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="9" 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" leftline="true" usebox="none">
4845 \begin_layout Plain Layout
4853 <cell alignment="center" valignment="top" topline="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
4878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4881 \begin_layout Plain Layout
4882 \begin_inset Formula $\iddots$
4892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4895 \begin_layout Plain Layout
4897 \begin_inset space \thinspace{}
4900 matrix with the different dots
4905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4908 \begin_layout Plain Layout
4909 \begin_inset Formula $\begin{array}{ccc}
4910 A_{11} & \cdots & A_{1m}\\
4911 \vdots & \ddots & \vdots\\
4912 A_{n1} & \cdots & A_{nm}
4929 \begin_layout Standard
4930 The ellipses available in menu
4932 Insert\SpecialChar \menuseparator
4934 \begin_inset space ~
4948 \begin_layout Standard
4949 \begin_inset VSpace medskip
4958 , one of the options
4960 Use mathdots package (automatically)
4962 must be set in the document settings under
4965 \begin_inset space ~
4971 \begin_inset Newline newline
4976 Use mathdots package
4978 will improve the appearance of all dots in the documents if their font
4979 style or size is not the default.
4982 \begin_layout Standard
4983 \begin_inset VSpace medskip
4986 Specially for matrices there are ellipses that span over several columns.
4987 They are created with the command
4994 \begin_inset Index idx
4997 \begin_layout Plain Layout
5005 , that has the following scheme:
5008 \begin_layout Standard
5013 hdotsfor[distance]{number of columns}
5016 \begin_layout Standard
5017 The number of columns specifies how many columns should be spanned.
5018 Distance is a factor for the distance between the dots.
5021 \begin_layout Standard
5022 In the following matrix the command
5028 was inserted in the first box of the second line, to get an ellipsis with
5029 a dot distance twice as long as with the command
5036 \begin_inset Formula \[
5037 \left(\begin{array}{cccc}
5041 \end{array}\right)\]
5045 Note that the matrix fields that should be spanned must be empty, otherwise
5046 you get LaTeX-errors.
5049 \begin_layout Standard
5050 \begin_inset VSpace bigskip
5053 Furthermore you can fill with the command
5060 \begin_inset Index idx
5063 \begin_layout Plain Layout
5071 the rest of a line with dots.
5072 The effect of these commands is the same like with
5079 \begin_inset CommandInset ref
5081 reference "sub:Variable-Space"
5088 \begin_layout Standard
5089 For example the command
5097 \begin_layout Plain Layout
5111 \begin_layout Standard
5112 \begin_inset Formula $A\dotfill B$
5118 \begin_layout Standard
5125 there is for a line the command
5132 \begin_inset Index idx
5135 \begin_layout Plain Layout
5146 \begin_layout Standard
5147 \begin_inset Formula $A\hrulefill B$
5153 \begin_layout Standard
5154 To use the commands for text, they have to be inserted in TeX-mode.
5157 \begin_layout Section
5159 \begin_inset CommandInset label
5166 \begin_inset Index idx
5169 \begin_layout Plain Layout
5178 \begin_layout Standard
5179 Matrices can be inserted via the math toolbar button
5180 \begin_inset Graphics
5181 filename ../images/dialog-show_mathmatrix.png
5188 Insert\SpecialChar \menuseparator
5189 Math\SpecialChar \menuseparator
5193 In the matrix dialog you can specify the number of columns and rows, the
5194 alignment and the decoration.
5195 The vertical alignment is hereby only of importance for matrices in inline
5199 \begin_layout Standard
5200 The first matrix is top
5201 \begin_inset Formula $\begin{array}[t]{cccc}
5209 \begin_inset Formula $\begin{array}{cccc}
5216 and the third bottom
5217 \begin_inset Formula $\begin{array}[b]{cccc}
5227 \begin_layout Standard
5228 The horizontal alignment specifies how the column entries should be aligned.
5229 It is set by entering a letter for every column.
5234 denotes left aligned,
5243 To create for example a 4
5248 \begin_inset space ~
5251 matrix where the first column is left aligned, the second and third are
5252 centered and the last one is right aligned, one enters for the horizontal
5258 Normally are in a matrix all columns centered, therefore the default is
5259 for every column is a
5266 \begin_layout Standard
5267 Horizontal alignment:
5270 \begin_layout Standard
5276 \begin_inset Formula $\begin{array}{lll}
5288 \begin_inset Formula $\begin{array}{ccc}
5300 \begin_inset Formula $\begin{array}{rrr}
5310 \begin_layout Standard
5311 To add or delete rows and columns subsequently, the math toolbar buttons
5313 \begin_inset Graphics
5314 filename ../images/tabular-feature_append-row.png
5320 \begin_inset Graphics
5321 filename ../images/tabular-feature_delete-row.png
5327 \begin_inset space \thinspace{}
5332 Edit\SpecialChar \menuseparator
5336 New rows can also be created with
5339 arg "newline-insert newline"
5345 \begin_layout Standard
5346 \begin_inset VSpace bigskip
5353 adds parentheses in the selected style around the matrix.
5354 Alternatively, parentheses can can either be created with the commands
5362 \begin_inset Index idx
5365 \begin_layout Plain Layout
5380 \begin_inset Index idx
5383 \begin_layout Plain Layout
5394 \begin_inset space ~
5400 \begin_inset CommandInset ref
5402 reference "sub:Automatic-Bracket-Size"
5406 , or by using the following commands:
5407 \begin_inset VSpace medskip
5413 \begin_layout Standard
5414 \begin_inset space \hfill{}
5418 \begin_inset Tabular
5419 <lyxtabular version="3" rows="4" columns="2">
5420 <features tabularvalignment="middle">
5421 <column alignment="center" valignment="top" width="0">
5422 <column alignment="center" valignment="top" width="0">
5424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5427 \begin_layout Plain Layout
5433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5436 \begin_layout Plain Layout
5438 \begin_inset Note Note
5441 \begin_layout Plain Layout
5448 is only used as spacer.
5460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5463 \begin_layout Plain Layout
5470 \begin_layout Plain Layout
5484 \begin_inset space \thinspace{}
5492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5495 \begin_layout Plain Layout
5496 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5497 0 & \textrm{-}\mathrm{i}\\
5499 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5512 \begin_layout Plain Layout
5519 \begin_layout Plain Layout
5533 \begin_inset space \thinspace{}
5541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5544 \begin_layout Plain Layout
5545 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5546 0 & \textrm{-}\mathrm{i}\\
5548 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5561 \begin_layout Plain Layout
5568 \begin_layout Plain Layout
5582 \begin_inset space \thinspace{}
5590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5593 \begin_layout Plain Layout
5594 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5595 0 & \textrm{-}\mathrm{i}\\
5597 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5611 \begin_inset space \hfill{}
5615 \begin_inset Tabular
5616 <lyxtabular version="3" rows="4" columns="2">
5617 <features tabularvalignment="middle">
5618 <column alignment="center" valignment="top" width="0">
5619 <column alignment="center" valignment="top" width="0">
5621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5624 \begin_layout Plain Layout
5630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5633 \begin_layout Plain Layout
5641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5644 \begin_layout Plain Layout
5651 \begin_layout Plain Layout
5665 \begin_inset space \thinspace{}
5673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5676 \begin_layout Plain Layout
5677 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5678 0 & \textrm{-}\mathrm{i}\\
5680 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5693 \begin_layout Plain Layout
5700 \begin_layout Plain Layout
5714 \begin_inset space \thinspace{}
5722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5725 \begin_layout Plain Layout
5726 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5727 0 & \textrm{-}\mathrm{i}\\
5729 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5742 \begin_layout Plain Layout
5749 \begin_layout Plain Layout
5763 \begin_inset space \thinspace{}
5771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5774 \begin_layout Plain Layout
5775 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5776 0 & \textrm{-}\mathrm{i}\\
5778 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5792 \begin_inset space \hfill{}
5798 \begin_layout Standard
5799 \begin_inset VSpace medskip
5803 \begin_inset space \thinspace{}
5807 \begin_inset space \space{}
5816 is inserted, a blue box appears between two vertical lines where the matrix
5818 \begin_inset Newline newline
5821 Note that decorated matrices ignore the vertical alignment.
5824 \begin_layout Standard
5825 \begin_inset VSpace bigskip
5828 As all multiline formulas are matrices, the length
5835 \begin_inset Index idx
5838 \begin_layout Plain Layout
5846 that is described in
5847 \begin_inset CommandInset ref
5849 reference "sub:Column-Separation"
5853 can also be used to change the column separation of matrices.
5856 \begin_layout Standard
5857 To change the row separation, the command
5864 \begin_inset Index idx
5867 \begin_layout Plain Layout
5876 It is used as follows:
5879 \begin_layout Standard
5886 arraystretch}{stretch factor}
5887 \begin_inset Index idx
5890 \begin_layout Plain Layout
5901 \begin_layout Standard
5908 assigns the stretch factor to the predefined command
5916 \begin_inset space \thinspace{}
5920 \begin_inset space \space{}
5923 the row separation, use the factor 2.
5924 This is then used for all following matrices.
5925 To go back to the original separation, assign the factor 1 to
5934 \begin_layout Standard
5935 To set matrices into a text line, the command
5942 \begin_inset Index idx
5945 \begin_layout Plain Layout
5954 When it is inserted a blue box with two dashed lines appears.
5955 In this box the matrix is inserted.
5958 \begin_layout Standard
5960 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5962 \end{smallmatrix}\right)$
5968 \begin_layout Section
5969 Brackets and Delimiters
5970 \begin_inset Index idx
5973 \begin_layout Plain Layout
5980 \begin_inset Index idx
5983 \begin_layout Plain Layout
5992 \begin_layout Subsection
5993 Vertical Brackets and Delimiters
5994 \begin_inset Index idx
5997 \begin_layout Plain Layout
6006 \begin_layout Standard
6007 \begin_inset space \hfill{}
6011 \begin_inset Tabular
6012 <lyxtabular version="3" rows="9" columns="2">
6013 <features tabularvalignment="middle">
6014 <column alignment="center" valignment="top" width="0pt">
6015 <column alignment="center" valignment="top" width="0pt">
6017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6020 \begin_layout Plain Layout
6026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6029 \begin_layout Plain Layout
6037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6040 \begin_layout Plain Layout
6046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6049 \begin_layout Plain Layout
6050 \begin_inset Formula $($
6060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6063 \begin_layout Plain Layout
6069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6072 \begin_layout Plain Layout
6073 \begin_inset Formula $\{$
6083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6086 \begin_layout Plain Layout
6092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6095 \begin_layout Plain Layout
6096 \begin_inset Formula $[$
6106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6109 \begin_layout Plain Layout
6117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6120 \begin_layout Plain Layout
6121 \begin_inset Formula $\langle$
6131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6134 \begin_layout Plain Layout
6142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6145 \begin_layout Plain Layout
6146 \begin_inset Formula $\lceil$
6156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6159 \begin_layout Plain Layout
6167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6170 \begin_layout Plain Layout
6171 \begin_inset Formula $\lfloor$
6181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6184 \begin_layout Plain Layout
6190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6193 \begin_layout Plain Layout
6194 \begin_inset Formula $/$
6204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6207 \begin_layout Plain Layout
6213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6216 \begin_layout Plain Layout
6217 \begin_inset Formula $|$
6231 \begin_inset space \hfill{}
6235 \begin_inset Tabular
6236 <lyxtabular version="3" rows="9" columns="2">
6237 <features tabularvalignment="middle">
6238 <column alignment="center" valignment="top" width="0pt">
6239 <column alignment="center" valignment="top" width="0pt">
6241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6244 \begin_layout Plain Layout
6250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6253 \begin_layout Plain Layout
6261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6264 \begin_layout Plain Layout
6270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6273 \begin_layout Plain Layout
6274 \begin_inset Formula $)$
6284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6287 \begin_layout Plain Layout
6293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6296 \begin_layout Plain Layout
6297 \begin_inset Formula $\}$
6307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6310 \begin_layout Plain Layout
6316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6319 \begin_layout Plain Layout
6320 \begin_inset Formula $]$
6330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6333 \begin_layout Plain Layout
6341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6344 \begin_layout Plain Layout
6345 \begin_inset Formula $\rangle$
6355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6358 \begin_layout Plain Layout
6366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6369 \begin_layout Plain Layout
6370 \begin_inset Formula $\rceil$
6380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6383 \begin_layout Plain Layout
6391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6394 \begin_layout Plain Layout
6395 \begin_inset Formula $\rfloor$
6405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6408 \begin_layout Plain Layout
6418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6421 \begin_layout Plain Layout
6422 \begin_inset Formula $\backslash$
6432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6435 \begin_layout Plain Layout
6443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6446 \begin_layout Plain Layout
6447 \begin_inset Formula $\|$
6461 \begin_inset space \hfill{}
6467 \begin_layout Standard
6470 \begin_inset Note Greyedout
6473 \begin_layout Plain Layout
6478 In TeX-mode the command
6485 \begin_inset Index idx
6488 \begin_layout Plain Layout
6496 must be used for the backslash, because the command
6504 produces there a line break.
6512 \begin_layout Standard
6513 For all characters listed above the size can be adjusted with the commands
6514 described in the following two subsections.
6515 When using these commands, the characters < and > can directly be used
6516 instead of the commands
6531 \begin_layout Subsubsection
6533 \begin_inset CommandInset label
6535 name "sub:Manual-Bracket-Size"
6540 \begin_inset Index idx
6543 \begin_layout Plain Layout
6544 Bracket size ! manual
6552 \begin_layout Standard
6553 The bracket size can be specified manually by the LaTeX-commands
6560 \begin_inset Index idx
6563 \begin_layout Plain Layout
6596 denotes the smallest and
6602 the largest bracket size.
6605 \begin_layout Standard
6606 These commands are used to emphasize levels of brackets:
6609 \begin_layout Standard
6611 \begin_inset Tabular
6612 <lyxtabular version="3" rows="2" columns="2">
6613 <features tabularvalignment="middle">
6614 <column alignment="center" valignment="top" width="0pt">
6615 <column alignment="center" valignment="top" width="0pt">
6617 <cell alignment="center" valignment="top" usebox="none">
6620 \begin_layout Plain Layout
6621 all brackets in the same size:
6626 <cell alignment="center" valignment="top" usebox="none">
6629 \begin_layout Plain Layout
6630 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6640 <cell alignment="center" valignment="top" usebox="none">
6643 \begin_layout Plain Layout
6649 <cell alignment="center" valignment="top" usebox="none">
6652 \begin_layout Plain Layout
6653 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6667 \begin_inset Note Note
6670 \begin_layout Plain Layout
6677 is only used as spacer.
6685 \begin_layout Standard
6686 For the second formula the command
6696 \begin_layout Plain Layout
6710 \begin_layout Standard
6711 Here is an overview about all bracket sizes:
6714 \begin_layout Standard
6734 \begin_layout Plain Layout
6751 \begin_layout Plain Layout
6764 \begin_layout Plain Layout
6780 \begin_layout Standard
6782 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6788 \begin_layout Standard
6795 -commands there is the variant
6802 \begin_inset Index idx
6805 \begin_layout Plain Layout
6813 that adds a bit more space between the bracket and its content, and the
6827 \begin_inset Index idx
6830 \begin_layout Plain Layout
6840 , that don't add additional space.
6845 at the end of the command
6851 is for a left bracket; for a right bracket this will be replaced by an
6857 A left or right bracket can each be an opening or closing bracket.
6860 \begin_layout Standard
6861 In the following table is a comparison of the variants:
6864 \begin_layout Standard
6866 \begin_inset Tabular
6867 <lyxtabular version="3" rows="5" columns="2">
6868 <features tabularvalignment="middle">
6869 <column alignment="center" valignment="middle" width="0">
6870 <column alignment="center" valignment="middle" width="0">
6872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6875 \begin_layout Plain Layout
6881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6884 \begin_layout Plain Layout
6886 \begin_inset Note Note
6889 \begin_layout Plain Layout
6896 is only used as spacer.
6908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6911 \begin_layout Plain Layout
6926 \begin_layout Plain Layout
6944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6947 \begin_layout Plain Layout
6948 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6961 \begin_layout Plain Layout
6976 \begin_layout Plain Layout
6994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6997 \begin_layout Plain Layout
6998 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7011 \begin_layout Plain Layout
7026 \begin_layout Plain Layout
7044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7047 \begin_layout Plain Layout
7048 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7061 \begin_layout Plain Layout
7073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7076 \begin_layout Plain Layout
7077 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7093 \begin_layout Subsubsection
7094 Automatic Bracket Size
7095 \begin_inset CommandInset label
7097 name "sub:Automatic-Bracket-Size"
7102 \begin_inset Index idx
7105 \begin_layout Plain Layout
7106 Bracket size ! automatic
7114 \begin_layout Standard
7115 Brackets with variable size can be inserted with the commands
7122 \begin_inset Index idx
7125 \begin_layout Plain Layout
7140 \begin_inset Index idx
7143 \begin_layout Plain Layout
7151 or via the math toolbar button
7152 \begin_inset Graphics
7153 filename ../images/dialog-show_mathdelimiter.png
7171 the wanted bracket must be inserted.
7172 The bracket size will then automatically be calculated for the output.
7175 \begin_layout Standard
7177 normal bracket: The command
7187 \begin_layout Plain Layout
7197 \begin_inset Formula $\downarrow$
7204 \begin_layout Plain Layout
7216 \begin_inset Formula \[
7224 \begin_layout Standard
7226 multiline bracket: The command
7238 \begin_layout Plain Layout
7248 \begin_inset Formula $\downarrow$
7255 \begin_layout Plain Layout
7269 \begin_inset Formula \[
7270 \ln\left(\frac{A}{C}\right)\]
7277 \begin_layout Standard
7293 \begin_inset space ~
7299 This has the advantage that you can see in LyX immediately the real bracket
7300 size and that the matching right bracket will be created too.
7301 \begin_inset Newline newline
7304 The command for the last example would then be:
7318 \begin_layout Plain Layout
7328 \begin_inset Formula $\downarrow$
7334 \begin_layout Standard
7335 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7336 For example the command
7346 \begin_layout Plain Layout
7356 \begin_inset Formula $\downarrow$
7363 \begin_layout Plain Layout
7379 \begin_inset Formula \[
7380 \left.\frac{A}{B}\right\} \]
7398 will be converted by LyX to brackets in the right size when the document
7399 is reloaded and an omitted bracket will appear as dashed line.
7402 \begin_layout Standard
7403 \begin_inset VSpace bigskip
7406 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7414 \begin_inset Index idx
7417 \begin_layout Plain Layout
7425 is additionally available for all brackets and limits.
7426 With this command the height of the following character is adapted to the
7427 one of the surrounding brackets, what is e.
7428 \begin_inset space \thinspace{}
7432 \begin_inset space \space{}
7435 needed for physical vectors:
7436 \begin_inset Formula \[
7437 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7441 For physical vectors there is a special LaTeX-package, described in
7442 \begin_inset CommandInset ref
7444 reference "sub:Physical-Vectors"
7451 \begin_layout Subsection
7453 \begin_inset Index idx
7456 \begin_layout Plain Layout
7457 Brackets ! horizontal
7465 \begin_layout Standard
7467 \begin_inset Tabular
7468 <lyxtabular version="3" rows="4" columns="2">
7469 <features tabularvalignment="middle">
7470 <column alignment="center" valignment="top" width="0pt">
7471 <column alignment="center" valignment="top" width="0pt">
7473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7476 \begin_layout Plain Layout
7478 \begin_inset Note Note
7481 \begin_layout Plain Layout
7488 is only used as spacer.
7498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7501 \begin_layout Plain Layout
7509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7512 \begin_layout Plain Layout
7516 \begin_layout Plain Layout
7531 \begin_layout Plain Layout
7544 \begin_layout Plain Layout
7557 \begin_layout Plain Layout
7570 \begin_layout Plain Layout
7578 \begin_inset Index idx
7581 \begin_layout Plain Layout
7594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7597 \begin_layout Plain Layout
7598 \begin_inset Formula $\overbrace{A+B}^{3}$
7608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7611 \begin_layout Plain Layout
7615 \begin_layout Plain Layout
7630 \begin_layout Plain Layout
7643 \begin_layout Plain Layout
7656 \begin_layout Plain Layout
7664 \begin_inset Index idx
7667 \begin_layout Plain Layout
7680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7683 \begin_layout Plain Layout
7684 \begin_inset Formula $\underbrace{A+B}_{5}$
7694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7697 \begin_layout Plain Layout
7704 \begin_layout Plain Layout
7719 \begin_layout Plain Layout
7732 \begin_layout Plain Layout
7745 \begin_layout Plain Layout
7758 \begin_layout Plain Layout
7771 \begin_layout Plain Layout
7784 \begin_layout Plain Layout
7798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7801 \begin_layout Plain Layout
7802 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7818 \begin_layout Standard
7819 In the last example it doesn't matter if
7831 is inserted at first.
7834 \begin_layout Standard
7835 \begin_inset VSpace bigskip
7838 When brackets are needed that overlap each other, multiline formulas, as
7840 \begin_inset CommandInset ref
7842 reference "sec:Multiline-Formulas"
7847 \begin_inset Formula \begin{eqnarray*}
7848 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7849 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7854 In the first row the formula is inserted together with the first brace.
7855 It is hereby important that the space command
7859 \begin_layout Plain Layout
7860 Space commands are explained in
7861 \begin_inset CommandInset ref
7863 reference "sub:Predefined-Space"
7878 is inserted before the first
7879 \begin_inset Formula $d$
7882 , because the brace that ends behind the
7883 \begin_inset Formula $q$
7886 prevents that the following
7887 \begin_inset Quotes eld
7891 \begin_inset Quotes erd
7894 is surrounded by space.
7898 \begin_layout Plain Layout
7899 because a bracket is not handled as character, see
7900 \begin_inset CommandInset ref
7902 reference "sub:Binary-Operators"
7911 In the second row the second brace is inserted.
7912 As it should begin before the
7913 \begin_inset Formula $b$
7928 \begin_layout Plain Layout
7936 \begin_inset CommandInset ref
7938 reference "sub:Placeholders"
7947 This space is needed because the
7948 \begin_inset Quotes eld
7952 \begin_inset Quotes erd
7955 is also surrounded by space in the formula.
7956 The brace is placed under the command
7965 \begin_layout Standard
7966 It gets more complicated when brackets overlap each other, like in the following
7971 \begin_layout Plain Layout
7983 \begin_inset Formula \begin{eqnarray*}
7984 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7985 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7994 \begin_layout Plain Layout
8005 The first formula row is the same as the second row of the previous example,
8006 with the difference that the brace is above.
8007 The second row contains the formula together with the second brace.
8008 To avoid that there is space between the upper brace in the first row and
8009 the formula, the row spacing need to be reduced.
8010 This is not easily possible due to a bug in LyX
8014 \begin_layout Plain Layout
8015 \begin_inset CommandInset href
8017 name "LyX-bug #1505"
8018 target "http://www.lyx.org/trac/ticket/1505"
8028 As solution for the problem, the global formula row separation
8035 \begin_inset Index idx
8038 \begin_layout Plain Layout
8046 must be changed to -6
8047 \begin_inset space \thinspace{}
8050 pt before the formula with the command
8065 is set back after the formula to the standard value of 3
8066 \begin_inset space \thinspace{}
8069 pt using the same command.
8070 More about the row separation in formulas is explained in
8071 \begin_inset CommandInset ref
8073 reference "sub:Line-Separation"
8080 \begin_layout Section
8082 \begin_inset Index idx
8085 \begin_layout Plain Layout
8094 \begin_layout Standard
8095 Arrows can be inserted via the math toolbar button
8096 \begin_inset Graphics
8097 filename ../images/math/leftarrow.png
8102 or the commands listed in the following subsections.
8105 \begin_layout Standard
8106 \begin_inset Newpage newpage
8112 \begin_layout Subsection
8114 \begin_inset Index idx
8117 \begin_layout Plain Layout
8126 \begin_layout Standard
8127 \begin_inset space \hfill{}
8131 \begin_inset Tabular
8132 <lyxtabular version="3" rows="8" columns="2">
8133 <features tabularvalignment="middle">
8134 <column alignment="center" valignment="top" width="0pt">
8135 <column alignment="center" valignment="top" width="0pt">
8137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8140 \begin_layout Plain Layout
8146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8149 \begin_layout Plain Layout
8157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8160 \begin_layout Plain Layout
8168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8171 \begin_layout Plain Layout
8172 \begin_inset Formula $\gets$
8182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8185 \begin_layout Plain Layout
8193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8196 \begin_layout Plain Layout
8197 \begin_inset Formula $\Leftarrow$
8207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8210 \begin_layout Plain Layout
8218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8221 \begin_layout Plain Layout
8222 \begin_inset Formula $\longleftarrow$
8232 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8235 \begin_layout Plain Layout
8243 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8246 \begin_layout Plain Layout
8247 \begin_inset Formula $\Longleftarrow$
8257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8260 \begin_layout Plain Layout
8268 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8271 \begin_layout Plain Layout
8272 \begin_inset Formula $\leftharpoonup$
8282 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8285 \begin_layout Plain Layout
8293 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8296 \begin_layout Plain Layout
8297 \begin_inset Formula $\leftharpoondown$
8307 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8310 \begin_layout Plain Layout
8318 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8321 \begin_layout Plain Layout
8322 \begin_inset Formula $\hookleftarrow$
8336 \begin_inset space \hfill{}
8340 \begin_inset Tabular
8341 <lyxtabular version="3" rows="8" columns="2">
8342 <features tabularvalignment="middle">
8343 <column alignment="center" valignment="top" width="0pt">
8344 <column alignment="center" valignment="top" width="0pt">
8346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8349 \begin_layout Plain Layout
8355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8358 \begin_layout Plain Layout
8366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8369 \begin_layout Plain Layout
8377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8380 \begin_layout Plain Layout
8381 \begin_inset Formula $\to$
8391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8394 \begin_layout Plain Layout
8402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8405 \begin_layout Plain Layout
8406 \begin_inset Formula $\Rightarrow$
8416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8419 \begin_layout Plain Layout
8427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8430 \begin_layout Plain Layout
8431 \begin_inset Formula $\longrightarrow$
8441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8444 \begin_layout Plain Layout
8452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8455 \begin_layout Plain Layout
8456 \begin_inset Formula $\Longrightarrow$
8466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8469 \begin_layout Plain Layout
8477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8480 \begin_layout Plain Layout
8481 \begin_inset Formula $\rightharpoonup$
8491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8494 \begin_layout Plain Layout
8502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8505 \begin_layout Plain Layout
8506 \begin_inset Formula $\rightharpoondown$
8516 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8519 \begin_layout Plain Layout
8527 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8530 \begin_layout Plain Layout
8531 \begin_inset Formula $\hookrightarrow$
8545 \begin_inset space \hfill{}
8551 \begin_layout Standard
8552 \begin_inset space \hfill{}
8556 \begin_inset Tabular
8557 <lyxtabular version="3" rows="6" columns="2">
8558 <features tabularvalignment="middle">
8559 <column alignment="center" valignment="top" width="0pt">
8560 <column alignment="center" valignment="top" width="0pt">
8562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8565 \begin_layout Plain Layout
8571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8574 \begin_layout Plain Layout
8582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8585 \begin_layout Plain Layout
8593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8596 \begin_layout Plain Layout
8597 \begin_inset Formula $\leftrightarrow$
8607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8610 \begin_layout Plain Layout
8618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8621 \begin_layout Plain Layout
8622 \begin_inset Formula $\Leftrightarrow$
8632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8635 \begin_layout Plain Layout
8643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8646 \begin_layout Plain Layout
8647 \begin_inset Formula $\longleftrightarrow$
8657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8660 \begin_layout Plain Layout
8668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8671 \begin_layout Plain Layout
8672 \begin_inset Formula $\Longleftrightarrow$
8682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8685 \begin_layout Plain Layout
8693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8696 \begin_layout Plain Layout
8697 \begin_inset Formula $\rightleftharpoons$
8711 \begin_inset space \hspace{}
8716 \begin_inset space \hfill{}
8720 \begin_inset Tabular
8721 <lyxtabular version="3" rows="5" columns="2">
8722 <features tabularvalignment="middle">
8723 <column alignment="center" valignment="top" width="0pt">
8724 <column alignment="center" valignment="top" width="0pt">
8726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8729 \begin_layout Plain Layout
8735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8738 \begin_layout Plain Layout
8746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8749 \begin_layout Plain Layout
8757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8760 \begin_layout Plain Layout
8761 \begin_inset Formula $\mapsto$
8771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8774 \begin_layout Plain Layout
8782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8785 \begin_layout Plain Layout
8786 \begin_inset Formula $\longmapsto$
8796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8799 \begin_layout Plain Layout
8807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8810 \begin_layout Plain Layout
8811 \begin_inset Formula $\leadsto$
8821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8824 \begin_layout Plain Layout
8832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8835 \begin_layout Plain Layout
8836 \begin_inset Formula $\dasharrow$
8850 \begin_inset space \hfill{}
8856 \begin_layout Standard
8857 \begin_inset VSpace medskip
8860 Arrows used as accent like e.
8861 \begin_inset space \thinspace{}
8865 \begin_inset space \space{}
8868 vector arrows are listed in
8869 \begin_inset CommandInset ref
8871 reference "sec:Accents"
8878 \begin_layout Standard
8879 \begin_inset VSpace bigskip
8882 Furthermore there are the labeled arrows
8883 \begin_inset Index idx
8886 \begin_layout Plain Layout
8899 \begin_inset Index idx
8902 \begin_layout Plain Layout
8917 \begin_inset Index idx
8920 \begin_layout Plain Layout
8927 \begin_layout Plain Layout
8942 When inserting one of these commands in a formula, an arrow with two blue
8943 boxes appear where the label can be inserted.
8944 The length of the arrow adapts to the label width.
8947 \begin_layout Standard
8949 \begin_inset Tabular
8950 <lyxtabular version="3" rows="3" columns="2">
8951 <features tabularvalignment="middle">
8952 <column alignment="center" valignment="top" width="0pt">
8953 <column alignment="center" valignment="top" width="0pt">
8955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8958 \begin_layout Plain Layout
8964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8967 \begin_layout Plain Layout
8969 \begin_inset Note Note
8972 \begin_layout Plain Layout
8979 is only used as spacer.
