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}
45 \renewcommand{\equationautorefname}{\hspace{-\abc}}
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{$\mathsurround =0pt #1{#2}$}}
116 % ------------------------------------
117 % used to check for needed LaTeX packages
120 % check for package eurosym
121 % used for the Euro symbol
123 \IfFileExists{eurosym.sty}
124 {\usepackage[gennarrow]{eurosym}
125 \setboolean{eurosym}{true}}
126 {\setboolean{eurosym}{false}}
128 % check for package braket
129 % used for physical vectors
131 \IfFileExists{braket.sty}
133 \setboolean{braket}{true}}
134 {\setboolean{braket}{false}}
136 % check for package cancel
138 \IfFileExists{cancel.sty}
140 \setboolean{cancel}{true}}
141 {\setboolean{cancel}{false}}
143 % check for package upgreek
145 \IfFileExists{upgreek.sty}
146 {\usepackage{upgreek}
147 \setboolean{upgreek}{true}}
148 {\setboolean{upgreek}{false}}
150 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
151 \use_default_options false
152 \maintain_unincluded_children false
158 \font_typewriter default
159 \font_default_family default
167 \default_output_format default
169 \bibtex_command default
170 \index_command default
174 \pdf_title "LyX's Math Manual"
175 \pdf_author "LyX Team, Uwe Stöhr"
176 \pdf_subject "LyX-documentation about math"
177 \pdf_keywords "LyX, Mathed"
179 \pdf_bookmarksnumbered true
180 \pdf_bookmarksopen true
181 \pdf_bookmarksopenlevel 1
182 \pdf_breaklinks false
186 \pdf_pdfusetitle false
187 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
197 \paperorientation portrait
199 \notefontcolor #0000ff
206 \paragraph_separation skip
208 \quotes_language english
211 \paperpagestyle plain
215 \tracking_changes false
216 \output_changes false
218 \html_be_strict false
224 LyX's detailed Math manual
232 \begin_layout Plain Layout
234 If you have comments or error corrections, please send them to the LyX Documenta
238 \begin_inset CommandInset href
240 name "lyx-docs@lists.lyx.org"
241 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
252 \begin_inset Note Note
255 \begin_layout Plain Layout
262 \begin_inset Newline newline
266 \begin_inset Newline newline
274 \begin_layout Standard
275 \begin_inset CommandInset toc
276 LatexCommand tableofcontents
283 \begin_layout Standard
284 \begin_inset Note Note
287 \begin_layout Plain Layout
288 To export this document to PDF, PS or DVI the LaTeX-packages
290 braket, cancel, eurosym,
301 If they are not installed the document can be export anyway but the sections
302 where the packages are required will not appear in the output.
307 ; if it is not installed, this file cannot be exported.
310 \begin_layout Plain Layout
311 The latest PDF-version of this document can be found here:
312 \begin_inset Newline newline
317 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
325 \begin_layout Standard
326 \begin_inset Newpage newpage
332 \begin_layout Section
336 \begin_layout Standard
337 This document explains LyX's math features and is furthermore a collection
338 of LaTeX-commands used for mathematical characters and constructs.
339 The explanations are designed for the usage of commands.
340 It is therefore required that you have read the section
351 \begin_layout Standard
352 Most of the characters and many constructs explained in this manual are
353 also accessible via the menu
357 \SpecialChar \menuseparator
373 But everybody who has to write lots of formulas will notice that it is
374 much faster to use commands instead of the math toolbar.
375 Therefore this manual is focused on commands but also mentions the correspondin
376 g toolbar buttons when available.
379 \begin_layout Standard
380 If not specially mentioned the commands are only available within formulas.
381 To be able to use all commands explained in this document, the option
385 must be used in the document settings (menu
387 Document\SpecialChar \menuseparator
388 Settings\SpecialChar \menuseparator
399 \begin_layout Plain Layout
402 Use AMS math package automatically
408 \begin_layout Plain Layout
417 -math when math constructs are found that are supported by LyX.
425 \begin_layout Standard
426 This document doesn't list all
430 \begin_layout Plain Layout
443 \begin_layout Plain Layout
448 \begin_layout Plain Layout
457 -math commands is in the file
460 \begin_inset CommandInset href
463 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
469 , which is part of every LaTeX standard installation.
474 for lucidity reasons.
477 \begin_layout Section
481 \begin_layout Standard
482 To create an inline formula
483 \begin_inset Index idx
486 \begin_layout Plain Layout
492 that is embedded into a text line, use one of the shortcuts
498 or the toolbar button
499 \begin_inset Graphics
500 filename ../images/math-mode.png
506 \begin_inset Newline newline
509 To create a display style formula
510 \begin_inset Index idx
513 \begin_layout Plain Layout
514 Formula ! display style
519 that will appear bigger and in an own paragraph, use one of these shortcuts:
529 \begin_layout Standard
530 To change a display style formula to an inline formula, set the cursor into
531 the formula and use one of the shortcuts
539 Edit\SpecialChar \menuseparator
540 Math\SpecialChar \menuseparator
544 The same way is used to change an inline formula to a display style formula.
547 \begin_layout Standard
548 To display parts of an inline formula in the size of a display style formula,
556 \begin_inset Index idx
559 \begin_layout Plain Layout
568 Then a new blue box appears in which the desired formula part is inserted.
571 \begin_layout Standard
572 Only inline formulas are allowed inside tables.
575 \begin_layout Standard
580 can be turned on in the menu
582 View\SpecialChar \menuseparator
586 When you click there on
587 \begin_inset Quotes eld
591 \begin_inset Quotes erd
594 the toolbar will be shown permanently at the bottom; this state is visualized
599 menu with a checkmark.
600 When you click in this state again on
601 \begin_inset Quotes eld
605 \begin_inset Quotes erd
616 is only shown when the cursor is within a formula; this state is visualized
617 by the renaming of the menu entry from
618 \begin_inset Quotes eld
622 \begin_inset Quotes erd
626 \begin_inset Quotes eld
634 \begin_inset Quotes erd
640 \begin_layout Standard
642 \begin_inset Index idx
645 \begin_layout Plain Layout
651 is invoked by pressing the toolbar button
652 \begin_inset Graphics
653 filename ../images/ert-insert.png
660 Insert\SpecialChar \menuseparator
665 \begin_layout Plain Layout
681 \begin_inset Note Note
684 \begin_layout Plain Layout
685 In LyX there are three
686 \begin_inset Quotes eld
690 \begin_inset Quotes erd
693 that appear in the output with sub- and superscript letters: TeX, LaTeX
697 \begin_layout Plain Layout
698 To avoid that these names are recognized as proper names, a TeX-brace pair
707 \begin_layout Standard
708 To change the LaTeX-preamble
709 \begin_inset Index idx
712 \begin_layout Plain Layout
720 Document\SpecialChar \menuseparator
721 Settings\SpecialChar \menuseparator
726 \begin_layout Plain Layout
742 \begin_layout Standard
743 To edit matrices, case differentiations and multiline formulas subsequently,
746 Edit\SpecialChar \menuseparator
751 Edit\SpecialChar \menuseparator
753 \begin_inset space \thinspace{}
757 \begin_inset space \thinspace{}
767 When lines and columns are swapped via the menu, the column or line where
768 the cursor is in is exchanged with the column to the right or the line
770 Is the cursor in the last column or row, the exchange is done with the
771 column to the left or the line above.
774 \begin_layout Standard
775 To write text in formulas
779 \begin_layout Plain Layout
780 For multiline formulas the command
787 \begin_inset CommandInset ref
789 reference "sub:Text-in-multiline"
803 \begin_inset Index idx
806 \begin_layout Plain Layout
813 \begin_inset Index idx
816 \begin_layout Plain Layout
823 This mode is invoked with the shortcut
829 or by the insertion of the command
836 \begin_inset Index idx
839 \begin_layout Plain Layout
848 The text appears black in LyX and can therefore be distinguished from the
849 other formula parts that appear blue.
850 In the output mathematical text is set upright, in contrary to other formula
854 \begin_layout Subsection*
858 \begin_layout Standard
859 Most of the LaTeX-commands for math constructs have the following scheme:
862 \begin_layout Standard
878 \begin_layout Standard
879 A command starts always with a backslash
880 \begin_inset Quotes gld
890 \begin_inset Quotes grd
894 To omit optional arguments, also omit the associated brackets.
895 The braces around the required arguments are named in this document as
897 \begin_inset Index idx
900 \begin_layout Plain Layout
907 If you add in a formula a left brace to a command name, LyX creates automatical
909 In all other cases TeX-braces are created in formulas with the command
917 TeX-braces appear red in LyX, in contrary to normal braces that appear
919 In TeX-mode no command is needed to get TeX-braces.
920 TeX-braces don't appear in the output.
923 \begin_layout Standard
924 When commands without arguments, like commands for symbols are entered in
925 TeX-mode, a space character must
929 be behind the command to end it.
930 This space doesn't appear in the output.
931 When the space should appear in the output, the space must be followed
932 by a protected space in normal text.
935 \begin_layout Standard
936 A protected space is inserted with
939 arg "space-insert protected"
945 \begin_layout Subsection*
946 \begin_inset Newpage newpage
952 \begin_layout Itemize
957 \begin_layout Plain Layout
958 This visible space character can be created with the command
965 \begin_inset Index idx
968 \begin_layout Plain Layout
976 , inserted in TeX-mode.
985 \begin_layout Plain Layout
998 denotes a space character to be input.
1001 \begin_layout Itemize
1003 \begin_inset Formula $\to$
1006 denotes the usage of the corresponding arrow key on the keyboard.
1009 \begin_layout Subsection*
1013 \begin_layout Standard
1015 \begin_inset Float table
1021 \begin_layout Plain Layout
1023 \begin_inset Caption
1025 \begin_layout Plain Layout
1026 \begin_inset CommandInset label
1028 name "tab:Available-units"
1040 \begin_layout Plain Layout
1042 \begin_inset Tabular
1043 <lyxtabular version="3" rows="13" columns="2">
1044 <features tabularvalignment="middle">
1045 <column alignment="center" valignment="top" width="0">
1046 <column alignment="center" valignment="top" width="0">
1048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1051 \begin_layout Plain Layout
1057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1060 \begin_layout Plain Layout
1068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1071 \begin_layout Plain Layout
1077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1080 \begin_layout Plain Layout
1088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1091 \begin_layout Plain Layout
1097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1100 \begin_layout Plain Layout
1108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1111 \begin_layout Plain Layout
1117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1120 \begin_layout Plain Layout
1122 \begin_inset space \thinspace{}
1126 \begin_inset space \thinspace{}
1136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1139 \begin_layout Plain Layout
1145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1148 \begin_layout Plain Layout
1150 \begin_inset space \thinspace{}
1154 \begin_inset space \thinspace{}
1164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1167 \begin_layout Plain Layout
1173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1176 \begin_layout Plain Layout
1178 \begin_inset space \thinspace{}
1182 \begin_inset space \thinspace{}
1192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1195 \begin_layout Plain Layout
1201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1204 \begin_layout Plain Layout
1206 \begin_inset space \thinspace{}
1210 \begin_inset space \thinspace{}
1220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1223 \begin_layout Plain Layout
1229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1232 \begin_layout Plain Layout
1234 \begin_inset space \thinspace{}
1238 \begin_inset space \thinspace{}
1248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1251 \begin_layout Plain Layout
1257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1260 \begin_layout Plain Layout
1262 \begin_inset space \thinspace{}
1266 \begin_inset Formula $\approx$
1270 \begin_inset space \thinspace{}
1280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1283 \begin_layout Plain Layout
1289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1292 \begin_layout Plain Layout
1294 \begin_inset space \thinspace{}
1298 \begin_inset space \thinspace{}
1308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1311 \begin_layout Plain Layout
1317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1320 \begin_layout Plain Layout
1324 \begin_inset Quotes eld
1330 \begin_inset Quotes erd
1340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1343 \begin_layout Plain Layout
1349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1352 \begin_layout Plain Layout
1354 \begin_inset Quotes eld
1362 \begin_inset Quotes erd
1372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1375 \begin_layout Plain Layout
1381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1384 \begin_layout Plain Layout
1386 \begin_inset space \thinspace{}
1390 \begin_inset Formula $\nicefrac{1}{18}$
1394 \begin_inset space \thinspace{}
1415 \begin_layout Standard
1416 \begin_inset Newpage newpage
1422 \begin_layout Section
1426 \begin_layout Subsection
1428 \begin_inset Index idx
1431 \begin_layout Plain Layout
1438 \begin_inset Index idx
1441 \begin_layout Plain Layout
1448 \begin_inset Index idx
1451 \begin_layout Plain Layout
1456 \begin_layout Plain Layout
1467 \begin_layout Plain Layout
1480 \begin_inset Index idx
1483 \begin_layout Plain Layout
1488 \begin_layout Plain Layout
1499 \begin_layout Plain Layout
1514 \begin_layout Standard
1515 Indices are created with an underscore
1516 \begin_inset Quotes eld
1520 \begin_inset Quotes erd
1523 or via the math toolbar button
1524 \begin_inset Graphics
1525 filename ../images/math-subscript.png
1530 , exponents with a caret
1531 \begin_inset Quotes eld
1535 \begin_inset Quotes erd
1538 or via the math toolbar button
1539 \begin_inset Graphics
1540 filename ../images/math-superscript.png
1548 \begin_layout Standard
1550 \begin_inset Tabular
1551 <lyxtabular version="3" rows="4" columns="2">
1552 <features tabularvalignment="middle">
1553 <column alignment="center" valignment="top" width="0pt">
1554 <column alignment="center" valignment="top" width="0pt">
1556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1559 \begin_layout Plain Layout
1565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1568 \begin_layout Plain Layout
1570 \begin_inset Note Note
1573 \begin_layout Plain Layout
1580 is only used as spacer.
1592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1595 \begin_layout Plain Layout
1601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1604 \begin_layout Plain Layout
1605 \begin_inset Formula $B_{V}$
1615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1618 \begin_layout Plain Layout
1624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1627 \begin_layout Plain Layout
1628 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1641 \begin_layout Plain Layout
1646 \begin_layout Plain Layout
1660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1663 \begin_layout Plain Layout
1664 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1680 \begin_layout Standard
1681 As the caret is in some languages an accent, vowels will be accentuated
1682 in this case and not set as exponents
1686 \begin_layout Plain Layout
1687 Depending on the used keyboard settings this can also happen for other character
1694 To get in this case exponents, press
1698 after the caret as in the last example.
1701 \begin_layout Subsection
1703 \begin_inset CommandInset label
1705 name "sub:Fractions"
1710 \begin_inset Index idx
1713 \begin_layout Plain Layout
1722 \begin_layout Standard
1723 Fractions are generated with the command
1730 \begin_inset Index idx
1733 \begin_layout Plain Layout
1741 or via the math toolbar button
1742 \begin_inset Graphics
1743 filename ../images/math/frac.png
1749 The font size is adjusted automatically, depending on whether the fraction
1750 is in an inline or display style formula.
1751 With the math toolbar button
1752 \begin_inset Graphics
1753 filename ../images/math/frac-square.png
1758 you can select different fraction types.
1761 \begin_layout Standard
1769 \begin_inset Index idx
1772 \begin_layout Plain Layout
1780 a fraction can be created that has in any case the size of a display style
1789 \begin_inset Index idx
1792 \begin_layout Plain Layout
1800 the fraction appears always with the size of an inline formula.
1804 \begin_layout Standard
1805 A line with the fraction
1806 \begin_inset Formula $\frac{1}{2}$
1809 that was created with the command
1818 \begin_layout Standard
1819 A line with the fraction
1820 \begin_inset Formula $\dfrac{1}{2}$
1823 that was created with the command
1832 \begin_layout Standard
1834 \begin_inset Tabular
1835 <lyxtabular version="3" rows="4" columns="2">
1836 <features tabularvalignment="middle">
1837 <column alignment="center" valignment="top" width="0pt">
1838 <column alignment="center" valignment="top" width="0pt">
1840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1843 \begin_layout Plain Layout
1849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1852 \begin_layout Plain Layout
1854 \begin_inset Note Note
1857 \begin_layout Plain Layout
1864 is only used as spacer.
1876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1879 \begin_layout Plain Layout
1886 \begin_layout Plain Layout
1896 \begin_inset Formula $\downarrow$
1904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1907 \begin_layout Plain Layout
1908 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1921 \begin_layout Plain Layout
1928 \begin_layout Plain Layout
1938 \begin_inset Formula $\downarrow$
1946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1949 \begin_layout Plain Layout
1950 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1963 \begin_layout Plain Layout
1970 \begin_layout Plain Layout
1983 \begin_layout Plain Layout
1998 \begin_layout Plain Layout
2008 \begin_inset Formula $\downarrow$
2012 \begin_inset Formula $\downarrow\downarrow$
2020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2023 \begin_layout Plain Layout
2024 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2040 \begin_layout Standard
2041 \begin_inset VSpace bigskip
2045 \begin_inset Newpage newpage
2048 For nested fractions the command
2055 \begin_inset Index idx
2058 \begin_layout Plain Layout
2068 \begin_inset VSpace -3mm
2074 \begin_layout Standard
2075 \begin_inset Formula \begin{align*}
2076 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2077 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2085 \begin_layout Standard
2086 The command for the example above is:
2089 \begin_layout Standard
2098 \begin_layout Plain Layout
2108 \begin_inset Formula $\downarrow$
2117 \begin_layout Plain Layout
2132 \begin_layout Plain Layout
2142 \begin_inset Formula $\downarrow$
2146 \begin_inset Formula $\downarrow$
2152 \begin_layout Standard
2153 \begin_inset VSpace medskip
2159 \begin_layout Standard
2166 sets the fraction always in the size of a displayed formula, also when
2167 it is part of another fraction.
2170 \begin_layout Standard
2171 It is possible to specify the alignment of the numerator.
2178 is used to left align it, the command
2191 centers the numerator.
2192 These fractions demonstrate the different alignments:
2195 \begin_layout Standard
2196 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2200 \begin_inset Formula $\cfrac{A}{B+C}$
2204 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2210 \begin_layout Standard
2211 \begin_inset Note Greyedout
2214 \begin_layout Plain Layout
2231 are no real LaTeX commands but represent the command
2235 cfrac[alignment]{numerator}{denominator}
2238 Therefore you cannot use them in TeX code.
2246 \begin_layout Standard
2247 \begin_inset VSpace medskip
2250 It is often advantageous to combine
2263 \begin_inset Formula \[
2264 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2271 \begin_layout Standard
2272 For inline fractions with a sloped fraction stroke you can use the command
2280 \begin_inset Index idx
2283 \begin_layout Plain Layout
2292 \begin_inset Formula $\nicefrac{5}{31}$
2302 \begin_inset Index idx
2305 \begin_layout Plain Layout
2314 \begin_inset Formula $\unitfrac{5}{31}$
2317 There is furthermore the command
2323 that offers to write a fraction in combination with a number:
2324 \begin_inset Formula $\unitfrac[2]{1}{3}$
2330 \begin_layout Standard
2331 \begin_inset Note Greyedout
2334 \begin_layout Plain Layout
2345 is not a real LaTeX command but the command
2346 \begin_inset Newline newline
2353 unitfrac[number]{numerator}{denominator}
2356 Therefore you cannot use it in TeX code.
2364 \begin_layout Standard
2365 How to define own fractions where the fraction stroke can be changed, is
2367 \begin_inset CommandInset ref
2369 reference "sub:Self-defined-Fractions"
2376 \begin_layout Subsection
2378 \begin_inset Index idx
2381 \begin_layout Plain Layout
2390 \begin_layout Standard
2391 Square roots are created with
2398 \begin_inset Index idx
2401 \begin_layout Plain Layout
2409 or the math toolbar button
2410 \begin_inset Graphics
2411 filename ../images/math/sqrt.png
2416 , all other roots with the command
2423 \begin_inset Index idx
2426 \begin_layout Plain Layout
2434 or with the math toolbar button
2435 \begin_inset Graphics
2436 filename ../images/math/root.png
2444 \begin_layout Standard
2446 \begin_inset Tabular
2447 <lyxtabular version="3" rows="3" columns="2">
2448 <features tabularvalignment="middle">
2449 <column alignment="center" valignment="top" width="0pt">
2450 <column alignment="center" valignment="top" width="0pt">
2452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2455 \begin_layout Plain Layout
2461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2464 \begin_layout Plain Layout
2466 \begin_inset Note Note
2469 \begin_layout Plain Layout
2476 is only used as spacer.
2488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2491 \begin_layout Plain Layout
2498 \begin_layout Plain Layout
2512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2515 \begin_layout Plain Layout
2516 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2529 \begin_layout Plain Layout
2536 \begin_layout Plain Layout
2546 \begin_inset Formula $\downarrow$
2554 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2557 \begin_layout Plain Layout
2558 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2574 \begin_layout Standard
2575 A square root can also be created with
2581 when the root index field is left empty.
2584 \begin_layout Standard
2585 With certain indices the distance to the root is too small, like in this
2587 \begin_inset Formula $\sqrt[\beta]{B}$
2591 \begin_inset Newline newline
2595 \begin_inset Formula $\beta$
2599 To avoid this, the commands
2606 \begin_inset Index idx
2609 \begin_layout Plain Layout
2624 \begin_inset Index idx
2627 \begin_layout Plain Layout
2635 are used with the following scheme:
2638 \begin_layout Standard
2652 \begin_layout Standard
2653 Distance is the number of Big Points (unit bp;
2654 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2657 ), that the index should be moved to the left or top, resp..
2658 The commands are written to the index.
2659 This way the command
2660 \begin_inset Newline newline
2670 \begin_inset Formula $\to$
2676 \begin_inset Formula $\to$
2685 \begin_layout Plain Layout
2695 \begin_inset Formula $\to$
2699 \begin_inset Newline newline
2704 produces a correct typeset formula:
2705 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2711 \begin_layout Subsection
2712 Binomial Coefficients
2713 \begin_inset Index idx
2716 \begin_layout Plain Layout
2717 Binomial coefficients
2725 \begin_layout Standard
2726 Binomial coefficients are inserted with the command
2733 \begin_inset Index idx
2736 \begin_layout Plain Layout
2744 or with the submenu of the math toolbar button
2745 \begin_inset Graphics
2746 filename ../images/math/frac-square.png
2752 Analog to fractions (
2771 \begin_inset Index idx
2774 \begin_layout Plain Layout
2789 \begin_inset Index idx
2792 \begin_layout Plain Layout
2801 For other brackets around binomial coeficients there are the commands
2808 \begin_inset Index idx
2811 \begin_layout Plain Layout
2826 \begin_inset Index idx
2829 \begin_layout Plain Layout
2840 \begin_layout Standard
2842 \begin_inset Tabular
2843 <lyxtabular version="3" rows="6" columns="2">
2844 <features tabularvalignment="middle">
2845 <column alignment="center" valignment="top" width="0pt">
2846 <column alignment="center" valignment="top" width="0pt">
2848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2851 \begin_layout Plain Layout
2857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2860 \begin_layout Plain Layout
2862 \begin_inset Note Note
2865 \begin_layout Plain Layout
2872 is only used as spacer.
2884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2887 \begin_layout Plain Layout
2894 \begin_layout Plain Layout
2904 \begin_inset Formula $\downarrow$
2912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2915 \begin_layout Plain Layout
2916 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2929 \begin_layout Plain Layout
2936 \begin_layout Plain Layout
2946 \begin_inset Formula $\downarrow$
2954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2957 \begin_layout Plain Layout
2958 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2971 \begin_layout Plain Layout
2978 \begin_layout Plain Layout
2988 \begin_inset Formula $\downarrow$
2996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2999 \begin_layout Plain Layout
3000 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3013 \begin_layout Plain Layout
3020 \begin_layout Plain Layout
3030 \begin_inset Formula $\downarrow$
3038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3041 \begin_layout Plain Layout
3042 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3055 \begin_layout Plain Layout
3062 \begin_layout Plain Layout
3072 \begin_inset Formula $\downarrow$
3080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3083 \begin_layout Plain Layout
3084 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3100 \begin_layout Subsection
3101 Case Differentiations
3102 \begin_inset Index idx
3105 \begin_layout Plain Layout
3106 Case differentiations
3114 \begin_layout Standard
3116 \begin_inset Tabular
3117 <lyxtabular version="3" rows="3" columns="2">
3118 <features tabularvalignment="middle">
3119 <column alignment="center" valignment="top" width="0pt">
3120 <column alignment="center" valignment="top" width="0pt">
3122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3125 \begin_layout Plain Layout
3131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3134 \begin_layout Plain Layout
3142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3145 \begin_layout Plain Layout
3152 \begin_layout Plain Layout
3162 \begin_inset Formula $\to$
3166 \begin_inset Index idx
3169 \begin_layout Plain Layout
3182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3185 \begin_layout Plain Layout
3186 \begin_inset Formula $\begin{cases}
3197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3200 \begin_layout Plain Layout
3207 \begin_layout Plain Layout
3219 arg "newline-insert newline"
3227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3230 \begin_layout Plain Layout
3231 \begin_inset Formula $\begin{cases}
3232 A & \textrm{for }x>0\\
3233 B & \textrm{for }x=0
3250 \begin_layout Standard
3257 or the usage of the math toolbar button
3258 \begin_inset Graphics
3259 filename ../images/math/cases.png
3264 you can create new lines with the shortcut
3267 arg "newline-insert newline"
3270 or the table toolbar button
3271 \begin_inset Graphics
3272 filename ../images/tabular-feature_append-row.png
3280 \begin_layout Standard
3287 is also available via the menu
3289 Insert\SpecialChar \menuseparator
3290 Math\SpecialChar \menuseparator
3296 \begin_layout Subsection
3298 \begin_inset Index idx
3301 \begin_layout Plain Layout
3310 \begin_layout Standard
3318 \begin_inset Index idx
3321 \begin_layout Plain Layout
3329 every character can be displayed canceled.
3330 The characters are quasi accentuated by a slash.
3333 \begin_layout Standard
3335 \begin_inset Tabular
3336 <lyxtabular version="3" rows="4" columns="2">
3337 <features tabularvalignment="middle">
3338 <column alignment="center" valignment="top" width="0pt">
3339 <column alignment="center" valignment="top" width="0pt">
3341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3344 \begin_layout Plain Layout
3350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3353 \begin_layout Plain Layout
3361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3364 \begin_layout Plain Layout
3372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3375 \begin_layout Plain Layout
3376 \begin_inset Formula $\not=$
3386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3389 \begin_layout Plain Layout
3399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3402 \begin_layout Plain Layout
3403 \begin_inset Formula $\not\le$
3413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3416 \begin_layout Plain Layout
3426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3429 \begin_layout Plain Layout
3430 \begin_inset Formula $\not\parallel$
3446 \begin_layout Standard
3447 The last example shows, that not all negations look good.
3448 Therefore there are for some negations special commands (see
3449 \begin_inset CommandInset ref
3451 reference "sub:Mathematical-Symbols"
3456 \begin_inset CommandInset ref
3458 reference "sec:Relations"
3465 \begin_layout Subsection
3467 \begin_inset CommandInset label
3469 name "sub:Placeholders"
3474 \begin_inset Index idx
3477 \begin_layout Plain Layout
3484 \begin_inset Index idx
3487 \begin_layout Plain Layout
3488 Chemical characters ! Isotopes
3494 \begin_inset Index idx
3497 \begin_layout Plain Layout
3502 \begin_layout Plain Layout
3513 \begin_layout Plain Layout
3528 \begin_layout Standard
3530 \begin_inset space \thinspace{}
3534 \begin_inset space \space{}
3541 \begin_layout Plain Layout
3542 Typesetting isotopes and chemical symbols is described in
3543 \begin_inset CommandInset ref
3545 reference "sub:Chemical-Symbols-and"
3554 the following problem occurs:
3557 \begin_layout Standard
3559 \begin_inset Tabular
3560 <lyxtabular version="3" rows="2" columns="2">
3561 <features tabularvalignment="middle">
3562 <column alignment="center" valignment="top" width="0pt">
3563 <column alignment="center" valignment="top" width="0pt">
3565 <cell alignment="center" valignment="top" usebox="none">
3568 \begin_layout Plain Layout
3569 Indices created with sub- and superscripts:
3574 <cell alignment="center" valignment="top" usebox="none">
3577 \begin_layout Plain Layout
3578 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3588 <cell alignment="center" valignment="top" usebox="none">
3591 \begin_layout Plain Layout
3597 <cell alignment="center" valignment="top" usebox="none">
3600 \begin_layout Plain Layout
3601 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3615 \begin_inset Note Note
3618 \begin_layout Plain Layout
3625 is only used as spacer.
3633 \begin_layout Standard
3634 The shorter index is by default placed below or above the first character
3635 of the longer index.
3636 To avoid this there is the command
3643 \begin_inset Index idx
3646 \begin_layout Plain Layout
3654 or the math toolbar button
3655 \begin_inset space \thinspace{}
3662 \begin_layout Plain Layout
3663 can be found in the submenu of the toolbar button
3664 \begin_inset Graphics
3665 filename ../images/math/space.png
3676 \begin_inset Graphics
3677 filename ../images/math/phantom.png
3682 that creates one or more phantom characters.
3689 a small blue box appears that is superposed with two red arrows.
3690 The arrows indicate that the complete width and height of the box content
3691 will be created as placeholder.
3692 Phantom characters are accordingly placeholders with the size of the characters.
3695 \begin_layout Standard
3697 \begin_inset Tabular
3698 <lyxtabular version="3" rows="4" columns="2">
3699 <features tabularvalignment="middle">
3700 <column alignment="center" valignment="top" width="0">
3701 <column alignment="center" valignment="top" width="0">
3703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3706 \begin_layout Plain Layout
3712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3715 \begin_layout Plain Layout
3717 \begin_inset Note Note
3720 \begin_layout Plain Layout
3727 is only used as spacer.
3739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3742 \begin_layout Plain Layout
3747 \begin_layout Plain Layout
3762 \begin_layout Plain Layout
3772 \begin_inset Formula $\to$
3779 \begin_layout Plain Layout
3793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3796 \begin_layout Plain Layout
3797 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3810 \begin_layout Plain Layout
3815 \begin_layout Plain Layout
3830 \begin_layout Plain Layout
3840 \begin_inset Formula $\to$
3847 \begin_layout Plain Layout
3861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3864 \begin_layout Plain Layout
3865 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3878 \begin_layout Plain Layout
3885 \begin_layout Plain Layout
3900 \begin_layout Plain Layout
3910 \begin_inset Formula $\to$
3917 \begin_layout Plain Layout
3931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3934 \begin_layout Plain Layout
3935 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3951 \begin_layout Standard
3952 Furthermore there are the commands
3959 \begin_inset Index idx
3962 \begin_layout Plain Layout
3971 \begin_inset space ~
3975 \begin_inset Graphics
3976 filename ../images/math/vphantom.png
3988 \begin_inset Index idx
3991 \begin_layout Plain Layout
4000 \begin_inset space ~
4004 \begin_inset Graphics
4005 filename ../images/math/hphantom.png
4017 creates only space for the maximal height of the characters in the box
4018 but not for its width.
4025 creates only space for the width of the box content.
4026 Therefore the boxes of both commands have only one red arrow.
4029 \begin_layout Standard
4040 \begin_layout Plain Layout
4055 space for the height of the integral sign,
4059 \begin_layout Plain Layout
4066 creates an integral sign, see
4067 \begin_inset CommandInset ref
4069 reference "sub:Big-Operators"
4078 because this is the larger character.
4079 An example application is in
4080 \begin_inset CommandInset ref
4082 reference "sub:Multiline-Brackets"
4089 \begin_layout Standard
4090 Placeholders can also be used for text when it is inserted via the menu
4093 Insert\SpecialChar \menuseparator
4094 Formatting\SpecialChar \menuseparator
4100 \begin_layout Standard
4102 \begin_inset Newline newline
4106 \begin_inset Phantom Phantom
4109 \begin_layout Plain Layout
4118 \begin_layout Subsection
4120 \begin_inset Index idx
4123 \begin_layout Plain Layout
4130 \begin_inset Index idx
4133 \begin_layout Plain Layout
4134 Formula ! underlined
4142 \begin_layout Standard
4144 \begin_inset Tabular
4145 <lyxtabular version="3" rows="4" columns="2">
4146 <features tabularvalignment="middle">
4147 <column alignment="center" valignment="top" width="0pt">
4148 <column alignment="center" valignment="top" width="0pt">
4150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4153 \begin_layout Plain Layout
4159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4162 \begin_layout Plain Layout
4164 \begin_inset Note Note
4167 \begin_layout Plain Layout
4174 is only used as spacer.
4186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4189 \begin_layout Plain Layout
4196 \begin_layout Plain Layout
4206 \begin_inset Index idx
4209 \begin_layout Plain Layout
4222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4225 \begin_layout Plain Layout
4226 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4236 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4239 \begin_layout Plain Layout
4246 \begin_layout Plain Layout
4256 \begin_inset Index idx
4259 \begin_layout Plain Layout
4272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4275 \begin_layout Plain Layout
4276 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4289 \begin_layout Plain Layout
4296 \begin_layout Plain Layout
4311 \begin_layout Plain Layout
4325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4328 \begin_layout Plain Layout
4329 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4345 \begin_layout Standard
4346 In the last example it doesn't matter if first
4361 \begin_layout Standard
4362 To double underline e.
4363 \begin_inset space \thinspace{}
4367 \begin_inset space \space{}
4379 \begin_layout Standard
4380 It is possible to place up to 6 lines above or below characters.
4383 \begin_layout Standard
4384 \begin_inset VSpace bigskip
4387 Custom lines can be created using the command
4394 \begin_inset Index idx
4397 \begin_layout Plain Layout
4405 which has the following scheme:
4408 \begin_layout Standard
4413 rule[vertical offset]{length}{thickness}
4416 \begin_layout Standard
4417 The optional vertical offset shifts the line upwards (or downwards, when
4418 the value is negative).
4420 \begin_inset CommandInset ref
4422 reference "tab:Available-units"
4426 can be used for the values.
4427 Here are two example lines created with the commands
4428 \begin_inset Newline newline
4435 rule[-2ex]{3cm}{2pt}
4446 \begin_layout Standard
4448 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4454 \begin_layout Standard
4461 can also be used for text when a line is inserted via the menu
4463 Insert\SpecialChar \menuseparator
4464 Formatting\SpecialChar \menuseparator
4466 \begin_inset space ~
4474 \begin_layout Standard
4476 \begin_inset CommandInset line
4487 \begin_layout Subsection
4489 \begin_inset CommandInset label
4496 \begin_inset Index idx
4499 \begin_layout Plain Layout
4508 \begin_layout Standard
4509 There are different types of ellipses available.
4513 \begin_layout Plain Layout
4514 In the math toolbar in the submenu of the button
4515 \begin_inset Graphics
4516 filename ../images/math/ldots.png
4526 For listings dots at the baseline are used (
4533 \begin_inset Index idx
4536 \begin_layout Plain Layout
4544 ), while for operations dots are needed that are on the same height as the
4552 \begin_inset Index idx
4555 \begin_layout Plain Layout
4564 When using the command
4571 \begin_inset Index idx
4574 \begin_layout Plain Layout
4582 , LaTeX decides on the basis of the next character what type is used.
