centering}
91 % define a color, used in sec.9.3
92 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
94 % declare operators (see sec. 10.4 and sec. 15.2)
95 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
96 \DeclareMathOperator{\sgn}{sgn}
98 \newcommand{\spce}{\textvisiblespace}
100 % example definitions for sec. 20.1
101 \newcommand{\gr}{\Longrightarrow}
102 \newcommand{\us}[1]{\underline{#1}}
103 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
104 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
105 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
107 % example macro from sec. 19.4
108 %\def\tagform@#1{\maketag@@@{|#1|}}
110 % macro from sec. 10.2
111 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
112 \def\mathclap {\mathpalette \mathclapinternal}
113 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
115 % redefine the greyed out note
116 \renewenvironment{lyxgreyedout}
117 {\textcolor{blue}\bgroup}{\egroup}
119 % ------------------------------------
120 % used to check for needed LaTeX packages
123 % check for package eurosym
124 % used for the Euro symbol
126 \IfFileExists{eurosym.sty}
127 {\usepackage[gennarrow]{eurosym}
128 \setboolean{eurosym}{true}}
129 {\setboolean{eurosym}{false}}
131 % check for package braket
132 % used for physical vectors
134 \IfFileExists{braket.sty}
136 \setboolean{braket}{true}}
137 {\setboolean{braket}{false}}
139 % check for package cancel
141 \IfFileExists{cancel.sty}
143 \setboolean{cancel}{true}}
144 {\setboolean{cancel}{false}}
146 % check for package upgreek
148 \IfFileExists{upgreek.sty}
149 {\usepackage{upgreek}
150 \setboolean{upgreek}{true}}
151 {\setboolean{upgreek}{false}}
153 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
154 \use_default_options false
155 \maintain_unincluded_children false
161 \font_typewriter default
162 \font_default_family default
170 \default_output_format default
172 \bibtex_command default
173 \index_command default
177 \pdf_title "LyX's Math Manual"
178 \pdf_author "LyX Team, Uwe Stöhr"
179 \pdf_subject "LyX-documentation about math"
180 \pdf_keywords "LyX, Mathed"
182 \pdf_bookmarksnumbered true
183 \pdf_bookmarksopen true
184 \pdf_bookmarksopenlevel 1
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200 \paperorientation portrait
208 \paragraph_separation skip
210 \quotes_language english
213 \paperpagestyle plain
217 \tracking_changes false
218 \output_changes false
220 \html_be_strict false
226 LyX's detailed Math manual
234 \begin_layout Plain Layout
236 If you have comments or error corrections, please send them to the LyX Documenta
240 \begin_inset CommandInset href
242 name "lyx-docs@lists.lyx.org"
243 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
254 \begin_inset Note Note
257 \begin_layout Plain Layout
264 \begin_inset Newline newline
268 \begin_inset Newline newline
276 \begin_layout Standard
277 \begin_inset CommandInset toc
278 LatexCommand tableofcontents
285 \begin_layout Standard
286 \begin_inset Note Note
289 \begin_layout Plain Layout
290 To export this document to PDF, PS or DVI the LaTeX-packages
292 braket, cancel, eurosym,
303 If they are not installed the document can be export anyway but the sections
304 where the packages are required will not appear in the output.
309 ; if it is not installed, this file cannot be exported.
312 \begin_layout Plain Layout
313 The latest PDF-version of this document can be found here:
314 \begin_inset Newline newline
319 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
327 \begin_layout Standard
328 \begin_inset Newpage newpage
334 \begin_layout Section
338 \begin_layout Standard
339 This document explains LyX's math features and is furthermore a collection
340 of LaTeX-commands used for mathematical characters and constructs.
341 The explanations are designed for the usage of commands.
342 It is therefore required that you have read the section
353 \begin_layout Standard
354 Most of the characters and many constructs explained in this manual are
355 also accessible via the menu
359 \SpecialChar \menuseparator
375 But everybody who has to write lots of formulas will notice that it is
376 much faster to use commands instead of the math toolbar.
377 Therefore this manual is focused on commands but also mentions the correspondin
378 g toolbar buttons when available.
381 \begin_layout Standard
382 If not specially mentioned the commands are only available within formulas.
383 To be able to use all commands explained in this document, the option
387 must be used in the document settings (menu
389 Document\SpecialChar \menuseparator
390 Settings\SpecialChar \menuseparator
401 \begin_layout Plain Layout
404 Use AMS math package automatically
410 \begin_layout Plain Layout
419 -math when math constructs are found that are supported by LyX.
427 \begin_layout Standard
428 This document doesn't list all
432 \begin_layout Plain Layout
445 \begin_layout Plain Layout
450 \begin_layout Plain Layout
459 -math commands is in the file
462 \begin_inset CommandInset href
465 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
471 , which is part of every LaTeX standard installation.
476 for lucidity reasons.
479 \begin_layout Section
483 \begin_layout Standard
484 To create an inline formula
485 \begin_inset Index idx
488 \begin_layout Plain Layout
494 that is embedded into a text line, use one of the shortcuts
500 or the toolbar button
501 \begin_inset Graphics
502 filename ../images/math-mode.png
508 \begin_inset Newline newline
511 To create a display style formula
512 \begin_inset Index idx
515 \begin_layout Plain Layout
516 Formula ! display style
521 that will appear bigger and in an own paragraph, use one of these shortcuts:
531 \begin_layout Standard
532 To change a display style formula to an inline formula, set the cursor into
533 the formula and use one of the shortcuts
541 Edit\SpecialChar \menuseparator
542 Math\SpecialChar \menuseparator
546 The same way is used to change an inline formula to a display style formula.
549 \begin_layout Standard
550 To display parts of an inline formula in the size of a display style formula,
558 \begin_inset Index idx
561 \begin_layout Plain Layout
570 Then a new blue box appears in which the desired formula part is inserted.
573 \begin_layout Standard
574 Only inline formulas are allowed inside tables.
577 \begin_layout Standard
582 can be turned on in the menu
584 View\SpecialChar \menuseparator
588 When you click there on
589 \begin_inset Quotes eld
593 \begin_inset Quotes erd
596 the toolbar will be shown permanently at the bottom; this state is visualized
601 menu with a checkmark.
602 When you click in this state again on
603 \begin_inset Quotes eld
607 \begin_inset Quotes erd
618 is only shown when the cursor is within a formula; this state is visualized
619 by the renaming of the menu entry from
620 \begin_inset Quotes eld
624 \begin_inset Quotes erd
628 \begin_inset Quotes eld
636 \begin_inset Quotes erd
642 \begin_layout Standard
644 \begin_inset Index idx
647 \begin_layout Plain Layout
653 is invoked by pressing the toolbar button
654 \begin_inset Graphics
655 filename ../images/ert-insert.png
662 Insert\SpecialChar \menuseparator
667 \begin_layout Plain Layout
683 \begin_inset Note Note
686 \begin_layout Plain Layout
687 In LyX there are three
688 \begin_inset Quotes eld
692 \begin_inset Quotes erd
695 that appear in the output with sub- and superscript letters: TeX, LaTeX
699 \begin_layout Plain Layout
700 To avoid that these names are recognized as proper names, a TeX-brace pair
709 \begin_layout Standard
710 To change the LaTeX-preamble
711 \begin_inset Index idx
714 \begin_layout Plain Layout
722 Document\SpecialChar \menuseparator
723 Settings\SpecialChar \menuseparator
728 \begin_layout Plain Layout
744 \begin_layout Standard
745 To edit matrices, case differentiations and multiline formulas subsequently,
748 Edit\SpecialChar \menuseparator
753 Edit\SpecialChar \menuseparator
755 \begin_inset space \thinspace{}
759 \begin_inset space \thinspace{}
769 When lines and columns are swapped via the menu, the column or line where
770 the cursor is in is exchanged with the column to the right or the line
772 Is the cursor in the last column or row, the exchange is done with the
773 column to the left or the line above.
776 \begin_layout Standard
777 To write text in formulas
781 \begin_layout Plain Layout
782 For multiline formulas the command
789 \begin_inset CommandInset ref
791 reference "sub:Text-in-multiline"
805 \begin_inset Index idx
808 \begin_layout Plain Layout
815 \begin_inset Index idx
818 \begin_layout Plain Layout
825 This mode is invoked with the shortcut
831 or by the insertion of the command
838 \begin_inset Index idx
841 \begin_layout Plain Layout
850 The text appears black in LyX and can therefore be distinguished from the
851 other formula parts that appear blue.
852 In the output mathematical text is set upright, in contrary to other formula
856 \begin_layout Subsection*
860 \begin_layout Standard
861 Most of the LaTeX-commands for math constructs have the following scheme:
864 \begin_layout Standard
880 \begin_layout Standard
881 A command starts always with a backslash
882 \begin_inset Quotes gld
892 \begin_inset Quotes grd
896 To omit optional arguments, also omit the associated brackets.
897 The braces around the required arguments are named in this document as
899 \begin_inset Index idx
902 \begin_layout Plain Layout
909 If you add in a formula a left brace to a command name, LyX creates automatical
911 In all other cases TeX-braces are created in formulas with the command
919 TeX-braces appear red in LyX, in contrary to normal braces that appear
921 In TeX-mode no command is needed to get TeX-braces.
922 TeX-braces don't appear in the output.
925 \begin_layout Standard
926 When commands without arguments, like commands for symbols are entered in
927 TeX-mode, a space character must
931 be behind the command to end it.
932 This space doesn't appear in the output.
933 When the space should appear in the output, the space must be followed
934 by a protected space in normal text.
937 \begin_layout Standard
938 A protected space is inserted with
941 arg "space-insert protected"
947 \begin_layout Subsection*
948 \begin_inset Newpage newpage
954 \begin_layout Itemize
959 \begin_layout Plain Layout
960 This visible space character can be created with the command
967 \begin_inset Index idx
970 \begin_layout Plain Layout
978 , inserted in TeX-mode.
987 \begin_layout Plain Layout
1000 denotes a space character to be input.
1003 \begin_layout Itemize
1005 \begin_inset Formula $\to$
1008 denotes the usage of the corresponding arrow key on the keyboard.
1011 \begin_layout Subsection*
1015 \begin_layout Standard
1017 \begin_inset Float table
1023 \begin_layout Plain Layout
1025 \begin_inset Caption
1027 \begin_layout Plain Layout
1028 \begin_inset CommandInset label
1030 name "tab:Available-units"
1042 \begin_layout Plain Layout
1044 \begin_inset Tabular
1045 <lyxtabular version="3" rows="13" columns="2">
1046 <features tabularvalignment="middle">
1047 <column alignment="center" valignment="top" width="0">
1048 <column alignment="center" valignment="top" width="0">
1050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1053 \begin_layout Plain Layout
1059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1062 \begin_layout Plain Layout
1070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1073 \begin_layout Plain Layout
1079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1082 \begin_layout Plain Layout
1090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1093 \begin_layout Plain Layout
1099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1102 \begin_layout Plain Layout
1110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1113 \begin_layout Plain Layout
1119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1122 \begin_layout Plain Layout
1124 \begin_inset space \thinspace{}
1128 \begin_inset space \thinspace{}
1138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1141 \begin_layout Plain Layout
1147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1150 \begin_layout Plain Layout
1152 \begin_inset space \thinspace{}
1156 \begin_inset space \thinspace{}
1166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1169 \begin_layout Plain Layout
1175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1178 \begin_layout Plain Layout
1180 \begin_inset space \thinspace{}
1184 \begin_inset space \thinspace{}
1194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1197 \begin_layout Plain Layout
1203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1206 \begin_layout Plain Layout
1208 \begin_inset space \thinspace{}
1212 \begin_inset space \thinspace{}
1222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1225 \begin_layout Plain Layout
1231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1234 \begin_layout Plain Layout
1236 \begin_inset space \thinspace{}
1240 \begin_inset space \thinspace{}
1250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1253 \begin_layout Plain Layout
1259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1262 \begin_layout Plain Layout
1264 \begin_inset space \thinspace{}
1268 \begin_inset Formula $\approx$
1272 \begin_inset space \thinspace{}
1282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1285 \begin_layout Plain Layout
1291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1294 \begin_layout Plain Layout
1296 \begin_inset space \thinspace{}
1300 \begin_inset space \thinspace{}
1310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1313 \begin_layout Plain Layout
1319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1322 \begin_layout Plain Layout
1326 \begin_inset Quotes eld
1332 \begin_inset Quotes erd
1342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1345 \begin_layout Plain Layout
1351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1354 \begin_layout Plain Layout
1356 \begin_inset Quotes eld
1364 \begin_inset Quotes erd
1374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1377 \begin_layout Plain Layout
1383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1386 \begin_layout Plain Layout
1388 \begin_inset space \thinspace{}
1392 \begin_inset Formula $\nicefrac{1}{18}$
1396 \begin_inset space \thinspace{}
1417 \begin_layout Standard
1418 \begin_inset Newpage newpage
1424 \begin_layout Section
1428 \begin_layout Subsection
1430 \begin_inset Index idx
1433 \begin_layout Plain Layout
1440 \begin_inset Index idx
1443 \begin_layout Plain Layout
1450 \begin_inset Index idx
1453 \begin_layout Plain Layout
1458 \begin_layout Plain Layout
1469 \begin_layout Plain Layout
1482 \begin_inset Index idx
1485 \begin_layout Plain Layout
1490 \begin_layout Plain Layout
1501 \begin_layout Plain Layout
1516 \begin_layout Standard
1517 Indices are created with an underscore
1518 \begin_inset Quotes eld
1522 \begin_inset Quotes erd
1525 or via the math toolbar button
1526 \begin_inset Graphics
1527 filename ../images/math-subscript.png
1532 , exponents with a caret
1533 \begin_inset Quotes eld
1537 \begin_inset Quotes erd
1540 or via the math toolbar button
1541 \begin_inset Graphics
1542 filename ../images/math-superscript.png
1550 \begin_layout Standard
1552 \begin_inset Tabular
1553 <lyxtabular version="3" rows="4" columns="2">
1554 <features tabularvalignment="middle">
1555 <column alignment="center" valignment="top" width="0pt">
1556 <column alignment="center" valignment="top" width="0pt">
1558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1561 \begin_layout Plain Layout
1567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1570 \begin_layout Plain Layout
1572 \begin_inset Note Note
1575 \begin_layout Plain Layout
1582 is only used as spacer.
1594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1597 \begin_layout Plain Layout
1603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1606 \begin_layout Plain Layout
1607 \begin_inset Formula $B_{V}$
1617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1620 \begin_layout Plain Layout
1626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1629 \begin_layout Plain Layout
1630 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1643 \begin_layout Plain Layout
1648 \begin_layout Plain Layout
1662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1665 \begin_layout Plain Layout
1666 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1682 \begin_layout Standard
1683 As the caret is in some languages an accent, vowels will be accentuated
1684 in this case and not set as exponents
1688 \begin_layout Plain Layout
1689 Depending on the used keyboard settings this can also happen for other character
1696 To get in this case exponents, press
1700 after the caret as in the last example.
1703 \begin_layout Subsection
1705 \begin_inset CommandInset label
1707 name "sub:Fractions"
1712 \begin_inset Index idx
1715 \begin_layout Plain Layout
1724 \begin_layout Standard
1725 Fractions are generated with the command
1732 \begin_inset Index idx
1735 \begin_layout Plain Layout
1743 or via the math toolbar button
1744 \begin_inset Graphics
1745 filename ../images/math/frac.png
1751 The font size is adjusted automatically, depending on whether the fraction
1752 is in an inline or display style formula.
1753 With the math toolbar button
1754 \begin_inset Graphics
1755 filename ../images/math/frac-square.png
1760 you can select different fraction types.
1763 \begin_layout Standard
1771 \begin_inset Index idx
1774 \begin_layout Plain Layout
1782 a fraction can be created that has in any case the size of a display style
1791 \begin_inset Index idx
1794 \begin_layout Plain Layout
1802 the fraction appears always with the size of an inline formula.
1806 \begin_layout Standard
1807 A line with the fraction
1808 \begin_inset Formula $\frac{1}{2}$
1811 that was created with the command
1820 \begin_layout Standard
1821 A line with the fraction
1822 \begin_inset Formula $\dfrac{1}{2}$
1825 that was created with the command
1834 \begin_layout Standard
1836 \begin_inset Tabular
1837 <lyxtabular version="3" rows="4" columns="2">
1838 <features tabularvalignment="middle">
1839 <column alignment="center" valignment="top" width="0pt">
1840 <column alignment="center" valignment="top" width="0pt">
1842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1845 \begin_layout Plain Layout
1851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1854 \begin_layout Plain Layout
1856 \begin_inset Note Note
1859 \begin_layout Plain Layout
1866 is only used as spacer.
1878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1881 \begin_layout Plain Layout
1888 \begin_layout Plain Layout
1898 \begin_inset Formula $\downarrow$
1906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1909 \begin_layout Plain Layout
1910 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1923 \begin_layout Plain Layout
1930 \begin_layout Plain Layout
1940 \begin_inset Formula $\downarrow$
1948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1951 \begin_layout Plain Layout
1952 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1965 \begin_layout Plain Layout
1972 \begin_layout Plain Layout
1985 \begin_layout Plain Layout
2000 \begin_layout Plain Layout
2010 \begin_inset Formula $\downarrow$
2014 \begin_inset Formula $\downarrow\downarrow$
2022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2025 \begin_layout Plain Layout
2026 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2042 \begin_layout Standard
2043 \begin_inset VSpace bigskip
2047 \begin_inset Newpage newpage
2050 For nested fractions the command
2057 \begin_inset Index idx
2060 \begin_layout Plain Layout
2070 \begin_inset VSpace -3mm
2076 \begin_layout Standard
2077 \begin_inset Formula \begin{align*}
2078 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2079 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2087 \begin_layout Standard
2088 The command for the example above is:
2091 \begin_layout Standard
2100 \begin_layout Plain Layout
2110 \begin_inset Formula $\downarrow$
2119 \begin_layout Plain Layout
2134 \begin_layout Plain Layout
2144 \begin_inset Formula $\downarrow$
2148 \begin_inset Formula $\downarrow$
2154 \begin_layout Standard
2155 \begin_inset VSpace medskip
2161 \begin_layout Standard
2168 sets the fraction always in the size of a displayed formula, also when
2169 it is part of another fraction.
2172 \begin_layout Standard
2173 It is possible to specify the alignment of the numerator.
2180 is used to left align it, the command
2193 centers the numerator.
2194 These fractions demonstrate the different alignments:
2197 \begin_layout Standard
2198 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2202 \begin_inset Formula $\cfrac{A}{B+C}$
2206 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2212 \begin_layout Standard
2213 \begin_inset Note Greyedout
2216 \begin_layout Plain Layout
2233 are no real LaTeX commands but represent the command
2237 cfrac[alignment]{numerator}{denominator}
2240 Therefore you cannot use them in TeX code.
2248 \begin_layout Standard
2249 \begin_inset VSpace medskip
2252 It is often advantageous to combine
2265 \begin_inset Formula \[
2266 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2273 \begin_layout Standard
2274 For inline fractions with a sloped fraction stroke you can use the command
2282 \begin_inset Index idx
2285 \begin_layout Plain Layout
2294 \begin_inset Formula $\nicefrac{5}{31}$
2304 \begin_inset Index idx
2307 \begin_layout Plain Layout
2316 \begin_inset Formula $\unitfrac{5}{31}$
2319 There is furthermore the command
2325 that offers to write a fraction in combination with a number:
2326 \begin_inset Formula $\unitfrac[2]{1}{3}$
2332 \begin_layout Standard
2333 \begin_inset Note Greyedout
2336 \begin_layout Plain Layout
2347 is not a real LaTeX command but the command
2348 \begin_inset Newline newline
2355 unitfrac[number]{numerator}{denominator}
2358 Therefore you cannot use it in TeX code.
2366 \begin_layout Standard
2367 How to define own fractions where the fraction stroke can be changed, is
2369 \begin_inset CommandInset ref
2371 reference "sub:Self-defined-Fractions"
2378 \begin_layout Subsection
2380 \begin_inset Index idx
2383 \begin_layout Plain Layout
2392 \begin_layout Standard
2393 Square roots are created with
2400 \begin_inset Index idx
2403 \begin_layout Plain Layout
2411 or the math toolbar button
2412 \begin_inset Graphics
2413 filename ../images/math/sqrt.png
2418 , all other roots with the command
2425 \begin_inset Index idx
2428 \begin_layout Plain Layout
2436 or with the math toolbar button
2437 \begin_inset Graphics
2438 filename ../images/math/root.png
2446 \begin_layout Standard
2448 \begin_inset Tabular
2449 <lyxtabular version="3" rows="3" columns="2">
2450 <features tabularvalignment="middle">
2451 <column alignment="center" valignment="top" width="0pt">
2452 <column alignment="center" valignment="top" width="0pt">
2454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2457 \begin_layout Plain Layout
2463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2466 \begin_layout Plain Layout
2468 \begin_inset Note Note
2471 \begin_layout Plain Layout
2478 is only used as spacer.
2490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2493 \begin_layout Plain Layout
2500 \begin_layout Plain Layout
2514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2517 \begin_layout Plain Layout
2518 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2531 \begin_layout Plain Layout
2538 \begin_layout Plain Layout
2548 \begin_inset Formula $\downarrow$
2556 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2559 \begin_layout Plain Layout
2560 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2576 \begin_layout Standard
2577 A square root can also be created with
2583 when the root index field is left empty.
2586 \begin_layout Standard
2587 With certain indices the distance to the root is too small, like in this
2589 \begin_inset Formula $\sqrt[\beta]{B}$
2593 \begin_inset Newline newline
2597 \begin_inset Formula $\beta$
2601 To avoid this, the commands
2608 \begin_inset Index idx
2611 \begin_layout Plain Layout
2626 \begin_inset Index idx
2629 \begin_layout Plain Layout
2637 are used with the following scheme:
2640 \begin_layout Standard
2654 \begin_layout Standard
2655 Distance is the number of Big Points (unit bp;
2656 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2659 ), that the index should be moved to the left or top, resp..
2660 The commands are written to the index.
2661 This way the command
2662 \begin_inset Newline newline
2672 \begin_inset Formula $\to$
2678 \begin_inset Formula $\to$
2687 \begin_layout Plain Layout
2697 \begin_inset Formula $\to$
2701 \begin_inset Newline newline
2706 produces a correct typeset formula:
2707 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2713 \begin_layout Subsection
2714 Binomial Coefficients
2715 \begin_inset Index idx
2718 \begin_layout Plain Layout
2719 Binomial coefficients
2727 \begin_layout Standard
2728 Binomial coefficients are inserted with the command
2735 \begin_inset Index idx
2738 \begin_layout Plain Layout
2746 or with the submenu of the math toolbar button
2747 \begin_inset Graphics
2748 filename ../images/math/frac-square.png
2754 Analog to fractions (
2773 \begin_inset Index idx
2776 \begin_layout Plain Layout
2791 \begin_inset Index idx
2794 \begin_layout Plain Layout
2803 For other brackets around binomial coeficients there are the commands
2810 \begin_inset Index idx
2813 \begin_layout Plain Layout
2828 \begin_inset Index idx
2831 \begin_layout Plain Layout
2842 \begin_layout Standard
2844 \begin_inset Tabular
2845 <lyxtabular version="3" rows="6" columns="2">
2846 <features tabularvalignment="middle">
2847 <column alignment="center" valignment="top" width="0pt">
2848 <column alignment="center" valignment="top" width="0pt">
2850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2853 \begin_layout Plain Layout
2859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2862 \begin_layout Plain Layout
2864 \begin_inset Note Note
2867 \begin_layout Plain Layout
2874 is only used as spacer.
2886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2889 \begin_layout Plain Layout
2896 \begin_layout Plain Layout
2906 \begin_inset Formula $\downarrow$
2914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2917 \begin_layout Plain Layout
2918 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2931 \begin_layout Plain Layout
2938 \begin_layout Plain Layout
2948 \begin_inset Formula $\downarrow$
2956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2959 \begin_layout Plain Layout
2960 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2973 \begin_layout Plain Layout
2980 \begin_layout Plain Layout
2990 \begin_inset Formula $\downarrow$
2998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3001 \begin_layout Plain Layout
3002 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3015 \begin_layout Plain Layout
3022 \begin_layout Plain Layout
3032 \begin_inset Formula $\downarrow$
3040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3043 \begin_layout Plain Layout
3044 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3057 \begin_layout Plain Layout
3064 \begin_layout Plain Layout
3074 \begin_inset Formula $\downarrow$
3082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3085 \begin_layout Plain Layout
3086 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3102 \begin_layout Subsection
3103 Case Differentiations
3104 \begin_inset Index idx
3107 \begin_layout Plain Layout
3108 Case differentiations
3116 \begin_layout Standard
3118 \begin_inset Tabular
3119 <lyxtabular version="3" rows="3" columns="2">
3120 <features tabularvalignment="middle">
3121 <column alignment="center" valignment="top" width="0pt">
3122 <column alignment="center" valignment="top" width="0pt">
3124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3127 \begin_layout Plain Layout
3133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3136 \begin_layout Plain Layout
3144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3147 \begin_layout Plain Layout
3154 \begin_layout Plain Layout
3164 \begin_inset Formula $\to$
3168 \begin_inset Index idx
3171 \begin_layout Plain Layout
3184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3187 \begin_layout Plain Layout
3188 \begin_inset Formula $\begin{cases}
3199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3202 \begin_layout Plain Layout
3209 \begin_layout Plain Layout
3221 arg "newline-insert newline"
3229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3232 \begin_layout Plain Layout
3233 \begin_inset Formula $\begin{cases}
3234 A & \textrm{for }x>0\\
3235 B & \textrm{for }x=0
3252 \begin_layout Standard
3259 or the usage of the math toolbar button
3260 \begin_inset Graphics
3261 filename ../images/math/cases.png
3266 you can create new lines with the shortcut
3269 arg "newline-insert newline"
3272 or the table toolbar button
3273 \begin_inset Graphics
3274 filename ../images/tabular-feature_append-row.png
3282 \begin_layout Standard
3289 is also available via the menu
3291 Insert\SpecialChar \menuseparator
3292 Math\SpecialChar \menuseparator
3298 \begin_layout Subsection
3300 \begin_inset Index idx
3303 \begin_layout Plain Layout
3312 \begin_layout Standard
3320 \begin_inset Index idx
3323 \begin_layout Plain Layout
3331 every character can be displayed canceled.
3332 The characters are quasi accentuated by a slash.
3335 \begin_layout Standard
3337 \begin_inset Tabular
3338 <lyxtabular version="3" rows="4" columns="2">
3339 <features tabularvalignment="middle">
3340 <column alignment="center" valignment="top" width="0pt">
3341 <column alignment="center" valignment="top" width="0pt">
3343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3346 \begin_layout Plain Layout
3352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3355 \begin_layout Plain Layout
3363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3366 \begin_layout Plain Layout
3374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3377 \begin_layout Plain Layout
3378 \begin_inset Formula $\not=$
3388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3391 \begin_layout Plain Layout
3401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3404 \begin_layout Plain Layout
3405 \begin_inset Formula $\not\le$
3415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3418 \begin_layout Plain Layout
3428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3431 \begin_layout Plain Layout
3432 \begin_inset Formula $\not\parallel$
3448 \begin_layout Standard
3449 The last example shows, that not all negations look good.
3450 Therefore there are for some negations special commands (see
3451 \begin_inset CommandInset ref
3453 reference "sub:Mathematical-Symbols"
3458 \begin_inset CommandInset ref
3460 reference "sec:Relations"
3467 \begin_layout Subsection
3469 \begin_inset CommandInset label
3471 name "sub:Placeholders"
3476 \begin_inset Index idx
3479 \begin_layout Plain Layout
3486 \begin_inset Index idx
3489 \begin_layout Plain Layout
3490 Chemical characters ! Isotopes
3496 \begin_inset Index idx
3499 \begin_layout Plain Layout
3504 \begin_layout Plain Layout
3515 \begin_layout Plain Layout
3530 \begin_layout Standard
3532 \begin_inset space \thinspace{}
3536 \begin_inset space \space{}
3543 \begin_layout Plain Layout
3544 Typesetting isotopes and chemical symbols is described in
3545 \begin_inset CommandInset ref
3547 reference "sub:Chemical-Symbols-and"
3556 the following problem occurs:
3559 \begin_layout Standard
3561 \begin_inset Tabular
3562 <lyxtabular version="3" rows="2" columns="2">
3563 <features tabularvalignment="middle">
3564 <column alignment="center" valignment="top" width="0pt">
3565 <column alignment="center" valignment="top" width="0pt">
3567 <cell alignment="center" valignment="top" usebox="none">
3570 \begin_layout Plain Layout
3571 Indices created with sub- and superscripts:
3576 <cell alignment="center" valignment="top" usebox="none">
3579 \begin_layout Plain Layout
3580 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3590 <cell alignment="center" valignment="top" usebox="none">
3593 \begin_layout Plain Layout
3599 <cell alignment="center" valignment="top" usebox="none">
3602 \begin_layout Plain Layout
3603 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3617 \begin_inset Note Note
3620 \begin_layout Plain Layout
3627 is only used as spacer.
3635 \begin_layout Standard
3636 The shorter index is by default placed below or above the first character
3637 of the longer index.
3638 To avoid this there is the command
3645 \begin_inset Index idx
3648 \begin_layout Plain Layout
3656 or the math toolbar button
3657 \begin_inset space \thinspace{}
3664 \begin_layout Plain Layout
3665 can be found in the submenu of the toolbar button
3666 \begin_inset Graphics
3667 filename ../images/math/space.png
3678 \begin_inset Graphics
3679 filename ../images/math/phantom.png
3684 that creates one or more phantom characters.
3691 a small blue box appears that is superposed with two red arrows.
3692 The arrows indicate that the complete width and height of the box content
3693 will be created as placeholder.
3694 Phantom characters are accordingly placeholders with the size of the characters.
3697 \begin_layout Standard
3699 \begin_inset Tabular
3700 <lyxtabular version="3" rows="4" columns="2">
3701 <features tabularvalignment="middle">
3702 <column alignment="center" valignment="top" width="0">
3703 <column alignment="center" valignment="top" width="0">
3705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3708 \begin_layout Plain Layout
3714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3717 \begin_layout Plain Layout
3719 \begin_inset Note Note
3722 \begin_layout Plain Layout
3729 is only used as spacer.
3741 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3744 \begin_layout Plain Layout
3749 \begin_layout Plain Layout
3764 \begin_layout Plain Layout
3774 \begin_inset Formula $\to$
3781 \begin_layout Plain Layout
3795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3798 \begin_layout Plain Layout
3799 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3812 \begin_layout Plain Layout
3817 \begin_layout Plain Layout
3832 \begin_layout Plain Layout
3842 \begin_inset Formula $\to$
3849 \begin_layout Plain Layout
3863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3866 \begin_layout Plain Layout
3867 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3880 \begin_layout Plain Layout
3887 \begin_layout Plain Layout
3902 \begin_layout Plain Layout
3912 \begin_inset Formula $\to$
3919 \begin_layout Plain Layout
3933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3936 \begin_layout Plain Layout
3937 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3953 \begin_layout Standard
3954 Furthermore there are the commands
3961 \begin_inset Index idx
3964 \begin_layout Plain Layout
3973 \begin_inset space ~
3977 \begin_inset Graphics
3978 filename ../images/math/vphantom.png
3990 \begin_inset Index idx
3993 \begin_layout Plain Layout
4002 \begin_inset space ~
4006 \begin_inset Graphics
4007 filename ../images/math/hphantom.png
4019 creates only space for the maximal height of the characters in the box
4020 but not for its width.
4027 creates only space for the width of the box content.
4028 Therefore the boxes of both commands have only one red arrow.
4031 \begin_layout Standard
4042 \begin_layout Plain Layout
4057 space for the height of the integral sign,
4061 \begin_layout Plain Layout
4068 creates an integral sign, see
4069 \begin_inset CommandInset ref
4071 reference "sub:Big-Operators"
4080 because this is the larger character.
4081 An example application is in
4082 \begin_inset CommandInset ref
4084 reference "sub:Multiline-Brackets"
4091 \begin_layout Standard
4092 Placeholders can also be used for text when it is inserted via the menu
4095 Insert\SpecialChar \menuseparator
4096 Formatting\SpecialChar \menuseparator
4102 \begin_layout Standard
4104 \begin_inset Newline newline
4108 \begin_inset Phantom Phantom
4111 \begin_layout Plain Layout
4120 \begin_layout Subsection
4122 \begin_inset Index idx
4125 \begin_layout Plain Layout
4132 \begin_inset Index idx
4135 \begin_layout Plain Layout
4136 Formula ! underlined
4144 \begin_layout Standard
4146 \begin_inset Tabular
4147 <lyxtabular version="3" rows="4" columns="2">
4148 <features tabularvalignment="middle">
4149 <column alignment="center" valignment="top" width="0pt">
4150 <column alignment="center" valignment="top" width="0pt">
4152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4155 \begin_layout Plain Layout
4161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4164 \begin_layout Plain Layout
4166 \begin_inset Note Note
4169 \begin_layout Plain Layout
4176 is only used as spacer.
4188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4191 \begin_layout Plain Layout
4198 \begin_layout Plain Layout
4208 \begin_inset Index idx
4211 \begin_layout Plain Layout
4224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4227 \begin_layout Plain Layout
4228 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4238 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4241 \begin_layout Plain Layout
4248 \begin_layout Plain Layout
4258 \begin_inset Index idx
4261 \begin_layout Plain Layout
4274 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4277 \begin_layout Plain Layout
4278 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4291 \begin_layout Plain Layout
4298 \begin_layout Plain Layout
4313 \begin_layout Plain Layout
4327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4330 \begin_layout Plain Layout
4331 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4347 \begin_layout Standard
4348 In the last example it doesn't matter if first
4363 \begin_layout Standard
4364 To double underline e.
4365 \begin_inset space \thinspace{}
4369 \begin_inset space \space{}
4381 \begin_layout Standard
4382 It is possible to place up to 6 lines above or below characters.
4385 \begin_layout Standard
4386 \begin_inset VSpace bigskip
4389 Custom lines can be created using the command
4396 \begin_inset Index idx
4399 \begin_layout Plain Layout
4407 which has the following scheme:
4410 \begin_layout Standard
4415 rule[vertical offset]{length}{thickness}
4418 \begin_layout Standard
4419 The optional vertical offset shifts the line upwards (or downwards, when
4420 the value is negative).
4422 \begin_inset CommandInset ref
4424 reference "tab:Available-units"
4428 can be used for the values.
4429 Here are two example lines created with the commands
4430 \begin_inset Newline newline
4437 rule[-2ex]{3cm}{2pt}
4448 \begin_layout Standard
4450 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4456 \begin_layout Standard
4463 can also be used for text when a line is inserted via the menu
4465 Insert\SpecialChar \menuseparator
4466 Formatting\SpecialChar \menuseparator
4468 \begin_inset space ~
4476 \begin_layout Standard
4478 \begin_inset CommandInset line
4489 \begin_layout Subsection
4491 \begin_inset CommandInset label
4498 \begin_inset Index idx
4501 \begin_layout Plain Layout
4510 \begin_layout Standard
4511 There are different types of ellipses available.
4515 \begin_layout Plain Layout
4516 In the math toolbar in the submenu of the button
4517 \begin_inset Graphics
4518 filename ../images/math/ldots.png
4528 For listings dots at the baseline are used (
4535 \begin_inset Index idx
4538 \begin_layout Plain Layout
4546 ), while for operations dots are needed that are on the same height as the
4554 \begin_inset Index idx
4557 \begin_layout Plain Layout
4566 When using the command
4573 \begin_inset Index idx
4576 \begin_layout Plain Layout
4584 , LaTeX decides on the basis of the next character what type is used.