8991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8994 \begin_layout Plain Layout
9001 \begin_layout Plain Layout
9011 \begin_inset Formula $\downarrow$
9015 \begin_inset Formula $\to$
9023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9026 \begin_layout Plain Layout
9027 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9040 \begin_layout Plain Layout
9047 \begin_layout Plain Layout
9057 \begin_inset Formula $\downarrow$
9061 \begin_inset Formula $\to$
9069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9072 \begin_layout Plain Layout
9073 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9089 \begin_layout Subsection
9090 Vertical and diagonal Arrows
9091 \begin_inset Index idx
9094 \begin_layout Plain Layout
9101 \begin_inset Index idx
9104 \begin_layout Plain Layout
9113 \begin_layout Standard
9114 \begin_inset space \hfill{}
9118 \begin_inset Tabular
9119 <lyxtabular version="3" rows="7" columns="2">
9120 <features tabularvalignment="middle">
9121 <column alignment="center" valignment="top" width="0pt">
9122 <column alignment="center" valignment="top" width="0pt">
9124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9127 \begin_layout Plain Layout
9133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9136 \begin_layout Plain Layout
9144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9147 \begin_layout Plain Layout
9155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9158 \begin_layout Plain Layout
9159 \begin_inset Formula $\uparrow$
9169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9172 \begin_layout Plain Layout
9180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9183 \begin_layout Plain Layout
9184 \begin_inset Formula $\Uparrow$
9194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9197 \begin_layout Plain Layout
9205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9208 \begin_layout Plain Layout
9209 \begin_inset Formula $\updownarrow$
9219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9222 \begin_layout Plain Layout
9230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9233 \begin_layout Plain Layout
9234 \begin_inset Formula $\Updownarrow$
9244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9247 \begin_layout Plain Layout
9255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9258 \begin_layout Plain Layout
9259 \begin_inset Formula $\Downarrow$
9269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9272 \begin_layout Plain Layout
9280 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9283 \begin_layout Plain Layout
9284 \begin_inset Formula $\downarrow$
9298 \begin_inset space \hfill{}
9302 \begin_inset Tabular
9303 <lyxtabular version="3" rows="5" columns="2">
9304 <features tabularvalignment="middle">
9305 <column alignment="center" valignment="top" width="0pt">
9306 <column alignment="center" valignment="top" width="0pt">
9308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9311 \begin_layout Plain Layout
9317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9320 \begin_layout Plain Layout
9328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9331 \begin_layout Plain Layout
9339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9342 \begin_layout Plain Layout
9343 \begin_inset Formula $\nearrow$
9353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9356 \begin_layout Plain Layout
9364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9367 \begin_layout Plain Layout
9368 \begin_inset Formula $\searrow$
9378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9381 \begin_layout Plain Layout
9389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9392 \begin_layout Plain Layout
9393 \begin_inset Formula $\swarrow$
9403 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9406 \begin_layout Plain Layout
9414 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9417 \begin_layout Plain Layout
9418 \begin_inset Formula $\nwarrow$
9432 \begin_inset space \hfill{}
9438 \begin_layout Standard
9439 \begin_inset VSpace medskip
9442 Vertical arrows can be used also as delimiter together with the commands
9444 \begin_inset CommandInset ref
9446 reference "sub:Manual-Bracket-Size"
9451 \begin_inset CommandInset ref
9453 reference "sub:Automatic-Bracket-Size"
9460 \begin_layout Standard
9461 \begin_inset Newpage newpage
9467 \begin_layout Section
9469 \begin_inset CommandInset label
9476 \begin_inset Index idx
9479 \begin_layout Plain Layout
9488 \begin_layout Standard
9489 Accents can be inserted via the math toolbar button
9490 \begin_inset Graphics
9491 filename ../images/math/hat.png
9496 or the commands listed in the following subsections.
9499 \begin_layout Subsection
9500 Accents for one Character
9504 \begin_layout Plain Layout
9517 \begin_layout Plain Layout
9519 \begin_inset CommandInset ref
9521 reference "sub:Accents-in-Text"
9534 \begin_layout Plain Layout
9542 \begin_inset Note Note
9545 \begin_layout Plain Layout
9548 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9551 \begin_layout Plain Layout
9554 texorpdfstring is in section
9555 \begin_inset CommandInset ref
9557 reference "sub:Formulas-in-Section"
9567 \begin_inset CommandInset label
9569 name "sub:Accents-for-one"
9574 \begin_inset Index idx
9577 \begin_layout Plain Layout
9578 Accents ! for one character
9586 \begin_layout Standard
9587 \begin_inset space \hfill{}
9591 \begin_inset Tabular
9592 <lyxtabular version="3" rows="8" columns="2">
9593 <features tabularvalignment="middle">
9594 <column alignment="center" valignment="top" width="0pt">
9595 <column alignment="center" valignment="top" width="0pt">
9597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9600 \begin_layout Plain Layout
9606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9609 \begin_layout Plain Layout
9611 \begin_inset Note Note
9614 \begin_layout Plain Layout
9621 is only used as spacer.
9633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9636 \begin_layout Plain Layout
9643 \begin_layout Plain Layout
9657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9660 \begin_layout Plain Layout
9661 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9671 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9674 \begin_layout Plain Layout
9681 \begin_layout Plain Layout
9695 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9698 \begin_layout Plain Layout
9699 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9709 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9712 \begin_layout Plain Layout
9719 \begin_layout Plain Layout
9733 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9736 \begin_layout Plain Layout
9737 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9747 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9750 \begin_layout Plain Layout
9757 \begin_layout Plain Layout
9771 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9774 \begin_layout Plain Layout
9775 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9785 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9788 \begin_layout Plain Layout
9795 \begin_layout Plain Layout
9805 \begin_inset Index idx
9808 \begin_layout Plain Layout
9819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9822 \begin_layout Plain Layout
9823 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9833 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9836 \begin_layout Plain Layout
9843 \begin_layout Plain Layout
9857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9860 \begin_layout Plain Layout
9861 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9871 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9874 \begin_layout Plain Layout
9881 \begin_layout Plain Layout
9895 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9898 \begin_layout Plain Layout
9899 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9913 \begin_inset space \hfill{}
9917 \begin_inset Tabular
9918 <lyxtabular version="3" rows="7" columns="2">
9919 <features tabularvalignment="middle">
9920 <column alignment="center" valignment="top" width="0pt">
9921 <column alignment="center" valignment="top" width="0pt">
9923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9926 \begin_layout Plain Layout
9932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9935 \begin_layout Plain Layout
9943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9946 \begin_layout Plain Layout
9953 \begin_layout Plain Layout
9967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9970 \begin_layout Plain Layout
9971 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9981 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9984 \begin_layout Plain Layout
9991 \begin_layout Plain Layout
10005 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10008 \begin_layout Plain Layout
10009 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10019 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10022 \begin_layout Plain Layout
10029 \begin_layout Plain Layout
10043 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10046 \begin_layout Plain Layout
10047 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10057 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10060 \begin_layout Plain Layout
10067 \begin_layout Plain Layout
10081 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10084 \begin_layout Plain Layout
10085 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10095 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10098 \begin_layout Plain Layout
10105 \begin_layout Plain Layout
10119 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10122 \begin_layout Plain Layout
10123 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10133 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10136 \begin_layout Plain Layout
10143 \begin_layout Plain Layout
10157 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10160 \begin_layout Plain Layout
10161 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10175 \begin_inset space \hfill{}
10181 \begin_layout Standard
10182 \begin_inset VSpace bigskip
10188 \begin_layout Standard
10189 You can directly insert accents like é to formulas.
10190 LyX will transform them to the corresponding accent command.
10192 \begin_inset Index idx
10195 \begin_layout Plain Layout
10201 it is better to insert a quotation mark before the vowel.
10202 These two characters are then treated by LaTeX as
10206 character when the formula part with the umlaut is marked as German.
10214 \begin_inset Quotes eld
10218 \begin_inset Quotes erd
10221 umlauts are created as demonstrated in the following example:
10224 \begin_layout Standard
10225 \begin_inset VSpace -2mm
10231 \begin_layout Standard
10233 \begin_inset Tabular
10234 <lyxtabular version="3" rows="3" columns="2">
10235 <features tabularvalignment="middle">
10236 <column alignment="center" valignment="top" width="0">
10237 <column alignment="center" valignment="top" width="0">
10239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10242 \begin_layout Plain Layout
10248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10251 \begin_layout Plain Layout
10253 \begin_inset Note Note
10256 \begin_layout Plain Layout
10264 \begin_inset space \thinspace{}
10267 pt space are only used as spacer.
10279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10282 \begin_layout Plain Layout
10285 \begin_inset Quotes grd
10293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10296 \begin_layout Plain Layout
10297 \begin_inset space \hspace{}
10304 \begin_inset Formula $"i$
10314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10317 \begin_layout Plain Layout
10324 \begin_layout Plain Layout
10338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10341 \begin_layout Plain Layout
10342 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10358 \begin_layout Standard
10359 Another advantage to
10365 is that umlauts can directly be converted to mathematical text because
10366 the accent commands above are
10372 in mathematical text
10375 To convert an accented character to mathematical text, only the character
10376 under the accent may be converted.
10377 This applies also for all other conversions, e.
10378 \begin_inset space \thinspace{}
10382 \begin_inset space \space{}
10388 \begin_layout Standard
10389 In mathematical text, umlauts and other accented characters can directly
10393 \begin_layout Subsection
10394 Accents for Operators
10395 \begin_inset Index idx
10398 \begin_layout Plain Layout
10399 Accents ! for operators
10407 \begin_layout Standard
10415 \begin_inset Index idx
10418 \begin_layout Plain Layout
10433 \begin_inset Index idx
10436 \begin_layout Plain Layout
10444 characters can be placed above or below an operator, respectively, to accent
10453 \begin_inset Index idx
10456 \begin_layout Plain Layout
10464 characters can be set before and behind an operator.
10465 The command scheme is:
10468 \begin_layout Standard
10484 \begin_layout Standard
10491 must always be before the operator that should be accented.
10492 You can accent with several characters and even with other operators and
10500 for example only characters behind an operator, write nothing between the
10501 first braces but don't omit the braces.
10504 \begin_layout Standard
10505 For example the command
10510 \begin_inset Formula $\to$
10520 \begin_inset Formula $\to$
10529 \begin_layout Plain Layout
10545 \begin_inset Formula \[
10546 \sideset{}{'}\sum_{k=1}^{n}\]
10553 \begin_layout Standard
10562 \begin_layout Plain Layout
10577 \begin_layout Plain Layout
10589 \begin_inset Formula $\uparrow$
10597 \begin_inset Formula \[
10598 \overset{a}{\maltese}\]
10602 As seen in the last example, with
10614 also symbols and characters can be accented; with
10620 this is not possible.
10623 \begin_layout Subsection
10624 Accents for several Characters
10625 \begin_inset Index idx
10628 \begin_layout Plain Layout
10629 Accents ! for several characters
10637 \begin_layout Standard
10638 \begin_inset space \hfill{}
10642 \begin_inset Tabular
10643 <lyxtabular version="3" rows="5" columns="2">
10644 <features tabularvalignment="middle">
10645 <column alignment="center" valignment="top" width="0pt">
10646 <column alignment="center" valignment="top" width="0pt">
10648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10651 \begin_layout Plain Layout
10657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10660 \begin_layout Plain Layout
10662 \begin_inset Note Note
10665 \begin_layout Plain Layout
10672 is only used as spacer.
10684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10687 \begin_layout Plain Layout
10694 \begin_layout Plain Layout
10708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10711 \begin_layout Plain Layout
10712 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10722 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10725 \begin_layout Plain Layout
10732 \begin_layout Plain Layout
10746 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10749 \begin_layout Plain Layout
10750 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10760 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10763 \begin_layout Plain Layout
10770 \begin_layout Plain Layout
10784 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10787 \begin_layout Plain Layout
10788 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10798 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10801 \begin_layout Plain Layout
10804 underleftrightarrow
10808 \begin_layout Plain Layout
10822 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10825 \begin_layout Plain Layout
10826 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10840 \begin_inset space \hfill{}
10844 \begin_inset Tabular
10845 <lyxtabular version="3" rows="5" columns="2">
10846 <features tabularvalignment="middle">
10847 <column alignment="center" valignment="top" width="0pt">
10848 <column alignment="center" valignment="top" width="0pt">
10850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10853 \begin_layout Plain Layout
10859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10862 \begin_layout Plain Layout
10870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10873 \begin_layout Plain Layout
10880 \begin_layout Plain Layout
10894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10897 \begin_layout Plain Layout
10898 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10908 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10911 \begin_layout Plain Layout
10918 \begin_layout Plain Layout
10932 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10935 \begin_layout Plain Layout
10936 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10946 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10949 \begin_layout Plain Layout
10956 \begin_layout Plain Layout
10970 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10973 \begin_layout Plain Layout
10974 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10987 \begin_layout Plain Layout
10994 \begin_layout Plain Layout
11008 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11011 \begin_layout Plain Layout
11012 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11026 \begin_inset space \hfill{}
11032 \begin_layout Standard
11033 \begin_inset VSpace medskip
11036 With these commands as many characters as you like can be accented.
11049 will only be set in the output with a length of three characters, as shown
11050 in the following example:
11051 \begin_inset Formula \[
11052 \widetilde{A+B=C-D}\]
11059 \begin_layout Standard
11067 \begin_inset Index idx
11070 \begin_layout Plain Layout
11085 \begin_inset Index idx
11088 \begin_layout Plain Layout
11096 described in the previous subsection it is also possible to accent several
11106 \begin_layout Plain Layout
11116 \begin_inset Formula $\downarrow$
11122 \begin_inset Formula \[
11123 \underset{***}{A=B}\]
11130 \begin_layout Section
11132 \begin_inset CommandInset label
11139 \begin_inset Index idx
11142 \begin_layout Plain Layout
11151 \begin_layout Subsection
11153 \begin_inset CommandInset label
11155 name "sub:Predefined-Space"
11160 \begin_inset Index idx
11163 \begin_layout Plain Layout
11164 Space ! horizontal ! predefined
11172 \begin_layout Standard
11173 Sometimes it is necessary to insert horizontal space to a formula.
11174 This is done by inserting a protected space (shortcut
11177 arg "space-insert protected"
11182 \begin_inset Quotes eld
11191 \begin_layout Plain Layout
11203 \begin_inset Quotes erd
11206 appears and by pressing
11210 several times one can select one of eight different space sizes.
11211 The spaces can also be inserted using the math toolbar button
11212 \begin_inset Graphics
11213 filename ../images/math/space.png
11218 or special commands.
11219 Independent from the inserted command, one can select the size again by
11227 \begin_layout Standard
11230 \begin_inset VSpace -5mm
11234 \begin_inset Tabular
11235 <lyxtabular version="3" rows="3" columns="7">
11236 <features tabularvalignment="middle">
11237 <column alignment="center" valignment="middle" width="6.8cm">
11238 <column alignment="center" valignment="top" width="0">
11239 <column alignment="center" valignment="top" width="0">
11240 <column alignment="center" valignment="top" width="0">
11241 <column alignment="center" valignment="top" width="0">
11242 <column alignment="center" valignment="top" width="0">
11243 <column alignment="center" valignment="top" width="0">
11245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11248 \begin_layout Plain Layout
11254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11257 \begin_layout Plain Layout
11265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11268 \begin_layout Plain Layout
11276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11279 \begin_layout Plain Layout
11287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11290 \begin_layout Plain Layout
11298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11301 \begin_layout Plain Layout
11309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11312 \begin_layout Plain Layout
11322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11325 \begin_layout Plain Layout
11330 keystrokes after inserting the protected space
11335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11338 \begin_layout Plain Layout
11344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11347 \begin_layout Plain Layout
11353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11356 \begin_layout Plain Layout
11362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11365 \begin_layout Plain Layout
11371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11374 \begin_layout Plain Layout
11380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11383 \begin_layout Plain Layout
11391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11394 \begin_layout Plain Layout
11400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11403 \begin_layout Plain Layout
11404 \begin_inset Formula $A\, B$
11412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11415 \begin_layout Plain Layout
11416 \begin_inset Formula $A\: B$
11424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11427 \begin_layout Plain Layout
11428 \begin_inset Formula $A\; B$
11436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11439 \begin_layout Plain Layout
11440 \begin_inset Formula $A\quad B$
11448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11451 \begin_layout Plain Layout
11452 \begin_inset Formula $A\qquad B$
11460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11463 \begin_layout Plain Layout
11464 \begin_inset Formula $A\! B$
11480 \begin_layout Standard
11481 The last size seem to produce no space.
11482 It is displayed red in LyX contrary to the other sizes, because it is a
11484 There are two more negative spaces:
11487 \begin_layout Standard
11489 \begin_inset Tabular
11490 <lyxtabular version="3" rows="3" columns="3">
11491 <features tabularvalignment="middle">
11492 <column alignment="center" valignment="middle" width="6.8cm">
11493 <column alignment="center" valignment="top" width="0pt">
11494 <column alignment="center" valignment="top" width="0pt">
11496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11499 \begin_layout Plain Layout
11505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11508 \begin_layout Plain Layout
11516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11519 \begin_layout Plain Layout
11529 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11532 \begin_layout Plain Layout
11537 keystrokes after inserting the protected space
11542 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11545 \begin_layout Plain Layout
11551 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11554 \begin_layout Plain Layout
11562 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11565 \begin_layout Plain Layout
11571 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11574 \begin_layout Plain Layout
11575 \begin_inset Formula $A\negmedspace B$
11583 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11586 \begin_layout Plain Layout
11587 \begin_inset Formula $A\negthickspace B$
11603 \begin_layout Standard
11604 Negative spaces can lead to characters overlapping each other.
11605 Thus they can be used to enforce ligatures, what is e.
11606 \begin_inset space \thinspace{}
11610 \begin_inset space \space{}
11613 useful for summation operators:
11616 \begin_layout Standard
11618 \begin_inset Tabular
11619 <lyxtabular version="3" rows="3" columns="2">
11620 <features tabularvalignment="middle">
11621 <column alignment="center" valignment="top" width="0">
11622 <column alignment="center" valignment="top" width="0">
11624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11627 \begin_layout Plain Layout
11633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11636 \begin_layout Plain Layout
11638 \begin_inset Note Note
11641 \begin_layout Plain Layout
11648 is only used as spacer.
11660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11663 \begin_layout Plain Layout
11672 \begin_layout Plain Layout
11686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11689 \begin_layout Plain Layout
11690 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11703 \begin_layout Plain Layout
11714 \begin_layout Plain Layout
11728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11731 \begin_layout Plain Layout
11732 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11748 \begin_layout Standard
11749 Relations like for example equal signs, are always surrounded by space.
11750 To suppress this, the equal sign is placed into a TeX-brace.
11751 The following example demonstrates this:
11754 \begin_layout Standard
11756 \begin_inset Tabular
11757 <lyxtabular version="3" rows="2" columns="2">
11758 <features tabularvalignment="middle">
11759 <column alignment="center" valignment="top" width="0pt">
11760 <column alignment="center" valignment="top" width="0pt">
11762 <cell alignment="center" valignment="top" usebox="none">
11765 \begin_layout Plain Layout
11771 <cell alignment="center" valignment="top" usebox="none">
11774 \begin_layout Plain Layout
11775 \begin_inset Formula $A=B$
11785 <cell alignment="center" valignment="top" usebox="none">
11788 \begin_layout Plain Layout
11789 \begin_inset Note Note
11792 \begin_layout Plain Layout
11799 is only used as spacer.
11805 \begin_inset Formula $\raisebox{5mm}{}$
11808 equation without space
11813 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11816 \begin_layout Plain Layout
11817 \begin_inset Formula $A{=}B$
11833 \begin_layout Standard
11835 The command for the last formula is:
11840 \begin_inset Formula $\to$
11846 \begin_layout Standard
11847 \begin_inset VSpace bigskip
11850 Spaces are needed for physical units, because the space between the value
11851 and the unit is the smallest one and not a normal space.
11852 For units in text, the smallest space is inserted via the menu
11854 Insert\SpecialChar \menuseparator
11855 Formatting\SpecialChar \menuseparator
11857 \begin_inset space ~
11865 arg "space-insert thin"
11871 \begin_layout Standard
11872 An example to visualize the difference:
11875 \begin_layout Standard
11876 \begin_inset Tabular
11877 <lyxtabular version="3" rows="2" columns="2">
11878 <features tabularvalignment="middle">
11879 <column alignment="left" valignment="top" width="0">
11880 <column alignment="left" valignment="top" width="0">
11882 <cell alignment="center" valignment="top" usebox="none">
11885 \begin_layout Plain Layout
11887 \begin_inset Formula $\cdot$
11895 <cell alignment="center" valignment="top" usebox="none">
11898 \begin_layout Plain Layout
11899 space between value and unit
11906 <cell alignment="center" valignment="top" usebox="none">
11909 \begin_layout Plain Layout
11911 \begin_inset space \thinspace{}
11915 \begin_inset Formula $\cdot$
11923 <cell alignment="center" valignment="top" usebox="none">
11926 \begin_layout Plain Layout
11927 smallest space between value and unit
11940 \begin_layout Subsection
11945 \begin_layout Plain Layout
11958 \begin_layout Plain Layout
11959 for vertical space in formulas see
11960 \begin_inset CommandInset ref
11962 reference "sub:Line-Separation"
11975 \begin_layout Plain Layout
11983 \begin_inset Note Note
11986 \begin_layout Plain Layout
11989 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11992 \begin_layout Plain Layout
11995 texorpdfstring is in section
11996 \begin_inset CommandInset ref
11998 reference "sub:Formulas-in-Section"
12008 \begin_inset CommandInset label
12010 name "sub:Variable-Space"
12015 \begin_inset Index idx
12018 \begin_layout Plain Layout
12019 Space ! horizontal ! variable
12027 \begin_layout Standard
12028 Space with a defined length can be inserted with the command
12035 \begin_inset Index idx
12038 \begin_layout Plain Layout
12048 \begin_inset Quotes eld
12057 \begin_layout Plain Layout
12069 \begin_inset Quotes erd
12073 The length can be specified by left-clicking on the
12074 \begin_inset Quotes eld
12083 \begin_layout Plain Layout
12095 \begin_inset Quotes erd
12099 The length may also be negative.
12100 To insert so many space that the formula uses all available space, the
12108 \begin_inset Index idx
12111 \begin_layout Plain Layout
12122 \begin_layout Standard
12123 \begin_inset VSpace -1mm
12129 \begin_layout Standard
12131 \begin_inset Tabular
12132 <lyxtabular version="3" rows="4" columns="2">
12133 <features tabularvalignment="middle">
12134 <column alignment="center" valignment="top" width="0">
12135 <column alignment="center" valignment="top" width="0">
12137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12140 \begin_layout Plain Layout
12148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12151 \begin_layout Plain Layout
12159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12162 \begin_layout Plain Layout
12169 \begin_layout Plain Layout
12179 \begin_inset Formula $\to$
12185 \begin_inset space \thinspace{}
12193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12196 \begin_layout Plain Layout
12197 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12210 \begin_layout Plain Layout
12217 \begin_layout Plain Layout
12227 \begin_inset Formula $\to$
12233 \begin_inset space \thinspace{}
12241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12244 \begin_layout Plain Layout
12245 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12258 \begin_layout Plain Layout
12265 \begin_layout Plain Layout
12279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12282 \begin_layout Plain Layout
12283 \begin_inset Formula $A=A\hfill B=B$
12299 \begin_layout Standard
12300 In the last example the available space is given by the longest column entry
12302 In an inline formula the space depends on the length of the line in which
12310 Thus, when the line uses the full width, no space will be created.
12317 only has an effect on displayed formulas when the formula style
12322 (Formula styles are explained in
12323 \begin_inset CommandInset ref
12325 reference "sec:Formula-Styles"
12332 \begin_layout Standard
12339 , there are the commands
12351 that fill the space with a pattern, see
12352 \begin_inset CommandInset ref
12354 reference "sub:Ellipses"
12361 \begin_layout Standard
12362 For text, variable space can be inserted via the menu
12364 Insert\SpecialChar \menuseparator
12365 Formatting\SpecialChar \menuseparator
12367 \begin_inset space ~
12375 \begin_layout Standard
12376 This is a line with
12377 \begin_inset space \hspace{}
12382 \begin_inset space \thinspace{}
12388 \begin_layout Standard
12389 This is a line with
12390 \begin_inset space \hfill{}
12396 \begin_layout Subsection
12397 Space besides inline Formulas
12398 \begin_inset Index idx
12401 \begin_layout Plain Layout
12402 Space ! besides inline formulas
12410 \begin_layout Standard
12411 The space that surrounds inline formulas can be adjusted with the length
12419 \begin_inset Index idx
12422 \begin_layout Plain Layout
12431 The value of a length is set with the command
12438 \begin_inset Index idx
12441 \begin_layout Plain Layout
12449 that has the following scheme:
12452 \begin_layout Standard
12457 setlength{length name}{value}
12460 \begin_layout Standard
12468 \begin_inset space \thinspace{}
12474 \begin_layout Standard
12484 \begin_layout Standard
12485 is inserted in TeX-mode.
12487 \begin_inset space \thinspace{}
12490 mm space will now be set around all inline formulas:
12494 \begin_layout Plain Layout
12508 \begin_layout Standard
12509 This is a line with an inline formula
12510 \begin_inset Formula $A=B$
12514 \begin_inset space \thinspace{}
12517 mm surrounding space.
12521 \begin_layout Plain Layout
12535 \begin_layout Standard
12536 To return to the predefined value,
12542 is set to the value 0
12543 \begin_inset space \thinspace{}
12549 \begin_layout Section
12551 \begin_inset Index idx
12554 \begin_layout Plain Layout
12561 \begin_inset Index idx
12564 \begin_layout Plain Layout
12569 \begin_layout Plain Layout
12580 \begin_layout Plain Layout
12595 \begin_layout Standard
12596 Boxes for text are described in chapter
12603 \begin_inset space ~
12611 \begin_layout Subsection
12613 \begin_inset CommandInset label
12615 name "sub:Boxes-with-Frame"
12620 \begin_inset Index idx
12623 \begin_layout Plain Layout
12632 \begin_layout Standard
12633 It is possible to frame formulas or parts of it with the commands
12640 \begin_inset Index idx
12643 \begin_layout Plain Layout
12658 \begin_inset Index idx
12661 \begin_layout Plain Layout
12672 \begin_layout Standard
12673 When one of these commands is inserted to a formula, a blue box appears
12674 within a frame to enter formula parts.
12681 an additional formula has to be created by
12685 within this box, because the box content will otherwise be treated as mathemati
12693 is used, a new formula is automatically created inside the frame.
12696 \begin_layout Standard
12703 is not suitable to frame displayed formulas because the formula will always
12704 be set in the size of the text.
12711 is in contrary not suitable to frame inline formulas, because the formula
12712 will always be set in the size of a displayed formula.
12715 \begin_layout Standard
12722 there is the command
12729 \begin_inset Index idx
12732 \begin_layout Plain Layout
12740 where additionally the frame width and the alignment can be specified.
12747 is used in the following scheme:
12750 \begin_layout Standard
12755 framebox[frame width][position]{box content}
12758 \begin_layout Standard
12759 The position can either be
12776 right aligns the formula in the box.
12777 When no position is given, the formula will be centered.
12778 \begin_inset Newline newline
12781 Is no width given, also no position can be given.
12782 In this case the frame width is adjusted to the box content like for
12791 \begin_layout Standard
12798 is inserted, a box appears containing three blue boxes.
12799 The first two boxes are surrounded by brackets and denote the two optional
12801 The third box is for formula parts like for
12810 \begin_layout Standard
12812 \begin_inset Tabular
12813 <lyxtabular version="3" rows="5" columns="2">
12814 <features tabularvalignment="middle">
12815 <column alignment="center" valignment="top" width="0">
12816 <column alignment="center" valignment="top" width="0">
12818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12821 \begin_layout Plain Layout
12827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12830 \begin_layout Plain Layout
12832 \begin_inset Note Note
12835 \begin_layout Plain Layout
12842 is only used as spacer.
12854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12857 \begin_layout Plain Layout
12864 \begin_layout Plain Layout
12883 \begin_layout Plain Layout
12897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12900 \begin_layout Plain Layout
12901 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12914 \begin_layout Plain Layout
12921 \begin_layout Plain Layout
12936 \begin_layout Plain Layout
12950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12953 \begin_layout Plain Layout
12954 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12967 \begin_layout Plain Layout
12974 \begin_layout Plain Layout
12988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12991 \begin_layout Plain Layout
12992 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13005 \begin_layout Plain Layout
13012 \begin_layout Plain Layout
13022 \begin_inset Formula $\to$
13026 \begin_inset Formula $\to$
13039 \begin_layout Plain Layout
13049 \begin_inset Formula $\downarrow$
13057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13060 \begin_layout Plain Layout
13061 \begin_inset Formula $\raisebox{6mm}{}$
13065 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13069 \begin_inset Formula $\raisebox{-4mm}{}$
13085 \begin_layout Standard
13086 The frame thickness can also be adjusted.
13087 To do this the following commands have to be inserted in TeX-mode before
13091 \begin_layout Standard
13101 \begin_inset Quotes eld
13105 \begin_inset Quotes erd
13119 \begin_inset Quotes eld
13123 \begin_inset Quotes erd
13129 \begin_layout Standard
13130 \begin_inset Quotes eld
13134 \begin_inset Quotes erd
13137 specifies the minimal distance between the frame and the first character
13139 An example for this is the following framed formula:
13143 \begin_layout Plain Layout
13155 \begin_inset Formula \[
13160 Before this formula the commands
13163 \begin_layout Standard
13185 \begin_layout Standard
13186 were inserted in TeX-mode.
13187 The given values are used for all following boxes.
13190 \begin_layout Standard
13191 To return to the standard frame size, the command
13194 \begin_layout Standard
13219 \begin_layout Plain Layout
13233 \begin_layout Standard
13234 is inserted in TeX-mode before the next formula.
13237 \begin_layout Subsection
13238 Boxes without Frame
13239 \begin_inset CommandInset label
13241 name "sub:Boxes-without-Frame"
13246 \begin_inset Index idx
13249 \begin_layout Plain Layout
13250 Boxes ! without frame
13258 \begin_layout Standard
13259 For boxes without a frame there are the following box commands:
13266 \begin_inset Index idx
13269 \begin_layout Plain Layout
13284 \begin_inset Index idx
13287 \begin_layout Plain Layout
13302 \begin_inset Index idx
13305 \begin_layout Plain Layout
13316 \begin_layout Standard
13323 a box can be super- or subscripted.
13324 But in contrary to normal super- and subscripting, the characters in the
13325 box keep their font size.
13332 is used in the following scheme:
13335 \begin_layout Standard
13340 raisebox{height}{box content}
13343 \begin_layout Standard
13344 When the box should contain a formula, an extra formula is needed like for
13355 \begin_inset Note Greyedout
13358 \begin_layout Plain Layout
13369 this extra formula is created by pressing
13373 twice instead of once because LyX doesn't yet support
13387 \begin_layout Standard
13389 \begin_inset Tabular
13390 <lyxtabular version="3" rows="4" columns="2">
13391 <features tabularvalignment="middle">
13392 <column alignment="center" valignment="top" width="0">
13393 <column alignment="center" valignment="top" width="0">
13395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13398 \begin_layout Plain Layout
13404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13407 \begin_layout Plain Layout
13415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13418 \begin_layout Plain Layout
13422 \begin_inset Formula $\to$
13428 \begin_inset Formula $\to$
13436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13439 \begin_layout Plain Layout
13440 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13453 \begin_layout Plain Layout
13457 \begin_inset Formula $\to$
13463 \begin_inset Formula $\to$
13471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13474 \begin_layout Plain Layout
13475 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13488 \begin_layout Plain Layout
13492 \begin_inset Formula $\to$
13511 \begin_layout Plain Layout
13525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13528 \begin_layout Plain Layout
13529 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13545 \begin_layout Standard
13570 , with the difference that there is no frame.