4585 \begin_layout Standard
4587 \begin_inset Tabular
4588 <lyxtabular version="3" rows="8" columns="2">
4589 <features tabularvalignment="middle">
4590 <column alignment="center" valignment="top" width="0pt">
4591 <column alignment="center" valignment="top" width="0pt">
4593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4596 \begin_layout Plain Layout
4602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4605 \begin_layout Plain Layout
4613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4616 \begin_layout Plain Layout
4621 \begin_layout Plain Layout
4636 \begin_layout Plain Layout
4650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4653 \begin_layout Plain Layout
4654 \begin_inset Formula $A_{1},\dots,A_{n}$
4664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4667 \begin_layout Plain Layout
4672 \begin_layout Plain Layout
4687 \begin_layout Plain Layout
4701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4704 \begin_layout Plain Layout
4705 \begin_inset Formula $A_{1}+\dots+A_{n}$
4715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4718 \begin_layout Plain Layout
4723 \begin_layout Plain Layout
4738 \begin_layout Plain Layout
4752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4755 \begin_layout Plain Layout
4756 \begin_inset Formula $A_{1},\ldots,A_{n}$
4766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4769 \begin_layout Plain Layout
4774 \begin_layout Plain Layout
4789 \begin_layout Plain Layout
4803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4806 \begin_layout Plain Layout
4807 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4820 \begin_layout Plain Layout
4828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4831 \begin_layout Plain Layout
4832 \begin_inset Formula $\vdots$
4842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4845 \begin_layout Plain Layout
4853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4856 \begin_layout Plain Layout
4857 \begin_inset Formula $\ddots$
4867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4870 \begin_layout Plain Layout
4872 \begin_inset space \thinspace{}
4875 matrix with the different dots
4880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4883 \begin_layout Plain Layout
4884 \begin_inset Formula $\begin{array}{ccc}
4885 A_{11} & \cdots & A_{1m}\\
4886 \vdots & \ddots & \vdots\\
4887 A_{n1} & \cdots & A_{nm}
4904 \begin_layout Standard
4905 The ellipses available in menu
4907 Insert\SpecialChar \menuseparator
4909 \begin_inset space ~
4923 \begin_layout Standard
4924 \begin_inset VSpace medskip
4927 Specially for matrices there are ellipses that span over several columns.
4928 They are created with the command
4935 \begin_inset Index idx
4938 \begin_layout Plain Layout
4946 , that has the following scheme:
4949 \begin_layout Standard
4954 hdotsfor[distance]{number of columns}
4957 \begin_layout Standard
4958 The number of columns specifies how many columns should be spanned.
4959 Distance is a factor for the distance between the dots.
4962 \begin_layout Standard
4963 In the following matrix the command
4969 was inserted in the first box of the second line, to get an ellipsis with
4970 a dot distance twice as long as with the command
4977 \begin_inset Formula \[
4978 \left(\begin{array}{cccc}
4982 \end{array}\right)\]
4986 Note that the matrix fields that should be spanned must be empty, otherwise
4987 you get LaTeX-errors.
4990 \begin_layout Standard
4991 \begin_inset VSpace bigskip
4994 Furthermore you can fill with the command
5001 \begin_inset Index idx
5004 \begin_layout Plain Layout
5012 the rest of a line with dots.
5013 The effect of these commands is the same like with
5020 \begin_inset CommandInset ref
5022 reference "sub:Variable-Space"
5029 \begin_layout Standard
5030 For example the command
5038 \begin_layout Plain Layout
5052 \begin_layout Standard
5053 \begin_inset Formula $A\dotfill B$
5059 \begin_layout Standard
5066 there is for a line the command
5073 \begin_inset Index idx
5076 \begin_layout Plain Layout
5087 \begin_layout Standard
5088 \begin_inset Formula $A\hrulefill B$
5094 \begin_layout Standard
5095 To use the commands for text, they have to be inserted in TeX-mode.
5098 \begin_layout Section
5100 \begin_inset CommandInset label
5107 \begin_inset Index idx
5110 \begin_layout Plain Layout
5119 \begin_layout Standard
5120 Matrices can be inserted via the math toolbar button
5121 \begin_inset Graphics
5122 filename ../images/dialog-show_mathmatrix.png
5129 Insert\SpecialChar \menuseparator
5130 Math\SpecialChar \menuseparator
5134 In the matrix dialog you can specify the number of columns and rows, the
5135 alignment and the decoration.
5136 The vertical alignment is hereby only of importance for matrices in inline
5140 \begin_layout Standard
5141 The first matrix is top
5142 \begin_inset Formula $\begin{array}[t]{cccc}
5150 \begin_inset Formula $\begin{array}{cccc}
5157 and the third bottom
5158 \begin_inset Formula $\begin{array}[b]{cccc}
5168 \begin_layout Standard
5169 The horizontal alignment specifies how the column entries should be aligned.
5170 It is set by entering a letter for every column.
5175 denotes left aligned,
5184 To create for example a 4
5189 \begin_inset space ~
5192 matrix where the first column is left aligned, the second and third are
5193 centered and the last one is right aligned, one enters for the horizontal
5199 Normally are in a matrix all columns centered, therefore the default is
5200 for every column is a
5207 \begin_layout Standard
5208 Horizontal alignment:
5211 \begin_layout Standard
5217 \begin_inset Formula $\begin{array}{lll}
5229 \begin_inset Formula $\begin{array}{ccc}
5241 \begin_inset Formula $\begin{array}{rrr}
5251 \begin_layout Standard
5252 To add or delete rows and columns subsequently, the math toolbar buttons
5254 \begin_inset Graphics
5255 filename ../images/tabular-feature_append-row.png
5261 \begin_inset Graphics
5262 filename ../images/tabular-feature_delete-row.png
5268 \begin_inset space \thinspace{}
5273 Edit\SpecialChar \menuseparator
5277 New rows can also be created with
5280 arg "newline-insert newline"
5286 \begin_layout Standard
5287 \begin_inset VSpace bigskip
5294 adds parentheses in the selected style around the matrix.
5295 Alternatively, parentheses can can either be created with the commands
5303 \begin_inset Index idx
5306 \begin_layout Plain Layout
5321 \begin_inset Index idx
5324 \begin_layout Plain Layout
5335 \begin_inset space ~
5341 \begin_inset CommandInset ref
5343 reference "sub:Automatic-Bracket-Size"
5347 , or by using the following commands:
5348 \begin_inset VSpace medskip
5354 \begin_layout Standard
5355 \begin_inset space \hfill{}
5359 \begin_inset Tabular
5360 <lyxtabular version="3" rows="4" columns="2">
5361 <features tabularvalignment="middle">
5362 <column alignment="center" valignment="top" width="0">
5363 <column alignment="center" valignment="top" width="0">
5365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5368 \begin_layout Plain Layout
5374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5377 \begin_layout Plain Layout
5379 \begin_inset Note Note
5382 \begin_layout Plain Layout
5389 is only used as spacer.
5401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5404 \begin_layout Plain Layout
5411 \begin_layout Plain Layout
5425 \begin_inset space \thinspace{}
5433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5436 \begin_layout Plain Layout
5437 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5438 0 & \textrm{-}\mathrm{i}\\
5440 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5453 \begin_layout Plain Layout
5460 \begin_layout Plain Layout
5474 \begin_inset space \thinspace{}
5482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5485 \begin_layout Plain Layout
5486 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5487 0 & \textrm{-}\mathrm{i}\\
5489 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5502 \begin_layout Plain Layout
5509 \begin_layout Plain Layout
5523 \begin_inset space \thinspace{}
5531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5534 \begin_layout Plain Layout
5535 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5536 0 & \textrm{-}\mathrm{i}\\
5538 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5552 \begin_inset space \hfill{}
5556 \begin_inset Tabular
5557 <lyxtabular version="3" rows="4" columns="2">
5558 <features tabularvalignment="middle">
5559 <column alignment="center" valignment="top" width="0">
5560 <column alignment="center" valignment="top" width="0">
5562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5565 \begin_layout Plain Layout
5571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5574 \begin_layout Plain Layout
5582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5585 \begin_layout Plain Layout
5592 \begin_layout Plain Layout
5606 \begin_inset space \thinspace{}
5614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5617 \begin_layout Plain Layout
5618 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5619 0 & \textrm{-}\mathrm{i}\\
5621 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5634 \begin_layout Plain Layout
5641 \begin_layout Plain Layout
5655 \begin_inset space \thinspace{}
5663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5666 \begin_layout Plain Layout
5667 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5668 0 & \textrm{-}\mathrm{i}\\
5670 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5683 \begin_layout Plain Layout
5690 \begin_layout Plain Layout
5704 \begin_inset space \thinspace{}
5712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5715 \begin_layout Plain Layout
5716 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5717 0 & \textrm{-}\mathrm{i}\\
5719 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5733 \begin_inset space \hfill{}
5739 \begin_layout Standard
5740 \begin_inset VSpace medskip
5744 \begin_inset space \thinspace{}
5748 \begin_inset space \space{}
5757 is inserted, a blue box appears between two vertical lines where the matrix
5759 \begin_inset Newline newline
5762 Note that decorated matrices ignore the vertical alignment.
5765 \begin_layout Standard
5766 \begin_inset VSpace bigskip
5769 As all multiline formulas are matrices, the length
5776 \begin_inset Index idx
5779 \begin_layout Plain Layout
5787 that is described in
5788 \begin_inset CommandInset ref
5790 reference "sub:Column-Separation"
5794 can also be used to change the column separation of matrices.
5797 \begin_layout Standard
5798 To change the row separation, the command
5805 \begin_inset Index idx
5808 \begin_layout Plain Layout
5817 It is used as follows:
5820 \begin_layout Standard
5827 arraystretch}{stretch factor}
5828 \begin_inset Index idx
5831 \begin_layout Plain Layout
5842 \begin_layout Standard
5849 assigns the stretch factor to the predefined command
5857 \begin_inset space \thinspace{}
5861 \begin_inset space \space{}
5864 the row separation, use the factor 2.
5865 This is then used for all following matrices.
5866 To go back to the original separation, assign the factor 1 to
5875 \begin_layout Standard
5876 To set matrices into a text line, the command
5883 \begin_inset Index idx
5886 \begin_layout Plain Layout
5895 When it is inserted a blue box with two dashed lines appears.
5896 In this box the matrix is inserted.
5899 \begin_layout Standard
5901 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5903 \end{smallmatrix}\right)$
5909 \begin_layout Section
5910 Brackets and Delimiters
5911 \begin_inset Index idx
5914 \begin_layout Plain Layout
5921 \begin_inset Index idx
5924 \begin_layout Plain Layout
5933 \begin_layout Subsection
5934 Vertical Brackets and Delimiters
5935 \begin_inset Index idx
5938 \begin_layout Plain Layout
5947 \begin_layout Standard
5948 \begin_inset space \hfill{}
5952 \begin_inset Tabular
5953 <lyxtabular version="3" rows="9" columns="2">
5954 <features tabularvalignment="middle">
5955 <column alignment="center" valignment="top" width="0pt">
5956 <column alignment="center" valignment="top" width="0pt">
5958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5961 \begin_layout Plain Layout
5967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5970 \begin_layout Plain Layout
5978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5981 \begin_layout Plain Layout
5987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5990 \begin_layout Plain Layout
5991 \begin_inset Formula $($
6001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6004 \begin_layout Plain Layout
6010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6013 \begin_layout Plain Layout
6014 \begin_inset Formula $\{$
6024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6027 \begin_layout Plain Layout
6033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6036 \begin_layout Plain Layout
6037 \begin_inset Formula $[$
6047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6050 \begin_layout Plain Layout
6058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6061 \begin_layout Plain Layout
6062 \begin_inset Formula $\langle$
6072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6075 \begin_layout Plain Layout
6083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6086 \begin_layout Plain Layout
6087 \begin_inset Formula $\lceil$
6097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6100 \begin_layout Plain Layout
6108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6111 \begin_layout Plain Layout
6112 \begin_inset Formula $\lfloor$
6122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6125 \begin_layout Plain Layout
6131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6134 \begin_layout Plain Layout
6135 \begin_inset Formula $/$
6145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6148 \begin_layout Plain Layout
6154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6157 \begin_layout Plain Layout
6158 \begin_inset Formula $|$
6172 \begin_inset space \hfill{}
6176 \begin_inset Tabular
6177 <lyxtabular version="3" rows="9" columns="2">
6178 <features tabularvalignment="middle">
6179 <column alignment="center" valignment="top" width="0pt">
6180 <column alignment="center" valignment="top" width="0pt">
6182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6185 \begin_layout Plain Layout
6191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6194 \begin_layout Plain Layout
6202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6205 \begin_layout Plain Layout
6211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6214 \begin_layout Plain Layout
6215 \begin_inset Formula $)$
6225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6228 \begin_layout Plain Layout
6234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6237 \begin_layout Plain Layout
6238 \begin_inset Formula $\}$
6248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6251 \begin_layout Plain Layout
6257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6260 \begin_layout Plain Layout
6261 \begin_inset Formula $]$
6271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6274 \begin_layout Plain Layout
6282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6285 \begin_layout Plain Layout
6286 \begin_inset Formula $\rangle$
6296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6299 \begin_layout Plain Layout
6307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6310 \begin_layout Plain Layout
6311 \begin_inset Formula $\rceil$
6321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6324 \begin_layout Plain Layout
6332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6335 \begin_layout Plain Layout
6336 \begin_inset Formula $\rfloor$
6346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6349 \begin_layout Plain Layout
6359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6362 \begin_layout Plain Layout
6363 \begin_inset Formula $\backslash$
6373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6376 \begin_layout Plain Layout
6384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6387 \begin_layout Plain Layout
6388 \begin_inset Formula $\|$
6402 \begin_inset space \hfill{}
6408 \begin_layout Standard
6411 \begin_inset Note Greyedout
6414 \begin_layout Plain Layout
6419 In TeX-mode the command
6426 \begin_inset Index idx
6429 \begin_layout Plain Layout
6437 must be used for the backslash, because the command
6445 produces there a line break.
6453 \begin_layout Standard
6454 For all characters listed above the size can be adjusted with the commands
6455 described in the following two subsections.
6456 When using these commands, the characters < and > can directly be used
6457 instead of the commands
6472 \begin_layout Subsubsection
6474 \begin_inset CommandInset label
6476 name "sub:Manual-Bracket-Size"
6481 \begin_inset Index idx
6484 \begin_layout Plain Layout
6485 Bracket size ! manual
6493 \begin_layout Standard
6494 The bracket size can be specified manually by the LaTeX-commands
6501 \begin_inset Index idx
6504 \begin_layout Plain Layout
6537 denotes the smallest and
6543 the largest bracket size.
6546 \begin_layout Standard
6547 These commands are used to emphasize levels of brackets:
6550 \begin_layout Standard
6552 \begin_inset Tabular
6553 <lyxtabular version="3" rows="2" columns="2">
6554 <features tabularvalignment="middle">
6555 <column alignment="center" valignment="top" width="0pt">
6556 <column alignment="center" valignment="top" width="0pt">
6558 <cell alignment="center" valignment="top" usebox="none">
6561 \begin_layout Plain Layout
6562 all brackets in the same size:
6567 <cell alignment="center" valignment="top" usebox="none">
6570 \begin_layout Plain Layout
6571 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6581 <cell alignment="center" valignment="top" usebox="none">
6584 \begin_layout Plain Layout
6590 <cell alignment="center" valignment="top" usebox="none">
6593 \begin_layout Plain Layout
6594 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6608 \begin_inset Note Note
6611 \begin_layout Plain Layout
6618 is only used as spacer.
6626 \begin_layout Standard
6627 For the second formula the command
6637 \begin_layout Plain Layout
6651 \begin_layout Standard
6652 Here is an overview about all bracket sizes:
6655 \begin_layout Standard
6675 \begin_layout Plain Layout
6692 \begin_layout Plain Layout
6705 \begin_layout Plain Layout
6721 \begin_layout Standard
6723 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6729 \begin_layout Standard
6736 -commands there is the variant
6743 \begin_inset Index idx
6746 \begin_layout Plain Layout
6754 that adds a bit more space between the bracket and its content, and the
6768 \begin_inset Index idx
6771 \begin_layout Plain Layout
6781 , that don't add additional space.
6786 at the end of the command
6792 is for a left bracket; for a right bracket this will be replaced by an
6798 A left or right bracket can each be an opening or closing bracket.
6801 \begin_layout Standard
6802 In the following table is a comparison of the variants:
6805 \begin_layout Standard
6807 \begin_inset Tabular
6808 <lyxtabular version="3" rows="5" columns="2">
6809 <features tabularvalignment="middle">
6810 <column alignment="center" valignment="middle" width="0">
6811 <column alignment="center" valignment="middle" width="0">
6813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6816 \begin_layout Plain Layout
6822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6825 \begin_layout Plain Layout
6827 \begin_inset Note Note
6830 \begin_layout Plain Layout
6837 is only used as spacer.
6849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6852 \begin_layout Plain Layout
6867 \begin_layout Plain Layout
6885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6888 \begin_layout Plain Layout
6889 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6902 \begin_layout Plain Layout
6917 \begin_layout Plain Layout
6935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6938 \begin_layout Plain Layout
6939 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6952 \begin_layout Plain Layout
6967 \begin_layout Plain Layout
6985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6988 \begin_layout Plain Layout
6989 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7002 \begin_layout Plain Layout
7014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7017 \begin_layout Plain Layout
7018 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7034 \begin_layout Subsubsection
7035 Automatic Bracket Size
7036 \begin_inset CommandInset label
7038 name "sub:Automatic-Bracket-Size"
7043 \begin_inset Index idx
7046 \begin_layout Plain Layout
7047 Bracket size ! automatic
7055 \begin_layout Standard
7056 Brackets with variable size can be inserted with the commands
7063 \begin_inset Index idx
7066 \begin_layout Plain Layout
7081 \begin_inset Index idx
7084 \begin_layout Plain Layout
7092 or via the math toolbar button
7093 \begin_inset Graphics
7094 filename ../images/dialog-show_mathdelimiter.png
7112 the wanted bracket must be inserted.
7113 The bracket size will then automatically be calculated for the output.
7116 \begin_layout Standard
7118 normal bracket: The command
7128 \begin_layout Plain Layout
7138 \begin_inset Formula $\downarrow$
7145 \begin_layout Plain Layout
7157 \begin_inset Formula \[
7165 \begin_layout Standard
7167 multiline bracket: The command
7179 \begin_layout Plain Layout
7189 \begin_inset Formula $\downarrow$
7196 \begin_layout Plain Layout
7210 \begin_inset Formula \[
7211 \ln\left(\frac{A}{C}\right)\]
7218 \begin_layout Standard
7234 \begin_inset space ~
7240 This has the advantage that you can see in LyX immediately the real bracket
7241 size and that the matching right bracket will be created too.
7242 \begin_inset Newline newline
7245 The command for the last example would then be:
7259 \begin_layout Plain Layout
7269 \begin_inset Formula $\downarrow$
7275 \begin_layout Standard
7276 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7277 For example the command
7287 \begin_layout Plain Layout
7297 \begin_inset Formula $\downarrow$
7304 \begin_layout Plain Layout
7320 \begin_inset Formula \[
7321 \left.\frac{A}{B}\right\} \]
7339 will be converted by LyX to brackets in the right size when the document
7340 is reloaded and an omitted bracket will appear as dashed line.
7343 \begin_layout Standard
7344 \begin_inset VSpace bigskip
7347 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7355 \begin_inset Index idx
7358 \begin_layout Plain Layout
7366 is additionally available for all brackets and limits.
7367 With this command the height of the following character is adapted to the
7368 one of the surrounding brackets, what is e.
7369 \begin_inset space \thinspace{}
7373 \begin_inset space \space{}
7376 needed for physical vectors:
7377 \begin_inset Formula \[
7378 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7382 For physical vectors there is a special LaTeX-package, described in
7383 \begin_inset CommandInset ref
7385 reference "sub:Physical-Vectors"
7392 \begin_layout Subsection
7394 \begin_inset Index idx
7397 \begin_layout Plain Layout
7398 Brackets ! horizontal
7406 \begin_layout Standard
7408 \begin_inset Tabular
7409 <lyxtabular version="3" rows="4" columns="2">
7410 <features tabularvalignment="middle">
7411 <column alignment="center" valignment="top" width="0pt">
7412 <column alignment="center" valignment="top" width="0pt">
7414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7417 \begin_layout Plain Layout
7419 \begin_inset Note Note
7422 \begin_layout Plain Layout
7429 is only used as spacer.
7439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7442 \begin_layout Plain Layout
7450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7453 \begin_layout Plain Layout
7457 \begin_layout Plain Layout
7472 \begin_layout Plain Layout
7485 \begin_layout Plain Layout
7498 \begin_layout Plain Layout
7511 \begin_layout Plain Layout
7519 \begin_inset Index idx
7522 \begin_layout Plain Layout
7535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7538 \begin_layout Plain Layout
7539 \begin_inset Formula $\overbrace{A+B}^{3}$
7549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7552 \begin_layout Plain Layout
7556 \begin_layout Plain Layout
7571 \begin_layout Plain Layout
7584 \begin_layout Plain Layout
7597 \begin_layout Plain Layout
7605 \begin_inset Index idx
7608 \begin_layout Plain Layout
7621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7624 \begin_layout Plain Layout
7625 \begin_inset Formula $\underbrace{A+B}_{5}$
7635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7638 \begin_layout Plain Layout
7645 \begin_layout Plain Layout
7660 \begin_layout Plain Layout
7673 \begin_layout Plain Layout
7686 \begin_layout Plain Layout
7699 \begin_layout Plain Layout
7712 \begin_layout Plain Layout
7725 \begin_layout Plain Layout
7739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7742 \begin_layout Plain Layout
7743 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7759 \begin_layout Standard
7760 In the last example it doesn't matter if
7772 is inserted at first.
7775 \begin_layout Standard
7776 \begin_inset VSpace bigskip
7779 When brackets are needed that overlap each other, multiline formulas, as
7781 \begin_inset CommandInset ref
7783 reference "sec:Multiline-Formulas"
7788 \begin_inset Formula \begin{eqnarray*}
7789 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7790 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7795 In the first row the formula is inserted together with the first brace.
7796 It is hereby important that the space command
7800 \begin_layout Plain Layout
7801 Space commands are explained in
7802 \begin_inset CommandInset ref
7804 reference "sub:Predefined-Space"
7819 is inserted before the first
7820 \begin_inset Formula $d$
7823 , because the brace that ends behind the
7824 \begin_inset Formula $q$
7827 prevents that the following
7828 \begin_inset Quotes eld
7832 \begin_inset Quotes erd
7835 is surrounded by space.
7839 \begin_layout Plain Layout
7840 because a bracket is not handled as character, see
7841 \begin_inset CommandInset ref
7843 reference "sub:Binary-Operators"
7852 In the second row the second brace is inserted.
7853 As it should begin before the
7854 \begin_inset Formula $b$
7869 \begin_layout Plain Layout
7877 \begin_inset CommandInset ref
7879 reference "sub:Placeholders"
7888 This space is needed because the
7889 \begin_inset Quotes eld
7893 \begin_inset Quotes erd
7896 is also surrounded by space in the formula.
7897 The brace is placed under the command
7906 \begin_layout Standard
7907 It gets more complicated when brackets overlap each other, like in the following
7912 \begin_layout Plain Layout
7924 \begin_inset Formula \begin{eqnarray*}
7925 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7926 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7935 \begin_layout Plain Layout
7946 The first formula row is the same as the second row of the previous example,
7947 with the difference that the brace is above.
7948 The second row contains the formula together with the second brace.
7949 To avoid that there is space between the upper brace in the first row and
7950 the formula, the row spacing need to be reduced.
7951 This is not easily possible due to a bug in LyX
7955 \begin_layout Plain Layout
7956 \begin_inset CommandInset href
7958 name "LyX-bug #1505"
7959 target "http://www.lyx.org/trac/ticket/1505"
7969 As solution for the problem, the global formula row separation
7976 \begin_inset Index idx
7979 \begin_layout Plain Layout
7987 must be changed to -6
7988 \begin_inset space \thinspace{}
7991 pt before the formula with the command
8006 is set back after the formula to the standard value of 3
8007 \begin_inset space \thinspace{}
8010 pt using the same command.
8011 More about the row separation in formulas is explained in
8012 \begin_inset CommandInset ref
8014 reference "sub:Line-Separation"
8021 \begin_layout Section
8023 \begin_inset Index idx
8026 \begin_layout Plain Layout
8035 \begin_layout Standard
8036 Arrows can be inserted via the math toolbar button
8037 \begin_inset Graphics
8038 filename ../images/math/leftarrow.png
8043 or the commands listed in the following subsections.
8046 \begin_layout Standard
8047 \begin_inset Newpage newpage
8053 \begin_layout Subsection
8055 \begin_inset Index idx
8058 \begin_layout Plain Layout
8067 \begin_layout Standard
8068 \begin_inset space \hfill{}
8072 \begin_inset Tabular
8073 <lyxtabular version="3" rows="8" columns="2">
8074 <features tabularvalignment="middle">
8075 <column alignment="center" valignment="top" width="0pt">
8076 <column alignment="center" valignment="top" width="0pt">
8078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8081 \begin_layout Plain Layout
8087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8090 \begin_layout Plain Layout
8098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8101 \begin_layout Plain Layout
8109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8112 \begin_layout Plain Layout
8113 \begin_inset Formula $\gets$
8123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8126 \begin_layout Plain Layout
8134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8137 \begin_layout Plain Layout
8138 \begin_inset Formula $\Leftarrow$
8148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8151 \begin_layout Plain Layout
8159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8162 \begin_layout Plain Layout
8163 \begin_inset Formula $\longleftarrow$
8173 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8176 \begin_layout Plain Layout
8184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8187 \begin_layout Plain Layout
8188 \begin_inset Formula $\Longleftarrow$
8198 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8201 \begin_layout Plain Layout
8209 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8212 \begin_layout Plain Layout
8213 \begin_inset Formula $\leftharpoonup$
8223 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8226 \begin_layout Plain Layout
8234 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8237 \begin_layout Plain Layout
8238 \begin_inset Formula $\leftharpoondown$
8248 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8251 \begin_layout Plain Layout
8259 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8262 \begin_layout Plain Layout
8263 \begin_inset Formula $\hookleftarrow$
8277 \begin_inset space \hfill{}
8281 \begin_inset Tabular
8282 <lyxtabular version="3" rows="8" columns="2">
8283 <features tabularvalignment="middle">
8284 <column alignment="center" valignment="top" width="0pt">
8285 <column alignment="center" valignment="top" width="0pt">
8287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8290 \begin_layout Plain Layout
8296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8299 \begin_layout Plain Layout
8307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8310 \begin_layout Plain Layout
8318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8321 \begin_layout Plain Layout
8322 \begin_inset Formula $\to$
8332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8335 \begin_layout Plain Layout
8343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8346 \begin_layout Plain Layout
8347 \begin_inset Formula $\Rightarrow$
8357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8360 \begin_layout Plain Layout
8368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8371 \begin_layout Plain Layout
8372 \begin_inset Formula $\longrightarrow$
8382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8385 \begin_layout Plain Layout
8393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8396 \begin_layout Plain Layout
8397 \begin_inset Formula $\Longrightarrow$
8407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8410 \begin_layout Plain Layout
8418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8421 \begin_layout Plain Layout
8422 \begin_inset Formula $\rightharpoonup$
8432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8435 \begin_layout Plain Layout
8443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8446 \begin_layout Plain Layout
8447 \begin_inset Formula $\rightharpoondown$
8457 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8460 \begin_layout Plain Layout
8468 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8471 \begin_layout Plain Layout
8472 \begin_inset Formula $\hookrightarrow$
8486 \begin_inset space \hfill{}
8492 \begin_layout Standard
8493 \begin_inset space \hfill{}
8497 \begin_inset Tabular
8498 <lyxtabular version="3" rows="6" columns="2">
8499 <features tabularvalignment="middle">
8500 <column alignment="center" valignment="top" width="0pt">
8501 <column alignment="center" valignment="top" width="0pt">
8503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8506 \begin_layout Plain Layout
8512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8515 \begin_layout Plain Layout
8523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8526 \begin_layout Plain Layout
8534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8537 \begin_layout Plain Layout
8538 \begin_inset Formula $\leftrightarrow$
8548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8551 \begin_layout Plain Layout
8559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8562 \begin_layout Plain Layout
8563 \begin_inset Formula $\Leftrightarrow$
8573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8576 \begin_layout Plain Layout
8584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8587 \begin_layout Plain Layout
8588 \begin_inset Formula $\longleftrightarrow$
8598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8601 \begin_layout Plain Layout
8609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8612 \begin_layout Plain Layout
8613 \begin_inset Formula $\Longleftrightarrow$
8623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8626 \begin_layout Plain Layout
8634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8637 \begin_layout Plain Layout
8638 \begin_inset Formula $\rightleftharpoons$
8652 \begin_inset space \hspace{}
8657 \begin_inset space \hfill{}
8661 \begin_inset Tabular
8662 <lyxtabular version="3" rows="5" columns="2">
8663 <features tabularvalignment="middle">
8664 <column alignment="center" valignment="top" width="0pt">
8665 <column alignment="center" valignment="top" width="0pt">
8667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8670 \begin_layout Plain Layout
8676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8679 \begin_layout Plain Layout
8687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8690 \begin_layout Plain Layout
8698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8701 \begin_layout Plain Layout
8702 \begin_inset Formula $\mapsto$
8712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8715 \begin_layout Plain Layout
8723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8726 \begin_layout Plain Layout
8727 \begin_inset Formula $\longmapsto$
8737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8740 \begin_layout Plain Layout
8748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8751 \begin_layout Plain Layout
8752 \begin_inset Formula $\leadsto$
8762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8765 \begin_layout Plain Layout
8773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8776 \begin_layout Plain Layout
8777 \begin_inset Formula $\dasharrow$
8791 \begin_inset space \hfill{}
8797 \begin_layout Standard
8798 \begin_inset VSpace medskip
8801 Arrows used as accent like e.
8802 \begin_inset space \thinspace{}
8806 \begin_inset space \space{}
8809 vector arrows are listed in
8810 \begin_inset CommandInset ref
8812 reference "sec:Accents"
8819 \begin_layout Standard
8820 \begin_inset VSpace bigskip
8823 Furthermore there are the labeled arrows
8824 \begin_inset Index idx
8827 \begin_layout Plain Layout
8840 \begin_inset Index idx
8843 \begin_layout Plain Layout
8858 \begin_inset Index idx
8861 \begin_layout Plain Layout
8868 \begin_layout Plain Layout
8883 When inserting one of these commands in a formula, an arrow with two blue
8884 boxes appear where the label can be inserted.
8885 The length of the arrow adapts to the label width.
8888 \begin_layout Standard
8890 \begin_inset Tabular
8891 <lyxtabular version="3" rows="3" columns="2">
8892 <features tabularvalignment="middle">
8893 <column alignment="center" valignment="top" width="0pt">
8894 <column alignment="center" valignment="top" width="0pt">
8896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8899 \begin_layout Plain Layout
8905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8908 \begin_layout Plain Layout
8910 \begin_inset Note Note
8913 \begin_layout Plain Layout
8920 is only used as spacer.
8932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8935 \begin_layout Plain Layout
8942 \begin_layout Plain Layout
8952 \begin_inset Formula $\downarrow$
8956 \begin_inset Formula $\to$
8964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8967 \begin_layout Plain Layout
8968 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8981 \begin_layout Plain Layout
8988 \begin_layout Plain Layout
8998 \begin_inset Formula $\downarrow$
9002 \begin_inset Formula $\to$
9010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9013 \begin_layout Plain Layout
9014 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9030 \begin_layout Subsection
9031 Vertical and diagonal Arrows
9032 \begin_inset Index idx
9035 \begin_layout Plain Layout
9042 \begin_inset Index idx
9045 \begin_layout Plain Layout
9054 \begin_layout Standard
9055 \begin_inset space \hfill{}
9059 \begin_inset Tabular
9060 <lyxtabular version="3" rows="7" columns="2">
9061 <features tabularvalignment="middle">
9062 <column alignment="center" valignment="top" width="0pt">
9063 <column alignment="center" valignment="top" width="0pt">
9065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9068 \begin_layout Plain Layout
9074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9077 \begin_layout Plain Layout
9085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9088 \begin_layout Plain Layout
9096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9099 \begin_layout Plain Layout
9100 \begin_inset Formula $\uparrow$
9110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9113 \begin_layout Plain Layout
9121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9124 \begin_layout Plain Layout
9125 \begin_inset Formula $\Uparrow$
9135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9138 \begin_layout Plain Layout
9146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9149 \begin_layout Plain Layout
9150 \begin_inset Formula $\updownarrow$
9160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9163 \begin_layout Plain Layout
9171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9174 \begin_layout Plain Layout
9175 \begin_inset Formula $\Updownarrow$
9185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9188 \begin_layout Plain Layout
9196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9199 \begin_layout Plain Layout
9200 \begin_inset Formula $\Downarrow$
9210 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9213 \begin_layout Plain Layout
9221 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9224 \begin_layout Plain Layout
9225 \begin_inset Formula $\downarrow$
9239 \begin_inset space \hfill{}
9243 \begin_inset Tabular
9244 <lyxtabular version="3" rows="5" columns="2">
9245 <features tabularvalignment="middle">
9246 <column alignment="center" valignment="top" width="0pt">
9247 <column alignment="center" valignment="top" width="0pt">
9249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9252 \begin_layout Plain Layout
9258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9261 \begin_layout Plain Layout
9269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9272 \begin_layout Plain Layout
9280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9283 \begin_layout Plain Layout
9284 \begin_inset Formula $\nearrow$
9294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9297 \begin_layout Plain Layout
9305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9308 \begin_layout Plain Layout
9309 \begin_inset Formula $\searrow$
9319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9322 \begin_layout Plain Layout
9330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9333 \begin_layout Plain Layout
9334 \begin_inset Formula $\swarrow$
9344 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9347 \begin_layout Plain Layout
9355 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9358 \begin_layout Plain Layout
9359 \begin_inset Formula $\nwarrow$
9373 \begin_inset space \hfill{}
9379 \begin_layout Standard
9380 \begin_inset VSpace medskip
9383 Vertical arrows can be used also as delimiter together with the commands
9385 \begin_inset CommandInset ref
9387 reference "sub:Manual-Bracket-Size"
9392 \begin_inset CommandInset ref
9394 reference "sub:Automatic-Bracket-Size"
9401 \begin_layout Standard
9402 \begin_inset Newpage newpage
9408 \begin_layout Section
9410 \begin_inset CommandInset label
9417 \begin_inset Index idx
9420 \begin_layout Plain Layout
9429 \begin_layout Standard
9430 Accents can be inserted via the math toolbar button
9431 \begin_inset Graphics
9432 filename ../images/math/hat.png
9437 or the commands listed in the following subsections.
9440 \begin_layout Subsection
9441 Accents for one Character
9445 \begin_layout Plain Layout
9458 \begin_layout Plain Layout
9460 \begin_inset CommandInset ref
9462 reference "sub:Accents-in-Text"
9475 \begin_layout Plain Layout
9483 \begin_inset Note Note
9486 \begin_layout Plain Layout
9489 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9492 \begin_layout Plain Layout
9495 texorpdfstring is in section
9496 \begin_inset CommandInset ref
9498 reference "sub:Formulas-in-Section"
9508 \begin_inset CommandInset label
9510 name "sub:Accents-for-one"
9515 \begin_inset Index idx
9518 \begin_layout Plain Layout
9519 Accents ! for one character
9527 \begin_layout Standard
9528 \begin_inset space \hfill{}
9532 \begin_inset Tabular
9533 <lyxtabular version="3" rows="8" columns="2">
9534 <features tabularvalignment="middle">
9535 <column alignment="center" valignment="top" width="0pt">
9536 <column alignment="center" valignment="top" width="0pt">
9538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9541 \begin_layout Plain Layout
9547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9550 \begin_layout Plain Layout
9552 \begin_inset Note Note
9555 \begin_layout Plain Layout
9562 is only used as spacer.