4587 \begin_layout Standard
4589 \begin_inset Tabular
4590 <lyxtabular version="3" rows="8" columns="2">
4591 <features tabularvalignment="middle">
4592 <column alignment="center" valignment="top" width="0pt">
4593 <column alignment="center" valignment="top" width="0pt">
4595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4598 \begin_layout Plain Layout
4604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4607 \begin_layout Plain Layout
4615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4618 \begin_layout Plain Layout
4623 \begin_layout Plain Layout
4638 \begin_layout Plain Layout
4652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4655 \begin_layout Plain Layout
4656 \begin_inset Formula $A_{1},\dots,A_{n}$
4666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4669 \begin_layout Plain Layout
4674 \begin_layout Plain Layout
4689 \begin_layout Plain Layout
4703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4706 \begin_layout Plain Layout
4707 \begin_inset Formula $A_{1}+\dots+A_{n}$
4717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4720 \begin_layout Plain Layout
4725 \begin_layout Plain Layout
4740 \begin_layout Plain Layout
4754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4757 \begin_layout Plain Layout
4758 \begin_inset Formula $A_{1},\ldots,A_{n}$
4768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4771 \begin_layout Plain Layout
4776 \begin_layout Plain Layout
4791 \begin_layout Plain Layout
4805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4808 \begin_layout Plain Layout
4809 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4822 \begin_layout Plain Layout
4830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4833 \begin_layout Plain Layout
4834 \begin_inset Formula $\vdots$
4844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4847 \begin_layout Plain Layout
4855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4858 \begin_layout Plain Layout
4859 \begin_inset Formula $\ddots$
4869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4872 \begin_layout Plain Layout
4874 \begin_inset space \thinspace{}
4877 matrix with the different dots
4882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4885 \begin_layout Plain Layout
4886 \begin_inset Formula $\begin{array}{ccc}
4887 A_{11} & \cdots & A_{1m}\\
4888 \vdots & \ddots & \vdots\\
4889 A_{n1} & \cdots & A_{nm}
4906 \begin_layout Standard
4907 The ellipses available in menu
4909 Insert\SpecialChar \menuseparator
4911 \begin_inset space ~
4925 \begin_layout Standard
4926 \begin_inset VSpace medskip
4929 Specially for matrices there are ellipses that span over several columns.
4930 They are created with the command
4937 \begin_inset Index idx
4940 \begin_layout Plain Layout
4948 , that has the following scheme:
4951 \begin_layout Standard
4956 hdotsfor[distance]{number of columns}
4959 \begin_layout Standard
4960 The number of columns specifies how many columns should be spanned.
4961 Distance is a factor for the distance between the dots.
4964 \begin_layout Standard
4965 In the following matrix the command
4971 was inserted in the first box of the second line, to get an ellipsis with
4972 a dot distance twice as long as with the command
4979 \begin_inset Formula \[
4980 \left(\begin{array}{cccc}
4984 \end{array}\right)\]
4988 Note that the matrix fields that should be spanned must be empty, otherwise
4989 you get LaTeX-errors.
4992 \begin_layout Standard
4993 \begin_inset VSpace bigskip
4996 Furthermore you can fill with the command
5003 \begin_inset Index idx
5006 \begin_layout Plain Layout
5014 the rest of a line with dots.
5015 The effect of these commands is the same like with
5022 \begin_inset CommandInset ref
5024 reference "sub:Variable-Space"
5031 \begin_layout Standard
5032 For example the command
5040 \begin_layout Plain Layout
5054 \begin_layout Standard
5055 \begin_inset Formula $A\dotfill B$
5061 \begin_layout Standard
5068 there is for a line the command
5075 \begin_inset Index idx
5078 \begin_layout Plain Layout
5089 \begin_layout Standard
5090 \begin_inset Formula $A\hrulefill B$
5096 \begin_layout Standard
5097 To use the commands for text, they have to be inserted in TeX-mode.
5100 \begin_layout Section
5102 \begin_inset CommandInset label
5109 \begin_inset Index idx
5112 \begin_layout Plain Layout
5121 \begin_layout Standard
5122 Matrices can be inserted via the math toolbar button
5123 \begin_inset Graphics
5124 filename ../images/dialog-show_mathmatrix.png
5131 Insert\SpecialChar \menuseparator
5132 Math\SpecialChar \menuseparator
5136 You will be asked for the number of matrix columns and rows and the alignment.
5137 The vertical alignment is hereby only of importance for matrices in inline
5141 \begin_layout Standard
5142 The first matrix is top
5143 \begin_inset Formula $\begin{array}[t]{cccc}
5151 \begin_inset Formula $\begin{array}{cccc}
5158 and the third bottom
5159 \begin_inset Formula $\begin{array}[b]{cccc}
5169 \begin_layout Standard
5170 The horizontal alignment specifies how the column entries should be aligned.
5171 It is set by entering a letter for every column.
5176 denotes left aligned,
5185 To create for example a 4
5190 \begin_inset space ~
5193 matrix where the first column is left aligned, the second and third are
5194 centered and the last one is right aligned, one enters for the horizontal
5200 Normally are in a matrix all columns centered, therefore the default is
5201 for every column is a
5208 \begin_layout Standard
5209 Horizontal alignment:
5212 \begin_layout Standard
5218 \begin_inset Formula $\begin{array}{lll}
5230 \begin_inset Formula $\begin{array}{ccc}
5242 \begin_inset Formula $\begin{array}{rrr}
5252 \begin_layout Standard
5253 To add or delete rows and columns subsequently, the math toolbar buttons
5255 \begin_inset Graphics
5256 filename ../images/tabular-feature_append-row.png
5262 \begin_inset Graphics
5263 filename ../images/tabular-feature_delete-row.png
5269 \begin_inset space \thinspace{}
5274 Edit\SpecialChar \menuseparator
5278 New rows can also be created with
5281 arg "newline-insert newline"
5287 \begin_layout Standard
5288 \begin_inset VSpace bigskip
5291 Parentheses around a matrix can can either be created with the commands
5299 \begin_inset Index idx
5302 \begin_layout Plain Layout
5317 \begin_inset Index idx
5320 \begin_layout Plain Layout
5331 \begin_inset space ~
5337 \begin_inset CommandInset ref
5339 reference "sub:Automatic-Bracket-Size"
5343 , or by using the following commands:
5344 \begin_inset VSpace medskip
5350 \begin_layout Standard
5351 \begin_inset space \hfill{}
5355 \begin_inset Tabular
5356 <lyxtabular version="3" rows="4" columns="2">
5357 <features tabularvalignment="middle">
5358 <column alignment="center" valignment="top" width="0">
5359 <column alignment="center" valignment="top" width="0">
5361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5364 \begin_layout Plain Layout
5370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5373 \begin_layout Plain Layout
5375 \begin_inset Note Note
5378 \begin_layout Plain Layout
5385 is only used as spacer.
5397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5400 \begin_layout Plain Layout
5407 \begin_layout Plain Layout
5421 \begin_inset space \thinspace{}
5429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5432 \begin_layout Plain Layout
5433 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5434 0 & \textrm{-}\mathrm{i}\\
5436 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5449 \begin_layout Plain Layout
5456 \begin_layout Plain Layout
5470 \begin_inset space \thinspace{}
5478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5481 \begin_layout Plain Layout
5482 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5483 0 & \textrm{-}\mathrm{i}\\
5485 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5498 \begin_layout Plain Layout
5505 \begin_layout Plain Layout
5519 \begin_inset space \thinspace{}
5527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5530 \begin_layout Plain Layout
5531 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5532 0 & \textrm{-}\mathrm{i}\\
5534 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5548 \begin_inset space \hfill{}
5552 \begin_inset Tabular
5553 <lyxtabular version="3" rows="4" columns="2">
5554 <features tabularvalignment="middle">
5555 <column alignment="center" valignment="top" width="0">
5556 <column alignment="center" valignment="top" width="0">
5558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5561 \begin_layout Plain Layout
5567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5570 \begin_layout Plain Layout
5578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5581 \begin_layout Plain Layout
5588 \begin_layout Plain Layout
5602 \begin_inset space \thinspace{}
5610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5613 \begin_layout Plain Layout
5614 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5615 0 & \textrm{-}\mathrm{i}\\
5617 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5630 \begin_layout Plain Layout
5637 \begin_layout Plain Layout
5651 \begin_inset space \thinspace{}
5659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5662 \begin_layout Plain Layout
5663 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5664 0 & \textrm{-}\mathrm{i}\\
5666 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5679 \begin_layout Plain Layout
5686 \begin_layout Plain Layout
5700 \begin_inset space \thinspace{}
5708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5711 \begin_layout Plain Layout
5712 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5713 0 & \textrm{-}\mathrm{i}\\
5715 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5729 \begin_inset space \hfill{}
5735 \begin_layout Standard
5736 \begin_inset VSpace medskip
5740 \begin_inset space \thinspace{}
5744 \begin_inset space \space{}
5753 is inserted, a blue box appears between two vertical lines where the matrix
5757 \begin_layout Standard
5758 \begin_inset VSpace bigskip
5761 As all multiline formulas are matrices, the length
5768 \begin_inset Index idx
5771 \begin_layout Plain Layout
5779 that is described in
5780 \begin_inset CommandInset ref
5782 reference "sub:Column-Separation"
5786 can also be used to change the column separation of matrices.
5789 \begin_layout Standard
5790 To change the row separation, the command
5797 \begin_inset Index idx
5800 \begin_layout Plain Layout
5809 It is used as follows:
5812 \begin_layout Standard
5819 arraystretch}{stretch factor}
5820 \begin_inset Index idx
5823 \begin_layout Plain Layout
5834 \begin_layout Standard
5841 assigns the stretch factor to the predefined command
5849 \begin_inset space \thinspace{}
5853 \begin_inset space \space{}
5856 the row separation, use the factor 2.
5857 This is then used for all following matrices.
5858 To go back to the original separation, assign the factor 1 to
5867 \begin_layout Standard
5868 To set matrices into a text line, the command
5875 \begin_inset Index idx
5878 \begin_layout Plain Layout
5887 When it is inserted a blue box with two dashed lines appears.
5888 In this box the matrix is inserted.
5891 \begin_layout Standard
5893 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5895 \end{smallmatrix}\right)$
5901 \begin_layout Section
5902 Brackets and Delimiters
5903 \begin_inset Index idx
5906 \begin_layout Plain Layout
5913 \begin_inset Index idx
5916 \begin_layout Plain Layout
5925 \begin_layout Subsection
5926 Vertical Brackets and Delimiters
5927 \begin_inset Index idx
5930 \begin_layout Plain Layout
5939 \begin_layout Standard
5940 \begin_inset space \hfill{}
5944 \begin_inset Tabular
5945 <lyxtabular version="3" rows="9" columns="2">
5946 <features tabularvalignment="middle">
5947 <column alignment="center" valignment="top" width="0pt">
5948 <column alignment="center" valignment="top" width="0pt">
5950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5953 \begin_layout Plain Layout
5959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5962 \begin_layout Plain Layout
5970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5973 \begin_layout Plain Layout
5979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5982 \begin_layout Plain Layout
5983 \begin_inset Formula $($
5993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5996 \begin_layout Plain Layout
6002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6005 \begin_layout Plain Layout
6006 \begin_inset Formula $\{$
6016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6019 \begin_layout Plain Layout
6025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6028 \begin_layout Plain Layout
6029 \begin_inset Formula $[$
6039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6042 \begin_layout Plain Layout
6050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6053 \begin_layout Plain Layout
6054 \begin_inset Formula $\langle$
6064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6067 \begin_layout Plain Layout
6075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6078 \begin_layout Plain Layout
6079 \begin_inset Formula $\lceil$
6089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6092 \begin_layout Plain Layout
6100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6103 \begin_layout Plain Layout
6104 \begin_inset Formula $\lfloor$
6114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6117 \begin_layout Plain Layout
6123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6126 \begin_layout Plain Layout
6127 \begin_inset Formula $/$
6137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6140 \begin_layout Plain Layout
6146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6149 \begin_layout Plain Layout
6150 \begin_inset Formula $|$
6164 \begin_inset space \hfill{}
6168 \begin_inset Tabular
6169 <lyxtabular version="3" rows="9" columns="2">
6170 <features tabularvalignment="middle">
6171 <column alignment="center" valignment="top" width="0pt">
6172 <column alignment="center" valignment="top" width="0pt">
6174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6177 \begin_layout Plain Layout
6183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6186 \begin_layout Plain Layout
6194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6197 \begin_layout Plain Layout
6203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6206 \begin_layout Plain Layout
6207 \begin_inset Formula $)$
6217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6220 \begin_layout Plain Layout
6226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6229 \begin_layout Plain Layout
6230 \begin_inset Formula $\}$
6240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6243 \begin_layout Plain Layout
6249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6252 \begin_layout Plain Layout
6253 \begin_inset Formula $]$
6263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6266 \begin_layout Plain Layout
6274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6277 \begin_layout Plain Layout
6278 \begin_inset Formula $\rangle$
6288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6291 \begin_layout Plain Layout
6299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6302 \begin_layout Plain Layout
6303 \begin_inset Formula $\rceil$
6313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6316 \begin_layout Plain Layout
6324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6327 \begin_layout Plain Layout
6328 \begin_inset Formula $\rfloor$
6338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6341 \begin_layout Plain Layout
6351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6354 \begin_layout Plain Layout
6355 \begin_inset Formula $\backslash$
6365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6368 \begin_layout Plain Layout
6376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6379 \begin_layout Plain Layout
6380 \begin_inset Formula $\|$
6394 \begin_inset space \hfill{}
6400 \begin_layout Standard
6403 \begin_inset Note Greyedout
6406 \begin_layout Plain Layout
6411 In TeX-mode the command
6418 \begin_inset Index idx
6421 \begin_layout Plain Layout
6429 must be used for the backslash, because the command
6437 produces there a line break.
6445 \begin_layout Standard
6446 For all characters listed above the size can be adjusted with the commands
6447 described in the following two subsections.
6448 When using these commands, the characters < and > can directly be used
6449 instead of the commands
6464 \begin_layout Subsubsection
6466 \begin_inset CommandInset label
6468 name "sub:Manual-Bracket-Size"
6473 \begin_inset Index idx
6476 \begin_layout Plain Layout
6477 Bracket size ! manual
6485 \begin_layout Standard
6486 The bracket size can be specified manually by the LaTeX-commands
6493 \begin_inset Index idx
6496 \begin_layout Plain Layout
6529 denotes the smallest and
6535 the largest bracket size.
6538 \begin_layout Standard
6539 These commands are used to emphasize levels of brackets:
6542 \begin_layout Standard
6544 \begin_inset Tabular
6545 <lyxtabular version="3" rows="2" columns="2">
6546 <features tabularvalignment="middle">
6547 <column alignment="center" valignment="top" width="0pt">
6548 <column alignment="center" valignment="top" width="0pt">
6550 <cell alignment="center" valignment="top" usebox="none">
6553 \begin_layout Plain Layout
6554 all brackets in the same size:
6559 <cell alignment="center" valignment="top" usebox="none">
6562 \begin_layout Plain Layout
6563 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6573 <cell alignment="center" valignment="top" usebox="none">
6576 \begin_layout Plain Layout
6582 <cell alignment="center" valignment="top" usebox="none">
6585 \begin_layout Plain Layout
6586 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6600 \begin_inset Note Note
6603 \begin_layout Plain Layout
6610 is only used as spacer.
6618 \begin_layout Standard
6619 For the second formula the command
6629 \begin_layout Plain Layout
6643 \begin_layout Standard
6644 Here is an overview about all bracket sizes:
6647 \begin_layout Standard
6667 \begin_layout Plain Layout
6684 \begin_layout Plain Layout
6697 \begin_layout Plain Layout
6713 \begin_layout Standard
6715 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6721 \begin_layout Standard
6728 -commands there is the variant
6735 \begin_inset Index idx
6738 \begin_layout Plain Layout
6746 that adds a bit more space between the bracket and its content, and the
6760 \begin_inset Index idx
6763 \begin_layout Plain Layout
6773 , that don't add additional space.
6778 at the end of the command
6784 is for a left bracket; for a right bracket this will be replaced by an
6790 A left or right bracket can each be an opening or closing bracket.
6793 \begin_layout Standard
6794 In the following table is a comparison of the variants:
6797 \begin_layout Standard
6799 \begin_inset Tabular
6800 <lyxtabular version="3" rows="5" columns="2">
6801 <features tabularvalignment="middle">
6802 <column alignment="center" valignment="middle" width="0">
6803 <column alignment="center" valignment="middle" width="0">
6805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6808 \begin_layout Plain Layout
6814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6817 \begin_layout Plain Layout
6819 \begin_inset Note Note
6822 \begin_layout Plain Layout
6829 is only used as spacer.
6841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6844 \begin_layout Plain Layout
6859 \begin_layout Plain Layout
6877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6880 \begin_layout Plain Layout
6881 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6894 \begin_layout Plain Layout
6909 \begin_layout Plain Layout
6927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6930 \begin_layout Plain Layout
6931 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6944 \begin_layout Plain Layout
6959 \begin_layout Plain Layout
6977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6980 \begin_layout Plain Layout
6981 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6994 \begin_layout Plain Layout
7006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7009 \begin_layout Plain Layout
7010 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7026 \begin_layout Subsubsection
7027 Automatic Bracket Size
7028 \begin_inset CommandInset label
7030 name "sub:Automatic-Bracket-Size"
7035 \begin_inset Index idx
7038 \begin_layout Plain Layout
7039 Bracket size ! automatic
7047 \begin_layout Standard
7048 Brackets with variable size can be inserted with the commands
7055 \begin_inset Index idx
7058 \begin_layout Plain Layout
7073 \begin_inset Index idx
7076 \begin_layout Plain Layout
7084 or via the math toolbar button
7085 \begin_inset Graphics
7086 filename ../images/dialog-show_mathdelimiter.png
7104 the wanted bracket must be inserted.
7105 The bracket size will then automatically be calculated for the output.
7108 \begin_layout Standard
7110 normal bracket: The command
7120 \begin_layout Plain Layout
7130 \begin_inset Formula $\downarrow$
7137 \begin_layout Plain Layout
7149 \begin_inset Formula \[
7157 \begin_layout Standard
7159 multiline bracket: The command
7171 \begin_layout Plain Layout
7181 \begin_inset Formula $\downarrow$
7188 \begin_layout Plain Layout
7202 \begin_inset Formula \[
7203 \ln\left(\frac{A}{C}\right)\]
7210 \begin_layout Standard
7226 \begin_inset space ~
7232 This has the advantage that you can see in LyX immediately the real bracket
7233 size and that the matching right bracket will be created too.
7234 \begin_inset Newline newline
7237 The command for the last example would then be:
7251 \begin_layout Plain Layout
7261 \begin_inset Formula $\downarrow$
7267 \begin_layout Standard
7268 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7269 For example the command
7279 \begin_layout Plain Layout
7289 \begin_inset Formula $\downarrow$
7296 \begin_layout Plain Layout
7312 \begin_inset Formula \[
7313 \left.\frac{A}{B}\right\} \]
7331 will be converted by LyX to brackets in the right size when the document
7332 is reloaded and an omitted bracket will appear as dashed line.
7335 \begin_layout Standard
7336 \begin_inset VSpace bigskip
7339 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7347 \begin_inset Index idx
7350 \begin_layout Plain Layout
7358 is additionally available for all brackets and limits.
7359 With this command the height of the following character is adapted to the
7360 one of the surrounding brackets, what is e.
7361 \begin_inset space \thinspace{}
7365 \begin_inset space \space{}
7368 needed for physical vectors:
7369 \begin_inset Formula \[
7370 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7374 For physical vectors there is a special LaTeX-package, described in
7375 \begin_inset CommandInset ref
7377 reference "sub:Physical-Vectors"
7384 \begin_layout Subsection
7386 \begin_inset Index idx
7389 \begin_layout Plain Layout
7390 Brackets ! horizontal
7398 \begin_layout Standard
7400 \begin_inset Tabular
7401 <lyxtabular version="3" rows="4" columns="2">
7402 <features tabularvalignment="middle">
7403 <column alignment="center" valignment="top" width="0pt">
7404 <column alignment="center" valignment="top" width="0pt">
7406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7409 \begin_layout Plain Layout
7411 \begin_inset Note Note
7414 \begin_layout Plain Layout
7421 is only used as spacer.
7431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7434 \begin_layout Plain Layout
7442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7445 \begin_layout Plain Layout
7449 \begin_layout Plain Layout
7464 \begin_layout Plain Layout
7477 \begin_layout Plain Layout
7490 \begin_layout Plain Layout
7503 \begin_layout Plain Layout
7511 \begin_inset Index idx
7514 \begin_layout Plain Layout
7527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7530 \begin_layout Plain Layout
7531 \begin_inset Formula $\overbrace{A+B}^{3}$
7541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7544 \begin_layout Plain Layout
7548 \begin_layout Plain Layout
7563 \begin_layout Plain Layout
7576 \begin_layout Plain Layout
7589 \begin_layout Plain Layout
7597 \begin_inset Index idx
7600 \begin_layout Plain Layout
7613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7616 \begin_layout Plain Layout
7617 \begin_inset Formula $\underbrace{A+B}_{5}$
7627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7630 \begin_layout Plain Layout
7637 \begin_layout Plain Layout
7652 \begin_layout Plain Layout
7665 \begin_layout Plain Layout
7678 \begin_layout Plain Layout
7691 \begin_layout Plain Layout
7704 \begin_layout Plain Layout
7717 \begin_layout Plain Layout
7731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7734 \begin_layout Plain Layout
7735 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7751 \begin_layout Standard
7752 In the last example it doesn't matter if
7764 is inserted at first.
7767 \begin_layout Standard
7768 \begin_inset VSpace bigskip
7771 When brackets are needed that overlap each other, multiline formulas, as
7773 \begin_inset CommandInset ref
7775 reference "sec:Multiline-Formulas"
7780 \begin_inset Formula \begin{eqnarray*}
7781 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7782 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7787 In the first row the formula is inserted together with the first brace.
7788 It is hereby important that the space command
7792 \begin_layout Plain Layout
7793 Space commands are explained in
7794 \begin_inset CommandInset ref
7796 reference "sub:Predefined-Space"
7811 is inserted before the first
7812 \begin_inset Formula $d$
7815 , because the brace that ends behind the
7816 \begin_inset Formula $q$
7819 prevents that the following
7820 \begin_inset Quotes eld
7824 \begin_inset Quotes erd
7827 is surrounded by space.
7831 \begin_layout Plain Layout
7832 because a bracket is not handled as character, see
7833 \begin_inset CommandInset ref
7835 reference "sub:Binary-Operators"
7844 In the second row the second brace is inserted.
7845 As it should begin before the
7846 \begin_inset Formula $b$
7861 \begin_layout Plain Layout
7869 \begin_inset CommandInset ref
7871 reference "sub:Placeholders"
7880 This space is needed because the
7881 \begin_inset Quotes eld
7885 \begin_inset Quotes erd
7888 is also surrounded by space in the formula.
7889 The brace is placed under the command
7898 \begin_layout Standard
7899 It gets more complicated when brackets overlap each other, like in the following
7904 \begin_layout Plain Layout
7916 \begin_inset Formula \begin{eqnarray*}
7917 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7918 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7927 \begin_layout Plain Layout
7938 The first formula row is the same as the second row of the previous example,
7939 with the difference that the brace is above.
7940 The second row contains the formula together with the second brace.
7941 To avoid that there is space between the upper brace in the first row and
7942 the formula, the row spacing need to be reduced.
7943 This is not easily possible due to a bug in LyX
7947 \begin_layout Plain Layout
7948 \begin_inset CommandInset href
7950 name "LyX-bug #1505"
7951 target "http://www.lyx.org/trac/ticket/1505"
7961 As solution for the problem, the global formula row separation
7968 \begin_inset Index idx
7971 \begin_layout Plain Layout
7979 must be changed to -6
7980 \begin_inset space \thinspace{}
7983 pt before the formula with the command
7998 is set back after the formula to the standard value of 3
7999 \begin_inset space \thinspace{}
8002 pt using the same command.
8003 More about the row separation in formulas is explained in
8004 \begin_inset CommandInset ref
8006 reference "sub:Line-Separation"
8013 \begin_layout Section
8015 \begin_inset Index idx
8018 \begin_layout Plain Layout
8027 \begin_layout Standard
8028 Arrows can be inserted via the math toolbar button
8029 \begin_inset Graphics
8030 filename ../images/math/leftarrow.png
8035 or the commands listed in the following subsections.
8038 \begin_layout Standard
8039 \begin_inset Newpage newpage
8045 \begin_layout Subsection
8047 \begin_inset Index idx
8050 \begin_layout Plain Layout
8059 \begin_layout Standard
8060 \begin_inset space \hfill{}
8064 \begin_inset Tabular
8065 <lyxtabular version="3" rows="8" columns="2">
8066 <features tabularvalignment="middle">
8067 <column alignment="center" valignment="top" width="0pt">
8068 <column alignment="center" valignment="top" width="0pt">
8070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8073 \begin_layout Plain Layout
8079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8082 \begin_layout Plain Layout
8090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8093 \begin_layout Plain Layout
8101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8104 \begin_layout Plain Layout
8105 \begin_inset Formula $\gets$
8115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8118 \begin_layout Plain Layout
8126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8129 \begin_layout Plain Layout
8130 \begin_inset Formula $\Leftarrow$
8140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8143 \begin_layout Plain Layout
8151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8154 \begin_layout Plain Layout
8155 \begin_inset Formula $\longleftarrow$
8165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8168 \begin_layout Plain Layout
8176 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8179 \begin_layout Plain Layout
8180 \begin_inset Formula $\Longleftarrow$
8190 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8193 \begin_layout Plain Layout
8201 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8204 \begin_layout Plain Layout
8205 \begin_inset Formula $\leftharpoonup$
8215 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8218 \begin_layout Plain Layout
8226 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8229 \begin_layout Plain Layout
8230 \begin_inset Formula $\leftharpoondown$
8240 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8243 \begin_layout Plain Layout
8251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8254 \begin_layout Plain Layout
8255 \begin_inset Formula $\hookleftarrow$
8269 \begin_inset space \hfill{}
8273 \begin_inset Tabular
8274 <lyxtabular version="3" rows="8" columns="2">
8275 <features tabularvalignment="middle">
8276 <column alignment="center" valignment="top" width="0pt">
8277 <column alignment="center" valignment="top" width="0pt">
8279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8282 \begin_layout Plain Layout
8288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8291 \begin_layout Plain Layout
8299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8302 \begin_layout Plain Layout
8310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8313 \begin_layout Plain Layout
8314 \begin_inset Formula $\to$
8324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8327 \begin_layout Plain Layout
8335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8338 \begin_layout Plain Layout
8339 \begin_inset Formula $\Rightarrow$
8349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8352 \begin_layout Plain Layout
8360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8363 \begin_layout Plain Layout
8364 \begin_inset Formula $\longrightarrow$
8374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8377 \begin_layout Plain Layout
8385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8388 \begin_layout Plain Layout
8389 \begin_inset Formula $\Longrightarrow$
8399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8402 \begin_layout Plain Layout
8410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8413 \begin_layout Plain Layout
8414 \begin_inset Formula $\rightharpoonup$
8424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8427 \begin_layout Plain Layout
8435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8438 \begin_layout Plain Layout
8439 \begin_inset Formula $\rightharpoondown$
8449 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8452 \begin_layout Plain Layout
8460 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8463 \begin_layout Plain Layout
8464 \begin_inset Formula $\hookrightarrow$
8478 \begin_inset space \hfill{}
8484 \begin_layout Standard
8485 \begin_inset space \hfill{}
8489 \begin_inset Tabular
8490 <lyxtabular version="3" rows="6" columns="2">
8491 <features tabularvalignment="middle">
8492 <column alignment="center" valignment="top" width="0pt">
8493 <column alignment="center" valignment="top" width="0pt">
8495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8498 \begin_layout Plain Layout
8504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8507 \begin_layout Plain Layout
8515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8518 \begin_layout Plain Layout
8526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8529 \begin_layout Plain Layout
8530 \begin_inset Formula $\leftrightarrow$
8540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8543 \begin_layout Plain Layout
8551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8554 \begin_layout Plain Layout
8555 \begin_inset Formula $\Leftrightarrow$
8565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8568 \begin_layout Plain Layout
8576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8579 \begin_layout Plain Layout
8580 \begin_inset Formula $\longleftrightarrow$
8590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8593 \begin_layout Plain Layout
8601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8604 \begin_layout Plain Layout
8605 \begin_inset Formula $\Longleftrightarrow$
8615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8618 \begin_layout Plain Layout
8626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8629 \begin_layout Plain Layout
8630 \begin_inset Formula $\rightleftharpoons$
8644 \begin_inset space \hspace{}
8649 \begin_inset space \hfill{}
8653 \begin_inset Tabular
8654 <lyxtabular version="3" rows="5" columns="2">
8655 <features tabularvalignment="middle">
8656 <column alignment="center" valignment="top" width="0pt">
8657 <column alignment="center" valignment="top" width="0pt">
8659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8662 \begin_layout Plain Layout
8668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8671 \begin_layout Plain Layout
8679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8682 \begin_layout Plain Layout
8690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8693 \begin_layout Plain Layout
8694 \begin_inset Formula $\mapsto$
8704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8707 \begin_layout Plain Layout
8715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8718 \begin_layout Plain Layout
8719 \begin_inset Formula $\longmapsto$
8729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8732 \begin_layout Plain Layout
8740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8743 \begin_layout Plain Layout
8744 \begin_inset Formula $\leadsto$
8754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8757 \begin_layout Plain Layout
8765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8768 \begin_layout Plain Layout
8769 \begin_inset Formula $\dasharrow$
8783 \begin_inset space \hfill{}
8789 \begin_layout Standard
8790 \begin_inset VSpace medskip
8793 Arrows used as accent like e.
8794 \begin_inset space \thinspace{}
8798 \begin_inset space \space{}
8801 vector arrows are listed in
8802 \begin_inset CommandInset ref
8804 reference "sec:Accents"
8811 \begin_layout Standard
8812 \begin_inset VSpace bigskip
8815 Furthermore there are the labeled arrows
8816 \begin_inset Index idx
8819 \begin_layout Plain Layout
8832 \begin_inset Index idx
8835 \begin_layout Plain Layout
8850 \begin_inset Index idx
8853 \begin_layout Plain Layout
8860 \begin_layout Plain Layout
8875 When inserting one of these commands in a formula, an arrow with two blue
8876 boxes appear where the label can be inserted.
8877 The length of the arrow adapts to the label width.
8880 \begin_layout Standard
8882 \begin_inset Tabular
8883 <lyxtabular version="3" rows="3" columns="2">
8884 <features tabularvalignment="middle">
8885 <column alignment="center" valignment="top" width="0pt">
8886 <column alignment="center" valignment="top" width="0pt">
8888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8891 \begin_layout Plain Layout
8897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8900 \begin_layout Plain Layout
8902 \begin_inset Note Note
8905 \begin_layout Plain Layout
8912 is only used as spacer.
8924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8927 \begin_layout Plain Layout
8934 \begin_layout Plain Layout
8944 \begin_inset Formula $\downarrow$
8948 \begin_inset Formula $\to$
8956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8959 \begin_layout Plain Layout
8960 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8973 \begin_layout Plain Layout
8980 \begin_layout Plain Layout
8990 \begin_inset Formula $\downarrow$
8994 \begin_inset Formula $\to$
9002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9005 \begin_layout Plain Layout
9006 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9022 \begin_layout Subsection
9023 Vertical and diagonal Arrows
9024 \begin_inset Index idx
9027 \begin_layout Plain Layout
9034 \begin_inset Index idx
9037 \begin_layout Plain Layout
9046 \begin_layout Standard
9047 \begin_inset space \hfill{}
9051 \begin_inset Tabular
9052 <lyxtabular version="3" rows="7" columns="2">
9053 <features tabularvalignment="middle">
9054 <column alignment="center" valignment="top" width="0pt">
9055 <column alignment="center" valignment="top" width="0pt">
9057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9060 \begin_layout Plain Layout
9066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9069 \begin_layout Plain Layout
9077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9080 \begin_layout Plain Layout
9088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9091 \begin_layout Plain Layout
9092 \begin_inset Formula $\uparrow$
9102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9105 \begin_layout Plain Layout
9113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9116 \begin_layout Plain Layout
9117 \begin_inset Formula $\Uparrow$
9127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9130 \begin_layout Plain Layout
9138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9141 \begin_layout Plain Layout
9142 \begin_inset Formula $\updownarrow$
9152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9155 \begin_layout Plain Layout
9163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9166 \begin_layout Plain Layout
9167 \begin_inset Formula $\Updownarrow$
9177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9180 \begin_layout Plain Layout
9188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9191 \begin_layout Plain Layout
9192 \begin_inset Formula $\Downarrow$
9202 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9205 \begin_layout Plain Layout
9213 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9216 \begin_layout Plain Layout
9217 \begin_inset Formula $\downarrow$
9231 \begin_inset space \hfill{}
9235 \begin_inset Tabular
9236 <lyxtabular version="3" rows="5" columns="2">
9237 <features tabularvalignment="middle">
9238 <column alignment="center" valignment="top" width="0pt">
9239 <column alignment="center" valignment="top" width="0pt">
9241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9244 \begin_layout Plain Layout
9250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9253 \begin_layout Plain Layout
9261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9264 \begin_layout Plain Layout
9272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9275 \begin_layout Plain Layout
9276 \begin_inset Formula $\nearrow$
9286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9289 \begin_layout Plain Layout
9297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9300 \begin_layout Plain Layout
9301 \begin_inset Formula $\searrow$
9311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9314 \begin_layout Plain Layout
9322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9325 \begin_layout Plain Layout
9326 \begin_inset Formula $\swarrow$
9336 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9339 \begin_layout Plain Layout
9347 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9350 \begin_layout Plain Layout
9351 \begin_inset Formula $\nwarrow$
9365 \begin_inset space \hfill{}
9371 \begin_layout Standard
9372 \begin_inset VSpace medskip
9375 Vertical arrows can be used also as delimiter together with the commands
9377 \begin_inset CommandInset ref
9379 reference "sub:Manual-Bracket-Size"
9384 \begin_inset CommandInset ref
9386 reference "sub:Automatic-Bracket-Size"
9393 \begin_layout Standard
9394 \begin_inset Newpage newpage
9400 \begin_layout Section
9402 \begin_inset CommandInset label
9409 \begin_inset Index idx
9412 \begin_layout Plain Layout
9421 \begin_layout Standard
9422 Accents can be inserted via the math toolbar button
9423 \begin_inset Graphics
9424 filename ../images/math/hat.png
9429 or the commands listed in the following subsections.
9432 \begin_layout Subsection
9433 Accents for one Character
9437 \begin_layout Plain Layout
9450 \begin_layout Plain Layout
9452 \begin_inset CommandInset ref
9454 reference "sub:Accents-in-Text"
9467 \begin_layout Plain Layout
9475 \begin_inset Note Note
9478 \begin_layout Plain Layout
9481 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9484 \begin_layout Plain Layout
9487 texorpdfstring is in section
9488 \begin_inset CommandInset ref
9490 reference "sub:Formulas-in-Section"
9500 \begin_inset CommandInset label
9502 name "sub:Accents-for-one"
9507 \begin_inset Index idx
9510 \begin_layout Plain Layout
9511 Accents ! for one character
9519 \begin_layout Standard
9520 \begin_inset space \hfill{}
9524 \begin_inset Tabular
9525 <lyxtabular version="3" rows="8" columns="2">
9526 <features tabularvalignment="middle">
9527 <column alignment="center" valignment="top" width="0pt">
9528 <column alignment="center" valignment="top" width="0pt">
9530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9533 \begin_layout Plain Layout
9539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9542 \begin_layout Plain Layout
9544 \begin_inset Note Note
9547 \begin_layout Plain Layout
9554 is only used as spacer.