13573 \begin_layout Subsection
13575 \begin_inset CommandInset label
13577 name "sub:Colored-Boxes"
13582 \begin_inset Index idx
13585 \begin_layout Plain Layout
13594 \begin_layout Standard
13595 To be able to use all commands explained in this section, the LaTeX-package
13604 \begin_layout Plain Layout
13609 is part of every LaTeX standard installation.
13615 \begin_inset Index idx
13618 \begin_layout Plain Layout
13624 has to be loaded in the LaTeX-preamble with the line
13628 \begin_layout Plain Layout
13629 When text is colored somewhere in the document with a predefined color,
13630 LyX loads the LaTeX-package
13635 Thus it is possible that the package is loaded twice, but this doesn't
13642 \begin_inset Note Note
13645 \begin_layout Plain Layout
13646 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13655 \begin_layout Standard
13663 \begin_layout Standard
13664 \begin_inset VSpace medskip
13667 To color boxes, the command
13674 \begin_inset Index idx
13677 \begin_layout Plain Layout
13685 is used in the following scheme:
13688 \begin_layout Standard
13693 colorbox{color}{box content}
13696 \begin_layout Standard
13697 The box content can also be a box and a
13703 can also be part of another box (see the 2nd and 3rd example).
13704 When the box should contain a formula, an extra formula has to be created,
13705 the same way as for
13715 \begin_layout Plain Layout
13716 This also applies for the command
13730 \begin_layout Standard
13731 One of the following predefined colors can be chosen:
13734 \begin_layout Standard
13768 \begin_layout Standard
13770 \begin_inset Tabular
13771 <lyxtabular version="3" rows="4" columns="2">
13772 <features tabularvalignment="middle">
13773 <column alignment="center" valignment="top" width="0">
13774 <column alignment="center" valignment="top" width="0">
13776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13779 \begin_layout Plain Layout
13785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13788 \begin_layout Plain Layout
13790 \begin_inset Note Note
13793 \begin_layout Plain Layout
13800 is only used as spacer.
13812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13815 \begin_layout Plain Layout
13819 \begin_inset Formula $\to$
13829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13832 \begin_layout Plain Layout
13833 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13846 \begin_layout Plain Layout
13850 \begin_inset Formula $\to$
13861 \begin_layout Plain Layout
13875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13878 \begin_layout Plain Layout
13879 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13892 \begin_layout Plain Layout
13899 \begin_layout Plain Layout
13911 \begin_inset Formula $\to$
13930 \begin_layout Plain Layout
13944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13947 \begin_layout Plain Layout
13948 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13964 \begin_layout Standard
13971 only colors the box but not the characters in the box.
13972 To color all characters, the whole formula is highlighted and the wanted
13973 color is chosen in the
13976 \begin_inset space ~
13982 The dialog can be called with the toolbar button
13983 \begin_inset Graphics
13984 filename ../images/dialog-show_character.png
13991 Edit\SpecialChar \menuseparator
13993 \begin_inset space ~
13996 Style\SpecialChar \menuseparator
14000 The formula number has then the same color as the formula.
14001 When the formula number should get another color than the formula characters,
14002 the color must be changed within the formula.
14005 \begin_layout Standard
14009 \begin_layout Standard
14012 \begin_inset Formula \begin{equation}
14013 \int A=B\label{eq:red}\end{equation}
14020 \begin_inset Formula \begin{equation}
14021 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
14028 \begin_layout Standard
14030 \begin_inset CommandInset ref
14036 is completely colored red.
14037 \begin_inset Newline newline
14041 \begin_inset CommandInset ref
14043 reference "eq:redgreen"
14047 was first completely colored green to set the color for the formula number.
14048 Subsequently the formula characters were colored red.
14051 \begin_layout Standard
14052 \begin_inset VSpace bigskip
14055 To color the frame different than the rest of the box, the command
14062 \begin_inset Index idx
14065 \begin_layout Plain Layout
14073 is used in the following scheme:
14076 \begin_layout Standard
14081 fcolorbox{frame color}{color}{box content}
14084 \begin_layout Standard
14091 is an extension of the command
14098 The frame width is set, like for
14121 \begin_layout Plain Layout
14133 \begin_inset Formula \[
14134 \fcolorbox{cyan}{magenta}{A=B}\]
14142 \begin_layout Plain Layout
14156 \begin_layout Standard
14157 This formula was created with the command
14158 \begin_inset Newline newline
14166 \begin_inset Formula $\to$
14172 \begin_inset Formula $\to$
14182 \begin_layout Standard
14183 \begin_inset VSpace bigskip
14186 To use other colors than the predefined ones, they have to be defined first.
14189 \begin_layout Standard
14190 One can for example define the color
14191 \begin_inset Quotes eld
14199 \begin_inset Quotes erd
14202 with the LaTeX-preamble line:
14205 \begin_layout Standard
14210 definecolor{darkgreen}{cmyk}{0.5,
14225 \begin_inset Index idx
14228 \begin_layout Plain Layout
14239 \begin_layout Standard
14244 is the color space that denotes the colors
14261 The four comma separated numbers are the portion factor for the corresponding
14262 colors of the color space.
14263 The factors can be in the range of 0
14264 \begin_inset space \thinspace{}
14268 \begin_inset space \thinspace{}
14276 also the color space
14280 can be used for definitions.
14297 , so that there are in this case three portion factors for the corresponding
14299 Furthermore there is the color space
14303 with one portion factor for the gray value.
14306 \begin_layout Standard
14307 As example a framed box with the new defined color
14311 where the characters have been colored
14316 \begin_inset Formula \begin{equation}
14317 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14324 \begin_layout Standard
14325 Self-defined colors can also be used for text with the help of the command
14333 \begin_inset Index idx
14336 \begin_layout Plain Layout
14345 \begin_layout Standard
14349 \begin_layout Plain Layout
14353 textcolor{darkgreen}{
14359 \begin_inset Quotes eld
14363 \begin_inset Quotes erd
14370 \begin_layout Plain Layout
14380 \begin_layout Standard
14388 \begin_inset Index idx
14391 \begin_layout Plain Layout
14399 is used in the scheme
14403 textcolor{color}{characters to color}
14408 \begin_layout Subsection
14410 \begin_inset CommandInset label
14412 name "sub:Paragraph-Boxes"
14417 \begin_inset Index idx
14420 \begin_layout Plain Layout
14421 Boxes ! as paragraph
14429 \begin_layout Standard
14430 A box that can contain several lines and paragraphs, a so called paragraph
14431 box (parbox), can be created with the menu
14433 Insert\SpecialChar \menuseparator
14436 or the toolbar button
14437 \begin_inset Graphics
14438 filename ../images/box-insert.png
14446 \begin_layout Standard
14447 The following example shows a framed parbox in a line:
14450 \begin_layout Standard
14451 \begin_inset VSpace medskip
14455 \begin_inset Box Boxed
14465 height_special "totalheight"
14468 \begin_layout Plain Layout
14469 This is a paragraph box.
14471 \begin_inset space \thinspace{}
14474 cm long and can also contain formulas:
14475 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14486 \begin_layout Standard
14487 \begin_inset VSpace medskip
14493 \begin_layout Standard
14494 Such a box is created by right-clicking on the gray box inset.
14495 A dialog pops up showing the box properties.
14509 \begin_inset space \thinspace{}
14514 Vertical Box Alignment
14519 \begin_layout Standard
14520 \begin_inset VSpace medskip
14523 In LaTeX a parbox is created with the command
14530 \begin_inset Index idx
14533 \begin_layout Plain Layout
14541 that has the following scheme:
14544 \begin_layout Standard
14549 parbox[position]{width}{box content}
14552 \begin_layout Standard
14566 for bottom means that the box is aligned within the surrounding text with
14572 for top this is done with the first line.
14573 When no position is given, the box will be vertically centered, see section
14581 \begin_inset space ~
14586 manual for examples.
14589 \begin_layout Standard
14590 \begin_inset VSpace bigskip
14593 To frame formulas completely, including the formula number, the formula
14594 must be set into a parbox.
14595 To do this, the command
14609 is inserted in TeX-mode before the formula.
14617 \begin_inset Index idx
14620 \begin_layout Plain Layout
14628 is hereby the line width set for the document.
14629 Because the frame is outside the parbox, 2
14630 \begin_inset space \thinspace{}
14633 times the frame separation and the frame thickness must be subtracted from
14635 As this is not automatically done by LyX due to a bug
14639 \begin_layout Plain Layout
14640 \begin_inset CommandInset href
14642 name "LyX-bug #4483"
14643 target "http://www.lyx.org/trac/ticket/4483"
14652 , TeX-mode has to be used.
14653 To be able to multiply and subtract in arguments, the LaTeX-package
14661 \begin_layout Plain Layout
14666 is part of every LaTeX standard installation.
14672 \begin_inset Index idx
14675 \begin_layout Plain Layout
14681 must be loaded in the LaTeX-preamble with the line
14684 \begin_layout Standard
14692 \begin_layout Standard
14693 Behind the formula both boxes are closed by entering
14698 Here is an example:
14702 \begin_layout Plain Layout
14716 \begin_layout Standard
14720 \begin_layout Plain Layout
14738 \begin_inset Formula \begin{equation}
14739 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14747 \begin_layout Plain Layout
14758 \begin_layout Plain Layout
14772 \begin_layout Standard
14773 \begin_inset VSpace medskip
14776 As a parbox is used as argument of
14782 , there is in this case no difference between
14797 \begin_layout Standard
14798 \begin_inset VSpace bigskip
14801 Paragraph boxes are very useful to comment formulas directly.
14808 is used in combination with the command
14822 \begin_inset CommandInset ref
14824 reference "sub:User-defined-Numbering"
14831 \begin_layout Standard
14832 An example of a formula commented with
14841 \begin_layout Standard
14845 \begin_layout Plain Layout
14858 This is a description.
14859 It is distinctly separated from the formula and multiline.
14863 \begin_layout Plain Layout
14875 \begin_layout Standard
14876 Such a formula must be inserted completely in TeX-mode because LyX does
14877 not yet support the command
14884 The formula is created with the following command sequence:
14887 \begin_layout Standard
14900 is inserted in TeX-mode.
14904 \begin_layout Plain Layout
14905 When the formula style
14917 can also be replaced by
14924 (formula styles see
14925 \begin_inset CommandInset ref
14927 reference "sec:Formula-Styles"
14936 Then the description follows as normal text and finally
14942 is inserted in TeX-mode.
14955 hereby create a displayed formula.
14958 \begin_layout Standard
14965 can be seen in this example that was
14966 \begin_inset Quotes eld
14970 \begin_inset Quotes erd
14973 using the mathematical textmode:
14974 \begin_inset Formula \[
14975 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14982 \begin_layout Section
14984 \begin_inset Index idx
14987 \begin_layout Plain Layout
14996 \begin_layout Subsection
14998 \begin_inset CommandInset label
15000 name "sub:Big-Operators"
15005 \begin_inset Index idx
15008 \begin_layout Plain Layout
15015 \begin_inset Index idx
15018 \begin_layout Plain Layout
15025 \begin_inset Index idx
15028 \begin_layout Plain Layout
15037 \begin_layout Standard
15038 To be able to use all integral operators listed here, the option
15040 Use esint package automatically
15042 must be set in the document settings under
15045 \begin_inset space ~
15053 \begin_layout Standard
15054 \begin_inset space \hfill{}
15058 \begin_inset Tabular
15059 <lyxtabular version="3" rows="11" columns="2">
15060 <features tabularvalignment="middle">
15061 <column alignment="center" valignment="top" width="0pt">
15062 <column alignment="center" valignment="top" width="0pt">
15064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15067 \begin_layout Plain Layout
15073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15076 \begin_layout Plain Layout
15084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15087 \begin_layout Plain Layout
15091 \begin_inset Index idx
15094 \begin_layout Plain Layout
15107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15110 \begin_layout Plain Layout
15111 \begin_inset Formula $\int$
15121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15124 \begin_layout Plain Layout
15132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15135 \begin_layout Plain Layout
15136 \begin_inset Formula $\oint$
15146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15149 \begin_layout Plain Layout
15157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15160 \begin_layout Plain Layout
15161 \begin_inset Formula $\ointctrclockwise$
15171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15174 \begin_layout Plain Layout
15182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15185 \begin_layout Plain Layout
15186 \begin_inset Formula $\ointclockwise$
15196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15199 \begin_layout Plain Layout
15207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15210 \begin_layout Plain Layout
15211 \begin_inset Formula $\sqint$
15221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15224 \begin_layout Plain Layout
15232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15235 \begin_layout Plain Layout
15237 \begin_inset Formula $\fint$
15247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15250 \begin_layout Plain Layout
15258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15261 \begin_layout Plain Layout
15263 \begin_inset Formula $\landupint$
15273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15276 \begin_layout Plain Layout
15284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15287 \begin_layout Plain Layout
15289 \begin_inset Formula $\landdownint$
15299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15302 \begin_layout Plain Layout
15310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15313 \begin_layout Plain Layout
15314 \begin_inset Formula $\bigcap$
15324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15327 \begin_layout Plain Layout
15335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15338 \begin_layout Plain Layout
15339 \begin_inset Formula $\bigcup$
15353 \begin_inset space \hfill{}
15357 \begin_inset Tabular
15358 <lyxtabular version="3" rows="11" columns="2">
15359 <features tabularvalignment="middle">
15360 <column alignment="center" valignment="top" width="0pt">
15361 <column alignment="center" valignment="top" width="0pt">
15363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15366 \begin_layout Plain Layout
15372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15375 \begin_layout Plain Layout
15383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15386 \begin_layout Plain Layout
15390 \begin_inset Index idx
15393 \begin_layout Plain Layout
15406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15409 \begin_layout Plain Layout
15410 \begin_inset Formula $\sum$
15420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15423 \begin_layout Plain Layout
15427 \begin_inset Index idx
15430 \begin_layout Plain Layout
15443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15446 \begin_layout Plain Layout
15447 \begin_inset Formula $\prod$
15457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15460 \begin_layout Plain Layout
15468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15471 \begin_layout Plain Layout
15472 \begin_inset Formula $\coprod$
15482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15485 \begin_layout Plain Layout
15493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15496 \begin_layout Plain Layout
15497 \begin_inset Formula $\bigodot$
15507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15510 \begin_layout Plain Layout
15518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15521 \begin_layout Plain Layout
15522 \begin_inset Formula $\bigotimes$
15532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15535 \begin_layout Plain Layout
15543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15546 \begin_layout Plain Layout
15547 \begin_inset Formula $\bigoplus$
15557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15560 \begin_layout Plain Layout
15568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15571 \begin_layout Plain Layout
15572 \begin_inset Formula $\bigwedge$
15582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15585 \begin_layout Plain Layout
15593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15596 \begin_layout Plain Layout
15597 \begin_inset Formula $\bigvee$
15607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15610 \begin_layout Plain Layout
15618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15621 \begin_layout Plain Layout
15622 \begin_inset Formula $\bigsqcup$
15632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15635 \begin_layout Plain Layout
15643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15646 \begin_layout Plain Layout
15647 \begin_inset Formula $\biguplus$
15661 \begin_inset space \hfill{}
15667 \begin_layout Standard
15668 All big operators can also be inserted via the math toolbar button
15669 \begin_inset Graphics
15670 filename ../images/math/intop.png
15678 \begin_layout Standard
15679 The operators are called big because they are bigger than the sometimes
15680 equal looking binary operators.
15681 All big operators can have limits as described in the next subsection.
15684 \begin_layout Standard
15685 For all integral operators there is a second version available, ending on
15703 These operators are different from
15710 \begin_inset space \space{}
15713 in the style the operator limits are displayed, see
15714 \begin_inset CommandInset ref
15716 reference "sub:Operator-Limits"
15724 \begin_layout Subsubsection*
15725 Advice for Integrals
15728 \begin_layout Standard
15733 in an integral is an operator, that therefore has to be set upright.
15734 This is done by highlighting the
15738 and using the keyboard shortcut
15748 \begin_layout Plain Layout
15754 \begin_inset CommandInset ref
15756 reference "sub:Font-Styles"
15766 Finally the smallest space is inserted before the
15770 , as this is usual for operators.
15774 \begin_layout Standard
15776 \begin_inset Formula $\int A(x)dx$
15780 \begin_inset Newline newline
15784 \begin_inset Phantom HPhantom
15787 \begin_layout Plain Layout
15794 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15800 \begin_layout Standard
15801 For multiple integrals there are the following commands:
15802 \begin_inset VSpace medskip
15808 \begin_layout Standard
15809 \begin_inset space \hfill{}
15813 \begin_inset Tabular
15814 <lyxtabular version="3" rows="4" columns="2">
15815 <features tabularvalignment="middle">
15816 <column alignment="center" valignment="top" width="0">
15817 <column alignment="center" valignment="top" width="0">
15819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15822 \begin_layout Plain Layout
15828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15831 \begin_layout Plain Layout
15833 \begin_inset Note Note
15836 \begin_layout Plain Layout
15843 is only used as spacer.
15855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15858 \begin_layout Plain Layout
15866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15869 \begin_layout Plain Layout
15870 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15883 \begin_layout Plain Layout
15891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15894 \begin_layout Plain Layout
15895 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15908 \begin_layout Plain Layout
15916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15919 \begin_layout Plain Layout
15920 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15934 \begin_inset space \hfill{}
15938 \begin_inset Tabular
15939 <lyxtabular version="3" rows="4" columns="2">
15940 <features tabularvalignment="middle">
15941 <column alignment="center" valignment="top" width="0">
15942 <column alignment="center" valignment="top" width="0">
15944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15947 \begin_layout Plain Layout
15953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15956 \begin_layout Plain Layout
15964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15967 \begin_layout Plain Layout
15975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15978 \begin_layout Plain Layout
15979 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15992 \begin_layout Plain Layout
16000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16003 \begin_layout Plain Layout
16004 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16017 \begin_layout Plain Layout
16025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16028 \begin_layout Plain Layout
16029 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16043 \begin_inset space \hfill{}
16049 \begin_layout Subsection
16051 \begin_inset CommandInset label
16053 name "sub:Operator-Limits"
16058 \begin_inset Index idx
16061 \begin_layout Plain Layout
16070 \begin_layout Standard
16071 Limits are created by super- and subscripts:
16074 \begin_layout Standard
16076 \begin_inset Tabular
16077 <lyxtabular version="3" rows="2" columns="2">
16078 <features tabularvalignment="middle">
16079 <column alignment="center" valignment="top" width="0pt">
16080 <column alignment="center" valignment="top" width="0pt">
16082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16085 \begin_layout Plain Layout
16091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16094 \begin_layout Plain Layout
16096 \begin_inset Note Note
16099 \begin_layout Plain Layout
16106 is only used as spacer.
16118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16121 \begin_layout Plain Layout
16130 \begin_layout Plain Layout
16140 \begin_inset Formula $\to$
16144 \begin_inset Formula $\to$
16152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16155 \begin_layout Plain Layout
16156 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16172 \begin_layout Standard
16173 Limits of inline formulas are set right beside the operator.
16174 Limits in displayed formulas are set above or below the operator, except
16175 for integral limits.
16178 \begin_layout Standard
16179 To force that the limits are set beside the operator, the cursor is set
16180 directly behind the operator and the limits type is changed with the menu
16183 Edit\SpecialChar \menuseparator
16184 Math\SpecialChar \menuseparator
16203 \begin_layout Standard
16204 The default limits type is this:
16205 \begin_inset Formula \[
16206 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16210 This is how it looks when the limits type was changed to
16217 \begin_inset Formula \[
16218 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16222 For integrals, except those ending with
16238 etc., the limits are by default set beside the operator.
16239 But for multiple integrals the limits are often set below the operator.
16240 In the following example the limits type was therefore set to
16244 and so set below the integrals:
16245 \begin_inset Formula \begin{equation}
16246 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16253 \begin_layout Standard
16254 \begin_inset VSpace medskip
16257 To specify conditions for limits, the commands
16264 \begin_inset Index idx
16267 \begin_layout Plain Layout
16282 \begin_inset Index idx
16285 \begin_layout Plain Layout
16294 To create for example this expression
16295 \begin_inset Formula \begin{equation}
16296 \sum_{\begin{subarray}{c}
16300 \end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16307 \begin_layout Standard
16308 the following has to be done:
16309 \begin_inset Newline newline
16324 \begin_layout Plain Layout
16336 One is now in a blue box under the summation operator and insert there
16345 \begin_layout Plain Layout
16357 The blue box is now within a purple box and now several lines can be written
16359 A new line is created by inserting a line break (
16362 arg "newline-insert newline"
16367 \begin_inset Newline newline
16372 0<k<1000 Ctrl+Return
16373 \begin_inset Newline newline
16378 is typed in, a new box appears below for the new line.
16381 \begin_layout Standard
16382 The alignment of the lines can be changed to left aligned with the
16392 Edit\SpecialChar \menuseparator
16396 To get right alignment,
16404 \begin_layout Plain Layout
16415 is inserted at the beginning of the line.
16418 \begin_layout Standard
16431 with the difference that the lines are always centered.
16434 \begin_layout Standard
16435 \begin_inset VSpace bigskip
16439 \begin_inset CommandInset ref
16441 reference "eq:substack"
16445 there can be too much space beside an operator, because the characters
16446 following the operator are set beside the limits.
16449 \begin_layout Standard
16450 To avoid this, the following macro can be used in the LaTeX-preamble:
16453 \begin_layout Standard
16467 \begin_inset Newline newline
16479 \begin_inset Newline newline
16486 mathclapinternal #1#2{
16490 mathsurround =0pt #1{#2}$}}
16493 \begin_layout Standard
16494 This defines the command
16501 \begin_inset Index idx
16504 \begin_layout Plain Layout
16512 that sets the width of the limit to 0
16513 \begin_inset space \thinspace{}
16517 The command scheme is
16520 \begin_layout Standard
16528 \begin_layout Standard
16529 where the limit can consist of several conditions.
16532 \begin_layout Standard
16534 \begin_inset CommandInset ref
16536 reference "eq:substack"
16540 , one uses the command
16543 \begin_layout Standard
16556 \begin_layout Plain Layout
16565 0<k<1000 Ctrl+Return
16568 \begin_layout Standard
16569 to create the lower limit.
16570 The summand is now directly behind the summation operator:
16571 \begin_inset Formula \[
16572 \sum_{\mathclap{\substack{0<k<1000\\
16583 \begin_layout Standard
16584 \begin_inset VSpace bigskip
16587 How to use one limit for several operators is described in
16588 \begin_inset CommandInset ref
16590 reference "sub:Self-defined-Operators"
16597 \begin_layout Subsection
16599 \begin_inset CommandInset label
16601 name "sub:Binary-Operators"
16606 \begin_inset Index idx
16609 \begin_layout Plain Layout
16618 \begin_layout Standard
16619 Binary operators are surrounded by space when there is a character before
16621 \begin_inset VSpace medskip
16627 \begin_layout Standard
16628 \begin_inset space \hfill{}
16632 \begin_inset Tabular
16633 <lyxtabular version="3" rows="13" columns="2">
16634 <features tabularvalignment="middle">
16635 <column alignment="center" valignment="top" width="0pt">
16636 <column alignment="center" valignment="top" width="0pt">
16638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16641 \begin_layout Plain Layout
16643 \begin_inset Note Note
16646 \begin_layout Plain Layout
16653 is only used as spacer.
16663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16666 \begin_layout Plain Layout
16674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16677 \begin_layout Plain Layout
16683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16686 \begin_layout Plain Layout
16687 \begin_inset Formula $+$
16697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16700 \begin_layout Plain Layout
16706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16709 \begin_layout Plain Layout
16710 \begin_inset Formula $-$
16720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16723 \begin_layout Plain Layout
16731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16734 \begin_layout Plain Layout
16735 \begin_inset Formula $\pm$
16745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16748 \begin_layout Plain Layout
16756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16759 \begin_layout Plain Layout
16760 \begin_inset Formula $\mp$
16770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16773 \begin_layout Plain Layout
16781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16784 \begin_layout Plain Layout
16785 \begin_inset Formula $\cdot$
16795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16798 \begin_layout Plain Layout
16806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16809 \begin_layout Plain Layout
16810 \begin_inset Formula $\times$
16820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16823 \begin_layout Plain Layout
16831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16834 \begin_layout Plain Layout
16835 \begin_inset Formula $\div$
16845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16848 \begin_layout Plain Layout
16852 \begin_layout Plain Layout
16865 \begin_layout Plain Layout
16877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16880 \begin_layout Plain Layout
16881 \begin_inset Formula $*$
16891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16894 \begin_layout Plain Layout
16902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16905 \begin_layout Plain Layout
16906 \begin_inset Formula $\star$
16916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16919 \begin_layout Plain Layout
16927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16930 \begin_layout Plain Layout
16931 \begin_inset Formula $\circ$
16941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16944 \begin_layout Plain Layout
16952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16955 \begin_layout Plain Layout
16956 \begin_inset Formula $\diamond$
16966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16969 \begin_layout Plain Layout
16977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16980 \begin_layout Plain Layout
16981 \begin_inset Formula $\bullet$
16995 \begin_inset space \hfill{}
16999 \begin_inset Tabular
17000 <lyxtabular version="3" rows="13" columns="2">
17001 <features tabularvalignment="middle">
17002 <column alignment="center" valignment="top" width="0pt">
17003 <column alignment="center" valignment="top" width="0pt">
17005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17008 \begin_layout Plain Layout
17014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17017 \begin_layout Plain Layout
17025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17028 \begin_layout Plain Layout
17036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17039 \begin_layout Plain Layout
17040 \begin_inset Formula $\nabla$
17050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17053 \begin_layout Plain Layout
17061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17064 \begin_layout Plain Layout
17065 \begin_inset Formula $\bigtriangledown$
17075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17078 \begin_layout Plain Layout
17086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17089 \begin_layout Plain Layout
17090 \begin_inset Formula $\bigtriangleup$
17100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17103 \begin_layout Plain Layout
17111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17114 \begin_layout Plain Layout
17115 \begin_inset Formula $\Box$
17125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17128 \begin_layout Plain Layout
17136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17139 \begin_layout Plain Layout
17140 \begin_inset Formula $\cap$
17150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17153 \begin_layout Plain Layout
17161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17164 \begin_layout Plain Layout
17165 \begin_inset Formula $\cup$
17175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17178 \begin_layout Plain Layout
17186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17189 \begin_layout Plain Layout
17190 \begin_inset Formula $\dagger$
17200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17203 \begin_layout Plain Layout
17211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17214 \begin_layout Plain Layout
17215 \begin_inset Formula $\ddagger$
17225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17228 \begin_layout Plain Layout
17236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17239 \begin_layout Plain Layout
17240 \begin_inset Formula $\wr$
17250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17253 \begin_layout Plain Layout
17261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17264 \begin_layout Plain Layout
17265 \begin_inset Formula $\bigcirc$
17275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17278 \begin_layout Plain Layout
17286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17289 \begin_layout Plain Layout
17290 \begin_inset Formula $\wedge$
17300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17303 \begin_layout Plain Layout
17311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17314 \begin_layout Plain Layout
17315 \begin_inset Formula $\vee$
17329 \begin_inset space \hfill{}
17333 \begin_inset Tabular
17334 <lyxtabular version="3" rows="13" columns="2">
17335 <features tabularvalignment="middle">
17336 <column alignment="center" valignment="top" width="0pt">
17337 <column alignment="center" valignment="top" width="0pt">
17339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17342 \begin_layout Plain Layout
17348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17351 \begin_layout Plain Layout
17359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17362 \begin_layout Plain Layout
17370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17373 \begin_layout Plain Layout
17374 \begin_inset Formula $\oplus$
17384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17387 \begin_layout Plain Layout
17395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17398 \begin_layout Plain Layout
17399 \begin_inset Formula $\ominus$
17409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17412 \begin_layout Plain Layout
17420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17423 \begin_layout Plain Layout
17424 \begin_inset Formula $\otimes$
17434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17437 \begin_layout Plain Layout
17445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17448 \begin_layout Plain Layout
17449 \begin_inset Formula $\oslash$
17459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17462 \begin_layout Plain Layout
17470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17473 \begin_layout Plain Layout
17474 \begin_inset Formula $\odot$
17484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17487 \begin_layout Plain Layout
17495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17498 \begin_layout Plain Layout
17499 \begin_inset Formula $\amalg$
17509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17512 \begin_layout Plain Layout
17520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17523 \begin_layout Plain Layout
17524 \begin_inset Formula $\uplus$
17534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17537 \begin_layout Plain Layout
17545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17548 \begin_layout Plain Layout
17549 \begin_inset Formula $\setminus$
17559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17562 \begin_layout Plain Layout
17570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17573 \begin_layout Plain Layout
17574 \begin_inset Formula $\sqcap$
17584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17587 \begin_layout Plain Layout
17595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17598 \begin_layout Plain Layout
17599 \begin_inset Formula $\sqcup$
17609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17612 \begin_layout Plain Layout
17620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17623 \begin_layout Plain Layout
17624 \begin_inset Formula $\triangleleft$
17634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17637 \begin_layout Plain Layout
17645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17648 \begin_layout Plain Layout
17649 \begin_inset Formula $\triangleright$
17663 \begin_inset space \hfill{}
17669 \begin_layout Standard
17670 All binary operators can also be inserted via the math toolbar button
17671 \begin_inset Graphics
17672 filename ../images/math/pm.png
17680 \begin_layout Standard
17681 To typeset the Laplace operator also
17698 \begin_inset Formula $\nabla^{2}$
17701 ) can be used instead of
17710 \begin_layout Standard
17717 Insert\SpecialChar \menuseparator
17729 \begin_layout Subsection
17730 Self-defined Operators
17731 \begin_inset CommandInset label
17733 name "sub:Self-defined-Operators"
17738 \begin_inset Index idx
17741 \begin_layout Plain Layout
17742 Operators ! self-defined
17750 \begin_layout Standard
17751 With the help of the command
17755 DeclareMathOperator
17758 \begin_inset Index idx
17761 \begin_layout Plain Layout
17766 DeclareMathOperator
17771 custom operators can be defined in the LaTeX-preamble.