9574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9577 \begin_layout Plain Layout
9584 \begin_layout Plain Layout
9598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9601 \begin_layout Plain Layout
9602 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9612 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9615 \begin_layout Plain Layout
9622 \begin_layout Plain Layout
9636 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9639 \begin_layout Plain Layout
9640 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9650 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9653 \begin_layout Plain Layout
9660 \begin_layout Plain Layout
9674 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9677 \begin_layout Plain Layout
9678 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9688 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9691 \begin_layout Plain Layout
9698 \begin_layout Plain Layout
9712 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9715 \begin_layout Plain Layout
9716 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9726 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9729 \begin_layout Plain Layout
9736 \begin_layout Plain Layout
9746 \begin_inset Index idx
9749 \begin_layout Plain Layout
9760 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9763 \begin_layout Plain Layout
9764 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9774 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9777 \begin_layout Plain Layout
9784 \begin_layout Plain Layout
9798 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9801 \begin_layout Plain Layout
9802 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9812 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9815 \begin_layout Plain Layout
9822 \begin_layout Plain Layout
9836 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9839 \begin_layout Plain Layout
9840 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9854 \begin_inset space \hfill{}
9858 \begin_inset Tabular
9859 <lyxtabular version="3" rows="7" columns="2">
9860 <features tabularvalignment="middle">
9861 <column alignment="center" valignment="top" width="0pt">
9862 <column alignment="center" valignment="top" width="0pt">
9864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9867 \begin_layout Plain Layout
9873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9876 \begin_layout Plain Layout
9884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9887 \begin_layout Plain Layout
9894 \begin_layout Plain Layout
9908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9911 \begin_layout Plain Layout
9912 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9922 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9925 \begin_layout Plain Layout
9932 \begin_layout Plain Layout
9946 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9949 \begin_layout Plain Layout
9950 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9960 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9963 \begin_layout Plain Layout
9970 \begin_layout Plain Layout
9984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9987 \begin_layout Plain Layout
9988 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10001 \begin_layout Plain Layout
10008 \begin_layout Plain Layout
10022 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10025 \begin_layout Plain Layout
10026 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10036 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10039 \begin_layout Plain Layout
10046 \begin_layout Plain Layout
10060 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10063 \begin_layout Plain Layout
10064 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10074 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10077 \begin_layout Plain Layout
10084 \begin_layout Plain Layout
10098 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10101 \begin_layout Plain Layout
10102 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10116 \begin_inset space \hfill{}
10122 \begin_layout Standard
10123 \begin_inset VSpace bigskip
10129 \begin_layout Standard
10130 You can directly insert accents like é to formulas.
10131 LyX will transform them to the corresponding accent command.
10133 \begin_inset Index idx
10136 \begin_layout Plain Layout
10142 it is better to insert a quotation mark before the vowel.
10143 These two characters are then treated by LaTeX as
10147 character when the formula part with the umlaut is marked as German.
10155 \begin_inset Quotes eld
10159 \begin_inset Quotes erd
10162 umlauts are created as demonstrated in the following example:
10165 \begin_layout Standard
10166 \begin_inset VSpace -2mm
10172 \begin_layout Standard
10174 \begin_inset Tabular
10175 <lyxtabular version="3" rows="3" columns="2">
10176 <features tabularvalignment="middle">
10177 <column alignment="center" valignment="top" width="0">
10178 <column alignment="center" valignment="top" width="0">
10180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10183 \begin_layout Plain Layout
10189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10192 \begin_layout Plain Layout
10194 \begin_inset Note Note
10197 \begin_layout Plain Layout
10205 \begin_inset space \thinspace{}
10208 pt space are only used as spacer.
10220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10223 \begin_layout Plain Layout
10226 \begin_inset Quotes grd
10234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10237 \begin_layout Plain Layout
10238 \begin_inset space \hspace{}
10245 \begin_inset Formula $"i$
10255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10258 \begin_layout Plain Layout
10265 \begin_layout Plain Layout
10279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10282 \begin_layout Plain Layout
10283 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10299 \begin_layout Standard
10300 Another advantage to
10306 is that umlauts can directly be converted to mathematical text because
10307 the accent commands above are
10313 in mathematical text
10316 To convert an accented character to mathematical text, only the character
10317 under the accent may be converted.
10318 This applies also for all other conversions, e.
10319 \begin_inset space \thinspace{}
10323 \begin_inset space \space{}
10329 \begin_layout Standard
10330 In mathematical text, umlauts and other accented characters can directly
10334 \begin_layout Subsection
10335 Accents for Operators
10336 \begin_inset Index idx
10339 \begin_layout Plain Layout
10340 Accents ! for operators
10348 \begin_layout Standard
10356 \begin_inset Index idx
10359 \begin_layout Plain Layout
10374 \begin_inset Index idx
10377 \begin_layout Plain Layout
10385 characters can be placed above or below an operator, respectively, to accent
10394 \begin_inset Index idx
10397 \begin_layout Plain Layout
10405 characters can be set before and behind an operator.
10406 The command scheme is:
10409 \begin_layout Standard
10425 \begin_layout Standard
10432 must always be before the operator that should be accented.
10433 You can accent with several characters and even with other operators and
10441 for example only characters behind an operator, write nothing between the
10442 first braces but don't omit the braces.
10445 \begin_layout Standard
10446 For example the command
10451 \begin_inset Formula $\to$
10461 \begin_inset Formula $\to$
10470 \begin_layout Plain Layout
10486 \begin_inset Formula \[
10487 \sideset{}{'}\sum_{k=1}^{n}\]
10494 \begin_layout Standard
10503 \begin_layout Plain Layout
10518 \begin_layout Plain Layout
10530 \begin_inset Formula $\uparrow$
10538 \begin_inset Formula \[
10539 \overset{a}{\maltese}\]
10543 As seen in the last example, with
10555 also symbols and characters can be accented; with
10561 this is not possible.
10564 \begin_layout Subsection
10565 Accents for several Characters
10566 \begin_inset Index idx
10569 \begin_layout Plain Layout
10570 Accents ! for several characters
10578 \begin_layout Standard
10579 \begin_inset space \hfill{}
10583 \begin_inset Tabular
10584 <lyxtabular version="3" rows="5" columns="2">
10585 <features tabularvalignment="middle">
10586 <column alignment="center" valignment="top" width="0pt">
10587 <column alignment="center" valignment="top" width="0pt">
10589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10592 \begin_layout Plain Layout
10598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10601 \begin_layout Plain Layout
10603 \begin_inset Note Note
10606 \begin_layout Plain Layout
10613 is only used as spacer.
10625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10628 \begin_layout Plain Layout
10635 \begin_layout Plain Layout
10649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10652 \begin_layout Plain Layout
10653 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10663 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10666 \begin_layout Plain Layout
10673 \begin_layout Plain Layout
10687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10690 \begin_layout Plain Layout
10691 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10701 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10704 \begin_layout Plain Layout
10711 \begin_layout Plain Layout
10725 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10728 \begin_layout Plain Layout
10729 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10739 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10742 \begin_layout Plain Layout
10745 underleftrightarrow
10749 \begin_layout Plain Layout
10763 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10766 \begin_layout Plain Layout
10767 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10781 \begin_inset space \hfill{}
10785 \begin_inset Tabular
10786 <lyxtabular version="3" rows="5" columns="2">
10787 <features tabularvalignment="middle">
10788 <column alignment="center" valignment="top" width="0pt">
10789 <column alignment="center" valignment="top" width="0pt">
10791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10794 \begin_layout Plain Layout
10800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10803 \begin_layout Plain Layout
10811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10814 \begin_layout Plain Layout
10821 \begin_layout Plain Layout
10835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10838 \begin_layout Plain Layout
10839 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10849 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10852 \begin_layout Plain Layout
10859 \begin_layout Plain Layout
10873 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10876 \begin_layout Plain Layout
10877 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10887 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10890 \begin_layout Plain Layout
10897 \begin_layout Plain Layout
10911 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10914 \begin_layout Plain Layout
10915 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10925 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10928 \begin_layout Plain Layout
10935 \begin_layout Plain Layout
10949 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10952 \begin_layout Plain Layout
10953 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10967 \begin_inset space \hfill{}
10973 \begin_layout Standard
10974 \begin_inset VSpace medskip
10977 With these commands as many characters as you like can be accented.
10990 will only be set in the output with a length of three characters, as shown
10991 in the following example:
10992 \begin_inset Formula \[
10993 \widetilde{A+B=C-D}\]
11000 \begin_layout Standard
11008 \begin_inset Index idx
11011 \begin_layout Plain Layout
11026 \begin_inset Index idx
11029 \begin_layout Plain Layout
11037 described in the previous subsection it is also possible to accent several
11047 \begin_layout Plain Layout
11057 \begin_inset Formula $\downarrow$
11063 \begin_inset Formula \[
11064 \underset{***}{A=B}\]
11071 \begin_layout Section
11073 \begin_inset CommandInset label
11080 \begin_inset Index idx
11083 \begin_layout Plain Layout
11092 \begin_layout Subsection
11094 \begin_inset CommandInset label
11096 name "sub:Predefined-Space"
11101 \begin_inset Index idx
11104 \begin_layout Plain Layout
11105 Space ! horizontal ! predefined
11113 \begin_layout Standard
11114 Sometimes it is necessary to insert horizontal space to a formula.
11115 This is done by inserting a protected space (shortcut
11118 arg "space-insert protected"
11123 \begin_inset Quotes eld
11132 \begin_layout Plain Layout
11144 \begin_inset Quotes erd
11147 appears and by pressing
11151 several times one can select one of eight different space sizes.
11152 The spaces can also be inserted using the math toolbar button
11153 \begin_inset Graphics
11154 filename ../images/math/space.png
11159 or special commands.
11160 Independent from the inserted command, one can select the size again by
11168 \begin_layout Standard
11171 \begin_inset VSpace -5mm
11175 \begin_inset Tabular
11176 <lyxtabular version="3" rows="3" columns="7">
11177 <features tabularvalignment="middle">
11178 <column alignment="center" valignment="middle" width="6.8cm">
11179 <column alignment="center" valignment="top" width="0">
11180 <column alignment="center" valignment="top" width="0">
11181 <column alignment="center" valignment="top" width="0">
11182 <column alignment="center" valignment="top" width="0">
11183 <column alignment="center" valignment="top" width="0">
11184 <column alignment="center" valignment="top" width="0">
11186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11189 \begin_layout Plain Layout
11195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11198 \begin_layout Plain Layout
11206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11209 \begin_layout Plain Layout
11217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11220 \begin_layout Plain Layout
11228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11231 \begin_layout Plain Layout
11239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11242 \begin_layout Plain Layout
11250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11253 \begin_layout Plain Layout
11263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11266 \begin_layout Plain Layout
11271 keystrokes after inserting the protected space
11276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11279 \begin_layout Plain Layout
11285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11288 \begin_layout Plain Layout
11294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11297 \begin_layout Plain Layout
11303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11306 \begin_layout Plain Layout
11312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11315 \begin_layout Plain Layout
11321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11324 \begin_layout Plain Layout
11332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11335 \begin_layout Plain Layout
11341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11344 \begin_layout Plain Layout
11345 \begin_inset Formula $A\, B$
11353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11356 \begin_layout Plain Layout
11357 \begin_inset Formula $A\: B$
11365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11368 \begin_layout Plain Layout
11369 \begin_inset Formula $A\; B$
11377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11380 \begin_layout Plain Layout
11381 \begin_inset Formula $A\quad B$
11389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11392 \begin_layout Plain Layout
11393 \begin_inset Formula $A\qquad B$
11401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11404 \begin_layout Plain Layout
11405 \begin_inset Formula $A\! B$
11421 \begin_layout Standard
11422 The last size seem to produce no space.
11423 It is displayed red in LyX contrary to the other sizes, because it is a
11425 There are two more negative spaces:
11428 \begin_layout Standard
11430 \begin_inset Tabular
11431 <lyxtabular version="3" rows="3" columns="3">
11432 <features tabularvalignment="middle">
11433 <column alignment="center" valignment="middle" width="6.8cm">
11434 <column alignment="center" valignment="top" width="0pt">
11435 <column alignment="center" valignment="top" width="0pt">
11437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11440 \begin_layout Plain Layout
11446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11449 \begin_layout Plain Layout
11457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11460 \begin_layout Plain Layout
11470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11473 \begin_layout Plain Layout
11478 keystrokes after inserting the protected space
11483 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11486 \begin_layout Plain Layout
11492 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11495 \begin_layout Plain Layout
11503 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11506 \begin_layout Plain Layout
11512 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11515 \begin_layout Plain Layout
11516 \begin_inset Formula $A\negmedspace B$
11524 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11527 \begin_layout Plain Layout
11528 \begin_inset Formula $A\negthickspace B$
11544 \begin_layout Standard
11545 Negative spaces can lead to characters overlapping each other.
11546 Thus they can be used to enforce ligatures, what is e.
11547 \begin_inset space \thinspace{}
11551 \begin_inset space \space{}
11554 useful for summation operators:
11557 \begin_layout Standard
11559 \begin_inset Tabular
11560 <lyxtabular version="3" rows="3" columns="2">
11561 <features tabularvalignment="middle">
11562 <column alignment="center" valignment="top" width="0">
11563 <column alignment="center" valignment="top" width="0">
11565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11568 \begin_layout Plain Layout
11574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11577 \begin_layout Plain Layout
11579 \begin_inset Note Note
11582 \begin_layout Plain Layout
11589 is only used as spacer.
11601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11604 \begin_layout Plain Layout
11613 \begin_layout Plain Layout
11627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11630 \begin_layout Plain Layout
11631 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11644 \begin_layout Plain Layout
11655 \begin_layout Plain Layout
11669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11672 \begin_layout Plain Layout
11673 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11689 \begin_layout Standard
11690 Relations like for example equal signs, are always surrounded by space.
11691 To suppress this, the equal sign is placed into a TeX-brace.
11692 The following example demonstrates this:
11695 \begin_layout Standard
11697 \begin_inset Tabular
11698 <lyxtabular version="3" rows="2" columns="2">
11699 <features tabularvalignment="middle">
11700 <column alignment="center" valignment="top" width="0pt">
11701 <column alignment="center" valignment="top" width="0pt">
11703 <cell alignment="center" valignment="top" usebox="none">
11706 \begin_layout Plain Layout
11712 <cell alignment="center" valignment="top" usebox="none">
11715 \begin_layout Plain Layout
11716 \begin_inset Formula $A=B$
11726 <cell alignment="center" valignment="top" usebox="none">
11729 \begin_layout Plain Layout
11730 \begin_inset Note Note
11733 \begin_layout Plain Layout
11740 is only used as spacer.
11746 \begin_inset Formula $\raisebox{5mm}{}$
11749 equation without space
11754 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11757 \begin_layout Plain Layout
11758 \begin_inset Formula $A{=}B$
11774 \begin_layout Standard
11776 The command for the last formula is:
11781 \begin_inset Formula $\to$
11787 \begin_layout Standard
11788 \begin_inset VSpace bigskip
11791 Spaces are needed for physical units, because the space between the value
11792 and the unit is the smallest one and not a normal space.
11793 For units in text, the smallest space is inserted via the menu
11795 Insert\SpecialChar \menuseparator
11796 Formatting\SpecialChar \menuseparator
11798 \begin_inset space ~
11806 arg "space-insert thin"
11812 \begin_layout Standard
11813 An example to visualize the difference:
11816 \begin_layout Standard
11817 \begin_inset Tabular
11818 <lyxtabular version="3" rows="2" columns="2">
11819 <features tabularvalignment="middle">
11820 <column alignment="left" valignment="top" width="0">
11821 <column alignment="left" valignment="top" width="0">
11823 <cell alignment="center" valignment="top" usebox="none">
11826 \begin_layout Plain Layout
11828 \begin_inset Formula $\cdot$
11836 <cell alignment="center" valignment="top" usebox="none">
11839 \begin_layout Plain Layout
11840 space between value and unit
11847 <cell alignment="center" valignment="top" usebox="none">
11850 \begin_layout Plain Layout
11852 \begin_inset space \thinspace{}
11856 \begin_inset Formula $\cdot$
11864 <cell alignment="center" valignment="top" usebox="none">
11867 \begin_layout Plain Layout
11868 smallest space between value and unit
11881 \begin_layout Subsection
11886 \begin_layout Plain Layout
11899 \begin_layout Plain Layout
11900 for vertical space in formulas see
11901 \begin_inset CommandInset ref
11903 reference "sub:Line-Separation"
11916 \begin_layout Plain Layout
11924 \begin_inset Note Note
11927 \begin_layout Plain Layout
11930 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11933 \begin_layout Plain Layout
11936 texorpdfstring is in section
11937 \begin_inset CommandInset ref
11939 reference "sub:Formulas-in-Section"
11949 \begin_inset CommandInset label
11951 name "sub:Variable-Space"
11956 \begin_inset Index idx
11959 \begin_layout Plain Layout
11960 Space ! horizontal ! variable
11968 \begin_layout Standard
11969 Space with a defined length can be inserted with the command
11976 \begin_inset Index idx
11979 \begin_layout Plain Layout
11989 \begin_inset Quotes eld
11998 \begin_layout Plain Layout
12010 \begin_inset Quotes erd
12014 The length can be specified by left-clicking on the
12015 \begin_inset Quotes eld
12024 \begin_layout Plain Layout
12036 \begin_inset Quotes erd
12040 The length may also be negative.
12041 To insert so many space that the formula uses all available space, the
12049 \begin_inset Index idx
12052 \begin_layout Plain Layout
12063 \begin_layout Standard
12064 \begin_inset VSpace -1mm
12070 \begin_layout Standard
12072 \begin_inset Tabular
12073 <lyxtabular version="3" rows="4" columns="2">
12074 <features tabularvalignment="middle">
12075 <column alignment="center" valignment="top" width="0">
12076 <column alignment="center" valignment="top" width="0">
12078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12081 \begin_layout Plain Layout
12089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12092 \begin_layout Plain Layout
12100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12103 \begin_layout Plain Layout
12110 \begin_layout Plain Layout
12120 \begin_inset Formula $\to$
12126 \begin_inset space \thinspace{}
12134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12137 \begin_layout Plain Layout
12138 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12151 \begin_layout Plain Layout
12158 \begin_layout Plain Layout
12168 \begin_inset Formula $\to$
12174 \begin_inset space \thinspace{}
12182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12185 \begin_layout Plain Layout
12186 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12199 \begin_layout Plain Layout
12206 \begin_layout Plain Layout
12220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12223 \begin_layout Plain Layout
12224 \begin_inset Formula $A=A\hfill B=B$
12240 \begin_layout Standard
12241 In the last example the available space is given by the longest column entry
12243 In an inline formula the space depends on the length of the line in which
12251 Thus, when the line uses the full width, no space will be created.
12258 only has an effect on displayed formulas when the formula style
12263 (Formula styles are explained in
12264 \begin_inset CommandInset ref
12266 reference "sec:Formula-Styles"
12273 \begin_layout Standard
12280 , there are the commands
12292 that fill the space with a pattern, see
12293 \begin_inset CommandInset ref
12295 reference "sub:Ellipses"
12302 \begin_layout Standard
12303 For text, variable space can be inserted via the menu
12305 Insert\SpecialChar \menuseparator
12306 Formatting\SpecialChar \menuseparator
12308 \begin_inset space ~
12316 \begin_layout Standard
12317 This is a line with
12318 \begin_inset space \hspace{}
12323 \begin_inset space \thinspace{}
12329 \begin_layout Standard
12330 This is a line with
12331 \begin_inset space \hfill{}
12337 \begin_layout Subsection
12338 Space besides inline Formulas
12339 \begin_inset Index idx
12342 \begin_layout Plain Layout
12343 Space ! besides inline formulas
12351 \begin_layout Standard
12352 The space that surrounds inline formulas can be adjusted with the length
12360 \begin_inset Index idx
12363 \begin_layout Plain Layout
12372 The value of a length is set with the command
12379 \begin_inset Index idx
12382 \begin_layout Plain Layout
12390 that has the following scheme:
12393 \begin_layout Standard
12398 setlength{length name}{value}
12401 \begin_layout Standard
12409 \begin_inset space \thinspace{}
12415 \begin_layout Standard
12425 \begin_layout Standard
12426 is inserted in TeX-mode.
12428 \begin_inset space \thinspace{}
12431 mm space will now be set around all inline formulas:
12435 \begin_layout Plain Layout
12449 \begin_layout Standard
12450 This is a line with an inline formula
12451 \begin_inset Formula $A=B$
12455 \begin_inset space \thinspace{}
12458 mm surrounding space.
12462 \begin_layout Plain Layout
12476 \begin_layout Standard
12477 To return to the predefined value,
12483 is set to the value 0
12484 \begin_inset space \thinspace{}
12490 \begin_layout Section
12492 \begin_inset Index idx
12495 \begin_layout Plain Layout
12502 \begin_inset Index idx
12505 \begin_layout Plain Layout
12510 \begin_layout Plain Layout
12521 \begin_layout Plain Layout
12536 \begin_layout Standard
12537 Boxes for text are described in chapter
12544 \begin_inset space ~
12552 \begin_layout Subsection
12554 \begin_inset CommandInset label
12556 name "sub:Boxes-with-Frame"
12561 \begin_inset Index idx
12564 \begin_layout Plain Layout
12573 \begin_layout Standard
12574 It is possible to frame formulas or parts of it with the commands
12581 \begin_inset Index idx
12584 \begin_layout Plain Layout
12599 \begin_inset Index idx
12602 \begin_layout Plain Layout
12613 \begin_layout Standard
12614 When one of these commands is inserted to a formula, a blue box appears
12615 within a frame to enter formula parts.
12622 an additional formula has to be created by
12626 within this box, because the box content will otherwise be treated as mathemati
12634 is used, a new formula is automatically created inside the frame.
12637 \begin_layout Standard
12644 is not suitable to frame displayed formulas because the formula will always
12645 be set in the size of the text.
12652 is in contrary not suitable to frame inline formulas, because the formula
12653 will always be set in the size of a displayed formula.
12656 \begin_layout Standard
12663 there is the command
12670 \begin_inset Index idx
12673 \begin_layout Plain Layout
12681 where additionally the frame width and the alignment can be specified.
12688 is used in the following scheme:
12691 \begin_layout Standard
12696 framebox[frame width][position]{box content}
12699 \begin_layout Standard
12700 The position can either be
12717 right aligns the formula in the box.
12718 When no position is given, the formula will be centered.
12719 \begin_inset Newline newline
12722 Is no width given, also no position can be given.
12723 In this case the frame width is adjusted to the box content like for
12732 \begin_layout Standard
12739 is inserted, a box appears containing three blue boxes.
12740 The first two boxes are surrounded by brackets and denote the two optional
12742 The third box is for formula parts like for
12751 \begin_layout Standard
12753 \begin_inset Tabular
12754 <lyxtabular version="3" rows="5" columns="2">
12755 <features tabularvalignment="middle">
12756 <column alignment="center" valignment="top" width="0">
12757 <column alignment="center" valignment="top" width="0">
12759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12762 \begin_layout Plain Layout
12768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12771 \begin_layout Plain Layout
12773 \begin_inset Note Note
12776 \begin_layout Plain Layout
12783 is only used as spacer.
12795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12798 \begin_layout Plain Layout
12805 \begin_layout Plain Layout
12824 \begin_layout Plain Layout
12838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12841 \begin_layout Plain Layout
12842 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12855 \begin_layout Plain Layout
12862 \begin_layout Plain Layout
12877 \begin_layout Plain Layout
12891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12894 \begin_layout Plain Layout
12895 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12908 \begin_layout Plain Layout
12915 \begin_layout Plain Layout
12929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12932 \begin_layout Plain Layout
12933 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12946 \begin_layout Plain Layout
12953 \begin_layout Plain Layout
12963 \begin_inset Formula $\to$
12967 \begin_inset Formula $\to$
12980 \begin_layout Plain Layout
12990 \begin_inset Formula $\downarrow$
12998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13001 \begin_layout Plain Layout
13002 \begin_inset Formula $\raisebox{6mm}{}$
13006 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13010 \begin_inset Formula $\raisebox{-4mm}{}$
13026 \begin_layout Standard
13027 The frame thickness can also be adjusted.
13028 To do this the following commands have to be inserted in TeX-mode before
13032 \begin_layout Standard
13042 \begin_inset Quotes eld
13046 \begin_inset Quotes erd
13060 \begin_inset Quotes eld
13064 \begin_inset Quotes erd
13070 \begin_layout Standard
13071 \begin_inset Quotes eld
13075 \begin_inset Quotes erd
13078 specifies the minimal distance between the frame and the first character
13080 An example for this is the following framed formula:
13084 \begin_layout Plain Layout
13096 \begin_inset Formula \[
13101 Before this formula the commands
13104 \begin_layout Standard
13126 \begin_layout Standard
13127 were inserted in TeX-mode.
13128 The given values are used for all following boxes.
13131 \begin_layout Standard
13132 To return to the standard frame size, the command
13135 \begin_layout Standard
13160 \begin_layout Plain Layout
13174 \begin_layout Standard
13175 is inserted in TeX-mode before the next formula.
13178 \begin_layout Subsection
13179 Boxes without Frame
13180 \begin_inset CommandInset label
13182 name "sub:Boxes-without-Frame"
13187 \begin_inset Index idx
13190 \begin_layout Plain Layout
13191 Boxes ! without frame
13199 \begin_layout Standard
13200 For boxes without a frame there are the following box commands:
13207 \begin_inset Index idx
13210 \begin_layout Plain Layout
13225 \begin_inset Index idx
13228 \begin_layout Plain Layout
13243 \begin_inset Index idx
13246 \begin_layout Plain Layout
13257 \begin_layout Standard
13264 a box can be super- or subscripted.
13265 But in contrary to normal super- and subscripting, the characters in the
13266 box keep their font size.
13273 is used in the following scheme:
13276 \begin_layout Standard
13281 raisebox{height}{box content}
13284 \begin_layout Standard
13285 When the box should contain a formula, an extra formula is needed like for
13296 \begin_inset Note Greyedout
13299 \begin_layout Plain Layout
13310 this extra formula is created by pressing
13314 twice instead of once because LyX doesn't yet support
13328 \begin_layout Standard
13330 \begin_inset Tabular
13331 <lyxtabular version="3" rows="4" columns="2">
13332 <features tabularvalignment="middle">
13333 <column alignment="center" valignment="top" width="0">
13334 <column alignment="center" valignment="top" width="0">
13336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13339 \begin_layout Plain Layout
13345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13348 \begin_layout Plain Layout
13356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13359 \begin_layout Plain Layout
13363 \begin_inset Formula $\to$
13369 \begin_inset Formula $\to$
13377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13380 \begin_layout Plain Layout
13381 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13394 \begin_layout Plain Layout
13398 \begin_inset Formula $\to$
13404 \begin_inset Formula $\to$
13412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13415 \begin_layout Plain Layout
13416 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13429 \begin_layout Plain Layout
13433 \begin_inset Formula $\to$
13452 \begin_layout Plain Layout
13466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13469 \begin_layout Plain Layout
13470 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13486 \begin_layout Standard
13511 , with the difference that there is no frame.
13514 \begin_layout Subsection
13516 \begin_inset CommandInset label
13518 name "sub:Colored-Boxes"
13523 \begin_inset Index idx
13526 \begin_layout Plain Layout
13535 \begin_layout Standard
13536 To be able to use all commands explained in this section, the LaTeX-package
13545 \begin_layout Plain Layout
13550 is part of every LaTeX standard installation.
13556 \begin_inset Index idx
13559 \begin_layout Plain Layout
13565 has to be loaded in the LaTeX-preamble with the line
13569 \begin_layout Plain Layout
13570 When text is colored somewhere in the document with a predefined color,
13571 LyX loads the LaTeX-package
13576 Thus it is possible that the package is loaded twice, but this doesn't
13583 \begin_inset Note Note
13586 \begin_layout Plain Layout
13587 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13596 \begin_layout Standard
13604 \begin_layout Standard
13605 \begin_inset VSpace medskip
13608 To color boxes, the command
13615 \begin_inset Index idx
13618 \begin_layout Plain Layout
13626 is used in the following scheme:
13629 \begin_layout Standard
13634 colorbox{color}{box content}
13637 \begin_layout Standard
13638 The box content can also be a box and a
13644 can also be part of another box (see the 2nd and 3rd example).
13645 When the box should contain a formula, an extra formula has to be created,
13646 the same way as for
13656 \begin_layout Plain Layout
13657 This also applies for the command
13671 \begin_layout Standard
13672 One of the following predefined colors can be chosen:
13675 \begin_layout Standard
13709 \begin_layout Standard
13711 \begin_inset Tabular
13712 <lyxtabular version="3" rows="4" columns="2">
13713 <features tabularvalignment="middle">
13714 <column alignment="center" valignment="top" width="0">
13715 <column alignment="center" valignment="top" width="0">
13717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13720 \begin_layout Plain Layout
13726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13729 \begin_layout Plain Layout
13731 \begin_inset Note Note
13734 \begin_layout Plain Layout
13741 is only used as spacer.
13753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13756 \begin_layout Plain Layout
13760 \begin_inset Formula $\to$
13770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13773 \begin_layout Plain Layout
13774 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13787 \begin_layout Plain Layout
13791 \begin_inset Formula $\to$
13802 \begin_layout Plain Layout
13816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13819 \begin_layout Plain Layout
13820 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13833 \begin_layout Plain Layout
13840 \begin_layout Plain Layout
13852 \begin_inset Formula $\to$
13871 \begin_layout Plain Layout
13885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13888 \begin_layout Plain Layout
13889 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13905 \begin_layout Standard
13912 only colors the box but not the characters in the box.
13913 To color all characters, the whole formula is highlighted and the wanted
13914 color is chosen in the
13917 \begin_inset space ~
13923 The dialog can be called with the toolbar button
13924 \begin_inset Graphics
13925 filename ../images/dialog-show_character.png
13932 Edit\SpecialChar \menuseparator
13934 \begin_inset space ~
13937 Style\SpecialChar \menuseparator
13941 The formula number has then the same color as the formula.
13942 When the formula number should get another color than the formula characters,
13943 the color must be changed within the formula.
13946 \begin_layout Standard
13950 \begin_layout Standard
13953 \begin_inset Formula \begin{equation}
13954 \int A=B\label{eq:red}\end{equation}
13961 \begin_inset Formula \begin{equation}
13962 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13969 \begin_layout Standard
13971 \begin_inset CommandInset ref
13977 is completely colored red.
13978 \begin_inset Newline newline
13982 \begin_inset CommandInset ref
13984 reference "eq:redgreen"
13988 was first completely colored green to set the color for the formula number.
13989 Subsequently the formula characters were colored red.
13992 \begin_layout Standard
13993 \begin_inset VSpace bigskip
13996 To color the frame different than the rest of the box, the command
14003 \begin_inset Index idx
14006 \begin_layout Plain Layout
14014 is used in the following scheme:
14017 \begin_layout Standard
14022 fcolorbox{frame color}{color}{box content}
14025 \begin_layout Standard
14032 is an extension of the command
14039 The frame width is set, like for
14062 \begin_layout Plain Layout
14074 \begin_inset Formula \[
14075 \fcolorbox{cyan}{magenta}{A=B}\]
14083 \begin_layout Plain Layout
14097 \begin_layout Standard
14098 This formula was created with the command
14099 \begin_inset Newline newline
14107 \begin_inset Formula $\to$
14113 \begin_inset Formula $\to$
14123 \begin_layout Standard
14124 \begin_inset VSpace bigskip
14127 To use other colors than the predefined ones, they have to be defined first.
14130 \begin_layout Standard
14131 One can for example define the color
14132 \begin_inset Quotes eld
14140 \begin_inset Quotes erd
14143 with the LaTeX-preamble line:
14146 \begin_layout Standard
14151 definecolor{darkgreen}{cmyk}{0.5,
14166 \begin_inset Index idx
14169 \begin_layout Plain Layout
14180 \begin_layout Standard
14185 is the color space that denotes the colors
14202 The four comma separated numbers are the portion factor for the corresponding
14203 colors of the color space.
14204 The factors can be in the range of 0
14205 \begin_inset space \thinspace{}
14209 \begin_inset space \thinspace{}
14217 also the color space
14221 can be used for definitions.
14238 , so that there are in this case three portion factors for the corresponding
14240 Furthermore there is the color space
14244 with one portion factor for the gray value.
14247 \begin_layout Standard
14248 As example a framed box with the new defined color
14252 where the characters have been colored
14257 \begin_inset Formula \begin{equation}
14258 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14265 \begin_layout Standard
14266 Self-defined colors can also be used for text with the help of the command
14274 \begin_inset Index idx
14277 \begin_layout Plain Layout
14286 \begin_layout Standard
14290 \begin_layout Plain Layout
14294 textcolor{darkgreen}{
14300 \begin_inset Quotes eld
14304 \begin_inset Quotes erd
14311 \begin_layout Plain Layout
14321 \begin_layout Standard
14329 \begin_inset Index idx
14332 \begin_layout Plain Layout
14340 is used in the scheme
14344 textcolor{color}{characters to color}
14349 \begin_layout Subsection
14351 \begin_inset CommandInset label
14353 name "sub:Paragraph-Boxes"
14358 \begin_inset Index idx
14361 \begin_layout Plain Layout
14362 Boxes ! as paragraph
14370 \begin_layout Standard
14371 A box that can contain several lines and paragraphs, a so called paragraph
14372 box (parbox), can be created with the menu
14374 Insert\SpecialChar \menuseparator
14377 or the toolbar button
14378 \begin_inset Graphics
14379 filename ../images/box-insert.png
14387 \begin_layout Standard
14388 The following example shows a framed parbox in a line:
14391 \begin_layout Standard
14392 \begin_inset VSpace medskip
14396 \begin_inset Box Boxed
14406 height_special "totalheight"
14409 \begin_layout Plain Layout
14410 This is a paragraph box.
14412 \begin_inset space \thinspace{}
14415 cm long and can also contain formulas:
14416 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14427 \begin_layout Standard
14428 \begin_inset VSpace medskip
14434 \begin_layout Standard
14435 Such a box is created by right-clicking on the gray box inset.
14436 A dialog pops up showing the box properties.
14450 \begin_inset space \thinspace{}
14455 Vertical Box Alignment
14460 \begin_layout Standard
14461 \begin_inset VSpace medskip
14464 In LaTeX a parbox is created with the command
14471 \begin_inset Index idx
14474 \begin_layout Plain Layout
14482 that has the following scheme:
14485 \begin_layout Standard
14490 parbox[position]{width}{box content}
14493 \begin_layout Standard
14507 for bottom means that the box is aligned within the surrounding text with
14513 for top this is done with the first line.
14514 When no position is given, the box will be vertically centered, see section
14522 \begin_inset space ~
14527 manual for examples.
14530 \begin_layout Standard
14531 \begin_inset VSpace bigskip
14534 To frame formulas completely, including the formula number, the formula
14535 must be set into a parbox.
14536 To do this, the command
14550 is inserted in TeX-mode before the formula.
14558 \begin_inset Index idx
14561 \begin_layout Plain Layout
14569 is hereby the line width set for the document.
14570 Because the frame is outside the parbox, 2
14571 \begin_inset space \thinspace{}
14574 times the frame separation and the frame thickness must be subtracted from
14576 As this is not automatically done by LyX due to a bug
14580 \begin_layout Plain Layout
14581 \begin_inset CommandInset href
14583 name "LyX-bug #4483"
14584 target "http://www.lyx.org/trac/ticket/4483"
14593 , TeX-mode has to be used.