9566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9569 \begin_layout Plain Layout
9576 \begin_layout Plain Layout
9590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9593 \begin_layout Plain Layout
9594 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9604 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9607 \begin_layout Plain Layout
9614 \begin_layout Plain Layout
9628 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9631 \begin_layout Plain Layout
9632 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9642 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9645 \begin_layout Plain Layout
9652 \begin_layout Plain Layout
9666 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9669 \begin_layout Plain Layout
9670 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9683 \begin_layout Plain Layout
9690 \begin_layout Plain Layout
9704 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9707 \begin_layout Plain Layout
9708 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9718 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9721 \begin_layout Plain Layout
9728 \begin_layout Plain Layout
9738 \begin_inset Index idx
9741 \begin_layout Plain Layout
9752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9755 \begin_layout Plain Layout
9756 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9766 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9769 \begin_layout Plain Layout
9776 \begin_layout Plain Layout
9790 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9793 \begin_layout Plain Layout
9794 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9804 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9807 \begin_layout Plain Layout
9814 \begin_layout Plain Layout
9828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9831 \begin_layout Plain Layout
9832 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9846 \begin_inset space \hfill{}
9850 \begin_inset Tabular
9851 <lyxtabular version="3" rows="7" columns="2">
9852 <features tabularvalignment="middle">
9853 <column alignment="center" valignment="top" width="0pt">
9854 <column alignment="center" valignment="top" width="0pt">
9856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9859 \begin_layout Plain Layout
9865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9868 \begin_layout Plain Layout
9876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9879 \begin_layout Plain Layout
9886 \begin_layout Plain Layout
9900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9903 \begin_layout Plain Layout
9904 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9914 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9917 \begin_layout Plain Layout
9924 \begin_layout Plain Layout
9938 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9941 \begin_layout Plain Layout
9942 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9952 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9955 \begin_layout Plain Layout
9962 \begin_layout Plain Layout
9976 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9979 \begin_layout Plain Layout
9980 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9990 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9993 \begin_layout Plain Layout
10000 \begin_layout Plain Layout
10014 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10017 \begin_layout Plain Layout
10018 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10028 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10031 \begin_layout Plain Layout
10038 \begin_layout Plain Layout
10052 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10055 \begin_layout Plain Layout
10056 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10066 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10069 \begin_layout Plain Layout
10076 \begin_layout Plain Layout
10090 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10093 \begin_layout Plain Layout
10094 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10108 \begin_inset space \hfill{}
10114 \begin_layout Standard
10115 \begin_inset VSpace bigskip
10121 \begin_layout Standard
10122 You can directly insert accents like é to formulas.
10123 LyX will transform them to the corresponding accent command.
10125 \begin_inset Index idx
10128 \begin_layout Plain Layout
10134 it is better to insert a quotation mark before the vowel.
10135 These two characters are then treated by LaTeX as
10139 character when the formula part with the umlaut is marked as German.
10147 \begin_inset Quotes eld
10151 \begin_inset Quotes erd
10154 umlauts are created as demonstrated in the following example:
10157 \begin_layout Standard
10158 \begin_inset VSpace -2mm
10164 \begin_layout Standard
10166 \begin_inset Tabular
10167 <lyxtabular version="3" rows="3" columns="2">
10168 <features tabularvalignment="middle">
10169 <column alignment="center" valignment="top" width="0">
10170 <column alignment="center" valignment="top" width="0">
10172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10175 \begin_layout Plain Layout
10181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10184 \begin_layout Plain Layout
10186 \begin_inset Note Note
10189 \begin_layout Plain Layout
10197 \begin_inset space \thinspace{}
10200 pt space are only used as spacer.
10212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10215 \begin_layout Plain Layout
10218 \begin_inset Quotes grd
10226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10229 \begin_layout Plain Layout
10230 \begin_inset space \hspace{}
10237 \begin_inset Formula $"i$
10247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10250 \begin_layout Plain Layout
10257 \begin_layout Plain Layout
10271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10274 \begin_layout Plain Layout
10275 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10291 \begin_layout Standard
10292 Another advantage to
10298 is that umlauts can directly be converted to mathematical text because
10299 the accent commands above are
10305 in mathematical text
10308 To convert an accented character to mathematical text, only the character
10309 under the accent may be converted.
10310 This applies also for all other conversions, e.
10311 \begin_inset space \thinspace{}
10315 \begin_inset space \space{}
10321 \begin_layout Standard
10322 In mathematical text, umlauts and other accented characters can directly
10326 \begin_layout Subsection
10327 Accents for Operators
10328 \begin_inset Index idx
10331 \begin_layout Plain Layout
10332 Accents ! for operators
10340 \begin_layout Standard
10348 \begin_inset Index idx
10351 \begin_layout Plain Layout
10366 \begin_inset Index idx
10369 \begin_layout Plain Layout
10377 characters can be placed above or below an operator, respectively, to accent
10386 \begin_inset Index idx
10389 \begin_layout Plain Layout
10397 characters can be set before and behind an operator.
10398 The command scheme is:
10401 \begin_layout Standard
10417 \begin_layout Standard
10424 must always be before the operator that should be accented.
10425 You can accent with several characters and even with other operators and
10433 for example only characters behind an operator, write nothing between the
10434 first braces but don't omit the braces.
10437 \begin_layout Standard
10438 For example the command
10443 \begin_inset Formula $\to$
10453 \begin_inset Formula $\to$
10462 \begin_layout Plain Layout
10478 \begin_inset Formula \[
10479 \sideset{}{'}\sum_{k=1}^{n}\]
10486 \begin_layout Standard
10495 \begin_layout Plain Layout
10510 \begin_layout Plain Layout
10522 \begin_inset Formula $\uparrow$
10530 \begin_inset Formula \[
10531 \overset{a}{\maltese}\]
10535 As seen in the last example, with
10547 also symbols and characters can be accented; with
10553 this is not possible.
10556 \begin_layout Subsection
10557 Accents for several Characters
10558 \begin_inset Index idx
10561 \begin_layout Plain Layout
10562 Accents ! for several characters
10570 \begin_layout Standard
10571 \begin_inset space \hfill{}
10575 \begin_inset Tabular
10576 <lyxtabular version="3" rows="5" columns="2">
10577 <features tabularvalignment="middle">
10578 <column alignment="center" valignment="top" width="0pt">
10579 <column alignment="center" valignment="top" width="0pt">
10581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10584 \begin_layout Plain Layout
10590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10593 \begin_layout Plain Layout
10595 \begin_inset Note Note
10598 \begin_layout Plain Layout
10605 is only used as spacer.
10617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10620 \begin_layout Plain Layout
10627 \begin_layout Plain Layout
10641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10644 \begin_layout Plain Layout
10645 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10655 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10658 \begin_layout Plain Layout
10665 \begin_layout Plain Layout
10679 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10682 \begin_layout Plain Layout
10683 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10693 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10696 \begin_layout Plain Layout
10703 \begin_layout Plain Layout
10717 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10720 \begin_layout Plain Layout
10721 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10731 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10734 \begin_layout Plain Layout
10737 underleftrightarrow
10741 \begin_layout Plain Layout
10755 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10758 \begin_layout Plain Layout
10759 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10773 \begin_inset space \hfill{}
10777 \begin_inset Tabular
10778 <lyxtabular version="3" rows="5" columns="2">
10779 <features tabularvalignment="middle">
10780 <column alignment="center" valignment="top" width="0pt">
10781 <column alignment="center" valignment="top" width="0pt">
10783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10786 \begin_layout Plain Layout
10792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10795 \begin_layout Plain Layout
10803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10806 \begin_layout Plain Layout
10813 \begin_layout Plain Layout
10827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10830 \begin_layout Plain Layout
10831 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10841 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10844 \begin_layout Plain Layout
10851 \begin_layout Plain Layout
10865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10868 \begin_layout Plain Layout
10869 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10879 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10882 \begin_layout Plain Layout
10889 \begin_layout Plain Layout
10903 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10906 \begin_layout Plain Layout
10907 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10917 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10920 \begin_layout Plain Layout
10927 \begin_layout Plain Layout
10941 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10944 \begin_layout Plain Layout
10945 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10959 \begin_inset space \hfill{}
10965 \begin_layout Standard
10966 \begin_inset VSpace medskip
10969 With these commands as many characters as you like can be accented.
10982 will only be set in the output with a length of three characters, as shown
10983 in the following example:
10984 \begin_inset Formula \[
10985 \widetilde{A+B=C-D}\]
10992 \begin_layout Standard
11000 \begin_inset Index idx
11003 \begin_layout Plain Layout
11018 \begin_inset Index idx
11021 \begin_layout Plain Layout
11029 described in the previous subsection it is also possible to accent several
11039 \begin_layout Plain Layout
11049 \begin_inset Formula $\downarrow$
11055 \begin_inset Formula \[
11056 \underset{***}{A=B}\]
11063 \begin_layout Section
11065 \begin_inset CommandInset label
11072 \begin_inset Index idx
11075 \begin_layout Plain Layout
11084 \begin_layout Subsection
11086 \begin_inset CommandInset label
11088 name "sub:Predefined-Space"
11093 \begin_inset Index idx
11096 \begin_layout Plain Layout
11097 Space ! horizontal ! predefined
11105 \begin_layout Standard
11106 Sometimes it is necessary to insert horizontal space to a formula.
11107 This is done by inserting a protected space (shortcut
11110 arg "space-insert protected"
11115 \begin_inset Quotes eld
11124 \begin_layout Plain Layout
11136 \begin_inset Quotes erd
11139 appears and by pressing
11143 several times one can select one of eight different space sizes.
11144 The spaces can also be inserted using the math toolbar button
11145 \begin_inset Graphics
11146 filename ../images/math/space.png
11151 or special commands.
11152 Independent from the inserted command, one can select the size again by
11160 \begin_layout Standard
11163 \begin_inset VSpace -5mm
11167 \begin_inset Tabular
11168 <lyxtabular version="3" rows="3" columns="7">
11169 <features tabularvalignment="middle">
11170 <column alignment="center" valignment="middle" width="6.8cm">
11171 <column alignment="center" valignment="top" width="0">
11172 <column alignment="center" valignment="top" width="0">
11173 <column alignment="center" valignment="top" width="0">
11174 <column alignment="center" valignment="top" width="0">
11175 <column alignment="center" valignment="top" width="0">
11176 <column alignment="center" valignment="top" width="0">
11178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11181 \begin_layout Plain Layout
11187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11190 \begin_layout Plain Layout
11198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11201 \begin_layout Plain Layout
11209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11212 \begin_layout Plain Layout
11220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11223 \begin_layout Plain Layout
11231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11234 \begin_layout Plain Layout
11242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11245 \begin_layout Plain Layout
11255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11258 \begin_layout Plain Layout
11263 keystrokes after inserting the protected space
11268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11271 \begin_layout Plain Layout
11277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11280 \begin_layout Plain Layout
11286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11289 \begin_layout Plain Layout
11295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11298 \begin_layout Plain Layout
11304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11307 \begin_layout Plain Layout
11313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11316 \begin_layout Plain Layout
11324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11327 \begin_layout Plain Layout
11333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11336 \begin_layout Plain Layout
11337 \begin_inset Formula $A\, B$
11345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11348 \begin_layout Plain Layout
11349 \begin_inset Formula $A\: B$
11357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11360 \begin_layout Plain Layout
11361 \begin_inset Formula $A\; B$
11369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11372 \begin_layout Plain Layout
11373 \begin_inset Formula $A\quad B$
11381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11384 \begin_layout Plain Layout
11385 \begin_inset Formula $A\qquad B$
11393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11396 \begin_layout Plain Layout
11397 \begin_inset Formula $A\! B$
11413 \begin_layout Standard
11414 The last size seem to produce no space.
11415 It is displayed red in LyX contrary to the other sizes, because it is a
11417 There are two more negative spaces:
11420 \begin_layout Standard
11422 \begin_inset Tabular
11423 <lyxtabular version="3" rows="3" columns="3">
11424 <features tabularvalignment="middle">
11425 <column alignment="center" valignment="middle" width="6.8cm">
11426 <column alignment="center" valignment="top" width="0pt">
11427 <column alignment="center" valignment="top" width="0pt">
11429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11432 \begin_layout Plain Layout
11438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11441 \begin_layout Plain Layout
11449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11452 \begin_layout Plain Layout
11462 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11465 \begin_layout Plain Layout
11470 keystrokes after inserting the protected space
11475 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11478 \begin_layout Plain Layout
11484 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11487 \begin_layout Plain Layout
11495 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11498 \begin_layout Plain Layout
11504 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11507 \begin_layout Plain Layout
11508 \begin_inset Formula $A\negmedspace B$
11516 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11519 \begin_layout Plain Layout
11520 \begin_inset Formula $A\negthickspace B$
11536 \begin_layout Standard
11537 Negative spaces can lead to characters overlapping each other.
11538 Thus they can be used to enforce ligatures, what is e.
11539 \begin_inset space \thinspace{}
11543 \begin_inset space \space{}
11546 useful for summation operators:
11549 \begin_layout Standard
11551 \begin_inset Tabular
11552 <lyxtabular version="3" rows="3" columns="2">
11553 <features tabularvalignment="middle">
11554 <column alignment="center" valignment="top" width="0">
11555 <column alignment="center" valignment="top" width="0">
11557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11560 \begin_layout Plain Layout
11566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11569 \begin_layout Plain Layout
11571 \begin_inset Note Note
11574 \begin_layout Plain Layout
11581 is only used as spacer.
11593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11596 \begin_layout Plain Layout
11605 \begin_layout Plain Layout
11619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11622 \begin_layout Plain Layout
11623 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11636 \begin_layout Plain Layout
11647 \begin_layout Plain Layout
11661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11664 \begin_layout Plain Layout
11665 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11681 \begin_layout Standard
11682 Relations like for example equal signs, are always surrounded by space.
11683 To suppress this, the equal sign is placed into a TeX-brace.
11684 The following example demonstrates this:
11687 \begin_layout Standard
11689 \begin_inset Tabular
11690 <lyxtabular version="3" rows="2" columns="2">
11691 <features tabularvalignment="middle">
11692 <column alignment="center" valignment="top" width="0pt">
11693 <column alignment="center" valignment="top" width="0pt">
11695 <cell alignment="center" valignment="top" usebox="none">
11698 \begin_layout Plain Layout
11704 <cell alignment="center" valignment="top" usebox="none">
11707 \begin_layout Plain Layout
11708 \begin_inset Formula $A=B$
11718 <cell alignment="center" valignment="top" usebox="none">
11721 \begin_layout Plain Layout
11722 \begin_inset Note Note
11725 \begin_layout Plain Layout
11732 is only used as spacer.
11738 \begin_inset Formula $\raisebox{5mm}{}$
11741 equation without space
11746 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11749 \begin_layout Plain Layout
11750 \begin_inset Formula $A{=}B$
11766 \begin_layout Standard
11768 The command for the last formula is:
11773 \begin_inset Formula $\to$
11779 \begin_layout Standard
11780 \begin_inset VSpace bigskip
11783 Spaces are needed for physical units, because the space between the value
11784 and the unit is the smallest one and not a normal space.
11785 For units in text, the smallest space is inserted via the menu
11787 Insert\SpecialChar \menuseparator
11788 Formatting\SpecialChar \menuseparator
11790 \begin_inset space ~
11798 arg "space-insert thin"
11804 \begin_layout Standard
11805 An example to visualize the difference:
11808 \begin_layout Standard
11809 \begin_inset Tabular
11810 <lyxtabular version="3" rows="2" columns="2">
11811 <features tabularvalignment="middle">
11812 <column alignment="left" valignment="top" width="0">
11813 <column alignment="left" valignment="top" width="0">
11815 <cell alignment="center" valignment="top" usebox="none">
11818 \begin_layout Plain Layout
11820 \begin_inset Formula $\cdot$
11828 <cell alignment="center" valignment="top" usebox="none">
11831 \begin_layout Plain Layout
11832 space between value and unit
11839 <cell alignment="center" valignment="top" usebox="none">
11842 \begin_layout Plain Layout
11844 \begin_inset space \thinspace{}
11848 \begin_inset Formula $\cdot$
11856 <cell alignment="center" valignment="top" usebox="none">
11859 \begin_layout Plain Layout
11860 smallest space between value and unit
11873 \begin_layout Subsection
11878 \begin_layout Plain Layout
11891 \begin_layout Plain Layout
11892 for vertical space in formulas see
11893 \begin_inset CommandInset ref
11895 reference "sub:Line-Separation"
11908 \begin_layout Plain Layout
11916 \begin_inset Note Note
11919 \begin_layout Plain Layout
11922 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11925 \begin_layout Plain Layout
11928 texorpdfstring is in section
11929 \begin_inset CommandInset ref
11931 reference "sub:Formulas-in-Section"
11941 \begin_inset CommandInset label
11943 name "sub:Variable-Space"
11948 \begin_inset Index idx
11951 \begin_layout Plain Layout
11952 Space ! horizontal ! variable
11960 \begin_layout Standard
11961 Space with a defined length can be inserted with the command
11968 \begin_inset Index idx
11971 \begin_layout Plain Layout
11981 \begin_inset Quotes eld
11990 \begin_layout Plain Layout
12002 \begin_inset Quotes erd
12006 The length can be specified by left-clicking on the
12007 \begin_inset Quotes eld
12016 \begin_layout Plain Layout
12028 \begin_inset Quotes erd
12032 The length may also be negative.
12033 To insert so many space that the formula uses all available space, the
12041 \begin_inset Index idx
12044 \begin_layout Plain Layout
12055 \begin_layout Standard
12056 \begin_inset VSpace -1mm
12062 \begin_layout Standard
12064 \begin_inset Tabular
12065 <lyxtabular version="3" rows="4" columns="2">
12066 <features tabularvalignment="middle">
12067 <column alignment="center" valignment="top" width="0">
12068 <column alignment="center" valignment="top" width="0">
12070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12073 \begin_layout Plain Layout
12081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12084 \begin_layout Plain Layout
12092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12095 \begin_layout Plain Layout
12102 \begin_layout Plain Layout
12112 \begin_inset Formula $\to$
12118 \begin_inset space \thinspace{}
12126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12129 \begin_layout Plain Layout
12130 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12143 \begin_layout Plain Layout
12150 \begin_layout Plain Layout
12160 \begin_inset Formula $\to$
12166 \begin_inset space \thinspace{}
12174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12177 \begin_layout Plain Layout
12178 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12191 \begin_layout Plain Layout
12198 \begin_layout Plain Layout
12212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12215 \begin_layout Plain Layout
12216 \begin_inset Formula $A=A\hfill B=B$
12232 \begin_layout Standard
12233 In the last example the available space is given by the longest column entry
12235 In an inline formula the space depends on the length of the line in which
12243 Thus, when the line uses the full width, no space will be created.
12250 only has an effect on displayed formulas when the formula style
12255 (Formula styles are explained in
12256 \begin_inset CommandInset ref
12258 reference "sec:Formula-Styles"
12265 \begin_layout Standard
12272 , there are the commands
12284 that fill the space with a pattern, see
12285 \begin_inset CommandInset ref
12287 reference "sub:Ellipses"
12294 \begin_layout Standard
12295 For text, variable space can be inserted via the menu
12297 Insert\SpecialChar \menuseparator
12298 Formatting\SpecialChar \menuseparator
12300 \begin_inset space ~
12308 \begin_layout Standard
12309 This is a line with
12310 \begin_inset space \hspace{}
12315 \begin_inset space \thinspace{}
12321 \begin_layout Standard
12322 This is a line with
12323 \begin_inset space \hfill{}
12329 \begin_layout Subsection
12330 Space besides inline Formulas
12331 \begin_inset Index idx
12334 \begin_layout Plain Layout
12335 Space ! besides inline formulas
12343 \begin_layout Standard
12344 The space that surrounds inline formulas can be adjusted with the length
12352 \begin_inset Index idx
12355 \begin_layout Plain Layout
12364 The value of a length is set with the command
12371 \begin_inset Index idx
12374 \begin_layout Plain Layout
12382 that has the following scheme:
12385 \begin_layout Standard
12390 setlength{length name}{value}
12393 \begin_layout Standard
12401 \begin_inset space \thinspace{}
12407 \begin_layout Standard
12417 \begin_layout Standard
12418 is inserted in TeX-mode.
12420 \begin_inset space \thinspace{}
12423 mm space will now be set around all inline formulas:
12427 \begin_layout Plain Layout
12441 \begin_layout Standard
12442 This is a line with an inline formula
12443 \begin_inset Formula $A=B$
12447 \begin_inset space \thinspace{}
12450 mm surrounding space.
12454 \begin_layout Plain Layout
12468 \begin_layout Standard
12469 To return to the predefined value,
12475 is set to the value 0
12476 \begin_inset space \thinspace{}
12482 \begin_layout Section
12484 \begin_inset Index idx
12487 \begin_layout Plain Layout
12494 \begin_inset Index idx
12497 \begin_layout Plain Layout
12502 \begin_layout Plain Layout
12513 \begin_layout Plain Layout
12528 \begin_layout Standard
12529 Boxes for text are described in chapter
12536 \begin_inset space ~
12544 \begin_layout Subsection
12546 \begin_inset CommandInset label
12548 name "sub:Boxes-with-Frame"
12553 \begin_inset Index idx
12556 \begin_layout Plain Layout
12565 \begin_layout Standard
12566 It is possible to frame formulas or parts of it with the commands
12573 \begin_inset Index idx
12576 \begin_layout Plain Layout
12591 \begin_inset Index idx
12594 \begin_layout Plain Layout
12605 \begin_layout Standard
12606 When one of these commands is inserted to a formula, a blue box appears
12607 within a frame to enter formula parts.
12614 an additional formula has to be created by
12618 within this box, because the box content will otherwise be treated as mathemati
12626 is used, a new formula is automatically created inside the frame.
12629 \begin_layout Standard
12636 is not suitable to frame displayed formulas because the formula will always
12637 be set in the size of the text.
12644 is in contrary not suitable to frame inline formulas, because the formula
12645 will always be set in the size of a displayed formula.
12648 \begin_layout Standard
12655 there is the command
12662 \begin_inset Index idx
12665 \begin_layout Plain Layout
12673 where additionally the frame width and the alignment can be specified.
12680 is used in the following scheme:
12683 \begin_layout Standard
12688 framebox[frame width][position]{box content}
12691 \begin_layout Standard
12692 The position can either be
12709 right aligns the formula in the box.
12710 When no position is given, the formula will be centered.
12711 \begin_inset Newline newline
12714 Is no width given, also no position can be given.
12715 In this case the frame width is adjusted to the box content like for
12724 \begin_layout Standard
12731 is inserted, a box appears containing three blue boxes.
12732 The first two boxes are surrounded by brackets and denote the two optional
12734 The third box is for formula parts like for
12743 \begin_layout Standard
12745 \begin_inset Tabular
12746 <lyxtabular version="3" rows="5" columns="2">
12747 <features tabularvalignment="middle">
12748 <column alignment="center" valignment="top" width="0">
12749 <column alignment="center" valignment="top" width="0">
12751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12754 \begin_layout Plain Layout
12760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12763 \begin_layout Plain Layout
12765 \begin_inset Note Note
12768 \begin_layout Plain Layout
12775 is only used as spacer.
12787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12790 \begin_layout Plain Layout
12797 \begin_layout Plain Layout
12816 \begin_layout Plain Layout
12830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12833 \begin_layout Plain Layout
12834 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12847 \begin_layout Plain Layout
12854 \begin_layout Plain Layout
12869 \begin_layout Plain Layout
12883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12886 \begin_layout Plain Layout
12887 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12900 \begin_layout Plain Layout
12907 \begin_layout Plain Layout
12921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12924 \begin_layout Plain Layout
12925 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12938 \begin_layout Plain Layout
12945 \begin_layout Plain Layout
12955 \begin_inset Formula $\to$
12959 \begin_inset Formula $\to$
12972 \begin_layout Plain Layout
12982 \begin_inset Formula $\downarrow$
12990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12993 \begin_layout Plain Layout
12994 \begin_inset Formula $\raisebox{6mm}{}$
12998 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13002 \begin_inset Formula $\raisebox{-4mm}{}$
13018 \begin_layout Standard
13019 The frame thickness can also be adjusted.
13020 To do this the following commands have to be inserted in TeX-mode before
13024 \begin_layout Standard
13034 \begin_inset Quotes eld
13038 \begin_inset Quotes erd
13052 \begin_inset Quotes eld
13056 \begin_inset Quotes erd
13062 \begin_layout Standard
13063 \begin_inset Quotes eld
13067 \begin_inset Quotes erd
13070 specifies the minimal distance between the frame and the first character
13072 An example for this is the following framed formula:
13076 \begin_layout Plain Layout
13088 \begin_inset Formula \[
13093 Before this formula the commands
13096 \begin_layout Standard
13118 \begin_layout Standard
13119 were inserted in TeX-mode.
13120 The given values are used for all following boxes.
13123 \begin_layout Standard
13124 To return to the standard frame size, the command
13127 \begin_layout Standard
13152 \begin_layout Plain Layout
13166 \begin_layout Standard
13167 is inserted in TeX-mode before the next formula.
13170 \begin_layout Subsection
13171 Boxes without Frame
13172 \begin_inset CommandInset label
13174 name "sub:Boxes-without-Frame"
13179 \begin_inset Index idx
13182 \begin_layout Plain Layout
13183 Boxes ! without frame
13191 \begin_layout Standard
13192 For boxes without a frame there are the following box commands:
13199 \begin_inset Index idx
13202 \begin_layout Plain Layout
13217 \begin_inset Index idx
13220 \begin_layout Plain Layout
13235 \begin_inset Index idx
13238 \begin_layout Plain Layout
13249 \begin_layout Standard
13256 a box can be super- or subscripted.
13257 But in contrary to normal super- and subscripting, the characters in the
13258 box keep their font size.
13265 is used in the following scheme:
13268 \begin_layout Standard
13273 raisebox{height}{box content}
13276 \begin_layout Standard
13277 When the box should contain a formula, an extra formula is needed like for
13288 \begin_inset Note Greyedout
13291 \begin_layout Plain Layout
13302 this extra formula is created by pressing
13306 twice instead of once because LyX doesn't yet support
13320 \begin_layout Standard
13322 \begin_inset Tabular
13323 <lyxtabular version="3" rows="4" columns="2">
13324 <features tabularvalignment="middle">
13325 <column alignment="center" valignment="top" width="0">
13326 <column alignment="center" valignment="top" width="0">
13328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13331 \begin_layout Plain Layout
13337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13340 \begin_layout Plain Layout
13348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13351 \begin_layout Plain Layout
13355 \begin_inset Formula $\to$
13361 \begin_inset Formula $\to$
13369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13372 \begin_layout Plain Layout
13373 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13386 \begin_layout Plain Layout
13390 \begin_inset Formula $\to$
13396 \begin_inset Formula $\to$
13404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13407 \begin_layout Plain Layout
13408 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13421 \begin_layout Plain Layout
13425 \begin_inset Formula $\to$
13444 \begin_layout Plain Layout
13458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13461 \begin_layout Plain Layout
13462 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13478 \begin_layout Standard
13503 , with the difference that there is no frame.
13506 \begin_layout Subsection
13508 \begin_inset CommandInset label
13510 name "sub:Colored-Boxes"
13515 \begin_inset Index idx
13518 \begin_layout Plain Layout
13527 \begin_layout Standard
13528 To be able to use all commands explained in this section, the LaTeX-package
13537 \begin_layout Plain Layout
13542 is part of every LaTeX standard installation.
13548 \begin_inset Index idx
13551 \begin_layout Plain Layout
13557 has to be loaded in the LaTeX-preamble with the line
13561 \begin_layout Plain Layout
13562 When text is colored somewhere in the document with a predefined color,
13563 LyX loads the LaTeX-package
13568 Thus it is possible that the package is loaded twice, but this doesn't
13575 \begin_inset Note Note
13578 \begin_layout Plain Layout
13579 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13588 \begin_layout Standard
13596 \begin_layout Standard
13597 \begin_inset VSpace medskip
13600 To color boxes, the command
13607 \begin_inset Index idx
13610 \begin_layout Plain Layout
13618 is used in the following scheme:
13621 \begin_layout Standard
13626 colorbox{color}{box content}
13629 \begin_layout Standard
13630 The box content can also be a box and a
13636 can also be part of another box (see the 2nd and 3rd example).
13637 When the box should contain a formula, an extra formula has to be created,
13638 the same way as for
13648 \begin_layout Plain Layout
13649 This also applies for the command
13663 \begin_layout Standard
13664 One of the following predefined colors can be chosen:
13667 \begin_layout Standard
13701 \begin_layout Standard
13703 \begin_inset Tabular
13704 <lyxtabular version="3" rows="4" columns="2">
13705 <features tabularvalignment="middle">
13706 <column alignment="center" valignment="top" width="0">
13707 <column alignment="center" valignment="top" width="0">
13709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13712 \begin_layout Plain Layout
13718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13721 \begin_layout Plain Layout
13723 \begin_inset Note Note
13726 \begin_layout Plain Layout
13733 is only used as spacer.
13745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13748 \begin_layout Plain Layout
13752 \begin_inset Formula $\to$
13762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13765 \begin_layout Plain Layout
13766 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13779 \begin_layout Plain Layout
13783 \begin_inset Formula $\to$
13794 \begin_layout Plain Layout
13808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13811 \begin_layout Plain Layout
13812 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13825 \begin_layout Plain Layout
13832 \begin_layout Plain Layout
13844 \begin_inset Formula $\to$
13863 \begin_layout Plain Layout
13877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13880 \begin_layout Plain Layout
13881 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13897 \begin_layout Standard
13904 only colors the box but not the characters in the box.
13905 To color all characters, the whole formula is highlighted and the wanted
13906 color is chosen in the
13909 \begin_inset space ~
13915 The dialog can be called with the toolbar button
13916 \begin_inset Graphics
13917 filename ../images/dialog-show_character.png
13924 Edit\SpecialChar \menuseparator
13926 \begin_inset space ~
13929 Style\SpecialChar \menuseparator
13933 The formula number has then the same color as the formula.
13934 When the formula number should get another color than the formula characters,
13935 the color must be changed within the formula.
13938 \begin_layout Standard
13942 \begin_layout Standard
13945 \begin_inset Formula \begin{equation}
13946 \int A=B\label{eq:red}\end{equation}
13953 \begin_inset Formula \begin{equation}
13954 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13961 \begin_layout Standard
13963 \begin_inset CommandInset ref
13969 is completely colored red.
13970 \begin_inset Newline newline
13974 \begin_inset CommandInset ref
13976 reference "eq:redgreen"
13980 was first completely colored green to set the color for the formula number.
13981 Subsequently the formula characters were colored red.
13984 \begin_layout Standard
13985 \begin_inset VSpace bigskip
13988 To color the frame different than the rest of the box, the command
13995 \begin_inset Index idx
13998 \begin_layout Plain Layout
14006 is used in the following scheme:
14009 \begin_layout Standard
14014 fcolorbox{frame color}{color}{box content}
14017 \begin_layout Standard
14024 is an extension of the command
14031 The frame width is set, like for
14054 \begin_layout Plain Layout
14066 \begin_inset Formula \[
14067 \fcolorbox{cyan}{magenta}{A=B}\]
14075 \begin_layout Plain Layout
14089 \begin_layout Standard
14090 This formula was created with the command
14091 \begin_inset Newline newline
14099 \begin_inset Formula $\to$
14105 \begin_inset Formula $\to$
14115 \begin_layout Standard
14116 \begin_inset VSpace bigskip
14119 To use other colors than the predefined ones, they have to be defined first.
14122 \begin_layout Standard
14123 One can for example define the color
14124 \begin_inset Quotes eld
14132 \begin_inset Quotes erd
14135 with the LaTeX-preamble line:
14138 \begin_layout Standard
14143 definecolor{darkgreen}{cmyk}{0.5,
14158 \begin_inset Index idx
14161 \begin_layout Plain Layout
14172 \begin_layout Standard
14177 is the color space that denotes the colors
14194 The four comma separated numbers are the portion factor for the corresponding
14195 colors of the color space.
14196 The factors can be in the range of 0
14197 \begin_inset space \thinspace{}
14201 \begin_inset space \thinspace{}
14209 also the color space
14213 can be used for definitions.
14230 , so that there are in this case three portion factors for the corresponding
14232 Furthermore there is the color space
14236 with one portion factor for the gray value.
14239 \begin_layout Standard
14240 As example a framed box with the new defined color
14244 where the characters have been colored
14249 \begin_inset Formula \begin{equation}
14250 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14257 \begin_layout Standard
14258 Self-defined colors can also be used for text with the help of the command
14266 \begin_inset Index idx
14269 \begin_layout Plain Layout
14278 \begin_layout Standard
14282 \begin_layout Plain Layout
14286 textcolor{darkgreen}{
14292 \begin_inset Quotes eld
14296 \begin_inset Quotes erd
14303 \begin_layout Plain Layout
14313 \begin_layout Standard
14321 \begin_inset Index idx
14324 \begin_layout Plain Layout
14332 is used in the scheme
14336 textcolor{color}{characters to color}
14341 \begin_layout Subsection
14343 \begin_inset CommandInset label
14345 name "sub:Paragraph-Boxes"
14350 \begin_inset Index idx
14353 \begin_layout Plain Layout
14354 Boxes ! as paragraph
14362 \begin_layout Standard
14363 A box that can contain several lines and paragraphs, a so called paragraph
14364 box (parbox), can be created with the menu
14366 Insert\SpecialChar \menuseparator
14369 or the toolbar button
14370 \begin_inset Graphics
14371 filename ../images/box-insert.png
14379 \begin_layout Standard
14380 The following example shows a framed parbox in a line:
14383 \begin_layout Standard
14384 \begin_inset VSpace medskip
14388 \begin_inset Box Boxed
14398 height_special "totalheight"
14401 \begin_layout Plain Layout
14402 This is a paragraph box.
14404 \begin_inset space \thinspace{}
14407 cm long and can also contain formulas:
14408 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14419 \begin_layout Standard
14420 \begin_inset VSpace medskip
14426 \begin_layout Standard
14427 Such a box is created by right-clicking on the gray box inset.
14428 A dialog pops up showing the box properties.
14442 \begin_inset space \thinspace{}
14447 Vertical Box Alignment
14452 \begin_layout Standard
14453 \begin_inset VSpace medskip
14456 In LaTeX a parbox is created with the command
14463 \begin_inset Index idx
14466 \begin_layout Plain Layout
14474 that has the following scheme:
14477 \begin_layout Standard
14482 parbox[position]{width}{box content}
14485 \begin_layout Standard
14499 for bottom means that the box is aligned within the surrounding text with
14505 for top this is done with the first line.
14506 When no position is given, the box will be vertically centered, see section
14514 \begin_inset space ~
14519 manual for examples.
14522 \begin_layout Standard
14523 \begin_inset VSpace bigskip
14526 To frame formulas completely, including the formula number, the formula
14527 must be set into a parbox.
14528 To do this, the command
14542 is inserted in TeX-mode before the formula.
14550 \begin_inset Index idx
14553 \begin_layout Plain Layout
14561 is hereby the line width set for the document.
14562 Because the frame is outside the parbox, 2
14563 \begin_inset space \thinspace{}
14566 times the frame separation and the frame thickness must be subtracted from
14568 As this is not automatically done by LyX due to a bug
14572 \begin_layout Plain Layout
14573 \begin_inset CommandInset href
14575 name "LyX-bug #4483"
14576 target "http://www.lyx.org/trac/ticket/4483"
14585 , TeX-mode has to be used.
14586 To be able to multiply and subtract in arguments, the LaTeX-package
14594 \begin_layout Plain Layout
14599 is part of every LaTeX standard installation.
14605 \begin_inset Index idx
14608 \begin_layout Plain Layout
14614 must be loaded in the LaTeX-preamble with the line
14617 \begin_layout Standard
14625 \begin_layout Standard
14626 Behind the formula both boxes are closed by entering
14631 Here is an example:
14635 \begin_layout Plain Layout
14649 \begin_layout Standard
14653 \begin_layout Plain Layout
14671 \begin_inset Formula \begin{equation}
14672 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14680 \begin_layout Plain Layout
14691 \begin_layout Plain Layout
14705 \begin_layout Standard
14706 \begin_inset VSpace medskip
14709 As a parbox is used as argument of
14715 , there is in this case no difference between
14730 \begin_layout Standard
14731 \begin_inset VSpace bigskip
14734 Paragraph boxes are very useful to comment formulas directly.
14741 is used in combination with the command
14755 \begin_inset CommandInset ref
14757 reference "sub:User-defined-Numbering"
14764 \begin_layout Standard
14765 An example of a formula commented with
14774 \begin_layout Standard
14778 \begin_layout Plain Layout
14791 This is a description.
14792 It is distinctly separated from the formula and multiline.
14796 \begin_layout Plain Layout
14808 \begin_layout Standard
14809 Such a formula must be inserted completely in TeX-mode because LyX does
14810 not yet support the command
14817 The formula is created with the following command sequence:
14820 \begin_layout Standard
14833 is inserted in TeX-mode.