17772 Its command scheme is:
17775 \begin_layout Standard
17780 DeclareMathOperator{new command}{display}
17783 \begin_layout Standard
17784 Display can be characters or symbols that define how the operator looks
17786 To define a big operator a * is set behind the command.
17787 All self-defined big operators can have limits as described in
17788 \begin_inset CommandInset ref
17790 reference "sub:Operator-Limits"
17797 \begin_layout Standard
17798 For example the LaTeX-preamble line
17801 \begin_layout Standard
17806 DeclareMathOperator*{
17813 \begin_layout Standard
17814 defines the command
17820 , that inserts a big operator consisting of the lozenge symbol from
17821 \begin_inset CommandInset ref
17823 reference "sub:Miscellaneous-Symbols"
17828 \begin_inset Formula \[
17829 \Lozenge_{n=1}^{\infty}\]
17833 The command for this formula is:
17844 \begin_inset Formula $\to$
17850 \begin_layout Standard
17851 \begin_inset VSpace bigskip
17854 When self-defined operators are not used several times in the document,
17855 they can also be defined with the commands
17862 \begin_inset Index idx
17865 \begin_layout Plain Layout
17880 \begin_inset Index idx
17883 \begin_layout Plain Layout
17891 , which have the following scheme:
17894 \begin_layout Standard
17908 \begin_layout Standard
17915 defines big operators,
17924 \begin_layout Standard
17932 \begin_inset space \thinspace{}
17936 \begin_inset space \space{}
17939 be used to use one limit for several operators:
17942 \begin_layout Standard
17943 \begin_inset Formula \[
17944 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17951 \begin_layout Standard
17952 The command for the formula above is:
17953 \begin_inset Newline newline
17972 \begin_layout Plain Layout
17984 \begin_inset Formula $\to$
17993 \begin_layout Plain Layout
18007 \begin_layout Section
18009 \begin_inset Index idx
18012 \begin_layout Plain Layout
18021 \begin_layout Subsection
18023 \begin_inset CommandInset label
18025 name "sub:Font-Styles"
18030 \begin_inset Index idx
18033 \begin_layout Plain Layout
18042 \begin_layout Standard
18043 Latin letters in formulas can be set in one of the following font styles:
18044 \begin_inset VSpace -2mm
18050 \begin_layout Standard
18052 \begin_inset Tabular
18053 <lyxtabular version="3" rows="7" columns="3">
18054 <features tabularvalignment="middle">
18055 <column alignment="center" valignment="top" width="0">
18056 <column alignment="center" valignment="top" width="0">
18057 <column alignment="center" valignment="top" width="0">
18059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18062 \begin_layout Plain Layout
18068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18071 \begin_layout Plain Layout
18077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18080 \begin_layout Plain Layout
18088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18091 \begin_layout Plain Layout
18100 \begin_layout Plain Layout
18116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18119 \begin_layout Plain Layout
18120 \begin_inset Formula $\mathbb{ABC}$
18128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18131 \begin_layout Plain Layout
18144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18147 \begin_layout Plain Layout
18156 \begin_layout Plain Layout
18172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18175 \begin_layout Plain Layout
18176 \begin_inset Formula $\mathbf{AbC}$
18184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18187 \begin_layout Plain Layout
18200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18203 \begin_layout Plain Layout
18212 \begin_layout Plain Layout
18228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18231 \begin_layout Plain Layout
18232 \begin_inset Formula $\boldsymbol{AbC}$
18240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18243 \begin_layout Plain Layout
18246 arg "font-boldsymbol"
18256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18259 \begin_layout Plain Layout
18268 \begin_layout Plain Layout
18284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18287 \begin_layout Plain Layout
18288 \begin_inset Formula $\mathcal{ABC}$
18296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18299 \begin_layout Plain Layout
18312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18315 \begin_layout Plain Layout
18324 \begin_layout Plain Layout
18340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18343 \begin_layout Plain Layout
18344 \begin_inset Formula $\mathfrak{AbC}$
18352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18355 \begin_layout Plain Layout
18363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18366 \begin_layout Plain Layout
18375 \begin_layout Plain Layout
18391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18394 \begin_layout Plain Layout
18395 \begin_inset Formula $\mathscr{AbC}$
18403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18406 \begin_layout Plain Layout
18420 \begin_layout Standard
18422 \begin_inset Tabular
18423 <lyxtabular version="3" rows="5" columns="3">
18424 <features tabularvalignment="middle">
18425 <column alignment="center" valignment="top" width="0">
18426 <column alignment="center" valignment="top" width="0">
18427 <column alignment="center" valignment="top" width="0">
18429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18432 \begin_layout Plain Layout
18438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18441 \begin_layout Plain Layout
18447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18450 \begin_layout Plain Layout
18458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18461 \begin_layout Plain Layout
18470 \begin_layout Plain Layout
18486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18489 \begin_layout Plain Layout
18490 \begin_inset Formula $\mathit{AbC}$
18498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18501 \begin_layout Plain Layout
18509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18512 \begin_layout Plain Layout
18521 \begin_layout Plain Layout
18537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18540 \begin_layout Plain Layout
18541 \begin_inset Formula $\mathrm{AbC}$
18549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18552 \begin_layout Plain Layout
18565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18568 \begin_layout Plain Layout
18577 \begin_layout Plain Layout
18593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18596 \begin_layout Plain Layout
18597 \begin_inset Formula $\mathsf{AbC}$
18605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18608 \begin_layout Plain Layout
18621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18624 \begin_layout Plain Layout
18633 \begin_layout Plain Layout
18649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18652 \begin_layout Plain Layout
18653 \begin_inset Formula $\mathtt{AbC}$
18661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18664 \begin_layout Plain Layout
18667 arg "font-typewriter"
18683 \begin_layout Standard
18684 \begin_inset Note Greyedout
18687 \begin_layout Plain Layout
18704 can only be used for big letters.
18712 \begin_layout Standard
18713 Predefined is the style
18722 \begin_layout Standard
18723 The style commands work also for letters in mathematical constructs:
18724 \begin_inset Formula \[
18725 \mathfrak{A=\frac{b}{C}}\]
18732 \begin_layout Standard
18733 Characters in mathematical text don't appear in a math font style but in
18734 the text font style
18741 That their style can't be set correctly via the text style dialog is a
18746 \begin_layout Plain Layout
18747 \begin_inset CommandInset href
18749 name "LyX-bug #4629"
18750 target "http://www.lyx.org/trac/ticket/4629"
18762 \begin_layout Standard
18763 Instead of the style commands the dialog
18765 Edit\SpecialChar \menuseparator
18766 Math\SpecialChar \menuseparator
18769 or the toolbar button
18770 \begin_inset Graphics
18771 filename ../images/math/font.png
18779 \begin_layout Subsection
18781 \begin_inset CommandInset label
18783 name "sub:Bold-Formulas"
18788 \begin_inset Index idx
18791 \begin_layout Plain Layout
18800 \begin_layout Standard
18801 To make a complete formula bold, the command
18807 from the previous subsection cannot be used, because it doesn't work for
18808 small Greek letters.
18809 Furthermore it prints Latin letters always upright, like in the following
18813 \begin_layout Standard
18814 \begin_inset Formula \[
18815 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18822 \begin_layout Standard
18823 To display the formula correctly, the command
18830 \begin_inset Formula \[
18831 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18835 It is also possible to set the formula in a
18837 boldmath environment
18840 This environment is created by inserting the command
18847 \begin_inset Index idx
18850 \begin_layout Plain Layout
18859 To end the environment, the command
18866 \begin_inset Index idx
18869 \begin_layout Plain Layout
18877 is inserted in TeX-mode.
18881 \begin_layout Plain Layout
18891 \begin_inset Formula \[
18892 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18900 \begin_layout Plain Layout
18912 \begin_layout Subsection
18914 \begin_inset Index idx
18917 \begin_layout Plain Layout
18926 \begin_layout Standard
18927 Formulas can be colored like normal text: Highlight a formula or a formula
18933 Here is a formula in magenta:
18934 \begin_inset Formula \[
18935 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18942 \begin_layout Standard
18943 You can also define your own colors as described in
18944 \begin_inset CommandInset ref
18946 reference "sub:Colored-Boxes"
18951 They can be used with the TeX code command
18958 \begin_inset Index idx
18961 \begin_layout Plain Layout
18972 \begin_layout Standard
18977 textcolor{color}{characters or formula}
18980 \begin_layout Standard
18981 The following example was colored completely dark green and partly red:
18984 \begin_layout Standard
18988 \begin_layout Plain Layout
18992 textcolor{darkgreen}{
18998 \begin_inset Formula \[
18999 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
19007 \begin_layout Plain Layout
19017 \begin_layout Standard
19018 Due to a bug in LyX only complete formulas can be colored with self-defined
19023 \begin_layout Plain Layout
19024 \begin_inset CommandInset href
19026 name "LyX-bug #5269"
19027 target "http://www.lyx.org/trac/ticket/5269"
19039 \begin_layout Subsection
19041 \begin_inset CommandInset label
19043 name "sub:Font-Sizes"
19048 \begin_inset Index idx
19051 \begin_layout Plain Layout
19060 \begin_layout Standard
19061 For characters in formulas there are, analog to characters in text, the
19062 following size commands:
19065 \begin_layout Standard
19109 \begin_inset Newline newline
19131 \begin_layout Standard
19132 The size produced by the commands depends on the document font size, that
19133 corresponds with the command
19140 The other commands produce smaller or larger sizes than
19147 The font size can however not exceed a certain value.
19148 Is for example the document font size 12
19149 \begin_inset space \thinspace{}
19158 switches to the same size as
19168 \begin_layout Standard
19169 A size command is inserted in TeX-mode before the formula and sets the size
19170 for all following formula and text characters.
19171 To switch back to the initial size, the command
19177 is inserted behind the formula in TeX-mode.
19180 \begin_layout Standard
19181 \begin_inset Newpage newpage
19187 \begin_layout Standard
19188 Within a formula the size can be changed using the following size commands:
19191 \begin_layout Standard
19194 \begin_inset Tabular
19195 <lyxtabular version="3" rows="5" columns="2">
19196 <features tabularvalignment="middle">
19197 <column alignment="center" valignment="top" width="0">
19198 <column alignment="center" valignment="top" width="0">
19200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19203 \begin_layout Plain Layout
19209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19212 \begin_layout Plain Layout
19214 \begin_inset Note Note
19217 \begin_layout Plain Layout
19224 is only used as spacer.
19236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19239 \begin_layout Plain Layout
19243 \begin_inset Index idx
19246 \begin_layout Plain Layout
19259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19262 \begin_layout Plain Layout
19263 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19276 \begin_layout Plain Layout
19284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19287 \begin_layout Plain Layout
19288 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19301 \begin_layout Plain Layout
19309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19312 \begin_layout Plain Layout
19313 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19326 \begin_layout Plain Layout
19334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19337 \begin_layout Plain Layout
19338 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19354 \begin_layout Standard
19355 After entering these commands, a blue box appears in which the formula parts
19359 \begin_layout Standard
19360 There is a further method to change the font size, that though only works
19361 for symbols or letters in mathematical text.
19362 To use it, one of the above text size commands is inserted in mathematical
19364 All following characters until the end of the mathematical text or until
19365 another size command will have the selected size.
19367 \begin_inset VSpace -2mm
19373 \begin_layout Standard
19377 \begin_layout Plain Layout
19387 \begin_inset Formula \[
19388 A=\frac{B}{c}\cdot\maltese\]
19393 \begin_inset Formula \[
19394 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
19402 \begin_layout Plain Layout
19414 \begin_layout Standard
19415 \begin_inset VSpace medskip
19418 Before both formulas the command
19425 The command for the second formula is:
19426 \begin_inset Newline newline
19437 \begin_layout Plain Layout
19452 \begin_layout Plain Layout
19467 \begin_layout Plain Layout
19482 \begin_layout Plain Layout
19492 \begin_inset Formula $\to$
19496 \begin_inset Formula $\to$
19500 \begin_inset Newline newline
19504 \begin_inset space \hspace*{}
19518 \begin_layout Plain Layout
19533 \begin_layout Plain Layout
19548 \begin_layout Plain Layout
19560 \begin_layout Standard
19561 If a symbol cannot be displayed in different sizes, it will always be displayed
19562 in the default size.
19565 \begin_layout Standard
19566 \begin_inset Newpage newpage
19572 \begin_layout Section
19574 \begin_inset Index idx
19577 \begin_layout Plain Layout
19586 \begin_layout Standard
19587 All Greek letters can also be inserted via the toolbar button
19588 \begin_inset Graphics
19589 filename ../images/math/alpha.png
19597 \begin_layout Subsection
19599 \begin_inset Index idx
19602 \begin_layout Plain Layout
19603 Greek letters ! small
19611 \begin_layout Standard
19612 \begin_inset space \hfill{}
19616 \begin_inset Tabular
19617 <lyxtabular version="3" rows="11" columns="2">
19618 <features tabularvalignment="middle">
19619 <column alignment="center" valignment="top" width="0pt">
19620 <column alignment="center" valignment="top" width="0pt">
19622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19625 \begin_layout Plain Layout
19631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19634 \begin_layout Plain Layout
19642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19645 \begin_layout Plain Layout
19653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19656 \begin_layout Plain Layout
19657 \begin_inset Formula $\alpha$
19667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19670 \begin_layout Plain Layout
19678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19681 \begin_layout Plain Layout
19682 \begin_inset Formula $\beta$
19692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19695 \begin_layout Plain Layout
19703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19706 \begin_layout Plain Layout
19707 \begin_inset Formula $\gamma$
19717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19720 \begin_layout Plain Layout
19728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19731 \begin_layout Plain Layout
19732 \begin_inset Formula $\delta$
19742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19745 \begin_layout Plain Layout
19753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19756 \begin_layout Plain Layout
19757 \begin_inset Formula $\epsilon$
19767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19770 \begin_layout Plain Layout
19778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19781 \begin_layout Plain Layout
19782 \begin_inset Formula $\varepsilon$
19792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19795 \begin_layout Plain Layout
19803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19806 \begin_layout Plain Layout
19807 \begin_inset Formula $\zeta$
19817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19820 \begin_layout Plain Layout
19828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19831 \begin_layout Plain Layout
19832 \begin_inset Formula $\eta$
19842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19845 \begin_layout Plain Layout
19853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19856 \begin_layout Plain Layout
19857 \begin_inset Formula $\theta$
19867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19870 \begin_layout Plain Layout
19878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19881 \begin_layout Plain Layout
19882 \begin_inset Formula $\vartheta$
19896 \begin_inset space \hfill{}
19900 \begin_inset Tabular
19901 <lyxtabular version="3" rows="12" columns="2">
19902 <features tabularvalignment="middle">
19903 <column alignment="center" valignment="top" width="0pt">
19904 <column alignment="center" valignment="top" width="0pt">
19906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19909 \begin_layout Plain Layout
19915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19918 \begin_layout Plain Layout
19926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19929 \begin_layout Plain Layout
19937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19940 \begin_layout Plain Layout
19941 \begin_inset Formula $\iota$
19951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19954 \begin_layout Plain Layout
19962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19965 \begin_layout Plain Layout
19966 \begin_inset Formula $\kappa$
19976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19979 \begin_layout Plain Layout
19987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19990 \begin_layout Plain Layout
19991 \begin_inset Formula $\varkappa$
20001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20004 \begin_layout Plain Layout
20012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20015 \begin_layout Plain Layout
20016 \begin_inset Formula $\lambda$
20026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20029 \begin_layout Plain Layout
20037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20040 \begin_layout Plain Layout
20041 \begin_inset Formula $\mu$
20051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20054 \begin_layout Plain Layout
20062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20065 \begin_layout Plain Layout
20066 \begin_inset Formula $\nu$
20076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20079 \begin_layout Plain Layout
20087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20090 \begin_layout Plain Layout
20091 \begin_inset Formula $\xi$
20101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20104 \begin_layout Plain Layout
20110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20113 \begin_layout Plain Layout
20114 \begin_inset Formula $o$
20124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20127 \begin_layout Plain Layout
20135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20138 \begin_layout Plain Layout
20139 \begin_inset Formula $\pi$
20149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20152 \begin_layout Plain Layout
20160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20163 \begin_layout Plain Layout
20164 \begin_inset Formula $\varpi$
20174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20177 \begin_layout Plain Layout
20185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20188 \begin_layout Plain Layout
20189 \begin_inset Formula $\rho$
20203 \begin_inset space \hfill{}
20207 \begin_inset Tabular
20208 <lyxtabular version="3" rows="11" columns="2">
20209 <features tabularvalignment="middle">
20210 <column alignment="center" valignment="top" width="0pt">
20211 <column alignment="center" valignment="top" width="0pt">
20213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20216 \begin_layout Plain Layout
20222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20225 \begin_layout Plain Layout
20233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20236 \begin_layout Plain Layout
20244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20247 \begin_layout Plain Layout
20248 \begin_inset Formula $\varrho$
20258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20261 \begin_layout Plain Layout
20269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20272 \begin_layout Plain Layout
20273 \begin_inset Formula $\sigma$
20283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20286 \begin_layout Plain Layout
20294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20297 \begin_layout Plain Layout
20298 \begin_inset Formula $\varsigma$
20308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20311 \begin_layout Plain Layout
20319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20322 \begin_layout Plain Layout
20323 \begin_inset Formula $\tau$
20333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20336 \begin_layout Plain Layout
20344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20347 \begin_layout Plain Layout
20348 \begin_inset Formula $\upsilon$
20358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20361 \begin_layout Plain Layout
20369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20372 \begin_layout Plain Layout
20373 \begin_inset Formula $\phi$
20383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20386 \begin_layout Plain Layout
20394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20397 \begin_layout Plain Layout
20398 \begin_inset Formula $\varphi$
20408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20411 \begin_layout Plain Layout
20419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20422 \begin_layout Plain Layout
20423 \begin_inset Formula $\chi$
20433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20436 \begin_layout Plain Layout
20444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20447 \begin_layout Plain Layout
20448 \begin_inset Formula $\psi$
20458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20461 \begin_layout Plain Layout
20469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20472 \begin_layout Plain Layout
20473 \begin_inset Formula $\omega$
20487 \begin_inset space \hfill{}
20493 \begin_layout Standard
20494 \begin_inset VSpace medskip
20500 \begin_layout Standard
20501 How to create upright Greek letters is explained in
20502 \begin_inset CommandInset ref
20504 reference "sub:Upright-small-Greek"
20511 \begin_layout Subsection
20513 \begin_inset Index idx
20516 \begin_layout Plain Layout
20517 Greek letters ! big
20525 \begin_layout Standard
20526 \begin_inset space \hfill{}
20530 \begin_inset Tabular
20531 <lyxtabular version="3" rows="7" columns="2">
20532 <features tabularvalignment="middle">
20533 <column alignment="center" valignment="top" width="0pt">
20534 <column alignment="center" valignment="top" width="0pt">
20536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20539 \begin_layout Plain Layout
20545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20548 \begin_layout Plain Layout
20556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20559 \begin_layout Plain Layout
20567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20570 \begin_layout Plain Layout
20571 \begin_inset Formula $\Gamma$
20581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20584 \begin_layout Plain Layout
20592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20595 \begin_layout Plain Layout
20596 \begin_inset Formula $\Delta$
20606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20609 \begin_layout Plain Layout
20617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20620 \begin_layout Plain Layout
20621 \begin_inset Formula $\Theta$
20631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20634 \begin_layout Plain Layout
20642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20645 \begin_layout Plain Layout
20646 \begin_inset Formula $\Lambda$
20656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20659 \begin_layout Plain Layout
20667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20670 \begin_layout Plain Layout
20671 \begin_inset Formula $\Xi$
20681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20684 \begin_layout Plain Layout
20692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20695 \begin_layout Plain Layout
20696 \begin_inset Formula $\Pi$
20710 \begin_inset space \hfill{}
20714 \begin_inset Tabular
20715 <lyxtabular version="3" rows="6" columns="2">
20716 <features tabularvalignment="middle">
20717 <column alignment="center" valignment="top" width="0pt">
20718 <column alignment="center" valignment="top" width="0pt">
20720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20723 \begin_layout Plain Layout
20729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20732 \begin_layout Plain Layout
20740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20743 \begin_layout Plain Layout
20751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20754 \begin_layout Plain Layout
20755 \begin_inset Formula $\Sigma$
20765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20768 \begin_layout Plain Layout
20776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20779 \begin_layout Plain Layout
20780 \begin_inset Formula $\Upsilon$
20790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20793 \begin_layout Plain Layout
20801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20804 \begin_layout Plain Layout
20805 \begin_inset Formula $\Phi$
20815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20818 \begin_layout Plain Layout
20826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20829 \begin_layout Plain Layout
20830 \begin_inset Formula $\Psi$
20840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20843 \begin_layout Plain Layout
20851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20854 \begin_layout Plain Layout
20855 \begin_inset Formula $\Omega$
20869 \begin_inset space \hfill{}
20875 \begin_layout Standard
20876 \begin_inset VSpace medskip
20879 That the big Greek letters appear upright is caused by a design bug when
20881 To get correct italic big letters, begin every command with
20886 For example the command
20893 \begin_inset Formula $\varGamma$
20899 \begin_layout Subsection
20901 \begin_inset Index idx
20904 \begin_layout Plain Layout
20905 Greek letters ! bold
20913 \begin_layout Standard
20914 Greek letters cannot be set with different font styles like Latin letters.
20915 They can only be made bold with the command
20922 \begin_inset Index idx
20925 \begin_layout Plain Layout
20936 \begin_layout Standard
20938 \begin_inset Tabular
20939 <lyxtabular version="3" rows="3" columns="2">
20940 <features tabularvalignment="middle">
20941 <column alignment="center" valignment="top" width="0">
20942 <column alignment="center" valignment="top" width="0">
20944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20947 \begin_layout Plain Layout
20953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20956 \begin_layout Plain Layout
20964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20967 \begin_layout Plain Layout
20979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20982 \begin_layout Plain Layout
20983 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20996 \begin_layout Plain Layout
21008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21011 \begin_layout Plain Layout
21012 \begin_inset Formula $\theta\boldsymbol{\theta}$
21028 \begin_layout Section
21033 \begin_layout Plain Layout
21046 \begin_layout Plain Layout
21047 A list with all symbols of most of the LaTeX-packages can be found in
21048 \begin_inset CommandInset citation
21063 \begin_layout Plain Layout
21071 \begin_inset Note Note
21074 \begin_layout Plain Layout
21077 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21080 \begin_layout Plain Layout
21083 texorpdfstring is in section
21084 \begin_inset CommandInset ref
21086 reference "sub:Formulas-in-Section"
21096 \begin_inset Index idx
21099 \begin_layout Plain Layout
21108 \begin_layout Standard
21109 Many of the symbols listed in this section can also be inserted via the
21111 \begin_inset Graphics
21112 filename ../images/math/nabla.png
21118 \begin_inset Graphics
21119 filename ../images/math/digamma.png
21127 \begin_layout Subsection
21128 Mathematical Symbols
21129 \begin_inset CommandInset label
21131 name "sub:Mathematical-Symbols"
21136 \begin_inset Index idx
21139 \begin_layout Plain Layout
21140 Symbols ! mathematical
21148 \begin_layout Standard
21149 \begin_inset space \hfill{}
21153 \begin_inset Tabular
21154 <lyxtabular version="3" rows="10" columns="2">
21155 <features tabularvalignment="middle">
21156 <column alignment="center" valignment="top" width="0pt">
21157 <column alignment="center" valignment="top" width="0pt">
21159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21162 \begin_layout Plain Layout
21168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21171 \begin_layout Plain Layout
21179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21182 \begin_layout Plain Layout
21190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21193 \begin_layout Plain Layout
21194 \begin_inset Formula $\neg$
21204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21207 \begin_layout Plain Layout
21215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21218 \begin_layout Plain Layout
21219 \begin_inset Formula $\Im$
21229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21232 \begin_layout Plain Layout
21240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21243 \begin_layout Plain Layout
21244 \begin_inset Formula $\Re$
21254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21257 \begin_layout Plain Layout
21265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21268 \begin_layout Plain Layout
21269 \begin_inset Formula $\aleph$
21279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21282 \begin_layout Plain Layout
21290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21293 \begin_layout Plain Layout
21294 \begin_inset Formula $\partial$
21304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21307 \begin_layout Plain Layout
21315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21318 \begin_layout Plain Layout
21319 \begin_inset Formula $\infty$
21329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21332 \begin_layout Plain Layout
21340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21343 \begin_layout Plain Layout
21344 \begin_inset Formula $\wp$
21354 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21357 \begin_layout Plain Layout
21365 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21368 \begin_layout Plain Layout
21369 \begin_inset Formula $\imath$
21379 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21382 \begin_layout Plain Layout
21390 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21393 \begin_layout Plain Layout
21394 \begin_inset Formula $\jmath$
21408 \begin_inset space \hfill{}
21412 \begin_inset Tabular
21413 <lyxtabular version="3" rows="10" columns="2">
21414 <features tabularvalignment="middle">
21415 <column alignment="center" valignment="top" width="0pt">
21416 <column alignment="center" valignment="top" width="0pt">
21418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21421 \begin_layout Plain Layout
21427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21430 \begin_layout Plain Layout
21432 \begin_inset Note Note
21435 \begin_layout Plain Layout
21442 is only used as spacer.
21454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21457 \begin_layout Plain Layout
21465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21468 \begin_layout Plain Layout
21469 \begin_inset Formula $\forall$
21479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21482 \begin_layout Plain Layout
21490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21493 \begin_layout Plain Layout
21494 \begin_inset Formula $\exists$
21504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21507 \begin_layout Plain Layout
21515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21518 \begin_layout Plain Layout
21519 \begin_inset Formula $\nexists$
21529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21532 \begin_layout Plain Layout
21540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21543 \begin_layout Plain Layout
21544 \begin_inset Formula $\emptyset$
21554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21557 \begin_layout Plain Layout
21565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21568 \begin_layout Plain Layout
21569 \begin_inset Formula $\varnothing$
21579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21582 \begin_layout Plain Layout
21590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21593 \begin_layout Plain Layout
21594 \begin_inset Formula $\dag$
21604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21607 \begin_layout Plain Layout
21615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21618 \begin_layout Plain Layout
21619 \begin_inset Formula $\ddag$
21629 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21632 \begin_layout Plain Layout
21640 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21643 \begin_layout Plain Layout
21647 \begin_layout Plain Layout
21657 \begin_inset Formula $\complement$
21664 \begin_layout Plain Layout
21678 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21681 \begin_layout Plain Layout
21689 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21692 \begin_layout Plain Layout
21693 \begin_inset Formula $\Bbbk$
21707 \begin_inset space \hfill{}
21711 \begin_inset Tabular
21712 <lyxtabular version="3" rows="10" columns="2">
21713 <features tabularvalignment="middle">
21714 <column alignment="center" valignment="top" width="0pt">
21715 <column alignment="center" valignment="top" width="0pt">
21717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21720 \begin_layout Plain Layout
21726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21729 \begin_layout Plain Layout
21737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21740 \begin_layout Plain Layout
21748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21751 \begin_layout Plain Layout
21752 \begin_inset Formula $\prime$
21762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21765 \begin_layout Plain Layout
21773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21776 \begin_layout Plain Layout
21777 \begin_inset Formula $\backprime$
21787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21790 \begin_layout Plain Layout
21798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21801 \begin_layout Plain Layout
21802 \begin_inset Formula $\mho$
21812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21815 \begin_layout Plain Layout
21823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21826 \begin_layout Plain Layout
21827 \begin_inset Formula $\triangle$
21837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21840 \begin_layout Plain Layout
21848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21851 \begin_layout Plain Layout
21852 \begin_inset Formula $\angle$
21862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21865 \begin_layout Plain Layout
21873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21876 \begin_layout Plain Layout
21877 \begin_inset Formula $\measuredangle$
21887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21890 \begin_layout Plain Layout
21898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21901 \begin_layout Plain Layout
21902 \begin_inset Formula $\sphericalangle$
21912 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21915 \begin_layout Plain Layout
21923 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21926 \begin_layout Plain Layout
21927 \begin_inset Formula $\top$
21937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21940 \begin_layout Plain Layout
21948 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21951 \begin_layout Plain Layout
21952 \begin_inset Formula $\bot$
21966 \begin_inset space \hfill{}
21972 \begin_layout Subsection
21973 Miscellaneous Symbols
21974 \begin_inset CommandInset label
21976 name "sub:Miscellaneous-Symbols"
21981 \begin_inset Index idx
21984 \begin_layout Plain Layout
21985 Symbols ! miscellaneous
21993 \begin_layout Standard
21996 \begin_inset Tabular
21997 <lyxtabular version="3" rows="10" columns="2">
21998 <features tabularvalignment="middle">
21999 <column alignment="center" valignment="top" width="0pt">
22000 <column alignment="center" valignment="top" width="0pt">
22002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22005 \begin_layout Plain Layout
22011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22014 \begin_layout Plain Layout
22022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22025 \begin_layout Plain Layout
22033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22036 \begin_layout Plain Layout
22037 \begin_inset Formula $\flat$
22047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22050 \begin_layout Plain Layout
22058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22061 \begin_layout Plain Layout
22062 \begin_inset Formula $\natural$
22072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22075 \begin_layout Plain Layout
22083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22086 \begin_layout Plain Layout
22087 \begin_inset Formula $\sharp$
22097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22100 \begin_layout Plain Layout
22108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22111 \begin_layout Plain Layout
22112 \begin_inset Formula $\surd$
22122 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22125 \begin_layout Plain Layout
22133 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22136 \begin_layout Plain Layout
22137 \begin_inset Formula $\checkmark$
22147 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22150 \begin_layout Plain Layout
22158 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22161 \begin_layout Plain Layout
22162 \begin_inset Formula $\yen$
22172 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22175 \begin_layout Plain Layout
22183 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22186 \begin_layout Plain Layout
22187 \begin_inset Formula $\pounds$
22197 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22200 \begin_layout Plain Layout
22206 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22209 \begin_layout Plain Layout
22210 \begin_inset Formula $\$$
22220 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22223 \begin_layout Plain Layout
22229 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22232 \begin_layout Plain Layout
22233 \begin_inset Formula $§$
22247 \begin_inset Tabular
22248 <lyxtabular version="3" rows="10" columns="2">
22249 <features tabularvalignment="middle">
22250 <column alignment="center" valignment="top" width="0">
22251 <column alignment="center" valignment="top" width="0">
22253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22256 \begin_layout Plain Layout
22262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22265 \begin_layout Plain Layout
22273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22276 \begin_layout Plain Layout
22284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22287 \begin_layout Plain Layout
22288 \begin_inset Formula $\hbar$
22298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22301 \begin_layout Plain Layout
22309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22312 \begin_layout Plain Layout
22313 \begin_inset Formula $\hslash$
22323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22326 \begin_layout Plain Layout
22334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22337 \begin_layout Plain Layout
22338 \begin_inset Formula $\clubsuit$
22348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22351 \begin_layout Plain Layout
22359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22362 \begin_layout Plain Layout
22363 \begin_inset Formula $\spadesuit$
22373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22376 \begin_layout Plain Layout
22384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22387 \begin_layout Plain Layout
22388 \begin_inset Formula $\bigstar$
22398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22401 \begin_layout Plain Layout
22409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22412 \begin_layout Plain Layout
22413 \begin_inset Formula $\blacklozenge$
22423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22426 \begin_layout Plain Layout
22434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22437 \begin_layout Plain Layout
22438 \begin_inset Formula $\blacktriangle$
22448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22451 \begin_layout Plain Layout
22459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22462 \begin_layout Plain Layout
22463 \begin_inset Formula $\blacktriangledown$
22473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22476 \begin_layout Plain Layout
22484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22487 \begin_layout Plain Layout
22488 \begin_inset Formula $\bullet$
22502 \begin_inset Tabular
22503 <lyxtabular version="3" rows="10" columns="2">
22504 <features tabularvalignment="middle">
22505 <column alignment="center" valignment="top" width="0pt">
22506 <column alignment="center" valignment="top" width="0pt">
22508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22511 \begin_layout Plain Layout
22517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22520 \begin_layout Plain Layout
22528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22531 \begin_layout Plain Layout
22539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22542 \begin_layout Plain Layout
22543 \begin_inset Formula $\diamondsuit$
22553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22556 \begin_layout Plain Layout
22564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22567 \begin_layout Plain Layout
22568 \begin_inset Formula $\Diamond$
22578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22581 \begin_layout Plain Layout
22589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22592 \begin_layout Plain Layout
22593 \begin_inset Formula $\heartsuit$
22603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22606 \begin_layout Plain Layout
22614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22617 \begin_layout Plain Layout
22618 \begin_inset Formula $\P$
22628 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22631 \begin_layout Plain Layout
22639 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22642 \begin_layout Plain Layout
22643 \begin_inset Formula $\copyright$
22653 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22656 \begin_layout Plain Layout
22664 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22667 \begin_layout Plain Layout
22668 \begin_inset Formula $\circledR$
22678 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22681 \begin_layout Plain Layout
22689 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22692 \begin_layout Plain Layout
22693 \begin_inset Formula $\maltese$
22703 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22706 \begin_layout Plain Layout
22714 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22717 \begin_layout Plain Layout
22718 \begin_inset Formula $\diagup$
22728 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22731 \begin_layout Plain Layout
22739 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22742 \begin_layout Plain Layout
22743 \begin_inset Formula $\diagdown$
22759 \begin_layout Standard
22760 \begin_inset VSpace medskip
22763 More symbols are listed in
22764 \begin_inset CommandInset ref
22766 reference "sub:Miscellaneous-special-Characters"
22773 \begin_layout Standard
22774 Some symbols can be displayed in different sizes, see
22775 \begin_inset CommandInset ref
22777 reference "sub:Font-Sizes"
22784 \begin_layout Subsection
22786 \begin_inset Index idx
22789 \begin_layout Plain Layout
22790 Symbols ! Euro-symbol
22796 \begin_inset Index idx
22799 \begin_layout Plain Layout
22806 \begin_layout Plain Layout
22823 \begin_layout Standard
22824 To use the Euro symbol in formulas, the LaTeX-package
22829 \begin_inset Index idx
22832 \begin_layout Plain Layout
22838 must be installed and loaded with the LaTeX-preamble line
22841 \begin_layout Standard
22846 usepackage[gennarrow]{eurosym}
22849 \begin_layout Standard
22850 The Euro symbol can now be inserted with the command
22857 \begin_inset Index idx
22860 \begin_layout Plain Layout
22871 \begin_layout Standard
22872 The Euro symbol can directly be inserted with the € key in mathematical
22873 text, without having
22888 can also be inserted in TeX-mode.