14594 To be able to multiply and subtract in arguments, the LaTeX-package
14602 \begin_layout Plain Layout
14607 is part of every LaTeX standard installation.
14613 \begin_inset Index idx
14616 \begin_layout Plain Layout
14622 must be loaded in the LaTeX-preamble with the line
14625 \begin_layout Standard
14633 \begin_layout Standard
14634 Behind the formula both boxes are closed by entering
14639 Here is an example:
14643 \begin_layout Plain Layout
14657 \begin_layout Standard
14661 \begin_layout Plain Layout
14679 \begin_inset Formula \begin{equation}
14680 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14688 \begin_layout Plain Layout
14699 \begin_layout Plain Layout
14713 \begin_layout Standard
14714 \begin_inset VSpace medskip
14717 As a parbox is used as argument of
14723 , there is in this case no difference between
14738 \begin_layout Standard
14739 \begin_inset VSpace bigskip
14742 Paragraph boxes are very useful to comment formulas directly.
14749 is used in combination with the command
14763 \begin_inset CommandInset ref
14765 reference "sub:User-defined-Numbering"
14772 \begin_layout Standard
14773 An example of a formula commented with
14782 \begin_layout Standard
14786 \begin_layout Plain Layout
14799 This is a description.
14800 It is distinctly separated from the formula and multiline.
14804 \begin_layout Plain Layout
14816 \begin_layout Standard
14817 Such a formula must be inserted completely in TeX-mode because LyX does
14818 not yet support the command
14825 The formula is created with the following command sequence:
14828 \begin_layout Standard
14841 is inserted in TeX-mode.
14845 \begin_layout Plain Layout
14846 When the formula style
14858 can also be replaced by
14865 (formula styles see
14866 \begin_inset CommandInset ref
14868 reference "sec:Formula-Styles"
14877 Then the description follows as normal text and finally
14883 is inserted in TeX-mode.
14896 hereby create a displayed formula.
14899 \begin_layout Standard
14906 can be seen in this example that was
14907 \begin_inset Quotes eld
14911 \begin_inset Quotes erd
14914 using the mathematical textmode:
14915 \begin_inset Formula \[
14916 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14923 \begin_layout Section
14925 \begin_inset Index idx
14928 \begin_layout Plain Layout
14937 \begin_layout Subsection
14939 \begin_inset CommandInset label
14941 name "sub:Big-Operators"
14946 \begin_inset Index idx
14949 \begin_layout Plain Layout
14956 \begin_inset Index idx
14959 \begin_layout Plain Layout
14966 \begin_inset Index idx
14969 \begin_layout Plain Layout
14978 \begin_layout Standard
14979 To be able to use all integral operators listed here, the option
14981 Use esint package automatically
14983 must be set in the document settings under
14986 \begin_inset space ~
14994 \begin_layout Standard
14995 \begin_inset space \hfill{}
14999 \begin_inset Tabular
15000 <lyxtabular version="3" rows="11" columns="2">
15001 <features tabularvalignment="middle">
15002 <column alignment="center" valignment="top" width="0pt">
15003 <column alignment="center" valignment="top" width="0pt">
15005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15008 \begin_layout Plain Layout
15014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15017 \begin_layout Plain Layout
15025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15028 \begin_layout Plain Layout
15032 \begin_inset Index idx
15035 \begin_layout Plain Layout
15048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15051 \begin_layout Plain Layout
15052 \begin_inset Formula $\int$
15062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15065 \begin_layout Plain Layout
15073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15076 \begin_layout Plain Layout
15077 \begin_inset Formula $\oint$
15087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15090 \begin_layout Plain Layout
15098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15101 \begin_layout Plain Layout
15102 \begin_inset Formula $\ointctrclockwise$
15112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15115 \begin_layout Plain Layout
15123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15126 \begin_layout Plain Layout
15127 \begin_inset Formula $\ointclockwise$
15137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15140 \begin_layout Plain Layout
15148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15151 \begin_layout Plain Layout
15152 \begin_inset Formula $\sqint$
15162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15165 \begin_layout Plain Layout
15173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15176 \begin_layout Plain Layout
15178 \begin_inset Formula $\fint$
15188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15191 \begin_layout Plain Layout
15199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15202 \begin_layout Plain Layout
15204 \begin_inset Formula $\landupint$
15214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15217 \begin_layout Plain Layout
15225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15228 \begin_layout Plain Layout
15230 \begin_inset Formula $\landdownint$
15240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15243 \begin_layout Plain Layout
15251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15254 \begin_layout Plain Layout
15255 \begin_inset Formula $\bigcap$
15265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15268 \begin_layout Plain Layout
15276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15279 \begin_layout Plain Layout
15280 \begin_inset Formula $\bigcup$
15294 \begin_inset space \hfill{}
15298 \begin_inset Tabular
15299 <lyxtabular version="3" rows="11" columns="2">
15300 <features tabularvalignment="middle">
15301 <column alignment="center" valignment="top" width="0pt">
15302 <column alignment="center" valignment="top" width="0pt">
15304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15307 \begin_layout Plain Layout
15313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15316 \begin_layout Plain Layout
15324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15327 \begin_layout Plain Layout
15331 \begin_inset Index idx
15334 \begin_layout Plain Layout
15347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15350 \begin_layout Plain Layout
15351 \begin_inset Formula $\sum$
15361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15364 \begin_layout Plain Layout
15368 \begin_inset Index idx
15371 \begin_layout Plain Layout
15384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15387 \begin_layout Plain Layout
15388 \begin_inset Formula $\prod$
15398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15401 \begin_layout Plain Layout
15409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15412 \begin_layout Plain Layout
15413 \begin_inset Formula $\coprod$
15423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15426 \begin_layout Plain Layout
15434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15437 \begin_layout Plain Layout
15438 \begin_inset Formula $\bigodot$
15448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15451 \begin_layout Plain Layout
15459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15462 \begin_layout Plain Layout
15463 \begin_inset Formula $\bigotimes$
15473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15476 \begin_layout Plain Layout
15484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15487 \begin_layout Plain Layout
15488 \begin_inset Formula $\bigoplus$
15498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15501 \begin_layout Plain Layout
15509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15512 \begin_layout Plain Layout
15513 \begin_inset Formula $\bigwedge$
15523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15526 \begin_layout Plain Layout
15534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15537 \begin_layout Plain Layout
15538 \begin_inset Formula $\bigvee$
15548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15551 \begin_layout Plain Layout
15559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15562 \begin_layout Plain Layout
15563 \begin_inset Formula $\bigsqcup$
15573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15576 \begin_layout Plain Layout
15584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15587 \begin_layout Plain Layout
15588 \begin_inset Formula $\biguplus$
15602 \begin_inset space \hfill{}
15608 \begin_layout Standard
15609 All big operators can also be inserted via the math toolbar button
15610 \begin_inset Graphics
15611 filename ../images/math/intop.png
15619 \begin_layout Standard
15620 The operators are called big because they are bigger than the sometimes
15621 equal looking binary operators.
15622 All big operators can have limits as described in the next subsection.
15625 \begin_layout Standard
15626 For all integral operators there is a second version available, ending on
15644 These operators are different from
15651 \begin_inset space \space{}
15654 in the style the operator limits are displayed, see
15655 \begin_inset CommandInset ref
15657 reference "sub:Operator-Limits"
15665 \begin_layout Subsubsection*
15666 Advice for Integrals
15669 \begin_layout Standard
15674 in an integral is an operator, that therefore has to be set upright.
15675 This is done by highlighting the
15679 and using the keyboard shortcut
15689 \begin_layout Plain Layout
15695 \begin_inset CommandInset ref
15697 reference "sub:Font-Styles"
15707 Finally the smallest space is inserted before the
15711 , as this is usual for operators.
15715 \begin_layout Standard
15717 \begin_inset Formula $\int A(x)dx$
15721 \begin_inset Newline newline
15725 \begin_inset Phantom HPhantom
15728 \begin_layout Plain Layout
15735 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15741 \begin_layout Standard
15742 For multiple integrals there are the following commands:
15743 \begin_inset VSpace medskip
15749 \begin_layout Standard
15750 \begin_inset space \hfill{}
15754 \begin_inset Tabular
15755 <lyxtabular version="3" rows="4" columns="2">
15756 <features tabularvalignment="middle">
15757 <column alignment="center" valignment="top" width="0">
15758 <column alignment="center" valignment="top" width="0">
15760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15763 \begin_layout Plain Layout
15769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15772 \begin_layout Plain Layout
15774 \begin_inset Note Note
15777 \begin_layout Plain Layout
15784 is only used as spacer.
15796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15799 \begin_layout Plain Layout
15807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15810 \begin_layout Plain Layout
15811 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15824 \begin_layout Plain Layout
15832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15835 \begin_layout Plain Layout
15836 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15849 \begin_layout Plain Layout
15857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15860 \begin_layout Plain Layout
15861 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15875 \begin_inset space \hfill{}
15879 \begin_inset Tabular
15880 <lyxtabular version="3" rows="4" columns="2">
15881 <features tabularvalignment="middle">
15882 <column alignment="center" valignment="top" width="0">
15883 <column alignment="center" valignment="top" width="0">
15885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15888 \begin_layout Plain Layout
15894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15897 \begin_layout Plain Layout
15905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15908 \begin_layout Plain Layout
15916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15919 \begin_layout Plain Layout
15920 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15933 \begin_layout Plain Layout
15941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15944 \begin_layout Plain Layout
15945 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15958 \begin_layout Plain Layout
15966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15969 \begin_layout Plain Layout
15970 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15984 \begin_inset space \hfill{}
15990 \begin_layout Subsection
15992 \begin_inset CommandInset label
15994 name "sub:Operator-Limits"
15999 \begin_inset Index idx
16002 \begin_layout Plain Layout
16011 \begin_layout Standard
16012 Limits are created by super- and subscripts:
16015 \begin_layout Standard
16017 \begin_inset Tabular
16018 <lyxtabular version="3" rows="2" columns="2">
16019 <features tabularvalignment="middle">
16020 <column alignment="center" valignment="top" width="0pt">
16021 <column alignment="center" valignment="top" width="0pt">
16023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16026 \begin_layout Plain Layout
16032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16035 \begin_layout Plain Layout
16037 \begin_inset Note Note
16040 \begin_layout Plain Layout
16047 is only used as spacer.
16059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16062 \begin_layout Plain Layout
16071 \begin_layout Plain Layout
16081 \begin_inset Formula $\to$
16085 \begin_inset Formula $\to$
16093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16096 \begin_layout Plain Layout
16097 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16113 \begin_layout Standard
16114 Limits of inline formulas are set right beside the operator.
16115 Limits in displayed formulas are set above or below the operator, except
16116 for integral limits.
16119 \begin_layout Standard
16120 To force that the limits are set beside the operator, the cursor is set
16121 directly behind the operator and the limits type is changed with the menu
16124 Edit\SpecialChar \menuseparator
16125 Math\SpecialChar \menuseparator
16144 \begin_layout Standard
16145 The default limits type is this:
16146 \begin_inset Formula \[
16147 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16151 This is how it looks when the limits type was changed to
16158 \begin_inset Formula \[
16159 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16163 For integrals, except those ending with
16179 etc., the limits are by default set beside the operator.
16180 But for multiple integrals the limits are often set below the operator.
16181 In the following example the limits type was therefore set to
16185 and so set below the integrals:
16186 \begin_inset Formula \begin{equation}
16187 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16194 \begin_layout Standard
16195 \begin_inset VSpace medskip
16198 To specify conditions for limits, the commands
16205 \begin_inset Index idx
16208 \begin_layout Plain Layout
16223 \begin_inset Index idx
16226 \begin_layout Plain Layout
16235 To create for example this expression
16236 \begin_inset Formula \begin{equation}
16237 \sum_{\begin{subarray}{c}
16241 \end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16248 \begin_layout Standard
16249 the following has to be done:
16250 \begin_inset Newline newline
16265 \begin_layout Plain Layout
16277 One is now in a blue box under the summation operator and insert there
16286 \begin_layout Plain Layout
16298 The blue box is now within a purple box and now several lines can be written
16300 A new line is created by inserting a line break (
16303 arg "newline-insert newline"
16308 \begin_inset Newline newline
16313 0<k<1000 Ctrl+Return
16314 \begin_inset Newline newline
16319 is typed in, a new box appears below for the new line.
16322 \begin_layout Standard
16323 The alignment of the lines can be changed to left aligned with the
16333 Edit\SpecialChar \menuseparator
16337 To get right alignment,
16345 \begin_layout Plain Layout
16356 is inserted at the beginning of the line.
16359 \begin_layout Standard
16372 with the difference that the lines are always centered.
16375 \begin_layout Standard
16376 \begin_inset VSpace bigskip
16380 \begin_inset CommandInset ref
16382 reference "eq:substack"
16386 there can be too much space beside an operator, because the characters
16387 following the operator are set beside the limits.
16390 \begin_layout Standard
16391 To avoid this, the following macro can be used in the LaTeX-preamble:
16394 \begin_layout Standard
16408 \begin_inset Newline newline
16420 \begin_inset Newline newline
16427 mathclapinternal #1#2{
16431 mathsurround =0pt #1{#2}$}}
16434 \begin_layout Standard
16435 This defines the command
16442 \begin_inset Index idx
16445 \begin_layout Plain Layout
16453 that sets the width of the limit to 0
16454 \begin_inset space \thinspace{}
16458 The command scheme is
16461 \begin_layout Standard
16469 \begin_layout Standard
16470 where the limit can consist of several conditions.
16473 \begin_layout Standard
16475 \begin_inset CommandInset ref
16477 reference "eq:substack"
16481 , one uses the command
16484 \begin_layout Standard
16497 \begin_layout Plain Layout
16506 0<k<1000 Ctrl+Return
16509 \begin_layout Standard
16510 to create the lower limit.
16511 The summand is now directly behind the summation operator:
16512 \begin_inset Formula \[
16513 \sum_{\mathclap{\substack{0<k<1000\\
16524 \begin_layout Standard
16525 \begin_inset VSpace bigskip
16528 How to use one limit for several operators is described in
16529 \begin_inset CommandInset ref
16531 reference "sub:Self-defined-Operators"
16538 \begin_layout Subsection
16540 \begin_inset CommandInset label
16542 name "sub:Binary-Operators"
16547 \begin_inset Index idx
16550 \begin_layout Plain Layout
16559 \begin_layout Standard
16560 Binary operators are surrounded by space when there is a character before
16562 \begin_inset VSpace medskip
16568 \begin_layout Standard
16569 \begin_inset space \hfill{}
16573 \begin_inset Tabular
16574 <lyxtabular version="3" rows="13" columns="2">
16575 <features tabularvalignment="middle">
16576 <column alignment="center" valignment="top" width="0pt">
16577 <column alignment="center" valignment="top" width="0pt">
16579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16582 \begin_layout Plain Layout
16584 \begin_inset Note Note
16587 \begin_layout Plain Layout
16594 is only used as spacer.
16604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16607 \begin_layout Plain Layout
16615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16618 \begin_layout Plain Layout
16624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16627 \begin_layout Plain Layout
16628 \begin_inset Formula $+$
16638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16641 \begin_layout Plain Layout
16647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16650 \begin_layout Plain Layout
16651 \begin_inset Formula $-$
16661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16664 \begin_layout Plain Layout
16672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16675 \begin_layout Plain Layout
16676 \begin_inset Formula $\pm$
16686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16689 \begin_layout Plain Layout
16697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16700 \begin_layout Plain Layout
16701 \begin_inset Formula $\mp$
16711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16714 \begin_layout Plain Layout
16722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16725 \begin_layout Plain Layout
16726 \begin_inset Formula $\cdot$
16736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16739 \begin_layout Plain Layout
16747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16750 \begin_layout Plain Layout
16751 \begin_inset Formula $\times$
16761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16764 \begin_layout Plain Layout
16772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16775 \begin_layout Plain Layout
16776 \begin_inset Formula $\div$
16786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16789 \begin_layout Plain Layout
16793 \begin_layout Plain Layout
16806 \begin_layout Plain Layout
16818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16821 \begin_layout Plain Layout
16822 \begin_inset Formula $*$
16832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16835 \begin_layout Plain Layout
16843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16846 \begin_layout Plain Layout
16847 \begin_inset Formula $\star$
16857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16860 \begin_layout Plain Layout
16868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16871 \begin_layout Plain Layout
16872 \begin_inset Formula $\circ$
16882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16885 \begin_layout Plain Layout
16893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16896 \begin_layout Plain Layout
16897 \begin_inset Formula $\diamond$
16907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16910 \begin_layout Plain Layout
16918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16921 \begin_layout Plain Layout
16922 \begin_inset Formula $\bullet$
16936 \begin_inset space \hfill{}
16940 \begin_inset Tabular
16941 <lyxtabular version="3" rows="13" columns="2">
16942 <features tabularvalignment="middle">
16943 <column alignment="center" valignment="top" width="0pt">
16944 <column alignment="center" valignment="top" width="0pt">
16946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16949 \begin_layout Plain Layout
16955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16958 \begin_layout Plain Layout
16966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16969 \begin_layout Plain Layout
16977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16980 \begin_layout Plain Layout
16981 \begin_inset Formula $\nabla$
16991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16994 \begin_layout Plain Layout
17002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17005 \begin_layout Plain Layout
17006 \begin_inset Formula $\bigtriangledown$
17016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17019 \begin_layout Plain Layout
17027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17030 \begin_layout Plain Layout
17031 \begin_inset Formula $\bigtriangleup$
17041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17044 \begin_layout Plain Layout
17052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17055 \begin_layout Plain Layout
17056 \begin_inset Formula $\Box$
17066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17069 \begin_layout Plain Layout
17077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17080 \begin_layout Plain Layout
17081 \begin_inset Formula $\cap$
17091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17094 \begin_layout Plain Layout
17102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17105 \begin_layout Plain Layout
17106 \begin_inset Formula $\cup$
17116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17119 \begin_layout Plain Layout
17127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17130 \begin_layout Plain Layout
17131 \begin_inset Formula $\dagger$
17141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17144 \begin_layout Plain Layout
17152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17155 \begin_layout Plain Layout
17156 \begin_inset Formula $\ddagger$
17166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17169 \begin_layout Plain Layout
17177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17180 \begin_layout Plain Layout
17181 \begin_inset Formula $\wr$
17191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17194 \begin_layout Plain Layout
17202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17205 \begin_layout Plain Layout
17206 \begin_inset Formula $\bigcirc$
17216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17219 \begin_layout Plain Layout
17227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17230 \begin_layout Plain Layout
17231 \begin_inset Formula $\wedge$
17241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17244 \begin_layout Plain Layout
17252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17255 \begin_layout Plain Layout
17256 \begin_inset Formula $\vee$
17270 \begin_inset space \hfill{}
17274 \begin_inset Tabular
17275 <lyxtabular version="3" rows="13" columns="2">
17276 <features tabularvalignment="middle">
17277 <column alignment="center" valignment="top" width="0pt">
17278 <column alignment="center" valignment="top" width="0pt">
17280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17283 \begin_layout Plain Layout
17289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17292 \begin_layout Plain Layout
17300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17303 \begin_layout Plain Layout
17311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17314 \begin_layout Plain Layout
17315 \begin_inset Formula $\oplus$
17325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17328 \begin_layout Plain Layout
17336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17339 \begin_layout Plain Layout
17340 \begin_inset Formula $\ominus$
17350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17353 \begin_layout Plain Layout
17361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17364 \begin_layout Plain Layout
17365 \begin_inset Formula $\otimes$
17375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17378 \begin_layout Plain Layout
17386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17389 \begin_layout Plain Layout
17390 \begin_inset Formula $\oslash$
17400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17403 \begin_layout Plain Layout
17411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17414 \begin_layout Plain Layout
17415 \begin_inset Formula $\odot$
17425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17428 \begin_layout Plain Layout
17436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17439 \begin_layout Plain Layout
17440 \begin_inset Formula $\amalg$
17450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17453 \begin_layout Plain Layout
17461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17464 \begin_layout Plain Layout
17465 \begin_inset Formula $\uplus$
17475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17478 \begin_layout Plain Layout
17486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17489 \begin_layout Plain Layout
17490 \begin_inset Formula $\setminus$
17500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17503 \begin_layout Plain Layout
17511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17514 \begin_layout Plain Layout
17515 \begin_inset Formula $\sqcap$
17525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17528 \begin_layout Plain Layout
17536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17539 \begin_layout Plain Layout
17540 \begin_inset Formula $\sqcup$
17550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17553 \begin_layout Plain Layout
17561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17564 \begin_layout Plain Layout
17565 \begin_inset Formula $\triangleleft$
17575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17578 \begin_layout Plain Layout
17586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17589 \begin_layout Plain Layout
17590 \begin_inset Formula $\triangleright$
17604 \begin_inset space \hfill{}
17610 \begin_layout Standard
17611 All binary operators can also be inserted via the math toolbar button
17612 \begin_inset Graphics
17613 filename ../images/math/pm.png
17621 \begin_layout Standard
17622 To typeset the Laplace operator also
17639 \begin_inset Formula $\nabla^{2}$
17642 ) can be used instead of
17651 \begin_layout Standard
17658 Insert\SpecialChar \menuseparator
17670 \begin_layout Subsection
17671 Self-defined Operators
17672 \begin_inset CommandInset label
17674 name "sub:Self-defined-Operators"
17679 \begin_inset Index idx
17682 \begin_layout Plain Layout
17683 Operators ! self-defined
17691 \begin_layout Standard
17692 With the help of the command
17696 DeclareMathOperator
17699 \begin_inset Index idx
17702 \begin_layout Plain Layout
17707 DeclareMathOperator
17712 custom operators can be defined in the LaTeX-preamble.
17713 Its command scheme is:
17716 \begin_layout Standard
17721 DeclareMathOperator{new command}{display}
17724 \begin_layout Standard
17725 Display can be characters or symbols that define how the operator looks
17727 To define a big operator a * is set behind the command.
17728 All self-defined big operators can have limits as described in
17729 \begin_inset CommandInset ref
17731 reference "sub:Operator-Limits"
17738 \begin_layout Standard
17739 For example the LaTeX-preamble line
17742 \begin_layout Standard
17747 DeclareMathOperator*{
17754 \begin_layout Standard
17755 defines the command
17761 , that inserts a big operator consisting of the lozenge symbol from
17762 \begin_inset CommandInset ref
17764 reference "sub:Miscellaneous-Symbols"
17769 \begin_inset Formula \[
17770 \Lozenge_{n=1}^{\infty}\]
17774 The command for this formula is:
17785 \begin_inset Formula $\to$
17791 \begin_layout Standard
17792 \begin_inset VSpace bigskip
17795 When self-defined operators are not used several times in the document,
17796 they can also be defined with the commands
17803 \begin_inset Index idx
17806 \begin_layout Plain Layout
17821 \begin_inset Index idx
17824 \begin_layout Plain Layout
17832 , which have the following scheme:
17835 \begin_layout Standard
17849 \begin_layout Standard
17856 defines big operators,
17865 \begin_layout Standard
17873 \begin_inset space \thinspace{}
17877 \begin_inset space \space{}
17880 be used to use one limit for several operators:
17883 \begin_layout Standard
17884 \begin_inset Formula \[
17885 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17892 \begin_layout Standard
17893 The command for the formula above is:
17894 \begin_inset Newline newline
17913 \begin_layout Plain Layout
17925 \begin_inset Formula $\to$
17934 \begin_layout Plain Layout
17948 \begin_layout Section
17950 \begin_inset Index idx
17953 \begin_layout Plain Layout
17962 \begin_layout Subsection
17964 \begin_inset CommandInset label
17966 name "sub:Font-Styles"
17971 \begin_inset Index idx
17974 \begin_layout Plain Layout
17983 \begin_layout Standard
17984 Latin letters in formulas can be set in one of the following font styles:
17985 \begin_inset VSpace -2mm
17991 \begin_layout Standard
17993 \begin_inset Tabular
17994 <lyxtabular version="3" rows="7" columns="3">
17995 <features tabularvalignment="middle">
17996 <column alignment="center" valignment="top" width="0">
17997 <column alignment="center" valignment="top" width="0">
17998 <column alignment="center" valignment="top" width="0">
18000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18003 \begin_layout Plain Layout
18009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18012 \begin_layout Plain Layout
18018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18021 \begin_layout Plain Layout
18029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18032 \begin_layout Plain Layout
18041 \begin_layout Plain Layout
18057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18060 \begin_layout Plain Layout
18061 \begin_inset Formula $\mathbb{ABC}$
18069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18072 \begin_layout Plain Layout
18085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18088 \begin_layout Plain Layout
18097 \begin_layout Plain Layout
18113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18116 \begin_layout Plain Layout
18117 \begin_inset Formula $\mathbf{AbC}$
18125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18128 \begin_layout Plain Layout
18141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18144 \begin_layout Plain Layout
18153 \begin_layout Plain Layout
18169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18172 \begin_layout Plain Layout
18173 \begin_inset Formula $\boldsymbol{AbC}$
18181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18184 \begin_layout Plain Layout
18187 arg "font-boldsymbol"
18197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18200 \begin_layout Plain Layout
18209 \begin_layout Plain Layout
18225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18228 \begin_layout Plain Layout
18229 \begin_inset Formula $\mathcal{ABC}$
18237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18240 \begin_layout Plain Layout
18253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18256 \begin_layout Plain Layout
18265 \begin_layout Plain Layout
18281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18284 \begin_layout Plain Layout
18285 \begin_inset Formula $\mathfrak{AbC}$
18293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18296 \begin_layout Plain Layout
18304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18307 \begin_layout Plain Layout
18316 \begin_layout Plain Layout
18332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18335 \begin_layout Plain Layout
18336 \begin_inset Formula $\mathscr{AbC}$
18344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18347 \begin_layout Plain Layout
18361 \begin_layout Standard
18363 \begin_inset Tabular
18364 <lyxtabular version="3" rows="5" columns="3">
18365 <features tabularvalignment="middle">
18366 <column alignment="center" valignment="top" width="0">
18367 <column alignment="center" valignment="top" width="0">
18368 <column alignment="center" valignment="top" width="0">
18370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18373 \begin_layout Plain Layout
18379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18382 \begin_layout Plain Layout
18388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18391 \begin_layout Plain Layout
18399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18402 \begin_layout Plain Layout
18411 \begin_layout Plain Layout
18427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18430 \begin_layout Plain Layout
18431 \begin_inset Formula $\mathit{AbC}$
18439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18442 \begin_layout Plain Layout
18450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18453 \begin_layout Plain Layout
18462 \begin_layout Plain Layout
18478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18481 \begin_layout Plain Layout
18482 \begin_inset Formula $\mathrm{AbC}$
18490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18493 \begin_layout Plain Layout
18506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18509 \begin_layout Plain Layout
18518 \begin_layout Plain Layout
18534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18537 \begin_layout Plain Layout
18538 \begin_inset Formula $\mathsf{AbC}$
18546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18549 \begin_layout Plain Layout
18562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18565 \begin_layout Plain Layout
18574 \begin_layout Plain Layout
18590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18593 \begin_layout Plain Layout
18594 \begin_inset Formula $\mathtt{AbC}$
18602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18605 \begin_layout Plain Layout
18608 arg "font-typewriter"
18624 \begin_layout Standard
18625 \begin_inset Note Greyedout
18628 \begin_layout Plain Layout
18645 can only be used for big letters.
18653 \begin_layout Standard
18654 Predefined is the style
18663 \begin_layout Standard
18664 The style commands work also for letters in mathematical constructs:
18665 \begin_inset Formula \[
18666 \mathfrak{A=\frac{b}{C}}\]
18673 \begin_layout Standard
18674 Characters in mathematical text don't appear in a math font style but in
18675 the text font style
18682 That their style can't be set correctly via the text style dialog is a
18687 \begin_layout Plain Layout
18688 \begin_inset CommandInset href
18690 name "LyX-bug #4629"
18691 target "http://www.lyx.org/trac/ticket/4629"
18703 \begin_layout Standard
18704 Instead of the style commands the dialog
18706 Edit\SpecialChar \menuseparator
18707 Math\SpecialChar \menuseparator
18710 or the toolbar button
18711 \begin_inset Graphics
18712 filename ../images/math/font.png
18720 \begin_layout Subsection
18722 \begin_inset CommandInset label
18724 name "sub:Bold-Formulas"
18729 \begin_inset Index idx
18732 \begin_layout Plain Layout
18741 \begin_layout Standard
18742 To make a complete formula bold, the command
18748 from the previous subsection cannot be used, because it doesn't work for
18749 small Greek letters.
18750 Furthermore it prints Latin letters always upright, like in the following
18754 \begin_layout Standard
18755 \begin_inset Formula \[
18756 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18763 \begin_layout Standard
18764 To display the formula correctly, the command
18771 \begin_inset Formula \[
18772 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18776 It is also possible to set the formula in a
18778 boldmath environment
18781 This environment is created by inserting the command
18788 \begin_inset Index idx
18791 \begin_layout Plain Layout
18800 To end the environment, the command
18807 \begin_inset Index idx
18810 \begin_layout Plain Layout
18818 is inserted in TeX-mode.
18822 \begin_layout Plain Layout
18832 \begin_inset Formula \[
18833 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18841 \begin_layout Plain Layout
18853 \begin_layout Subsection
18855 \begin_inset Index idx
18858 \begin_layout Plain Layout
18867 \begin_layout Standard
18868 Formulas can be colored like normal text: Highlight a formula or a formula
18874 Here is a formula in magenta:
18875 \begin_inset Formula \[
18876 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18883 \begin_layout Standard
18884 You can also define your own colors as described in
18885 \begin_inset CommandInset ref
18887 reference "sub:Colored-Boxes"
18892 They can be used with the TeX code command
18899 \begin_inset Index idx
18902 \begin_layout Plain Layout
18913 \begin_layout Standard
18918 textcolor{color}{characters or formula}
18921 \begin_layout Standard
18922 The following example was colored completely dark green and partly red:
18925 \begin_layout Standard
18929 \begin_layout Plain Layout
18933 textcolor{darkgreen}{
18939 \begin_inset Formula \[
18940 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18948 \begin_layout Plain Layout
18958 \begin_layout Standard
18959 Due to a bug in LyX only complete formulas can be colored with self-defined
18964 \begin_layout Plain Layout
18965 \begin_inset CommandInset href
18967 name "LyX-bug #5269"
18968 target "http://www.lyx.org/trac/ticket/5269"
18980 \begin_layout Subsection
18982 \begin_inset CommandInset label
18984 name "sub:Font-Sizes"
18989 \begin_inset Index idx
18992 \begin_layout Plain Layout
19001 \begin_layout Standard
19002 For characters in formulas there are, analog to characters in text, the
19003 following size commands:
19006 \begin_layout Standard
19050 \begin_inset Newline newline
19072 \begin_layout Standard
19073 The size produced by the commands depends on the document font size, that
19074 corresponds with the command
19081 The other commands produce smaller or larger sizes than
19088 The font size can however not exceed a certain value.
19089 Is for example the document font size 12
19090 \begin_inset space \thinspace{}
19099 switches to the same size as
19109 \begin_layout Standard
19110 A size command is inserted in TeX-mode before the formula and sets the size
19111 for all following formula and text characters.
19112 To switch back to the initial size, the command
19118 is inserted behind the formula in TeX-mode.
19121 \begin_layout Standard
19122 \begin_inset Newpage newpage
19128 \begin_layout Standard
19129 Within a formula the size can be changed using the following size commands:
19132 \begin_layout Standard
19135 \begin_inset Tabular
19136 <lyxtabular version="3" rows="5" columns="2">
19137 <features tabularvalignment="middle">
19138 <column alignment="center" valignment="top" width="0">
19139 <column alignment="center" valignment="top" width="0">
19141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19144 \begin_layout Plain Layout
19150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19153 \begin_layout Plain Layout
19155 \begin_inset Note Note
19158 \begin_layout Plain Layout
19165 is only used as spacer.
19177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19180 \begin_layout Plain Layout
19184 \begin_inset Index idx
19187 \begin_layout Plain Layout
19200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19203 \begin_layout Plain Layout
19204 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19217 \begin_layout Plain Layout
19225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19228 \begin_layout Plain Layout
19229 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19242 \begin_layout Plain Layout
19250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19253 \begin_layout Plain Layout
19254 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19267 \begin_layout Plain Layout
19275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19278 \begin_layout Plain Layout
19279 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19295 \begin_layout Standard
19296 After entering these commands, a blue box appears in which the formula parts
19300 \begin_layout Standard
19301 There is a further method to change the font size, that though only works
19302 for symbols or letters in mathematical text.
19303 To use it, one of the above text size commands is inserted in mathematical
19305 All following characters until the end of the mathematical text or until
19306 another size command will have the selected size.
19308 \begin_inset VSpace -2mm
19314 \begin_layout Standard
19318 \begin_layout Plain Layout
19328 \begin_inset Formula \[
19329 A=\frac{B}{c}\cdot\maltese\]
19334 \begin_inset Formula \[
19335 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
19343 \begin_layout Plain Layout
19355 \begin_layout Standard
19356 \begin_inset VSpace medskip
19359 Before both formulas the command
19366 The command for the second formula is:
19367 \begin_inset Newline newline
19378 \begin_layout Plain Layout
19393 \begin_layout Plain Layout
19408 \begin_layout Plain Layout
19423 \begin_layout Plain Layout
19433 \begin_inset Formula $\to$
19437 \begin_inset Formula $\to$
19441 \begin_inset Newline newline
19445 \begin_inset space \hspace*{}
19459 \begin_layout Plain Layout
19474 \begin_layout Plain Layout
19489 \begin_layout Plain Layout
19501 \begin_layout Standard
19502 If a symbol cannot be displayed in different sizes, it will always be displayed
19503 in the default size.