14837 \begin_layout Plain Layout
14838 When the formula style
14850 can also be replaced by
14857 (formula styles see
14858 \begin_inset CommandInset ref
14860 reference "sec:Formula-Styles"
14869 Then the description follows as normal text and finally
14875 is inserted in TeX-mode.
14888 hereby create a displayed formula.
14891 \begin_layout Standard
14898 can be seen in this example that was
14899 \begin_inset Quotes eld
14903 \begin_inset Quotes erd
14906 using the mathematical textmode:
14907 \begin_inset Formula \[
14908 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14915 \begin_layout Section
14917 \begin_inset Index idx
14920 \begin_layout Plain Layout
14929 \begin_layout Subsection
14931 \begin_inset CommandInset label
14933 name "sub:Big-Operators"
14938 \begin_inset Index idx
14941 \begin_layout Plain Layout
14948 \begin_inset Index idx
14951 \begin_layout Plain Layout
14958 \begin_inset Index idx
14961 \begin_layout Plain Layout
14970 \begin_layout Standard
14971 To be able to use all integral operators listed here, the option
14973 Use esint package automatically
14975 must be set in the document settings under
14978 \begin_inset space ~
14986 \begin_layout Standard
14987 \begin_inset space \hfill{}
14991 \begin_inset Tabular
14992 <lyxtabular version="3" rows="11" columns="2">
14993 <features tabularvalignment="middle">
14994 <column alignment="center" valignment="top" width="0pt">
14995 <column alignment="center" valignment="top" width="0pt">
14997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15000 \begin_layout Plain Layout
15006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15009 \begin_layout Plain Layout
15017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15020 \begin_layout Plain Layout
15024 \begin_inset Index idx
15027 \begin_layout Plain Layout
15040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15043 \begin_layout Plain Layout
15044 \begin_inset Formula $\int$
15054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15057 \begin_layout Plain Layout
15065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15068 \begin_layout Plain Layout
15069 \begin_inset Formula $\oint$
15079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15082 \begin_layout Plain Layout
15090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15093 \begin_layout Plain Layout
15094 \begin_inset Formula $\ointctrclockwise$
15104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15107 \begin_layout Plain Layout
15115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15118 \begin_layout Plain Layout
15119 \begin_inset Formula $\ointclockwise$
15129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15132 \begin_layout Plain Layout
15140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15143 \begin_layout Plain Layout
15144 \begin_inset Formula $\sqint$
15154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15157 \begin_layout Plain Layout
15165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15168 \begin_layout Plain Layout
15170 \begin_inset Formula $\fint$
15180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15183 \begin_layout Plain Layout
15191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15194 \begin_layout Plain Layout
15196 \begin_inset Formula $\landupint$
15206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15209 \begin_layout Plain Layout
15217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15220 \begin_layout Plain Layout
15222 \begin_inset Formula $\landdownint$
15232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15235 \begin_layout Plain Layout
15243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15246 \begin_layout Plain Layout
15247 \begin_inset Formula $\bigcap$
15257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15260 \begin_layout Plain Layout
15268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15271 \begin_layout Plain Layout
15272 \begin_inset Formula $\bigcup$
15286 \begin_inset space \hfill{}
15290 \begin_inset Tabular
15291 <lyxtabular version="3" rows="11" columns="2">
15292 <features tabularvalignment="middle">
15293 <column alignment="center" valignment="top" width="0pt">
15294 <column alignment="center" valignment="top" width="0pt">
15296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15299 \begin_layout Plain Layout
15305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15308 \begin_layout Plain Layout
15316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15319 \begin_layout Plain Layout
15323 \begin_inset Index idx
15326 \begin_layout Plain Layout
15339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15342 \begin_layout Plain Layout
15343 \begin_inset Formula $\sum$
15353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15356 \begin_layout Plain Layout
15360 \begin_inset Index idx
15363 \begin_layout Plain Layout
15376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15379 \begin_layout Plain Layout
15380 \begin_inset Formula $\prod$
15390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15393 \begin_layout Plain Layout
15401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15404 \begin_layout Plain Layout
15405 \begin_inset Formula $\coprod$
15415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15418 \begin_layout Plain Layout
15426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15429 \begin_layout Plain Layout
15430 \begin_inset Formula $\bigodot$
15440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15443 \begin_layout Plain Layout
15451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15454 \begin_layout Plain Layout
15455 \begin_inset Formula $\bigotimes$
15465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15468 \begin_layout Plain Layout
15476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15479 \begin_layout Plain Layout
15480 \begin_inset Formula $\bigoplus$
15490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15493 \begin_layout Plain Layout
15501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15504 \begin_layout Plain Layout
15505 \begin_inset Formula $\bigwedge$
15515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15518 \begin_layout Plain Layout
15526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15529 \begin_layout Plain Layout
15530 \begin_inset Formula $\bigvee$
15540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15543 \begin_layout Plain Layout
15551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15554 \begin_layout Plain Layout
15555 \begin_inset Formula $\bigsqcup$
15565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15568 \begin_layout Plain Layout
15576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15579 \begin_layout Plain Layout
15580 \begin_inset Formula $\biguplus$
15594 \begin_inset space \hfill{}
15600 \begin_layout Standard
15601 All big operators can also be inserted via the math toolbar button
15602 \begin_inset Graphics
15603 filename ../images/math/intop.png
15611 \begin_layout Standard
15612 The operators are called big because they are bigger than the sometimes
15613 equal looking binary operators.
15614 All big operators can have limits as described in the next subsection.
15617 \begin_layout Standard
15618 For all integral operators there is a second version available, ending on
15636 These operators are different from
15643 \begin_inset space \space{}
15646 in the style the operator limits are displayed, see
15647 \begin_inset CommandInset ref
15649 reference "sub:Operator-Limits"
15657 \begin_layout Subsubsection*
15658 Advice for Integrals
15661 \begin_layout Standard
15666 in an integral is an operator, that therefore has to be set upright.
15667 This is done by highlighting the
15671 and using the keyboard shortcut
15681 \begin_layout Plain Layout
15687 \begin_inset CommandInset ref
15689 reference "sub:Font-Styles"
15699 Finally the smallest space is inserted before the
15703 , as this is usual for operators.
15707 \begin_layout Standard
15709 \begin_inset Formula $\int A(x)dx$
15713 \begin_inset Newline newline
15717 \begin_inset Phantom HPhantom
15720 \begin_layout Plain Layout
15727 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15733 \begin_layout Standard
15734 For multiple integrals there are the following commands:
15735 \begin_inset VSpace medskip
15741 \begin_layout Standard
15742 \begin_inset space \hfill{}
15746 \begin_inset Tabular
15747 <lyxtabular version="3" rows="4" columns="2">
15748 <features tabularvalignment="middle">
15749 <column alignment="center" valignment="top" width="0">
15750 <column alignment="center" valignment="top" width="0">
15752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15755 \begin_layout Plain Layout
15761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15764 \begin_layout Plain Layout
15766 \begin_inset Note Note
15769 \begin_layout Plain Layout
15776 is only used as spacer.
15788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15791 \begin_layout Plain Layout
15799 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15802 \begin_layout Plain Layout
15803 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15816 \begin_layout Plain Layout
15824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15827 \begin_layout Plain Layout
15828 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15841 \begin_layout Plain Layout
15849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15852 \begin_layout Plain Layout
15853 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15867 \begin_inset space \hfill{}
15871 \begin_inset Tabular
15872 <lyxtabular version="3" rows="4" columns="2">
15873 <features tabularvalignment="middle">
15874 <column alignment="center" valignment="top" width="0">
15875 <column alignment="center" valignment="top" width="0">
15877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15880 \begin_layout Plain Layout
15886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15889 \begin_layout Plain Layout
15897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15900 \begin_layout Plain Layout
15908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15911 \begin_layout Plain Layout
15912 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15925 \begin_layout Plain Layout
15933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15936 \begin_layout Plain Layout
15937 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15950 \begin_layout Plain Layout
15958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15961 \begin_layout Plain Layout
15962 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15976 \begin_inset space \hfill{}
15982 \begin_layout Subsection
15984 \begin_inset CommandInset label
15986 name "sub:Operator-Limits"
15991 \begin_inset Index idx
15994 \begin_layout Plain Layout
16003 \begin_layout Standard
16004 Limits are created by super- and subscripts:
16007 \begin_layout Standard
16009 \begin_inset Tabular
16010 <lyxtabular version="3" rows="2" columns="2">
16011 <features tabularvalignment="middle">
16012 <column alignment="center" valignment="top" width="0pt">
16013 <column alignment="center" valignment="top" width="0pt">
16015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16018 \begin_layout Plain Layout
16024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16027 \begin_layout Plain Layout
16029 \begin_inset Note Note
16032 \begin_layout Plain Layout
16039 is only used as spacer.
16051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16054 \begin_layout Plain Layout
16063 \begin_layout Plain Layout
16073 \begin_inset Formula $\to$
16077 \begin_inset Formula $\to$
16085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16088 \begin_layout Plain Layout
16089 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16105 \begin_layout Standard
16106 Limits of inline formulas are set right beside the operator.
16107 Limits in displayed formulas are set above or below the operator, except
16108 for integral limits.
16111 \begin_layout Standard
16112 To force that the limits are set beside the operator, the cursor is set
16113 directly behind the operator and the limits type is changed with the menu
16116 Edit\SpecialChar \menuseparator
16117 Math\SpecialChar \menuseparator
16136 \begin_layout Standard
16137 The default limits type is this:
16138 \begin_inset Formula \[
16139 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16143 This is how it looks when the limits type was changed to
16150 \begin_inset Formula \[
16151 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16155 For integrals, except those ending with
16171 etc., the limits are by default set beside the operator.
16172 But for multiple integrals the limits are often set below the operator.
16173 In the following example the limits type was therefore set to
16177 and so set below the integrals:
16178 \begin_inset Formula \begin{equation}
16179 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16186 \begin_layout Standard
16187 \begin_inset VSpace medskip
16190 To specify conditions for limits, the commands
16197 \begin_inset Index idx
16200 \begin_layout Plain Layout
16215 \begin_inset Index idx
16218 \begin_layout Plain Layout
16227 To create for example this expression
16228 \begin_inset Formula \begin{equation}
16229 \sum_{\begin{subarray}{c}
16233 \end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16240 \begin_layout Standard
16241 the following has to be done:
16242 \begin_inset Newline newline
16257 \begin_layout Plain Layout
16269 One is now in a blue box under the summation operator and insert there
16278 \begin_layout Plain Layout
16290 The blue box is now within a purple box and now several lines can be written
16292 A new line is created by inserting a line break (
16295 arg "newline-insert newline"
16300 \begin_inset Newline newline
16305 0<k<1000 Ctrl+Return
16306 \begin_inset Newline newline
16311 is typed in, a new box appears below for the new line.
16314 \begin_layout Standard
16315 The alignment of the lines can be changed to left aligned with the
16325 Edit\SpecialChar \menuseparator
16329 To get right alignment,
16337 \begin_layout Plain Layout
16348 is inserted at the beginning of the line.
16351 \begin_layout Standard
16364 with the difference that the lines are always centered.
16367 \begin_layout Standard
16368 \begin_inset VSpace bigskip
16372 \begin_inset CommandInset ref
16374 reference "eq:substack"
16378 there can be too much space beside an operator, because the characters
16379 following the operator are set beside the limits.
16382 \begin_layout Standard
16383 To avoid this, the following macro can be used in the LaTeX-preamble:
16386 \begin_layout Standard
16400 \begin_inset Newline newline
16412 \begin_inset Newline newline
16419 mathclapinternal #1#2{
16423 mathsurround =0pt #1{#2}$}}
16426 \begin_layout Standard
16427 This defines the command
16434 \begin_inset Index idx
16437 \begin_layout Plain Layout
16445 that sets the width of the limit to 0
16446 \begin_inset space \thinspace{}
16450 The command scheme is
16453 \begin_layout Standard
16461 \begin_layout Standard
16462 where the limit can consist of several conditions.
16465 \begin_layout Standard
16467 \begin_inset CommandInset ref
16469 reference "eq:substack"
16473 , one uses the command
16476 \begin_layout Standard
16489 \begin_layout Plain Layout
16498 0<k<1000 Ctrl+Return
16501 \begin_layout Standard
16502 to create the lower limit.
16503 The summand is now directly behind the summation operator:
16504 \begin_inset Formula \[
16505 \sum_{\mathclap{\substack{0<k<1000\\
16516 \begin_layout Standard
16517 \begin_inset VSpace bigskip
16520 How to use one limit for several operators is described in
16521 \begin_inset CommandInset ref
16523 reference "sub:Self-defined-Operators"
16530 \begin_layout Subsection
16532 \begin_inset CommandInset label
16534 name "sub:Binary-Operators"
16539 \begin_inset Index idx
16542 \begin_layout Plain Layout
16551 \begin_layout Standard
16552 Binary operators are surrounded by space when there is a character before
16554 \begin_inset VSpace medskip
16560 \begin_layout Standard
16561 \begin_inset space \hfill{}
16565 \begin_inset Tabular
16566 <lyxtabular version="3" rows="13" columns="2">
16567 <features tabularvalignment="middle">
16568 <column alignment="center" valignment="top" width="0pt">
16569 <column alignment="center" valignment="top" width="0pt">
16571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16574 \begin_layout Plain Layout
16576 \begin_inset Note Note
16579 \begin_layout Plain Layout
16586 is only used as spacer.
16596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16599 \begin_layout Plain Layout
16607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16610 \begin_layout Plain Layout
16616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16619 \begin_layout Plain Layout
16620 \begin_inset Formula $+$
16630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16633 \begin_layout Plain Layout
16639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16642 \begin_layout Plain Layout
16643 \begin_inset Formula $-$
16653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16656 \begin_layout Plain Layout
16664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16667 \begin_layout Plain Layout
16668 \begin_inset Formula $\pm$
16678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16681 \begin_layout Plain Layout
16689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16692 \begin_layout Plain Layout
16693 \begin_inset Formula $\mp$
16703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16706 \begin_layout Plain Layout
16714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16717 \begin_layout Plain Layout
16718 \begin_inset Formula $\cdot$
16728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16731 \begin_layout Plain Layout
16739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16742 \begin_layout Plain Layout
16743 \begin_inset Formula $\times$
16753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16756 \begin_layout Plain Layout
16764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16767 \begin_layout Plain Layout
16768 \begin_inset Formula $\div$
16778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16781 \begin_layout Plain Layout
16785 \begin_layout Plain Layout
16798 \begin_layout Plain Layout
16810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16813 \begin_layout Plain Layout
16814 \begin_inset Formula $*$
16824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16827 \begin_layout Plain Layout
16835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16838 \begin_layout Plain Layout
16839 \begin_inset Formula $\star$
16849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16852 \begin_layout Plain Layout
16860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16863 \begin_layout Plain Layout
16864 \begin_inset Formula $\circ$
16874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16877 \begin_layout Plain Layout
16885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16888 \begin_layout Plain Layout
16889 \begin_inset Formula $\diamond$
16899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16902 \begin_layout Plain Layout
16910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16913 \begin_layout Plain Layout
16914 \begin_inset Formula $\bullet$
16928 \begin_inset space \hfill{}
16932 \begin_inset Tabular
16933 <lyxtabular version="3" rows="13" columns="2">
16934 <features tabularvalignment="middle">
16935 <column alignment="center" valignment="top" width="0pt">
16936 <column alignment="center" valignment="top" width="0pt">
16938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16941 \begin_layout Plain Layout
16947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16950 \begin_layout Plain Layout
16958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16961 \begin_layout Plain Layout
16969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16972 \begin_layout Plain Layout
16973 \begin_inset Formula $\nabla$
16983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16986 \begin_layout Plain Layout
16994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16997 \begin_layout Plain Layout
16998 \begin_inset Formula $\bigtriangledown$
17008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17011 \begin_layout Plain Layout
17019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17022 \begin_layout Plain Layout
17023 \begin_inset Formula $\bigtriangleup$
17033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17036 \begin_layout Plain Layout
17044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17047 \begin_layout Plain Layout
17048 \begin_inset Formula $\Box$
17058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17061 \begin_layout Plain Layout
17069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17072 \begin_layout Plain Layout
17073 \begin_inset Formula $\cap$
17083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17086 \begin_layout Plain Layout
17094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17097 \begin_layout Plain Layout
17098 \begin_inset Formula $\cup$
17108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17111 \begin_layout Plain Layout
17119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17122 \begin_layout Plain Layout
17123 \begin_inset Formula $\dagger$
17133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17136 \begin_layout Plain Layout
17144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17147 \begin_layout Plain Layout
17148 \begin_inset Formula $\ddagger$
17158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17161 \begin_layout Plain Layout
17169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17172 \begin_layout Plain Layout
17173 \begin_inset Formula $\wr$
17183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17186 \begin_layout Plain Layout
17194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17197 \begin_layout Plain Layout
17198 \begin_inset Formula $\bigcirc$
17208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17211 \begin_layout Plain Layout
17219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17222 \begin_layout Plain Layout
17223 \begin_inset Formula $\wedge$
17233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17236 \begin_layout Plain Layout
17244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17247 \begin_layout Plain Layout
17248 \begin_inset Formula $\vee$
17262 \begin_inset space \hfill{}
17266 \begin_inset Tabular
17267 <lyxtabular version="3" rows="13" columns="2">
17268 <features tabularvalignment="middle">
17269 <column alignment="center" valignment="top" width="0pt">
17270 <column alignment="center" valignment="top" width="0pt">
17272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17275 \begin_layout Plain Layout
17281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17284 \begin_layout Plain Layout
17292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17295 \begin_layout Plain Layout
17303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17306 \begin_layout Plain Layout
17307 \begin_inset Formula $\oplus$
17317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17320 \begin_layout Plain Layout
17328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17331 \begin_layout Plain Layout
17332 \begin_inset Formula $\ominus$
17342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17345 \begin_layout Plain Layout
17353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17356 \begin_layout Plain Layout
17357 \begin_inset Formula $\otimes$
17367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17370 \begin_layout Plain Layout
17378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17381 \begin_layout Plain Layout
17382 \begin_inset Formula $\oslash$
17392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17395 \begin_layout Plain Layout
17403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17406 \begin_layout Plain Layout
17407 \begin_inset Formula $\odot$
17417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17420 \begin_layout Plain Layout
17428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17431 \begin_layout Plain Layout
17432 \begin_inset Formula $\amalg$
17442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17445 \begin_layout Plain Layout
17453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17456 \begin_layout Plain Layout
17457 \begin_inset Formula $\uplus$
17467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17470 \begin_layout Plain Layout
17478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17481 \begin_layout Plain Layout
17482 \begin_inset Formula $\setminus$
17492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17495 \begin_layout Plain Layout
17503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17506 \begin_layout Plain Layout
17507 \begin_inset Formula $\sqcap$
17517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17520 \begin_layout Plain Layout
17528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17531 \begin_layout Plain Layout
17532 \begin_inset Formula $\sqcup$
17542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17545 \begin_layout Plain Layout
17553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17556 \begin_layout Plain Layout
17557 \begin_inset Formula $\triangleleft$
17567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17570 \begin_layout Plain Layout
17578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17581 \begin_layout Plain Layout
17582 \begin_inset Formula $\triangleright$
17596 \begin_inset space \hfill{}
17602 \begin_layout Standard
17603 All binary operators can also be inserted via the math toolbar button
17604 \begin_inset Graphics
17605 filename ../images/math/pm.png
17613 \begin_layout Standard
17614 To typeset the Laplace operator also
17631 \begin_inset Formula $\nabla^{2}$
17634 ) can be used instead of
17643 \begin_layout Standard
17650 Insert\SpecialChar \menuseparator
17662 \begin_layout Subsection
17663 Self-defined Operators
17664 \begin_inset CommandInset label
17666 name "sub:Self-defined-Operators"
17671 \begin_inset Index idx
17674 \begin_layout Plain Layout
17675 Operators ! self-defined
17683 \begin_layout Standard
17684 With the help of the command
17688 DeclareMathOperator
17691 \begin_inset Index idx
17694 \begin_layout Plain Layout
17699 DeclareMathOperator
17704 custom operators can be defined in the LaTeX-preamble.
17705 Its command scheme is:
17708 \begin_layout Standard
17713 DeclareMathOperator{new command}{display}
17716 \begin_layout Standard
17717 Display can be characters or symbols that define how the operator looks
17719 To define a big operator a * is set behind the command.
17720 All self-defined big operators can have limits as described in
17721 \begin_inset CommandInset ref
17723 reference "sub:Operator-Limits"
17730 \begin_layout Standard
17731 For example the LaTeX-preamble line
17734 \begin_layout Standard
17739 DeclareMathOperator*{
17746 \begin_layout Standard
17747 defines the command
17753 , that inserts a big operator consisting of the lozenge symbol from
17754 \begin_inset CommandInset ref
17756 reference "sub:Miscellaneous-Symbols"
17761 \begin_inset Formula \[
17762 \Lozenge_{n=1}^{\infty}\]
17766 The command for this formula is:
17777 \begin_inset Formula $\to$
17783 \begin_layout Standard
17784 \begin_inset VSpace bigskip
17787 When self-defined operators are not used several times in the document,
17788 they can also be defined with the commands
17795 \begin_inset Index idx
17798 \begin_layout Plain Layout
17813 \begin_inset Index idx
17816 \begin_layout Plain Layout
17824 , which have the following scheme:
17827 \begin_layout Standard
17841 \begin_layout Standard
17848 defines big operators,
17857 \begin_layout Standard
17865 \begin_inset space \thinspace{}
17869 \begin_inset space \space{}
17872 be used to use one limit for several operators:
17875 \begin_layout Standard
17876 \begin_inset Formula \[
17877 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17884 \begin_layout Standard
17885 The command for the formula above is:
17886 \begin_inset Newline newline
17905 \begin_layout Plain Layout
17917 \begin_inset Formula $\to$
17926 \begin_layout Plain Layout
17940 \begin_layout Section
17942 \begin_inset Index idx
17945 \begin_layout Plain Layout
17954 \begin_layout Subsection
17956 \begin_inset CommandInset label
17958 name "sub:Font-Styles"
17963 \begin_inset Index idx
17966 \begin_layout Plain Layout
17975 \begin_layout Standard
17976 Latin letters in formulas can be set in one of the following font styles:
17977 \begin_inset VSpace -2mm
17983 \begin_layout Standard
17985 \begin_inset Tabular
17986 <lyxtabular version="3" rows="6" columns="3">
17987 <features tabularvalignment="middle">
17988 <column alignment="center" valignment="top" width="0">
17989 <column alignment="center" valignment="top" width="0">
17990 <column alignment="center" valignment="top" width="0">
17992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17995 \begin_layout Plain Layout
18001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18004 \begin_layout Plain Layout
18010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18013 \begin_layout Plain Layout
18021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18024 \begin_layout Plain Layout
18033 \begin_layout Plain Layout
18049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18052 \begin_layout Plain Layout
18053 \begin_inset Formula $\mathbb{ABC}$
18061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18064 \begin_layout Plain Layout
18077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18080 \begin_layout Plain Layout
18089 \begin_layout Plain Layout
18105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18108 \begin_layout Plain Layout
18109 \begin_inset Formula $\mathbf{AbC}$
18117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18120 \begin_layout Plain Layout
18133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18136 \begin_layout Plain Layout
18145 \begin_layout Plain Layout
18161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18164 \begin_layout Plain Layout
18165 \begin_inset Formula $\boldsymbol{AbC}$
18173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18176 \begin_layout Plain Layout
18179 arg "font-boldsymbol"
18189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18192 \begin_layout Plain Layout
18201 \begin_layout Plain Layout
18217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18220 \begin_layout Plain Layout
18221 \begin_inset Formula $\mathcal{ABC}$
18229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18232 \begin_layout Plain Layout
18245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18248 \begin_layout Plain Layout
18257 \begin_layout Plain Layout
18273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18276 \begin_layout Plain Layout
18277 \begin_inset Formula $\mathfrak{AbC}$
18285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18288 \begin_layout Plain Layout
18302 \begin_layout Standard
18304 \begin_inset Tabular
18305 <lyxtabular version="3" rows="5" columns="3">
18306 <features tabularvalignment="middle">
18307 <column alignment="center" valignment="top" width="0">
18308 <column alignment="center" valignment="top" width="0">
18309 <column alignment="center" valignment="top" width="0">
18311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18314 \begin_layout Plain Layout
18320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18323 \begin_layout Plain Layout
18329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18332 \begin_layout Plain Layout
18340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18343 \begin_layout Plain Layout
18352 \begin_layout Plain Layout
18368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18371 \begin_layout Plain Layout
18372 \begin_inset Formula $\mathit{AbC}$
18380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18383 \begin_layout Plain Layout
18391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18394 \begin_layout Plain Layout
18403 \begin_layout Plain Layout
18419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18422 \begin_layout Plain Layout
18423 \begin_inset Formula $\mathrm{AbC}$
18431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18434 \begin_layout Plain Layout
18447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18450 \begin_layout Plain Layout
18459 \begin_layout Plain Layout
18475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18478 \begin_layout Plain Layout
18479 \begin_inset Formula $\mathsf{AbC}$
18487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18490 \begin_layout Plain Layout
18503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18506 \begin_layout Plain Layout
18515 \begin_layout Plain Layout
18531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18534 \begin_layout Plain Layout
18535 \begin_inset Formula $\mathtt{AbC}$
18543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18546 \begin_layout Plain Layout
18549 arg "font-typewriter"
18565 \begin_layout Standard
18566 \begin_inset Note Greyedout
18569 \begin_layout Plain Layout
18586 can only be used for big letters.
18594 \begin_layout Standard
18595 Predefined is the style
18604 \begin_layout Standard
18605 The style commands work also for letters in mathematical constructs:
18606 \begin_inset Formula \[
18607 \mathfrak{A=\frac{b}{C}}\]
18614 \begin_layout Standard
18615 Characters in mathematical text don't appear in a math font style but in
18616 the text font style
18623 That their style can't be set correctly via the text style dialog is a
18628 \begin_layout Plain Layout
18629 \begin_inset CommandInset href
18631 name "LyX-bug #4629"
18632 target "http://www.lyx.org/trac/ticket/4629"
18644 \begin_layout Standard
18645 Instead of the style commands the dialog
18647 Edit\SpecialChar \menuseparator
18648 Math\SpecialChar \menuseparator
18651 or the toolbar button
18652 \begin_inset Graphics
18653 filename ../images/math/font.png
18661 \begin_layout Subsection
18663 \begin_inset CommandInset label
18665 name "sub:Bold-Formulas"
18670 \begin_inset Index idx
18673 \begin_layout Plain Layout
18682 \begin_layout Standard
18683 To make a complete formula bold, the command
18689 from the previous subsection cannot be used, because it doesn't work for
18690 small Greek letters.
18691 Furthermore it prints Latin letters always upright, like in the following
18695 \begin_layout Standard
18696 \begin_inset Formula \[
18697 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18704 \begin_layout Standard
18705 To display the formula correctly, the command
18712 \begin_inset Formula \[
18713 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18717 It is also possible to set the formula in a
18719 boldmath environment
18722 This environment is created by inserting the command
18729 \begin_inset Index idx
18732 \begin_layout Plain Layout
18741 To end the environment, the command
18748 \begin_inset Index idx
18751 \begin_layout Plain Layout
18759 is inserted in TeX-mode.
18763 \begin_layout Plain Layout
18773 \begin_inset Formula \[
18774 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18782 \begin_layout Plain Layout
18794 \begin_layout Subsection
18796 \begin_inset Index idx
18799 \begin_layout Plain Layout
18808 \begin_layout Standard
18809 Formulas can be colored like normal text: Highlight a formula or a formula
18815 Here is a formula in magenta:
18816 \begin_inset Formula \[
18817 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18824 \begin_layout Standard
18825 You can also define your own colors as described in
18826 \begin_inset CommandInset ref
18828 reference "sub:Colored-Boxes"
18833 They can be used with the TeX code command
18840 \begin_inset Index idx
18843 \begin_layout Plain Layout
18854 \begin_layout Standard
18859 textcolor{color}{characters or formula}
18862 \begin_layout Standard
18863 The following example was colored completely dark green and partly red:
18866 \begin_layout Standard
18870 \begin_layout Plain Layout
18874 textcolor{darkgreen}{
18880 \begin_inset Formula \[
18881 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18889 \begin_layout Plain Layout
18899 \begin_layout Standard
18900 Due to a bug in LyX only complete formulas can be colored with self-defined
18905 \begin_layout Plain Layout
18906 \begin_inset CommandInset href
18908 name "LyX-bug #5269"
18909 target "http://www.lyx.org/trac/ticket/5269"
18921 \begin_layout Subsection
18923 \begin_inset CommandInset label
18925 name "sub:Font-Sizes"
18930 \begin_inset Index idx
18933 \begin_layout Plain Layout
18942 \begin_layout Standard
18943 For characters in formulas there are, analog to characters in text, the
18944 following size commands:
18947 \begin_layout Standard
18991 \begin_inset Newline newline
19013 \begin_layout Standard
19014 The size produced by the commands depends on the document font size, that
19015 corresponds with the command
19022 The other commands produce smaller or larger sizes than
19029 The font size can however not exceed a certain value.
19030 Is for example the document font size 12
19031 \begin_inset space \thinspace{}
19040 switches to the same size as
19050 \begin_layout Standard
19051 A size command is inserted in TeX-mode before the formula and sets the size
19052 for all following formula and text characters.
19053 To switch back to the initial size, the command
19059 is inserted behind the formula in TeX-mode.
19062 \begin_layout Standard
19063 \begin_inset Newpage newpage
19069 \begin_layout Standard
19070 Within a formula the size can be changed using the following size commands:
19073 \begin_layout Standard
19076 \begin_inset Tabular
19077 <lyxtabular version="3" rows="5" columns="2">
19078 <features tabularvalignment="middle">
19079 <column alignment="center" valignment="top" width="0">
19080 <column alignment="center" valignment="top" width="0">
19082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19085 \begin_layout Plain Layout
19091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19094 \begin_layout Plain Layout
19096 \begin_inset Note Note
19099 \begin_layout Plain Layout
19106 is only used as spacer.
19118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19121 \begin_layout Plain Layout
19125 \begin_inset Index idx
19128 \begin_layout Plain Layout
19141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19144 \begin_layout Plain Layout
19145 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19158 \begin_layout Plain Layout
19166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19169 \begin_layout Plain Layout
19170 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19183 \begin_layout Plain Layout
19191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19194 \begin_layout Plain Layout
19195 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19208 \begin_layout Plain Layout
19216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19219 \begin_layout Plain Layout
19220 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19236 \begin_layout Standard
19237 After entering these commands, a blue box appears in which the formula parts
19241 \begin_layout Standard
19242 There is a further method to change the font size, that though only works
19243 for symbols or letters in mathematical text.
19244 To use it, one of the above text size commands is inserted in mathematical
19246 All following characters until the end of the mathematical text or until
19247 another size command will have the selected size.
19249 \begin_inset VSpace -2mm
19255 \begin_layout Standard
19259 \begin_layout Plain Layout
19269 \begin_inset Formula \[
19270 A=\frac{B}{c}\cdot\maltese\]
19275 \begin_inset Formula \[
19276 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
19284 \begin_layout Plain Layout
19296 \begin_layout Standard
19297 \begin_inset VSpace medskip
19300 Before both formulas the command
19307 The command for the second formula is:
19308 \begin_inset Newline newline
19319 \begin_layout Plain Layout
19334 \begin_layout Plain Layout
19349 \begin_layout Plain Layout
19364 \begin_layout Plain Layout
19374 \begin_inset Formula $\to$
19378 \begin_inset Formula $\to$
19382 \begin_inset Newline newline
19386 \begin_inset space \hspace*{}
19400 \begin_layout Plain Layout
19415 \begin_layout Plain Layout
19430 \begin_layout Plain Layout
19442 \begin_layout Standard
19443 If a symbol cannot be displayed in different sizes, it will always be displayed
19444 in the default size.