22889 The official currency symbol can then be inserted with the command
22896 \begin_inset Index idx
22899 \begin_layout Plain Layout
22907 , that is only available in TeX-mode.
22910 \begin_layout Standard
22914 \begin_layout Plain Layout
22924 \begin_inset Note Note
22927 \begin_layout Plain Layout
22928 The following table will only be displayed when the LaTeX-package
22940 \begin_layout Standard
22941 An overview about the different Euro symbols:
22944 \begin_layout Standard
22946 \begin_inset Tabular
22947 <lyxtabular version="3" rows="4" columns="3">
22948 <features tabularvalignment="middle">
22949 <column alignment="center" valignment="top" width="0pt">
22950 <column alignment="center" valignment="top" width="0pt">
22951 <column alignment="center" valignment="top" width="0pt">
22953 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22956 \begin_layout Plain Layout
22962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22965 \begin_layout Plain Layout
22971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22974 \begin_layout Plain Layout
22982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22985 \begin_layout Plain Layout
22991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22994 \begin_layout Plain Layout
23002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23005 \begin_layout Plain Layout
23006 \begin_inset Formula $\euro$
23016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23019 \begin_layout Plain Layout
23025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23028 \begin_layout Plain Layout
23034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23037 \begin_layout Plain Layout
23038 \begin_inset Formula $\mbox{€}$
23048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23051 \begin_layout Plain Layout
23057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23060 \begin_layout Plain Layout
23068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23071 \begin_layout Plain Layout
23075 \begin_layout Plain Layout
23097 \begin_layout Standard
23101 \begin_layout Plain Layout
23111 \begin_inset Note Note
23114 \begin_layout Plain Layout
23115 The following will be displayed when the LaTeX-package
23127 \begin_layout Standard
23128 You need to install the LaTeX-package
23132 to see the rest of this subsection in the output.
23135 \begin_layout Standard
23139 \begin_layout Plain Layout
23151 \begin_layout Section
23153 \begin_inset CommandInset label
23155 name "sec:Relations"
23160 \begin_inset Index idx
23163 \begin_layout Plain Layout
23170 \begin_inset Index idx
23173 \begin_layout Plain Layout
23178 \begin_layout Plain Layout
23189 \begin_layout Plain Layout
23204 \begin_layout Standard
23205 All relations can also be inserted via the toolbar button
23206 \begin_inset Graphics
23207 filename ../images/math/leq.png
23215 \begin_layout Standard
23216 \begin_inset space \hfill{}
23220 \begin_inset Tabular
23221 <lyxtabular version="3" rows="17" columns="2">
23222 <features tabularvalignment="middle">
23223 <column alignment="center" valignment="top" width="0pt">
23224 <column alignment="center" valignment="top" width="0pt">
23226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23229 \begin_layout Plain Layout
23235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23238 \begin_layout Plain Layout
23246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23249 \begin_layout Plain Layout
23255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23258 \begin_layout Plain Layout
23259 \begin_inset Formula $<$
23269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23272 \begin_layout Plain Layout
23280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23283 \begin_layout Plain Layout
23284 \begin_inset Formula $\le$
23294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23297 \begin_layout Plain Layout
23305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23308 \begin_layout Plain Layout
23309 \begin_inset Formula $\ll$
23319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23322 \begin_layout Plain Layout
23330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23333 \begin_layout Plain Layout
23334 \begin_inset Formula $\prec$
23344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23347 \begin_layout Plain Layout
23355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23358 \begin_layout Plain Layout
23359 \begin_inset Formula $\preceq$
23369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23372 \begin_layout Plain Layout
23380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23383 \begin_layout Plain Layout
23384 \begin_inset Formula $\subset$
23394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23397 \begin_layout Plain Layout
23405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23408 \begin_layout Plain Layout
23409 \begin_inset Formula $\subseteq$
23419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23422 \begin_layout Plain Layout
23430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23433 \begin_layout Plain Layout
23434 \begin_inset Formula $\sqsubseteq$
23444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23447 \begin_layout Plain Layout
23455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23458 \begin_layout Plain Layout
23459 \begin_inset Formula $\in$
23469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23472 \begin_layout Plain Layout
23480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23483 \begin_layout Plain Layout
23484 \begin_inset Formula $\vdash$
23494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23497 \begin_layout Plain Layout
23505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23508 \begin_layout Plain Layout
23509 \begin_inset Formula $\smile$
23519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23522 \begin_layout Plain Layout
23530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23533 \begin_layout Plain Layout
23534 \begin_inset Formula $\lhd$
23544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23547 \begin_layout Plain Layout
23555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23558 \begin_layout Plain Layout
23559 \begin_inset Formula $\unlhd$
23569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23572 \begin_layout Plain Layout
23580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23583 \begin_layout Plain Layout
23584 \begin_inset Formula $\gtrless$
23594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23597 \begin_layout Plain Layout
23605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23608 \begin_layout Plain Layout
23609 \begin_inset Formula $\mid$
23619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23622 \begin_layout Plain Layout
23630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23633 \begin_layout Plain Layout
23634 \begin_inset Formula $\nmid$
23648 \begin_inset space \hfill{}
23652 \begin_inset Tabular
23653 <lyxtabular version="3" rows="17" columns="2">
23654 <features tabularvalignment="middle">
23655 <column alignment="center" valignment="top" width="0pt">
23656 <column alignment="center" valignment="top" width="0pt">
23658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23661 \begin_layout Plain Layout
23667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23670 \begin_layout Plain Layout
23678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23681 \begin_layout Plain Layout
23687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23690 \begin_layout Plain Layout
23691 \begin_inset Formula $=$
23701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23704 \begin_layout Plain Layout
23712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23715 \begin_layout Plain Layout
23716 \begin_inset Formula $\not=$
23726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23729 \begin_layout Plain Layout
23737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23740 \begin_layout Plain Layout
23741 \begin_inset Formula $\equiv$
23751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23754 \begin_layout Plain Layout
23762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23765 \begin_layout Plain Layout
23766 \begin_inset Formula $\sim$
23776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23779 \begin_layout Plain Layout
23787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23790 \begin_layout Plain Layout
23791 \begin_inset Formula $\simeq$
23801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23804 \begin_layout Plain Layout
23812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23815 \begin_layout Plain Layout
23816 \begin_inset Formula $\approx$
23826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23829 \begin_layout Plain Layout
23837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23840 \begin_layout Plain Layout
23841 \begin_inset Formula $\cong$
23851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23854 \begin_layout Plain Layout
23862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23865 \begin_layout Plain Layout
23866 \begin_inset Formula $\bowtie$
23876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23879 \begin_layout Plain Layout
23887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23890 \begin_layout Plain Layout
23891 \begin_inset Formula $\notin$
23901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23904 \begin_layout Plain Layout
23912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23915 \begin_layout Plain Layout
23916 \begin_inset Formula $\perp$
23926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23929 \begin_layout Plain Layout
23937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23940 \begin_layout Plain Layout
23941 \begin_inset Formula $\propto$
23951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23954 \begin_layout Plain Layout
23962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23965 \begin_layout Plain Layout
23966 \begin_inset Formula $\asymp$
23976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23979 \begin_layout Plain Layout
23987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23990 \begin_layout Plain Layout
23991 \begin_inset Formula $\doteq$
24001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24004 \begin_layout Plain Layout
24012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24015 \begin_layout Plain Layout
24016 \begin_inset Formula $\circeq$
24026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24029 \begin_layout Plain Layout
24037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24040 \begin_layout Plain Layout
24041 \begin_inset Formula $\models$
24051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24054 \begin_layout Plain Layout
24062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24065 \begin_layout Plain Layout
24066 \begin_inset Formula $\widehat{=}$
24080 \begin_inset space \hfill{}
24084 \begin_inset Tabular
24085 <lyxtabular version="3" rows="17" columns="2">
24086 <features tabularvalignment="middle">
24087 <column alignment="center" valignment="top" width="0pt">
24088 <column alignment="center" valignment="top" width="0pt">
24090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24093 \begin_layout Plain Layout
24099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24102 \begin_layout Plain Layout
24110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24113 \begin_layout Plain Layout
24119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24122 \begin_layout Plain Layout
24123 \begin_inset Formula $>$
24133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24136 \begin_layout Plain Layout
24144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24147 \begin_layout Plain Layout
24148 \begin_inset Formula $\ge$
24158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24161 \begin_layout Plain Layout
24169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24172 \begin_layout Plain Layout
24173 \begin_inset Formula $\gg$
24183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24186 \begin_layout Plain Layout
24194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24197 \begin_layout Plain Layout
24198 \begin_inset Formula $\succ$
24208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24211 \begin_layout Plain Layout
24219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24222 \begin_layout Plain Layout
24223 \begin_inset Formula $\succeq$
24233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24236 \begin_layout Plain Layout
24244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24247 \begin_layout Plain Layout
24248 \begin_inset Formula $\supset$
24258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24261 \begin_layout Plain Layout
24269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24272 \begin_layout Plain Layout
24273 \begin_inset Formula $\supseteq$
24283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24286 \begin_layout Plain Layout
24294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24297 \begin_layout Plain Layout
24298 \begin_inset Formula $\sqsupseteq$
24308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24311 \begin_layout Plain Layout
24319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24322 \begin_layout Plain Layout
24323 \begin_inset Formula $\ni$
24333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24336 \begin_layout Plain Layout
24344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24347 \begin_layout Plain Layout
24348 \begin_inset Formula $\dashv$
24358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24361 \begin_layout Plain Layout
24369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24372 \begin_layout Plain Layout
24373 \begin_inset Formula $\frown$
24383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24386 \begin_layout Plain Layout
24394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24397 \begin_layout Plain Layout
24398 \begin_inset Formula $\rhd$
24408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24411 \begin_layout Plain Layout
24419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24422 \begin_layout Plain Layout
24423 \begin_inset Formula $\unrhd$
24433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24436 \begin_layout Plain Layout
24444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24447 \begin_layout Plain Layout
24448 \begin_inset Formula $\lessgtr$
24458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24461 \begin_layout Plain Layout
24469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24472 \begin_layout Plain Layout
24473 \begin_inset Formula $\parallel$
24483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24486 \begin_layout Plain Layout
24494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24497 \begin_layout Plain Layout
24498 \begin_inset Formula $\nparallel$
24512 \begin_inset space \hfill{}
24518 \begin_layout Standard
24519 \begin_inset VSpace medskip
24534 are bigger than the equal looking operators
24549 \begin_layout Standard
24550 Relations are, in contrary to symbols, always surrounded by space.
24553 \begin_layout Standard
24554 Relations with labels can be created with the command
24561 \begin_inset Index idx
24564 \begin_layout Plain Layout
24575 \begin_layout Standard
24577 \begin_inset Tabular
24578 <lyxtabular version="3" rows="2" columns="2">
24579 <features tabularvalignment="middle">
24580 <column alignment="center" valignment="top" width="0">
24581 <column alignment="center" valignment="top" width="0">
24583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24586 \begin_layout Plain Layout
24592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24595 \begin_layout Plain Layout
24597 \begin_inset Note Note
24600 \begin_layout Plain Layout
24607 is only used as spacer.
24619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24622 \begin_layout Plain Layout
24629 \begin_layout Plain Layout
24646 \begin_layout Plain Layout
24656 \begin_inset Formula $\downarrow$
24665 \begin_layout Plain Layout
24678 \begin_layout Plain Layout
24692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24695 \begin_layout Plain Layout
24696 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24712 \begin_layout Section
24716 \begin_layout Subsection
24717 Predefined Functions
24718 \begin_inset CommandInset label
24720 name "sub:Predefined-Functions"
24725 \begin_inset Index idx
24728 \begin_layout Plain Layout
24729 Functions ! predefined
24737 \begin_layout Standard
24738 In general, variables are set
24742 in mathematical expressions, but not function names, because
24743 \begin_inset Formula $sin$
24746 could be misunderstood as
24747 \begin_inset Formula $s\cdot i\cdot n$
24751 Therefore there are predefined functions, that are additionally a bit separated
24753 They are inserted as commands starting with a backslash before their name.
24756 \begin_layout Standard
24758 \begin_inset Tabular
24759 <lyxtabular version="3" rows="2" columns="4">
24760 <features tabularvalignment="middle">
24761 <column alignment="center" valignment="top" width="0pt">
24762 <column alignment="center" valignment="top" width="0pt">
24763 <column alignment="center" valignment="top" width="0pt">
24764 <column alignment="center" valignment="top" width="0pt">
24766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24769 \begin_layout Plain Layout
24775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24778 \begin_layout Plain Layout
24784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24787 \begin_layout Plain Layout
24793 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24796 \begin_layout Plain Layout
24804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24807 \begin_layout Plain Layout
24813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24816 \begin_layout Plain Layout
24817 \begin_inset Formula $Asin(x)+B$
24825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24828 \begin_layout Plain Layout
24836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24839 \begin_layout Plain Layout
24840 \begin_inset Formula $A\sin(x)+B$
24856 \begin_layout Standard
24857 The following functions are predefined:
24860 \begin_layout Standard
24861 \begin_inset VSpace -2mm
24867 \begin_layout Standard
24869 \begin_inset Tabular
24870 <lyxtabular version="3" rows="9" columns="4">
24871 <features tabularvalignment="middle">
24872 <column alignment="center" valignment="top" width="0pt">
24873 <column alignment="center" valignment="top" width="0pt">
24874 <column alignment="center" valignment="top" width="0pt">
24875 <column alignment="center" valignment="top" width="0pt">
24877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24880 \begin_layout Plain Layout
24886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24889 \begin_layout Plain Layout
24895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24898 \begin_layout Plain Layout
24904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24907 \begin_layout Plain Layout
24915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24918 \begin_layout Plain Layout
24926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24929 \begin_layout Plain Layout
24937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24940 \begin_layout Plain Layout
24948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24951 \begin_layout Plain Layout
24961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24964 \begin_layout Plain Layout
24972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24975 \begin_layout Plain Layout
24983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24986 \begin_layout Plain Layout
24994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24997 \begin_layout Plain Layout
25007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25010 \begin_layout Plain Layout
25018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25021 \begin_layout Plain Layout
25029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25032 \begin_layout Plain Layout
25040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25043 \begin_layout Plain Layout
25053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25056 \begin_layout Plain Layout
25064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25067 \begin_layout Plain Layout
25075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25078 \begin_layout Plain Layout
25086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25089 \begin_layout Plain Layout
25099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25102 \begin_layout Plain Layout
25110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25113 \begin_layout Plain Layout
25121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25124 \begin_layout Plain Layout
25132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25135 \begin_layout Plain Layout
25145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25148 \begin_layout Plain Layout
25156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25159 \begin_layout Plain Layout
25167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25170 \begin_layout Plain Layout
25178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25181 \begin_layout Plain Layout
25191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25194 \begin_layout Plain Layout
25202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25205 \begin_layout Plain Layout
25213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25216 \begin_layout Plain Layout
25224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25227 \begin_layout Plain Layout
25237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25240 \begin_layout Plain Layout
25248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25251 \begin_layout Plain Layout
25259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25262 \begin_layout Plain Layout
25270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25273 \begin_layout Plain Layout
25289 \begin_layout Standard
25290 They can also be inserted with the math toolbar button
25291 \begin_inset Graphics
25292 filename ../images/math/functions.png
25300 \begin_layout Subsection
25301 Self-defined Functions
25302 \begin_inset Index idx
25305 \begin_layout Plain Layout
25306 Functions ! self-defined
25314 \begin_layout Standard
25315 To use a function that is not predefined, like for example the sign function
25316 sgn(x), there are two possibilities:
25319 \begin_layout Itemize
25320 Define the function by inserting the following line to the LaTeX-preamble
25324 \begin_layout Plain Layout
25329 DeclareMathOperator
25332 \begin_inset CommandInset ref
25334 reference "sub:Self-defined-Operators"
25344 \begin_inset Newline newline
25348 \begin_inset VSpace -3mm
25352 \begin_inset Newline newline
25359 DeclareMathOperator{
25364 \begin_inset Index idx
25367 \begin_layout Plain Layout
25372 DeclareMathOperator
25378 \begin_inset Newline newline
25382 \begin_inset VSpace -2mm
25386 \begin_inset Newline newline
25389 Now the new defined function can be called with the command
25398 \begin_layout Itemize
25399 Write the formula as usual, mark the formula name, in our example the letters
25404 , and change it to mathematical text.
25405 At last a space is inserted between prefactor and function.
25408 \begin_layout Standard
25409 The result is the same with both methods as with a predefined function
25413 \begin_layout Plain Layout
25414 In LyX self-defined functions are displayed red, predefined ones black.
25422 \begin_layout Standard
25424 \begin_inset Tabular
25425 <lyxtabular version="3" rows="3" columns="2">
25426 <features tabularvalignment="middle">
25427 <column alignment="center" valignment="top" width="0pt">
25428 <column alignment="center" valignment="top" width="0pt">
25430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25433 \begin_layout Plain Layout
25439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25442 \begin_layout Plain Layout
25450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25453 \begin_layout Plain Layout
25461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25464 \begin_layout Plain Layout
25465 \begin_inset Formula $A\sgn(x)+B$
25475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25478 \begin_layout Plain Layout
25482 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25493 \begin_layout Plain Layout
25494 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25510 \begin_layout Standard
25511 The first method is more suitable when the self-defined function should
25512 be used several times.
25515 \begin_layout Subsection
25517 \begin_inset Index idx
25520 \begin_layout Plain Layout
25529 \begin_layout Standard
25530 For limits there are defined besides
25537 \begin_inset Index idx
25540 \begin_layout Plain Layout
25560 furthermore the following functions:
25563 \begin_layout Standard
25565 \begin_inset Tabular
25566 <lyxtabular version="3" rows="5" columns="2">
25567 <features tabularvalignment="middle">
25568 <column alignment="center" valignment="top" width="0">
25569 <column alignment="center" valignment="top" width="0">
25571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25574 \begin_layout Plain Layout
25580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25583 \begin_layout Plain Layout
25585 \begin_inset Note Note
25588 \begin_layout Plain Layout
25595 is only used as spacer.
25607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25610 \begin_layout Plain Layout
25618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25621 \begin_layout Plain Layout
25622 \begin_inset Formula $\varliminf$
25632 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25635 \begin_layout Plain Layout
25643 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25646 \begin_layout Plain Layout
25647 \begin_inset Formula $\varlimsup$
25657 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25660 \begin_layout Plain Layout
25668 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25671 \begin_layout Plain Layout
25672 \begin_inset Formula $\varprojlim$
25682 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25685 \begin_layout Plain Layout
25693 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25696 \begin_layout Plain Layout
25697 \begin_inset Formula $\varinjlim$
25701 \begin_inset Formula $\raisebox{-2.5mm}{}$
25717 \begin_layout Standard
25718 \begin_inset VSpace medskip
25721 The limit is created by inserting a subscript.
25722 It is set right beside the function in an inline formula:
25725 \begin_layout Standard
25727 \begin_inset Tabular
25728 <lyxtabular version="3" rows="2" columns="2">
25729 <features tabularvalignment="middle">
25730 <column alignment="center" valignment="top" width="0pt">
25731 <column alignment="center" valignment="top" width="0pt">
25733 <cell alignment="center" valignment="top" usebox="none">
25736 \begin_layout Plain Layout
25742 <cell alignment="center" valignment="top" usebox="none">
25745 \begin_layout Plain Layout
25746 \begin_inset space \hspace{}
25751 \begin_inset Note Note
25754 \begin_layout Plain Layout
25761 are used here as spacer.
25773 <cell alignment="center" valignment="top" usebox="none">
25776 \begin_layout Plain Layout
25785 \begin_layout Plain Layout
25798 \begin_layout Plain Layout
25812 <cell alignment="center" valignment="top" usebox="none">
25815 \begin_layout Plain Layout
25816 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25832 \begin_layout Standard
25833 In a displayed formula the limit is set below the formula, as usual:
25834 \begin_inset Formula \[
25842 \begin_layout Subsection
25844 \begin_inset Index idx
25847 \begin_layout Plain Layout
25848 Functions ! modulo-
25856 \begin_layout Standard
25857 The modulo-function is special, because it exists in four variants.
25860 \begin_layout Standard
25861 The variants in a displayed formula:
25862 \begin_inset Formula \begin{align*}
25863 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25864 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25865 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25866 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25867 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
25875 \begin_layout Standard
25876 In an inline formula less space is set before the function names for all
25880 \begin_layout Section
25882 \begin_inset Index idx
25885 \begin_layout Plain Layout
25894 \begin_layout Subsection
25895 Special Characters in Mathematical Text
25898 \begin_layout Standard
25899 The following commands can only be used in mathematical text or in TeX-mode:
25902 \begin_layout Standard
25903 \begin_inset space \hfill{}
25907 \begin_inset Tabular
25908 <lyxtabular version="3" rows="8" columns="2">
25909 <features tabularvalignment="middle">
25910 <column alignment="block" valignment="top" width="0">
25911 <column alignment="block" valignment="top" width="0">
25913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25916 \begin_layout Plain Layout
25922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25925 \begin_layout Plain Layout
25933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25936 \begin_layout Plain Layout
25944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25947 \begin_layout Plain Layout
25948 \begin_inset Formula $\textrm{œ}$
25958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25961 \begin_layout Plain Layout
25969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25972 \begin_layout Plain Layout
25973 \begin_inset Formula $\textrm{Œ}$
25983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25986 \begin_layout Plain Layout
25994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25997 \begin_layout Plain Layout
25998 \begin_inset Formula $\textrm{æ}$
26008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26011 \begin_layout Plain Layout
26019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26022 \begin_layout Plain Layout
26023 \begin_inset Formula $\textrm{Æ}$
26033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26036 \begin_layout Plain Layout
26044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26047 \begin_layout Plain Layout
26048 \begin_inset Formula $\textrm{\aa}$
26058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26061 \begin_layout Plain Layout
26065 \begin_inset Index idx
26068 \begin_layout Plain Layout
26075 \begin_layout Plain Layout
26096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26099 \begin_layout Plain Layout
26100 \begin_inset Formula $\textrm{Å}$
26110 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26113 \begin_layout Plain Layout
26121 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26124 \begin_layout Plain Layout
26125 \begin_inset Formula $\textrm{ı}$
26139 \begin_inset space \hfill{}
26143 \begin_inset Tabular
26144 <lyxtabular version="3" rows="8" columns="2">
26145 <features tabularvalignment="middle">
26146 <column alignment="block" valignment="top" width="0">
26147 <column alignment="center" valignment="top" width="0">
26149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26152 \begin_layout Plain Layout
26154 \begin_inset Note Note
26157 \begin_layout Plain Layout
26159 \begin_inset space \thinspace{}
26162 mm is used for separation, because otherwise the output will be ¡ and ¿
26173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26176 \begin_layout Plain Layout
26184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26187 \begin_layout Plain Layout
26195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26198 \begin_layout Plain Layout
26199 \begin_inset Formula $\textrm{ø}$
26209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26212 \begin_layout Plain Layout
26220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26223 \begin_layout Plain Layout
26224 \begin_inset Formula $\textrm{Ø}$
26234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26237 \begin_layout Plain Layout
26245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26248 \begin_layout Plain Layout
26249 \begin_inset Formula $\textrm{ł}$
26259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26262 \begin_layout Plain Layout
26270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26273 \begin_layout Plain Layout
26274 \begin_inset Formula $\textrm{Ł}$
26284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26287 \begin_layout Plain Layout
26289 \begin_inset space \hspace{}
26297 \begin_layout Plain Layout
26311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26314 \begin_layout Plain Layout
26315 \begin_inset Formula $\textrm{!`}$
26325 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26328 \begin_layout Plain Layout
26330 \begin_inset space \hspace{}
26338 \begin_layout Plain Layout
26352 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26355 \begin_layout Plain Layout
26356 \begin_inset Formula $\textrm{?`}$
26366 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26369 \begin_layout Plain Layout
26377 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26380 \begin_layout Plain Layout
26381 \begin_inset Formula $\textrm{ȷ}$
26395 \begin_inset space \hfill{}
26401 \begin_layout Standard
26403 \begin_inset Formula $\textrm{\textrm{Å}}$
26407 \begin_inset Formula $\textrm{\textrm{Ø}}$
26410 can also be inserted via the math toolbar button
26411 \begin_inset Graphics
26412 filename ../images/math/digamma.png
26420 \begin_layout Standard
26421 An exception are the commands
26424 \begin_inset space \hspace{}
26433 \begin_inset space \hspace{}
26439 , because they can be inserted in LyX directly to text.
26442 \begin_layout Subsection
26444 \begin_inset CommandInset label
26446 name "sub:Accents-in-Text"
26451 \begin_inset Index idx
26454 \begin_layout Plain Layout
26463 \begin_layout Standard
26464 With the following commands all letters can be accented.
26465 The commands must be inserted in TeX-mode.
26468 \begin_layout Standard
26469 \begin_inset space \hfill{}
26473 \begin_inset Tabular
26474 <lyxtabular version="3" rows="8" columns="2">
26475 <features tabularvalignment="middle">
26476 <column alignment="block" valignment="top" width="0">
26477 <column alignment="block" valignment="top" width="0">
26479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26482 \begin_layout Plain Layout
26488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26491 \begin_layout Plain Layout
26499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26502 \begin_layout Plain Layout
26506 \begin_inset Quotes grd
26514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26517 \begin_layout Plain Layout
26521 \begin_layout Plain Layout
26537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26540 \begin_layout Plain Layout
26548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26551 \begin_layout Plain Layout
26555 \begin_layout Plain Layout
26571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26574 \begin_layout Plain Layout
26581 \begin_layout Plain Layout
26595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26598 \begin_layout Plain Layout
26602 \begin_layout Plain Layout
26618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26621 \begin_layout Plain Layout
26629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26632 \begin_layout Plain Layout
26636 \begin_layout Plain Layout
26652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26655 \begin_layout Plain Layout
26662 \begin_layout Plain Layout
26676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26679 \begin_layout Plain Layout
26683 \begin_layout Plain Layout
26699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26702 \begin_layout Plain Layout
26709 \begin_layout Plain Layout
26723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26726 \begin_layout Plain Layout
26730 \begin_layout Plain Layout
26746 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26749 \begin_layout Plain Layout
26756 \begin_layout Plain Layout
26770 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26773 \begin_layout Plain Layout
26777 \begin_layout Plain Layout
26797 \begin_inset space \hfill{}
26801 \begin_inset Tabular
26802 <lyxtabular version="3" rows="8" columns="2">
26803 <features tabularvalignment="middle">
26804 <column alignment="block" valignment="top" width="0">
26805 <column alignment="center" valignment="top" width="0">
26807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26810 \begin_layout Plain Layout
26816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26819 \begin_layout Plain Layout
26827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26830 \begin_layout Plain Layout
26837 \begin_layout Plain Layout
26851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26854 \begin_layout Plain Layout
26858 \begin_layout Plain Layout
26874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26877 \begin_layout Plain Layout
26885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26888 \begin_layout Plain Layout
26892 \begin_layout Plain Layout
26908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26911 \begin_layout Plain Layout
26915 \begin_inset Index idx
26918 \begin_layout Plain Layout
26929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26932 \begin_layout Plain Layout
26936 \begin_layout Plain Layout
26952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26955 \begin_layout Plain Layout
26963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26966 \begin_layout Plain Layout
26970 \begin_layout Plain Layout
26986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26989 \begin_layout Plain Layout
26996 \begin_layout Plain Layout
27010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27013 \begin_layout Plain Layout
27017 \begin_layout Plain Layout
27033 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27036 \begin_layout Plain Layout
27043 \begin_layout Plain Layout
27057 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27060 \begin_layout Plain Layout
27064 \begin_layout Plain Layout
27080 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27083 \begin_layout Plain Layout
27090 \begin_layout Plain Layout
27104 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27107 \begin_layout Plain Layout
27111 \begin_layout Plain Layout
27131 \begin_inset space \hfill{}
27137 \begin_layout Standard
27138 \begin_inset VSpace medskip
27147 also two different characters can be accented.
27156 \begin_layout Plain Layout
27171 \begin_layout Plain Layout
27183 \begin_layout Standard
27196 can in combination with vowels directly be inserted with the keyboard without
27198 The same applies for the tilde
27202 \begin_layout Plain Layout
27203 This only applies for keyboards where the tilde is defined as accent.
27212 in combination with
27227 \begin_layout Standard
27270 and accents that are inserted directly with the keyboard are also available
27271 in mathematical text.