19506 \begin_layout Standard
19507 \begin_inset Newpage newpage
19513 \begin_layout Section
19515 \begin_inset Index idx
19518 \begin_layout Plain Layout
19527 \begin_layout Standard
19528 All Greek letters can also be inserted via the toolbar button
19529 \begin_inset Graphics
19530 filename ../images/math/alpha.png
19538 \begin_layout Subsection
19540 \begin_inset Index idx
19543 \begin_layout Plain Layout
19544 Greek letters ! small
19552 \begin_layout Standard
19553 \begin_inset space \hfill{}
19557 \begin_inset Tabular
19558 <lyxtabular version="3" rows="11" columns="2">
19559 <features tabularvalignment="middle">
19560 <column alignment="center" valignment="top" width="0pt">
19561 <column alignment="center" valignment="top" width="0pt">
19563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19566 \begin_layout Plain Layout
19572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19575 \begin_layout Plain Layout
19583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19586 \begin_layout Plain Layout
19594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19597 \begin_layout Plain Layout
19598 \begin_inset Formula $\alpha$
19608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19611 \begin_layout Plain Layout
19619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19622 \begin_layout Plain Layout
19623 \begin_inset Formula $\beta$
19633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19636 \begin_layout Plain Layout
19644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19647 \begin_layout Plain Layout
19648 \begin_inset Formula $\gamma$
19658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19661 \begin_layout Plain Layout
19669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19672 \begin_layout Plain Layout
19673 \begin_inset Formula $\delta$
19683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19686 \begin_layout Plain Layout
19694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19697 \begin_layout Plain Layout
19698 \begin_inset Formula $\epsilon$
19708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19711 \begin_layout Plain Layout
19719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19722 \begin_layout Plain Layout
19723 \begin_inset Formula $\varepsilon$
19733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19736 \begin_layout Plain Layout
19744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19747 \begin_layout Plain Layout
19748 \begin_inset Formula $\zeta$
19758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19761 \begin_layout Plain Layout
19769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19772 \begin_layout Plain Layout
19773 \begin_inset Formula $\eta$
19783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19786 \begin_layout Plain Layout
19794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19797 \begin_layout Plain Layout
19798 \begin_inset Formula $\theta$
19808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19811 \begin_layout Plain Layout
19819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19822 \begin_layout Plain Layout
19823 \begin_inset Formula $\vartheta$
19837 \begin_inset space \hfill{}
19841 \begin_inset Tabular
19842 <lyxtabular version="3" rows="12" columns="2">
19843 <features tabularvalignment="middle">
19844 <column alignment="center" valignment="top" width="0pt">
19845 <column alignment="center" valignment="top" width="0pt">
19847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19850 \begin_layout Plain Layout
19856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19859 \begin_layout Plain Layout
19867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19870 \begin_layout Plain Layout
19878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19881 \begin_layout Plain Layout
19882 \begin_inset Formula $\iota$
19892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19895 \begin_layout Plain Layout
19903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19906 \begin_layout Plain Layout
19907 \begin_inset Formula $\kappa$
19917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19920 \begin_layout Plain Layout
19928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19931 \begin_layout Plain Layout
19932 \begin_inset Formula $\varkappa$
19942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19945 \begin_layout Plain Layout
19953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19956 \begin_layout Plain Layout
19957 \begin_inset Formula $\lambda$
19967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19970 \begin_layout Plain Layout
19978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19981 \begin_layout Plain Layout
19982 \begin_inset Formula $\mu$
19992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19995 \begin_layout Plain Layout
20003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20006 \begin_layout Plain Layout
20007 \begin_inset Formula $\nu$
20017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20020 \begin_layout Plain Layout
20028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20031 \begin_layout Plain Layout
20032 \begin_inset Formula $\xi$
20042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20045 \begin_layout Plain Layout
20051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20054 \begin_layout Plain Layout
20055 \begin_inset Formula $o$
20065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20068 \begin_layout Plain Layout
20076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20079 \begin_layout Plain Layout
20080 \begin_inset Formula $\pi$
20090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20093 \begin_layout Plain Layout
20101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20104 \begin_layout Plain Layout
20105 \begin_inset Formula $\varpi$
20115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20118 \begin_layout Plain Layout
20126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20129 \begin_layout Plain Layout
20130 \begin_inset Formula $\rho$
20144 \begin_inset space \hfill{}
20148 \begin_inset Tabular
20149 <lyxtabular version="3" rows="11" columns="2">
20150 <features tabularvalignment="middle">
20151 <column alignment="center" valignment="top" width="0pt">
20152 <column alignment="center" valignment="top" width="0pt">
20154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20157 \begin_layout Plain Layout
20163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20166 \begin_layout Plain Layout
20174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20177 \begin_layout Plain Layout
20185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20188 \begin_layout Plain Layout
20189 \begin_inset Formula $\varrho$
20199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20202 \begin_layout Plain Layout
20210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20213 \begin_layout Plain Layout
20214 \begin_inset Formula $\sigma$
20224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20227 \begin_layout Plain Layout
20235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20238 \begin_layout Plain Layout
20239 \begin_inset Formula $\varsigma$
20249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20252 \begin_layout Plain Layout
20260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20263 \begin_layout Plain Layout
20264 \begin_inset Formula $\tau$
20274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20277 \begin_layout Plain Layout
20285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20288 \begin_layout Plain Layout
20289 \begin_inset Formula $\upsilon$
20299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20302 \begin_layout Plain Layout
20310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20313 \begin_layout Plain Layout
20314 \begin_inset Formula $\phi$
20324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20327 \begin_layout Plain Layout
20335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20338 \begin_layout Plain Layout
20339 \begin_inset Formula $\varphi$
20349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20352 \begin_layout Plain Layout
20360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20363 \begin_layout Plain Layout
20364 \begin_inset Formula $\chi$
20374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20377 \begin_layout Plain Layout
20385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20388 \begin_layout Plain Layout
20389 \begin_inset Formula $\psi$
20399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20402 \begin_layout Plain Layout
20410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20413 \begin_layout Plain Layout
20414 \begin_inset Formula $\omega$
20428 \begin_inset space \hfill{}
20434 \begin_layout Standard
20435 \begin_inset VSpace medskip
20441 \begin_layout Standard
20442 How to create upright Greek letters is explained in
20443 \begin_inset CommandInset ref
20445 reference "sub:Upright-small-Greek"
20452 \begin_layout Subsection
20454 \begin_inset Index idx
20457 \begin_layout Plain Layout
20458 Greek letters ! big
20466 \begin_layout Standard
20467 \begin_inset space \hfill{}
20471 \begin_inset Tabular
20472 <lyxtabular version="3" rows="7" columns="2">
20473 <features tabularvalignment="middle">
20474 <column alignment="center" valignment="top" width="0pt">
20475 <column alignment="center" valignment="top" width="0pt">
20477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20480 \begin_layout Plain Layout
20486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20489 \begin_layout Plain Layout
20497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20500 \begin_layout Plain Layout
20508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20511 \begin_layout Plain Layout
20512 \begin_inset Formula $\Gamma$
20522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20525 \begin_layout Plain Layout
20533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20536 \begin_layout Plain Layout
20537 \begin_inset Formula $\Delta$
20547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20550 \begin_layout Plain Layout
20558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20561 \begin_layout Plain Layout
20562 \begin_inset Formula $\Theta$
20572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20575 \begin_layout Plain Layout
20583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20586 \begin_layout Plain Layout
20587 \begin_inset Formula $\Lambda$
20597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20600 \begin_layout Plain Layout
20608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20611 \begin_layout Plain Layout
20612 \begin_inset Formula $\Xi$
20622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20625 \begin_layout Plain Layout
20633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20636 \begin_layout Plain Layout
20637 \begin_inset Formula $\Pi$
20651 \begin_inset space \hfill{}
20655 \begin_inset Tabular
20656 <lyxtabular version="3" rows="6" columns="2">
20657 <features tabularvalignment="middle">
20658 <column alignment="center" valignment="top" width="0pt">
20659 <column alignment="center" valignment="top" width="0pt">
20661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20664 \begin_layout Plain Layout
20670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20673 \begin_layout Plain Layout
20681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20684 \begin_layout Plain Layout
20692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20695 \begin_layout Plain Layout
20696 \begin_inset Formula $\Sigma$
20706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20709 \begin_layout Plain Layout
20717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20720 \begin_layout Plain Layout
20721 \begin_inset Formula $\Upsilon$
20731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20734 \begin_layout Plain Layout
20742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20745 \begin_layout Plain Layout
20746 \begin_inset Formula $\Phi$
20756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20759 \begin_layout Plain Layout
20767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20770 \begin_layout Plain Layout
20771 \begin_inset Formula $\Psi$
20781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20784 \begin_layout Plain Layout
20792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20795 \begin_layout Plain Layout
20796 \begin_inset Formula $\Omega$
20810 \begin_inset space \hfill{}
20816 \begin_layout Standard
20817 \begin_inset VSpace medskip
20820 That the big Greek letters appear upright is caused by a design bug when
20822 To get correct italic big letters, begin every command with
20827 For example the command
20834 \begin_inset Formula $\varGamma$
20840 \begin_layout Subsection
20842 \begin_inset Index idx
20845 \begin_layout Plain Layout
20846 Greek letters ! bold
20854 \begin_layout Standard
20855 Greek letters cannot be set with different font styles like Latin letters.
20856 They can only be made bold with the command
20863 \begin_inset Index idx
20866 \begin_layout Plain Layout
20877 \begin_layout Standard
20879 \begin_inset Tabular
20880 <lyxtabular version="3" rows="3" columns="2">
20881 <features tabularvalignment="middle">
20882 <column alignment="center" valignment="top" width="0">
20883 <column alignment="center" valignment="top" width="0">
20885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20888 \begin_layout Plain Layout
20894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20897 \begin_layout Plain Layout
20905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20908 \begin_layout Plain Layout
20920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20923 \begin_layout Plain Layout
20924 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20937 \begin_layout Plain Layout
20949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20952 \begin_layout Plain Layout
20953 \begin_inset Formula $\theta\boldsymbol{\theta}$
20969 \begin_layout Section
20974 \begin_layout Plain Layout
20987 \begin_layout Plain Layout
20988 A list with all symbols of most of the LaTeX-packages can be found in
20989 \begin_inset CommandInset citation
21004 \begin_layout Plain Layout
21012 \begin_inset Note Note
21015 \begin_layout Plain Layout
21018 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21021 \begin_layout Plain Layout
21024 texorpdfstring is in section
21025 \begin_inset CommandInset ref
21027 reference "sub:Formulas-in-Section"
21037 \begin_inset Index idx
21040 \begin_layout Plain Layout
21049 \begin_layout Standard
21050 Many of the symbols listed in this section can also be inserted via the
21052 \begin_inset Graphics
21053 filename ../images/math/nabla.png
21059 \begin_inset Graphics
21060 filename ../images/math/digamma.png
21068 \begin_layout Subsection
21069 Mathematical Symbols
21070 \begin_inset CommandInset label
21072 name "sub:Mathematical-Symbols"
21077 \begin_inset Index idx
21080 \begin_layout Plain Layout
21081 Symbols ! mathematical
21089 \begin_layout Standard
21090 \begin_inset space \hfill{}
21094 \begin_inset Tabular
21095 <lyxtabular version="3" rows="10" columns="2">
21096 <features tabularvalignment="middle">
21097 <column alignment="center" valignment="top" width="0pt">
21098 <column alignment="center" valignment="top" width="0pt">
21100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21103 \begin_layout Plain Layout
21109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21112 \begin_layout Plain Layout
21120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21123 \begin_layout Plain Layout
21131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21134 \begin_layout Plain Layout
21135 \begin_inset Formula $\neg$
21145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21148 \begin_layout Plain Layout
21156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21159 \begin_layout Plain Layout
21160 \begin_inset Formula $\Im$
21170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21173 \begin_layout Plain Layout
21181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21184 \begin_layout Plain Layout
21185 \begin_inset Formula $\Re$
21195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21198 \begin_layout Plain Layout
21206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21209 \begin_layout Plain Layout
21210 \begin_inset Formula $\aleph$
21220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21223 \begin_layout Plain Layout
21231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21234 \begin_layout Plain Layout
21235 \begin_inset Formula $\partial$
21245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21248 \begin_layout Plain Layout
21256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21259 \begin_layout Plain Layout
21260 \begin_inset Formula $\infty$
21270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21273 \begin_layout Plain Layout
21281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21284 \begin_layout Plain Layout
21285 \begin_inset Formula $\wp$
21295 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21298 \begin_layout Plain Layout
21306 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21309 \begin_layout Plain Layout
21310 \begin_inset Formula $\imath$
21320 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21323 \begin_layout Plain Layout
21331 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21334 \begin_layout Plain Layout
21335 \begin_inset Formula $\jmath$
21349 \begin_inset space \hfill{}
21353 \begin_inset Tabular
21354 <lyxtabular version="3" rows="10" columns="2">
21355 <features tabularvalignment="middle">
21356 <column alignment="center" valignment="top" width="0pt">
21357 <column alignment="center" valignment="top" width="0pt">
21359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21362 \begin_layout Plain Layout
21368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21371 \begin_layout Plain Layout
21373 \begin_inset Note Note
21376 \begin_layout Plain Layout
21383 is only used as spacer.
21395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21398 \begin_layout Plain Layout
21406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21409 \begin_layout Plain Layout
21410 \begin_inset Formula $\forall$
21420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21423 \begin_layout Plain Layout
21431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21434 \begin_layout Plain Layout
21435 \begin_inset Formula $\exists$
21445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21448 \begin_layout Plain Layout
21456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21459 \begin_layout Plain Layout
21460 \begin_inset Formula $\nexists$
21470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21473 \begin_layout Plain Layout
21481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21484 \begin_layout Plain Layout
21485 \begin_inset Formula $\emptyset$
21495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21498 \begin_layout Plain Layout
21506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21509 \begin_layout Plain Layout
21510 \begin_inset Formula $\varnothing$
21520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21523 \begin_layout Plain Layout
21531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21534 \begin_layout Plain Layout
21535 \begin_inset Formula $\dag$
21545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21548 \begin_layout Plain Layout
21556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21559 \begin_layout Plain Layout
21560 \begin_inset Formula $\ddag$
21570 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21573 \begin_layout Plain Layout
21581 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21584 \begin_layout Plain Layout
21588 \begin_layout Plain Layout
21598 \begin_inset Formula $\complement$
21605 \begin_layout Plain Layout
21619 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21622 \begin_layout Plain Layout
21630 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21633 \begin_layout Plain Layout
21634 \begin_inset Formula $\Bbbk$
21648 \begin_inset space \hfill{}
21652 \begin_inset Tabular
21653 <lyxtabular version="3" rows="10" columns="2">
21654 <features tabularvalignment="middle">
21655 <column alignment="center" valignment="top" width="0pt">
21656 <column alignment="center" valignment="top" width="0pt">
21658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21661 \begin_layout Plain Layout
21667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21670 \begin_layout Plain Layout
21678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21681 \begin_layout Plain Layout
21689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21692 \begin_layout Plain Layout
21693 \begin_inset Formula $\prime$
21703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21706 \begin_layout Plain Layout
21714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21717 \begin_layout Plain Layout
21718 \begin_inset Formula $\backprime$
21728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21731 \begin_layout Plain Layout
21739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21742 \begin_layout Plain Layout
21743 \begin_inset Formula $\mho$
21753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21756 \begin_layout Plain Layout
21764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21767 \begin_layout Plain Layout
21768 \begin_inset Formula $\triangle$
21778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21781 \begin_layout Plain Layout
21789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21792 \begin_layout Plain Layout
21793 \begin_inset Formula $\angle$
21803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21806 \begin_layout Plain Layout
21814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21817 \begin_layout Plain Layout
21818 \begin_inset Formula $\measuredangle$
21828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21831 \begin_layout Plain Layout
21839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21842 \begin_layout Plain Layout
21843 \begin_inset Formula $\sphericalangle$
21853 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21856 \begin_layout Plain Layout
21864 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21867 \begin_layout Plain Layout
21868 \begin_inset Formula $\top$
21878 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21881 \begin_layout Plain Layout
21889 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21892 \begin_layout Plain Layout
21893 \begin_inset Formula $\bot$
21907 \begin_inset space \hfill{}
21913 \begin_layout Subsection
21914 Miscellaneous Symbols
21915 \begin_inset CommandInset label
21917 name "sub:Miscellaneous-Symbols"
21922 \begin_inset Index idx
21925 \begin_layout Plain Layout
21926 Symbols ! miscellaneous
21934 \begin_layout Standard
21937 \begin_inset Tabular
21938 <lyxtabular version="3" rows="10" columns="2">
21939 <features tabularvalignment="middle">
21940 <column alignment="center" valignment="top" width="0pt">
21941 <column alignment="center" valignment="top" width="0pt">
21943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21946 \begin_layout Plain Layout
21952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21955 \begin_layout Plain Layout
21963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21966 \begin_layout Plain Layout
21974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21977 \begin_layout Plain Layout
21978 \begin_inset Formula $\flat$
21988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21991 \begin_layout Plain Layout
21999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22002 \begin_layout Plain Layout
22003 \begin_inset Formula $\natural$
22013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22016 \begin_layout Plain Layout
22024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22027 \begin_layout Plain Layout
22028 \begin_inset Formula $\sharp$
22038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22041 \begin_layout Plain Layout
22049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22052 \begin_layout Plain Layout
22053 \begin_inset Formula $\surd$
22063 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22066 \begin_layout Plain Layout
22074 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22077 \begin_layout Plain Layout
22078 \begin_inset Formula $\checkmark$
22088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22091 \begin_layout Plain Layout
22099 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22102 \begin_layout Plain Layout
22103 \begin_inset Formula $\yen$
22113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22116 \begin_layout Plain Layout
22124 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22127 \begin_layout Plain Layout
22128 \begin_inset Formula $\pounds$
22138 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22141 \begin_layout Plain Layout
22147 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22150 \begin_layout Plain Layout
22151 \begin_inset Formula $\$$
22161 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22164 \begin_layout Plain Layout
22170 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22173 \begin_layout Plain Layout
22174 \begin_inset Formula $§$
22188 \begin_inset Tabular
22189 <lyxtabular version="3" rows="10" columns="2">
22190 <features tabularvalignment="middle">
22191 <column alignment="center" valignment="top" width="0">
22192 <column alignment="center" valignment="top" width="0">
22194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22197 \begin_layout Plain Layout
22203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22206 \begin_layout Plain Layout
22214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22217 \begin_layout Plain Layout
22225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22228 \begin_layout Plain Layout
22229 \begin_inset Formula $\hbar$
22239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22242 \begin_layout Plain Layout
22250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22253 \begin_layout Plain Layout
22254 \begin_inset Formula $\hslash$
22264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22267 \begin_layout Plain Layout
22275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22278 \begin_layout Plain Layout
22279 \begin_inset Formula $\clubsuit$
22289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22292 \begin_layout Plain Layout
22300 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22303 \begin_layout Plain Layout
22304 \begin_inset Formula $\spadesuit$
22314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22317 \begin_layout Plain Layout
22325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22328 \begin_layout Plain Layout
22329 \begin_inset Formula $\bigstar$
22339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22342 \begin_layout Plain Layout
22350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22353 \begin_layout Plain Layout
22354 \begin_inset Formula $\blacklozenge$
22364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22367 \begin_layout Plain Layout
22375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22378 \begin_layout Plain Layout
22379 \begin_inset Formula $\blacktriangle$
22389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22392 \begin_layout Plain Layout
22400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22403 \begin_layout Plain Layout
22404 \begin_inset Formula $\blacktriangledown$
22414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22417 \begin_layout Plain Layout
22425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22428 \begin_layout Plain Layout
22429 \begin_inset Formula $\bullet$
22443 \begin_inset Tabular
22444 <lyxtabular version="3" rows="10" columns="2">
22445 <features tabularvalignment="middle">
22446 <column alignment="center" valignment="top" width="0pt">
22447 <column alignment="center" valignment="top" width="0pt">
22449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22452 \begin_layout Plain Layout
22458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22461 \begin_layout Plain Layout
22469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22472 \begin_layout Plain Layout
22480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22483 \begin_layout Plain Layout
22484 \begin_inset Formula $\diamondsuit$
22494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22497 \begin_layout Plain Layout
22505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22508 \begin_layout Plain Layout
22509 \begin_inset Formula $\Diamond$
22519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22522 \begin_layout Plain Layout
22530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22533 \begin_layout Plain Layout
22534 \begin_inset Formula $\heartsuit$
22544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22547 \begin_layout Plain Layout
22555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22558 \begin_layout Plain Layout
22559 \begin_inset Formula $\P$
22569 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22572 \begin_layout Plain Layout
22580 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22583 \begin_layout Plain Layout
22584 \begin_inset Formula $\copyright$
22594 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22597 \begin_layout Plain Layout
22605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22608 \begin_layout Plain Layout
22609 \begin_inset Formula $\circledR$
22619 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22622 \begin_layout Plain Layout
22630 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22633 \begin_layout Plain Layout
22634 \begin_inset Formula $\maltese$
22644 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22647 \begin_layout Plain Layout
22655 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22658 \begin_layout Plain Layout
22659 \begin_inset Formula $\diagup$
22669 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22672 \begin_layout Plain Layout
22680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22683 \begin_layout Plain Layout
22684 \begin_inset Formula $\diagdown$
22700 \begin_layout Standard
22701 \begin_inset VSpace medskip
22704 More symbols are listed in
22705 \begin_inset CommandInset ref
22707 reference "sub:Miscellaneous-special-Characters"
22714 \begin_layout Standard
22715 Some symbols can be displayed in different sizes, see
22716 \begin_inset CommandInset ref
22718 reference "sub:Font-Sizes"
22725 \begin_layout Subsection
22727 \begin_inset Index idx
22730 \begin_layout Plain Layout
22731 Symbols ! Euro-symbol
22737 \begin_inset Index idx
22740 \begin_layout Plain Layout
22747 \begin_layout Plain Layout
22764 \begin_layout Standard
22765 To use the Euro symbol in formulas, the LaTeX-package
22770 \begin_inset Index idx
22773 \begin_layout Plain Layout
22779 must be installed and loaded with the LaTeX-preamble line
22782 \begin_layout Standard
22787 usepackage[gennarrow]{eurosym}
22790 \begin_layout Standard
22791 The Euro symbol can now be inserted with the command
22798 \begin_inset Index idx
22801 \begin_layout Plain Layout
22812 \begin_layout Standard
22813 The Euro symbol can directly be inserted with the € key in mathematical
22814 text, without having
22829 can also be inserted in TeX-mode.
22830 The official currency symbol can then be inserted with the command
22837 \begin_inset Index idx
22840 \begin_layout Plain Layout
22848 , that is only available in TeX-mode.
22851 \begin_layout Standard
22855 \begin_layout Plain Layout
22865 \begin_inset Note Note
22868 \begin_layout Plain Layout
22869 The following table will only be displayed when the LaTeX-package
22881 \begin_layout Standard
22882 An overview about the different Euro symbols:
22885 \begin_layout Standard
22887 \begin_inset Tabular
22888 <lyxtabular version="3" rows="4" columns="3">
22889 <features tabularvalignment="middle">
22890 <column alignment="center" valignment="top" width="0pt">
22891 <column alignment="center" valignment="top" width="0pt">
22892 <column alignment="center" valignment="top" width="0pt">
22894 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22897 \begin_layout Plain Layout
22903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22906 \begin_layout Plain Layout
22912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22915 \begin_layout Plain Layout
22923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22926 \begin_layout Plain Layout
22932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22935 \begin_layout Plain Layout
22943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22946 \begin_layout Plain Layout
22947 \begin_inset Formula $\euro$
22957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22960 \begin_layout Plain Layout
22966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22969 \begin_layout Plain Layout
22975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22978 \begin_layout Plain Layout
22979 \begin_inset Formula $\mbox{€}$
22989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22992 \begin_layout Plain Layout
22998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23001 \begin_layout Plain Layout
23009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23012 \begin_layout Plain Layout
23016 \begin_layout Plain Layout
23038 \begin_layout Standard
23042 \begin_layout Plain Layout
23052 \begin_inset Note Note
23055 \begin_layout Plain Layout
23056 The following will be displayed when the LaTeX-package
23068 \begin_layout Standard
23069 You need to install the LaTeX-package
23073 to see the rest of this subsection in the output.
23076 \begin_layout Standard
23080 \begin_layout Plain Layout
23092 \begin_layout Section
23094 \begin_inset CommandInset label
23096 name "sec:Relations"
23101 \begin_inset Index idx
23104 \begin_layout Plain Layout
23111 \begin_inset Index idx
23114 \begin_layout Plain Layout
23119 \begin_layout Plain Layout
23130 \begin_layout Plain Layout
23145 \begin_layout Standard
23146 All relations can also be inserted via the toolbar button
23147 \begin_inset Graphics
23148 filename ../images/math/leq.png
23156 \begin_layout Standard
23157 \begin_inset space \hfill{}
23161 \begin_inset Tabular
23162 <lyxtabular version="3" rows="17" columns="2">
23163 <features tabularvalignment="middle">
23164 <column alignment="center" valignment="top" width="0pt">
23165 <column alignment="center" valignment="top" width="0pt">
23167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23170 \begin_layout Plain Layout
23176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23179 \begin_layout Plain Layout
23187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23190 \begin_layout Plain Layout
23196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23199 \begin_layout Plain Layout
23200 \begin_inset Formula $<$
23210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23213 \begin_layout Plain Layout
23221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23224 \begin_layout Plain Layout
23225 \begin_inset Formula $\le$
23235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23238 \begin_layout Plain Layout
23246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23249 \begin_layout Plain Layout
23250 \begin_inset Formula $\ll$
23260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23263 \begin_layout Plain Layout
23271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23274 \begin_layout Plain Layout
23275 \begin_inset Formula $\prec$
23285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23288 \begin_layout Plain Layout
23296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23299 \begin_layout Plain Layout
23300 \begin_inset Formula $\preceq$
23310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23313 \begin_layout Plain Layout
23321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23324 \begin_layout Plain Layout
23325 \begin_inset Formula $\subset$
23335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23338 \begin_layout Plain Layout
23346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23349 \begin_layout Plain Layout
23350 \begin_inset Formula $\subseteq$
23360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23363 \begin_layout Plain Layout
23371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23374 \begin_layout Plain Layout
23375 \begin_inset Formula $\sqsubseteq$
23385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23388 \begin_layout Plain Layout
23396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23399 \begin_layout Plain Layout
23400 \begin_inset Formula $\in$
23410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23413 \begin_layout Plain Layout
23421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23424 \begin_layout Plain Layout
23425 \begin_inset Formula $\vdash$
23435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23438 \begin_layout Plain Layout
23446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23449 \begin_layout Plain Layout
23450 \begin_inset Formula $\smile$
23460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23463 \begin_layout Plain Layout
23471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23474 \begin_layout Plain Layout
23475 \begin_inset Formula $\lhd$
23485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23488 \begin_layout Plain Layout
23496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23499 \begin_layout Plain Layout
23500 \begin_inset Formula $\unlhd$
23510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23513 \begin_layout Plain Layout
23521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23524 \begin_layout Plain Layout
23525 \begin_inset Formula $\gtrless$
23535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23538 \begin_layout Plain Layout
23546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23549 \begin_layout Plain Layout
23550 \begin_inset Formula $\mid$
23560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23563 \begin_layout Plain Layout
23571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23574 \begin_layout Plain Layout
23575 \begin_inset Formula $\nmid$
23589 \begin_inset space \hfill{}
23593 \begin_inset Tabular
23594 <lyxtabular version="3" rows="17" columns="2">
23595 <features tabularvalignment="middle">
23596 <column alignment="center" valignment="top" width="0pt">
23597 <column alignment="center" valignment="top" width="0pt">
23599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23602 \begin_layout Plain Layout
23608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23611 \begin_layout Plain Layout
23619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23622 \begin_layout Plain Layout
23628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23631 \begin_layout Plain Layout
23632 \begin_inset Formula $=$
23642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23645 \begin_layout Plain Layout
23653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23656 \begin_layout Plain Layout
23657 \begin_inset Formula $\not=$
23667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23670 \begin_layout Plain Layout
23678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23681 \begin_layout Plain Layout
23682 \begin_inset Formula $\equiv$
23692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23695 \begin_layout Plain Layout
23703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23706 \begin_layout Plain Layout
23707 \begin_inset Formula $\sim$
23717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23720 \begin_layout Plain Layout
23728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23731 \begin_layout Plain Layout
23732 \begin_inset Formula $\simeq$
23742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23745 \begin_layout Plain Layout
23753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23756 \begin_layout Plain Layout
23757 \begin_inset Formula $\approx$
23767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23770 \begin_layout Plain Layout
23778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23781 \begin_layout Plain Layout
23782 \begin_inset Formula $\cong$
23792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23795 \begin_layout Plain Layout
23803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23806 \begin_layout Plain Layout
23807 \begin_inset Formula $\bowtie$
23817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23820 \begin_layout Plain Layout
23828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23831 \begin_layout Plain Layout
23832 \begin_inset Formula $\notin$
23842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23845 \begin_layout Plain Layout
23853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23856 \begin_layout Plain Layout
23857 \begin_inset Formula $\perp$
23867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23870 \begin_layout Plain Layout
23878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23881 \begin_layout Plain Layout
23882 \begin_inset Formula $\propto$
23892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23895 \begin_layout Plain Layout
23903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23906 \begin_layout Plain Layout
23907 \begin_inset Formula $\asymp$
23917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23920 \begin_layout Plain Layout
23928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23931 \begin_layout Plain Layout
23932 \begin_inset Formula $\doteq$
23942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23945 \begin_layout Plain Layout
23953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23956 \begin_layout Plain Layout
23957 \begin_inset Formula $\circeq$
23967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23970 \begin_layout Plain Layout
23978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23981 \begin_layout Plain Layout
23982 \begin_inset Formula $\models$
23992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23995 \begin_layout Plain Layout
24003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24006 \begin_layout Plain Layout
24007 \begin_inset Formula $\widehat{=}$
24021 \begin_inset space \hfill{}
24025 \begin_inset Tabular
24026 <lyxtabular version="3" rows="17" columns="2">
24027 <features tabularvalignment="middle">
24028 <column alignment="center" valignment="top" width="0pt">
24029 <column alignment="center" valignment="top" width="0pt">
24031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24034 \begin_layout Plain Layout
24040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24043 \begin_layout Plain Layout
24051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24054 \begin_layout Plain Layout
24060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24063 \begin_layout Plain Layout
24064 \begin_inset Formula $>$
24074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24077 \begin_layout Plain Layout
24085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24088 \begin_layout Plain Layout
24089 \begin_inset Formula $\ge$
24099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24102 \begin_layout Plain Layout
24110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24113 \begin_layout Plain Layout
24114 \begin_inset Formula $\gg$
24124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24127 \begin_layout Plain Layout
24135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24138 \begin_layout Plain Layout
24139 \begin_inset Formula $\succ$
24149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24152 \begin_layout Plain Layout
24160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24163 \begin_layout Plain Layout
24164 \begin_inset Formula $\succeq$
24174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24177 \begin_layout Plain Layout
24185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24188 \begin_layout Plain Layout
24189 \begin_inset Formula $\supset$
24199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24202 \begin_layout Plain Layout
24210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24213 \begin_layout Plain Layout
24214 \begin_inset Formula $\supseteq$
24224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24227 \begin_layout Plain Layout
24235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24238 \begin_layout Plain Layout
24239 \begin_inset Formula $\sqsupseteq$
24249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24252 \begin_layout Plain Layout
24260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24263 \begin_layout Plain Layout
24264 \begin_inset Formula $\ni$
24274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24277 \begin_layout Plain Layout
24285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24288 \begin_layout Plain Layout
24289 \begin_inset Formula $\dashv$
24299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24302 \begin_layout Plain Layout
24310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24313 \begin_layout Plain Layout
24314 \begin_inset Formula $\frown$
24324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24327 \begin_layout Plain Layout
24335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24338 \begin_layout Plain Layout
24339 \begin_inset Formula $\rhd$
24349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24352 \begin_layout Plain Layout
24360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24363 \begin_layout Plain Layout
24364 \begin_inset Formula $\unrhd$
24374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24377 \begin_layout Plain Layout
24385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24388 \begin_layout Plain Layout
24389 \begin_inset Formula $\lessgtr$
24399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24402 \begin_layout Plain Layout
24410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24413 \begin_layout Plain Layout
24414 \begin_inset Formula $\parallel$
24424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24427 \begin_layout Plain Layout
24435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24438 \begin_layout Plain Layout
24439 \begin_inset Formula $\nparallel$
24453 \begin_inset space \hfill{}
24459 \begin_layout Standard
24460 \begin_inset VSpace medskip
24475 are bigger than the equal looking operators
24490 \begin_layout Standard
24491 Relations are, in contrary to symbols, always surrounded by space.
24494 \begin_layout Standard
24495 Relations with labels can be created with the command
24502 \begin_inset Index idx
24505 \begin_layout Plain Layout
24516 \begin_layout Standard
24518 \begin_inset Tabular
24519 <lyxtabular version="3" rows="2" columns="2">
24520 <features tabularvalignment="middle">
24521 <column alignment="center" valignment="top" width="0">
24522 <column alignment="center" valignment="top" width="0">
24524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24527 \begin_layout Plain Layout
24533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24536 \begin_layout Plain Layout
24538 \begin_inset Note Note
24541 \begin_layout Plain Layout
24548 is only used as spacer.
24560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24563 \begin_layout Plain Layout
24570 \begin_layout Plain Layout
24587 \begin_layout Plain Layout
24597 \begin_inset Formula $\downarrow$
24606 \begin_layout Plain Layout
24619 \begin_layout Plain Layout
24633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24636 \begin_layout Plain Layout
24637 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24653 \begin_layout Section
24657 \begin_layout Subsection
24658 Predefined Functions
24659 \begin_inset CommandInset label
24661 name "sub:Predefined-Functions"
24666 \begin_inset Index idx
24669 \begin_layout Plain Layout
24670 Functions ! predefined
24678 \begin_layout Standard
24679 In general, variables are set
24683 in mathematical expressions, but not function names, because
24684 \begin_inset Formula $sin$
24687 could be misunderstood as
24688 \begin_inset Formula $s\cdot i\cdot n$
24692 Therefore there are predefined functions, that are additionally a bit separated
24694 They are inserted as commands starting with a backslash before their name.
24697 \begin_layout Standard
24699 \begin_inset Tabular
24700 <lyxtabular version="3" rows="2" columns="4">
24701 <features tabularvalignment="middle">
24702 <column alignment="center" valignment="top" width="0pt">
24703 <column alignment="center" valignment="top" width="0pt">
24704 <column alignment="center" valignment="top" width="0pt">
24705 <column alignment="center" valignment="top" width="0pt">
24707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24710 \begin_layout Plain Layout
24716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24719 \begin_layout Plain Layout
24725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24728 \begin_layout Plain Layout
24734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24737 \begin_layout Plain Layout
24745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24748 \begin_layout Plain Layout
24754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24757 \begin_layout Plain Layout
24758 \begin_inset Formula $Asin(x)+B$
24766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24769 \begin_layout Plain Layout
24777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24780 \begin_layout Plain Layout
24781 \begin_inset Formula $A\sin(x)+B$
24797 \begin_layout Standard
24798 The following functions are predefined:
24801 \begin_layout Standard
24802 \begin_inset VSpace -2mm
24808 \begin_layout Standard
24810 \begin_inset Tabular
24811 <lyxtabular version="3" rows="9" columns="4">
24812 <features tabularvalignment="middle">
24813 <column alignment="center" valignment="top" width="0pt">
24814 <column alignment="center" valignment="top" width="0pt">
24815 <column alignment="center" valignment="top" width="0pt">
24816 <column alignment="center" valignment="top" width="0pt">
24818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24821 \begin_layout Plain Layout
24827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24830 \begin_layout Plain Layout
24836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24839 \begin_layout Plain Layout
24845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24848 \begin_layout Plain Layout
24856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24859 \begin_layout Plain Layout
24867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24870 \begin_layout Plain Layout
24878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24881 \begin_layout Plain Layout
24889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24892 \begin_layout Plain Layout
24902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24905 \begin_layout Plain Layout
24913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24916 \begin_layout Plain Layout
24924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24927 \begin_layout Plain Layout
24935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24938 \begin_layout Plain Layout
24948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24951 \begin_layout Plain Layout
24959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24962 \begin_layout Plain Layout
24970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24973 \begin_layout Plain Layout
24981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24984 \begin_layout Plain Layout
24994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24997 \begin_layout Plain Layout
25005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25008 \begin_layout Plain Layout
25016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25019 \begin_layout Plain Layout
25027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25030 \begin_layout Plain Layout
25040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25043 \begin_layout Plain Layout
25051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25054 \begin_layout Plain Layout
25062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25065 \begin_layout Plain Layout
25073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25076 \begin_layout Plain Layout
25086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25089 \begin_layout Plain Layout
25097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25100 \begin_layout Plain Layout
25108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25111 \begin_layout Plain Layout
25119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25122 \begin_layout Plain Layout
25132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25135 \begin_layout Plain Layout
25143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25146 \begin_layout Plain Layout
25154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25157 \begin_layout Plain Layout
25165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25168 \begin_layout Plain Layout
25178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25181 \begin_layout Plain Layout
25189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25192 \begin_layout Plain Layout
25200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25203 \begin_layout Plain Layout
25211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25214 \begin_layout Plain Layout
25230 \begin_layout Standard
25231 They can also be inserted with the math toolbar button
25232 \begin_inset Graphics
25233 filename ../images/math/functions.png
25241 \begin_layout Subsection
25242 Self-defined Functions
25243 \begin_inset Index idx
25246 \begin_layout Plain Layout
25247 Functions ! self-defined
25255 \begin_layout Standard
25256 To use a function that is not predefined, like for example the sign function
25257 sgn(x), there are two possibilities:
25260 \begin_layout Itemize
25261 Define the function by inserting the following line to the LaTeX-preamble
25265 \begin_layout Plain Layout
25270 DeclareMathOperator
25273 \begin_inset CommandInset ref
25275 reference "sub:Self-defined-Operators"
25285 \begin_inset Newline newline
25289 \begin_inset VSpace -3mm
25293 \begin_inset Newline newline
25300 DeclareMathOperator{
25305 \begin_inset Index idx
25308 \begin_layout Plain Layout
25313 DeclareMathOperator
25319 \begin_inset Newline newline
25323 \begin_inset VSpace -2mm
25327 \begin_inset Newline newline
25330 Now the new defined function can be called with the command
25339 \begin_layout Itemize
25340 Write the formula as usual, mark the formula name, in our example the letters
25345 , and change it to mathematical text.