19447 \begin_layout Standard
19448 \begin_inset Newpage newpage
19454 \begin_layout Section
19456 \begin_inset Index idx
19459 \begin_layout Plain Layout
19468 \begin_layout Standard
19469 All Greek letters can also be inserted via the toolbar button
19470 \begin_inset Graphics
19471 filename ../images/math/alpha.png
19479 \begin_layout Subsection
19481 \begin_inset Index idx
19484 \begin_layout Plain Layout
19485 Greek letters ! small
19493 \begin_layout Standard
19494 \begin_inset space \hfill{}
19498 \begin_inset Tabular
19499 <lyxtabular version="3" rows="11" columns="2">
19500 <features tabularvalignment="middle">
19501 <column alignment="center" valignment="top" width="0pt">
19502 <column alignment="center" valignment="top" width="0pt">
19504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19507 \begin_layout Plain Layout
19513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19516 \begin_layout Plain Layout
19524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19527 \begin_layout Plain Layout
19535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19538 \begin_layout Plain Layout
19539 \begin_inset Formula $\alpha$
19549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19552 \begin_layout Plain Layout
19560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19563 \begin_layout Plain Layout
19564 \begin_inset Formula $\beta$
19574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19577 \begin_layout Plain Layout
19585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19588 \begin_layout Plain Layout
19589 \begin_inset Formula $\gamma$
19599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19602 \begin_layout Plain Layout
19610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19613 \begin_layout Plain Layout
19614 \begin_inset Formula $\delta$
19624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19627 \begin_layout Plain Layout
19635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19638 \begin_layout Plain Layout
19639 \begin_inset Formula $\epsilon$
19649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19652 \begin_layout Plain Layout
19660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19663 \begin_layout Plain Layout
19664 \begin_inset Formula $\varepsilon$
19674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19677 \begin_layout Plain Layout
19685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19688 \begin_layout Plain Layout
19689 \begin_inset Formula $\zeta$
19699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19702 \begin_layout Plain Layout
19710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19713 \begin_layout Plain Layout
19714 \begin_inset Formula $\eta$
19724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19727 \begin_layout Plain Layout
19735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19738 \begin_layout Plain Layout
19739 \begin_inset Formula $\theta$
19749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19752 \begin_layout Plain Layout
19760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19763 \begin_layout Plain Layout
19764 \begin_inset Formula $\vartheta$
19778 \begin_inset space \hfill{}
19782 \begin_inset Tabular
19783 <lyxtabular version="3" rows="12" columns="2">
19784 <features tabularvalignment="middle">
19785 <column alignment="center" valignment="top" width="0pt">
19786 <column alignment="center" valignment="top" width="0pt">
19788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19791 \begin_layout Plain Layout
19797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19800 \begin_layout Plain Layout
19808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19811 \begin_layout Plain Layout
19819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19822 \begin_layout Plain Layout
19823 \begin_inset Formula $\iota$
19833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19836 \begin_layout Plain Layout
19844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19847 \begin_layout Plain Layout
19848 \begin_inset Formula $\kappa$
19858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19861 \begin_layout Plain Layout
19869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19872 \begin_layout Plain Layout
19873 \begin_inset Formula $\varkappa$
19883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19886 \begin_layout Plain Layout
19894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19897 \begin_layout Plain Layout
19898 \begin_inset Formula $\lambda$
19908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19911 \begin_layout Plain Layout
19919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19922 \begin_layout Plain Layout
19923 \begin_inset Formula $\mu$
19933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19936 \begin_layout Plain Layout
19944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19947 \begin_layout Plain Layout
19948 \begin_inset Formula $\nu$
19958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19961 \begin_layout Plain Layout
19969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19972 \begin_layout Plain Layout
19973 \begin_inset Formula $\xi$
19983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19986 \begin_layout Plain Layout
19992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19995 \begin_layout Plain Layout
19996 \begin_inset Formula $o$
20006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20009 \begin_layout Plain Layout
20017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20020 \begin_layout Plain Layout
20021 \begin_inset Formula $\pi$
20031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20034 \begin_layout Plain Layout
20042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20045 \begin_layout Plain Layout
20046 \begin_inset Formula $\varpi$
20056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20059 \begin_layout Plain Layout
20067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20070 \begin_layout Plain Layout
20071 \begin_inset Formula $\rho$
20085 \begin_inset space \hfill{}
20089 \begin_inset Tabular
20090 <lyxtabular version="3" rows="11" columns="2">
20091 <features tabularvalignment="middle">
20092 <column alignment="center" valignment="top" width="0pt">
20093 <column alignment="center" valignment="top" width="0pt">
20095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20098 \begin_layout Plain Layout
20104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20107 \begin_layout Plain Layout
20115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20118 \begin_layout Plain Layout
20126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20129 \begin_layout Plain Layout
20130 \begin_inset Formula $\varrho$
20140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20143 \begin_layout Plain Layout
20151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20154 \begin_layout Plain Layout
20155 \begin_inset Formula $\sigma$
20165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20168 \begin_layout Plain Layout
20176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20179 \begin_layout Plain Layout
20180 \begin_inset Formula $\varsigma$
20190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20193 \begin_layout Plain Layout
20201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20204 \begin_layout Plain Layout
20205 \begin_inset Formula $\tau$
20215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20218 \begin_layout Plain Layout
20226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20229 \begin_layout Plain Layout
20230 \begin_inset Formula $\upsilon$
20240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20243 \begin_layout Plain Layout
20251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20254 \begin_layout Plain Layout
20255 \begin_inset Formula $\phi$
20265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20268 \begin_layout Plain Layout
20276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20279 \begin_layout Plain Layout
20280 \begin_inset Formula $\varphi$
20290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20293 \begin_layout Plain Layout
20301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20304 \begin_layout Plain Layout
20305 \begin_inset Formula $\chi$
20315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20318 \begin_layout Plain Layout
20326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20329 \begin_layout Plain Layout
20330 \begin_inset Formula $\psi$
20340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20343 \begin_layout Plain Layout
20351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20354 \begin_layout Plain Layout
20355 \begin_inset Formula $\omega$
20369 \begin_inset space \hfill{}
20375 \begin_layout Standard
20376 \begin_inset VSpace medskip
20382 \begin_layout Standard
20383 How to create upright Greek letters is explained in
20384 \begin_inset CommandInset ref
20386 reference "sub:Upright-small-Greek"
20393 \begin_layout Subsection
20395 \begin_inset Index idx
20398 \begin_layout Plain Layout
20399 Greek letters ! big
20407 \begin_layout Standard
20408 \begin_inset space \hfill{}
20412 \begin_inset Tabular
20413 <lyxtabular version="3" rows="7" columns="2">
20414 <features tabularvalignment="middle">
20415 <column alignment="center" valignment="top" width="0pt">
20416 <column alignment="center" valignment="top" width="0pt">
20418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20421 \begin_layout Plain Layout
20427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20430 \begin_layout Plain Layout
20438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20441 \begin_layout Plain Layout
20449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20452 \begin_layout Plain Layout
20453 \begin_inset Formula $\Gamma$
20463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20466 \begin_layout Plain Layout
20474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20477 \begin_layout Plain Layout
20478 \begin_inset Formula $\Delta$
20488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20491 \begin_layout Plain Layout
20499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20502 \begin_layout Plain Layout
20503 \begin_inset Formula $\Theta$
20513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20516 \begin_layout Plain Layout
20524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20527 \begin_layout Plain Layout
20528 \begin_inset Formula $\Lambda$
20538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20541 \begin_layout Plain Layout
20549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20552 \begin_layout Plain Layout
20553 \begin_inset Formula $\Xi$
20563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20566 \begin_layout Plain Layout
20574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20577 \begin_layout Plain Layout
20578 \begin_inset Formula $\Pi$
20592 \begin_inset space \hfill{}
20596 \begin_inset Tabular
20597 <lyxtabular version="3" rows="6" columns="2">
20598 <features tabularvalignment="middle">
20599 <column alignment="center" valignment="top" width="0pt">
20600 <column alignment="center" valignment="top" width="0pt">
20602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20605 \begin_layout Plain Layout
20611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20614 \begin_layout Plain Layout
20622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20625 \begin_layout Plain Layout
20633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20636 \begin_layout Plain Layout
20637 \begin_inset Formula $\Sigma$
20647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20650 \begin_layout Plain Layout
20658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20661 \begin_layout Plain Layout
20662 \begin_inset Formula $\Upsilon$
20672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20675 \begin_layout Plain Layout
20683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20686 \begin_layout Plain Layout
20687 \begin_inset Formula $\Phi$
20697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20700 \begin_layout Plain Layout
20708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20711 \begin_layout Plain Layout
20712 \begin_inset Formula $\Psi$
20722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20725 \begin_layout Plain Layout
20733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20736 \begin_layout Plain Layout
20737 \begin_inset Formula $\Omega$
20751 \begin_inset space \hfill{}
20757 \begin_layout Standard
20758 \begin_inset VSpace medskip
20761 That the big Greek letters appear upright is caused by a design bug when
20763 To get correct italic big letters, begin every command with
20768 For example the command
20775 \begin_inset Formula $\varGamma$
20781 \begin_layout Subsection
20783 \begin_inset Index idx
20786 \begin_layout Plain Layout
20787 Greek letters ! bold
20795 \begin_layout Standard
20796 Greek letters cannot be set with different font styles like Latin letters.
20797 They can only be made bold with the command
20804 \begin_inset Index idx
20807 \begin_layout Plain Layout
20818 \begin_layout Standard
20820 \begin_inset Tabular
20821 <lyxtabular version="3" rows="3" columns="2">
20822 <features tabularvalignment="middle">
20823 <column alignment="center" valignment="top" width="0">
20824 <column alignment="center" valignment="top" width="0">
20826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20829 \begin_layout Plain Layout
20835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20838 \begin_layout Plain Layout
20846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20849 \begin_layout Plain Layout
20861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20864 \begin_layout Plain Layout
20865 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20878 \begin_layout Plain Layout
20890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20893 \begin_layout Plain Layout
20894 \begin_inset Formula $\theta\boldsymbol{\theta}$
20910 \begin_layout Section
20915 \begin_layout Plain Layout
20928 \begin_layout Plain Layout
20929 A list with all symbols of most of the LaTeX-packages can be found in
20930 \begin_inset CommandInset citation
20945 \begin_layout Plain Layout
20953 \begin_inset Note Note
20956 \begin_layout Plain Layout
20959 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20962 \begin_layout Plain Layout
20965 texorpdfstring is in section
20966 \begin_inset CommandInset ref
20968 reference "sub:Formulas-in-Section"
20978 \begin_inset Index idx
20981 \begin_layout Plain Layout
20990 \begin_layout Standard
20991 Many of the symbols listed in this section can also be inserted via the
20993 \begin_inset Graphics
20994 filename ../images/math/nabla.png
21000 \begin_inset Graphics
21001 filename ../images/math/digamma.png
21009 \begin_layout Subsection
21010 Mathematical Symbols
21011 \begin_inset CommandInset label
21013 name "sub:Mathematical-Symbols"
21018 \begin_inset Index idx
21021 \begin_layout Plain Layout
21022 Symbols ! mathematical
21030 \begin_layout Standard
21031 \begin_inset space \hfill{}
21035 \begin_inset Tabular
21036 <lyxtabular version="3" rows="10" columns="2">
21037 <features tabularvalignment="middle">
21038 <column alignment="center" valignment="top" width="0pt">
21039 <column alignment="center" valignment="top" width="0pt">
21041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21044 \begin_layout Plain Layout
21050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21053 \begin_layout Plain Layout
21061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21064 \begin_layout Plain Layout
21072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21075 \begin_layout Plain Layout
21076 \begin_inset Formula $\neg$
21086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21089 \begin_layout Plain Layout
21097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21100 \begin_layout Plain Layout
21101 \begin_inset Formula $\Im$
21111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21114 \begin_layout Plain Layout
21122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21125 \begin_layout Plain Layout
21126 \begin_inset Formula $\Re$
21136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21139 \begin_layout Plain Layout
21147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21150 \begin_layout Plain Layout
21151 \begin_inset Formula $\aleph$
21161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21164 \begin_layout Plain Layout
21172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21175 \begin_layout Plain Layout
21176 \begin_inset Formula $\partial$
21186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21189 \begin_layout Plain Layout
21197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21200 \begin_layout Plain Layout
21201 \begin_inset Formula $\infty$
21211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21214 \begin_layout Plain Layout
21222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21225 \begin_layout Plain Layout
21226 \begin_inset Formula $\wp$
21236 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21239 \begin_layout Plain Layout
21247 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21250 \begin_layout Plain Layout
21251 \begin_inset Formula $\imath$
21261 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21264 \begin_layout Plain Layout
21272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21275 \begin_layout Plain Layout
21276 \begin_inset Formula $\jmath$
21290 \begin_inset space \hfill{}
21294 \begin_inset Tabular
21295 <lyxtabular version="3" rows="10" columns="2">
21296 <features tabularvalignment="middle">
21297 <column alignment="center" valignment="top" width="0pt">
21298 <column alignment="center" valignment="top" width="0pt">
21300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21303 \begin_layout Plain Layout
21309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21312 \begin_layout Plain Layout
21314 \begin_inset Note Note
21317 \begin_layout Plain Layout
21324 is only used as spacer.
21336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21339 \begin_layout Plain Layout
21347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21350 \begin_layout Plain Layout
21351 \begin_inset Formula $\forall$
21361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21364 \begin_layout Plain Layout
21372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21375 \begin_layout Plain Layout
21376 \begin_inset Formula $\exists$
21386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21389 \begin_layout Plain Layout
21397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21400 \begin_layout Plain Layout
21401 \begin_inset Formula $\nexists$
21411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21414 \begin_layout Plain Layout
21422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21425 \begin_layout Plain Layout
21426 \begin_inset Formula $\emptyset$
21436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21439 \begin_layout Plain Layout
21447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21450 \begin_layout Plain Layout
21451 \begin_inset Formula $\varnothing$
21461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21464 \begin_layout Plain Layout
21472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21475 \begin_layout Plain Layout
21476 \begin_inset Formula $\dag$
21486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21489 \begin_layout Plain Layout
21497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21500 \begin_layout Plain Layout
21501 \begin_inset Formula $\ddag$
21511 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21514 \begin_layout Plain Layout
21522 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21525 \begin_layout Plain Layout
21529 \begin_layout Plain Layout
21539 \begin_inset Formula $\complement$
21546 \begin_layout Plain Layout
21560 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21563 \begin_layout Plain Layout
21571 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21574 \begin_layout Plain Layout
21575 \begin_inset Formula $\Bbbk$
21589 \begin_inset space \hfill{}
21593 \begin_inset Tabular
21594 <lyxtabular version="3" rows="10" columns="2">
21595 <features tabularvalignment="middle">
21596 <column alignment="center" valignment="top" width="0pt">
21597 <column alignment="center" valignment="top" width="0pt">
21599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21602 \begin_layout Plain Layout
21608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21611 \begin_layout Plain Layout
21619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21622 \begin_layout Plain Layout
21630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21633 \begin_layout Plain Layout
21634 \begin_inset Formula $\prime$
21644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21647 \begin_layout Plain Layout
21655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21658 \begin_layout Plain Layout
21659 \begin_inset Formula $\backprime$
21669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21672 \begin_layout Plain Layout
21680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21683 \begin_layout Plain Layout
21684 \begin_inset Formula $\mho$
21694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21697 \begin_layout Plain Layout
21705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21708 \begin_layout Plain Layout
21709 \begin_inset Formula $\triangle$
21719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21722 \begin_layout Plain Layout
21730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21733 \begin_layout Plain Layout
21734 \begin_inset Formula $\angle$
21744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21747 \begin_layout Plain Layout
21755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21758 \begin_layout Plain Layout
21759 \begin_inset Formula $\measuredangle$
21769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21772 \begin_layout Plain Layout
21780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21783 \begin_layout Plain Layout
21784 \begin_inset Formula $\sphericalangle$
21794 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21797 \begin_layout Plain Layout
21805 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21808 \begin_layout Plain Layout
21809 \begin_inset Formula $\top$
21819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21822 \begin_layout Plain Layout
21830 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21833 \begin_layout Plain Layout
21834 \begin_inset Formula $\bot$
21848 \begin_inset space \hfill{}
21854 \begin_layout Subsection
21855 Miscellaneous Symbols
21856 \begin_inset CommandInset label
21858 name "sub:Miscellaneous-Symbols"
21863 \begin_inset Index idx
21866 \begin_layout Plain Layout
21867 Symbols ! miscellaneous
21875 \begin_layout Standard
21878 \begin_inset Tabular
21879 <lyxtabular version="3" rows="10" columns="2">
21880 <features tabularvalignment="middle">
21881 <column alignment="center" valignment="top" width="0pt">
21882 <column alignment="center" valignment="top" width="0pt">
21884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21887 \begin_layout Plain Layout
21893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21896 \begin_layout Plain Layout
21904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21907 \begin_layout Plain Layout
21915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21918 \begin_layout Plain Layout
21919 \begin_inset Formula $\flat$
21929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21932 \begin_layout Plain Layout
21940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21943 \begin_layout Plain Layout
21944 \begin_inset Formula $\natural$
21954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21957 \begin_layout Plain Layout
21965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21968 \begin_layout Plain Layout
21969 \begin_inset Formula $\sharp$
21979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21982 \begin_layout Plain Layout
21990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21993 \begin_layout Plain Layout
21994 \begin_inset Formula $\surd$
22004 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22007 \begin_layout Plain Layout
22015 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22018 \begin_layout Plain Layout
22019 \begin_inset Formula $\checkmark$
22029 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22032 \begin_layout Plain Layout
22040 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22043 \begin_layout Plain Layout
22044 \begin_inset Formula $\yen$
22054 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22057 \begin_layout Plain Layout
22065 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22068 \begin_layout Plain Layout
22069 \begin_inset Formula $\pounds$
22079 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22082 \begin_layout Plain Layout
22088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22091 \begin_layout Plain Layout
22092 \begin_inset Formula $\$$
22102 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22105 \begin_layout Plain Layout
22111 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22114 \begin_layout Plain Layout
22115 \begin_inset Formula $§$
22129 \begin_inset Tabular
22130 <lyxtabular version="3" rows="10" columns="2">
22131 <features tabularvalignment="middle">
22132 <column alignment="center" valignment="top" width="0">
22133 <column alignment="center" valignment="top" width="0">
22135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22138 \begin_layout Plain Layout
22144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22147 \begin_layout Plain Layout
22155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22158 \begin_layout Plain Layout
22166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22169 \begin_layout Plain Layout
22170 \begin_inset Formula $\hbar$
22180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22183 \begin_layout Plain Layout
22191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22194 \begin_layout Plain Layout
22195 \begin_inset Formula $\hslash$
22205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22208 \begin_layout Plain Layout
22216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22219 \begin_layout Plain Layout
22220 \begin_inset Formula $\clubsuit$
22230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22233 \begin_layout Plain Layout
22241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22244 \begin_layout Plain Layout
22245 \begin_inset Formula $\spadesuit$
22255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22258 \begin_layout Plain Layout
22266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22269 \begin_layout Plain Layout
22270 \begin_inset Formula $\bigstar$
22280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22283 \begin_layout Plain Layout
22291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22294 \begin_layout Plain Layout
22295 \begin_inset Formula $\blacklozenge$
22305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22308 \begin_layout Plain Layout
22316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22319 \begin_layout Plain Layout
22320 \begin_inset Formula $\blacktriangle$
22330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22333 \begin_layout Plain Layout
22341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22344 \begin_layout Plain Layout
22345 \begin_inset Formula $\blacktriangledown$
22355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22358 \begin_layout Plain Layout
22366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22369 \begin_layout Plain Layout
22370 \begin_inset Formula $\bullet$
22384 \begin_inset Tabular
22385 <lyxtabular version="3" rows="10" columns="2">
22386 <features tabularvalignment="middle">
22387 <column alignment="center" valignment="top" width="0pt">
22388 <column alignment="center" valignment="top" width="0pt">
22390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22393 \begin_layout Plain Layout
22399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22402 \begin_layout Plain Layout
22410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22413 \begin_layout Plain Layout
22421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22424 \begin_layout Plain Layout
22425 \begin_inset Formula $\diamondsuit$
22435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22438 \begin_layout Plain Layout
22446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22449 \begin_layout Plain Layout
22450 \begin_inset Formula $\Diamond$
22460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22463 \begin_layout Plain Layout
22471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22474 \begin_layout Plain Layout
22475 \begin_inset Formula $\heartsuit$
22485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22488 \begin_layout Plain Layout
22496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22499 \begin_layout Plain Layout
22500 \begin_inset Formula $\P$
22510 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22513 \begin_layout Plain Layout
22521 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22524 \begin_layout Plain Layout
22525 \begin_inset Formula $\copyright$
22535 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22538 \begin_layout Plain Layout
22546 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22549 \begin_layout Plain Layout
22550 \begin_inset Formula $\circledR$
22560 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22563 \begin_layout Plain Layout
22571 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22574 \begin_layout Plain Layout
22575 \begin_inset Formula $\maltese$
22585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22588 \begin_layout Plain Layout
22596 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22599 \begin_layout Plain Layout
22600 \begin_inset Formula $\diagup$
22610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22613 \begin_layout Plain Layout
22621 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22624 \begin_layout Plain Layout
22625 \begin_inset Formula $\diagdown$
22641 \begin_layout Standard
22642 \begin_inset VSpace medskip
22645 More symbols are listed in
22646 \begin_inset CommandInset ref
22648 reference "sub:Miscellaneous-special-Characters"
22655 \begin_layout Standard
22656 Some symbols can be displayed in different sizes, see
22657 \begin_inset CommandInset ref
22659 reference "sub:Font-Sizes"
22666 \begin_layout Subsection
22668 \begin_inset Index idx
22671 \begin_layout Plain Layout
22672 Symbols ! Euro-symbol
22678 \begin_inset Index idx
22681 \begin_layout Plain Layout
22688 \begin_layout Plain Layout
22705 \begin_layout Standard
22706 To use the Euro symbol in formulas, the LaTeX-package
22711 \begin_inset Index idx
22714 \begin_layout Plain Layout
22720 must be installed and loaded with the LaTeX-preamble line
22723 \begin_layout Standard
22728 usepackage[gennarrow]{eurosym}
22731 \begin_layout Standard
22732 The Euro symbol can now be inserted with the command
22739 \begin_inset Index idx
22742 \begin_layout Plain Layout
22753 \begin_layout Standard
22754 The Euro symbol can directly be inserted with the € key in mathematical
22755 text, without having
22770 can also be inserted in TeX-mode.
22771 The official currency symbol can then be inserted with the command
22778 \begin_inset Index idx
22781 \begin_layout Plain Layout
22789 , that is only available in TeX-mode.
22792 \begin_layout Standard
22796 \begin_layout Plain Layout
22806 \begin_inset Note Note
22809 \begin_layout Plain Layout
22810 The following table will only be displayed when the LaTeX-package
22822 \begin_layout Standard
22823 An overview about the different Euro symbols:
22826 \begin_layout Standard
22828 \begin_inset Tabular
22829 <lyxtabular version="3" rows="4" columns="3">
22830 <features tabularvalignment="middle">
22831 <column alignment="center" valignment="top" width="0pt">
22832 <column alignment="center" valignment="top" width="0pt">
22833 <column alignment="center" valignment="top" width="0pt">
22835 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22838 \begin_layout Plain Layout
22844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22847 \begin_layout Plain Layout
22853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22856 \begin_layout Plain Layout
22864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22867 \begin_layout Plain Layout
22873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22876 \begin_layout Plain Layout
22884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22887 \begin_layout Plain Layout
22888 \begin_inset Formula $\euro$
22898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22901 \begin_layout Plain Layout
22907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22910 \begin_layout Plain Layout
22916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22919 \begin_layout Plain Layout
22920 \begin_inset Formula $\mbox{€}$
22930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22933 \begin_layout Plain Layout
22939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22942 \begin_layout Plain Layout
22950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22953 \begin_layout Plain Layout
22957 \begin_layout Plain Layout
22979 \begin_layout Standard
22983 \begin_layout Plain Layout
22993 \begin_inset Note Note
22996 \begin_layout Plain Layout
22997 The following will be displayed when the LaTeX-package
23009 \begin_layout Standard
23010 You need to install the LaTeX-package
23014 to see the rest of this subsection in the output.
23017 \begin_layout Standard
23021 \begin_layout Plain Layout
23033 \begin_layout Section
23035 \begin_inset CommandInset label
23037 name "sec:Relations"
23042 \begin_inset Index idx
23045 \begin_layout Plain Layout
23052 \begin_inset Index idx
23055 \begin_layout Plain Layout
23060 \begin_layout Plain Layout
23071 \begin_layout Plain Layout
23086 \begin_layout Standard
23087 All relations can also be inserted via the toolbar button
23088 \begin_inset Graphics
23089 filename ../images/math/leq.png
23097 \begin_layout Standard
23098 \begin_inset space \hfill{}
23102 \begin_inset Tabular
23103 <lyxtabular version="3" rows="17" columns="2">
23104 <features tabularvalignment="middle">
23105 <column alignment="center" valignment="top" width="0pt">
23106 <column alignment="center" valignment="top" width="0pt">
23108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23111 \begin_layout Plain Layout
23117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23120 \begin_layout Plain Layout
23128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23131 \begin_layout Plain Layout
23137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23140 \begin_layout Plain Layout
23141 \begin_inset Formula $<$
23151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23154 \begin_layout Plain Layout
23162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23165 \begin_layout Plain Layout
23166 \begin_inset Formula $\le$
23176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23179 \begin_layout Plain Layout
23187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23190 \begin_layout Plain Layout
23191 \begin_inset Formula $\ll$
23201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23204 \begin_layout Plain Layout
23212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23215 \begin_layout Plain Layout
23216 \begin_inset Formula $\prec$
23226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23229 \begin_layout Plain Layout
23237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23240 \begin_layout Plain Layout
23241 \begin_inset Formula $\preceq$
23251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23254 \begin_layout Plain Layout
23262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23265 \begin_layout Plain Layout
23266 \begin_inset Formula $\subset$
23276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23279 \begin_layout Plain Layout
23287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23290 \begin_layout Plain Layout
23291 \begin_inset Formula $\subseteq$
23301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23304 \begin_layout Plain Layout
23312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23315 \begin_layout Plain Layout
23316 \begin_inset Formula $\sqsubseteq$
23326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23329 \begin_layout Plain Layout
23337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23340 \begin_layout Plain Layout
23341 \begin_inset Formula $\in$
23351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23354 \begin_layout Plain Layout
23362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23365 \begin_layout Plain Layout
23366 \begin_inset Formula $\vdash$
23376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23379 \begin_layout Plain Layout
23387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23390 \begin_layout Plain Layout
23391 \begin_inset Formula $\smile$
23401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23404 \begin_layout Plain Layout
23412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23415 \begin_layout Plain Layout
23416 \begin_inset Formula $\lhd$
23426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23429 \begin_layout Plain Layout
23437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23440 \begin_layout Plain Layout
23441 \begin_inset Formula $\unlhd$
23451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23454 \begin_layout Plain Layout
23462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23465 \begin_layout Plain Layout
23466 \begin_inset Formula $\gtrless$
23476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23479 \begin_layout Plain Layout
23487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23490 \begin_layout Plain Layout
23491 \begin_inset Formula $\mid$
23501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23504 \begin_layout Plain Layout
23512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23515 \begin_layout Plain Layout
23516 \begin_inset Formula $\nmid$
23530 \begin_inset space \hfill{}
23534 \begin_inset Tabular
23535 <lyxtabular version="3" rows="17" columns="2">
23536 <features tabularvalignment="middle">
23537 <column alignment="center" valignment="top" width="0pt">
23538 <column alignment="center" valignment="top" width="0pt">
23540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23543 \begin_layout Plain Layout
23549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23552 \begin_layout Plain Layout
23560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23563 \begin_layout Plain Layout
23569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23572 \begin_layout Plain Layout
23573 \begin_inset Formula $=$
23583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23586 \begin_layout Plain Layout
23594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23597 \begin_layout Plain Layout
23598 \begin_inset Formula $\not=$
23608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23611 \begin_layout Plain Layout
23619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23622 \begin_layout Plain Layout
23623 \begin_inset Formula $\equiv$
23633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23636 \begin_layout Plain Layout
23644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23647 \begin_layout Plain Layout
23648 \begin_inset Formula $\sim$
23658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23661 \begin_layout Plain Layout
23669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23672 \begin_layout Plain Layout
23673 \begin_inset Formula $\simeq$
23683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23686 \begin_layout Plain Layout
23694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23697 \begin_layout Plain Layout
23698 \begin_inset Formula $\approx$
23708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23711 \begin_layout Plain Layout
23719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23722 \begin_layout Plain Layout
23723 \begin_inset Formula $\cong$
23733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23736 \begin_layout Plain Layout
23744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23747 \begin_layout Plain Layout
23748 \begin_inset Formula $\bowtie$
23758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23761 \begin_layout Plain Layout
23769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23772 \begin_layout Plain Layout
23773 \begin_inset Formula $\notin$
23783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23786 \begin_layout Plain Layout
23794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23797 \begin_layout Plain Layout
23798 \begin_inset Formula $\perp$
23808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23811 \begin_layout Plain Layout
23819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23822 \begin_layout Plain Layout
23823 \begin_inset Formula $\propto$
23833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23836 \begin_layout Plain Layout
23844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23847 \begin_layout Plain Layout
23848 \begin_inset Formula $\asymp$
23858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23861 \begin_layout Plain Layout
23869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23872 \begin_layout Plain Layout
23873 \begin_inset Formula $\doteq$
23883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23886 \begin_layout Plain Layout
23894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23897 \begin_layout Plain Layout
23898 \begin_inset Formula $\circeq$
23908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23911 \begin_layout Plain Layout
23919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23922 \begin_layout Plain Layout
23923 \begin_inset Formula $\models$
23933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23936 \begin_layout Plain Layout
23944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23947 \begin_layout Plain Layout
23948 \begin_inset Formula $\widehat{=}$
23962 \begin_inset space \hfill{}
23966 \begin_inset Tabular
23967 <lyxtabular version="3" rows="17" columns="2">
23968 <features tabularvalignment="middle">
23969 <column alignment="center" valignment="top" width="0pt">
23970 <column alignment="center" valignment="top" width="0pt">
23972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23975 \begin_layout Plain Layout
23981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23984 \begin_layout Plain Layout
23992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23995 \begin_layout Plain Layout
24001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24004 \begin_layout Plain Layout
24005 \begin_inset Formula $>$
24015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24018 \begin_layout Plain Layout
24026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24029 \begin_layout Plain Layout
24030 \begin_inset Formula $\ge$
24040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24043 \begin_layout Plain Layout
24051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24054 \begin_layout Plain Layout
24055 \begin_inset Formula $\gg$
24065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24068 \begin_layout Plain Layout
24076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24079 \begin_layout Plain Layout
24080 \begin_inset Formula $\succ$
24090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24093 \begin_layout Plain Layout
24101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24104 \begin_layout Plain Layout
24105 \begin_inset Formula $\succeq$
24115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24118 \begin_layout Plain Layout
24126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24129 \begin_layout Plain Layout
24130 \begin_inset Formula $\supset$
24140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24143 \begin_layout Plain Layout
24151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24154 \begin_layout Plain Layout
24155 \begin_inset Formula $\supseteq$
24165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24168 \begin_layout Plain Layout
24176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24179 \begin_layout Plain Layout
24180 \begin_inset Formula $\sqsupseteq$
24190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24193 \begin_layout Plain Layout
24201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24204 \begin_layout Plain Layout
24205 \begin_inset Formula $\ni$
24215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24218 \begin_layout Plain Layout
24226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24229 \begin_layout Plain Layout
24230 \begin_inset Formula $\dashv$
24240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24243 \begin_layout Plain Layout
24251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24254 \begin_layout Plain Layout
24255 \begin_inset Formula $\frown$
24265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24268 \begin_layout Plain Layout
24276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24279 \begin_layout Plain Layout
24280 \begin_inset Formula $\rhd$
24290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24293 \begin_layout Plain Layout
24301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24304 \begin_layout Plain Layout
24305 \begin_inset Formula $\unrhd$
24315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24318 \begin_layout Plain Layout
24326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24329 \begin_layout Plain Layout
24330 \begin_inset Formula $\lessgtr$
24340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24343 \begin_layout Plain Layout
24351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24354 \begin_layout Plain Layout
24355 \begin_inset Formula $\parallel$
24365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24368 \begin_layout Plain Layout
24376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24379 \begin_layout Plain Layout
24380 \begin_inset Formula $\nparallel$
24394 \begin_inset space \hfill{}
24400 \begin_layout Standard
24401 \begin_inset VSpace medskip
24416 are bigger than the equal looking operators
24431 \begin_layout Standard
24432 Relations are, in contrary to symbols, always surrounded by space.
24435 \begin_layout Standard
24436 Relations with labels can be created with the command
24443 \begin_inset Index idx
24446 \begin_layout Plain Layout
24457 \begin_layout Standard
24459 \begin_inset Tabular
24460 <lyxtabular version="3" rows="2" columns="2">
24461 <features tabularvalignment="middle">
24462 <column alignment="center" valignment="top" width="0">
24463 <column alignment="center" valignment="top" width="0">
24465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24468 \begin_layout Plain Layout
24474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24477 \begin_layout Plain Layout
24479 \begin_inset Note Note
24482 \begin_layout Plain Layout
24489 is only used as spacer.
24501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24504 \begin_layout Plain Layout
24511 \begin_layout Plain Layout
24528 \begin_layout Plain Layout
24538 \begin_inset Formula $\downarrow$
24547 \begin_layout Plain Layout
24560 \begin_layout Plain Layout
24574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24577 \begin_layout Plain Layout
24578 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24594 \begin_layout Section
24598 \begin_layout Subsection
24599 Predefined Functions
24600 \begin_inset CommandInset label
24602 name "sub:Predefined-Functions"
24607 \begin_inset Index idx
24610 \begin_layout Plain Layout
24611 Functions ! predefined
24619 \begin_layout Standard
24620 In general, variables are set
24624 in mathematical expressions, but not function names, because
24625 \begin_inset Formula $sin$
24628 could be misunderstood as
24629 \begin_inset Formula $s\cdot i\cdot n$
24633 Therefore there are predefined functions, that are additionally a bit separated
24635 They are inserted as commands starting with a backslash before their name.
24638 \begin_layout Standard
24640 \begin_inset Tabular
24641 <lyxtabular version="3" rows="2" columns="4">
24642 <features tabularvalignment="middle">
24643 <column alignment="center" valignment="top" width="0pt">
24644 <column alignment="center" valignment="top" width="0pt">
24645 <column alignment="center" valignment="top" width="0pt">
24646 <column alignment="center" valignment="top" width="0pt">
24648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24651 \begin_layout Plain Layout
24657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24660 \begin_layout Plain Layout
24666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24669 \begin_layout Plain Layout
24675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24678 \begin_layout Plain Layout
24686 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24689 \begin_layout Plain Layout
24695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24698 \begin_layout Plain Layout
24699 \begin_inset Formula $Asin(x)+B$
24707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24710 \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
24722 \begin_inset Formula $A\sin(x)+B$
24738 \begin_layout Standard
24739 The following functions are predefined:
24742 \begin_layout Standard
24743 \begin_inset VSpace -2mm
24749 \begin_layout Standard
24751 \begin_inset Tabular
24752 <lyxtabular version="3" rows="9" columns="4">
24753 <features tabularvalignment="middle">
24754 <column alignment="center" valignment="top" width="0pt">
24755 <column alignment="center" valignment="top" width="0pt">
24756 <column alignment="center" valignment="top" width="0pt">
24757 <column alignment="center" valignment="top" width="0pt">
24759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24762 \begin_layout Plain Layout
24768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24771 \begin_layout Plain Layout
24777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24780 \begin_layout Plain Layout
24786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24789 \begin_layout Plain Layout
24797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24800 \begin_layout Plain Layout
24808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24811 \begin_layout Plain Layout
24819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24822 \begin_layout Plain Layout
24830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24833 \begin_layout Plain Layout
24843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24846 \begin_layout Plain Layout
24854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24857 \begin_layout Plain Layout
24865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24868 \begin_layout Plain Layout
24876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24879 \begin_layout Plain Layout
24889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24892 \begin_layout Plain Layout
24900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24903 \begin_layout Plain Layout
24911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24914 \begin_layout Plain Layout
24922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24925 \begin_layout Plain Layout
24935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24938 \begin_layout Plain Layout
24946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24949 \begin_layout Plain Layout
24957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24960 \begin_layout Plain Layout
24968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24971 \begin_layout Plain Layout
24981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24984 \begin_layout Plain Layout
24992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24995 \begin_layout Plain Layout
25003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25006 \begin_layout Plain Layout
25014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25017 \begin_layout Plain Layout
25027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25030 \begin_layout Plain Layout
25038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25041 \begin_layout Plain Layout
25049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25052 \begin_layout Plain Layout
25060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25063 \begin_layout Plain Layout
25073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25076 \begin_layout Plain Layout
25084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25087 \begin_layout Plain Layout
25095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25098 \begin_layout Plain Layout
25106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25109 \begin_layout Plain Layout
25119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25122 \begin_layout Plain Layout
25130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25133 \begin_layout Plain Layout
25141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25144 \begin_layout Plain Layout
25152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25155 \begin_layout Plain Layout
25171 \begin_layout Standard
25172 They can also be inserted with the math toolbar button
25173 \begin_inset Graphics
25174 filename ../images/math/functions.png
25182 \begin_layout Subsection
25183 Self-defined Functions
25184 \begin_inset Index idx
25187 \begin_layout Plain Layout
25188 Functions ! self-defined
25196 \begin_layout Standard
25197 To use a function that is not predefined, like for example the sign function
25198 sgn(x), there are two possibilities:
25201 \begin_layout Itemize
25202 Define the function by inserting the following line to the LaTeX-preamble
25206 \begin_layout Plain Layout
25211 DeclareMathOperator
25214 \begin_inset CommandInset ref
25216 reference "sub:Self-defined-Operators"
25226 \begin_inset Newline newline
25230 \begin_inset VSpace -3mm
25234 \begin_inset Newline newline
25241 DeclareMathOperator{
25246 \begin_inset Index idx
25249 \begin_layout Plain Layout
25254 DeclareMathOperator
25260 \begin_inset Newline newline
25264 \begin_inset VSpace -2mm
25268 \begin_inset Newline newline
25271 Now the new defined function can be called with the command
25280 \begin_layout Itemize
25281 Write the formula as usual, mark the formula name, in our example the letters
25286 , and change it to mathematical text.
25287 At last a space is inserted between prefactor and function.
25290 \begin_layout Standard
25291 The result is the same with both methods as with a predefined function
25295 \begin_layout Plain Layout
25296 In LyX self-defined functions are displayed red, predefined ones black.
25304 \begin_layout Standard
25306 \begin_inset Tabular
25307 <lyxtabular version="3" rows="3" columns="2">
25308 <features tabularvalignment="middle">
25309 <column alignment="center" valignment="top" width="0pt">
25310 <column alignment="center" valignment="top" width="0pt">
25312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25315 \begin_layout Plain Layout
25321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25324 \begin_layout Plain Layout
25332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25335 \begin_layout Plain Layout
25343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25346 \begin_layout Plain Layout
25347 \begin_inset Formula $A\sgn(x)+B$
25357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25360 \begin_layout Plain Layout
25364 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25375 \begin_layout Plain Layout
25376 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25392 \begin_layout Standard
25393 The first method is more suitable when the self-defined function should
25394 be used several times.