27272 For the other accents there are special math commands to be used in formulas,
27274 \begin_inset CommandInset ref
27276 reference "sub:Accents-for-one"
27283 \begin_layout Standard
27284 \begin_inset VSpace bigskip
27287 Furthermore, with the command
27294 \begin_inset Index idx
27297 \begin_layout Plain Layout
27305 all numbers and letters can be set into a circle, quasi accented with a
27306 circle, similar to the copyright symbol.
27309 \begin_layout Standard
27311 \begin_inset Tabular
27312 <lyxtabular version="3" rows="3" columns="2">
27313 <features tabularvalignment="middle">
27314 <column alignment="center" valignment="top" width="0">
27315 <column alignment="center" valignment="top" width="0">
27317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27320 \begin_layout Plain Layout
27326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27329 \begin_layout Plain Layout
27331 \begin_inset Note Note
27334 \begin_layout Plain Layout
27341 is only used as spacer.
27353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27356 \begin_layout Plain Layout
27364 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27367 \begin_layout Plain Layout
27371 \begin_layout Plain Layout
27387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27390 \begin_layout Plain Layout
27401 raisebox{-1.5pt}{W}}
27406 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27409 \begin_layout Plain Layout
27410 \begin_inset Formula $\raisebox{4.5mm}{}$
27417 \begin_layout Plain Layout
27435 \begin_inset Formula $\raisebox{-2mm}{}$
27451 \begin_layout Standard
27452 One has to take care that the character fits in the circle.
27463 \begin_layout Plain Layout
27465 \begin_inset CommandInset ref
27467 reference "sub:Font-Sizes"
27476 specifies thereby the size of the circle.
27487 \begin_layout Plain Layout
27489 \begin_inset CommandInset ref
27491 reference "sub:Boxes-without-Frame"
27500 the character can be centered.
27503 \begin_layout Subsection
27505 \begin_inset Index idx
27508 \begin_layout Plain Layout
27517 \begin_layout Standard
27518 Minuscule numbers are created with the command
27525 \begin_inset Index idx
27528 \begin_layout Plain Layout
27537 The command can be used in formulas and in TeX-mode.
27538 The command scheme is:
27541 \begin_layout Standard
27546 oldstylenums{number}
27549 \begin_layout Standard
27554 oldstylenums{0123456789
27557 \begin_inset Formula $\oldstylenums{0123456789}$
27563 \begin_layout Subsection
27564 Miscellaneous special Characters
27565 \begin_inset CommandInset label
27567 name "sub:Miscellaneous-special-Characters"
27572 \begin_inset Index idx
27575 \begin_layout Plain Layout
27576 Special characters ! miscellaneous
27584 \begin_layout Standard
27585 The following characters can only be inserted to formulas by using commands:
27588 \begin_layout Standard
27590 \begin_inset Tabular
27591 <lyxtabular version="3" rows="4" columns="2">
27592 <features tabularvalignment="middle">
27593 <column alignment="center" valignment="top" width="0">
27594 <column alignment="center" valignment="top" width="0">
27596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27599 \begin_layout Plain Layout
27605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27608 \begin_layout Plain Layout
27616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27619 \begin_layout Plain Layout
27626 \begin_layout Plain Layout
27640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27643 \begin_layout Plain Layout
27644 \begin_inset Formula $\mathcircumflex$
27654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27657 \begin_layout Plain Layout
27665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27668 \begin_layout Plain Layout
27669 \begin_inset Formula $\_$
27679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27682 \begin_layout Plain Layout
27687 \begin_layout Plain Layout
27699 \begin_inset Index idx
27702 \begin_layout Plain Layout
27715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27718 \begin_layout Plain Layout
27719 \begin_inset Formula $^{\circ}$
27735 \begin_layout Standard
27736 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27737 contains the following line
27741 \begin_layout Plain Layout
27742 More about this is described in
27743 \begin_inset CommandInset ref
27745 reference "sub:Text-Characters-in"
27757 \begin_layout Standard
27762 DeclareInputtext{176}{
27775 \begin_layout Section
27777 \begin_inset CommandInset label
27779 name "sec:Formula-Styles"
27784 \begin_inset Index idx
27787 \begin_layout Plain Layout
27796 \begin_layout Itemize
27797 There are two different alignment styles:
27801 \begin_layout Description
27802 Centered is the predefined standard
27805 \begin_layout Description
27806 Indented for this the option
27810 must be inserted in the menu
27812 Document\SpecialChar \menuseparator
27818 \begin_inset space ~
27824 \begin_layout Standard
27829 is used, the indentation can be adjusted with the length
27836 \begin_inset Index idx
27839 \begin_layout Plain Layout
27848 Should the distance be 15
27849 \begin_inset space \thinspace{}
27852 mm, the following command line is inserted in the LaTeX-preamble
27855 \begin_layout Standard
27865 \begin_layout Standard
27866 When no length is specified, the predefined value of 30
27867 \begin_inset space \thinspace{}
27874 \begin_layout Itemize
27875 And two different numbering styles:
27879 \begin_layout Description
27880 Right is the predefined standard
27883 \begin_layout Description
27884 Left for this the option
27888 must be inserted in the menu
27890 Document\SpecialChar \menuseparator
27896 \begin_inset space ~
27903 \begin_layout Standard
27912 can also be used together.
27913 In this case both options are inserted, separated by a comma.
27916 \begin_layout Standard
27917 The chosen styles are used for all displayed formulas of the document.
27918 When both, centered and indented formulas should be created in a document,
27924 The indented formulas are then set in a flalign environment, see
27925 \begin_inset CommandInset ref
27927 reference "sub:Flalign-Environment"
27934 \begin_layout Section
27936 \begin_inset CommandInset label
27938 name "sec:Multiline-Formulas"
27943 \begin_inset Index idx
27946 \begin_layout Plain Layout
27947 Formula ! multiline
27955 \begin_layout Subsection
27959 \begin_layout Standard
27960 In LyX multiline formulas are created by pressing
27965 arg "newline-insert newline"
27971 This creates either an
27973 eqnarray environment
27975 that is described in
27976 \begin_inset CommandInset ref
27978 reference "sub:Eqnarray-Environment"
27982 or, when the option
27984 Use AMS math package
27986 in the document settings is selected, an
27990 that is described in
27991 \begin_inset CommandInset ref
27993 reference "sub:Standard-align-Environment"
28000 \begin_layout Standard
28001 There are other multiline formula environments that can be created via the
28004 Insert\SpecialChar \menuseparator
28008 These environments are described in the following sections.
28011 \begin_layout Standard
28012 In all multiline formula environments a new line is created by pressing
28016 arg "newline-insert newline"
28020 To add or delete lines, the math toolbar buttons
28021 \begin_inset Graphics
28022 filename ../images/tabular-feature_append-row.png
28028 \begin_inset Graphics
28029 filename ../images/tabular-feature_delete-row.png
28034 , respectively, or the menu
28036 Edit\SpecialChar \menuseparator
28042 \begin_layout Subsubsection
28044 \begin_inset CommandInset label
28046 name "sub:Line-Separation"
28051 \begin_inset Index idx
28054 \begin_layout Plain Layout
28055 Formula ! multiline ! Line separation
28063 \begin_layout Standard
28064 There is sometimes not enough space in multiline formulas between the lines:
28065 \begin_inset Formula \begin{eqnarray*}
28066 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}\\
28067 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
28075 \begin_layout Standard
28076 In LaTeX additional line space is specified as optional argument of the
28078 This is not yet possible in LyX
28082 \begin_layout Plain Layout
28084 \begin_inset CommandInset href
28086 name "LyX-bug #1505"
28087 target "http://www.lyx.org/trac/ticket/1505"
28096 , therefore the whole formula must be inserted in TeX-mode.
28097 To add in our example space, the command
28105 is inserted at the end of the first line.
28110 \begin_layout Plain Layout
28117 \begin_layout Plain Layout
28119 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28122 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28129 \begin_layout Plain Layout
28133 left(B^{2}+x_{0}^{2}
28141 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28146 \begin_layout Plain Layout
28158 \begin_layout Standard
28159 \begin_inset VSpace bigskip
28162 To set the line separation for all lines in a formula, the length
28169 \begin_inset Index idx
28172 \begin_layout Plain Layout
28182 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28193 \begin_inset space \thinspace{}
28198 \begin_inset space \thinspace{}
28201 mm additional line separation as in the previous example, the command
28204 \begin_layout Standard
28214 \begin_layout Standard
28215 is inserted in TeX-mode before the formula.
28216 This requires that the LaTeX-package
28224 \begin_layout Plain Layout
28229 is part of every LaTeX standard installation.
28235 \begin_inset Index idx
28238 \begin_layout Plain Layout
28244 was loaded in LaTeX-preamble with the line
28247 \begin_layout Standard
28255 \begin_layout Standard
28260 \begin_layout Plain Layout
28272 \begin_inset Formula \begin{eqnarray*}
28273 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}\\
28274 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
28282 \begin_layout Standard
28286 \begin_layout Plain Layout
28297 To get back to the predefined distance,
28303 is set to the value 3
28304 \begin_inset space \thinspace{}
28310 \begin_layout Subsubsection
28312 \begin_inset CommandInset label
28314 name "sub:Column-Separation"
28319 \begin_inset Index idx
28322 \begin_layout Plain Layout
28323 Formula ! multiline ! Column separation
28331 \begin_layout Standard
28332 Multiline formulas form a matrix.
28333 A formula in the eqnarray environment is for example a matrix with three
28335 By changing the column separation in this environment, the space beside
28336 the relation sign can be changed.
28339 \begin_layout Standard
28340 The column separation is specified with the length
28347 \begin_inset Index idx
28350 \begin_layout Plain Layout
28359 \begin_inset Newline newline
28362 column separation = 2
28363 \begin_inset space \thinspace{}
28373 \begin_inset Newline newline
28379 \begin_layout Standard
28389 \begin_layout Standard
28390 inserted in TeX-mode, sets for all following formulas a column separation
28392 \begin_inset space \thinspace{}
28396 To get back to the predefined distance,
28403 \begin_inset space \thinspace{}
28409 \begin_layout Standard
28411 \begin_inset space \thinspace{}
28414 cm column separation:
28418 \begin_layout Plain Layout
28430 \begin_inset Formula \begin{eqnarray*}
28437 A formula with the predefined column separation for matrices of 10
28438 \begin_inset space \thinspace{}
28445 \begin_layout Plain Layout
28457 \begin_inset Formula \begin{eqnarray*}
28467 \begin_layout Subsubsection
28469 \begin_inset Index idx
28472 \begin_layout Plain Layout
28481 \begin_layout Standard
28482 Long formulas can be typeset using these methods:
28485 \begin_layout Itemize
28486 When one side of the equation is much shorther than the line width, this
28487 one is chosen for the left side and the right side is typeset over two
28489 \begin_inset Formula \begin{eqnarray}
28490 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 \\
28491 & & -\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}
28496 The minus sign at the beginning of the second line does normally not appear
28497 as operator because it is the first character of the line.
28498 Thus it would not be surrounded by space and could not be distinguished
28499 from the fraction bar.
28501 \begin_inset space \thinspace{}
28504 pt space was inserted behind the minus sign with the command
28514 \begin_layout Plain Layout
28522 \begin_inset CommandInset ref
28524 reference "sub:Variable-Space"
28534 \begin_inset Index idx
28537 \begin_layout Plain Layout
28548 \begin_layout Itemize
28549 When both sides of the equation are too long, the command
28556 \begin_inset Index idx
28559 \begin_layout Plain Layout
28568 It is inserted to the first column of the first line and effects that all
28569 further insertions overwrite the following columns:
28570 \begin_inset Formula \begin{eqnarray}
28571 \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 \\
28572 & & -\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 \\
28573 & & =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}
28578 After the insertion of
28584 , the cursor is in a purple box that is a bit shifted to the left from the
28586 In this the formula is inserted.
28587 \begin_inset Newline newline
28590 The content of the further lines is inserted to the second or another formula
28592 The greater the column number where it was inserted, the larger the indentation.
28593 \begin_inset VSpace medskip
28597 \begin_inset Newline newline
28601 \begin_inset Note Greyedout
28604 \begin_layout Plain Layout
28605 Note the following when using
28614 \begin_layout Itemize
28615 The formula doesn't use the full page width.
28617 \begin_inset space \thinspace{}
28621 \begin_inset space \space{}
28625 \begin_inset Formula $-B^{2}$
28628 is added to the first line in the above example, it would have been outside
28630 To better use the width, negative space can be inserted at the beginning
28634 \begin_layout Itemize
28635 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28640 \begin_layout Plain Layout
28641 \begin_inset CommandInset href
28643 name "LyX-bug #1429"
28644 target "http://www.lyx.org/trac/ticket/1429"
28653 One can only set the cursor at the beginning of the line and move it with
28662 \begin_layout Itemize
28663 Other methods to set long formulas are offered by the environments described
28665 \begin_inset CommandInset ref
28667 reference "sub:Multline-Environment"
28672 \begin_inset CommandInset ref
28674 reference "sub:Multiline-Formula-Parts"
28681 \begin_layout Subsubsection
28683 \begin_inset CommandInset label
28685 name "sub:Multiline-Brackets"
28690 \begin_inset Index idx
28693 \begin_layout Plain Layout
28694 Brackets ! for multiline expressions
28702 \begin_layout Standard
28703 For brackets spanning multiple lines the following problem occurs:
28704 \begin_inset Formula \begin{eqnarray*}
28705 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28706 & & \left.\cdots+B-D\right]
28714 \begin_layout Standard
28715 The closing bracket is smaller than the opening bracket because brackets
28716 with variable size may not span multiple lines.
28719 \begin_layout Standard
28720 To set the bracket size for the second line correctly, the first line is
28728 \begin_inset Index idx
28731 \begin_layout Plain Layout
28739 and the second line with
28747 \begin_layout Plain Layout
28761 \begin_inset CommandInset ref
28763 reference "sub:Automatic-Bracket-Size"
28775 \begin_inset Index idx
28778 \begin_layout Plain Layout
28804 \begin_layout Plain Layout
28823 \begin_layout Plain Layout
28842 \begin_layout Plain Layout
28854 \begin_inset Formula $\downarrow$
28860 \begin_inset Index idx
28863 \begin_layout Plain Layout
28871 is inserted, because the multiplication operator with its limits is the
28872 largest symbol in the first line and this should be the size for the bracket
28873 in the second line.
28876 \begin_layout Standard
28877 The result is this:
28878 \begin_inset Formula \begin{eqnarray*}
28879 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28880 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28888 \begin_layout Subsection
28892 \begin_layout Standard
28893 Align environments can be used for every kind of multiline formulas.
28894 They are specially useful to set several formulas side by side.
28897 \begin_layout Standard
28898 Align environments consist of columns.
28899 The odd columns are right aligned, the even ones left aligned.
28900 Every line in an Align environment can be numbered.
28903 \begin_layout Standard
28904 Align environments are created via the menu
28906 Insert\SpecialChar \menuseparator
28912 Edit\SpecialChar \menuseparator
28913 Math\SpecialChar \menuseparator
28914 Change Formula Type
28916 already existing formulas can be converted to Align environments.
28919 \begin_layout Standard
28920 To add or delete columns, the math toolbar buttons
28921 \begin_inset Graphics
28922 filename ../images/tabular-feature_append-column.png
28928 \begin_inset Graphics
28929 filename ../images/tabular-feature_delete-column.png
28934 , respectively, or the menu
28936 Edit\SpecialChar \menuseparator
28942 \begin_layout Subsubsection
28943 Standard align Environment
28944 \begin_inset CommandInset label
28946 name "sub:Standard-align-Environment"
28951 \begin_inset Index idx
28954 \begin_layout Plain Layout
28955 Formula ! multiline ! align environment
28963 \begin_layout Standard
28964 This Align environment is created by presssing
28967 arg "newline-insert newline"
28970 in a formula or by the menu
28972 Insert\SpecialChar \menuseparator
28973 Math\SpecialChar \menuseparator
28974 AMS align Environment
28979 \begin_layout Standard
28980 An example for two formulas set side by side, that are created with a four
28981 column align environment:
28982 \begin_inset Formula \begin{align*}
28983 A & =\sin(B) & C & =D\\
28984 C & \ne A & B & \ne D
28989 As it can be seen, the formulas in this environment are placed so as if
28998 \begin_layout Plain Layout
29006 \begin_inset CommandInset ref
29008 reference "sub:Variable-Space"
29019 before the first and after every even column.
29020 When the formula style
29026 \begin_layout Plain Layout
29028 \begin_inset CommandInset ref
29030 reference "sec:Formula-Styles"
29041 is used, the formula is set without the
29047 before the first column.
29050 \begin_layout Subsubsection
29051 Alignat Environment
29052 \begin_inset Index idx
29055 \begin_layout Plain Layout
29056 Formula ! multiline ! alignat environment
29064 \begin_layout Standard
29065 The alignat environment has no predefined column separation.
29066 It can be inserted manually with the spaces that are described
29067 \begin_inset CommandInset ref
29069 reference "sub:Space"
29076 \begin_layout Standard
29077 The above example in the alignat environment where 1
29078 \begin_inset space \thinspace{}
29081 cm space was inserted at the beginning of the second formula:
29082 \begin_inset Formula \begin{alignat*}{2}
29083 A & =\sin(B) & \hspace{1cm}C & =D\\
29084 C & \ne A & B & \ne D
29089 Because the column separation can be set separately for every column, this
29090 environment is especially suitable to set three and more formulas side
29094 \begin_layout Subsubsection
29095 Flalign Environment
29096 \begin_inset CommandInset label
29098 name "sub:Flalign-Environment"
29103 \begin_inset Index idx
29106 \begin_layout Plain Layout
29107 Formula ! multiline ! flalign environment
29115 \begin_layout Standard
29116 In this environment the first two columns are always set as much as possible
29117 to the left and the last two ones to the right.
29119 \begin_inset Formula \begin{flalign*}
29120 A & =1 & B & =2 & C & =3\\
29121 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29129 \begin_layout Standard
29130 By creating a flalign environment with an odd number of columns where an
29131 empty TeX-brace is inserted to the last column, several formulas in a document
29132 can be set to the left, although the formula style
29137 As example the indented formula
29138 \begin_inset CommandInset ref
29140 reference "eq:VolInt"
29145 \begin_inset Formula \begin{flalign}
29146 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
29150 The first two columns contain the formula.
29151 To indent it as with the formula style
29156 \begin_inset space \thinspace{}
29159 pt space was inserted at the beginning of the first column.
29162 \begin_layout Subsection
29163 Eqnarray Environment
29164 \begin_inset CommandInset label
29166 name "sub:Eqnarray-Environment"
29171 \begin_inset Index idx
29174 \begin_layout Plain Layout
29175 Formula ! multiline ! eqnarray environment
29183 \begin_layout Standard
29184 When this environment has been created, three blue boxes appear.
29185 The content of the first box is right aligned, the content of the last
29187 The content of the middle box appears centered and a bit smaller, because
29188 it is designed to insert there only relation characters.
29189 \begin_inset Formula \begin{eqnarray*}
29190 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29200 \begin_layout Subsection
29202 \begin_inset Index idx
29205 \begin_layout Plain Layout
29206 Formula ! multiline ! gather environment
29214 \begin_layout Standard
29215 This environment consists of only one centered column.
29216 Every line can be numbered.
29217 \begin_inset Formula \begin{gather}
29227 \begin_layout Subsection
29228 Multline Environment
29229 \begin_inset CommandInset label
29231 name "sub:Multline-Environment"
29236 \begin_inset Index idx
29239 \begin_layout Plain Layout
29240 Formula ! multiline ! multline environment
29248 \begin_layout Standard
29249 The multline environment consists, like the gather environment, of only
29251 But the first line is left aligned, the last one right aligned.
29252 All other lines are centered.
29253 Therefore this environment is suitable for long formulas.
29255 \begin_inset CommandInset ref
29257 reference "eq:lefteqn"
29261 in the multline environment:
29262 \begin_inset Formula \begin{multline}
29263 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}\\
29264 -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}\\
29265 =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}}
29273 \begin_layout Standard
29274 In the output only the last (first) line of a multline environment appears
29275 numbered when the document numbering is right (left).
29279 \begin_layout Plain Layout
29280 numbering styles see
29281 \begin_inset CommandInset ref
29283 reference "sec:Formula-Styles"
29295 \begin_layout Standard
29303 \begin_inset Index idx
29306 \begin_layout Plain Layout
29321 \begin_inset Index idx
29324 \begin_layout Plain Layout
29332 a centered line can be right or left aligned, respectively.
29333 The commands are used as follows:
29336 \begin_layout Standard
29341 shoveright{line content}
29347 shoveleft{line content}
29350 \begin_layout Standard
29351 \begin_inset VSpace medskip
29361 \begin_inset Index idx
29364 \begin_layout Plain Layout
29372 specifies the distance of the first line from the left page margin.
29373 Predefined is the length 0
29374 \begin_inset space \thinspace{}
29380 \begin_layout Standard
29381 As example the above formula where the command
29384 \begin_layout Standard
29394 \begin_layout Standard
29395 was inserted in TeX-mode before:
29399 \begin_layout Plain Layout
29411 \begin_inset Formula \begin{multline}
29412 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}\\
29413 \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}}\\
29414 =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}}
29423 \begin_layout Plain Layout
29434 The second line was left aligned using
29443 \begin_layout Subsection
29444 Multiline Formula Parts
29445 \begin_inset CommandInset label
29447 name "sub:Multiline-Formula-Parts"
29452 \begin_inset Index idx
29455 \begin_layout Plain Layout
29456 Formula ! multiline ! formula parts
29464 \begin_layout Standard
29465 To display only parts of a formula with multiple lines, one of the following
29466 environments are used:
29483 They can be inserted via the menu
29485 Insert\SpecialChar \menuseparator
29488 or by using the commands described in this section.
29491 \begin_layout Standard
29492 The first three have the same properties as the corresponding multiline
29493 formula environments, but it is possible to set further formula parts beside
29496 \begin_inset Formula \[
29497 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29498 \Delta E\Delta t & \ge\frac{\hbar}{2}
29500 \right\} \textrm{Uncertainty relations}\]
29507 \begin_layout Standard
29508 To get this formula, a displayed formula is created where the command
29515 \begin_inset Index idx
29518 \begin_layout Plain Layout
29527 A purple box appears around the blue formula box where now columns and
29528 lines can be added.
29529 Outside the multiline environment other formula parts can be set, like
29533 \begin_layout Standard
29534 The aligned environment is also suitable for long formulas whose lines are
29535 horizontally aligned.
29536 Using aligned in a displayed formula has the advantage that the formula
29537 number is vertically centered behind the lines.
29539 \begin_inset CommandInset ref
29541 reference "eq:shortlong"
29545 in the aligned environment:
29546 \begin_inset Formula \begin{equation}
29547 \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}|}\\
29548 & -\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}|}
29557 \begin_layout Standard
29558 To use the environments
29577 \begin_inset Index idx
29580 \begin_layout Plain Layout
29595 \begin_inset Index idx
29598 \begin_layout Plain Layout
29613 \begin_inset Index idx
29616 \begin_layout Plain Layout
29624 are inserted, respectively.
29625 The split environment has the same properties as the aligned environment
29626 but it can only have two columns.
29629 \begin_layout Subsection
29630 Text in multiline Formulas
29631 \begin_inset CommandInset label
29633 name "sub:Text-in-multiline"
29638 \begin_inset Index idx
29641 \begin_layout Plain Layout
29648 \begin_inset Index idx
29651 \begin_layout Plain Layout
29652 Formula ! multiline ! text
29660 \begin_layout Standard
29661 In the Align environments, and the multline and gather environment, text
29662 can be inserted that will appear in a separate line and doesn't affect
29663 the column alignment.
29664 To do this, the command
29671 \begin_inset Index idx
29674 \begin_layout Plain Layout
29682 is used in the following scheme:
29685 \begin_layout Standard
29693 \begin_layout Standard
29694 The text should not be longer than a line because it cannot be hyphenated.
29695 As LyX doesn't yet support
29701 directly, the text is written as mathematical text.
29708 must hereby be at the beginning of a line and appears in the output above
29710 An example where the text was inserted at the beginning of the second line:
29711 \begin_inset Formula \begin{align}
29712 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29713 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29721 \begin_layout Section
29723 \begin_inset Index idx
29726 \begin_layout Plain Layout
29733 \begin_inset Index idx
29736 \begin_layout Plain Layout
29737 Formula ! numbering|see
29741 \begin_layout Plain Layout
29752 \begin_layout Plain Layout
29767 \begin_layout Subsection
29771 \begin_layout Standard
29772 Numbered formulas can be created with the menu
29774 Insert\SpecialChar \menuseparator
29775 Math\SpecialChar \menuseparator
29777 \begin_inset space ~
29785 \begin_inset space ~
29791 Existing formulas can be numbered with the menu
29793 Edit\SpecialChar \menuseparator
29794 Math\SpecialChar \menuseparator
29796 \begin_inset space ~
29804 arg "math-number-toggle"
29808 The formula number is displayed in LyX behind the formula as number sign
29810 The number sign is replaced in the output by the formula number.
29813 \begin_layout Standard
29814 When numbering is turned on in multiline formulas, all lines will be numbered.
29815 But the numbering can be controlled with the menu
29817 Edit\SpecialChar \menuseparator
29818 Math\SpecialChar \menuseparator
29820 \begin_inset space ~
29824 \begin_inset space ~
29828 \begin_inset space ~
29836 arg "math-number-line-toggle"
29842 \begin_layout Standard
29843 Except for inline formulas, all formulas can be numbered with two different
29845 \begin_inset CommandInset ref
29847 reference "sec:Formula-Styles"
29854 \begin_layout Subsection
29856 \begin_inset Index idx
29859 \begin_layout Plain Layout
29860 Cross-references ! to formulas
29868 \begin_layout Standard
29869 All labeled formulas can be cross-referenced.
29870 A label is added by the menu
29872 Insert\SpecialChar \menuseparator
29875 or the toolbar button
29876 \begin_inset Graphics
29877 filename ../images/label-insert.png
29883 The cursor must hereby be inside a displayed formula.
29884 A dialog pops up displaying the prefix
29889 The label is inserted there behind the prefix.
29890 The predefined prefix means
29891 \begin_inset Quotes eld
29895 \begin_inset Quotes erd
29898 and makes it easier to find labels in large documents because it marks
29899 it as formula label to divide it from e.
29900 \begin_inset space \thinspace{}
29904 \begin_inset space \space{}
29908 To change a label, the menu
29910 Insert\SpecialChar \menuseparator
29916 \begin_layout Standard
29917 The name of the label is displayed in LyX within two parentheses behind
29919 A formula with a label is always numbered.
29922 \begin_layout Standard
29923 Cross-references are inserted via the menu
29925 Insert\SpecialChar \menuseparator
29928 or with the toolbar button
29929 \begin_inset Graphics
29930 filename ../images/dialog-show-new-inset_ref.png
29936 A formula cross-reference appears in the output as formula number.
29937 When in the cross-reference dialog window the format
29941 is chosen, the cross-reference appears in the output as formula number
29943 \begin_inset Newline newline
29946 By right-clicking on a cross-reference in LyX, one jumps to the formula
29947 that is referenced.
29950 \begin_layout Standard
29951 Here are as examples cross-references to formulas of the following subsections:
29952 \begin_inset Note Note
29955 \begin_layout Plain Layout
29956 Note the different cross-reference types.
29964 \begin_layout Standard
29966 \begin_inset CommandInset ref
29973 \begin_inset CommandInset ref
29981 \begin_inset CommandInset ref
29987 ) big Latin letters are used for the numbering in contrary to (
29988 \begin_inset CommandInset ref
29997 \begin_layout Standard
29998 \begin_inset VSpace medskip
30001 When the argument of
30009 \begin_layout Plain Layout
30017 \begin_inset CommandInset ref
30019 reference "sub:User-defined-Numbering"
30030 contains a box like in
30031 \begin_inset CommandInset ref
30033 reference "sub:Paragraph-Boxes"
30037 , the formula cannot be referenced.
30040 \begin_layout Subsection
30042 \begin_inset Index idx
30045 \begin_layout Plain Layout
30046 Formula numbering ! subnumbering
30054 \begin_layout Standard
30055 With the help of the commands
30059 begin{subequations}
30067 formulas can be subnumbered.
30068 Both commands are inserted in TeX-mode.
30071 \begin_layout Standard
30073 \begin_inset Formula \begin{equation}
30074 A=C-B\label{eq:a}\end{equation}
30082 \begin_layout Plain Layout
30086 addtocounter{equation}{-1}
30095 \begin_layout Plain Layout
30099 begin{subequations}
30105 \begin_inset VSpace -5mm
30109 \begin_inset Formula \begin{equation}
30110 B=C-A\label{eq:b}\end{equation}
30115 \begin_inset Formula \begin{equation}
30116 C=A+B\label{eq:c}\end{equation}
30123 \begin_layout Standard
30127 \begin_layout Plain Layout
30139 \begin_layout Standard
30140 To create the example, the following is done:
30143 \begin_layout Enumerate
30144 first formula is inserted
30147 \begin_layout Enumerate
30152 addtocounter{equation}{-1}
30154 begin{subequations}
30155 \begin_inset Index idx
30158 \begin_layout Plain Layout
30167 \begin_inset Newline newline
30172 is inserted after the first formula
30175 \begin_layout Enumerate
30176 second formula is inserted
30179 \begin_layout Enumerate
30180 third formula is inserted
30183 \begin_layout Enumerate
30190 is inserted after the third formula
30193 \begin_layout Standard
30194 Every formula between the commands
30206 is subnumbered as a, b,
30207 \begin_inset Newline linebreak
30210 c, \SpecialChar \ldots{}
30211 For multiline formulas every line will be subnumbered.
30212 All subnumbered formulas are treated as
30217 But as every numbered formula increases the counter
30221 by one, the command
30227 is needed to decrease it.
30228 Otherwise the formulas
30229 \begin_inset CommandInset ref
30236 \begin_inset CommandInset ref
30243 \begin_inset CommandInset ref
30249 would be numbered as
30250 \begin_inset CommandInset ref
30257 \begin_inset CommandInset ref
30264 \begin_inset CommandInset ref
30273 \begin_layout Standard
30274 By inserting the commands in TeX-mode, a space is created between the first
30277 \begin_inset space \thinspace{}
30280 mm vertical space is inserted after the command
30284 begin{subequations}
30287 When the formula style
30293 \begin_layout Plain Layout
30295 \begin_inset CommandInset ref
30297 reference "sec:Formula-Styles"
30309 \begin_inset space \thinspace{}
30312 mm space is inserted instead.