25346 At last a space is inserted between prefactor and function.
25349 \begin_layout Standard
25350 The result is the same with both methods as with a predefined function
25354 \begin_layout Plain Layout
25355 In LyX self-defined functions are displayed red, predefined ones black.
25363 \begin_layout Standard
25365 \begin_inset Tabular
25366 <lyxtabular version="3" rows="3" columns="2">
25367 <features tabularvalignment="middle">
25368 <column alignment="center" valignment="top" width="0pt">
25369 <column alignment="center" valignment="top" width="0pt">
25371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25374 \begin_layout Plain Layout
25380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25383 \begin_layout Plain Layout
25391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25394 \begin_layout Plain Layout
25402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25405 \begin_layout Plain Layout
25406 \begin_inset Formula $A\sgn(x)+B$
25416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25419 \begin_layout Plain Layout
25423 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25434 \begin_layout Plain Layout
25435 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25451 \begin_layout Standard
25452 The first method is more suitable when the self-defined function should
25453 be used several times.
25456 \begin_layout Subsection
25458 \begin_inset Index idx
25461 \begin_layout Plain Layout
25470 \begin_layout Standard
25471 For limits there are defined besides
25478 \begin_inset Index idx
25481 \begin_layout Plain Layout
25501 furthermore the following functions:
25504 \begin_layout Standard
25506 \begin_inset Tabular
25507 <lyxtabular version="3" rows="5" columns="2">
25508 <features tabularvalignment="middle">
25509 <column alignment="center" valignment="top" width="0">
25510 <column alignment="center" valignment="top" width="0">
25512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25515 \begin_layout Plain Layout
25521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25524 \begin_layout Plain Layout
25526 \begin_inset Note Note
25529 \begin_layout Plain Layout
25536 is only used as spacer.
25548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25551 \begin_layout Plain Layout
25559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25562 \begin_layout Plain Layout
25563 \begin_inset Formula $\varliminf$
25573 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25576 \begin_layout Plain Layout
25584 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25587 \begin_layout Plain Layout
25588 \begin_inset Formula $\varlimsup$
25598 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25601 \begin_layout Plain Layout
25609 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25612 \begin_layout Plain Layout
25613 \begin_inset Formula $\varprojlim$
25623 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25626 \begin_layout Plain Layout
25634 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25637 \begin_layout Plain Layout
25638 \begin_inset Formula $\varinjlim$
25642 \begin_inset Formula $\raisebox{-2.5mm}{}$
25658 \begin_layout Standard
25659 \begin_inset VSpace medskip
25662 The limit is created by inserting a subscript.
25663 It is set right beside the function in an inline formula:
25666 \begin_layout Standard
25668 \begin_inset Tabular
25669 <lyxtabular version="3" rows="2" columns="2">
25670 <features tabularvalignment="middle">
25671 <column alignment="center" valignment="top" width="0pt">
25672 <column alignment="center" valignment="top" width="0pt">
25674 <cell alignment="center" valignment="top" usebox="none">
25677 \begin_layout Plain Layout
25683 <cell alignment="center" valignment="top" usebox="none">
25686 \begin_layout Plain Layout
25687 \begin_inset space \hspace{}
25692 \begin_inset Note Note
25695 \begin_layout Plain Layout
25702 are used here as spacer.
25714 <cell alignment="center" valignment="top" usebox="none">
25717 \begin_layout Plain Layout
25726 \begin_layout Plain Layout
25739 \begin_layout Plain Layout
25753 <cell alignment="center" valignment="top" usebox="none">
25756 \begin_layout Plain Layout
25757 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25773 \begin_layout Standard
25774 In a displayed formula the limit is set below the formula, as usual:
25775 \begin_inset Formula \[
25783 \begin_layout Subsection
25785 \begin_inset Index idx
25788 \begin_layout Plain Layout
25789 Functions ! modulo-
25797 \begin_layout Standard
25798 The modulo-function is special, because it exists in four variants.
25801 \begin_layout Standard
25802 The variants in a displayed formula:
25803 \begin_inset Formula \begin{align*}
25804 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25805 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25806 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25807 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25808 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
25816 \begin_layout Standard
25817 In an inline formula less space is set before the function names for all
25821 \begin_layout Section
25823 \begin_inset Index idx
25826 \begin_layout Plain Layout
25835 \begin_layout Subsection
25836 Special Characters in Mathematical Text
25839 \begin_layout Standard
25840 The following commands can only be used in mathematical text or in TeX-mode:
25843 \begin_layout Standard
25844 \begin_inset space \hfill{}
25848 \begin_inset Tabular
25849 <lyxtabular version="3" rows="8" columns="2">
25850 <features tabularvalignment="middle">
25851 <column alignment="block" valignment="top" width="0">
25852 <column alignment="block" valignment="top" width="0">
25854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25857 \begin_layout Plain Layout
25863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25866 \begin_layout Plain Layout
25874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25877 \begin_layout Plain Layout
25885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25888 \begin_layout Plain Layout
25889 \begin_inset Formula $\textrm{œ}$
25899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25902 \begin_layout Plain Layout
25910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25913 \begin_layout Plain Layout
25914 \begin_inset Formula $\textrm{Œ}$
25924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25927 \begin_layout Plain Layout
25935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25938 \begin_layout Plain Layout
25939 \begin_inset Formula $\textrm{æ}$
25949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25952 \begin_layout Plain Layout
25960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25963 \begin_layout Plain Layout
25964 \begin_inset Formula $\textrm{Æ}$
25974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25977 \begin_layout Plain Layout
25985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25988 \begin_layout Plain Layout
25989 \begin_inset Formula $\textrm{\aa}$
25999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26002 \begin_layout Plain Layout
26006 \begin_inset Index idx
26009 \begin_layout Plain Layout
26016 \begin_layout Plain Layout
26037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26040 \begin_layout Plain Layout
26041 \begin_inset Formula $\textrm{Å}$
26051 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26054 \begin_layout Plain Layout
26062 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26065 \begin_layout Plain Layout
26066 \begin_inset Formula $\textrm{ı}$
26080 \begin_inset space \hfill{}
26084 \begin_inset Tabular
26085 <lyxtabular version="3" rows="8" columns="2">
26086 <features tabularvalignment="middle">
26087 <column alignment="block" valignment="top" width="0">
26088 <column alignment="center" valignment="top" width="0">
26090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26093 \begin_layout Plain Layout
26095 \begin_inset Note Note
26098 \begin_layout Plain Layout
26100 \begin_inset space \thinspace{}
26103 mm is used for separation, because otherwise the output will be ¡ and ¿
26114 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26117 \begin_layout Plain Layout
26125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26128 \begin_layout Plain Layout
26136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26139 \begin_layout Plain Layout
26140 \begin_inset Formula $\textrm{ø}$
26150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26153 \begin_layout Plain Layout
26161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26164 \begin_layout Plain Layout
26165 \begin_inset Formula $\textrm{Ø}$
26175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26178 \begin_layout Plain Layout
26186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26189 \begin_layout Plain Layout
26190 \begin_inset Formula $\textrm{ł}$
26200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26203 \begin_layout Plain Layout
26211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26214 \begin_layout Plain Layout
26215 \begin_inset Formula $\textrm{Ł}$
26225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26228 \begin_layout Plain Layout
26230 \begin_inset space \hspace{}
26238 \begin_layout Plain Layout
26252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26255 \begin_layout Plain Layout
26256 \begin_inset Formula $\textrm{!`}$
26266 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26269 \begin_layout Plain Layout
26271 \begin_inset space \hspace{}
26279 \begin_layout Plain Layout
26293 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26296 \begin_layout Plain Layout
26297 \begin_inset Formula $\textrm{?`}$
26307 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26310 \begin_layout Plain Layout
26318 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26321 \begin_layout Plain Layout
26322 \begin_inset Formula $\textrm{ȷ}$
26336 \begin_inset space \hfill{}
26342 \begin_layout Standard
26344 \begin_inset Formula $\textrm{\textrm{Å}}$
26348 \begin_inset Formula $\textrm{\textrm{Ø}}$
26351 can also be inserted via the math toolbar button
26352 \begin_inset Graphics
26353 filename ../images/math/digamma.png
26361 \begin_layout Standard
26362 An exception are the commands
26365 \begin_inset space \hspace{}
26374 \begin_inset space \hspace{}
26380 , because they can be inserted in LyX directly to text.
26383 \begin_layout Subsection
26385 \begin_inset CommandInset label
26387 name "sub:Accents-in-Text"
26392 \begin_inset Index idx
26395 \begin_layout Plain Layout
26404 \begin_layout Standard
26405 With the following commands all letters can be accented.
26406 The commands must be inserted in TeX-mode.
26409 \begin_layout Standard
26410 \begin_inset space \hfill{}
26414 \begin_inset Tabular
26415 <lyxtabular version="3" rows="8" columns="2">
26416 <features tabularvalignment="middle">
26417 <column alignment="block" valignment="top" width="0">
26418 <column alignment="block" valignment="top" width="0">
26420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26423 \begin_layout Plain Layout
26429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26432 \begin_layout Plain Layout
26440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26443 \begin_layout Plain Layout
26447 \begin_inset Quotes grd
26455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26458 \begin_layout Plain Layout
26462 \begin_layout Plain Layout
26478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26481 \begin_layout Plain Layout
26489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26492 \begin_layout Plain Layout
26496 \begin_layout Plain Layout
26512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26515 \begin_layout Plain Layout
26522 \begin_layout Plain Layout
26536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26539 \begin_layout Plain Layout
26543 \begin_layout Plain Layout
26559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26562 \begin_layout Plain Layout
26570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26573 \begin_layout Plain Layout
26577 \begin_layout Plain Layout
26593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26596 \begin_layout Plain Layout
26603 \begin_layout Plain Layout
26617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26620 \begin_layout Plain Layout
26624 \begin_layout Plain Layout
26640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26643 \begin_layout Plain Layout
26650 \begin_layout Plain Layout
26664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26667 \begin_layout Plain Layout
26671 \begin_layout Plain Layout
26687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26690 \begin_layout Plain Layout
26697 \begin_layout Plain Layout
26711 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26714 \begin_layout Plain Layout
26718 \begin_layout Plain Layout
26738 \begin_inset space \hfill{}
26742 \begin_inset Tabular
26743 <lyxtabular version="3" rows="8" columns="2">
26744 <features tabularvalignment="middle">
26745 <column alignment="block" valignment="top" width="0">
26746 <column alignment="center" valignment="top" width="0">
26748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26751 \begin_layout Plain Layout
26757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26760 \begin_layout Plain Layout
26768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26771 \begin_layout Plain Layout
26778 \begin_layout Plain Layout
26792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26795 \begin_layout Plain Layout
26799 \begin_layout Plain Layout
26815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26818 \begin_layout Plain Layout
26826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26829 \begin_layout Plain Layout
26833 \begin_layout Plain Layout
26849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26852 \begin_layout Plain Layout
26856 \begin_inset Index idx
26859 \begin_layout Plain Layout
26870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26873 \begin_layout Plain Layout
26877 \begin_layout Plain Layout
26893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26896 \begin_layout Plain Layout
26904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26907 \begin_layout Plain Layout
26911 \begin_layout Plain Layout
26927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26930 \begin_layout Plain Layout
26937 \begin_layout Plain Layout
26951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26954 \begin_layout Plain Layout
26958 \begin_layout Plain Layout
26974 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26977 \begin_layout Plain Layout
26984 \begin_layout Plain Layout
26998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27001 \begin_layout Plain Layout
27005 \begin_layout Plain Layout
27021 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27024 \begin_layout Plain Layout
27031 \begin_layout Plain Layout
27045 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27048 \begin_layout Plain Layout
27052 \begin_layout Plain Layout
27072 \begin_inset space \hfill{}
27078 \begin_layout Standard
27079 \begin_inset VSpace medskip
27088 also two different characters can be accented.
27097 \begin_layout Plain Layout
27112 \begin_layout Plain Layout
27124 \begin_layout Standard
27137 can in combination with vowels directly be inserted with the keyboard without
27139 The same applies for the tilde
27143 \begin_layout Plain Layout
27144 This only applies for keyboards where the tilde is defined as accent.
27153 in combination with
27168 \begin_layout Standard
27211 and accents that are inserted directly with the keyboard are also available
27212 in mathematical text.
27213 For the other accents there are special math commands to be used in formulas,
27215 \begin_inset CommandInset ref
27217 reference "sub:Accents-for-one"
27224 \begin_layout Standard
27225 \begin_inset VSpace bigskip
27228 Furthermore, with the command
27235 \begin_inset Index idx
27238 \begin_layout Plain Layout
27246 all numbers and letters can be set into a circle, quasi accented with a
27247 circle, similar to the copyright symbol.
27250 \begin_layout Standard
27252 \begin_inset Tabular
27253 <lyxtabular version="3" rows="3" columns="2">
27254 <features tabularvalignment="middle">
27255 <column alignment="center" valignment="top" width="0">
27256 <column alignment="center" valignment="top" width="0">
27258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27261 \begin_layout Plain Layout
27267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27270 \begin_layout Plain Layout
27272 \begin_inset Note Note
27275 \begin_layout Plain Layout
27282 is only used as spacer.
27294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27297 \begin_layout Plain Layout
27305 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27308 \begin_layout Plain Layout
27312 \begin_layout Plain Layout
27328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27331 \begin_layout Plain Layout
27342 raisebox{-1.5pt}{W}}
27347 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27350 \begin_layout Plain Layout
27351 \begin_inset Formula $\raisebox{4.5mm}{}$
27358 \begin_layout Plain Layout
27376 \begin_inset Formula $\raisebox{-2mm}{}$
27392 \begin_layout Standard
27393 One has to take care that the character fits in the circle.
27404 \begin_layout Plain Layout
27406 \begin_inset CommandInset ref
27408 reference "sub:Font-Sizes"
27417 specifies thereby the size of the circle.
27428 \begin_layout Plain Layout
27430 \begin_inset CommandInset ref
27432 reference "sub:Boxes-without-Frame"
27441 the character can be centered.
27444 \begin_layout Subsection
27446 \begin_inset Index idx
27449 \begin_layout Plain Layout
27458 \begin_layout Standard
27459 Minuscule numbers are created with the command
27466 \begin_inset Index idx
27469 \begin_layout Plain Layout
27478 The command can be used in formulas and in TeX-mode.
27479 The command scheme is:
27482 \begin_layout Standard
27487 oldstylenums{number}
27490 \begin_layout Standard
27495 oldstylenums{0123456789
27498 \begin_inset Formula $\oldstylenums{0123456789}$
27504 \begin_layout Subsection
27505 Miscellaneous special Characters
27506 \begin_inset CommandInset label
27508 name "sub:Miscellaneous-special-Characters"
27513 \begin_inset Index idx
27516 \begin_layout Plain Layout
27517 Special characters ! miscellaneous
27525 \begin_layout Standard
27526 The following characters can only be inserted to formulas by using commands:
27529 \begin_layout Standard
27531 \begin_inset Tabular
27532 <lyxtabular version="3" rows="4" columns="2">
27533 <features tabularvalignment="middle">
27534 <column alignment="center" valignment="top" width="0">
27535 <column alignment="center" valignment="top" width="0">
27537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27540 \begin_layout Plain Layout
27546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27549 \begin_layout Plain Layout
27557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27560 \begin_layout Plain Layout
27567 \begin_layout Plain Layout
27581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27584 \begin_layout Plain Layout
27585 \begin_inset Formula $\mathcircumflex$
27595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27598 \begin_layout Plain Layout
27606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27609 \begin_layout Plain Layout
27610 \begin_inset Formula $\_$
27620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27623 \begin_layout Plain Layout
27628 \begin_layout Plain Layout
27640 \begin_inset Index idx
27643 \begin_layout Plain Layout
27656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27659 \begin_layout Plain Layout
27660 \begin_inset Formula $^{\circ}$
27676 \begin_layout Standard
27677 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27678 contains the following line
27682 \begin_layout Plain Layout
27683 More about this is described in
27684 \begin_inset CommandInset ref
27686 reference "sub:Text-Characters-in"
27698 \begin_layout Standard
27703 DeclareInputtext{176}{
27716 \begin_layout Section
27718 \begin_inset CommandInset label
27720 name "sec:Formula-Styles"
27725 \begin_inset Index idx
27728 \begin_layout Plain Layout
27737 \begin_layout Itemize
27738 There are two different alignment styles:
27742 \begin_layout Description
27743 Centered is the predefined standard
27746 \begin_layout Description
27747 Indented for this the option
27751 must be inserted in the menu
27753 Document\SpecialChar \menuseparator
27759 \begin_inset space ~
27765 \begin_layout Standard
27770 is used, the indentation can be adjusted with the length
27777 \begin_inset Index idx
27780 \begin_layout Plain Layout
27789 Should the distance be 15
27790 \begin_inset space \thinspace{}
27793 mm, the following command line is inserted in the LaTeX-preamble
27796 \begin_layout Standard
27806 \begin_layout Standard
27807 When no length is specified, the predefined value of 30
27808 \begin_inset space \thinspace{}
27815 \begin_layout Itemize
27816 And two different numbering styles:
27820 \begin_layout Description
27821 Right is the predefined standard
27824 \begin_layout Description
27825 Left for this the option
27829 must be inserted in the menu
27831 Document\SpecialChar \menuseparator
27837 \begin_inset space ~
27844 \begin_layout Standard
27853 can also be used together.
27854 In this case both options are inserted, separated by a comma.
27857 \begin_layout Standard
27858 The chosen styles are used for all displayed formulas of the document.
27859 When both, centered and indented formulas should be created in a document,
27865 The indented formulas are then set in a flalign environment, see
27866 \begin_inset CommandInset ref
27868 reference "sub:Flalign-Environment"
27875 \begin_layout Section
27877 \begin_inset CommandInset label
27879 name "sec:Multiline-Formulas"
27884 \begin_inset Index idx
27887 \begin_layout Plain Layout
27888 Formula ! multiline
27896 \begin_layout Subsection
27900 \begin_layout Standard
27901 In LyX multiline formulas are created by pressing
27906 arg "newline-insert newline"
27912 This creates either an
27914 eqnarray environment
27916 that is described in
27917 \begin_inset CommandInset ref
27919 reference "sub:Eqnarray-Environment"
27923 or, when the option
27925 Use AMS math package
27927 in the document settings is selected, an
27931 that is described in
27932 \begin_inset CommandInset ref
27934 reference "sub:Standard-align-Environment"
27941 \begin_layout Standard
27942 There are other multiline formula environments that can be created via the
27945 Insert\SpecialChar \menuseparator
27949 These environments are described in the following sections.
27952 \begin_layout Standard
27953 In all multiline formula environments a new line is created by pressing
27957 arg "newline-insert newline"
27961 To add or delete lines, the math toolbar buttons
27962 \begin_inset Graphics
27963 filename ../images/tabular-feature_append-row.png
27969 \begin_inset Graphics
27970 filename ../images/tabular-feature_delete-row.png
27975 , respectively, or the menu
27977 Edit\SpecialChar \menuseparator
27983 \begin_layout Subsubsection
27985 \begin_inset CommandInset label
27987 name "sub:Line-Separation"
27992 \begin_inset Index idx
27995 \begin_layout Plain Layout
27996 Formula ! multiline ! Line separation
28004 \begin_layout Standard
28005 There is sometimes not enough space in multiline formulas between the lines:
28006 \begin_inset Formula \begin{eqnarray*}
28007 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}\\
28008 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
28016 \begin_layout Standard
28017 In LaTeX additional line space is specified as optional argument of the
28019 This is not yet possible in LyX
28023 \begin_layout Plain Layout
28025 \begin_inset CommandInset href
28027 name "LyX-bug #1505"
28028 target "http://www.lyx.org/trac/ticket/1505"
28037 , therefore the whole formula must be inserted in TeX-mode.
28038 To add in our example space, the command
28046 is inserted at the end of the first line.
28051 \begin_layout Plain Layout
28058 \begin_layout Plain Layout
28060 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28063 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28070 \begin_layout Plain Layout
28074 left(B^{2}+x_{0}^{2}
28082 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28087 \begin_layout Plain Layout
28099 \begin_layout Standard
28100 \begin_inset VSpace bigskip
28103 To set the line separation for all lines in a formula, the length
28110 \begin_inset Index idx
28113 \begin_layout Plain Layout
28123 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28134 \begin_inset space \thinspace{}
28139 \begin_inset space \thinspace{}
28142 mm additional line separation as in the previous example, the command
28145 \begin_layout Standard
28155 \begin_layout Standard
28156 is inserted in TeX-mode before the formula.
28157 This requires that the LaTeX-package
28165 \begin_layout Plain Layout
28170 is part of every LaTeX standard installation.
28176 \begin_inset Index idx
28179 \begin_layout Plain Layout
28185 was loaded in LaTeX-preamble with the line
28188 \begin_layout Standard
28196 \begin_layout Standard
28201 \begin_layout Plain Layout
28213 \begin_inset Formula \begin{eqnarray*}
28214 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}\\
28215 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
28223 \begin_layout Standard
28227 \begin_layout Plain Layout
28238 To get back to the predefined distance,
28244 is set to the value 3
28245 \begin_inset space \thinspace{}
28251 \begin_layout Subsubsection
28253 \begin_inset CommandInset label
28255 name "sub:Column-Separation"
28260 \begin_inset Index idx
28263 \begin_layout Plain Layout
28264 Formula ! multiline ! Column separation
28272 \begin_layout Standard
28273 Multiline formulas form a matrix.
28274 A formula in the eqnarray environment is for example a matrix with three
28276 By changing the column separation in this environment, the space beside
28277 the relation sign can be changed.
28280 \begin_layout Standard
28281 The column separation is specified with the length
28288 \begin_inset Index idx
28291 \begin_layout Plain Layout
28300 \begin_inset Newline newline
28303 column separation = 2
28304 \begin_inset space \thinspace{}
28314 \begin_inset Newline newline
28320 \begin_layout Standard
28330 \begin_layout Standard
28331 inserted in TeX-mode, sets for all following formulas a column separation
28333 \begin_inset space \thinspace{}
28337 To get back to the predefined distance,
28344 \begin_inset space \thinspace{}
28350 \begin_layout Standard
28352 \begin_inset space \thinspace{}
28355 cm column separation:
28359 \begin_layout Plain Layout
28371 \begin_inset Formula \begin{eqnarray*}
28378 A formula with the predefined column separation for matrices of 10
28379 \begin_inset space \thinspace{}
28386 \begin_layout Plain Layout
28398 \begin_inset Formula \begin{eqnarray*}
28408 \begin_layout Subsubsection
28410 \begin_inset Index idx
28413 \begin_layout Plain Layout
28422 \begin_layout Standard
28423 Long formulas can be typeset using these methods:
28426 \begin_layout Itemize
28427 When one side of the equation is much shorther than the line width, this
28428 one is chosen for the left side and the right side is typeset over two
28430 \begin_inset Formula \begin{eqnarray}
28431 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 \\
28432 & & -\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}
28437 The minus sign at the beginning of the second line does normally not appear
28438 as operator because it is the first character of the line.
28439 Thus it would not be surrounded by space and could not be distinguished
28440 from the fraction bar.
28442 \begin_inset space \thinspace{}
28445 pt space was inserted behind the minus sign with the command
28455 \begin_layout Plain Layout
28463 \begin_inset CommandInset ref
28465 reference "sub:Variable-Space"
28475 \begin_inset Index idx
28478 \begin_layout Plain Layout
28489 \begin_layout Itemize
28490 When both sides of the equation are too long, the command
28497 \begin_inset Index idx
28500 \begin_layout Plain Layout
28509 It is inserted to the first column of the first line and effects that all
28510 further insertions overwrite the following columns:
28511 \begin_inset Formula \begin{eqnarray}
28512 \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 \\
28513 & & -\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 \\
28514 & & =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}
28519 After the insertion of
28525 , the cursor is in a purple box that is a bit shifted to the left from the
28527 In this the formula is inserted.
28528 \begin_inset Newline newline
28531 The content of the further lines is inserted to the second or another formula
28533 The greater the column number where it was inserted, the larger the indentation.
28534 \begin_inset VSpace medskip
28538 \begin_inset Newline newline
28542 \begin_inset Note Greyedout
28545 \begin_layout Plain Layout
28546 Note the following when using
28555 \begin_layout Itemize
28556 The formula doesn't use the full page width.
28558 \begin_inset space \thinspace{}
28562 \begin_inset space \space{}
28566 \begin_inset Formula $-B^{2}$
28569 is added to the first line in the above example, it would have been outside
28571 To better use the width, negative space can be inserted at the beginning
28575 \begin_layout Itemize
28576 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28581 \begin_layout Plain Layout
28582 \begin_inset CommandInset href
28584 name "LyX-bug #1429"
28585 target "http://www.lyx.org/trac/ticket/1429"
28594 One can only set the cursor at the beginning of the line and move it with
28603 \begin_layout Itemize
28604 Other methods to set long formulas are offered by the environments described
28606 \begin_inset CommandInset ref
28608 reference "sub:Multline-Environment"
28613 \begin_inset CommandInset ref
28615 reference "sub:Multiline-Formula-Parts"
28622 \begin_layout Subsubsection
28624 \begin_inset CommandInset label
28626 name "sub:Multiline-Brackets"
28631 \begin_inset Index idx
28634 \begin_layout Plain Layout
28635 Brackets ! for multiline expressions
28643 \begin_layout Standard
28644 For brackets spanning multiple lines the following problem occurs:
28645 \begin_inset Formula \begin{eqnarray*}
28646 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28647 & & \left.\cdots+B-D\right]
28655 \begin_layout Standard
28656 The closing bracket is smaller than the opening bracket because brackets
28657 with variable size may not span multiple lines.
28660 \begin_layout Standard
28661 To set the bracket size for the second line correctly, the first line is
28669 \begin_inset Index idx
28672 \begin_layout Plain Layout
28680 and the second line with
28688 \begin_layout Plain Layout
28702 \begin_inset CommandInset ref
28704 reference "sub:Automatic-Bracket-Size"
28716 \begin_inset Index idx
28719 \begin_layout Plain Layout
28745 \begin_layout Plain Layout
28764 \begin_layout Plain Layout
28783 \begin_layout Plain Layout
28795 \begin_inset Formula $\downarrow$
28801 \begin_inset Index idx
28804 \begin_layout Plain Layout
28812 is inserted, because the multiplication operator with its limits is the
28813 largest symbol in the first line and this should be the size for the bracket
28814 in the second line.
28817 \begin_layout Standard
28818 The result is this:
28819 \begin_inset Formula \begin{eqnarray*}
28820 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28821 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28829 \begin_layout Subsection
28833 \begin_layout Standard
28834 Align environments can be used for every kind of multiline formulas.
28835 They are specially useful to set several formulas side by side.
28838 \begin_layout Standard
28839 Align environments consist of columns.
28840 The odd columns are right aligned, the even ones left aligned.
28841 Every line in an Align environment can be numbered.
28844 \begin_layout Standard
28845 Align environments are created via the menu
28847 Insert\SpecialChar \menuseparator
28853 Edit\SpecialChar \menuseparator
28854 Math\SpecialChar \menuseparator
28855 Change Formula Type
28857 already existing formulas can be converted to Align environments.
28860 \begin_layout Standard
28861 To add or delete columns, the math toolbar buttons
28862 \begin_inset Graphics
28863 filename ../images/tabular-feature_append-column.png
28869 \begin_inset Graphics
28870 filename ../images/tabular-feature_delete-column.png
28875 , respectively, or the menu
28877 Edit\SpecialChar \menuseparator
28883 \begin_layout Subsubsection
28884 Standard align Environment
28885 \begin_inset CommandInset label
28887 name "sub:Standard-align-Environment"
28892 \begin_inset Index idx
28895 \begin_layout Plain Layout
28896 Formula ! multiline ! align environment
28904 \begin_layout Standard
28905 This Align environment is created by presssing
28908 arg "newline-insert newline"
28911 in a formula or by the menu
28913 Insert\SpecialChar \menuseparator
28914 Math\SpecialChar \menuseparator
28915 AMS align Environment
28920 \begin_layout Standard
28921 An example for two formulas set side by side, that are created with a four
28922 column align environment:
28923 \begin_inset Formula \begin{align*}
28924 A & =\sin(B) & C & =D\\
28925 C & \ne A & B & \ne D
28930 As it can be seen, the formulas in this environment are placed so as if
28939 \begin_layout Plain Layout
28947 \begin_inset CommandInset ref
28949 reference "sub:Variable-Space"
28960 before the first and after every even column.
28961 When the formula style
28967 \begin_layout Plain Layout
28969 \begin_inset CommandInset ref
28971 reference "sec:Formula-Styles"
28982 is used, the formula is set without the
28988 before the first column.
28991 \begin_layout Subsubsection
28992 Alignat Environment
28993 \begin_inset Index idx
28996 \begin_layout Plain Layout
28997 Formula ! multiline ! alignat environment
29005 \begin_layout Standard
29006 The alignat environment has no predefined column separation.
29007 It can be inserted manually with the spaces that are described
29008 \begin_inset CommandInset ref
29010 reference "sub:Space"
29017 \begin_layout Standard
29018 The above example in the alignat environment where 1
29019 \begin_inset space \thinspace{}
29022 cm space was inserted at the beginning of the second formula:
29023 \begin_inset Formula \begin{alignat*}{2}
29024 A & =\sin(B) & \hspace{1cm}C & =D\\
29025 C & \ne A & B & \ne D
29030 Because the column separation can be set separately for every column, this
29031 environment is especially suitable to set three and more formulas side
29035 \begin_layout Subsubsection
29036 Flalign Environment
29037 \begin_inset CommandInset label
29039 name "sub:Flalign-Environment"
29044 \begin_inset Index idx
29047 \begin_layout Plain Layout
29048 Formula ! multiline ! flalign environment
29056 \begin_layout Standard
29057 In this environment the first two columns are always set as much as possible
29058 to the left and the last two ones to the right.
29060 \begin_inset Formula \begin{flalign*}
29061 A & =1 & B & =2 & C & =3\\
29062 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29070 \begin_layout Standard
29071 By creating a flalign environment with an odd number of columns where an
29072 empty TeX-brace is inserted to the last column, several formulas in a document
29073 can be set to the left, although the formula style
29078 As example the indented formula
29079 \begin_inset CommandInset ref
29081 reference "eq:VolInt"
29086 \begin_inset Formula \begin{flalign}
29087 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
29091 The first two columns contain the formula.
29092 To indent it as with the formula style
29097 \begin_inset space \thinspace{}
29100 pt space was inserted at the beginning of the first column.
29103 \begin_layout Subsection
29104 Eqnarray Environment
29105 \begin_inset CommandInset label
29107 name "sub:Eqnarray-Environment"
29112 \begin_inset Index idx
29115 \begin_layout Plain Layout
29116 Formula ! multiline ! eqnarray environment
29124 \begin_layout Standard
29125 When this environment has been created, three blue boxes appear.
29126 The content of the first box is right aligned, the content of the last
29128 The content of the middle box appears centered and a bit smaller, because
29129 it is designed to insert there only relation characters.
29130 \begin_inset Formula \begin{eqnarray*}
29131 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29141 \begin_layout Subsection
29143 \begin_inset Index idx
29146 \begin_layout Plain Layout
29147 Formula ! multiline ! gather environment
29155 \begin_layout Standard
29156 This environment consists of only one centered column.
29157 Every line can be numbered.
29158 \begin_inset Formula \begin{gather}
29168 \begin_layout Subsection
29169 Multline Environment
29170 \begin_inset CommandInset label
29172 name "sub:Multline-Environment"
29177 \begin_inset Index idx
29180 \begin_layout Plain Layout
29181 Formula ! multiline ! multline environment
29189 \begin_layout Standard
29190 The multline environment consists, like the gather environment, of only
29192 But the first line is left aligned, the last one right aligned.
29193 All other lines are centered.
29194 Therefore this environment is suitable for long formulas.
29196 \begin_inset CommandInset ref
29198 reference "eq:lefteqn"
29202 in the multline environment:
29203 \begin_inset Formula \begin{multline}
29204 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}\\
29205 -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}\\
29206 =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}}
29214 \begin_layout Standard
29215 In the output only the last (first) line of a multline environment appears
29216 numbered when the document numbering is right (left).
29220 \begin_layout Plain Layout
29221 numbering styles see
29222 \begin_inset CommandInset ref
29224 reference "sec:Formula-Styles"
29236 \begin_layout Standard
29244 \begin_inset Index idx
29247 \begin_layout Plain Layout
29262 \begin_inset Index idx
29265 \begin_layout Plain Layout
29273 a centered line can be right or left aligned, respectively.
29274 The commands are used as follows:
29277 \begin_layout Standard
29282 shoveright{line content}
29288 shoveleft{line content}
29291 \begin_layout Standard
29292 \begin_inset VSpace medskip
29302 \begin_inset Index idx
29305 \begin_layout Plain Layout
29313 specifies the distance of the first line from the left page margin.
29314 Predefined is the length 0
29315 \begin_inset space \thinspace{}
29321 \begin_layout Standard
29322 As example the above formula where the command
29325 \begin_layout Standard
29335 \begin_layout Standard
29336 was inserted in TeX-mode before:
29340 \begin_layout Plain Layout
29352 \begin_inset Formula \begin{multline}
29353 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}\\
29354 \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}}\\
29355 =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}}
29364 \begin_layout Plain Layout
29375 The second line was left aligned using
29384 \begin_layout Subsection
29385 Multiline Formula Parts
29386 \begin_inset CommandInset label
29388 name "sub:Multiline-Formula-Parts"
29393 \begin_inset Index idx
29396 \begin_layout Plain Layout
29397 Formula ! multiline ! formula parts
29405 \begin_layout Standard
29406 To display only parts of a formula with multiple lines, one of the following
29407 environments are used:
29424 They can be inserted via the menu
29426 Insert\SpecialChar \menuseparator
29429 or by using the commands described in this section.