25397 \begin_layout Subsection
25399 \begin_inset Index idx
25402 \begin_layout Plain Layout
25411 \begin_layout Standard
25412 For limits there are defined besides
25419 \begin_inset Index idx
25422 \begin_layout Plain Layout
25442 furthermore the following functions:
25445 \begin_layout Standard
25447 \begin_inset Tabular
25448 <lyxtabular version="3" rows="5" columns="2">
25449 <features tabularvalignment="middle">
25450 <column alignment="center" valignment="top" width="0">
25451 <column alignment="center" valignment="top" width="0">
25453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25456 \begin_layout Plain Layout
25462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25465 \begin_layout Plain Layout
25467 \begin_inset Note Note
25470 \begin_layout Plain Layout
25477 is only used as spacer.
25489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25492 \begin_layout Plain Layout
25500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25503 \begin_layout Plain Layout
25504 \begin_inset Formula $\varliminf$
25514 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25517 \begin_layout Plain Layout
25525 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25528 \begin_layout Plain Layout
25529 \begin_inset Formula $\varlimsup$
25539 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25542 \begin_layout Plain Layout
25550 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25553 \begin_layout Plain Layout
25554 \begin_inset Formula $\varprojlim$
25564 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25567 \begin_layout Plain Layout
25575 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25578 \begin_layout Plain Layout
25579 \begin_inset Formula $\varinjlim$
25583 \begin_inset Formula $\raisebox{-2.5mm}{}$
25599 \begin_layout Standard
25600 \begin_inset VSpace medskip
25603 The limit is created by inserting a subscript.
25604 It is set right beside the function in an inline formula:
25607 \begin_layout Standard
25609 \begin_inset Tabular
25610 <lyxtabular version="3" rows="2" columns="2">
25611 <features tabularvalignment="middle">
25612 <column alignment="center" valignment="top" width="0pt">
25613 <column alignment="center" valignment="top" width="0pt">
25615 <cell alignment="center" valignment="top" usebox="none">
25618 \begin_layout Plain Layout
25624 <cell alignment="center" valignment="top" usebox="none">
25627 \begin_layout Plain Layout
25628 \begin_inset space \hspace{}
25633 \begin_inset Note Note
25636 \begin_layout Plain Layout
25643 are used here as spacer.
25655 <cell alignment="center" valignment="top" usebox="none">
25658 \begin_layout Plain Layout
25667 \begin_layout Plain Layout
25680 \begin_layout Plain Layout
25694 <cell alignment="center" valignment="top" usebox="none">
25697 \begin_layout Plain Layout
25698 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25714 \begin_layout Standard
25715 In a displayed formula the limit is set below the formula, as usual:
25716 \begin_inset Formula \[
25724 \begin_layout Subsection
25726 \begin_inset Index idx
25729 \begin_layout Plain Layout
25730 Functions ! modulo-
25738 \begin_layout Standard
25739 The modulo-function is special, because it exists in four variants.
25742 \begin_layout Standard
25743 The variants in a displayed formula:
25744 \begin_inset Formula \begin{align*}
25745 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25746 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25747 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25748 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25749 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
25757 \begin_layout Standard
25758 In an inline formula less space is set before the function names for all
25762 \begin_layout Section
25764 \begin_inset Index idx
25767 \begin_layout Plain Layout
25776 \begin_layout Subsection
25777 Special Characters in Mathematical Text
25780 \begin_layout Standard
25781 The following commands can only be used in mathematical text or in TeX-mode:
25784 \begin_layout Standard
25785 \begin_inset space \hfill{}
25789 \begin_inset Tabular
25790 <lyxtabular version="3" rows="8" columns="2">
25791 <features tabularvalignment="middle">
25792 <column alignment="block" valignment="top" width="0">
25793 <column alignment="block" valignment="top" width="0">
25795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25798 \begin_layout Plain Layout
25804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25807 \begin_layout Plain Layout
25815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25818 \begin_layout Plain Layout
25826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25829 \begin_layout Plain Layout
25830 \begin_inset Formula $\textrm{œ}$
25840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25843 \begin_layout Plain Layout
25851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25854 \begin_layout Plain Layout
25855 \begin_inset Formula $\textrm{Œ}$
25865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25868 \begin_layout Plain Layout
25876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25879 \begin_layout Plain Layout
25880 \begin_inset Formula $\textrm{æ}$
25890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25893 \begin_layout Plain Layout
25901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25904 \begin_layout Plain Layout
25905 \begin_inset Formula $\textrm{Æ}$
25915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25918 \begin_layout Plain Layout
25926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25929 \begin_layout Plain Layout
25930 \begin_inset Formula $\textrm{\aa}$
25940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25943 \begin_layout Plain Layout
25947 \begin_inset Index idx
25950 \begin_layout Plain Layout
25957 \begin_layout Plain Layout
25978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25981 \begin_layout Plain Layout
25982 \begin_inset Formula $\textrm{Å}$
25992 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25995 \begin_layout Plain Layout
26003 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26006 \begin_layout Plain Layout
26007 \begin_inset Formula $\textrm{ı}$
26021 \begin_inset space \hfill{}
26025 \begin_inset Tabular
26026 <lyxtabular version="3" rows="8" columns="2">
26027 <features tabularvalignment="middle">
26028 <column alignment="block" valignment="top" width="0">
26029 <column alignment="center" valignment="top" width="0">
26031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26034 \begin_layout Plain Layout
26036 \begin_inset Note Note
26039 \begin_layout Plain Layout
26041 \begin_inset space \thinspace{}
26044 mm is used for separation, because otherwise the output will be ¡ and ¿
26055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26058 \begin_layout Plain Layout
26066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26069 \begin_layout Plain Layout
26077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26080 \begin_layout Plain Layout
26081 \begin_inset Formula $\textrm{ø}$
26091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26094 \begin_layout Plain Layout
26102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26105 \begin_layout Plain Layout
26106 \begin_inset Formula $\textrm{Ø}$
26116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26119 \begin_layout Plain Layout
26127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26130 \begin_layout Plain Layout
26131 \begin_inset Formula $\textrm{ł}$
26141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26144 \begin_layout Plain Layout
26152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26155 \begin_layout Plain Layout
26156 \begin_inset Formula $\textrm{Ł}$
26166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26169 \begin_layout Plain Layout
26171 \begin_inset space \hspace{}
26179 \begin_layout Plain Layout
26193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26196 \begin_layout Plain Layout
26197 \begin_inset Formula $\textrm{!`}$
26207 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26210 \begin_layout Plain Layout
26212 \begin_inset space \hspace{}
26220 \begin_layout Plain Layout
26234 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26237 \begin_layout Plain Layout
26238 \begin_inset Formula $\textrm{?`}$
26248 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26251 \begin_layout Plain Layout
26259 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26262 \begin_layout Plain Layout
26263 \begin_inset Formula $\textrm{ȷ}$
26277 \begin_inset space \hfill{}
26283 \begin_layout Standard
26285 \begin_inset Formula $\textrm{\textrm{Å}}$
26289 \begin_inset Formula $\textrm{\textrm{Ø}}$
26292 can also be inserted via the math toolbar button
26293 \begin_inset Graphics
26294 filename ../images/math/digamma.png
26302 \begin_layout Standard
26303 An exception are the commands
26306 \begin_inset space \hspace{}
26315 \begin_inset space \hspace{}
26321 , because they can be inserted in LyX directly to text.
26324 \begin_layout Subsection
26326 \begin_inset CommandInset label
26328 name "sub:Accents-in-Text"
26333 \begin_inset Index idx
26336 \begin_layout Plain Layout
26345 \begin_layout Standard
26346 With the following commands all letters can be accented.
26347 The commands must be inserted in TeX-mode.
26350 \begin_layout Standard
26351 \begin_inset space \hfill{}
26355 \begin_inset Tabular
26356 <lyxtabular version="3" rows="8" columns="2">
26357 <features tabularvalignment="middle">
26358 <column alignment="block" valignment="top" width="0">
26359 <column alignment="block" valignment="top" width="0">
26361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26364 \begin_layout Plain Layout
26370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26373 \begin_layout Plain Layout
26381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26384 \begin_layout Plain Layout
26388 \begin_inset Quotes grd
26396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26399 \begin_layout Plain Layout
26403 \begin_layout Plain Layout
26419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26422 \begin_layout Plain Layout
26430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26433 \begin_layout Plain Layout
26437 \begin_layout Plain Layout
26453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26456 \begin_layout Plain Layout
26463 \begin_layout Plain Layout
26477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26480 \begin_layout Plain Layout
26484 \begin_layout Plain Layout
26500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26503 \begin_layout Plain Layout
26511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26514 \begin_layout Plain Layout
26518 \begin_layout Plain Layout
26534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26537 \begin_layout Plain Layout
26544 \begin_layout Plain Layout
26558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26561 \begin_layout Plain Layout
26565 \begin_layout Plain Layout
26581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26584 \begin_layout Plain Layout
26591 \begin_layout Plain Layout
26605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26608 \begin_layout Plain Layout
26612 \begin_layout Plain Layout
26628 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26631 \begin_layout Plain Layout
26638 \begin_layout Plain Layout
26652 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26655 \begin_layout Plain Layout
26659 \begin_layout Plain Layout
26679 \begin_inset space \hfill{}
26683 \begin_inset Tabular
26684 <lyxtabular version="3" rows="8" columns="2">
26685 <features tabularvalignment="middle">
26686 <column alignment="block" valignment="top" width="0">
26687 <column alignment="center" valignment="top" width="0">
26689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26692 \begin_layout Plain Layout
26698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26701 \begin_layout Plain Layout
26709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26712 \begin_layout Plain Layout
26719 \begin_layout Plain Layout
26733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26736 \begin_layout Plain Layout
26740 \begin_layout Plain Layout
26756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26759 \begin_layout Plain Layout
26767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26770 \begin_layout Plain Layout
26774 \begin_layout Plain Layout
26790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26793 \begin_layout Plain Layout
26797 \begin_inset Index idx
26800 \begin_layout Plain Layout
26811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26814 \begin_layout Plain Layout
26818 \begin_layout Plain Layout
26834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26837 \begin_layout Plain Layout
26845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26848 \begin_layout Plain Layout
26852 \begin_layout Plain Layout
26868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26871 \begin_layout Plain Layout
26878 \begin_layout Plain Layout
26892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26895 \begin_layout Plain Layout
26899 \begin_layout Plain Layout
26915 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26918 \begin_layout Plain Layout
26925 \begin_layout Plain Layout
26939 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26942 \begin_layout Plain Layout
26946 \begin_layout Plain Layout
26962 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26965 \begin_layout Plain Layout
26972 \begin_layout Plain Layout
26986 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26989 \begin_layout Plain Layout
26993 \begin_layout Plain Layout
27013 \begin_inset space \hfill{}
27019 \begin_layout Standard
27020 \begin_inset VSpace medskip
27029 also two different characters can be accented.
27038 \begin_layout Plain Layout
27053 \begin_layout Plain Layout
27065 \begin_layout Standard
27078 can in combination with vowels directly be inserted with the keyboard without
27080 The same applies for the tilde
27084 \begin_layout Plain Layout
27085 This only applies for keyboards where the tilde is defined as accent.
27094 in combination with
27109 \begin_layout Standard
27152 and accents that are inserted directly with the keyboard are also available
27153 in mathematical text.
27154 For the other accents there are special math commands to be used in formulas,
27156 \begin_inset CommandInset ref
27158 reference "sub:Accents-for-one"
27165 \begin_layout Standard
27166 \begin_inset VSpace bigskip
27169 Furthermore, with the command
27176 \begin_inset Index idx
27179 \begin_layout Plain Layout
27187 all numbers and letters can be set into a circle, quasi accented with a
27188 circle, similar to the copyright symbol.
27191 \begin_layout Standard
27193 \begin_inset Tabular
27194 <lyxtabular version="3" rows="3" columns="2">
27195 <features tabularvalignment="middle">
27196 <column alignment="center" valignment="top" width="0">
27197 <column alignment="center" valignment="top" width="0">
27199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27202 \begin_layout Plain Layout
27208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27211 \begin_layout Plain Layout
27213 \begin_inset Note Note
27216 \begin_layout Plain Layout
27223 is only used as spacer.
27235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27238 \begin_layout Plain Layout
27246 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27249 \begin_layout Plain Layout
27253 \begin_layout Plain Layout
27269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27272 \begin_layout Plain Layout
27283 raisebox{-1.5pt}{W}}
27288 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27291 \begin_layout Plain Layout
27292 \begin_inset Formula $\raisebox{4.5mm}{}$
27299 \begin_layout Plain Layout
27317 \begin_inset Formula $\raisebox{-2mm}{}$
27333 \begin_layout Standard
27334 One has to take care that the character fits in the circle.
27345 \begin_layout Plain Layout
27347 \begin_inset CommandInset ref
27349 reference "sub:Font-Sizes"
27358 specifies thereby the size of the circle.
27369 \begin_layout Plain Layout
27371 \begin_inset CommandInset ref
27373 reference "sub:Boxes-without-Frame"
27382 the character can be centered.
27385 \begin_layout Subsection
27387 \begin_inset Index idx
27390 \begin_layout Plain Layout
27399 \begin_layout Standard
27400 Minuscule numbers are created with the command
27407 \begin_inset Index idx
27410 \begin_layout Plain Layout
27419 The command can be used in formulas and in TeX-mode.
27420 The command scheme is:
27423 \begin_layout Standard
27428 oldstylenums{number}
27431 \begin_layout Standard
27436 oldstylenums{0123456789
27439 \begin_inset Formula $\oldstylenums{0123456789}$
27445 \begin_layout Subsection
27446 Miscellaneous special Characters
27447 \begin_inset CommandInset label
27449 name "sub:Miscellaneous-special-Characters"
27454 \begin_inset Index idx
27457 \begin_layout Plain Layout
27458 Special characters ! miscellaneous
27466 \begin_layout Standard
27467 The following characters can only be inserted to formulas by using commands:
27470 \begin_layout Standard
27472 \begin_inset Tabular
27473 <lyxtabular version="3" rows="4" columns="2">
27474 <features tabularvalignment="middle">
27475 <column alignment="center" valignment="top" width="0">
27476 <column alignment="center" valignment="top" width="0">
27478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27481 \begin_layout Plain Layout
27487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27490 \begin_layout Plain Layout
27498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27501 \begin_layout Plain Layout
27508 \begin_layout Plain Layout
27522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27525 \begin_layout Plain Layout
27526 \begin_inset Formula $\mathcircumflex$
27536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27539 \begin_layout Plain Layout
27547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27550 \begin_layout Plain Layout
27551 \begin_inset Formula $\_$
27561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27564 \begin_layout Plain Layout
27569 \begin_layout Plain Layout
27581 \begin_inset Index idx
27584 \begin_layout Plain Layout
27597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27600 \begin_layout Plain Layout
27601 \begin_inset Formula $^{\circ}$
27617 \begin_layout Standard
27618 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27619 contains the following line
27623 \begin_layout Plain Layout
27624 More about this is described in
27625 \begin_inset CommandInset ref
27627 reference "sub:Text-Characters-in"
27639 \begin_layout Standard
27644 DeclareInputtext{176}{
27657 \begin_layout Section
27659 \begin_inset CommandInset label
27661 name "sec:Formula-Styles"
27666 \begin_inset Index idx
27669 \begin_layout Plain Layout
27678 \begin_layout Itemize
27679 There are two different alignment styles:
27683 \begin_layout Description
27684 Centered is the predefined standard
27687 \begin_layout Description
27688 Indented for this the option
27692 must be inserted in the menu
27694 Document\SpecialChar \menuseparator
27700 \begin_inset space ~
27706 \begin_layout Standard
27711 is used, the indentation can be adjusted with the length
27718 \begin_inset Index idx
27721 \begin_layout Plain Layout
27730 Should the distance be 15
27731 \begin_inset space \thinspace{}
27734 mm, the following command line is inserted in the LaTeX-preamble
27737 \begin_layout Standard
27747 \begin_layout Standard
27748 When no length is specified, the predefined value of 30
27749 \begin_inset space \thinspace{}
27756 \begin_layout Itemize
27757 And two different numbering styles:
27761 \begin_layout Description
27762 Right is the predefined standard
27765 \begin_layout Description
27766 Left for this the option
27770 must be inserted in the menu
27772 Document\SpecialChar \menuseparator
27778 \begin_inset space ~
27785 \begin_layout Standard
27794 can also be used together.
27795 In this case both options are inserted, separated by a comma.
27798 \begin_layout Standard
27799 The chosen styles are used for all displayed formulas of the document.
27800 When both, centered and indented formulas should be created in a document,
27806 The indented formulas are then set in a flalign environment, see
27807 \begin_inset CommandInset ref
27809 reference "sub:Flalign-Environment"
27816 \begin_layout Section
27818 \begin_inset CommandInset label
27820 name "sec:Multiline-Formulas"
27825 \begin_inset Index idx
27828 \begin_layout Plain Layout
27829 Formula ! multiline
27837 \begin_layout Subsection
27841 \begin_layout Standard
27842 In LyX multiline formulas are created by pressing
27847 arg "newline-insert newline"
27853 This creates either an
27855 eqnarray environment
27857 that is described in
27858 \begin_inset CommandInset ref
27860 reference "sub:Eqnarray-Environment"
27864 or, when the option
27866 Use AMS math package
27868 in the document settings is selected, an
27872 that is described in
27873 \begin_inset CommandInset ref
27875 reference "sub:Standard-align-Environment"
27882 \begin_layout Standard
27883 There are other multiline formula environments that can be created via the
27886 Insert\SpecialChar \menuseparator
27890 These environments are described in the following sections.
27893 \begin_layout Standard
27894 In all multiline formula environments a new line is created by pressing
27898 arg "newline-insert newline"
27902 To add or delete lines, the math toolbar buttons
27903 \begin_inset Graphics
27904 filename ../images/tabular-feature_append-row.png
27910 \begin_inset Graphics
27911 filename ../images/tabular-feature_delete-row.png
27916 , respectively, or the menu
27918 Edit\SpecialChar \menuseparator
27924 \begin_layout Subsubsection
27926 \begin_inset CommandInset label
27928 name "sub:Line-Separation"
27933 \begin_inset Index idx
27936 \begin_layout Plain Layout
27937 Formula ! multiline ! Line separation
27945 \begin_layout Standard
27946 There is sometimes not enough space in multiline formulas between the lines:
27947 \begin_inset Formula \begin{eqnarray*}
27948 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}\\
27949 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
27957 \begin_layout Standard
27958 In LaTeX additional line space is specified as optional argument of the
27960 This is not yet possible in LyX
27964 \begin_layout Plain Layout
27966 \begin_inset CommandInset href
27968 name "LyX-bug #1505"
27969 target "http://www.lyx.org/trac/ticket/1505"
27978 , therefore the whole formula must be inserted in TeX-mode.
27979 To add in our example space, the command
27987 is inserted at the end of the first line.
27992 \begin_layout Plain Layout
27999 \begin_layout Plain Layout
28001 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28004 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28011 \begin_layout Plain Layout
28015 left(B^{2}+x_{0}^{2}
28023 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28028 \begin_layout Plain Layout
28040 \begin_layout Standard
28041 \begin_inset VSpace bigskip
28044 To set the line separation for all lines in a formula, the length
28051 \begin_inset Index idx
28054 \begin_layout Plain Layout
28064 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28075 \begin_inset space \thinspace{}
28080 \begin_inset space \thinspace{}
28083 mm additional line separation as in the previous example, the command
28086 \begin_layout Standard
28096 \begin_layout Standard
28097 is inserted in TeX-mode before the formula.
28098 This requires that the LaTeX-package
28106 \begin_layout Plain Layout
28111 is part of every LaTeX standard installation.
28117 \begin_inset Index idx
28120 \begin_layout Plain Layout
28126 was loaded in LaTeX-preamble with the line
28129 \begin_layout Standard
28137 \begin_layout Standard
28142 \begin_layout Plain Layout
28154 \begin_inset Formula \begin{eqnarray*}
28155 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}\\
28156 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
28164 \begin_layout Standard
28168 \begin_layout Plain Layout
28179 To get back to the predefined distance,
28185 is set to the value 3
28186 \begin_inset space \thinspace{}
28192 \begin_layout Subsubsection
28194 \begin_inset CommandInset label
28196 name "sub:Column-Separation"
28201 \begin_inset Index idx
28204 \begin_layout Plain Layout
28205 Formula ! multiline ! Column separation
28213 \begin_layout Standard
28214 Multiline formulas form a matrix.
28215 A formula in the eqnarray environment is for example a matrix with three
28217 By changing the column separation in this environment, the space beside
28218 the relation sign can be changed.
28221 \begin_layout Standard
28222 The column separation is specified with the length
28229 \begin_inset Index idx
28232 \begin_layout Plain Layout
28241 \begin_inset Newline newline
28244 column separation = 2
28245 \begin_inset space \thinspace{}
28255 \begin_inset Newline newline
28261 \begin_layout Standard
28271 \begin_layout Standard
28272 inserted in TeX-mode, sets for all following formulas a column separation
28274 \begin_inset space \thinspace{}
28278 To get back to the predefined distance,
28285 \begin_inset space \thinspace{}
28291 \begin_layout Standard
28293 \begin_inset space \thinspace{}
28296 cm column separation:
28300 \begin_layout Plain Layout
28312 \begin_inset Formula \begin{eqnarray*}
28319 A formula with the predefined column separation for matrices of 10
28320 \begin_inset space \thinspace{}
28327 \begin_layout Plain Layout
28339 \begin_inset Formula \begin{eqnarray*}
28349 \begin_layout Subsubsection
28351 \begin_inset Index idx
28354 \begin_layout Plain Layout
28363 \begin_layout Standard
28364 Long formulas can be typeset using these methods:
28367 \begin_layout Itemize
28368 When one side of the equation is much shorther than the line width, this
28369 one is chosen for the left side and the right side is typeset over two
28371 \begin_inset Formula \begin{eqnarray}
28372 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 \\
28373 & & -\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}
28378 The minus sign at the beginning of the second line does normally not appear
28379 as operator because it is the first character of the line.
28380 Thus it would not be surrounded by space and could not be distinguished
28381 from the fraction bar.
28383 \begin_inset space \thinspace{}
28386 pt space was inserted behind the minus sign with the command
28396 \begin_layout Plain Layout
28404 \begin_inset CommandInset ref
28406 reference "sub:Variable-Space"
28416 \begin_inset Index idx
28419 \begin_layout Plain Layout
28430 \begin_layout Itemize
28431 When both sides of the equation are too long, the command
28438 \begin_inset Index idx
28441 \begin_layout Plain Layout
28450 It is inserted to the first column of the first line and effects that all
28451 further insertions overwrite the following columns:
28452 \begin_inset Formula \begin{eqnarray}
28453 \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 \\
28454 & & -\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 \\
28455 & & =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}
28460 After the insertion of
28466 , the cursor is in a purple box that is a bit shifted to the left from the
28468 In this the formula is inserted.
28469 \begin_inset Newline newline
28472 The content of the further lines is inserted to the second or another formula
28474 The greater the column number where it was inserted, the larger the indentation.
28475 \begin_inset VSpace medskip
28479 \begin_inset Newline newline
28483 \begin_inset Note Greyedout
28486 \begin_layout Plain Layout
28487 Note the following when using
28496 \begin_layout Itemize
28497 The formula doesn't use the full page width.
28499 \begin_inset space \thinspace{}
28503 \begin_inset space \space{}
28507 \begin_inset Formula $-B^{2}$
28510 is added to the first line in the above example, it would have been outside
28512 To better use the width, negative space can be inserted at the beginning
28516 \begin_layout Itemize
28517 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28522 \begin_layout Plain Layout
28523 \begin_inset CommandInset href
28525 name "LyX-bug #1429"
28526 target "http://www.lyx.org/trac/ticket/1429"
28535 One can only set the cursor at the beginning of the line and move it with
28544 \begin_layout Itemize
28545 Other methods to set long formulas are offered by the environments described
28547 \begin_inset CommandInset ref
28549 reference "sub:Multline-Environment"
28554 \begin_inset CommandInset ref
28556 reference "sub:Multiline-Formula-Parts"
28563 \begin_layout Subsubsection
28565 \begin_inset CommandInset label
28567 name "sub:Multiline-Brackets"
28572 \begin_inset Index idx
28575 \begin_layout Plain Layout
28576 Brackets ! for multiline expressions
28584 \begin_layout Standard
28585 For brackets spanning multiple lines the following problem occurs:
28586 \begin_inset Formula \begin{eqnarray*}
28587 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28588 & & \left.\cdots+B-D\right]
28596 \begin_layout Standard
28597 The closing bracket is smaller than the opening bracket because brackets
28598 with variable size may not span multiple lines.
28601 \begin_layout Standard
28602 To set the bracket size for the second line correctly, the first line is
28610 \begin_inset Index idx
28613 \begin_layout Plain Layout
28621 and the second line with
28629 \begin_layout Plain Layout
28643 \begin_inset CommandInset ref
28645 reference "sub:Automatic-Bracket-Size"
28657 \begin_inset Index idx
28660 \begin_layout Plain Layout
28686 \begin_layout Plain Layout
28705 \begin_layout Plain Layout
28724 \begin_layout Plain Layout
28736 \begin_inset Formula $\downarrow$
28742 \begin_inset Index idx
28745 \begin_layout Plain Layout
28753 is inserted, because the multiplication operator with its limits is the
28754 largest symbol in the first line and this should be the size for the bracket
28755 in the second line.
28758 \begin_layout Standard
28759 The result is this:
28760 \begin_inset Formula \begin{eqnarray*}
28761 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28762 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28770 \begin_layout Subsection
28774 \begin_layout Standard
28775 Align environments can be used for every kind of multiline formulas.
28776 They are specially useful to set several formulas side by side.
28779 \begin_layout Standard
28780 Align environments consist of columns.
28781 The odd columns are right aligned, the even ones left aligned.
28782 Every line in an Align environment can be numbered.
28785 \begin_layout Standard
28786 Align environments are created via the menu
28788 Insert\SpecialChar \menuseparator
28794 Edit\SpecialChar \menuseparator
28795 Math\SpecialChar \menuseparator
28796 Change Formula Type
28798 already existing formulas can be converted to Align environments.
28801 \begin_layout Standard
28802 To add or delete columns, the math toolbar buttons
28803 \begin_inset Graphics
28804 filename ../images/tabular-feature_append-column.png
28810 \begin_inset Graphics
28811 filename ../images/tabular-feature_delete-column.png
28816 , respectively, or the menu
28818 Edit\SpecialChar \menuseparator
28824 \begin_layout Subsubsection
28825 Standard align Environment
28826 \begin_inset CommandInset label
28828 name "sub:Standard-align-Environment"
28833 \begin_inset Index idx
28836 \begin_layout Plain Layout
28837 Formula ! multiline ! align environment
28845 \begin_layout Standard
28846 This Align environment is created by presssing
28849 arg "newline-insert newline"
28852 in a formula or by the menu
28854 Insert\SpecialChar \menuseparator
28855 Math\SpecialChar \menuseparator
28856 AMS align Environment
28861 \begin_layout Standard
28862 An example for two formulas set side by side, that are created with a four
28863 column align environment:
28864 \begin_inset Formula \begin{align*}
28865 A & =\sin(B) & C & =D\\
28866 C & \ne A & B & \ne D
28871 As it can be seen, the formulas in this environment are placed so as if
28880 \begin_layout Plain Layout
28888 \begin_inset CommandInset ref
28890 reference "sub:Variable-Space"
28901 before the first and after every even column.
28902 When the formula style
28908 \begin_layout Plain Layout
28910 \begin_inset CommandInset ref
28912 reference "sec:Formula-Styles"
28923 is used, the formula is set without the
28929 before the first column.
28932 \begin_layout Subsubsection
28933 Alignat Environment
28934 \begin_inset Index idx
28937 \begin_layout Plain Layout
28938 Formula ! multiline ! alignat environment
28946 \begin_layout Standard
28947 The alignat environment has no predefined column separation.
28948 It can be inserted manually with the spaces that are described
28949 \begin_inset CommandInset ref
28951 reference "sub:Space"
28958 \begin_layout Standard
28959 The above example in the alignat environment where 1
28960 \begin_inset space \thinspace{}
28963 cm space was inserted at the beginning of the second formula:
28964 \begin_inset Formula \begin{alignat*}{2}
28965 A & =\sin(B) & \hspace{1cm}C & =D\\
28966 C & \ne A & B & \ne D
28971 Because the column separation can be set separately for every column, this
28972 environment is especially suitable to set three and more formulas side
28976 \begin_layout Subsubsection
28977 Flalign Environment
28978 \begin_inset CommandInset label
28980 name "sub:Flalign-Environment"
28985 \begin_inset Index idx
28988 \begin_layout Plain Layout
28989 Formula ! multiline ! flalign environment
28997 \begin_layout Standard
28998 In this environment the first two columns are always set as much as possible
28999 to the left and the last two ones to the right.
29001 \begin_inset Formula \begin{flalign*}
29002 A & =1 & B & =2 & C & =3\\
29003 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29011 \begin_layout Standard
29012 By creating a flalign environment with an odd number of columns where an
29013 empty TeX-brace is inserted to the last column, several formulas in a document
29014 can be set to the left, although the formula style
29019 As example the indented formula
29020 \begin_inset CommandInset ref
29022 reference "eq:VolInt"
29027 \begin_inset Formula \begin{flalign}
29028 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
29032 The first two columns contain the formula.
29033 To indent it as with the formula style
29038 \begin_inset space \thinspace{}
29041 pt space was inserted at the beginning of the first column.
29044 \begin_layout Subsection
29045 Eqnarray Environment
29046 \begin_inset CommandInset label
29048 name "sub:Eqnarray-Environment"
29053 \begin_inset Index idx
29056 \begin_layout Plain Layout
29057 Formula ! multiline ! eqnarray environment
29065 \begin_layout Standard
29066 When this environment has been created, three blue boxes appear.
29067 The content of the first box is right aligned, the content of the last
29069 The content of the middle box appears centered and a bit smaller, because
29070 it is designed to insert there only relation characters.
29071 \begin_inset Formula \begin{eqnarray*}
29072 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29082 \begin_layout Subsection
29084 \begin_inset Index idx
29087 \begin_layout Plain Layout
29088 Formula ! multiline ! gather environment
29096 \begin_layout Standard
29097 This environment consists of only one centered column.
29098 Every line can be numbered.
29099 \begin_inset Formula \begin{gather}
29109 \begin_layout Subsection
29110 Multline Environment
29111 \begin_inset CommandInset label
29113 name "sub:Multline-Environment"
29118 \begin_inset Index idx
29121 \begin_layout Plain Layout
29122 Formula ! multiline ! multline environment
29130 \begin_layout Standard
29131 The multline environment consists, like the gather environment, of only
29133 But the first line is left aligned, the last one right aligned.
29134 All other lines are centered.
29135 Therefore this environment is suitable for long formulas.
29137 \begin_inset CommandInset ref
29139 reference "eq:lefteqn"
29143 in the multline environment:
29144 \begin_inset Formula \begin{multline}
29145 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}\\
29146 -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}\\
29147 =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}}
29155 \begin_layout Standard
29156 In the output only the last (first) line of a multline environment appears
29157 numbered when the document numbering is right (left).
29161 \begin_layout Plain Layout
29162 numbering styles see
29163 \begin_inset CommandInset ref
29165 reference "sec:Formula-Styles"
29177 \begin_layout Standard
29185 \begin_inset Index idx
29188 \begin_layout Plain Layout
29203 \begin_inset Index idx
29206 \begin_layout Plain Layout
29214 a centered line can be right or left aligned, respectively.
29215 The commands are used as follows:
29218 \begin_layout Standard
29223 shoveright{line content}
29229 shoveleft{line content}
29232 \begin_layout Standard
29233 \begin_inset VSpace medskip
29243 \begin_inset Index idx
29246 \begin_layout Plain Layout
29254 specifies the distance of the first line from the left page margin.
29255 Predefined is the length 0
29256 \begin_inset space \thinspace{}
29262 \begin_layout Standard
29263 As example the above formula where the command
29266 \begin_layout Standard
29276 \begin_layout Standard
29277 was inserted in TeX-mode before:
29281 \begin_layout Plain Layout
29293 \begin_inset Formula \begin{multline}
29294 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}\\
29295 \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}}\\
29296 =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}}
29305 \begin_layout Plain Layout
29316 The second line was left aligned using
29325 \begin_layout Subsection
29326 Multiline Formula Parts
29327 \begin_inset CommandInset label
29329 name "sub:Multiline-Formula-Parts"
29334 \begin_inset Index idx
29337 \begin_layout Plain Layout
29338 Formula ! multiline ! formula parts
29346 \begin_layout Standard
29347 To display only parts of a formula with multiple lines, one of the following
29348 environments are used:
29365 They can be inserted via the menu
29367 Insert\SpecialChar \menuseparator
29370 or by using the commands described in this section.
29373 \begin_layout Standard
29374 The first three have the same properties as the corresponding multiline
29375 formula environments, but it is possible to set further formula parts beside
29378 \begin_inset Formula \[
29379 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29380 \Delta E\Delta t & \ge\frac{\hbar}{2}
29382 \right\} \textrm{Uncertainty relations}\]
29389 \begin_layout Standard
29390 To get this formula, a displayed formula is created where the command
29397 \begin_inset Index idx
29400 \begin_layout Plain Layout
29409 A purple box appears around the blue formula box where now columns and
29410 lines can be added.
29411 Outside the multiline environment other formula parts can be set, like
29415 \begin_layout Standard
29416 The aligned environment is also suitable for long formulas whose lines are
29417 horizontally aligned.
29418 Using aligned in a displayed formula has the advantage that the formula
29419 number is vertically centered behind the lines.
29421 \begin_inset CommandInset ref
29423 reference "eq:shortlong"
29427 in the aligned environment:
29428 \begin_inset Formula \begin{equation}
29429 \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}|}\\
29430 & -\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}|}
29439 \begin_layout Standard
29440 To use the environments
29459 \begin_inset Index idx
29462 \begin_layout Plain Layout
29477 \begin_inset Index idx
29480 \begin_layout Plain Layout
29495 \begin_inset Index idx
29498 \begin_layout Plain Layout
29506 are inserted, respectively.
29507 The split environment has the same properties as the aligned environment
29508 but it can only have two columns.
29511 \begin_layout Subsection
29512 Text in multiline Formulas
29513 \begin_inset CommandInset label
29515 name "sub:Text-in-multiline"
29520 \begin_inset Index idx
29523 \begin_layout Plain Layout
29530 \begin_inset Index idx
29533 \begin_layout Plain Layout
29534 Formula ! multiline ! text
29542 \begin_layout Standard
29543 In the Align environments, and the multline and gather environment, text
29544 can be inserted that will appear in a separate line and doesn't affect
29545 the column alignment.
29546 To do this, the command
29553 \begin_inset Index idx
29556 \begin_layout Plain Layout
29564 is used in the following scheme:
29567 \begin_layout Standard
29575 \begin_layout Standard
29576 The text should not be longer than a line because it cannot be hyphenated.
29577 As LyX doesn't yet support
29583 directly, the text is written as mathematical text.