30315 \begin_layout Standard
30316 Here is an example for a multiline formula where the numbering was turned
30317 off for the second line:
30321 \begin_layout Plain Layout
30325 begin{subequations}
30331 \begin_inset Formula \begin{eqnarray}
30332 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30333 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30334 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30343 \begin_layout Plain Layout
30355 \begin_layout Subsection
30356 User-defined Numbering
30357 \begin_inset CommandInset label
30359 name "sub:User-defined-Numbering"
30364 \begin_inset Index idx
30367 \begin_layout Plain Layout
30368 Formula numbering ! user-defined
30376 \begin_layout Standard
30377 \begin_inset Index idx
30380 \begin_layout Plain Layout
30381 Formula numbering ! self-defined delimiters
30386 With the standard numbering parentheses are set around the formula number.
30387 To replace the parentheses for example by vertical bars, the following
30388 line is added to the LaTeX-preamble:
30391 \begin_layout Standard
30403 \begin_inset Note Note
30406 \begin_layout Plain Layout
30407 This macro is already declared in the LaTeX-preamble for testing.
30408 To activate it, remove the percent sign at the beginning.
30416 \begin_layout Standard
30417 To use other characters, the vertical bars besides the
30421 are replaced by one ore more characters.
30422 To get only the formula number the vertical bars are omitted.
30425 \begin_layout Standard
30426 \begin_inset VSpace bigskip
30429 When there should be an expression of your choice instead of the consecutive
30430 formula number in parentheses behind the formula, the command
30437 \begin_inset Index idx
30440 \begin_layout Plain Layout
30449 \begin_inset Formula \begin{equation}
30450 A+B=C\tag{something}\label{eq:tag}\end{equation}
30454 In this example the command
30462 \begin_layout Plain Layout
30473 was inserted to the formula.
30476 \begin_layout Standard
30485 \begin_layout Plain Layout
30496 is inserted instead, the star prevents the parentheses around the expression:
30497 \begin_inset Formula \[
30498 A+B=C\tag*{something}\]
30505 \begin_layout Standard
30506 \begin_inset VSpace bigskip
30509 To restart the formula numbering with new document parts or sections, the
30510 following command is used:
30513 \begin_layout Standard
30518 @addtoreset{equation}{part}
30521 \begin_inset Index idx
30524 \begin_layout Plain Layout
30529 \begin_layout Plain Layout
30540 \begin_layout Plain Layout
30553 \begin_layout Plain Layout
30564 \begin_layout Plain Layout
30577 \begin_inset Newline newline
30581 \begin_inset Newline newline
30588 @addtoreset{equation}{section}
30591 \begin_layout Standard
30592 To be able to use these commands in TeX-mode, the
30593 \begin_inset Quotes eld
30597 \begin_inset Quotes erd
30600 character has to be made
30601 \begin_inset Quotes eld
30605 \begin_inset Quotes erd
30608 for LaTeX using the command
30622 So the command sequence in TeX-mode is:
30625 \begin_layout Standard
30631 \begin_inset Newline newline
30636 @addtoreset{equation}{section}
30637 \begin_inset Newline newline
30645 \begin_layout Standard
30646 In the LaTeX-preamble
30658 can be omitted as they are automatically internally inserted by LyX.
30661 \begin_layout Standard
30676 \begin_layout Plain Layout
30681 is part of the LaTeX-package
30686 \begin_inset Index idx
30689 \begin_layout Plain Layout
30690 Packages ! carlisle
30695 that is part of every LaTeX standard installation.
30701 \begin_inset Index idx
30704 \begin_layout Plain Layout
30705 Packages ! remreset
30710 has to be loaded in the LaTeX-preamble with the line
30713 \begin_layout Standard
30718 usepackage{remreset}
30721 \begin_layout Standard
30729 \begin_inset Index idx
30732 \begin_layout Plain Layout
30737 \begin_layout Plain Layout
30748 \begin_layout Plain Layout
30761 \begin_layout Plain Layout
30772 \begin_layout Plain Layout
30784 can be used with the same scheme as
30793 \begin_layout Standard
30794 \begin_inset VSpace bigskip
30797 Sometimes formulas should be numbered in the following form:
30800 \begin_layout Standard
30803 (section number.formula number)
30806 \begin_layout Standard
30807 The formula number should start with every section with
30808 \begin_inset Quotes eld
30812 \begin_inset Quotes erd
30818 \begin_layout Standard
30819 For this case there is the command
30826 \begin_inset Index idx
30829 \begin_layout Plain Layout
30837 , which is used with the following scheme:
30840 \begin_layout Standard
30845 numberwithin{counter}{sectioning}
30848 \begin_layout Standard
30849 Counter denotes what kind of numbering is affected, sectioning denotes what
30850 number is before the dot.
30853 \begin_layout Standard
30854 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30857 \begin_layout Standard
30862 numberwithin{equation}{section}
30865 \begin_layout Standard
30866 This is the result:
30870 \begin_layout Plain Layout
30874 numberwithin{equation}{section}
30880 \begin_inset Formula \begin{equation}
30881 A+B=C\end{equation}
30888 \begin_layout Standard
30890 \begin_inset space \thinspace{}
30894 \begin_inset space \space{}
30897 tables so that the number of the part is the sectioning,
30898 \begin_inset Newline newline
30905 numberwithin{table}{part}
30910 \begin_layout Standard
30911 To go back to the standard numbering or to prevent this kind of numbering
30912 when it is defined by the document class, the following command is inserted
30913 as TeX-Code or to the LaTeX-preamble:
30916 \begin_layout Standard
30926 \begin_inset Index idx
30929 \begin_layout Plain Layout
30943 \begin_layout Plain Layout
30959 \begin_inset Newline newline
30967 \begin_inset Newline newline
30979 \begin_layout Standard
30986 uses internally the command
30992 , described above, that also needs to be reverted.
30996 \begin_layout Plain Layout
31003 \begin_layout Plain Layout
31007 @removefromreset{equation}{section}
31010 \begin_layout Plain Layout
31022 \begin_layout Subsection
31023 Numbering with Roman Numbers and Letters
31024 \begin_inset Index idx
31027 \begin_layout Plain Layout
31028 Formula numbering ! with letters
31034 \begin_inset Index idx
31037 \begin_layout Plain Layout
31038 Formula numbering ! with Roman numbers
31046 \begin_layout Standard
31047 Formulas can also be numbered with Roman numbers and Latin letters.
31048 To number for example with small Roman numbers, the command
31051 \begin_layout Standard
31063 \begin_layout Standard
31064 is inserted before the formula in TeX-mode.
31072 \begin_inset Index idx
31075 \begin_layout Plain Layout
31083 redefines the predefined command
31099 \begin_layout Plain Layout
31106 has the same scheme like the command
31112 that is described in
31113 \begin_inset CommandInset ref
31115 reference "sub:The-Command-newcommand"
31128 is the formula counter.
31135 is used as prefix for a counter, the value of the counter is output as
31137 When a formula is numbered, LaTeX sets internally the command
31143 behind the formula.
31149 \begin_inset Index idx
31152 \begin_layout Plain Layout
31162 outputs the counter as small Roman number.
31165 \begin_layout Standard
31166 All formulas behind the command
31176 are now numbered Roman.
31177 To switch to numbering with big Roman numbers, the command is inserted
31191 \begin_inset Index idx
31194 \begin_layout Plain Layout
31206 \begin_inset Quotes eld
31210 \begin_inset Quotes erd
31213 with small Latin letters there is the command
31220 \begin_inset Index idx
31223 \begin_layout Plain Layout
31231 , for big ones there is the command
31238 \begin_inset Index idx
31241 \begin_layout Plain Layout
31254 \begin_layout Standard
31255 \begin_inset Note Greyedout
31258 \begin_layout Plain Layout
31263 Only maximal 26 formulas can be numbered with Latin letters in one document.
31271 \begin_layout Standard
31275 \begin_layout Plain Layout
31291 \begin_layout Standard
31292 \begin_inset Formula \begin{equation}
31293 A=\textrm{small roman}\end{equation}
31301 \begin_layout Plain Layout
31315 \begin_inset Formula \begin{equation}
31316 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
31324 \begin_layout Plain Layout
31338 \begin_inset Formula \begin{equation}
31339 C=\textrm{small Latin}\end{equation}
31347 \begin_layout Plain Layout
31361 \begin_inset Formula \begin{equation}
31362 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
31369 \begin_layout Standard
31370 To switch back to the default numbering, insert the command:
31373 \begin_layout Standard
31383 \begin_inset Index idx
31386 \begin_layout Plain Layout
31397 \begin_layout Standard
31401 \begin_layout Plain Layout
31415 \begin_inset Formula \begin{equation}
31416 E=\textrm{Arabic}\end{equation}
31423 \begin_layout Standard
31424 \begin_inset VSpace medskip
31427 As you see, formulas are numbered serially independent from the numbering
31429 When then numbering should start with
31430 \begin_inset Quotes eld
31434 \begin_inset Quotes erd
31437 when the style is changed, new equation counters have to be defined.
31438 A description about this can be found in the file
31439 \begin_inset CommandInset href
31441 name "Formula-numbering.lyx"
31442 target "run:Formula-numbering.lyx"
31449 \begin_layout Section
31450 Chemical Symbols and Equations
31451 \begin_inset CommandInset label
31453 name "sub:Chemical-Symbols-and"
31458 \begin_inset Index idx
31461 \begin_layout Plain Layout
31462 Chemical characters ! Symbols
31468 \begin_inset Index idx
31471 \begin_layout Plain Layout
31478 \begin_inset Index idx
31481 \begin_layout Plain Layout
31490 \begin_layout Standard
31491 An example text from chemistry:
31494 \begin_layout Quote
31496 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31499 -ion reacts with two
31500 \begin_inset Formula $\mathrm{Na^{+}}$
31503 -ions to sodium sulfate
31504 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31508 The chemical equation for this is:
31509 \begin_inset Formula \begin{equation}
31510 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
31517 \begin_layout Standard
31518 This chemical equation can directly be created as formula.
31519 To avoid that the symbols appear italic, everything is highlighted and
31520 changed by the shortcut
31526 to the upright font style.
31530 \begin_layout Plain Layout
31536 \begin_inset CommandInset ref
31538 reference "sub:Font-Styles"
31550 \begin_layout Standard
31551 A more convenient way to typeset chemical formulas is to use the command
31559 \begin_inset Index idx
31562 \begin_layout Plain Layout
31570 that is available when the LaTeX-package
31575 \begin_inset Index idx
31578 \begin_layout Plain Layout
31591 to a formula a new blue box appears where chemical formulas can be inserted
31592 in an intuitive way.
31595 \begin_layout Standard
31597 \begin_inset Tabular
31598 <lyxtabular version="3" rows="9" columns="2">
31599 <features tabularvalignment="middle">
31600 <column alignment="center" valignment="top" width="0">
31601 <column alignment="center" valignment="top" width="0">
31603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31606 \begin_layout Plain Layout
31612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31615 \begin_layout Plain Layout
31617 \begin_inset Note Note
31620 \begin_layout Plain Layout
31627 is only used as spacer.
31639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31642 \begin_layout Plain Layout
31649 \begin_layout Plain Layout
31663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31666 \begin_layout Plain Layout
31667 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31680 \begin_layout Plain Layout
31687 \begin_layout Plain Layout
31701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31704 \begin_layout Plain Layout
31705 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31718 \begin_layout Plain Layout
31725 \begin_layout Plain Layout
31739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31742 \begin_layout Plain Layout
31743 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31756 \begin_layout Plain Layout
31763 \begin_layout Plain Layout
31777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31780 \begin_layout Plain Layout
31781 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31794 \begin_layout Plain Layout
31801 \begin_layout Plain Layout
31816 \begin_layout Plain Layout
31831 \begin_layout Plain Layout
31845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31848 \begin_layout Plain Layout
31849 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31862 \begin_layout Plain Layout
31869 \begin_layout Plain Layout
31879 \begin_inset Formula $\downarrow$
31883 \begin_inset Formula $\to$
31891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31894 \begin_layout Plain Layout
31895 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31908 \begin_layout Plain Layout
31915 \begin_layout Plain Layout
31928 \begin_layout Plain Layout
31941 \begin_layout Plain Layout
31954 \begin_layout Plain Layout
31967 \begin_layout Plain Layout
31981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31984 \begin_layout Plain Layout
31985 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
31995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31998 \begin_layout Plain Layout
32005 \begin_layout Plain Layout
32018 \begin_layout Plain Layout
32031 \begin_layout Plain Layout
32044 \begin_layout Plain Layout
32061 \begin_layout Plain Layout
32075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32078 \begin_layout Plain Layout
32079 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32095 \begin_layout Standard
32096 \begin_inset Note Greyedout
32099 \begin_layout Plain Layout
32104 Inserting a formula to a
32110 box will lead to LaTeX errors.
32111 In this case TeX code has to be used like for
32125 \begin_layout Plain Layout
32146 \begin_layout Standard
32153 the command for equation
32154 \begin_inset space ~
32158 \begin_inset CommandInset ref
32160 reference "eq:chem-reaction"
32165 \begin_inset Newline newline
32176 \begin_layout Plain Layout
32189 \begin_layout Plain Layout
32202 \begin_layout Plain Layout
32215 \begin_layout Plain Layout
32228 \begin_layout Plain Layout
32241 \begin_layout Plain Layout
32253 \begin_layout Standard
32254 To create multiline chemical equations first a multiline formula is created
32256 \begin_inset CommandInset ref
32258 reference "sec:Multiline-Formulas"
32263 Afterwards the command
32269 is used in every small blue box of the formula.
32271 \begin_inset CommandInset ref
32273 reference "eq:TEOS-reaction-1"
32278 \begin_inset CommandInset ref
32280 reference "eq:TEOS-reaction-2"
32284 are an example of a multi-stage chemical reaction where every equation
32285 has its own number.
32286 \begin_inset Formula \begin{eqnarray}
32287 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32288 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32296 \begin_layout Standard
32307 package provides the command
32314 \begin_inset Index idx
32317 \begin_layout Plain Layout
32325 that has to be used for special cases.
32326 For more information about
32332 and more examples have a look at the documentation of
32337 \begin_inset CommandInset citation
32346 \begin_layout Standard
32347 \begin_inset Newpage newpage
32353 \begin_layout Section
32357 \begin_layout Standard
32358 LyX supports two types of commutative diagrams:
32366 that are explained in the following.
32369 \begin_layout Subsection
32371 \begin_inset Index idx
32374 \begin_layout Plain Layout
32383 \begin_layout Standard
32384 Diagrams of this type visualize relations by vertical and horizontal lines
32386 \begin_inset Formula \[
32387 \begin{CD}A@>>>B@>>>C\\
32397 \begin_layout Standard
32398 To get them, the command
32403 \begin_inset Index idx
32406 \begin_layout Plain Layout
32416 is inserted to a formula.
32417 A blue box appears with two dashed lines where further commands can be
32422 arg "newline-insert newline"
32425 a new line is created.
32426 Horizontal relations are inserted in odd, vertical in even formula lines.
32429 \begin_layout Standard
32430 To create the relations there are the following commands:
32433 \begin_layout Itemize
32438 creates a left arrow,
32449 \begin_layout Itemize
32454 creates an up arrow,
32462 a vertical equal sign
32465 \begin_layout Itemize
32471 is a placeholder for non-existent relations
32474 \begin_layout Standard
32475 All arrows can be labeled as follows:
32478 \begin_layout Itemize
32479 Is text inserted between the first and second < or >, resp., it is placed
32481 When it is inserted between the second and third one, it appears under
32485 \begin_layout Itemize
32486 When text for vertical arrows is inserted between the first and second A
32487 or V, resp., it is placed left beside the arrow.
32488 When it is inserted between the second and third one, it appears right
32490 If the text contains an A or V, these letters must be set into a TeX-brace.
32493 \begin_layout Standard
32494 As example a diagram with all possible relations:
32497 \begin_layout Standard
32498 \begin_inset Formula \[
32499 \begin{CD}A@>j>>B@>>k>C@=F\\
32509 \begin_layout Standard
32510 The command for this is:
32511 \begin_inset Newline newline
32522 \begin_layout Plain Layout
32531 A@>j>>B@>>k>C@=F Ctrl+Return
32532 \begin_inset Newline newline
32536 \begin_inset Phantom HPhantom
32539 \begin_layout Plain Layout
32548 \begin_layout Plain Layout
32567 \begin_inset Formula $\to$
32573 \begin_inset Newline newline
32577 \begin_inset Phantom HPhantom
32580 \begin_layout Plain Layout
32589 \begin_layout Plain Layout
32606 \begin_layout Subsection
32608 \begin_inset Index idx
32611 \begin_layout Plain Layout
32612 Diagrams ! xymatrix
32620 \begin_layout Standard
32621 To be able to use xymatrices, the LaTeX-package
32626 A xymatrix is created by inserting the command
32633 Then you are able to add new matrix columns and rows like for normal matrices,
32635 \begin_inset CommandInset ref
32637 reference "sec:Matrices"
32644 \begin_layout Standard
32645 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32647 All possibilities to create commutative diagrams and decorations are explained
32652 that you find in the menu
32654 Help\SpecialChar \menuseparator
32656 \begin_inset space ~
32664 \begin_layout Subsection
32670 \begin_inset Index idx
32673 \begin_layout Plain Layout
32682 \begin_layout Standard
32687 -diagrams, the LaTeX-package
32696 -diagram is created by inserting the command
32703 Then you are able to add new matrix columns and rows like for normal matrices,
32705 \begin_inset CommandInset ref
32707 reference "sec:Matrices"
32714 \begin_layout Standard
32715 Examples how to create
32719 diagrams in LyX is given in the
32721 Feynman-diagram manual
32723 that you find in the menu
32725 Help\SpecialChar \menuseparator
32727 \begin_inset space ~
32735 \begin_layout Section
32736 User-defined Commands
32737 \begin_inset Index idx
32740 \begin_layout Plain Layout
32741 User-defined commands
32749 \begin_layout Standard
32750 \begin_inset Note Greyedout
32753 \begin_layout Plain Layout
32758 The names of user-defined commands and macros may only consist of Latin
32767 \begin_layout Subsection
32771 \begin_inset CommandInset label
32773 name "sub:The-Command-newcommand"
32778 \begin_inset Index idx
32781 \begin_layout Plain Layout
32782 User-defined commands !
32790 \begin_inset Index idx
32793 \begin_layout Plain Layout
32804 \begin_layout Standard
32805 Many LaTeX-commands are too long to be used frequently.
32806 But it is possible to define with the command
32812 new shorter commands.
32815 \begin_layout Standard
32816 The command scheme of
32825 \begin_layout Standard
32830 newcommand{new command name}[number of arguments][optional
32835 \begin_inset Newline newline
32839 \begin_inset Phantom HPhantom
32842 \begin_layout Plain Layout
32852 {command definition}
32855 \begin_layout Standard
32856 \begin_inset Note Greyedout
32859 \begin_layout Plain Layout
32864 Assure that the name of the new command is not already used in your document
32865 or by LaTeX-packages that you use.
32866 When you for example define the command
32878 , you get an error message because
32884 is already defined as command for
32885 \begin_inset Quotes eld
32889 \begin_inset Formula $\le$
32893 \begin_inset Quotes erd
32904 \begin_layout Standard
32905 The number of arguments is an integer in the range 0
32906 \begin_inset space \thinspace{}
32910 \begin_inset space \thinspace{}
32913 9 and specifies how many arguments the new command should have.
32914 With the optional value a value for an optional argument can be predefined.
32915 When this is done, the
32923 rgument of the new command is automatically an optional one.
32926 \begin_layout Standard
32927 Here are some examples:
32930 \begin_layout Itemize
32931 To define the command
32943 , the LaTeX-preamble line is:
32944 \begin_inset VSpace medskip
32948 \begin_inset Newline newline
32962 \begin_layout Itemize
32963 To define the command
32975 , the argument (that should be underlined) must be taken into account.
32976 For this the preamble line is:
32977 \begin_inset VSpace medskip
32981 \begin_inset Newline newline
32995 \begin_inset VSpace medskip
32999 \begin_inset Newline newline
33006 acts as argument placeholder, the
33010 behind it denotes that it is the placeholder for the first argument.
33013 \begin_layout Itemize
33021 \begin_inset space \thinspace{}
33025 \begin_inset space \space{}
33035 \begin_inset VSpace medskip
33039 \begin_inset Newline newline
33050 framebox#1#2{$#3$}}
33053 \begin_inset VSpace medskip
33057 \begin_inset Newline newline
33060 The two Dollar signs creates the extra formula needed for
33067 \begin_inset CommandInset ref
33069 reference "sub:Boxes-with-Frame"
33076 \begin_layout Itemize
33077 To create a new command for
33083 where the color for the box needn't to be specified, the argument for the
33084 color is defined optional:
33085 \begin_inset VSpace medskip
33089 \begin_inset Newline newline
33100 fcolorbox{#2}{#1}{$#3$}}
33103 \begin_inset VSpace medskip
33107 \begin_inset Newline newline
33110 When the color is not specified when using
33116 , the predefined color
33123 \begin_layout Standard
33124 A test of the new defined commands:
33127 \begin_layout Standard
33129 \begin_inset Tabular
33130 <lyxtabular version="3" rows="6" columns="2">
33131 <features tabularvalignment="middle">
33132 <column alignment="center" valignment="top" width="0">
33133 <column alignment="center" valignment="top" width="0">
33135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33138 \begin_layout Plain Layout
33144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33147 \begin_layout Plain Layout
33149 \begin_inset Note Note
33152 \begin_layout Plain Layout
33159 is only used as spacer.
33171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33174 \begin_layout Plain Layout
33181 \begin_layout Plain Layout
33195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33198 \begin_layout Plain Layout
33199 \begin_inset Formula $A\gr B$
33209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33212 \begin_layout Plain Layout
33220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33223 \begin_layout Plain Layout
33224 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33237 \begin_layout Plain Layout
33241 \begin_inset Formula $\to$
33247 \begin_inset Formula $\to$
33258 \begin_layout Plain Layout
33272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33275 \begin_layout Plain Layout
33276 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33289 \begin_layout Plain Layout
33293 \begin_inset Formula $\to$
33304 \begin_layout Plain Layout
33318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33321 \begin_layout Plain Layout
33322 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33335 \begin_layout Plain Layout
33341 \begin_inset Formula $\to$
33352 \begin_layout Plain Layout
33366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33369 \begin_layout Plain Layout
33370 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33386 \begin_layout Subsection
33388 \begin_inset Index idx
33391 \begin_layout Plain Layout
33392 User-defined commands! Math macros
33398 \begin_inset Index idx
33401 \begin_layout Plain Layout
33410 \begin_layout Standard
33411 User-defined commands are especially convenient for complex expressions.
33412 When you are for example dealing in a document with quadratic equations,
33413 the same solution type occurs several times.
33414 The general form of a quadratic equation is
33415 \begin_inset Formula \[
33416 0=\lambda^{2}+p\lambda+q\]
33420 The general form of the solution is
33421 \begin_inset Formula \[
33422 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
33429 \begin_layout Standard
33430 To define a command for the solution formula where only the three parameters
33432 \begin_inset Formula $\lambda$
33436 \begin_inset Formula $p$
33440 \begin_inset Formula $q$
33443 need to be specified and the index of
33444 \begin_inset Formula $\lambda$
33447 can be given optionally, the LaTeX-preamble line is
33448 \begin_inset Newline newline
33464 \begin_inset Newline newline
33468 \begin_inset Phantom HPhantom
33471 \begin_layout Plain Layout
33485 frac{#3^{2}}{4}-#4}}
33488 \begin_layout Standard
33489 To create with this the solution formula, the command
33490 \begin_inset Newline newline
33500 \begin_inset Formula $\to$
33506 \begin_inset Formula $\to$
33513 is inserted to a formula
33518 \begin_layout Standard
33519 The definition of the new command is unintuitive because one has to know
33520 the schemes of all used LaTeX commands, e.
33521 \begin_inset space \thinspace{}
33525 \begin_inset space \space{}
33528 that a fraction is inserted in LaTeX as
33532 frac{numerator}{denominator}
33535 Furthermore one can easily forget a brace in the definition and cannot
33536 see in LyX what the new command is doing.
33537 To avoid these problems LyX offers the possibility to use math macros instead
33547 \begin_layout Standard
33548 A math macro is created by using the menu
33550 Insert\SpecialChar \menuseparator
33551 Math\SpecialChar \menuseparator
33554 or the toolbar button
33555 \begin_inset Graphics
33556 filename ../images/math-macro_newmacroname_newcommand.png
33562 The math macro toolbar appears together with the following box where the
33564 \begin_inset Newline newline
33568 \begin_inset space \hspace*{\fill}
33572 \begin_inset Graphics
33573 filename clipart/macrobox.png
33578 \begin_inset space \hspace*{\fill}
33582 \begin_inset Newline newline
33586 \begin_inset FormulaMacro
33587 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33592 newmacroname is the default name of the macro that should be changed to
33593 something sensible.
33594 The wanted formula is inserted in the first blue box.
33595 An argument placeholder is inserted with the command
33602 \begin_inset space \thinspace{}
33606 \begin_inset space \space{}
33615 or by using the macro toolbar button
33616 \begin_inset Graphics
33617 filename ../images/math-macro-add-param.png
33623 Argument placeholders are displayed red.
33624 Maximum 9 arguments are possible.
33625 Optional arguments are created with the toolbar button
33626 \begin_inset Graphics
33627 filename ../images/math-macro-add-optional-param.png
33633 The first non-optional argument can be transformed to an optional one with
33635 \begin_inset Graphics
33636 filename ../images/math-macro-make-optional.png
33642 In the second blue box the appearance of the macro in LyX can be defined.
33643 Normally you want to see it as it is defined, so the box is kept empty.
33644 But when you have created a macro that needs lot of space on the screen,
33645 you can insert in the box for example
33646 \begin_inset Newline newline
33676 \begin_inset Newline newline
33681 For the macro only the arguments with the macro name in front of them will
33682 then be displayed in LyX, leading to a better overview.
33683 The formula appears in the output as defined in the first box.
33684 \begin_inset Newline newline
33687 The appearance of macros in formulas can furthermore be changed for single
33688 macros by setting the cursor in the macro and using the menu
33690 View\SpecialChar \menuseparator
33692 \begin_inset space ~
33696 \begin_inset space ~
33704 \begin_layout Standard
33705 To use a macro, the macro name is inserted as command to a formula, in our
33713 Our macro looks in LyX like this:
33714 \begin_inset Newline newline
33718 \begin_inset space \hspace*{\fill}
33722 \begin_inset Graphics
33723 filename clipart/macrouse.png
33728 \begin_inset space \hspace*{\fill}
33732 \begin_inset Newline newline
33735 Here is our macro example with the arguments
33736 \begin_inset Formula $x$
33740 \begin_inset Formula $\ln(x)$
33744 \begin_inset Formula $B$
33750 \begin_layout Standard
33751 \begin_inset Formula \[
33759 \begin_layout Standard
33760 LyX offers in the menu
33762 Tools\SpecialChar \menuseparator
33763 Preferences\SpecialChar \menuseparator
33764 Editing\SpecialChar \menuseparator
33767 different styles to edit macros.
33768 To find the style that suits you the most, choose a style and set the cursor
33769 in a macro formula to see the difference.
33772 \begin_layout Standard
33773 A math macro is transformed internally to a
33779 command when exporting the document.
33786 command is not placed in the LaTeX-preamble, therefore macros can only
33787 be used in formulas that are in the document below the macro definition
33791 \begin_layout Standard
33792 Math macros can also be directly be created from a
33799 When writing for example the command
33802 \begin_inset Newline newline
33811 xleftarrow[#2]{#1}}
33812 \begin_inset Newline newline
33817 in LyX as normal text, highlighting it completely and using then the shortcut
33822 , the command will be transformed to a math macro.
33823 Using this method you need to be careful that the
33829 command is typed correctly, otherwise you get a faulty macro leading to
33833 \begin_layout Standard
33834 Math macros currently yet have the problem that further formulas in macro
33835 definitions are handled wrongly.
33836 Therefore the example
33843 \begin_inset CommandInset ref
33845 reference "sub:The-Command-newcommand"
33849 cannot be created as macro.
33852 \begin_layout Standard
33853 When the cursor is in a macro definition box, you will see the macro toolbar
33857 \begin_layout Standard
33858 \begin_inset VSpace defskip
33864 \begin_layout Standard
33865 \begin_inset Graphics
33866 filename clipart/MacroToolbar.png
33871 \begin_inset Index idx
33874 \begin_layout Plain Layout
33883 \begin_layout Standard
33884 \begin_inset VSpace defskip
33890 \begin_layout Standard
33891 The macro toolbar contains from left to right the following buttons:
33894 \begin_layout Standard
33895 \begin_inset VSpace defskip
33901 \begin_layout Standard
33902 \begin_inset Tabular
33903 <lyxtabular version="3" rows="9" columns="2">
33904 <features islongtable="true" longtabularalignment="center">
33905 <column alignment="left" valignment="top" width="0">
33906 <column alignment="left" valignment="top" width="85col%">
33907 <row interlinespace="2.5mm">
33908 <cell alignment="center" valignment="top" usebox="none">
33911 \begin_layout Plain Layout
33912 \begin_inset Graphics
33913 filename ../images/math-macro-remove-param.png
33914 BoundingBox 0bp 5bp 20bp 25bp
33915 rotateOrigin center
33924 <cell alignment="center" valignment="top" usebox="none">
33927 \begin_layout Plain Layout
33930 Edit\SpecialChar \menuseparator
33931 Math\SpecialChar \menuseparator
33933 \begin_inset space ~
33936 Definition\SpecialChar \menuseparator
33937 Remove Last Argument
33943 <row interlinespace="2.5mm">
33944 <cell alignment="center" valignment="top" usebox="none">
33947 \begin_layout Plain Layout
33948 \begin_inset Graphics
33949 filename ../images/math-macro-add-param.png
33950 BoundingBox 0bp 5bp 20bp 25bp
33951 rotateOrigin center
33960 <cell alignment="center" valignment="top" usebox="none">
33963 \begin_layout Plain Layout
33966 Edit\SpecialChar \menuseparator
33967 Math\SpecialChar \menuseparator
33969 \begin_inset space ~
33972 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-optional.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 First Non-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
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-make-nonoptional.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 Make Last Optional into
34069 \begin_inset Newline newline
34073 \begin_inset Phantom HPhantom
34076 \begin_layout Plain Layout
34079 Edit\SpecialChar \menuseparator
34080 Math\SpecialChar \menuseparator
34082 \begin_inset space ~
34085 Definition\SpecialChar \menuseparator
34091 Non-Optional Argument
34097 <row interlinespace="2.5mm">
34098 <cell alignment="center" valignment="top" usebox="none">
34101 \begin_layout Plain Layout
34102 \begin_inset Graphics
34103 filename ../images/math-macro-remove-optional-param.png
34104 BoundingBox 0bp 5bp 20bp 25bp
34105 rotateOrigin center
34114 <cell alignment="center" valignment="top" usebox="none">
34117 \begin_layout Plain Layout
34120 Edit\SpecialChar \menuseparator
34121 Math\SpecialChar \menuseparator
34123 \begin_inset space ~
34126 Definition\SpecialChar \menuseparator
34127 Remove Optional Argument
34133 <row interlinespace="2.5mm">
34134 <cell alignment="center" valignment="top" usebox="none">
34137 \begin_layout Plain Layout
34138 \begin_inset Graphics
34139 filename ../images/math-macro-add-optional-param.png
34140 BoundingBox 0bp 5bp 20bp 25bp
34141 rotateOrigin center
34150 <cell alignment="center" valignment="top" usebox="none">
34153 \begin_layout Plain Layout
34156 Edit\SpecialChar \menuseparator
34157 Math\SpecialChar \menuseparator
34159 \begin_inset space ~
34162 Definition\SpecialChar \menuseparator
34163 Insert Optional Argument
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-remove-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
34199 Remove Last Argument
34200 \begin_inset Newline newline
34204 \begin_inset Phantom HPhantom
34207 \begin_layout Plain Layout
34210 Edit\SpecialChar \menuseparator
34211 Math\SpecialChar \menuseparator
34213 \begin_inset space ~
34216 Definition\SpecialChar \menuseparator
34222 Spitting Out To 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-append-greedy-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
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
34287 <row interlinespace="2.5mm">
34288 <cell alignment="center" valignment="top" usebox="none">
34291 \begin_layout Plain Layout
34292 \begin_inset Graphics
34293 filename ../images/math-macro-add-greedy-optional-param.png
34294 BoundingBox 0bp 5bp 20bp 25bp
34295 rotateOrigin center
34304 <cell alignment="center" valignment="top" usebox="none">
34307 \begin_layout Plain Layout
34310 Edit\SpecialChar \menuseparator
34311 Math\SpecialChar \menuseparator
34313 \begin_inset space ~
34316 Definition\SpecialChar \menuseparator
34317 Append Optional Argument
34318 \begin_inset Newline newline
34322 \begin_inset Phantom HPhantom
34325 \begin_layout Plain Layout
34328 Edit\SpecialChar \menuseparator
34329 Math\SpecialChar \menuseparator
34331 \begin_inset space ~
34334 Definition\SpecialChar \menuseparator
34340 Eating From The Right
34353 \begin_layout Standard
34354 \begin_inset Newpage newpage
34360 \begin_layout Section
34362 \begin_inset Index idx
34365 \begin_layout Plain Layout
34374 \begin_layout Subsection
34376 \begin_inset Index idx
34379 \begin_layout Plain Layout
34388 \begin_layout Standard
34389 Negative numbers often look ugly in formulas because the minus sign before
34390 the number is set with the same length as the minus operator sign.