29432 \begin_layout Standard
29433 The first three have the same properties as the corresponding multiline
29434 formula environments, but it is possible to set further formula parts beside
29437 \begin_inset Formula \[
29438 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29439 \Delta E\Delta t & \ge\frac{\hbar}{2}
29441 \right\} \textrm{Uncertainty relations}\]
29448 \begin_layout Standard
29449 To get this formula, a displayed formula is created where the command
29456 \begin_inset Index idx
29459 \begin_layout Plain Layout
29468 A purple box appears around the blue formula box where now columns and
29469 lines can be added.
29470 Outside the multiline environment other formula parts can be set, like
29474 \begin_layout Standard
29475 The aligned environment is also suitable for long formulas whose lines are
29476 horizontally aligned.
29477 Using aligned in a displayed formula has the advantage that the formula
29478 number is vertically centered behind the lines.
29480 \begin_inset CommandInset ref
29482 reference "eq:shortlong"
29486 in the aligned environment:
29487 \begin_inset Formula \begin{equation}
29488 \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}|}\\
29489 & -\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}|}
29498 \begin_layout Standard
29499 To use the environments
29518 \begin_inset Index idx
29521 \begin_layout Plain Layout
29536 \begin_inset Index idx
29539 \begin_layout Plain Layout
29554 \begin_inset Index idx
29557 \begin_layout Plain Layout
29565 are inserted, respectively.
29566 The split environment has the same properties as the aligned environment
29567 but it can only have two columns.
29570 \begin_layout Subsection
29571 Text in multiline Formulas
29572 \begin_inset CommandInset label
29574 name "sub:Text-in-multiline"
29579 \begin_inset Index idx
29582 \begin_layout Plain Layout
29589 \begin_inset Index idx
29592 \begin_layout Plain Layout
29593 Formula ! multiline ! text
29601 \begin_layout Standard
29602 In the Align environments, and the multline and gather environment, text
29603 can be inserted that will appear in a separate line and doesn't affect
29604 the column alignment.
29605 To do this, the command
29612 \begin_inset Index idx
29615 \begin_layout Plain Layout
29623 is used in the following scheme:
29626 \begin_layout Standard
29634 \begin_layout Standard
29635 The text should not be longer than a line because it cannot be hyphenated.
29636 As LyX doesn't yet support
29642 directly, the text is written as mathematical text.
29649 must hereby be at the beginning of a line and appears in the output above
29651 An example where the text was inserted at the beginning of the second line:
29652 \begin_inset Formula \begin{align}
29653 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29654 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29662 \begin_layout Section
29664 \begin_inset Index idx
29667 \begin_layout Plain Layout
29674 \begin_inset Index idx
29677 \begin_layout Plain Layout
29678 Formula ! numbering|see
29682 \begin_layout Plain Layout
29693 \begin_layout Plain Layout
29708 \begin_layout Subsection
29712 \begin_layout Standard
29713 Numbered formulas can be created with the menu
29715 Insert\SpecialChar \menuseparator
29716 Math\SpecialChar \menuseparator
29718 \begin_inset space ~
29726 \begin_inset space ~
29732 Existing formulas can be numbered with the menu
29734 Edit\SpecialChar \menuseparator
29735 Math\SpecialChar \menuseparator
29737 \begin_inset space ~
29745 arg "math-number-toggle"
29749 The formula number is displayed in LyX behind the formula as number sign
29751 The number sign is replaced in the output by the formula number.
29754 \begin_layout Standard
29755 When numbering is turned on in multiline formulas, all lines will be numbered.
29756 But the numbering can be controlled with the menu
29758 Edit\SpecialChar \menuseparator
29759 Math\SpecialChar \menuseparator
29761 \begin_inset space ~
29765 \begin_inset space ~
29769 \begin_inset space ~
29777 arg "math-number-line-toggle"
29783 \begin_layout Standard
29784 Except for inline formulas, all formulas can be numbered with two different
29786 \begin_inset CommandInset ref
29788 reference "sec:Formula-Styles"
29795 \begin_layout Subsection
29797 \begin_inset Index idx
29800 \begin_layout Plain Layout
29801 Cross-references ! to formulas
29809 \begin_layout Standard
29810 All labeled formulas can be cross-referenced.
29811 A label is added by the menu
29813 Insert\SpecialChar \menuseparator
29816 or the toolbar button
29817 \begin_inset Graphics
29818 filename ../images/label-insert.png
29824 The cursor must hereby be inside a displayed formula.
29825 A dialog pops up displaying the prefix
29830 The label is inserted there behind the prefix.
29831 The predefined prefix means
29832 \begin_inset Quotes eld
29836 \begin_inset Quotes erd
29839 and makes it easier to find labels in large documents because it marks
29840 it as formula label to divide it from e.
29841 \begin_inset space \thinspace{}
29845 \begin_inset space \space{}
29849 To change a label, the menu
29851 Insert\SpecialChar \menuseparator
29857 \begin_layout Standard
29858 The name of the label is displayed in LyX within two parentheses behind
29860 A formula with a label is always numbered.
29863 \begin_layout Standard
29864 Cross-references are inserted via the menu
29866 Insert\SpecialChar \menuseparator
29869 or with the toolbar button
29870 \begin_inset Graphics
29871 filename ../images/dialog-show-new-inset_ref.png
29877 A formula cross-reference appears in the output as formula number.
29878 When in the cross-reference dialog window the format
29882 is chosen, the cross-reference appears in the output as formula number
29884 \begin_inset Newline newline
29887 By right-clicking on a cross-reference in LyX, one jumps to the formula
29888 that is referenced.
29891 \begin_layout Standard
29892 Here are as examples cross-references to formulas of the following subsections:
29893 \begin_inset Note Note
29896 \begin_layout Plain Layout
29897 Note the different cross-reference types.
29905 \begin_layout Standard
29907 \begin_inset CommandInset ref
29914 \begin_inset CommandInset ref
29922 \begin_inset CommandInset ref
29928 ) big Latin letters are used for the numbering in contrary to (
29929 \begin_inset CommandInset ref
29938 \begin_layout Standard
29939 \begin_inset VSpace medskip
29942 When the argument of
29950 \begin_layout Plain Layout
29958 \begin_inset CommandInset ref
29960 reference "sub:User-defined-Numbering"
29971 contains a box like in
29972 \begin_inset CommandInset ref
29974 reference "sub:Paragraph-Boxes"
29978 , the formula cannot be referenced.
29981 \begin_layout Subsection
29983 \begin_inset Index idx
29986 \begin_layout Plain Layout
29987 Formula numbering ! subnumbering
29995 \begin_layout Standard
29996 With the help of the commands
30000 begin{subequations}
30008 formulas can be subnumbered.
30009 Both commands are inserted in TeX-mode.
30012 \begin_layout Standard
30014 \begin_inset Formula \begin{equation}
30015 A=C-B\label{eq:a}\end{equation}
30023 \begin_layout Plain Layout
30027 addtocounter{equation}{-1}
30036 \begin_layout Plain Layout
30040 begin{subequations}
30046 \begin_inset VSpace -5mm
30050 \begin_inset Formula \begin{equation}
30051 B=C-A\label{eq:b}\end{equation}
30056 \begin_inset Formula \begin{equation}
30057 C=A+B\label{eq:c}\end{equation}
30064 \begin_layout Standard
30068 \begin_layout Plain Layout
30080 \begin_layout Standard
30081 To create the example, the following is done:
30084 \begin_layout Enumerate
30085 first formula is inserted
30088 \begin_layout Enumerate
30093 addtocounter{equation}{-1}
30095 begin{subequations}
30096 \begin_inset Index idx
30099 \begin_layout Plain Layout
30108 \begin_inset Newline newline
30113 is inserted after the first formula
30116 \begin_layout Enumerate
30117 second formula is inserted
30120 \begin_layout Enumerate
30121 third formula is inserted
30124 \begin_layout Enumerate
30131 is inserted after the third formula
30134 \begin_layout Standard
30135 Every formula between the commands
30147 is subnumbered as a, b,
30148 \begin_inset Newline linebreak
30151 c, \SpecialChar \ldots{}
30152 For multiline formulas every line will be subnumbered.
30153 All subnumbered formulas are treated as
30158 But as every numbered formula increases the counter
30162 by one, the command
30168 is needed to decrease it.
30169 Otherwise the formulas
30170 \begin_inset CommandInset ref
30177 \begin_inset CommandInset ref
30184 \begin_inset CommandInset ref
30190 would be numbered as
30191 \begin_inset CommandInset ref
30198 \begin_inset CommandInset ref
30205 \begin_inset CommandInset ref
30214 \begin_layout Standard
30215 By inserting the commands in TeX-mode, a space is created between the first
30218 \begin_inset space \thinspace{}
30221 mm vertical space is inserted after the command
30225 begin{subequations}
30228 When the formula style
30234 \begin_layout Plain Layout
30236 \begin_inset CommandInset ref
30238 reference "sec:Formula-Styles"
30250 \begin_inset space \thinspace{}
30253 mm space is inserted instead.
30256 \begin_layout Standard
30257 Here is an example for a multiline formula where the numbering was turned
30258 off for the second line:
30262 \begin_layout Plain Layout
30266 begin{subequations}
30272 \begin_inset Formula \begin{eqnarray}
30273 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30274 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30275 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30284 \begin_layout Plain Layout
30296 \begin_layout Subsection
30297 User-defined Numbering
30298 \begin_inset CommandInset label
30300 name "sub:User-defined-Numbering"
30305 \begin_inset Index idx
30308 \begin_layout Plain Layout
30309 Formula numbering ! user-defined
30317 \begin_layout Standard
30318 \begin_inset Index idx
30321 \begin_layout Plain Layout
30322 Formula numbering ! self-defined delimiters
30327 With the standard numbering parentheses are set around the formula number.
30328 To replace the parentheses for example by vertical bars, the following
30329 line is added to the LaTeX-preamble:
30332 \begin_layout Standard
30344 \begin_inset Note Note
30347 \begin_layout Plain Layout
30348 This macro is already declared in the LaTeX-preamble for testing.
30349 To activate it, remove the percent sign at the beginning.
30357 \begin_layout Standard
30358 To use other characters, the vertical bars besides the
30362 are replaced by one ore more characters.
30363 To get only the formula number the vertical bars are omitted.
30366 \begin_layout Standard
30367 \begin_inset VSpace bigskip
30370 When there should be an expression of your choice instead of the consecutive
30371 formula number in parentheses behind the formula, the command
30378 \begin_inset Index idx
30381 \begin_layout Plain Layout
30390 \begin_inset Formula \begin{equation}
30391 A+B=C\tag{something}\label{eq:tag}\end{equation}
30395 In this example the command
30403 \begin_layout Plain Layout
30414 was inserted to the formula.
30417 \begin_layout Standard
30426 \begin_layout Plain Layout
30437 is inserted instead, the star prevents the parentheses around the expression:
30438 \begin_inset Formula \[
30439 A+B=C\tag*{something}\]
30446 \begin_layout Standard
30447 \begin_inset VSpace bigskip
30450 To restart the formula numbering with new document parts or sections, the
30451 following command is used:
30454 \begin_layout Standard
30459 @addtoreset{equation}{part}
30462 \begin_inset Index idx
30465 \begin_layout Plain Layout
30470 \begin_layout Plain Layout
30481 \begin_layout Plain Layout
30494 \begin_layout Plain Layout
30505 \begin_layout Plain Layout
30518 \begin_inset Newline newline
30522 \begin_inset Newline newline
30529 @addtoreset{equation}{section}
30532 \begin_layout Standard
30533 To be able to use these commands in TeX-mode, the
30534 \begin_inset Quotes eld
30538 \begin_inset Quotes erd
30541 character has to be made
30542 \begin_inset Quotes eld
30546 \begin_inset Quotes erd
30549 for LaTeX using the command
30563 So the command sequence in TeX-mode is:
30566 \begin_layout Standard
30572 \begin_inset Newline newline
30577 @addtoreset{equation}{section}
30578 \begin_inset Newline newline
30586 \begin_layout Standard
30587 In the LaTeX-preamble
30599 can be omitted as they are automatically internally inserted by LyX.
30602 \begin_layout Standard
30617 \begin_layout Plain Layout
30622 is part of the LaTeX-package
30627 \begin_inset Index idx
30630 \begin_layout Plain Layout
30631 Packages ! carlisle
30636 that is part of every LaTeX standard installation.
30642 \begin_inset Index idx
30645 \begin_layout Plain Layout
30646 Packages ! remreset
30651 has to be loaded in the LaTeX-preamble with the line
30654 \begin_layout Standard
30659 usepackage{remreset}
30662 \begin_layout Standard
30670 \begin_inset Index idx
30673 \begin_layout Plain Layout
30678 \begin_layout Plain Layout
30689 \begin_layout Plain Layout
30702 \begin_layout Plain Layout
30713 \begin_layout Plain Layout
30725 can be used with the same scheme as
30734 \begin_layout Standard
30735 \begin_inset VSpace bigskip
30738 Sometimes formulas should be numbered in the following form:
30741 \begin_layout Standard
30744 (section number.formula number)
30747 \begin_layout Standard
30748 The formula number should start with every section with
30749 \begin_inset Quotes eld
30753 \begin_inset Quotes erd
30759 \begin_layout Standard
30760 For this case there is the command
30767 \begin_inset Index idx
30770 \begin_layout Plain Layout
30778 , which is used with the following scheme:
30781 \begin_layout Standard
30786 numberwithin{counter}{sectioning}
30789 \begin_layout Standard
30790 Counter denotes what kind of numbering is affected, sectioning denotes what
30791 number is before the dot.
30794 \begin_layout Standard
30795 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30798 \begin_layout Standard
30803 numberwithin{equation}{section}
30806 \begin_layout Standard
30807 This is the result:
30811 \begin_layout Plain Layout
30815 numberwithin{equation}{section}
30821 \begin_inset Formula \begin{equation}
30822 A+B=C\end{equation}
30829 \begin_layout Standard
30831 \begin_inset space \thinspace{}
30835 \begin_inset space \space{}
30838 tables so that the number of the part is the sectioning,
30839 \begin_inset Newline newline
30846 numberwithin{table}{part}
30851 \begin_layout Standard
30852 To go back to the standard numbering or to prevent this kind of numbering
30853 when it is defined by the document class, the following command is inserted
30854 as TeX-Code or to the LaTeX-preamble:
30857 \begin_layout Standard
30867 \begin_inset Index idx
30870 \begin_layout Plain Layout
30884 \begin_layout Plain Layout
30900 \begin_inset Newline newline
30908 \begin_inset Newline newline
30920 \begin_layout Standard
30927 uses internally the command
30933 , described above, that also needs to be reverted.
30937 \begin_layout Plain Layout
30944 \begin_layout Plain Layout
30948 @removefromreset{equation}{section}
30951 \begin_layout Plain Layout
30963 \begin_layout Subsection
30964 Numbering with Roman Numbers and Letters
30965 \begin_inset Index idx
30968 \begin_layout Plain Layout
30969 Formula numbering ! with letters
30975 \begin_inset Index idx
30978 \begin_layout Plain Layout
30979 Formula numbering ! with Roman numbers
30987 \begin_layout Standard
30988 Formulas can also be numbered with Roman numbers and Latin letters.
30989 To number for example with small Roman numbers, the command
30992 \begin_layout Standard
31004 \begin_layout Standard
31005 is inserted before the formula in TeX-mode.
31013 \begin_inset Index idx
31016 \begin_layout Plain Layout
31024 redefines the predefined command
31040 \begin_layout Plain Layout
31047 has the same scheme like the command
31053 that is described in
31054 \begin_inset CommandInset ref
31056 reference "sub:The-Command-newcommand"
31069 is the formula counter.
31076 is used as prefix for a counter, the value of the counter is output as
31078 When a formula is numbered, LaTeX sets internally the command
31084 behind the formula.
31090 \begin_inset Index idx
31093 \begin_layout Plain Layout
31103 outputs the counter as small Roman number.
31106 \begin_layout Standard
31107 All formulas behind the command
31117 are now numbered Roman.
31118 To switch to numbering with big Roman numbers, the command is inserted
31132 \begin_inset Index idx
31135 \begin_layout Plain Layout
31147 \begin_inset Quotes eld
31151 \begin_inset Quotes erd
31154 with small Latin letters there is the command
31161 \begin_inset Index idx
31164 \begin_layout Plain Layout
31172 , for big ones there is the command
31179 \begin_inset Index idx
31182 \begin_layout Plain Layout
31195 \begin_layout Standard
31196 \begin_inset Note Greyedout
31199 \begin_layout Plain Layout
31204 Only maximal 26 formulas can be numbered with Latin letters in one document.
31212 \begin_layout Standard
31216 \begin_layout Plain Layout
31232 \begin_layout Standard
31233 \begin_inset Formula \begin{equation}
31234 A=\textrm{small roman}\end{equation}
31242 \begin_layout Plain Layout
31256 \begin_inset Formula \begin{equation}
31257 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
31265 \begin_layout Plain Layout
31279 \begin_inset Formula \begin{equation}
31280 C=\textrm{small Latin}\end{equation}
31288 \begin_layout Plain Layout
31302 \begin_inset Formula \begin{equation}
31303 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
31310 \begin_layout Standard
31311 To switch back to the default numbering, insert the command:
31314 \begin_layout Standard
31324 \begin_inset Index idx
31327 \begin_layout Plain Layout
31338 \begin_layout Standard
31342 \begin_layout Plain Layout
31356 \begin_inset Formula \begin{equation}
31357 E=\textrm{Arabic}\end{equation}
31364 \begin_layout Standard
31365 \begin_inset VSpace medskip
31368 As you see, formulas are numbered serially independent from the numbering
31370 When then numbering should start with
31371 \begin_inset Quotes eld
31375 \begin_inset Quotes erd
31378 when the style is changed, new equation counters have to be defined.
31379 A description about this can be found in the file
31380 \begin_inset CommandInset href
31382 name "Formula-numbering.lyx"
31383 target "run:Formula-numbering.lyx"
31390 \begin_layout Section
31391 Chemical Symbols and Equations
31392 \begin_inset CommandInset label
31394 name "sub:Chemical-Symbols-and"
31399 \begin_inset Index idx
31402 \begin_layout Plain Layout
31403 Chemical characters ! Symbols
31409 \begin_inset Index idx
31412 \begin_layout Plain Layout
31419 \begin_inset Index idx
31422 \begin_layout Plain Layout
31431 \begin_layout Standard
31432 An example text from chemistry:
31435 \begin_layout Quote
31437 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31440 -ion reacts with two
31441 \begin_inset Formula $\mathrm{Na^{+}}$
31444 -ions to sodium sulfate
31445 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31449 The chemical equation for this is:
31450 \begin_inset Formula \begin{equation}
31451 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
31458 \begin_layout Standard
31459 This chemical equation can directly be created as formula.
31460 To avoid that the symbols appear italic, everything is highlighted and
31461 changed by the shortcut
31467 to the upright font style.
31471 \begin_layout Plain Layout
31477 \begin_inset CommandInset ref
31479 reference "sub:Font-Styles"
31491 \begin_layout Standard
31492 A more convenient way to typeset chemical formulas is to use the command
31500 \begin_inset Index idx
31503 \begin_layout Plain Layout
31511 that is available when the LaTeX-package
31516 \begin_inset Index idx
31519 \begin_layout Plain Layout
31532 to a formula a new blue box appears where chemical formulas can be inserted
31533 in an intuitive way.
31536 \begin_layout Standard
31538 \begin_inset Tabular
31539 <lyxtabular version="3" rows="9" columns="2">
31540 <features tabularvalignment="middle">
31541 <column alignment="center" valignment="top" width="0">
31542 <column alignment="center" valignment="top" width="0">
31544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31547 \begin_layout Plain Layout
31553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31556 \begin_layout Plain Layout
31558 \begin_inset Note Note
31561 \begin_layout Plain Layout
31568 is only used as spacer.
31580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31583 \begin_layout Plain Layout
31590 \begin_layout Plain Layout
31604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31607 \begin_layout Plain Layout
31608 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31621 \begin_layout Plain Layout
31628 \begin_layout Plain Layout
31642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31645 \begin_layout Plain Layout
31646 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31659 \begin_layout Plain Layout
31666 \begin_layout Plain Layout
31680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31683 \begin_layout Plain Layout
31684 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31697 \begin_layout Plain Layout
31704 \begin_layout Plain Layout
31718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31721 \begin_layout Plain Layout
31722 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31735 \begin_layout Plain Layout
31742 \begin_layout Plain Layout
31757 \begin_layout Plain Layout
31772 \begin_layout Plain Layout
31786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31789 \begin_layout Plain Layout
31790 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31803 \begin_layout Plain Layout
31810 \begin_layout Plain Layout
31820 \begin_inset Formula $\downarrow$
31824 \begin_inset Formula $\to$
31832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31835 \begin_layout Plain Layout
31836 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31849 \begin_layout Plain Layout
31856 \begin_layout Plain Layout
31869 \begin_layout Plain Layout
31882 \begin_layout Plain Layout
31895 \begin_layout Plain Layout
31908 \begin_layout Plain Layout
31922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31925 \begin_layout Plain Layout
31926 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
31936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31939 \begin_layout Plain Layout
31946 \begin_layout Plain Layout
31959 \begin_layout Plain Layout
31972 \begin_layout Plain Layout
31985 \begin_layout Plain Layout
32002 \begin_layout Plain Layout
32016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32019 \begin_layout Plain Layout
32020 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32036 \begin_layout Standard
32037 \begin_inset Note Greyedout
32040 \begin_layout Plain Layout
32045 Inserting a formula to a
32051 box will lead to LaTeX errors.
32052 In this case TeX code has to be used like for
32066 \begin_layout Plain Layout
32087 \begin_layout Standard
32094 the command for equation
32095 \begin_inset space ~
32099 \begin_inset CommandInset ref
32101 reference "eq:chem-reaction"
32106 \begin_inset Newline newline
32117 \begin_layout Plain Layout
32130 \begin_layout Plain Layout
32143 \begin_layout Plain Layout
32156 \begin_layout Plain Layout
32169 \begin_layout Plain Layout
32182 \begin_layout Plain Layout
32194 \begin_layout Standard
32195 To create multiline chemical equations first a multiline formula is created
32197 \begin_inset CommandInset ref
32199 reference "sec:Multiline-Formulas"
32204 Afterwards the command
32210 is used in every small blue box of the formula.
32212 \begin_inset CommandInset ref
32214 reference "eq:TEOS-reaction-1"
32219 \begin_inset CommandInset ref
32221 reference "eq:TEOS-reaction-2"
32225 are an example of a multi-stage chemical reaction where every equation
32226 has its own number.
32227 \begin_inset Formula \begin{eqnarray}
32228 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32229 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32237 \begin_layout Standard
32248 package provides the command
32255 \begin_inset Index idx
32258 \begin_layout Plain Layout
32266 that has to be used for special cases.
32267 For more information about
32273 and more examples have a look at the documentation of
32278 \begin_inset CommandInset citation
32287 \begin_layout Standard
32288 \begin_inset Newpage newpage
32294 \begin_layout Section
32298 \begin_layout Standard
32299 LyX supports two types of commutative diagrams:
32307 that are explained in the following.
32310 \begin_layout Subsection
32312 \begin_inset Index idx
32315 \begin_layout Plain Layout
32324 \begin_layout Standard
32325 Diagrams of this type visualize relations by vertical and horizontal lines
32327 \begin_inset Formula \[
32328 \begin{CD}A@>>>B@>>>C\\
32338 \begin_layout Standard
32339 To get them, the command
32344 \begin_inset Index idx
32347 \begin_layout Plain Layout
32357 is inserted to a formula.
32358 A blue box appears with two dashed lines where further commands can be
32363 arg "newline-insert newline"
32366 a new line is created.
32367 Horizontal relations are inserted in odd, vertical in even formula lines.
32370 \begin_layout Standard
32371 To create the relations there are the following commands:
32374 \begin_layout Itemize
32379 creates a left arrow,
32390 \begin_layout Itemize
32395 creates an up arrow,
32403 a vertical equal sign
32406 \begin_layout Itemize
32412 is a placeholder for non-existent relations
32415 \begin_layout Standard
32416 All arrows can be labeled as follows:
32419 \begin_layout Itemize
32420 Is text inserted between the first and second < or >, resp., it is placed
32422 When it is inserted between the second and third one, it appears under
32426 \begin_layout Itemize
32427 When text for vertical arrows is inserted between the first and second A
32428 or V, resp., it is placed left beside the arrow.
32429 When it is inserted between the second and third one, it appears right
32431 If the text contains an A or V, these letters must be set into a TeX-brace.
32434 \begin_layout Standard
32435 As example a diagram with all possible relations:
32438 \begin_layout Standard
32439 \begin_inset Formula \[
32440 \begin{CD}A@>j>>B@>>k>C@=F\\
32450 \begin_layout Standard
32451 The command for this is:
32452 \begin_inset Newline newline
32463 \begin_layout Plain Layout
32472 A@>j>>B@>>k>C@=F Ctrl+Return
32473 \begin_inset Newline newline
32477 \begin_inset Phantom HPhantom
32480 \begin_layout Plain Layout
32489 \begin_layout Plain Layout
32508 \begin_inset Formula $\to$
32514 \begin_inset Newline newline
32518 \begin_inset Phantom HPhantom
32521 \begin_layout Plain Layout
32530 \begin_layout Plain Layout
32547 \begin_layout Subsection
32549 \begin_inset Index idx
32552 \begin_layout Plain Layout
32553 Diagrams ! xymatrix
32561 \begin_layout Standard
32562 To be able to use xymatrices, the LaTeX-package
32567 A xymatrix is created by inserting the command
32574 Then you are able to add new matrix columns and rows like for normal matrices,
32576 \begin_inset CommandInset ref
32578 reference "sec:Matrices"
32585 \begin_layout Standard
32586 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32588 All possibilities to create commutative diagrams and decorations are explained
32593 that you find in the menu
32595 Help\SpecialChar \menuseparator
32597 \begin_inset space ~
32605 \begin_layout Subsection
32611 \begin_inset Index idx
32614 \begin_layout Plain Layout
32623 \begin_layout Standard
32628 -diagrams, the LaTeX-package
32637 -diagram is created by inserting the command
32644 Then you are able to add new matrix columns and rows like for normal matrices,
32646 \begin_inset CommandInset ref
32648 reference "sec:Matrices"
32655 \begin_layout Standard
32656 Examples how to create
32660 diagrams in LyX is given in the
32662 Feynman-diagram manual
32664 that you find in the menu
32666 Help\SpecialChar \menuseparator
32668 \begin_inset space ~
32676 \begin_layout Section
32677 User-defined Commands
32678 \begin_inset Index idx
32681 \begin_layout Plain Layout
32682 User-defined commands
32690 \begin_layout Standard
32691 \begin_inset Note Greyedout
32694 \begin_layout Plain Layout
32699 The names of user-defined commands and macros may only consist of Latin
32708 \begin_layout Subsection
32712 \begin_inset CommandInset label
32714 name "sub:The-Command-newcommand"
32719 \begin_inset Index idx
32722 \begin_layout Plain Layout
32723 User-defined commands !
32731 \begin_inset Index idx
32734 \begin_layout Plain Layout
32745 \begin_layout Standard
32746 Many LaTeX-commands are too long to be used frequently.
32747 But it is possible to define with the command
32753 new shorter commands.
32756 \begin_layout Standard
32757 The command scheme of
32766 \begin_layout Standard
32771 newcommand{new command name}[number of arguments][optional
32776 \begin_inset Newline newline
32780 \begin_inset Phantom HPhantom
32783 \begin_layout Plain Layout
32793 {command definition}
32796 \begin_layout Standard
32797 \begin_inset Note Greyedout
32800 \begin_layout Plain Layout
32805 Assure that the name of the new command is not already used in your document
32806 or by LaTeX-packages that you use.
32807 When you for example define the command
32819 , you get an error message because
32825 is already defined as command for
32826 \begin_inset Quotes eld
32830 \begin_inset Formula $\le$
32834 \begin_inset Quotes erd
32845 \begin_layout Standard
32846 The number of arguments is an integer in the range 0
32847 \begin_inset space \thinspace{}
32851 \begin_inset space \thinspace{}
32854 9 and specifies how many arguments the new command should have.
32855 With the optional value a value for an optional argument can be predefined.
32856 When this is done, the
32864 rgument of the new command is automatically an optional one.
32867 \begin_layout Standard
32868 Here are some examples:
32871 \begin_layout Itemize
32872 To define the command
32884 , the LaTeX-preamble line is:
32885 \begin_inset VSpace medskip
32889 \begin_inset Newline newline
32903 \begin_layout Itemize
32904 To define the command
32916 , the argument (that should be underlined) must be taken into account.
32917 For this the preamble line is:
32918 \begin_inset VSpace medskip
32922 \begin_inset Newline newline
32936 \begin_inset VSpace medskip
32940 \begin_inset Newline newline
32947 acts as argument placeholder, the
32951 behind it denotes that it is the placeholder for the first argument.
32954 \begin_layout Itemize
32962 \begin_inset space \thinspace{}
32966 \begin_inset space \space{}
32976 \begin_inset VSpace medskip
32980 \begin_inset Newline newline
32991 framebox#1#2{$#3$}}
32994 \begin_inset VSpace medskip
32998 \begin_inset Newline newline
33001 The two Dollar signs creates the extra formula needed for
33008 \begin_inset CommandInset ref
33010 reference "sub:Boxes-with-Frame"
33017 \begin_layout Itemize
33018 To create a new command for
33024 where the color for the box needn't to be specified, the argument for the
33025 color is defined optional:
33026 \begin_inset VSpace medskip
33030 \begin_inset Newline newline
33041 fcolorbox{#2}{#1}{$#3$}}
33044 \begin_inset VSpace medskip
33048 \begin_inset Newline newline
33051 When the color is not specified when using
33057 , the predefined color
33064 \begin_layout Standard
33065 A test of the new defined commands:
33068 \begin_layout Standard
33070 \begin_inset Tabular
33071 <lyxtabular version="3" rows="6" columns="2">
33072 <features tabularvalignment="middle">
33073 <column alignment="center" valignment="top" width="0">
33074 <column alignment="center" valignment="top" width="0">
33076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33079 \begin_layout Plain Layout
33085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33088 \begin_layout Plain Layout
33090 \begin_inset Note Note
33093 \begin_layout Plain Layout
33100 is only used as spacer.
33112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33115 \begin_layout Plain Layout
33122 \begin_layout Plain Layout
33136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33139 \begin_layout Plain Layout
33140 \begin_inset Formula $A\gr B$
33150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33153 \begin_layout Plain Layout
33161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33164 \begin_layout Plain Layout
33165 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33178 \begin_layout Plain Layout
33182 \begin_inset Formula $\to$
33188 \begin_inset Formula $\to$
33199 \begin_layout Plain Layout
33213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33216 \begin_layout Plain Layout
33217 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33230 \begin_layout Plain Layout
33234 \begin_inset Formula $\to$
33245 \begin_layout Plain Layout
33259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33262 \begin_layout Plain Layout
33263 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33276 \begin_layout Plain Layout
33282 \begin_inset Formula $\to$
33293 \begin_layout Plain Layout
33307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33310 \begin_layout Plain Layout
33311 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33327 \begin_layout Subsection
33329 \begin_inset Index idx
33332 \begin_layout Plain Layout
33333 User-defined commands! Math macros
33339 \begin_inset Index idx
33342 \begin_layout Plain Layout
33351 \begin_layout Standard
33352 User-defined commands are especially convenient for complex expressions.
33353 When you are for example dealing in a document with quadratic equations,
33354 the same solution type occurs several times.
33355 The general form of a quadratic equation is
33356 \begin_inset Formula \[
33357 0=\lambda^{2}+p\lambda+q\]
33361 The general form of the solution is
33362 \begin_inset Formula \[
33363 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
33370 \begin_layout Standard
33371 To define a command for the solution formula where only the three parameters
33373 \begin_inset Formula $\lambda$
33377 \begin_inset Formula $p$
33381 \begin_inset Formula $q$
33384 need to be specified and the index of
33385 \begin_inset Formula $\lambda$
33388 can be given optionally, the LaTeX-preamble line is
33389 \begin_inset Newline newline
33405 \begin_inset Newline newline
33409 \begin_inset Phantom HPhantom
33412 \begin_layout Plain Layout
33426 frac{#3^{2}}{4}-#4}}
33429 \begin_layout Standard
33430 To create with this the solution formula, the command
33431 \begin_inset Newline newline
33441 \begin_inset Formula $\to$
33447 \begin_inset Formula $\to$
33454 is inserted to a formula
33459 \begin_layout Standard
33460 The definition of the new command is unintuitive because one has to know
33461 the schemes of all used LaTeX commands, e.
33462 \begin_inset space \thinspace{}
33466 \begin_inset space \space{}
33469 that a fraction is inserted in LaTeX as
33473 frac{numerator}{denominator}
33476 Furthermore one can easily forget a brace in the definition and cannot
33477 see in LyX what the new command is doing.
33478 To avoid these problems LyX offers the possibility to use math macros instead
33488 \begin_layout Standard
33489 A math macro is created by using the menu
33491 Insert\SpecialChar \menuseparator
33492 Math\SpecialChar \menuseparator
33495 or the toolbar button
33496 \begin_inset Graphics
33497 filename ../images/math-macro_newmacroname_newcommand.png
33503 The math macro toolbar appears together with the following box where the
33505 \begin_inset Newline newline
33509 \begin_inset space \hspace*{\fill}
33513 \begin_inset Graphics
33514 filename clipart/macrobox.png
33519 \begin_inset space \hspace*{\fill}
33523 \begin_inset Newline newline
33527 \begin_inset FormulaMacro
33528 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33533 newmacroname is the default name of the macro that should be changed to
33534 something sensible.
33535 The wanted formula is inserted in the first blue box.
33536 An argument placeholder is inserted with the command
33543 \begin_inset space \thinspace{}
33547 \begin_inset space \space{}
33556 or by using the macro toolbar button
33557 \begin_inset Graphics
33558 filename ../images/math-macro-add-param.png
33564 Argument placeholders are displayed red.
33565 Maximum 9 arguments are possible.
33566 Optional arguments are created with the toolbar button
33567 \begin_inset Graphics
33568 filename ../images/math-macro-add-optional-param.png
33574 The first non-optional argument can be transformed to an optional one with
33576 \begin_inset Graphics
33577 filename ../images/math-macro-make-optional.png
33583 In the second blue box the appearance of the macro in LyX can be defined.
33584 Normally you want to see it as it is defined, so the box is kept empty.
33585 But when you have created a macro that needs lot of space on the screen,
33586 you can insert in the box for example
33587 \begin_inset Newline newline
33617 \begin_inset Newline newline
33622 For the macro only the arguments with the macro name in front of them will
33623 then be displayed in LyX, leading to a better overview.
33624 The formula appears in the output as defined in the first box.
33625 \begin_inset Newline newline
33628 The appearance of macros in formulas can furthermore be changed for single
33629 macros by setting the cursor in the macro and using the menu
33631 View\SpecialChar \menuseparator
33633 \begin_inset space ~
33637 \begin_inset space ~
33645 \begin_layout Standard
33646 To use a macro, the macro name is inserted as command to a formula, in our
33654 Our macro looks in LyX like this:
33655 \begin_inset Newline newline
33659 \begin_inset space \hspace*{\fill}
33663 \begin_inset Graphics
33664 filename clipart/macrouse.png
33669 \begin_inset space \hspace*{\fill}
33673 \begin_inset Newline newline
33676 Here is our macro example with the arguments
33677 \begin_inset Formula $x$
33681 \begin_inset Formula $\ln(x)$
33685 \begin_inset Formula $B$
33691 \begin_layout Standard
33692 \begin_inset Formula \[
33700 \begin_layout Standard
33701 LyX offers in the menu
33703 Tools\SpecialChar \menuseparator
33704 Preferences\SpecialChar \menuseparator
33705 Editing\SpecialChar \menuseparator
33708 different styles to edit macros.