29590 must hereby be at the beginning of a line and appears in the output above
29592 An example where the text was inserted at the beginning of the second line:
29593 \begin_inset Formula \begin{align}
29594 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29595 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29603 \begin_layout Section
29605 \begin_inset Index idx
29608 \begin_layout Plain Layout
29615 \begin_inset Index idx
29618 \begin_layout Plain Layout
29619 Formula ! numbering|see
29623 \begin_layout Plain Layout
29634 \begin_layout Plain Layout
29649 \begin_layout Subsection
29653 \begin_layout Standard
29654 Numbered formulas can be created with the menu
29656 Insert\SpecialChar \menuseparator
29657 Math\SpecialChar \menuseparator
29659 \begin_inset space ~
29667 \begin_inset space ~
29673 Existing formulas can be numbered with the menu
29675 Edit\SpecialChar \menuseparator
29676 Math\SpecialChar \menuseparator
29678 \begin_inset space ~
29686 arg "math-number-toggle"
29690 The formula number is displayed in LyX behind the formula as number sign
29692 The number sign is replaced in the output by the formula number.
29695 \begin_layout Standard
29696 When numbering is turned on in multiline formulas, all lines will be numbered.
29697 But the numbering can be controlled with the menu
29699 Edit\SpecialChar \menuseparator
29700 Math\SpecialChar \menuseparator
29702 \begin_inset space ~
29706 \begin_inset space ~
29710 \begin_inset space ~
29718 arg "math-number-line-toggle"
29724 \begin_layout Standard
29725 Except for inline formulas, all formulas can be numbered with two different
29727 \begin_inset CommandInset ref
29729 reference "sec:Formula-Styles"
29736 \begin_layout Subsection
29738 \begin_inset Index idx
29741 \begin_layout Plain Layout
29742 Cross-references ! to formulas
29750 \begin_layout Standard
29751 All labeled formulas can be cross-referenced.
29752 A label is added by the menu
29754 Insert\SpecialChar \menuseparator
29757 or the toolbar button
29758 \begin_inset Graphics
29759 filename ../images/label-insert.png
29765 The cursor must hereby be inside a displayed formula.
29766 A dialog pops up displaying the prefix
29771 The label is inserted there behind the prefix.
29772 The predefined prefix means
29773 \begin_inset Quotes eld
29777 \begin_inset Quotes erd
29780 and makes it easier to find labels in large documents because it marks
29781 it as formula label to divide it from e.
29782 \begin_inset space \thinspace{}
29786 \begin_inset space \space{}
29790 To change a label, the menu
29792 Insert\SpecialChar \menuseparator
29798 \begin_layout Standard
29799 The name of the label is displayed in LyX within two parentheses behind
29801 A formula with a label is always numbered.
29804 \begin_layout Standard
29805 Cross-references are inserted via the menu
29807 Insert\SpecialChar \menuseparator
29810 or with the toolbar button
29811 \begin_inset Graphics
29812 filename ../images/dialog-show-new-inset_ref.png
29818 A formula cross-reference appears in the output as formula number.
29819 When in the cross-reference dialog window the format
29823 is chosen, the cross-reference appears in the output as formula number
29825 \begin_inset Newline newline
29828 By right-clicking on a cross-reference in LyX, one jumps to the formula
29829 that is referenced.
29832 \begin_layout Standard
29833 Here are as examples cross-references to formulas of the following subsections:
29834 \begin_inset Note Note
29837 \begin_layout Plain Layout
29838 Note the different cross-reference types.
29846 \begin_layout Standard
29848 \begin_inset CommandInset ref
29855 \begin_inset CommandInset ref
29863 \begin_inset CommandInset ref
29869 ) big Latin letters are used for the numbering in contrary to (
29870 \begin_inset CommandInset ref
29879 \begin_layout Standard
29880 \begin_inset VSpace medskip
29883 When the argument of
29891 \begin_layout Plain Layout
29899 \begin_inset CommandInset ref
29901 reference "sub:User-defined-Numbering"
29912 contains a box like in
29913 \begin_inset CommandInset ref
29915 reference "sub:Paragraph-Boxes"
29919 , the formula cannot be referenced.
29922 \begin_layout Subsection
29924 \begin_inset Index idx
29927 \begin_layout Plain Layout
29928 Formula numbering ! subnumbering
29936 \begin_layout Standard
29937 With the help of the commands
29941 begin{subequations}
29949 formulas can be subnumbered.
29950 Both commands are inserted in TeX-mode.
29953 \begin_layout Standard
29955 \begin_inset Formula \begin{equation}
29956 A=C-B\label{eq:a}\end{equation}
29964 \begin_layout Plain Layout
29968 addtocounter{equation}{-1}
29977 \begin_layout Plain Layout
29981 begin{subequations}
29987 \begin_inset VSpace -5mm
29991 \begin_inset Formula \begin{equation}
29992 B=C-A\label{eq:b}\end{equation}
29997 \begin_inset Formula \begin{equation}
29998 C=A+B\label{eq:c}\end{equation}
30005 \begin_layout Standard
30009 \begin_layout Plain Layout
30021 \begin_layout Standard
30022 To create the example, the following is done:
30025 \begin_layout Enumerate
30026 first formula is inserted
30029 \begin_layout Enumerate
30034 addtocounter{equation}{-1}
30036 begin{subequations}
30037 \begin_inset Index idx
30040 \begin_layout Plain Layout
30049 \begin_inset Newline newline
30054 is inserted after the first formula
30057 \begin_layout Enumerate
30058 second formula is inserted
30061 \begin_layout Enumerate
30062 third formula is inserted
30065 \begin_layout Enumerate
30072 is inserted after the third formula
30075 \begin_layout Standard
30076 Every formula between the commands
30088 is subnumbered as a, b,
30089 \begin_inset Newline linebreak
30092 c, \SpecialChar \ldots{}
30093 For multiline formulas every line will be subnumbered.
30094 All subnumbered formulas are treated as
30099 But as every numbered formula increases the counter
30103 by one, the command
30109 is needed to decrease it.
30110 Otherwise the formulas
30111 \begin_inset CommandInset ref
30118 \begin_inset CommandInset ref
30125 \begin_inset CommandInset ref
30131 would be numbered as
30132 \begin_inset CommandInset ref
30139 \begin_inset CommandInset ref
30146 \begin_inset CommandInset ref
30155 \begin_layout Standard
30156 By inserting the commands in TeX-mode, a space is created between the first
30159 \begin_inset space \thinspace{}
30162 mm vertical space is inserted after the command
30166 begin{subequations}
30169 When the formula style
30175 \begin_layout Plain Layout
30177 \begin_inset CommandInset ref
30179 reference "sec:Formula-Styles"
30191 \begin_inset space \thinspace{}
30194 mm space is inserted instead.
30197 \begin_layout Standard
30198 Here is an example for a multiline formula where the numbering was turned
30199 off for the second line:
30203 \begin_layout Plain Layout
30207 begin{subequations}
30213 \begin_inset Formula \begin{eqnarray}
30214 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30215 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30216 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30225 \begin_layout Plain Layout
30237 \begin_layout Subsection
30238 User-defined Numbering
30239 \begin_inset CommandInset label
30241 name "sub:User-defined-Numbering"
30246 \begin_inset Index idx
30249 \begin_layout Plain Layout
30250 Formula numbering ! user-defined
30258 \begin_layout Standard
30259 \begin_inset Index idx
30262 \begin_layout Plain Layout
30263 Formula numbering ! self-defined delimiters
30268 With the standard numbering parentheses are set around the formula number.
30269 To replace the parentheses for example by vertical bars, the following
30270 line is added to the LaTeX-preamble:
30273 \begin_layout Standard
30285 \begin_inset Note Note
30288 \begin_layout Plain Layout
30289 This macro is already declared in the LaTeX-preamble for testing.
30290 To activate it, remove the percent sign at the beginning.
30298 \begin_layout Standard
30299 To use other characters, the vertical bars besides the
30303 are replaced by one ore more characters.
30304 To get only the formula number the vertical bars are omitted.
30307 \begin_layout Standard
30308 \begin_inset VSpace bigskip
30311 When there should be an expression of your choice instead of the consecutive
30312 formula number in parentheses behind the formula, the command
30319 \begin_inset Index idx
30322 \begin_layout Plain Layout
30331 \begin_inset Formula \begin{equation}
30332 A+B=C\tag{something}\label{eq:tag}\end{equation}
30336 In this example the command
30344 \begin_layout Plain Layout
30355 was inserted to the formula.
30358 \begin_layout Standard
30367 \begin_layout Plain Layout
30378 is inserted instead, the star prevents the parentheses around the expression:
30379 \begin_inset Formula \[
30380 A+B=C\tag*{something}\]
30387 \begin_layout Standard
30388 \begin_inset VSpace bigskip
30391 To restart the formula numbering with new document parts or sections, the
30392 following command is used:
30395 \begin_layout Standard
30400 @addtoreset{equation}{part}
30403 \begin_inset Index idx
30406 \begin_layout Plain Layout
30411 \begin_layout Plain Layout
30422 \begin_layout Plain Layout
30435 \begin_layout Plain Layout
30446 \begin_layout Plain Layout
30459 \begin_inset Newline newline
30463 \begin_inset Newline newline
30470 @addtoreset{equation}{section}
30473 \begin_layout Standard
30474 To be able to use these commands in TeX-mode, the
30475 \begin_inset Quotes eld
30479 \begin_inset Quotes erd
30482 character has to be made
30483 \begin_inset Quotes eld
30487 \begin_inset Quotes erd
30490 for LaTeX using the command
30504 So the command sequence in TeX-mode is:
30507 \begin_layout Standard
30513 \begin_inset Newline newline
30518 @addtoreset{equation}{section}
30519 \begin_inset Newline newline
30527 \begin_layout Standard
30528 In the LaTeX-preamble
30540 can be omitted as they are automatically internally inserted by LyX.
30543 \begin_layout Standard
30558 \begin_layout Plain Layout
30563 is part of the LaTeX-package
30568 \begin_inset Index idx
30571 \begin_layout Plain Layout
30572 Packages ! carlisle
30577 that is part of every LaTeX standard installation.
30583 \begin_inset Index idx
30586 \begin_layout Plain Layout
30587 Packages ! remreset
30592 has to be loaded in the LaTeX-preamble with the line
30595 \begin_layout Standard
30600 usepackage{remreset}
30603 \begin_layout Standard
30611 \begin_inset Index idx
30614 \begin_layout Plain Layout
30619 \begin_layout Plain Layout
30630 \begin_layout Plain Layout
30643 \begin_layout Plain Layout
30654 \begin_layout Plain Layout
30666 can be used with the same scheme as
30675 \begin_layout Standard
30676 \begin_inset VSpace bigskip
30679 Sometimes formulas should be numbered in the following form:
30682 \begin_layout Standard
30685 (section number.formula number)
30688 \begin_layout Standard
30689 The formula number should start with every section with
30690 \begin_inset Quotes eld
30694 \begin_inset Quotes erd
30700 \begin_layout Standard
30701 For this case there is the command
30708 \begin_inset Index idx
30711 \begin_layout Plain Layout
30719 , which is used with the following scheme:
30722 \begin_layout Standard
30727 numberwithin{counter}{sectioning}
30730 \begin_layout Standard
30731 Counter denotes what kind of numbering is affected, sectioning denotes what
30732 number is before the dot.
30735 \begin_layout Standard
30736 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30739 \begin_layout Standard
30744 numberwithin{equation}{section}
30747 \begin_layout Standard
30748 This is the result:
30752 \begin_layout Plain Layout
30756 numberwithin{equation}{section}
30762 \begin_inset Formula \begin{equation}
30763 A+B=C\end{equation}
30770 \begin_layout Standard
30772 \begin_inset space \thinspace{}
30776 \begin_inset space \space{}
30779 tables so that the number of the part is the sectioning,
30780 \begin_inset Newline newline
30787 numberwithin{table}{part}
30792 \begin_layout Standard
30793 To go back to the standard numbering or to prevent this kind of numbering
30794 when it is defined by the document class, the following command is inserted
30795 as TeX-Code or to the LaTeX-preamble:
30798 \begin_layout Standard
30808 \begin_inset Index idx
30811 \begin_layout Plain Layout
30825 \begin_layout Plain Layout
30841 \begin_inset Newline newline
30849 \begin_inset Newline newline
30861 \begin_layout Standard
30868 uses internally the command
30874 , described above, that also needs to be reverted.
30878 \begin_layout Plain Layout
30885 \begin_layout Plain Layout
30889 @removefromreset{equation}{section}
30892 \begin_layout Plain Layout
30904 \begin_layout Subsection
30905 Numbering with Roman Numbers and Letters
30906 \begin_inset Index idx
30909 \begin_layout Plain Layout
30910 Formula numbering ! with letters
30916 \begin_inset Index idx
30919 \begin_layout Plain Layout
30920 Formula numbering ! with Roman numbers
30928 \begin_layout Standard
30929 Formulas can also be numbered with Roman numbers and Latin letters.
30930 To number for example with small Roman numbers, the command
30933 \begin_layout Standard
30945 \begin_layout Standard
30946 is inserted before the formula in TeX-mode.
30954 \begin_inset Index idx
30957 \begin_layout Plain Layout
30965 redefines the predefined command
30981 \begin_layout Plain Layout
30988 has the same scheme like the command
30994 that is described in
30995 \begin_inset CommandInset ref
30997 reference "sub:The-Command-newcommand"
31010 is the formula counter.
31017 is used as prefix for a counter, the value of the counter is output as
31019 When a formula is numbered, LaTeX sets internally the command
31025 behind the formula.
31031 \begin_inset Index idx
31034 \begin_layout Plain Layout
31044 outputs the counter as small Roman number.
31047 \begin_layout Standard
31048 All formulas behind the command
31058 are now numbered Roman.
31059 To switch to numbering with big Roman numbers, the command is inserted
31073 \begin_inset Index idx
31076 \begin_layout Plain Layout
31088 \begin_inset Quotes eld
31092 \begin_inset Quotes erd
31095 with small Latin letters there is the command
31102 \begin_inset Index idx
31105 \begin_layout Plain Layout
31113 , for big ones there is the command
31120 \begin_inset Index idx
31123 \begin_layout Plain Layout
31136 \begin_layout Standard
31137 \begin_inset Note Greyedout
31140 \begin_layout Plain Layout
31145 Only maximal 26 formulas can be numbered with Latin letters in one document.
31153 \begin_layout Standard
31157 \begin_layout Plain Layout
31173 \begin_layout Standard
31174 \begin_inset Formula \begin{equation}
31175 A=\textrm{small roman}\end{equation}
31183 \begin_layout Plain Layout
31197 \begin_inset Formula \begin{equation}
31198 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
31206 \begin_layout Plain Layout
31220 \begin_inset Formula \begin{equation}
31221 C=\textrm{small Latin}\end{equation}
31229 \begin_layout Plain Layout
31243 \begin_inset Formula \begin{equation}
31244 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
31251 \begin_layout Standard
31252 To switch back to the default numbering, insert the command:
31255 \begin_layout Standard
31265 \begin_inset Index idx
31268 \begin_layout Plain Layout
31279 \begin_layout Standard
31283 \begin_layout Plain Layout
31297 \begin_inset Formula \begin{equation}
31298 E=\textrm{Arabic}\end{equation}
31305 \begin_layout Standard
31306 \begin_inset VSpace medskip
31309 As you see, formulas are numbered serially independent from the numbering
31311 When then numbering should start with
31312 \begin_inset Quotes eld
31316 \begin_inset Quotes erd
31319 when the style is changed, new equation counters have to be defined.
31320 A description about this can be found in the file
31321 \begin_inset CommandInset href
31323 name "Formula-numbering.lyx"
31324 target "run:Formula-numbering.lyx"
31331 \begin_layout Section
31332 Chemical Symbols and Equations
31333 \begin_inset CommandInset label
31335 name "sub:Chemical-Symbols-and"
31340 \begin_inset Index idx
31343 \begin_layout Plain Layout
31344 Chemical characters ! Symbols
31350 \begin_inset Index idx
31353 \begin_layout Plain Layout
31360 \begin_inset Index idx
31363 \begin_layout Plain Layout
31372 \begin_layout Standard
31373 An example text from chemistry:
31376 \begin_layout Quote
31378 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31381 -ion reacts with two
31382 \begin_inset Formula $\mathrm{Na^{+}}$
31385 -ions to sodium sulfate
31386 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31390 The chemical equation for this is:
31391 \begin_inset Formula \begin{equation}
31392 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
31399 \begin_layout Standard
31400 This chemical equation can directly be created as formula.
31401 To avoid that the symbols appear italic, everything is highlighted and
31402 changed by the shortcut
31408 to the upright font style.
31412 \begin_layout Plain Layout
31418 \begin_inset CommandInset ref
31420 reference "sub:Font-Styles"
31432 \begin_layout Standard
31433 A more convenient way to typeset chemical formulas is to use the command
31441 \begin_inset Index idx
31444 \begin_layout Plain Layout
31452 that is available when the LaTeX-package
31457 \begin_inset Index idx
31460 \begin_layout Plain Layout
31473 to a formula a new blue box appears where chemical formulas can be inserted
31474 in an intuitive way.
31477 \begin_layout Standard
31479 \begin_inset Tabular
31480 <lyxtabular version="3" rows="9" columns="2">
31481 <features tabularvalignment="middle">
31482 <column alignment="center" valignment="top" width="0">
31483 <column alignment="center" valignment="top" width="0">
31485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31488 \begin_layout Plain Layout
31494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31497 \begin_layout Plain Layout
31499 \begin_inset Note Note
31502 \begin_layout Plain Layout
31509 is only used as spacer.
31521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31524 \begin_layout Plain Layout
31531 \begin_layout Plain Layout
31545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31548 \begin_layout Plain Layout
31549 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31562 \begin_layout Plain Layout
31569 \begin_layout Plain Layout
31583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31586 \begin_layout Plain Layout
31587 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31600 \begin_layout Plain Layout
31607 \begin_layout Plain Layout
31621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31624 \begin_layout Plain Layout
31625 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31638 \begin_layout Plain Layout
31645 \begin_layout Plain Layout
31659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31662 \begin_layout Plain Layout
31663 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31676 \begin_layout Plain Layout
31683 \begin_layout Plain Layout
31698 \begin_layout Plain Layout
31713 \begin_layout Plain Layout
31727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31730 \begin_layout Plain Layout
31731 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31744 \begin_layout Plain Layout
31751 \begin_layout Plain Layout
31761 \begin_inset Formula $\downarrow$
31765 \begin_inset Formula $\to$
31773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31776 \begin_layout Plain Layout
31777 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31790 \begin_layout Plain Layout
31797 \begin_layout Plain Layout
31810 \begin_layout Plain Layout
31823 \begin_layout Plain Layout
31836 \begin_layout Plain Layout
31849 \begin_layout Plain Layout
31863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31866 \begin_layout Plain Layout
31867 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
31877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31880 \begin_layout Plain Layout
31887 \begin_layout Plain Layout
31900 \begin_layout Plain Layout
31913 \begin_layout Plain Layout
31926 \begin_layout Plain Layout
31943 \begin_layout Plain Layout
31957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31960 \begin_layout Plain Layout
31961 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
31977 \begin_layout Standard
31978 \begin_inset Note Greyedout
31981 \begin_layout Plain Layout
31986 Inserting a formula to a
31992 box will lead to LaTeX errors.
31993 In this case TeX code has to be used like for
32007 \begin_layout Plain Layout
32028 \begin_layout Standard
32035 the command for equation
32036 \begin_inset space ~
32040 \begin_inset CommandInset ref
32042 reference "eq:chem-reaction"
32047 \begin_inset Newline newline
32058 \begin_layout Plain Layout
32071 \begin_layout Plain Layout
32084 \begin_layout Plain Layout
32097 \begin_layout Plain Layout
32110 \begin_layout Plain Layout
32123 \begin_layout Plain Layout
32135 \begin_layout Standard
32136 To create multiline chemical equations first a multiline formula is created
32138 \begin_inset CommandInset ref
32140 reference "sec:Multiline-Formulas"
32145 Afterwards the command
32151 is used in every small blue box of the formula.
32153 \begin_inset CommandInset ref
32155 reference "eq:TEOS-reaction-1"
32160 \begin_inset CommandInset ref
32162 reference "eq:TEOS-reaction-2"
32166 are an example of a multi-stage chemical reaction where every equation
32167 has its own number.
32168 \begin_inset Formula \begin{eqnarray}
32169 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32170 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32178 \begin_layout Standard
32189 package provides the command
32196 \begin_inset Index idx
32199 \begin_layout Plain Layout
32207 that has to be used for special cases.
32208 For more information about
32214 and more examples have a look at the documentation of
32219 \begin_inset CommandInset citation
32228 \begin_layout Standard
32229 \begin_inset Newpage newpage
32235 \begin_layout Section
32239 \begin_layout Standard
32240 LyX supports two types of commutative diagrams:
32248 that are explained in the following.
32251 \begin_layout Subsection
32253 \begin_inset Index idx
32256 \begin_layout Plain Layout
32265 \begin_layout Standard
32266 Diagrams of this type visualize relations by vertical and horizontal lines
32268 \begin_inset Formula \[
32269 \begin{CD}A@>>>B@>>>C\\
32279 \begin_layout Standard
32280 To get them, the command
32285 \begin_inset Index idx
32288 \begin_layout Plain Layout
32298 is inserted to a formula.
32299 A blue box appears with two dashed lines where further commands can be
32304 arg "newline-insert newline"
32307 a new line is created.
32308 Horizontal relations are inserted in odd, vertical in even formula lines.
32311 \begin_layout Standard
32312 To create the relations there are the following commands:
32315 \begin_layout Itemize
32320 creates a left arrow,
32331 \begin_layout Itemize
32336 creates an up arrow,
32344 a vertical equal sign
32347 \begin_layout Itemize
32353 is a placeholder for non-existent relations
32356 \begin_layout Standard
32357 All arrows can be labeled as follows:
32360 \begin_layout Itemize
32361 Is text inserted between the first and second < or >, resp., it is placed
32363 When it is inserted between the second and third one, it appears under
32367 \begin_layout Itemize
32368 When text for vertical arrows is inserted between the first and second A
32369 or V, resp., it is placed left beside the arrow.
32370 When it is inserted between the second and third one, it appears right
32372 If the text contains an A or V, these letters must be set into a TeX-brace.
32375 \begin_layout Standard
32376 As example a diagram with all possible relations:
32379 \begin_layout Standard
32380 \begin_inset Formula \[
32381 \begin{CD}A@>j>>B@>>k>C@=F\\
32391 \begin_layout Standard
32392 The command for this is:
32393 \begin_inset Newline newline
32404 \begin_layout Plain Layout
32413 A@>j>>B@>>k>C@=F Ctrl+Return
32414 \begin_inset Newline newline
32418 \begin_inset Phantom HPhantom
32421 \begin_layout Plain Layout
32430 \begin_layout Plain Layout
32449 \begin_inset Formula $\to$
32455 \begin_inset Newline newline
32459 \begin_inset Phantom HPhantom
32462 \begin_layout Plain Layout
32471 \begin_layout Plain Layout
32488 \begin_layout Subsection
32490 \begin_inset Index idx
32493 \begin_layout Plain Layout
32494 Diagrams ! xymatrix
32502 \begin_layout Standard
32503 To be able to use xymatrices, the LaTeX-package
32508 A xymatrix is created by inserting the command
32515 Then you are able to add new matrix columns and rows like for normal matrices,
32517 \begin_inset CommandInset ref
32519 reference "sec:Matrices"
32526 \begin_layout Standard
32527 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32529 All possibilities to create commutative diagrams and decorations are explained
32534 that you find in the menu
32536 Help\SpecialChar \menuseparator
32538 \begin_inset space ~
32546 \begin_layout Subsection
32552 \begin_inset Index idx
32555 \begin_layout Plain Layout
32564 \begin_layout Standard
32569 -diagrams, the LaTeX-package
32578 -diagram is created by inserting the command
32585 Then you are able to add new matrix columns and rows like for normal matrices,
32587 \begin_inset CommandInset ref
32589 reference "sec:Matrices"
32596 \begin_layout Standard
32597 Examples how to create
32601 diagrams in LyX is given in the
32603 Feynman-diagram manual
32605 that you find in the menu
32607 Help\SpecialChar \menuseparator
32609 \begin_inset space ~
32617 \begin_layout Section
32618 User-defined Commands
32619 \begin_inset Index idx
32622 \begin_layout Plain Layout
32623 User-defined commands
32631 \begin_layout Standard
32632 \begin_inset Note Greyedout
32635 \begin_layout Plain Layout
32640 The names of user-defined commands and macros may only consist of Latin
32649 \begin_layout Subsection
32653 \begin_inset CommandInset label
32655 name "sub:The-Command-newcommand"
32660 \begin_inset Index idx
32663 \begin_layout Plain Layout
32664 User-defined commands !
32672 \begin_inset Index idx
32675 \begin_layout Plain Layout
32686 \begin_layout Standard
32687 Many LaTeX-commands are too long to be used frequently.
32688 But it is possible to define with the command
32694 new shorter commands.
32697 \begin_layout Standard
32698 The command scheme of
32707 \begin_layout Standard
32712 newcommand{new command name}[number of arguments][optional
32717 \begin_inset Newline newline
32721 \begin_inset Phantom HPhantom
32724 \begin_layout Plain Layout
32734 {command definition}
32737 \begin_layout Standard
32738 \begin_inset Note Greyedout
32741 \begin_layout Plain Layout
32746 Assure that the name of the new command is not already used in your document
32747 or by LaTeX-packages that you use.
32748 When you for example define the command
32760 , you get an error message because
32766 is already defined as command for
32767 \begin_inset Quotes eld
32771 \begin_inset Formula $\le$
32775 \begin_inset Quotes erd
32786 \begin_layout Standard
32787 The number of arguments is an integer in the range 0
32788 \begin_inset space \thinspace{}
32792 \begin_inset space \thinspace{}
32795 9 and specifies how many arguments the new command should have.
32796 With the optional value a value for an optional argument can be predefined.
32797 When this is done, the
32805 rgument of the new command is automatically an optional one.
32808 \begin_layout Standard
32809 Here are some examples:
32812 \begin_layout Itemize
32813 To define the command
32825 , the LaTeX-preamble line is:
32826 \begin_inset VSpace medskip
32830 \begin_inset Newline newline
32844 \begin_layout Itemize
32845 To define the command
32857 , the argument (that should be underlined) must be taken into account.
32858 For this the preamble line is:
32859 \begin_inset VSpace medskip
32863 \begin_inset Newline newline
32877 \begin_inset VSpace medskip
32881 \begin_inset Newline newline
32888 acts as argument placeholder, the
32892 behind it denotes that it is the placeholder for the first argument.
32895 \begin_layout Itemize
32903 \begin_inset space \thinspace{}
32907 \begin_inset space \space{}
32917 \begin_inset VSpace medskip
32921 \begin_inset Newline newline
32932 framebox#1#2{$#3$}}
32935 \begin_inset VSpace medskip
32939 \begin_inset Newline newline
32942 The two Dollar signs creates the extra formula needed for
32949 \begin_inset CommandInset ref
32951 reference "sub:Boxes-with-Frame"
32958 \begin_layout Itemize
32959 To create a new command for
32965 where the color for the box needn't to be specified, the argument for the
32966 color is defined optional:
32967 \begin_inset VSpace medskip
32971 \begin_inset Newline newline
32982 fcolorbox{#2}{#1}{$#3$}}
32985 \begin_inset VSpace medskip
32989 \begin_inset Newline newline
32992 When the color is not specified when using
32998 , the predefined color
33005 \begin_layout Standard
33006 A test of the new defined commands:
33009 \begin_layout Standard
33011 \begin_inset Tabular
33012 <lyxtabular version="3" rows="6" columns="2">
33013 <features tabularvalignment="middle">
33014 <column alignment="center" valignment="top" width="0">
33015 <column alignment="center" valignment="top" width="0">
33017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33020 \begin_layout Plain Layout
33026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33029 \begin_layout Plain Layout
33031 \begin_inset Note Note
33034 \begin_layout Plain Layout
33041 is only used as spacer.
33053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33056 \begin_layout Plain Layout
33063 \begin_layout Plain Layout
33077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33080 \begin_layout Plain Layout
33081 \begin_inset Formula $A\gr B$
33091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33094 \begin_layout Plain Layout
33102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33105 \begin_layout Plain Layout
33106 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33119 \begin_layout Plain Layout
33123 \begin_inset Formula $\to$
33129 \begin_inset Formula $\to$
33140 \begin_layout Plain Layout
33154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33157 \begin_layout Plain Layout
33158 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33171 \begin_layout Plain Layout
33175 \begin_inset Formula $\to$
33186 \begin_layout Plain Layout
33200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33203 \begin_layout Plain Layout
33204 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33217 \begin_layout Plain Layout
33223 \begin_inset Formula $\to$
33234 \begin_layout Plain Layout
33248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33251 \begin_layout Plain Layout
33252 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33268 \begin_layout Subsection
33270 \begin_inset Index idx
33273 \begin_layout Plain Layout
33274 User-defined commands! Math macros
33280 \begin_inset Index idx
33283 \begin_layout Plain Layout
33292 \begin_layout Standard
33293 User-defined commands are especially convenient for complex expressions.
33294 When you are for example dealing in a document with quadratic equations,
33295 the same solution type occurs several times.
33296 The general form of a quadratic equation is
33297 \begin_inset Formula \[
33298 0=\lambda^{2}+p\lambda+q\]
33302 The general form of the solution is
33303 \begin_inset Formula \[
33304 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
33311 \begin_layout Standard
33312 To define a command for the solution formula where only the three parameters
33314 \begin_inset Formula $\lambda$
33318 \begin_inset Formula $p$
33322 \begin_inset Formula $q$
33325 need to be specified and the index of
33326 \begin_inset Formula $\lambda$
33329 can be given optionally, the LaTeX-preamble line is
33330 \begin_inset Newline newline
33346 \begin_inset Newline newline
33350 \begin_inset Phantom HPhantom
33353 \begin_layout Plain Layout
33367 frac{#3^{2}}{4}-#4}}
33370 \begin_layout Standard
33371 To create with this the solution formula, the command
33372 \begin_inset Newline newline
33382 \begin_inset Formula $\to$
33388 \begin_inset Formula $\to$
33395 is inserted to a formula
33400 \begin_layout Standard
33401 The definition of the new command is unintuitive because one has to know
33402 the schemes of all used LaTeX commands, e.
33403 \begin_inset space \thinspace{}
33407 \begin_inset space \space{}
33410 that a fraction is inserted in LaTeX as
33414 frac{numerator}{denominator}
33417 Furthermore one can easily forget a brace in the definition and cannot
33418 see in LyX what the new command is doing.
33419 To avoid these problems LyX offers the possibility to use math macros instead
33429 \begin_layout Standard
33430 A math macro is created by using the menu
33432 Insert\SpecialChar \menuseparator
33433 Math\SpecialChar \menuseparator
33436 or the toolbar button
33437 \begin_inset Graphics
33438 filename ../images/math-macro_newmacroname_newcommand.png
33444 The math macro toolbar appears together with the following box where the
33446 \begin_inset Newline newline
33450 \begin_inset space \hspace*{\fill}
33454 \begin_inset Graphics
33455 filename clipart/macrobox.png
33460 \begin_inset space \hspace*{\fill}
33464 \begin_inset Newline newline
33468 \begin_inset FormulaMacro
33469 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33474 newmacroname is the default name of the macro that should be changed to
33475 something sensible.
33476 The wanted formula is inserted in the first blue box.
33477 An argument placeholder is inserted with the command
33484 \begin_inset space \thinspace{}
33488 \begin_inset space \space{}
33497 or by using the macro toolbar button
33498 \begin_inset Graphics
33499 filename ../images/math-macro-add-param.png
33505 Argument placeholders are displayed red.
33506 Maximum 9 arguments are possible.
33507 Optional arguments are created with the toolbar button
33508 \begin_inset Graphics
33509 filename ../images/math-macro-add-optional-param.png
33515 The first non-optional argument can be transformed to an optional one with
33517 \begin_inset Graphics
33518 filename ../images/math-macro-make-optional.png
33524 In the second blue box the appearance of the macro in LyX can be defined.
33525 Normally you want to see it as it is defined, so the box is kept empty.
33526 But when you have created a macro that needs lot of space on the screen,
33527 you can insert in the box for example
33528 \begin_inset Newline newline
33558 \begin_inset Newline newline
33563 For the macro only the arguments with the macro name in front of them will
33564 then be displayed in LyX, leading to a better overview.
33565 The formula appears in the output as defined in the first box.
33566 \begin_inset Newline newline
33569 The appearance of macros in formulas can furthermore be changed for single
33570 macros by setting the cursor in the macro and using the menu
33572 View\SpecialChar \menuseparator
33574 \begin_inset space ~
33578 \begin_inset space ~
33586 \begin_layout Standard
33587 To use a macro, the macro name is inserted as command to a formula, in our
33595 Our macro looks in LyX like this:
33596 \begin_inset Newline newline
33600 \begin_inset space \hspace*{\fill}
33604 \begin_inset Graphics
33605 filename clipart/macrouse.png
33610 \begin_inset space \hspace*{\fill}
33614 \begin_inset Newline newline
33617 Here is our macro example with the arguments
33618 \begin_inset Formula $x$
33622 \begin_inset Formula $\ln(x)$
33626 \begin_inset Formula $B$
33632 \begin_layout Standard
33633 \begin_inset Formula \[
33641 \begin_layout Standard
33642 LyX offers in the menu
33644 Tools\SpecialChar \menuseparator
33645 Preferences\SpecialChar \menuseparator
33646 Editing\SpecialChar \menuseparator
33649 different styles to edit macros.
33650 To find the style that suits you the most, choose a style and set the cursor
33651 in a macro formula to see the difference.
33654 \begin_layout Standard
33655 A math macro is transformed internally to a
33661 command when exporting the document.
33668 command is not placed in the LaTeX-preamble, therefore macros can only
33669 be used in formulas that are in the document below the macro definition
33673 \begin_layout Standard
33674 Math macros can also be directly be created from a
33681 When writing for example the command
33684 \begin_inset Newline newline
33693 xleftarrow[#2]{#1}}
33694 \begin_inset Newline newline
33699 in LyX as normal text, highlighting it completely and using then the shortcut
33704 , the command will be transformed to a math macro.
33705 Using this method you need to be careful that the
33711 command is typed correctly, otherwise you get a faulty macro leading to
33715 \begin_layout Standard
33716 Math macros currently yet have the problem that further formulas in macro
33717 definitions are handled wrongly.
33718 Therefore the example
33725 \begin_inset CommandInset ref
33727 reference "sub:The-Command-newcommand"
33731 cannot be created as macro.