34391 When writing the negative number in normal text, the minus sign appears
34395 \begin_layout Standard
34396 Thus, the problem disappears when converting the minus sign to mathematical
34400 \begin_layout Standard
34401 An example to visualize the problem:
34404 \begin_layout Standard
34406 \begin_inset Tabular
34407 <lyxtabular version="3" rows="3" columns="2">
34408 <features tabularvalignment="middle">
34409 <column alignment="right" valignment="top" width="0">
34410 <column alignment="left" valignment="top" width="0">
34412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34415 \begin_layout Plain Layout
34421 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34424 \begin_layout Plain Layout
34432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34435 \begin_layout Plain Layout
34441 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34444 \begin_layout Plain Layout
34445 \begin_inset Formula $x=-2$
34455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34458 \begin_layout Plain Layout
34464 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34467 \begin_layout Plain Layout
34468 \begin_inset Formula $x=\textrm{-}2$
34484 \begin_layout Subsection
34485 Comma as decimal Separator
34486 \begin_inset Index idx
34489 \begin_layout Plain Layout
34498 \begin_layout Standard
34499 In LaTeX a comma inside a formula is used, according to the English convention,
34500 as number group separator.
34501 So there will be space added behind all commas in formulas.
34504 \begin_layout Standard
34505 To avoid this, the comma is highlighted and changed to mathematical text
34515 \begin_layout Standard
34516 To use all formula commas in the document as decimal separator, the file
34525 \begin_layout Plain Layout
34530 is part of the LaTeX-package
34535 \begin_inset Index idx
34538 \begin_layout Plain Layout
34543 \begin_layout Plain Layout
34563 \begin_inset Index idx
34566 \begin_layout Plain Layout
34572 is loaded with the LaTeX-preamble line
34575 \begin_layout Standard
34583 \begin_layout Subsection
34585 \begin_inset CommandInset label
34587 name "sub:Physical-Vectors"
34592 \begin_inset Index idx
34595 \begin_layout Plain Layout
34604 \begin_layout Standard
34605 Predefined vectors are offered by the LaTeX-package
34610 \begin_inset Index idx
34613 \begin_layout Plain Layout
34619 that is loaded with the LaTeX-preamble line
34622 \begin_layout Standard
34630 \begin_layout Standard
34634 \begin_layout Plain Layout
34644 \begin_inset Note Note
34647 \begin_layout Plain Layout
34648 The following table will only be displayed when the LaTeX-package
34660 \begin_layout Standard
34661 The following commands are defined:
34664 \begin_layout Standard
34666 \begin_inset Tabular
34667 <lyxtabular version="3" rows="4" columns="2">
34668 <features tabularvalignment="middle">
34669 <column alignment="center" valignment="top" width="0">
34670 <column alignment="center" valignment="top" width="0">
34672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34675 \begin_layout Plain Layout
34681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34684 \begin_layout Plain Layout
34692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34695 \begin_layout Plain Layout
34705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34708 \begin_layout Plain Layout
34709 \begin_inset Formula $\Bra{\psi}$
34719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34722 \begin_layout Plain Layout
34732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34735 \begin_layout Plain Layout
34736 \begin_inset Formula $\Ket{\psi}$
34746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34749 \begin_layout Plain Layout
34761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34764 \begin_layout Plain Layout
34765 \begin_inset Formula $\Braket{\psi|\phi}$
34781 \begin_layout Standard
34788 assures that all vertical bars are set in the size of the surrounding brackets:
34789 \begin_inset Formula \[
34790 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
34798 \begin_layout Plain Layout
34808 \begin_inset Note Note
34811 \begin_layout Plain Layout
34812 The following will be displayed when the LaTeX-package
34824 \begin_layout Standard
34825 You need to install the LaTeX-package
34829 to see the rest of this subsection in the output.
34832 \begin_layout Standard
34836 \begin_layout Plain Layout
34848 \begin_layout Standard
34855 can also be achieved using the command
34861 , that is described in
34862 \begin_inset CommandInset ref
34864 reference "sub:Automatic-Bracket-Size"
34871 \begin_layout Subsection
34872 Self-defined Fractions
34873 \begin_inset CommandInset label
34875 name "sub:Self-defined-Fractions"
34880 \begin_inset Index idx
34883 \begin_layout Plain Layout
34884 Fractions ! self-defined
34892 \begin_layout Standard
34893 To define custom commands for fractions, the command
34900 \begin_inset Index idx
34903 \begin_layout Plain Layout
34911 is used in the following scheme:
34914 \begin_layout Standard
34927 bracket}{fraction bar thickness}{style}
34928 \begin_inset Newline newline
34932 \begin_inset Phantom HPhantom
34935 \begin_layout Plain Layout
34945 {numerator}{denominator}
34948 \begin_layout Standard
34949 The style is a number in the range of 0
34950 \begin_inset space \thinspace{}
34954 \begin_inset space \thinspace{}
34960 \begin_layout Standard
34962 \begin_inset Tabular
34963 <lyxtabular version="3" rows="5" columns="2">
34964 <features tabularvalignment="middle">
34965 <column alignment="center" valignment="top" width="0">
34966 <column alignment="center" valignment="top" width="0">
34968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34971 \begin_layout Plain Layout
34977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34980 \begin_layout Plain Layout
34988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34991 \begin_layout Plain Layout
34997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35000 \begin_layout Plain Layout
35001 display style formula
35008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35011 \begin_layout Plain Layout
35017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35020 \begin_layout Plain Layout
35028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35031 \begin_layout Plain Layout
35037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35040 \begin_layout Plain Layout
35048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35051 \begin_layout Plain Layout
35057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35060 \begin_layout Plain Layout
35074 \begin_layout Standard
35075 When no style is given, the size is adjusted to the surrounding environment
35076 like for the command
35085 \begin_layout Standard
35086 When no fraction bar thickness is given, the predefined value of 0.4
35087 \begin_inset space \thinspace{}
35093 \begin_layout Standard
35094 \begin_inset VSpace medskip
35097 For example, the commands
35110 \begin_inset CommandInset ref
35112 reference "sub:Fractions"
35116 are defined with the commands
35119 \begin_layout Standard
35128 genfrac{}{}{}{0}{#1}{#2}}
35131 \begin_layout Standard
35135 \begin_layout Standard
35144 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35147 \begin_layout Standard
35148 \begin_inset VSpace medskip
35151 To define a fraction where the fraction bar thickness can be given as optional
35152 argument, the following line is inserted to the LaTeX-preamble:
35155 \begin_layout Standard
35164 genfrac{}{}{#1}{}{#2}{#3}}
35167 \begin_layout Standard
35169 \begin_inset Formula \begin{align*}
35170 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35171 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35176 As one can see, the distance of the numerator and the denominator to the
35177 fraction bar is round about three times the bar thickness.
35180 \begin_layout Subsection
35182 \begin_inset Index idx
35185 \begin_layout Plain Layout
35194 \begin_layout Standard
35195 To cancel formulas or formula parts, the LaTeX-package
35200 \begin_inset Index idx
35203 \begin_layout Plain Layout
35209 has to be loaded with the LaTeX-preamble line
35212 \begin_layout Standard
35217 usepackage[samesize]{cancel}
35220 \begin_layout Standard
35224 \begin_layout Plain Layout
35234 \begin_inset Note Note
35237 \begin_layout Plain Layout
35238 The following table will only be displayed when the LaTeX-package
35250 \begin_layout Standard
35251 There are four ways to cancel formulas:
35254 \begin_layout Standard
35256 \begin_inset Tabular
35257 <lyxtabular version="3" rows="5" columns="2">
35258 <features tabularvalignment="middle">
35259 <column alignment="center" valignment="top" width="0">
35260 <column alignment="center" valignment="top" width="0">
35262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35265 \begin_layout Plain Layout
35271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35274 \begin_layout Plain Layout
35276 \begin_inset Note Note
35279 \begin_layout Plain Layout
35286 are used here as spacer.
35298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35301 \begin_layout Plain Layout
35310 \begin_layout Plain Layout
35324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35327 \begin_layout Plain Layout
35328 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35341 \begin_layout Plain Layout
35350 \begin_layout Plain Layout
35364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35367 \begin_layout Plain Layout
35368 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35381 \begin_layout Plain Layout
35390 \begin_layout Plain Layout
35404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35407 \begin_layout Plain Layout
35408 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35421 \begin_layout Plain Layout
35425 \begin_inset Formula $\to$
35436 \begin_layout Plain Layout
35450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35453 \begin_layout Plain Layout
35454 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35470 \begin_layout Standard
35477 is especially suitable to visualize the reduction of fractions within formulas:
35478 \begin_inset Formula \[
35479 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
35486 \begin_layout Standard
35490 \begin_layout Plain Layout
35500 \begin_inset Note Note
35503 \begin_layout Plain Layout
35504 The following will be displayed when the LaTeX-package
35516 \begin_layout Standard
35517 You need to install the LaTeX-package
35521 to see the rest of this subsection in the output.
35524 \begin_layout Standard
35528 \begin_layout Plain Layout
35540 \begin_layout Subsection
35541 Formulas in Section Headings
35542 \begin_inset CommandInset label
35544 name "sub:Formulas-in-Section"
35549 \begin_inset Index idx
35552 \begin_layout Plain Layout
35553 Formula ! in section headings
35561 \begin_layout Standard
35562 When formulas are used in section headings, the following has to be taken
35566 \begin_layout Standard
35567 \begin_inset Note Greyedout
35570 \begin_layout Plain Layout
35576 \begin_inset Index idx
35579 \begin_layout Plain Layout
35580 Packages ! hyperref
35585 support is enabled in the document settings dialog under
35588 \begin_inset space ~
35593 , PDF-bookmarks are created for every section heading in the table of contents.
35594 If a section heading contains formulas, they are incorrectly displayed
35595 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35604 \begin_layout Standard
35605 Both problems can be solved by inserting at the end of the section heading
35606 a short title with the menu
35608 Insert\SpecialChar \menuseparator
35610 \begin_inset space ~
35616 Short titles are used as alternative for multiline section headings to
35617 keep the table of contents clearly arranged.
35618 Only the short title appears in the table of contents and therefore also
35619 in the PDF-bookmark.
35622 \begin_layout Standard
35623 When formulas should be used in the table of contents but
35627 is used, one can use the following command in TeX-mode:
35630 \begin_layout Standard
35635 texorpdfstring{part}{alternative}
35636 \begin_inset Index idx
35639 \begin_layout Plain Layout
35650 \begin_layout Standard
35651 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35652 This can be characters, formulas, footnotes, but also cross-references.
35653 The alternative is used instead of the part for the bookmark.
35656 \begin_layout Standard
35657 Here are two example headings:
35658 \begin_inset VSpace -3mm
35665 \begin_layout Plain Layout
35677 \begin_layout Subsubsection
35678 Heading without formula in table of contents
35679 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35683 \begin_inset Argument
35686 \begin_layout Plain Layout
35687 Heading without formula in table of contents
35695 \begin_layout Subsubsection
35696 Heading with formula in table of contents
35700 \begin_layout Plain Layout
35710 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35717 \begin_layout Plain Layout
35727 \begin_layout Standard
35731 \begin_layout Plain Layout
35740 In the first heading a short title was used, in the second one
35749 \begin_layout Standard
35750 To get the same formatting as for the other headings, the complete heading
35759 \begin_layout Plain Layout
35761 \begin_inset CommandInset ref
35763 reference "sub:Bold-Formulas"
35775 \begin_layout Subsection
35776 Formulas in multi-column Text
35777 \begin_inset Index idx
35780 \begin_layout Plain Layout
35781 Formula ! in multi-column text
35789 \begin_layout Standard
35790 Formulas in multi-column text are often too wide to fit into a column and
35791 thus need to be set over the whole page width.
35792 This is done by using the LaTeX-package
35800 \begin_layout Plain Layout
35805 is part of every LaTeX standard installation.
35811 \begin_inset Index idx
35814 \begin_layout Plain Layout
35815 Packages ! multicol
35820 , that is loaded with the LaTeX-preamble line
35823 \begin_layout Standard
35828 usepackage{multicol}
35831 \begin_layout Standard
35832 \begin_inset Note Greyedout
35835 \begin_layout Plain Layout
35836 Note herby that the setting
35839 \begin_inset space ~
35846 Document\SpecialChar \menuseparator
35852 \begin_inset space ~
35872 \begin_layout Standard
35873 Before the multi-column text the command
35876 \begin_layout Standard
35881 begin{multicols}{column number}
35884 \begin_layout Standard
35885 is written in TeX-mode.
35886 The column number is a number in the range of 2
35887 \begin_inset space \thinspace{}
35891 \begin_inset space \thinspace{}
35895 Before the formula the multi-column text is ended by inserting the command
35898 \begin_layout Standard
35906 \begin_layout Standard
35910 \begin_layout Standard
35911 Due to the command some space is automatically added before the formula.
35913 \begin_inset space \thinspace{}
35916 mm vertical space is inserted before the formula.
35917 When the formula style
35923 \begin_layout Plain Layout
35925 \begin_inset CommandInset ref
35927 reference "sec:Formula-Styles"
35939 \begin_inset space \thinspace{}
35942 mm space is inserted instead.
35945 \begin_layout Standard
35946 As example a multi-column text with a displayed formula:
35949 \begin_layout Standard
35955 \begin_layout Plain Layout
35959 begin{multicols}{2}
35964 Das Spektrum wird fouriertransformiert.
35965 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35966 , Lösungsmittel) zu trennen.
35967 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35968 nun das Aussehen des Ausgangssignals.
35969 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35970 über alle Phasen integrieren muss.
35972 \begin_inset Formula $S$
35975 unser normiertes Ausgangssignal und
35976 \begin_inset Formula $P$
35979 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35983 \begin_layout Plain Layout
35993 \begin_inset VSpace -6mm
35997 \begin_inset Formula \begin{equation}
35998 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
36006 \begin_layout Plain Layout
36010 begin{multicols}{2}
36016 \begin_inset Formula $S_{0}$
36019 das Signal ohne Gradient ist und die Normierungsbedingung
36020 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36024 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36026 \begin_inset Formula $\nicefrac{\pi}{2}$
36030 \begin_inset space \thinspace{}
36033 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36034 das Signal zusätzlich abschwächt.
36035 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36037 \begin_inset Formula $T_{2}$
36043 \begin_layout Standard
36049 \begin_layout Plain Layout
36061 \begin_layout Subsection
36062 Formulas with Description of Variables
36063 \begin_inset Index idx
36066 \begin_layout Plain Layout
36067 Formula ! with description of variables
36075 \begin_layout Standard
36076 To describe variables within a formula, like in formula
36077 \begin_inset CommandInset ref
36079 reference "eq:within"
36088 \begin_inset Formula $n$
36092 \begin_inset space ~
36095 matrix is used with left aligned columns for the
36096 \begin_inset Formula $n$
36103 \begin_layout Plain Layout
36105 \begin_inset CommandInset ref
36107 reference "sec:Matrices"
36116 To set the description in a smaller size, before the matrix e.
36117 \begin_inset space \thinspace{}
36121 \begin_inset space \space{}
36134 \begin_layout Plain Layout
36136 \begin_inset CommandInset ref
36138 reference "sub:Font-Sizes"
36150 \begin_layout Standard
36151 When the formula style
36157 \begin_layout Plain Layout
36159 \begin_inset CommandInset ref
36161 reference "sec:Formula-Styles"
36182 \begin_layout Plain Layout
36189 only works in formulas with the style
36194 \begin_inset CommandInset ref
36196 reference "sub:Variable-Space"
36205 is inserted before and after the matrix to have the same separation of
36206 the matrix from the equation and the side margin.
36209 \begin_layout Standard
36210 When the formula style
36214 is used, the method described in
36215 \begin_inset CommandInset ref
36217 reference "sub:Flalign-Environment"
36221 is used to indent formulas.
36223 \begin_inset CommandInset ref
36225 reference "eq:within"
36229 consists of five columns whereas in the first two columns contain the equation,
36230 the third the matrix and the last one an empty TeX-brace.
36231 \begin_inset Formula \begin{flalign}
36232 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36233 \rho & \textrm{density}\\
36234 V & \textrm{volume}\\
36235 g & \textrm{gravitational acceleration}
36236 \end{array} & & {}\label{eq:within}\end{flalign}
36243 \begin_layout Subsection
36244 Upright small Greek Letters
36245 \begin_inset CommandInset label
36247 name "sub:Upright-small-Greek"
36252 \begin_inset Index idx
36255 \begin_layout Plain Layout
36256 Greek letters ! upright
36264 \begin_layout Standard
36265 Most of the math fonts only provide italic small Greek letters.
36266 But for symbols of elementary particles like pions and neutrinos, upright
36267 Greek letters are needed.
36276 \begin_layout Plain Layout
36281 is part of the LaTeX-package
36286 \begin_inset Index idx
36289 \begin_layout Plain Layout
36294 \begin_layout Plain Layout
36314 \begin_inset Index idx
36317 \begin_layout Plain Layout
36323 that is loaded with the LaTeX-preamble line
36326 \begin_layout Standard
36331 usepackage{upgreek}
36334 \begin_layout Standard
36340 \begin_layout Plain Layout
36350 \begin_inset Note Note
36353 \begin_layout Plain Layout
36354 The following table will only be displayed when the LaTeX-package
36363 They are created when the command for a small Greek letters is started
36369 For example the command
36376 \begin_inset Formula $\uptau$
36382 \begin_layout Standard
36383 With these commands reactions of elementary particles can be typeset:
36384 \begin_inset Formula \[
36385 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
36392 \begin_layout Standard
36393 The upright letters are more bold and wider than the italic ones.
36394 They should therefore not be used for units like
36395 \begin_inset Quotes eld
36399 \begin_inset Quotes erd
36405 \begin_layout Standard
36409 \begin_layout Plain Layout
36419 \begin_inset Note Note
36422 \begin_layout Plain Layout
36423 The following will be displayed when the LaTeX-package
36435 \begin_layout Standard
36436 You need to install the LaTeX-package
36440 to see the rest of this subsection in the output.
36443 \begin_layout Standard
36447 \begin_layout Plain Layout
36459 \begin_layout Subsection
36460 Text Characters in Formulas
36461 \begin_inset CommandInset label
36463 name "sub:Text-Characters-in"
36468 \begin_inset Index idx
36471 \begin_layout Plain Layout
36480 \begin_layout Standard
36481 In some cases you might want to insert text characters directly into formulas.
36482 When for example the centered dot · is often used in formulas like
36483 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36486 , one would have to insert the command
36496 \begin_layout Plain Layout
36498 \begin_inset CommandInset ref
36500 reference "sub:Binary-Operators"
36509 all the time, because this character is defined in all encodings as text
36511 But the encoding can be changed by this LaTeX-preamble line:
36514 \begin_layout Standard
36519 Declare Inputtext{183}{
36529 f\SpecialChar \textcompwordmark{}
36533 \begin_layout Standard
36534 The character encoding (menu
36536 Document\SpecialChar \menuseparator
36537 Settings\SpecialChar \menuseparator
36540 ) specifies what character appears when a keyboard key is pressed.
36541 When the key for the character '·' is pressed, internally the command
36548 But this command is not available in a formula so that you would get LaTeX-erro
36550 With the changed encoding the right command is chosen automatically, depending
36551 on if the character was inserted into a formula or not.
36554 \begin_layout Standard
36555 The encoding of several characters is saved in definition files.
36556 Fore example the encoding
36560 is defined in the file
36564 that is in the installation folder of LaTeX.
36565 Encodings should only be changed via the LaTeX-preamble and not in the
36567 Otherwise own documents could not be edited by other LyX users working
36568 on other computers.
36571 \begin_layout Standard
36572 \begin_inset VSpace medskip
36575 Besides the centered dot, in this document the degree sign ° is defined
36576 with the following LaTeX-preamble line so that it can directly be inserted
36580 \begin_layout Standard
36585 DeclareInputtext{176}{
36595 f\SpecialChar \textcompwordmark{}
36599 \begin_layout Standard
36600 \begin_inset Newpage newpage
36606 \begin_layout Section
36609 \begin_inset Index idx
36612 \begin_layout Plain Layout
36621 \begin_layout Standard
36622 This section is a summary of the most important typographic rules, listed
36627 \begin_layout Plain Layout
36628 This collection was partly taken from the German semi-official dictionary
36630 \begin_inset Quotes eld
36634 \begin_inset Quotes erd
36638 \begin_inset CommandInset citation
36644 that lists some of the ISO rules.
36645 More rules are listed in
36646 \begin_inset CommandInset citation
36660 \begin_layout Itemize
36669 \begin_layout Plain Layout
36670 done with font styles, see
36671 \begin_inset CommandInset ref
36673 reference "sub:Font-Styles"
36682 , no matter if they appear in italic text: 30
36683 \begin_inset space \thinspace{}
36687 \begin_inset Newline newline
36690 Between the value and the unit is the smallest space, see
36691 \begin_inset CommandInset ref
36693 reference "sub:Predefined-Space"
36698 \begin_inset Newline newline
36701 This convention is automatically fulfilled when the command
36708 When it is entered to a formula, two boxes appear.
36709 In the first one the value is inserted, in the second one the unit, and
36711 \begin_inset Formula $\unit[30]{km/h}$
36715 \begin_inset space \thinspace{}
36725 is not a real LaTeX command but the command
36731 , therefore you cannot use it in TeX code.
36734 \begin_layout Itemize
36735 Percent and perthousand signs are set like physical units:
36736 \begin_inset Newline newline
36740 \begin_inset space \thinspace{}
36746 \begin_layout Itemize
36747 The degree sign follows directly on the value: 15°, but not when it is used
36749 \begin_inset space \thinspace{}
36755 \begin_layout Itemize
36756 In numbers with more than four digits the smallest space is inserted before
36757 every third digit to group them:
36767 \begin_inset space \thinspace{}
36771 \begin_inset space \thinspace{}
36777 \begin_layout Itemize
36778 For dimensions like 120×90×40
36779 \begin_inset space \thinspace{}
36782 cm the multiplication sign
36783 \begin_inset Quotes eld
36787 \begin_inset Quotes erd
36791 It is available either via the command
36799 Insert\SpecialChar \menuseparator
36800 Special Character\SpecialChar \menuseparator
36806 \begin_layout Itemize
36807 Functions with names consisting of several letters are set upright to avoid
36809 \begin_inset CommandInset ref
36811 reference "sub:Predefined-Functions"
36818 \begin_layout Itemize
36819 Indices consisting of several letters, are set upright:
36820 \begin_inset Formula $E_{\mathrm{kin}}$
36824 \begin_inset Newline newline
36827 Components of matrices are set italic:
36828 \begin_inset Formula $\hat{H}_{kl}$
36834 \begin_layout Itemize
36835 The differentiation/integration operator 'd', the Euler's number 'e' and
36836 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36840 \begin_layout Itemize
36841 The character that denotes a
36845 transformation is inserted either by the command
36853 \begin_layout Plain Layout
36866 Insert\SpecialChar \menuseparator
36867 Special Character\SpecialChar \menuseparator
36868 Symbols\SpecialChar \menuseparator
36870 \begin_inset space ~
36876 \begin_inset Formula $\mathscr{F}$
36882 \begin_layout Standard
36883 \begin_inset Newpage newpage
36889 \begin_layout Section
36891 \begin_inset Index idx
36894 \begin_layout Plain Layout
36903 \begin_layout Standard
36904 Some characters and symbols can be created with several commands.
36905 Here is a list of the synonym commands:
36908 \begin_layout Standard
36909 \begin_inset VSpace bigskip
36913 \begin_inset space \hfill{}
36917 \begin_inset Tabular
36918 <lyxtabular version="3" rows="12" columns="2">
36919 <features tabularvalignment="middle">
36920 <column alignment="center" valignment="top" width="0pt">
36921 <column alignment="center" valignment="top" width="0pt">
36923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36926 \begin_layout Plain Layout
36932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36935 \begin_layout Plain Layout
36937 \begin_inset Note Note
36940 \begin_layout Plain Layout
36947 is only used as spacer.
36959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36962 \begin_layout Plain Layout
36970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36973 \begin_layout Plain Layout
36977 \begin_layout Plain Layout
36990 \begin_layout Plain Layout
37004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37007 \begin_layout Plain Layout
37015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37018 \begin_layout Plain Layout
37028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37031 \begin_layout Plain Layout
37039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37042 \begin_layout Plain Layout
37052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37055 \begin_layout Plain Layout
37063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37066 \begin_layout Plain Layout
37074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37077 \begin_layout Plain Layout
37085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37088 \begin_layout Plain Layout
37096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37099 \begin_layout Plain Layout
37107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37110 \begin_layout Plain Layout
37120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37123 \begin_layout Plain Layout
37131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37134 \begin_layout Plain Layout
37144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37147 \begin_layout Plain Layout
37155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37158 \begin_layout Plain Layout
37168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37171 \begin_layout Plain Layout
37179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37182 \begin_layout Plain Layout
37192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37195 \begin_layout Plain Layout
37203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37206 \begin_layout Plain Layout
37214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37217 \begin_layout Plain Layout
37225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37228 \begin_layout Plain Layout
37240 \begin_inset space \hfill{}
37244 \begin_inset Tabular
37245 <lyxtabular version="3" rows="12" columns="2">
37246 <features tabularvalignment="middle">
37247 <column alignment="center" valignment="top" width="0pt">
37248 <column alignment="center" valignment="top" width="0pt">
37250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37253 \begin_layout Plain Layout
37259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37262 \begin_layout Plain Layout
37270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37273 \begin_layout Plain Layout
37281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37284 \begin_layout Plain Layout
37296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37299 \begin_layout Plain Layout
37307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37310 \begin_layout Plain Layout
37320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37323 \begin_layout Plain Layout
37331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37334 \begin_layout Plain Layout
37344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37347 \begin_layout Plain Layout
37355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37358 \begin_layout Plain Layout
37366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37369 \begin_layout Plain Layout
37377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37380 \begin_layout Plain Layout
37388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37391 \begin_layout Plain Layout
37399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37402 \begin_layout Plain Layout
37412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37415 \begin_layout Plain Layout
37423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37426 \begin_layout Plain Layout
37436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37439 \begin_layout Plain Layout
37447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37450 \begin_layout Plain Layout
37460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37463 \begin_layout Plain Layout
37471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37474 \begin_layout Plain Layout
37484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37487 \begin_layout Plain Layout
37495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37498 \begin_layout Plain Layout
37508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37511 \begin_layout Plain Layout
37519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37522 \begin_layout Plain Layout
37536 \begin_inset space \hfill{}
37542 \begin_layout Standard
37543 \begin_inset Newpage newpage
37549 \begin_layout Bibliography
37550 \labelwidthstring References
37551 \begin_inset CommandInset bibitem
37552 LatexCommand bibitem
37564 The LaTeX Companion
37567 Addison Wesley, 2004
37570 \begin_layout Bibliography
37571 \labelwidthstring References
37572 \begin_inset CommandInset bibitem
37573 LatexCommand bibitem
37579 \begin_inset CommandInset href
37582 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37586 of LaTeX's math abilities
37589 \begin_layout Bibliography
37590 \labelwidthstring References
37591 \begin_inset CommandInset bibitem
37592 LatexCommand bibitem
37598 \begin_inset CommandInset href
37601 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37609 \begin_layout Plain Layout
37621 \begin_layout Bibliography
37622 \labelwidthstring References
37623 \begin_inset CommandInset bibitem
37624 LatexCommand bibitem
37630 \begin_inset CommandInset href
37633 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37637 of all symbols available with LaTeX-packages
37640 \begin_layout Bibliography
37641 \labelwidthstring References
37642 \begin_inset CommandInset bibitem
37643 LatexCommand bibitem
37649 \begin_inset CommandInset href
37651 name "Documentation"
37652 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37656 of the LaTeX-package
37661 \begin_inset Index idx
37664 \begin_layout Plain Layout
37665 Packages ! hyperref
37673 \begin_layout Bibliography
37674 \labelwidthstring References
37675 \begin_inset CommandInset bibitem
37676 LatexCommand bibitem
37682 \begin_inset CommandInset href
37684 name "Documentation"
37685 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37689 of the LaTeX-package
37694 \begin_inset Index idx
37697 \begin_layout Plain Layout
37706 \begin_layout Bibliography
37707 \labelwidthstring References
37708 \begin_inset CommandInset bibitem
37709 LatexCommand bibitem
37715 \begin_inset CommandInset href
37718 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
37729 \begin_inset CommandInset ref
37731 reference "sub:Operator-Limits"
37736 \begin_inset Index idx
37739 \begin_layout Plain Layout
37750 \begin_layout Bibliography
37751 \labelwidthstring References
37752 \begin_inset CommandInset bibitem
37753 LatexCommand bibitem
37764 Auflage, Duden 2001
37767 \begin_layout Bibliography
37768 \labelwidthstring References
37769 \begin_inset CommandInset bibitem
37770 LatexCommand bibitem
37776 \begin_inset CommandInset href
37779 target "http://physics.nist.gov/Document/checklist.pdf"
37783 for reviewing manuscripts
37786 \begin_layout Standard
37787 \begin_inset CommandInset index_print
37788 LatexCommand printindex