33709 To find the style that suits you the most, choose a style and set the cursor
33710 in a macro formula to see the difference.
33713 \begin_layout Standard
33714 A math macro is transformed internally to a
33720 command when exporting the document.
33727 command is not placed in the LaTeX-preamble, therefore macros can only
33728 be used in formulas that are in the document below the macro definition
33732 \begin_layout Standard
33733 Math macros can also be directly be created from a
33740 When writing for example the command
33743 \begin_inset Newline newline
33752 xleftarrow[#2]{#1}}
33753 \begin_inset Newline newline
33758 in LyX as normal text, highlighting it completely and using then the shortcut
33763 , the command will be transformed to a math macro.
33764 Using this method you need to be careful that the
33770 command is typed correctly, otherwise you get a faulty macro leading to
33774 \begin_layout Standard
33775 Math macros currently yet have the problem that further formulas in macro
33776 definitions are handled wrongly.
33777 Therefore the example
33784 \begin_inset CommandInset ref
33786 reference "sub:The-Command-newcommand"
33790 cannot be created as macro.
33793 \begin_layout Standard
33794 When the cursor is in a macro definition box, you will see the macro toolbar
33798 \begin_layout Standard
33799 \begin_inset VSpace defskip
33805 \begin_layout Standard
33806 \begin_inset Graphics
33807 filename clipart/MacroToolbar.png
33812 \begin_inset Index idx
33815 \begin_layout Plain Layout
33824 \begin_layout Standard
33825 \begin_inset VSpace defskip
33831 \begin_layout Standard
33832 The macro toolbar contains from left to right the following buttons:
33835 \begin_layout Standard
33836 \begin_inset VSpace defskip
33842 \begin_layout Standard
33843 \begin_inset Tabular
33844 <lyxtabular version="3" rows="9" columns="2">
33845 <features islongtable="true" longtabularalignment="center">
33846 <column alignment="left" valignment="top" width="0">
33847 <column alignment="left" valignment="top" width="85col%">
33848 <row interlinespace="2.5mm">
33849 <cell alignment="center" valignment="top" usebox="none">
33852 \begin_layout Plain Layout
33853 \begin_inset Graphics
33854 filename ../images/math-macro-remove-param.png
33855 BoundingBox 0bp 5bp 20bp 25bp
33856 rotateOrigin center
33865 <cell alignment="center" valignment="top" usebox="none">
33868 \begin_layout Plain Layout
33871 Edit\SpecialChar \menuseparator
33872 Math\SpecialChar \menuseparator
33874 \begin_inset space ~
33877 Definition\SpecialChar \menuseparator
33878 Remove Last Argument
33884 <row interlinespace="2.5mm">
33885 <cell alignment="center" valignment="top" usebox="none">
33888 \begin_layout Plain Layout
33889 \begin_inset Graphics
33890 filename ../images/math-macro-add-param.png
33891 BoundingBox 0bp 5bp 20bp 25bp
33892 rotateOrigin center
33901 <cell alignment="center" valignment="top" usebox="none">
33904 \begin_layout Plain Layout
33907 Edit\SpecialChar \menuseparator
33908 Math\SpecialChar \menuseparator
33910 \begin_inset space ~
33913 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-optional.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 First Non-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
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-make-nonoptional.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 Make Last Optional into
34010 \begin_inset Newline newline
34014 \begin_inset Phantom HPhantom
34017 \begin_layout Plain Layout
34020 Edit\SpecialChar \menuseparator
34021 Math\SpecialChar \menuseparator
34023 \begin_inset space ~
34026 Definition\SpecialChar \menuseparator
34032 Non-Optional Argument
34038 <row interlinespace="2.5mm">
34039 <cell alignment="center" valignment="top" usebox="none">
34042 \begin_layout Plain Layout
34043 \begin_inset Graphics
34044 filename ../images/math-macro-remove-optional-param.png
34045 BoundingBox 0bp 5bp 20bp 25bp
34046 rotateOrigin center
34055 <cell alignment="center" valignment="top" usebox="none">
34058 \begin_layout Plain Layout
34061 Edit\SpecialChar \menuseparator
34062 Math\SpecialChar \menuseparator
34064 \begin_inset space ~
34067 Definition\SpecialChar \menuseparator
34068 Remove Optional Argument
34074 <row interlinespace="2.5mm">
34075 <cell alignment="center" valignment="top" usebox="none">
34078 \begin_layout Plain Layout
34079 \begin_inset Graphics
34080 filename ../images/math-macro-add-optional-param.png
34081 BoundingBox 0bp 5bp 20bp 25bp
34082 rotateOrigin center
34091 <cell alignment="center" valignment="top" usebox="none">
34094 \begin_layout Plain Layout
34097 Edit\SpecialChar \menuseparator
34098 Math\SpecialChar \menuseparator
34100 \begin_inset space ~
34103 Definition\SpecialChar \menuseparator
34104 Insert Optional Argument
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-remove-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
34140 Remove Last Argument
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 Spitting Out To 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-append-greedy-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
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
34228 <row interlinespace="2.5mm">
34229 <cell alignment="center" valignment="top" usebox="none">
34232 \begin_layout Plain Layout
34233 \begin_inset Graphics
34234 filename ../images/math-macro-add-greedy-optional-param.png
34235 BoundingBox 0bp 5bp 20bp 25bp
34236 rotateOrigin center
34245 <cell alignment="center" valignment="top" usebox="none">
34248 \begin_layout Plain Layout
34251 Edit\SpecialChar \menuseparator
34252 Math\SpecialChar \menuseparator
34254 \begin_inset space ~
34257 Definition\SpecialChar \menuseparator
34258 Append Optional Argument
34259 \begin_inset Newline newline
34263 \begin_inset Phantom HPhantom
34266 \begin_layout Plain Layout
34269 Edit\SpecialChar \menuseparator
34270 Math\SpecialChar \menuseparator
34272 \begin_inset space ~
34275 Definition\SpecialChar \menuseparator
34281 Eating From The Right
34294 \begin_layout Standard
34295 \begin_inset Newpage newpage
34301 \begin_layout Section
34303 \begin_inset Index idx
34306 \begin_layout Plain Layout
34315 \begin_layout Subsection
34317 \begin_inset Index idx
34320 \begin_layout Plain Layout
34329 \begin_layout Standard
34330 Negative numbers often look ugly in formulas because the minus sign before
34331 the number is set with the same length as the minus operator sign.
34332 When writing the negative number in normal text, the minus sign appears
34336 \begin_layout Standard
34337 Thus, the problem disappears when converting the minus sign to mathematical
34341 \begin_layout Standard
34342 An example to visualize the problem:
34345 \begin_layout Standard
34347 \begin_inset Tabular
34348 <lyxtabular version="3" rows="3" columns="2">
34349 <features tabularvalignment="middle">
34350 <column alignment="right" valignment="top" width="0">
34351 <column alignment="left" valignment="top" width="0">
34353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34356 \begin_layout Plain Layout
34362 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34365 \begin_layout Plain Layout
34373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34376 \begin_layout Plain Layout
34382 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34385 \begin_layout Plain Layout
34386 \begin_inset Formula $x=-2$
34396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34399 \begin_layout Plain Layout
34405 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34408 \begin_layout Plain Layout
34409 \begin_inset Formula $x=\textrm{-}2$
34425 \begin_layout Subsection
34426 Comma as decimal Separator
34427 \begin_inset Index idx
34430 \begin_layout Plain Layout
34439 \begin_layout Standard
34440 In LaTeX a comma inside a formula is used, according to the English convention,
34441 as number group separator.
34442 So there will be space added behind all commas in formulas.
34445 \begin_layout Standard
34446 To avoid this, the comma is highlighted and changed to mathematical text
34456 \begin_layout Standard
34457 To use all formula commas in the document as decimal separator, the file
34466 \begin_layout Plain Layout
34471 is part of the LaTeX-package
34476 \begin_inset Index idx
34479 \begin_layout Plain Layout
34484 \begin_layout Plain Layout
34504 \begin_inset Index idx
34507 \begin_layout Plain Layout
34513 is loaded with the LaTeX-preamble line
34516 \begin_layout Standard
34524 \begin_layout Subsection
34526 \begin_inset CommandInset label
34528 name "sub:Physical-Vectors"
34533 \begin_inset Index idx
34536 \begin_layout Plain Layout
34545 \begin_layout Standard
34546 Predefined vectors are offered by the LaTeX-package
34551 \begin_inset Index idx
34554 \begin_layout Plain Layout
34560 that is loaded with the LaTeX-preamble line
34563 \begin_layout Standard
34571 \begin_layout Standard
34575 \begin_layout Plain Layout
34585 \begin_inset Note Note
34588 \begin_layout Plain Layout
34589 The following table will only be displayed when the LaTeX-package
34601 \begin_layout Standard
34602 The following commands are defined:
34605 \begin_layout Standard
34607 \begin_inset Tabular
34608 <lyxtabular version="3" rows="4" columns="2">
34609 <features tabularvalignment="middle">
34610 <column alignment="center" valignment="top" width="0">
34611 <column alignment="center" valignment="top" width="0">
34613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34616 \begin_layout Plain Layout
34622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34625 \begin_layout Plain Layout
34633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34636 \begin_layout Plain Layout
34646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34649 \begin_layout Plain Layout
34650 \begin_inset Formula $\Bra{\psi}$
34660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34663 \begin_layout Plain Layout
34673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34676 \begin_layout Plain Layout
34677 \begin_inset Formula $\Ket{\psi}$
34687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34690 \begin_layout Plain Layout
34702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34705 \begin_layout Plain Layout
34706 \begin_inset Formula $\Braket{\psi|\phi}$
34722 \begin_layout Standard
34729 assures that all vertical bars are set in the size of the surrounding brackets:
34730 \begin_inset Formula \[
34731 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
34739 \begin_layout Plain Layout
34749 \begin_inset Note Note
34752 \begin_layout Plain Layout
34753 The following will be displayed when the LaTeX-package
34765 \begin_layout Standard
34766 You need to install the LaTeX-package
34770 to see the rest of this subsection in the output.
34773 \begin_layout Standard
34777 \begin_layout Plain Layout
34789 \begin_layout Standard
34796 can also be achieved using the command
34802 , that is described in
34803 \begin_inset CommandInset ref
34805 reference "sub:Automatic-Bracket-Size"
34812 \begin_layout Subsection
34813 Self-defined Fractions
34814 \begin_inset CommandInset label
34816 name "sub:Self-defined-Fractions"
34821 \begin_inset Index idx
34824 \begin_layout Plain Layout
34825 Fractions ! self-defined
34833 \begin_layout Standard
34834 To define custom commands for fractions, the command
34841 \begin_inset Index idx
34844 \begin_layout Plain Layout
34852 is used in the following scheme:
34855 \begin_layout Standard
34868 bracket}{fraction bar thickness}{style}
34869 \begin_inset Newline newline
34873 \begin_inset Phantom HPhantom
34876 \begin_layout Plain Layout
34886 {numerator}{denominator}
34889 \begin_layout Standard
34890 The style is a number in the range of 0
34891 \begin_inset space \thinspace{}
34895 \begin_inset space \thinspace{}
34901 \begin_layout Standard
34903 \begin_inset Tabular
34904 <lyxtabular version="3" rows="5" columns="2">
34905 <features tabularvalignment="middle">
34906 <column alignment="center" valignment="top" width="0">
34907 <column alignment="center" valignment="top" width="0">
34909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34912 \begin_layout Plain Layout
34918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34921 \begin_layout Plain Layout
34929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34932 \begin_layout Plain Layout
34938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34941 \begin_layout Plain Layout
34942 display style formula
34949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34952 \begin_layout Plain Layout
34958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34961 \begin_layout Plain Layout
34969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34972 \begin_layout Plain Layout
34978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34981 \begin_layout Plain Layout
34989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34992 \begin_layout Plain Layout
34998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35001 \begin_layout Plain Layout
35015 \begin_layout Standard
35016 When no style is given, the size is adjusted to the surrounding environment
35017 like for the command
35026 \begin_layout Standard
35027 When no fraction bar thickness is given, the predefined value of 0.4
35028 \begin_inset space \thinspace{}
35034 \begin_layout Standard
35035 \begin_inset VSpace medskip
35038 For example, the commands
35051 \begin_inset CommandInset ref
35053 reference "sub:Fractions"
35057 are defined with the commands
35060 \begin_layout Standard
35069 genfrac{}{}{}{0}{#1}{#2}}
35072 \begin_layout Standard
35076 \begin_layout Standard
35085 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35088 \begin_layout Standard
35089 \begin_inset VSpace medskip
35092 To define a fraction where the fraction bar thickness can be given as optional
35093 argument, the following line is inserted to the LaTeX-preamble:
35096 \begin_layout Standard
35105 genfrac{}{}{#1}{}{#2}{#3}}
35108 \begin_layout Standard
35110 \begin_inset Formula \begin{align*}
35111 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35112 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35117 As one can see, the distance of the numerator and the denominator to the
35118 fraction bar is round about three times the bar thickness.
35121 \begin_layout Subsection
35123 \begin_inset Index idx
35126 \begin_layout Plain Layout
35135 \begin_layout Standard
35136 To cancel formulas or formula parts, the LaTeX-package
35141 \begin_inset Index idx
35144 \begin_layout Plain Layout
35150 has to be loaded with the LaTeX-preamble line
35153 \begin_layout Standard
35158 usepackage[samesize]{cancel}
35161 \begin_layout Standard
35165 \begin_layout Plain Layout
35175 \begin_inset Note Note
35178 \begin_layout Plain Layout
35179 The following table will only be displayed when the LaTeX-package
35191 \begin_layout Standard
35192 There are four ways to cancel formulas:
35195 \begin_layout Standard
35197 \begin_inset Tabular
35198 <lyxtabular version="3" rows="5" columns="2">
35199 <features tabularvalignment="middle">
35200 <column alignment="center" valignment="top" width="0">
35201 <column alignment="center" valignment="top" width="0">
35203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35206 \begin_layout Plain Layout
35212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35215 \begin_layout Plain Layout
35217 \begin_inset Note Note
35220 \begin_layout Plain Layout
35227 are used here as spacer.
35239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35242 \begin_layout Plain Layout
35251 \begin_layout Plain Layout
35265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35268 \begin_layout Plain Layout
35269 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35282 \begin_layout Plain Layout
35291 \begin_layout Plain Layout
35305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35308 \begin_layout Plain Layout
35309 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35322 \begin_layout Plain Layout
35331 \begin_layout Plain Layout
35345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35348 \begin_layout Plain Layout
35349 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35362 \begin_layout Plain Layout
35366 \begin_inset Formula $\to$
35377 \begin_layout Plain Layout
35391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35394 \begin_layout Plain Layout
35395 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35411 \begin_layout Standard
35418 is especially suitable to visualize the reduction of fractions within formulas:
35419 \begin_inset Formula \[
35420 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
35427 \begin_layout Standard
35431 \begin_layout Plain Layout
35441 \begin_inset Note Note
35444 \begin_layout Plain Layout
35445 The following will be displayed when the LaTeX-package
35457 \begin_layout Standard
35458 You need to install the LaTeX-package
35462 to see the rest of this subsection in the output.
35465 \begin_layout Standard
35469 \begin_layout Plain Layout
35481 \begin_layout Subsection
35482 Formulas in Section Headings
35483 \begin_inset CommandInset label
35485 name "sub:Formulas-in-Section"
35490 \begin_inset Index idx
35493 \begin_layout Plain Layout
35494 Formula ! in section headings
35502 \begin_layout Standard
35503 When formulas are used in section headings, the following has to be taken
35507 \begin_layout Standard
35508 \begin_inset Note Greyedout
35511 \begin_layout Plain Layout
35517 \begin_inset Index idx
35520 \begin_layout Plain Layout
35521 Packages ! hyperref
35526 support is enabled in the document settings dialog under
35529 \begin_inset space ~
35534 , PDF-bookmarks are created for every section heading in the table of contents.
35535 If a section heading contains formulas, they are incorrectly displayed
35536 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35545 \begin_layout Standard
35546 Both problems can be solved by inserting at the end of the section heading
35547 a short title with the menu
35549 Insert\SpecialChar \menuseparator
35551 \begin_inset space ~
35557 Short titles are used as alternative for multiline section headings to
35558 keep the table of contents clearly arranged.
35559 Only the short title appears in the table of contents and therefore also
35560 in the PDF-bookmark.
35563 \begin_layout Standard
35564 When formulas should be used in the table of contents but
35568 is used, one can use the following command in TeX-mode:
35571 \begin_layout Standard
35576 texorpdfstring{part}{alternative}
35577 \begin_inset Index idx
35580 \begin_layout Plain Layout
35591 \begin_layout Standard
35592 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35593 This can be characters, formulas, footnotes, but also cross-references.
35594 The alternative is used instead of the part for the bookmark.
35597 \begin_layout Standard
35598 Here are two example headings:
35599 \begin_inset VSpace -3mm
35606 \begin_layout Plain Layout
35618 \begin_layout Subsubsection
35619 Heading without formula in table of contents
35620 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35624 \begin_inset Argument
35627 \begin_layout Plain Layout
35628 Heading without formula in table of contents
35636 \begin_layout Subsubsection
35637 Heading with formula in table of contents
35641 \begin_layout Plain Layout
35651 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35658 \begin_layout Plain Layout
35668 \begin_layout Standard
35672 \begin_layout Plain Layout
35681 In the first heading a short title was used, in the second one
35690 \begin_layout Standard
35691 To get the same formatting as for the other headings, the complete heading
35700 \begin_layout Plain Layout
35702 \begin_inset CommandInset ref
35704 reference "sub:Bold-Formulas"
35716 \begin_layout Subsection
35717 Formulas in multi-column Text
35718 \begin_inset Index idx
35721 \begin_layout Plain Layout
35722 Formula ! in multi-column text
35730 \begin_layout Standard
35731 Formulas in multi-column text are often too wide to fit into a column and
35732 thus need to be set over the whole page width.
35733 This is done by using the LaTeX-package
35741 \begin_layout Plain Layout
35746 is part of every LaTeX standard installation.
35752 \begin_inset Index idx
35755 \begin_layout Plain Layout
35756 Packages ! multicol
35761 , that is loaded with the LaTeX-preamble line
35764 \begin_layout Standard
35769 usepackage{multicol}
35772 \begin_layout Standard
35773 \begin_inset Note Greyedout
35776 \begin_layout Plain Layout
35777 Note herby that the setting
35780 \begin_inset space ~
35787 Document\SpecialChar \menuseparator
35793 \begin_inset space ~
35813 \begin_layout Standard
35814 Before the multi-column text the command
35817 \begin_layout Standard
35822 begin{multicols}{column number}
35825 \begin_layout Standard
35826 is written in TeX-mode.
35827 The column number is a number in the range of 2
35828 \begin_inset space \thinspace{}
35832 \begin_inset space \thinspace{}
35836 Before the formula the multi-column text is ended by inserting the command
35839 \begin_layout Standard
35847 \begin_layout Standard
35851 \begin_layout Standard
35852 Due to the command some space is automatically added before the formula.
35854 \begin_inset space \thinspace{}
35857 mm vertical space is inserted before the formula.
35858 When the formula style
35864 \begin_layout Plain Layout
35866 \begin_inset CommandInset ref
35868 reference "sec:Formula-Styles"
35880 \begin_inset space \thinspace{}
35883 mm space is inserted instead.
35886 \begin_layout Standard
35887 As example a multi-column text with a displayed formula:
35890 \begin_layout Standard
35896 \begin_layout Plain Layout
35900 begin{multicols}{2}
35905 Das Spektrum wird fouriertransformiert.
35906 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35907 , Lösungsmittel) zu trennen.
35908 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35909 nun das Aussehen des Ausgangssignals.
35910 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35911 über alle Phasen integrieren muss.
35913 \begin_inset Formula $S$
35916 unser normiertes Ausgangssignal und
35917 \begin_inset Formula $P$
35920 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35924 \begin_layout Plain Layout
35934 \begin_inset VSpace -6mm
35938 \begin_inset Formula \begin{equation}
35939 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
35947 \begin_layout Plain Layout
35951 begin{multicols}{2}
35957 \begin_inset Formula $S_{0}$
35960 das Signal ohne Gradient ist und die Normierungsbedingung
35961 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35965 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35967 \begin_inset Formula $\nicefrac{\pi}{2}$
35971 \begin_inset space \thinspace{}
35974 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35975 das Signal zusätzlich abschwächt.
35976 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35978 \begin_inset Formula $T_{2}$
35984 \begin_layout Standard
35990 \begin_layout Plain Layout
36002 \begin_layout Subsection
36003 Formulas with Description of Variables
36004 \begin_inset Index idx
36007 \begin_layout Plain Layout
36008 Formula ! with description of variables
36016 \begin_layout Standard
36017 To describe variables within a formula, like in formula
36018 \begin_inset CommandInset ref
36020 reference "eq:within"
36029 \begin_inset Formula $n$
36033 \begin_inset space ~
36036 matrix is used with left aligned columns for the
36037 \begin_inset Formula $n$
36044 \begin_layout Plain Layout
36046 \begin_inset CommandInset ref
36048 reference "sec:Matrices"
36057 To set the description in a smaller size, before the matrix e.
36058 \begin_inset space \thinspace{}
36062 \begin_inset space \space{}
36075 \begin_layout Plain Layout
36077 \begin_inset CommandInset ref
36079 reference "sub:Font-Sizes"
36091 \begin_layout Standard
36092 When the formula style
36098 \begin_layout Plain Layout
36100 \begin_inset CommandInset ref
36102 reference "sec:Formula-Styles"
36123 \begin_layout Plain Layout
36130 only works in formulas with the style
36135 \begin_inset CommandInset ref
36137 reference "sub:Variable-Space"
36146 is inserted before and after the matrix to have the same separation of
36147 the matrix from the equation and the side margin.
36150 \begin_layout Standard
36151 When the formula style
36155 is used, the method described in
36156 \begin_inset CommandInset ref
36158 reference "sub:Flalign-Environment"
36162 is used to indent formulas.
36164 \begin_inset CommandInset ref
36166 reference "eq:within"
36170 consists of five columns whereas in the first two columns contain the equation,
36171 the third the matrix and the last one an empty TeX-brace.
36172 \begin_inset Formula \begin{flalign}
36173 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36174 \rho & \textrm{density}\\
36175 V & \textrm{volume}\\
36176 g & \textrm{gravitational acceleration}
36177 \end{array} & & {}\label{eq:within}\end{flalign}
36184 \begin_layout Subsection
36185 Upright small Greek Letters
36186 \begin_inset CommandInset label
36188 name "sub:Upright-small-Greek"
36193 \begin_inset Index idx
36196 \begin_layout Plain Layout
36197 Greek letters ! upright
36205 \begin_layout Standard
36206 Most of the math fonts only provide italic small Greek letters.
36207 But for symbols of elementary particles like pions and neutrinos, upright
36208 Greek letters are needed.
36217 \begin_layout Plain Layout
36222 is part of the LaTeX-package
36227 \begin_inset Index idx
36230 \begin_layout Plain Layout
36235 \begin_layout Plain Layout
36255 \begin_inset Index idx
36258 \begin_layout Plain Layout
36264 that is loaded with the LaTeX-preamble line
36267 \begin_layout Standard
36272 usepackage{upgreek}
36275 \begin_layout Standard
36281 \begin_layout Plain Layout
36291 \begin_inset Note Note
36294 \begin_layout Plain Layout
36295 The following table will only be displayed when the LaTeX-package
36304 They are created when the command for a small Greek letters is started
36310 For example the command
36317 \begin_inset Formula $\uptau$
36323 \begin_layout Standard
36324 With these commands reactions of elementary particles can be typeset:
36325 \begin_inset Formula \[
36326 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
36333 \begin_layout Standard
36334 The upright letters are more bold and wider than the italic ones.
36335 They should therefore not be used for units like
36336 \begin_inset Quotes eld
36340 \begin_inset Quotes erd
36346 \begin_layout Standard
36350 \begin_layout Plain Layout
36360 \begin_inset Note Note
36363 \begin_layout Plain Layout
36364 The following will be displayed when the LaTeX-package
36376 \begin_layout Standard
36377 You need to install the LaTeX-package
36381 to see the rest of this subsection in the output.
36384 \begin_layout Standard
36388 \begin_layout Plain Layout
36400 \begin_layout Subsection
36401 Text Characters in Formulas
36402 \begin_inset CommandInset label
36404 name "sub:Text-Characters-in"
36409 \begin_inset Index idx
36412 \begin_layout Plain Layout
36421 \begin_layout Standard
36422 In some cases you might want to insert text characters directly into formulas.
36423 When for example the centered dot · is often used in formulas like
36424 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36427 , one would have to insert the command
36437 \begin_layout Plain Layout
36439 \begin_inset CommandInset ref
36441 reference "sub:Binary-Operators"
36450 all the time, because this character is defined in all encodings as text
36452 But the encoding can be changed by this LaTeX-preamble line:
36455 \begin_layout Standard
36460 Declare Inputtext{183}{
36470 f\SpecialChar \textcompwordmark{}
36474 \begin_layout Standard
36475 The character encoding (menu
36477 Document\SpecialChar \menuseparator
36478 Settings\SpecialChar \menuseparator
36481 ) specifies what character appears when a keyboard key is pressed.
36482 When the key for the character '·' is pressed, internally the command
36489 But this command is not available in a formula so that you would get LaTeX-erro
36491 With the changed encoding the right command is chosen automatically, depending
36492 on if the character was inserted into a formula or not.
36495 \begin_layout Standard
36496 The encoding of several characters is saved in definition files.
36497 Fore example the encoding
36501 is defined in the file
36505 that is in the installation folder of LaTeX.
36506 Encodings should only be changed via the LaTeX-preamble and not in the
36508 Otherwise own documents could not be edited by other LyX users working
36509 on other computers.
36512 \begin_layout Standard
36513 \begin_inset VSpace medskip
36516 Besides the centered dot, in this document the degree sign ° is defined
36517 with the following LaTeX-preamble line so that it can directly be inserted
36521 \begin_layout Standard
36526 DeclareInputtext{176}{
36536 f\SpecialChar \textcompwordmark{}
36540 \begin_layout Standard
36541 \begin_inset Newpage newpage
36547 \begin_layout Section
36550 \begin_inset Index idx
36553 \begin_layout Plain Layout
36562 \begin_layout Standard
36563 This section is a summary of the most important typographic rules, listed
36568 \begin_layout Plain Layout
36569 This collection was partly taken from the German semi-official dictionary
36571 \begin_inset Quotes eld
36575 \begin_inset Quotes erd
36579 \begin_inset CommandInset citation
36585 that lists some of the ISO rules.
36586 More rules are listed in
36587 \begin_inset CommandInset citation
36601 \begin_layout Itemize
36610 \begin_layout Plain Layout
36611 done with font styles, see
36612 \begin_inset CommandInset ref
36614 reference "sub:Font-Styles"
36623 , no matter if they appear in italic text: 30
36624 \begin_inset space \thinspace{}
36628 \begin_inset Newline newline
36631 Between the value and the unit is the smallest space, see
36632 \begin_inset CommandInset ref
36634 reference "sub:Predefined-Space"
36639 \begin_inset Newline newline
36642 This convention is automatically fulfilled when the command
36649 When it is entered to a formula, two boxes appear.
36650 In the first one the value is inserted, in the second one the unit, and
36652 \begin_inset Formula $\unit[30]{km/h}$
36656 \begin_inset space \thinspace{}
36666 is not a real LaTeX command but the command
36672 , therefore you cannot use it in TeX code.
36675 \begin_layout Itemize
36676 Percent and perthousand signs are set like physical units:
36677 \begin_inset Newline newline
36681 \begin_inset space \thinspace{}
36687 \begin_layout Itemize
36688 The degree sign follows directly on the value: 15°, but not when it is used
36690 \begin_inset space \thinspace{}
36696 \begin_layout Itemize
36697 In numbers with more than four digits the smallest space is inserted before
36698 every third digit to group them:
36708 \begin_inset space \thinspace{}
36712 \begin_inset space \thinspace{}
36718 \begin_layout Itemize
36719 For dimensions like 120×90×40
36720 \begin_inset space \thinspace{}
36723 cm the multiplication sign
36724 \begin_inset Quotes eld
36728 \begin_inset Quotes erd
36732 It is available either via the command
36740 Insert\SpecialChar \menuseparator
36741 Special Character\SpecialChar \menuseparator
36747 \begin_layout Itemize
36748 Functions with names consisting of several letters are set upright to avoid
36750 \begin_inset CommandInset ref
36752 reference "sub:Predefined-Functions"
36759 \begin_layout Itemize
36760 Indices consisting of several letters, are set upright:
36761 \begin_inset Formula $E_{\mathrm{kin}}$
36765 \begin_inset Newline newline
36768 Components of matrices are set italic:
36769 \begin_inset Formula $\hat{H}_{kl}$
36775 \begin_layout Itemize
36776 The differentiation/integration operator 'd', the Euler's number 'e' and
36777 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36781 \begin_layout Itemize
36782 The character that denotes a
36786 transformation is inserted either by the command
36794 \begin_layout Plain Layout
36807 Insert\SpecialChar \menuseparator
36808 Special Character\SpecialChar \menuseparator
36809 Symbols\SpecialChar \menuseparator
36811 \begin_inset space ~
36817 \begin_inset Formula $\mathscr{F}$
36823 \begin_layout Standard
36824 \begin_inset Newpage newpage
36830 \begin_layout Section
36832 \begin_inset Index idx
36835 \begin_layout Plain Layout
36844 \begin_layout Standard
36845 Some characters and symbols can be created with several commands.
36846 Here is a list of the synonym commands:
36849 \begin_layout Standard
36850 \begin_inset VSpace bigskip
36854 \begin_inset space \hfill{}
36858 \begin_inset Tabular
36859 <lyxtabular version="3" rows="12" columns="2">
36860 <features tabularvalignment="middle">
36861 <column alignment="center" valignment="top" width="0pt">
36862 <column alignment="center" valignment="top" width="0pt">
36864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36867 \begin_layout Plain Layout
36873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36876 \begin_layout Plain Layout
36878 \begin_inset Note Note
36881 \begin_layout Plain Layout
36888 is only used as spacer.
36900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36903 \begin_layout Plain Layout
36911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36914 \begin_layout Plain Layout
36918 \begin_layout Plain Layout
36931 \begin_layout Plain Layout
36945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36948 \begin_layout Plain Layout
36956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36959 \begin_layout Plain Layout
36969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36972 \begin_layout Plain Layout
36980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36983 \begin_layout Plain Layout
36993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36996 \begin_layout Plain Layout
37004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37007 \begin_layout Plain Layout
37015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37018 \begin_layout Plain Layout
37026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37029 \begin_layout Plain Layout
37037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37040 \begin_layout Plain Layout
37048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37051 \begin_layout Plain Layout
37061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37064 \begin_layout Plain Layout
37072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37075 \begin_layout Plain Layout
37085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37088 \begin_layout Plain Layout
37096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37099 \begin_layout Plain Layout
37109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37112 \begin_layout Plain Layout
37120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37123 \begin_layout Plain Layout
37133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37136 \begin_layout Plain Layout
37144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37147 \begin_layout Plain Layout
37155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37158 \begin_layout Plain Layout
37166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37169 \begin_layout Plain Layout
37181 \begin_inset space \hfill{}
37185 \begin_inset Tabular
37186 <lyxtabular version="3" rows="12" columns="2">
37187 <features tabularvalignment="middle">
37188 <column alignment="center" valignment="top" width="0pt">
37189 <column alignment="center" valignment="top" width="0pt">
37191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37194 \begin_layout Plain Layout
37200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37203 \begin_layout Plain Layout
37211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37214 \begin_layout Plain Layout
37222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37225 \begin_layout Plain Layout
37237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37240 \begin_layout Plain Layout
37248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37251 \begin_layout Plain Layout
37261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37264 \begin_layout Plain Layout
37272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37275 \begin_layout Plain Layout
37285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37288 \begin_layout Plain Layout
37296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37299 \begin_layout Plain Layout
37307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37310 \begin_layout Plain Layout
37318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37321 \begin_layout Plain Layout
37329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37332 \begin_layout Plain Layout
37340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37343 \begin_layout Plain Layout
37353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37356 \begin_layout Plain Layout
37364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37367 \begin_layout Plain Layout
37377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37380 \begin_layout Plain Layout
37388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37391 \begin_layout Plain Layout
37401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37404 \begin_layout Plain Layout
37412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37415 \begin_layout Plain Layout
37425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37428 \begin_layout Plain Layout
37436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37439 \begin_layout Plain Layout
37449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37452 \begin_layout Plain Layout
37460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37463 \begin_layout Plain Layout
37477 \begin_inset space \hfill{}
37483 \begin_layout Standard
37484 \begin_inset Newpage newpage
37490 \begin_layout Bibliography
37491 \labelwidthstring References
37492 \begin_inset CommandInset bibitem
37493 LatexCommand bibitem
37505 The LaTeX Companion
37508 Addison Wesley, 2004
37511 \begin_layout Bibliography
37512 \labelwidthstring References
37513 \begin_inset CommandInset bibitem
37514 LatexCommand bibitem
37520 \begin_inset CommandInset href
37523 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37527 of LaTeX's math abilities
37530 \begin_layout Bibliography
37531 \labelwidthstring References
37532 \begin_inset CommandInset bibitem
37533 LatexCommand bibitem
37539 \begin_inset CommandInset href
37542 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37550 \begin_layout Plain Layout
37562 \begin_layout Bibliography
37563 \labelwidthstring References
37564 \begin_inset CommandInset bibitem
37565 LatexCommand bibitem
37571 \begin_inset CommandInset href
37574 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37578 of all symbols available with LaTeX-packages
37581 \begin_layout Bibliography
37582 \labelwidthstring References
37583 \begin_inset CommandInset bibitem
37584 LatexCommand bibitem
37590 \begin_inset CommandInset href
37592 name "Documentation"
37593 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37597 of the LaTeX-package
37602 \begin_inset Index idx
37605 \begin_layout Plain Layout
37606 Packages ! hyperref
37614 \begin_layout Bibliography
37615 \labelwidthstring References
37616 \begin_inset CommandInset bibitem
37617 LatexCommand bibitem
37623 \begin_inset CommandInset href
37625 name "Documentation"
37626 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37630 of the LaTeX-package
37635 \begin_inset Index idx
37638 \begin_layout Plain Layout
37647 \begin_layout Bibliography
37648 \labelwidthstring References
37649 \begin_inset CommandInset bibitem
37650 LatexCommand bibitem
37656 \begin_inset CommandInset href
37659 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
37670 \begin_inset CommandInset ref
37672 reference "sub:Operator-Limits"
37677 \begin_inset Index idx
37680 \begin_layout Plain Layout
37691 \begin_layout Bibliography
37692 \labelwidthstring References
37693 \begin_inset CommandInset bibitem
37694 LatexCommand bibitem
37705 Auflage, Duden 2001
37708 \begin_layout Bibliography
37709 \labelwidthstring References
37710 \begin_inset CommandInset bibitem
37711 LatexCommand bibitem
37717 \begin_inset CommandInset href
37720 target "http://physics.nist.gov/Document/checklist.pdf"
37724 for reviewing manuscripts
37727 \begin_layout Standard
37728 \begin_inset CommandInset index_print
37729 LatexCommand printindex