33734 \begin_layout Standard
33735 When the cursor is in a macro definition box, you will see the macro toolbar
33739 \begin_layout Standard
33740 \begin_inset VSpace defskip
33746 \begin_layout Standard
33747 \begin_inset Graphics
33748 filename clipart/MacroToolbar.png
33753 \begin_inset Index idx
33756 \begin_layout Plain Layout
33765 \begin_layout Standard
33766 \begin_inset VSpace defskip
33772 \begin_layout Standard
33773 The macro toolbar contains from left to right the following buttons:
33776 \begin_layout Standard
33777 \begin_inset VSpace defskip
33783 \begin_layout Standard
33784 \begin_inset Tabular
33785 <lyxtabular version="3" rows="9" columns="2">
33786 <features islongtable="true" longtabularalignment="center">
33787 <column alignment="left" valignment="top" width="0">
33788 <column alignment="left" valignment="top" width="85col%">
33789 <row interlinespace="2.5mm">
33790 <cell alignment="center" valignment="top" usebox="none">
33793 \begin_layout Plain Layout
33794 \begin_inset Graphics
33795 filename ../images/math-macro-remove-param.png
33796 BoundingBox 0bp 5bp 20bp 25bp
33797 rotateOrigin center
33806 <cell alignment="center" valignment="top" usebox="none">
33809 \begin_layout Plain Layout
33812 Edit\SpecialChar \menuseparator
33813 Math\SpecialChar \menuseparator
33815 \begin_inset space ~
33818 Definition\SpecialChar \menuseparator
33819 Remove Last Argument
33825 <row interlinespace="2.5mm">
33826 <cell alignment="center" valignment="top" usebox="none">
33829 \begin_layout Plain Layout
33830 \begin_inset Graphics
33831 filename ../images/math-macro-add-param.png
33832 BoundingBox 0bp 5bp 20bp 25bp
33833 rotateOrigin center
33842 <cell alignment="center" valignment="top" usebox="none">
33845 \begin_layout Plain Layout
33848 Edit\SpecialChar \menuseparator
33849 Math\SpecialChar \menuseparator
33851 \begin_inset space ~
33854 Definition\SpecialChar \menuseparator
33861 <row interlinespace="2.5mm">
33862 <cell alignment="center" valignment="top" usebox="none">
33865 \begin_layout Plain Layout
33866 \begin_inset Graphics
33867 filename ../images/math-macro-make-optional.png
33868 BoundingBox 0bp 5bp 20bp 25bp
33869 rotateOrigin center
33878 <cell alignment="center" valignment="top" usebox="none">
33881 \begin_layout Plain Layout
33884 Edit\SpecialChar \menuseparator
33885 Math\SpecialChar \menuseparator
33887 \begin_inset space ~
33890 Definition\SpecialChar \menuseparator
33891 Make First Non-Optional into
33892 \begin_inset Newline newline
33896 \begin_inset Phantom HPhantom
33899 \begin_layout Plain Layout
33902 Edit\SpecialChar \menuseparator
33903 Math\SpecialChar \menuseparator
33905 \begin_inset space ~
33908 Definition\SpecialChar \menuseparator
33920 <row interlinespace="2.5mm">
33921 <cell alignment="center" valignment="top" usebox="none">
33924 \begin_layout Plain Layout
33925 \begin_inset Graphics
33926 filename ../images/math-macro-make-nonoptional.png
33927 BoundingBox 0bp 5bp 20bp 25bp
33928 rotateOrigin center
33937 <cell alignment="center" valignment="top" usebox="none">
33940 \begin_layout Plain Layout
33943 Edit\SpecialChar \menuseparator
33944 Math\SpecialChar \menuseparator
33946 \begin_inset space ~
33949 Definition\SpecialChar \menuseparator
33950 Make Last Optional into
33951 \begin_inset Newline newline
33955 \begin_inset Phantom HPhantom
33958 \begin_layout Plain Layout
33961 Edit\SpecialChar \menuseparator
33962 Math\SpecialChar \menuseparator
33964 \begin_inset space ~
33967 Definition\SpecialChar \menuseparator
33973 Non-Optional Argument
33979 <row interlinespace="2.5mm">
33980 <cell alignment="center" valignment="top" usebox="none">
33983 \begin_layout Plain Layout
33984 \begin_inset Graphics
33985 filename ../images/math-macro-remove-optional-param.png
33986 BoundingBox 0bp 5bp 20bp 25bp
33987 rotateOrigin center
33996 <cell alignment="center" valignment="top" usebox="none">
33999 \begin_layout Plain Layout
34002 Edit\SpecialChar \menuseparator
34003 Math\SpecialChar \menuseparator
34005 \begin_inset space ~
34008 Definition\SpecialChar \menuseparator
34009 Remove Optional Argument
34015 <row interlinespace="2.5mm">
34016 <cell alignment="center" valignment="top" usebox="none">
34019 \begin_layout Plain Layout
34020 \begin_inset Graphics
34021 filename ../images/math-macro-add-optional-param.png
34022 BoundingBox 0bp 5bp 20bp 25bp
34023 rotateOrigin center
34032 <cell alignment="center" valignment="top" usebox="none">
34035 \begin_layout Plain Layout
34038 Edit\SpecialChar \menuseparator
34039 Math\SpecialChar \menuseparator
34041 \begin_inset space ~
34044 Definition\SpecialChar \menuseparator
34045 Insert Optional Argument
34051 <row interlinespace="2.5mm">
34052 <cell alignment="center" valignment="top" usebox="none">
34055 \begin_layout Plain Layout
34056 \begin_inset Graphics
34057 filename ../images/math-macro-remove-greedy-param.png
34058 BoundingBox 0bp 5bp 20bp 25bp
34059 rotateOrigin center
34068 <cell alignment="center" valignment="top" usebox="none">
34071 \begin_layout Plain Layout
34074 Edit\SpecialChar \menuseparator
34075 Math\SpecialChar \menuseparator
34077 \begin_inset space ~
34080 Definition\SpecialChar \menuseparator
34081 Remove Last Argument
34082 \begin_inset Newline newline
34086 \begin_inset Phantom HPhantom
34089 \begin_layout Plain Layout
34092 Edit\SpecialChar \menuseparator
34093 Math\SpecialChar \menuseparator
34095 \begin_inset space ~
34098 Definition\SpecialChar \menuseparator
34104 Spitting Out To The Right
34110 <row interlinespace="2.5mm">
34111 <cell alignment="center" valignment="top" usebox="none">
34114 \begin_layout Plain Layout
34115 \begin_inset Graphics
34116 filename ../images/math-macro-append-greedy-param.png
34117 BoundingBox 0bp 5bp 20bp 25bp
34118 rotateOrigin center
34127 <cell alignment="center" valignment="top" usebox="none">
34130 \begin_layout Plain Layout
34133 Edit\SpecialChar \menuseparator
34134 Math\SpecialChar \menuseparator
34136 \begin_inset space ~
34139 Definition\SpecialChar \menuseparator
34141 \begin_inset Newline newline
34145 \begin_inset Phantom HPhantom
34148 \begin_layout Plain Layout
34151 Edit\SpecialChar \menuseparator
34152 Math\SpecialChar \menuseparator
34154 \begin_inset space ~
34157 Definition\SpecialChar \menuseparator
34163 Eating From The Right
34169 <row interlinespace="2.5mm">
34170 <cell alignment="center" valignment="top" usebox="none">
34173 \begin_layout Plain Layout
34174 \begin_inset Graphics
34175 filename ../images/math-macro-add-greedy-optional-param.png
34176 BoundingBox 0bp 5bp 20bp 25bp
34177 rotateOrigin center
34186 <cell alignment="center" valignment="top" usebox="none">
34189 \begin_layout Plain Layout
34192 Edit\SpecialChar \menuseparator
34193 Math\SpecialChar \menuseparator
34195 \begin_inset space ~
34198 Definition\SpecialChar \menuseparator
34199 Append Optional Argument
34200 \begin_inset Newline newline
34204 \begin_inset Phantom HPhantom
34207 \begin_layout Plain Layout
34210 Edit\SpecialChar \menuseparator
34211 Math\SpecialChar \menuseparator
34213 \begin_inset space ~
34216 Definition\SpecialChar \menuseparator
34222 Eating From The Right
34235 \begin_layout Standard
34236 \begin_inset Newpage newpage
34242 \begin_layout Section
34244 \begin_inset Index idx
34247 \begin_layout Plain Layout
34256 \begin_layout Subsection
34258 \begin_inset Index idx
34261 \begin_layout Plain Layout
34270 \begin_layout Standard
34271 Negative numbers often look ugly in formulas because the minus sign before
34272 the number is set with the same length as the minus operator sign.
34273 When writing the negative number in normal text, the minus sign appears
34277 \begin_layout Standard
34278 Thus, the problem disappears when converting the minus sign to mathematical
34282 \begin_layout Standard
34283 An example to visualize the problem:
34286 \begin_layout Standard
34288 \begin_inset Tabular
34289 <lyxtabular version="3" rows="3" columns="2">
34290 <features tabularvalignment="middle">
34291 <column alignment="right" valignment="top" width="0">
34292 <column alignment="left" valignment="top" width="0">
34294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34297 \begin_layout Plain Layout
34303 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34306 \begin_layout Plain Layout
34314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34317 \begin_layout Plain Layout
34323 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34326 \begin_layout Plain Layout
34327 \begin_inset Formula $x=-2$
34337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34340 \begin_layout Plain Layout
34346 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34349 \begin_layout Plain Layout
34350 \begin_inset Formula $x=\textrm{-}2$
34366 \begin_layout Subsection
34367 Comma as decimal Separator
34368 \begin_inset Index idx
34371 \begin_layout Plain Layout
34380 \begin_layout Standard
34381 In LaTeX a comma inside a formula is used, according to the English convention,
34382 as number group separator.
34383 So there will be space added behind all commas in formulas.
34386 \begin_layout Standard
34387 To avoid this, the comma is highlighted and changed to mathematical text
34397 \begin_layout Standard
34398 To use all formula commas in the document as decimal separator, the file
34407 \begin_layout Plain Layout
34412 is part of the LaTeX-package
34417 \begin_inset Index idx
34420 \begin_layout Plain Layout
34425 \begin_layout Plain Layout
34445 \begin_inset Index idx
34448 \begin_layout Plain Layout
34454 is loaded with the LaTeX-preamble line
34457 \begin_layout Standard
34465 \begin_layout Subsection
34467 \begin_inset CommandInset label
34469 name "sub:Physical-Vectors"
34474 \begin_inset Index idx
34477 \begin_layout Plain Layout
34486 \begin_layout Standard
34487 Predefined vectors are offered by the LaTeX-package
34492 \begin_inset Index idx
34495 \begin_layout Plain Layout
34501 that is loaded with the LaTeX-preamble line
34504 \begin_layout Standard
34512 \begin_layout Standard
34516 \begin_layout Plain Layout
34526 \begin_inset Note Note
34529 \begin_layout Plain Layout
34530 The following table will only be displayed when the LaTeX-package
34542 \begin_layout Standard
34543 The following commands are defined:
34546 \begin_layout Standard
34548 \begin_inset Tabular
34549 <lyxtabular version="3" rows="4" columns="2">
34550 <features tabularvalignment="middle">
34551 <column alignment="center" valignment="top" width="0">
34552 <column alignment="center" valignment="top" width="0">
34554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34557 \begin_layout Plain Layout
34563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34566 \begin_layout Plain Layout
34574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34577 \begin_layout Plain Layout
34587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34590 \begin_layout Plain Layout
34591 \begin_inset Formula $\Bra{\psi}$
34601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34604 \begin_layout Plain Layout
34614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34617 \begin_layout Plain Layout
34618 \begin_inset Formula $\Ket{\psi}$
34628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34631 \begin_layout Plain Layout
34643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34646 \begin_layout Plain Layout
34647 \begin_inset Formula $\Braket{\psi|\phi}$
34663 \begin_layout Standard
34670 assures that all vertical bars are set in the size of the surrounding brackets:
34671 \begin_inset Formula \[
34672 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
34680 \begin_layout Plain Layout
34690 \begin_inset Note Note
34693 \begin_layout Plain Layout
34694 The following will be displayed when the LaTeX-package
34706 \begin_layout Standard
34707 You need to install the LaTeX-package
34711 to see the rest of this subsection in the output.
34714 \begin_layout Standard
34718 \begin_layout Plain Layout
34730 \begin_layout Standard
34737 can also be achieved using the command
34743 , that is described in
34744 \begin_inset CommandInset ref
34746 reference "sub:Automatic-Bracket-Size"
34753 \begin_layout Subsection
34754 Self-defined Fractions
34755 \begin_inset CommandInset label
34757 name "sub:Self-defined-Fractions"
34762 \begin_inset Index idx
34765 \begin_layout Plain Layout
34766 Fractions ! self-defined
34774 \begin_layout Standard
34775 To define custom commands for fractions, the command
34782 \begin_inset Index idx
34785 \begin_layout Plain Layout
34793 is used in the following scheme:
34796 \begin_layout Standard
34809 bracket}{fraction bar thickness}{style}
34810 \begin_inset Newline newline
34814 \begin_inset Phantom HPhantom
34817 \begin_layout Plain Layout
34827 {numerator}{denominator}
34830 \begin_layout Standard
34831 The style is a number in the range of 0
34832 \begin_inset space \thinspace{}
34836 \begin_inset space \thinspace{}
34842 \begin_layout Standard
34844 \begin_inset Tabular
34845 <lyxtabular version="3" rows="5" columns="2">
34846 <features tabularvalignment="middle">
34847 <column alignment="center" valignment="top" width="0">
34848 <column alignment="center" valignment="top" width="0">
34850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34853 \begin_layout Plain Layout
34859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34862 \begin_layout Plain Layout
34870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34873 \begin_layout Plain Layout
34879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34882 \begin_layout Plain Layout
34883 display style formula
34890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34893 \begin_layout Plain Layout
34899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34902 \begin_layout Plain Layout
34910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34913 \begin_layout Plain Layout
34919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34922 \begin_layout Plain Layout
34930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34933 \begin_layout Plain Layout
34939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34942 \begin_layout Plain Layout
34956 \begin_layout Standard
34957 When no style is given, the size is adjusted to the surrounding environment
34958 like for the command
34967 \begin_layout Standard
34968 When no fraction bar thickness is given, the predefined value of 0.4
34969 \begin_inset space \thinspace{}
34975 \begin_layout Standard
34976 \begin_inset VSpace medskip
34979 For example, the commands
34992 \begin_inset CommandInset ref
34994 reference "sub:Fractions"
34998 are defined with the commands
35001 \begin_layout Standard
35010 genfrac{}{}{}{0}{#1}{#2}}
35013 \begin_layout Standard
35017 \begin_layout Standard
35026 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35029 \begin_layout Standard
35030 \begin_inset VSpace medskip
35033 To define a fraction where the fraction bar thickness can be given as optional
35034 argument, the following line is inserted to the LaTeX-preamble:
35037 \begin_layout Standard
35046 genfrac{}{}{#1}{}{#2}{#3}}
35049 \begin_layout Standard
35051 \begin_inset Formula \begin{align*}
35052 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35053 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35058 As one can see, the distance of the numerator and the denominator to the
35059 fraction bar is round about three times the bar thickness.
35062 \begin_layout Subsection
35064 \begin_inset Index idx
35067 \begin_layout Plain Layout
35076 \begin_layout Standard
35077 To cancel formulas or formula parts, the LaTeX-package
35082 \begin_inset Index idx
35085 \begin_layout Plain Layout
35091 has to be loaded with the LaTeX-preamble line
35094 \begin_layout Standard
35099 usepackage[samesize]{cancel}
35102 \begin_layout Standard
35106 \begin_layout Plain Layout
35116 \begin_inset Note Note
35119 \begin_layout Plain Layout
35120 The following table will only be displayed when the LaTeX-package
35132 \begin_layout Standard
35133 There are four ways to cancel formulas:
35136 \begin_layout Standard
35138 \begin_inset Tabular
35139 <lyxtabular version="3" rows="5" columns="2">
35140 <features tabularvalignment="middle">
35141 <column alignment="center" valignment="top" width="0">
35142 <column alignment="center" valignment="top" width="0">
35144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35147 \begin_layout Plain Layout
35153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35156 \begin_layout Plain Layout
35158 \begin_inset Note Note
35161 \begin_layout Plain Layout
35168 are used here as spacer.
35180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35183 \begin_layout Plain Layout
35192 \begin_layout Plain Layout
35206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35209 \begin_layout Plain Layout
35210 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35223 \begin_layout Plain Layout
35232 \begin_layout Plain Layout
35246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35249 \begin_layout Plain Layout
35250 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35263 \begin_layout Plain Layout
35272 \begin_layout Plain Layout
35286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35289 \begin_layout Plain Layout
35290 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35303 \begin_layout Plain Layout
35307 \begin_inset Formula $\to$
35318 \begin_layout Plain Layout
35332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35335 \begin_layout Plain Layout
35336 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35352 \begin_layout Standard
35359 is especially suitable to visualize the reduction of fractions within formulas:
35360 \begin_inset Formula \[
35361 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
35368 \begin_layout Standard
35372 \begin_layout Plain Layout
35382 \begin_inset Note Note
35385 \begin_layout Plain Layout
35386 The following will be displayed when the LaTeX-package
35398 \begin_layout Standard
35399 You need to install the LaTeX-package
35403 to see the rest of this subsection in the output.
35406 \begin_layout Standard
35410 \begin_layout Plain Layout
35422 \begin_layout Subsection
35423 Formulas in Section Headings
35424 \begin_inset CommandInset label
35426 name "sub:Formulas-in-Section"
35431 \begin_inset Index idx
35434 \begin_layout Plain Layout
35435 Formula ! in section headings
35443 \begin_layout Standard
35444 When formulas are used in section headings, the following has to be taken
35448 \begin_layout Standard
35449 \begin_inset Note Greyedout
35452 \begin_layout Plain Layout
35458 \begin_inset Index idx
35461 \begin_layout Plain Layout
35462 Packages ! hyperref
35467 support is enabled in the document settings dialog under
35470 \begin_inset space ~
35475 , PDF-bookmarks are created for every section heading in the table of contents.
35476 If a section heading contains formulas, they are incorrectly displayed
35477 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35486 \begin_layout Standard
35487 Both problems can be solved by inserting at the end of the section heading
35488 a short title with the menu
35490 Insert\SpecialChar \menuseparator
35492 \begin_inset space ~
35498 Short titles are used as alternative for multiline section headings to
35499 keep the table of contents clearly arranged.
35500 Only the short title appears in the table of contents and therefore also
35501 in the PDF-bookmark.
35504 \begin_layout Standard
35505 When formulas should be used in the table of contents but
35509 is used, one can use the following command in TeX-mode:
35512 \begin_layout Standard
35517 texorpdfstring{part}{alternative}
35518 \begin_inset Index idx
35521 \begin_layout Plain Layout
35532 \begin_layout Standard
35533 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35534 This can be characters, formulas, footnotes, but also cross-references.
35535 The alternative is used instead of the part for the bookmark.
35538 \begin_layout Standard
35539 Here are two example headings:
35540 \begin_inset VSpace -3mm
35547 \begin_layout Plain Layout
35559 \begin_layout Subsubsection
35560 Heading without formula in table of contents
35561 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35565 \begin_inset Argument
35568 \begin_layout Plain Layout
35569 Heading without formula in table of contents
35577 \begin_layout Subsubsection
35578 Heading with formula in table of contents
35582 \begin_layout Plain Layout
35592 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35599 \begin_layout Plain Layout
35609 \begin_layout Standard
35613 \begin_layout Plain Layout
35622 In the first heading a short title was used, in the second one
35631 \begin_layout Standard
35632 To get the same formatting as for the other headings, the complete heading
35641 \begin_layout Plain Layout
35643 \begin_inset CommandInset ref
35645 reference "sub:Bold-Formulas"
35657 \begin_layout Subsection
35658 Formulas in multi-column Text
35659 \begin_inset Index idx
35662 \begin_layout Plain Layout
35663 Formula ! in multi-column text
35671 \begin_layout Standard
35672 Formulas in multi-column text are often too wide to fit into a column and
35673 thus need to be set over the whole page width.
35674 This is done by using the LaTeX-package
35682 \begin_layout Plain Layout
35687 is part of every LaTeX standard installation.
35693 \begin_inset Index idx
35696 \begin_layout Plain Layout
35697 Packages ! multicol
35702 , that is loaded with the LaTeX-preamble line
35705 \begin_layout Standard
35710 usepackage{multicol}
35713 \begin_layout Standard
35714 \begin_inset Note Greyedout
35717 \begin_layout Plain Layout
35718 Note herby that the setting
35721 \begin_inset space ~
35728 Document\SpecialChar \menuseparator
35734 \begin_inset space ~
35754 \begin_layout Standard
35755 Before the multi-column text the command
35758 \begin_layout Standard
35763 begin{multicols}{column number}
35766 \begin_layout Standard
35767 is written in TeX-mode.
35768 The column number is a number in the range of 2
35769 \begin_inset space \thinspace{}
35773 \begin_inset space \thinspace{}
35777 Before the formula the multi-column text is ended by inserting the command
35780 \begin_layout Standard
35788 \begin_layout Standard
35792 \begin_layout Standard
35793 Due to the command some space is automatically added before the formula.
35795 \begin_inset space \thinspace{}
35798 mm vertical space is inserted before the formula.
35799 When the formula style
35805 \begin_layout Plain Layout
35807 \begin_inset CommandInset ref
35809 reference "sec:Formula-Styles"
35821 \begin_inset space \thinspace{}
35824 mm space is inserted instead.
35827 \begin_layout Standard
35828 As example a multi-column text with a displayed formula:
35831 \begin_layout Standard
35837 \begin_layout Plain Layout
35841 begin{multicols}{2}
35846 Das Spektrum wird fouriertransformiert.
35847 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35848 , Lösungsmittel) zu trennen.
35849 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35850 nun das Aussehen des Ausgangssignals.
35851 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35852 über alle Phasen integrieren muss.
35854 \begin_inset Formula $S$
35857 unser normiertes Ausgangssignal und
35858 \begin_inset Formula $P$
35861 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35865 \begin_layout Plain Layout
35875 \begin_inset VSpace -6mm
35879 \begin_inset Formula \begin{equation}
35880 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
35888 \begin_layout Plain Layout
35892 begin{multicols}{2}
35898 \begin_inset Formula $S_{0}$
35901 das Signal ohne Gradient ist und die Normierungsbedingung
35902 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35906 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35908 \begin_inset Formula $\nicefrac{\pi}{2}$
35912 \begin_inset space \thinspace{}
35915 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35916 das Signal zusätzlich abschwächt.
35917 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35919 \begin_inset Formula $T_{2}$
35925 \begin_layout Standard
35931 \begin_layout Plain Layout
35943 \begin_layout Subsection
35944 Formulas with Description of Variables
35945 \begin_inset Index idx
35948 \begin_layout Plain Layout
35949 Formula ! with description of variables
35957 \begin_layout Standard
35958 To describe variables within a formula, like in formula
35959 \begin_inset CommandInset ref
35961 reference "eq:within"
35970 \begin_inset Formula $n$
35974 \begin_inset space ~
35977 matrix is used with left aligned columns for the
35978 \begin_inset Formula $n$
35985 \begin_layout Plain Layout
35987 \begin_inset CommandInset ref
35989 reference "sec:Matrices"
35998 To set the description in a smaller size, before the matrix e.
35999 \begin_inset space \thinspace{}
36003 \begin_inset space \space{}
36016 \begin_layout Plain Layout
36018 \begin_inset CommandInset ref
36020 reference "sub:Font-Sizes"
36032 \begin_layout Standard
36033 When the formula style
36039 \begin_layout Plain Layout
36041 \begin_inset CommandInset ref
36043 reference "sec:Formula-Styles"
36064 \begin_layout Plain Layout
36071 only works in formulas with the style
36076 \begin_inset CommandInset ref
36078 reference "sub:Variable-Space"
36087 is inserted before and after the matrix to have the same separation of
36088 the matrix from the equation and the side margin.
36091 \begin_layout Standard
36092 When the formula style
36096 is used, the method described in
36097 \begin_inset CommandInset ref
36099 reference "sub:Flalign-Environment"
36103 is used to indent formulas.
36105 \begin_inset CommandInset ref
36107 reference "eq:within"
36111 consists of five columns whereas in the first two columns contain the equation,
36112 the third the matrix and the last one an empty TeX-brace.
36113 \begin_inset Formula \begin{flalign}
36114 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36115 \rho & \textrm{density}\\
36116 V & \textrm{volume}\\
36117 g & \textrm{gravitational acceleration}
36118 \end{array} & & {}\label{eq:within}\end{flalign}
36125 \begin_layout Subsection
36126 Upright small Greek Letters
36127 \begin_inset CommandInset label
36129 name "sub:Upright-small-Greek"
36134 \begin_inset Index idx
36137 \begin_layout Plain Layout
36138 Greek letters ! upright
36146 \begin_layout Standard
36147 Most of the math fonts only provide italic small Greek letters.
36148 But for symbols of elementary particles like pions and neutrinos, upright
36149 Greek letters are needed.
36158 \begin_layout Plain Layout
36163 is part of the LaTeX-package
36168 \begin_inset Index idx
36171 \begin_layout Plain Layout
36176 \begin_layout Plain Layout
36196 \begin_inset Index idx
36199 \begin_layout Plain Layout
36205 that is loaded with the LaTeX-preamble line
36208 \begin_layout Standard
36213 usepackage{upgreek}
36216 \begin_layout Standard
36222 \begin_layout Plain Layout
36232 \begin_inset Note Note
36235 \begin_layout Plain Layout
36236 The following table will only be displayed when the LaTeX-package
36245 They are created when the command for a small Greek letters is started
36251 For example the command
36258 \begin_inset Formula $\uptau$
36264 \begin_layout Standard
36265 With these commands reactions of elementary particles can be typeset:
36266 \begin_inset Formula \[
36267 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
36274 \begin_layout Standard
36275 The upright letters are more bold and wider than the italic ones.
36276 They should therefore not be used for units like
36277 \begin_inset Quotes eld
36281 \begin_inset Quotes erd
36287 \begin_layout Standard
36291 \begin_layout Plain Layout
36301 \begin_inset Note Note
36304 \begin_layout Plain Layout
36305 The following will be displayed when the LaTeX-package
36317 \begin_layout Standard
36318 You need to install the LaTeX-package
36322 to see the rest of this subsection in the output.
36325 \begin_layout Standard
36329 \begin_layout Plain Layout
36341 \begin_layout Subsection
36342 Text Characters in Formulas
36343 \begin_inset CommandInset label
36345 name "sub:Text-Characters-in"
36350 \begin_inset Index idx
36353 \begin_layout Plain Layout
36362 \begin_layout Standard
36363 In some cases you might want to insert text characters directly into formulas.
36364 When for example the centered dot · is often used in formulas like
36365 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36368 , one would have to insert the command
36378 \begin_layout Plain Layout
36380 \begin_inset CommandInset ref
36382 reference "sub:Binary-Operators"
36391 all the time, because this character is defined in all encodings as text
36393 But the encoding can be changed by this LaTeX-preamble line:
36396 \begin_layout Standard
36401 Declare Inputtext{183}{
36411 f\SpecialChar \textcompwordmark{}
36415 \begin_layout Standard
36416 The character encoding (menu
36418 Document\SpecialChar \menuseparator
36419 Settings\SpecialChar \menuseparator
36422 ) specifies what character appears when a keyboard key is pressed.
36423 When the key for the character '·' is pressed, internally the command
36430 But this command is not available in a formula so that you would get LaTeX-erro
36432 With the changed encoding the right command is chosen automatically, depending
36433 on if the character was inserted into a formula or not.
36436 \begin_layout Standard
36437 The encoding of several characters is saved in definition files.
36438 Fore example the encoding
36442 is defined in the file
36446 that is in the installation folder of LaTeX.
36447 Encodings should only be changed via the LaTeX-preamble and not in the
36449 Otherwise own documents could not be edited by other LyX users working
36450 on other computers.
36453 \begin_layout Standard
36454 \begin_inset VSpace medskip
36457 Besides the centered dot, in this document the degree sign ° is defined
36458 with the following LaTeX-preamble line so that it can directly be inserted
36462 \begin_layout Standard
36467 DeclareInputtext{176}{
36477 f\SpecialChar \textcompwordmark{}
36481 \begin_layout Standard
36482 \begin_inset Newpage newpage
36488 \begin_layout Section
36491 \begin_inset Index idx
36494 \begin_layout Plain Layout
36503 \begin_layout Standard
36504 This section is a summary of the most important typographic rules, listed
36509 \begin_layout Plain Layout
36510 This collection was partly taken from the German semi-official dictionary
36512 \begin_inset Quotes eld
36516 \begin_inset Quotes erd
36520 \begin_inset CommandInset citation
36526 that lists some of the ISO rules.
36527 More rules are listed in
36528 \begin_inset CommandInset citation
36542 \begin_layout Itemize
36551 \begin_layout Plain Layout
36552 done with font styles, see
36553 \begin_inset CommandInset ref
36555 reference "sub:Font-Styles"
36564 , no matter if they appear in italic text: 30
36565 \begin_inset space \thinspace{}
36569 \begin_inset Newline newline
36572 Between the value and the unit is the smallest space, see
36573 \begin_inset CommandInset ref
36575 reference "sub:Predefined-Space"
36580 \begin_inset Newline newline
36583 This convention is automatically fulfilled when the command
36590 When it is entered to a formula, two boxes appear.
36591 In the first one the value is inserted, in the second one the unit, and
36593 \begin_inset Formula $\unit[30]{km/h}$
36597 \begin_inset space \thinspace{}
36607 is not a real LaTeX command but the command
36613 , therefore you cannot use it in TeX code.
36616 \begin_layout Itemize
36617 Percent and perthousand signs are set like physical units:
36618 \begin_inset Newline newline
36622 \begin_inset space \thinspace{}
36628 \begin_layout Itemize
36629 The degree sign follows directly on the value: 15°, but not when it is used
36631 \begin_inset space \thinspace{}
36637 \begin_layout Itemize
36638 In numbers with more than four digits the smallest space is inserted before
36639 every third digit to group them:
36649 \begin_inset space \thinspace{}
36653 \begin_inset space \thinspace{}
36659 \begin_layout Itemize
36660 For dimensions like 120×90×40
36661 \begin_inset space \thinspace{}
36664 cm the multiplication sign
36665 \begin_inset Quotes eld
36669 \begin_inset Quotes erd
36673 It is available either via the command
36681 Insert\SpecialChar \menuseparator
36682 Special Character\SpecialChar \menuseparator
36688 \begin_layout Itemize
36689 Functions with names consisting of several letters are set upright to avoid
36691 \begin_inset CommandInset ref
36693 reference "sub:Predefined-Functions"
36700 \begin_layout Itemize
36701 Indices consisting of several letters, are set upright:
36702 \begin_inset Formula $E_{\mathrm{kin}}$
36706 \begin_inset Newline newline
36709 Components of matrices are set italic:
36710 \begin_inset Formula $\hat{H}_{kl}$
36716 \begin_layout Itemize
36717 The differentiation/integration operator 'd', the Euler's number 'e' and
36718 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36722 \begin_layout Itemize
36723 The character that denotes a
36727 transformation is inserted either by the command
36735 \begin_layout Plain Layout
36749 \begin_inset Index idx
36752 \begin_layout Plain Layout
36762 Insert\SpecialChar \menuseparator
36763 Special Character\SpecialChar \menuseparator
36764 Symbols\SpecialChar \menuseparator
36766 \begin_inset space ~
36772 \begin_inset Formula $\mathscr{F}$
36776 \begin_inset Newline newline
36779 To be able to use the command
36785 , the LaTeX package
36790 \begin_inset Index idx
36793 \begin_layout Plain Layout
36794 Packages ! mathrsfs
36799 needs to be loaded with the LaTeX-preamble line
36803 usepackage{mathrsfs}
36808 \begin_layout Standard
36809 \begin_inset Newpage newpage
36815 \begin_layout Section
36817 \begin_inset Index idx
36820 \begin_layout Plain Layout
36829 \begin_layout Standard
36830 Some characters and symbols can be created with several commands.
36831 Here is a list of the synonym commands:
36834 \begin_layout Standard
36835 \begin_inset VSpace bigskip
36839 \begin_inset space \hfill{}
36843 \begin_inset Tabular
36844 <lyxtabular version="3" rows="12" columns="2">
36845 <features tabularvalignment="middle">
36846 <column alignment="center" valignment="top" width="0pt">
36847 <column alignment="center" valignment="top" width="0pt">
36849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36852 \begin_layout Plain Layout
36858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36861 \begin_layout Plain Layout
36863 \begin_inset Note Note
36866 \begin_layout Plain Layout
36873 is only used as spacer.
36885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36888 \begin_layout Plain Layout
36896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36899 \begin_layout Plain Layout
36903 \begin_layout Plain Layout
36916 \begin_layout Plain Layout
36930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36933 \begin_layout Plain Layout
36941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36944 \begin_layout Plain Layout
36954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36957 \begin_layout Plain Layout
36965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36968 \begin_layout Plain Layout
36978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36981 \begin_layout Plain Layout
36989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36992 \begin_layout Plain Layout
37000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37003 \begin_layout Plain Layout
37011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37014 \begin_layout Plain Layout
37022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37025 \begin_layout Plain Layout
37033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37036 \begin_layout Plain Layout
37046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37049 \begin_layout Plain Layout
37057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37060 \begin_layout Plain Layout
37070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37073 \begin_layout Plain Layout
37081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37084 \begin_layout Plain Layout
37094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37097 \begin_layout Plain Layout
37105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37108 \begin_layout Plain Layout
37118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37121 \begin_layout Plain Layout
37129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37132 \begin_layout Plain Layout
37140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37143 \begin_layout Plain Layout
37151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37154 \begin_layout Plain Layout
37166 \begin_inset space \hfill{}
37170 \begin_inset Tabular
37171 <lyxtabular version="3" rows="12" columns="2">
37172 <features tabularvalignment="middle">
37173 <column alignment="center" valignment="top" width="0pt">
37174 <column alignment="center" valignment="top" width="0pt">
37176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37179 \begin_layout Plain Layout
37185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37188 \begin_layout Plain Layout
37196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37199 \begin_layout Plain Layout
37207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37210 \begin_layout Plain Layout
37222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37225 \begin_layout Plain Layout
37233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37236 \begin_layout Plain Layout
37246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37249 \begin_layout Plain Layout
37257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37260 \begin_layout Plain Layout
37270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37273 \begin_layout Plain Layout
37281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37284 \begin_layout Plain Layout
37292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37295 \begin_layout Plain Layout
37303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37306 \begin_layout Plain Layout
37314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37317 \begin_layout Plain Layout
37325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37328 \begin_layout Plain Layout
37338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37341 \begin_layout Plain Layout
37349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37352 \begin_layout Plain Layout
37362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37365 \begin_layout Plain Layout
37373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37376 \begin_layout Plain Layout
37386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37389 \begin_layout Plain Layout
37397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37400 \begin_layout Plain Layout
37410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37413 \begin_layout Plain Layout
37421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37424 \begin_layout Plain Layout
37434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37437 \begin_layout Plain Layout
37445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37448 \begin_layout Plain Layout
37462 \begin_inset space \hfill{}
37468 \begin_layout Standard
37469 \begin_inset Newpage newpage
37475 \begin_layout Bibliography
37476 \labelwidthstring References
37477 \begin_inset CommandInset bibitem
37478 LatexCommand bibitem
37490 The LaTeX Companion
37493 Addison Wesley, 2004
37496 \begin_layout Bibliography
37497 \labelwidthstring References
37498 \begin_inset CommandInset bibitem
37499 LatexCommand bibitem
37505 \begin_inset CommandInset href
37508 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37512 of LaTeX's math abilities
37515 \begin_layout Bibliography
37516 \labelwidthstring References
37517 \begin_inset CommandInset bibitem
37518 LatexCommand bibitem
37524 \begin_inset CommandInset href
37527 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37535 \begin_layout Plain Layout
37547 \begin_layout Bibliography
37548 \labelwidthstring References
37549 \begin_inset CommandInset bibitem
37550 LatexCommand bibitem
37556 \begin_inset CommandInset href
37559 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37563 of all symbols available with LaTeX-packages
37566 \begin_layout Bibliography
37567 \labelwidthstring References
37568 \begin_inset CommandInset bibitem
37569 LatexCommand bibitem
37575 \begin_inset CommandInset href
37577 name "Documentation"
37578 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37582 of the LaTeX-package
37587 \begin_inset Index idx
37590 \begin_layout Plain Layout
37591 Packages ! hyperref
37599 \begin_layout Bibliography
37600 \labelwidthstring References
37601 \begin_inset CommandInset bibitem
37602 LatexCommand bibitem
37608 \begin_inset CommandInset href
37610 name "Documentation"
37611 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37615 of the LaTeX-package
37620 \begin_inset Index idx
37623 \begin_layout Plain Layout
37632 \begin_layout Bibliography
37633 \labelwidthstring References
37634 \begin_inset CommandInset bibitem
37635 LatexCommand bibitem
37641 \begin_inset CommandInset href
37644 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
37655 \begin_inset CommandInset ref
37657 reference "sub:Operator-Limits"
37662 \begin_inset Index idx
37665 \begin_layout Plain Layout
37676 \begin_layout Bibliography
37677 \labelwidthstring References
37678 \begin_inset CommandInset bibitem
37679 LatexCommand bibitem
37690 Auflage, Duden 2001
37693 \begin_layout Bibliography
37694 \labelwidthstring References
37695 \begin_inset CommandInset bibitem
37696 LatexCommand bibitem
37702 \begin_inset CommandInset href
37705 target "http://physics.nist.gov/Document/checklist.pdf"
37709 for reviewing manuscripts
37712 \begin_layout Standard
37713 \begin_inset CommandInset index_print
37714 LatexCommand printindex